15. A polygon has the dimensions shown.
(2b + a) in.
W
X
(4a-3) in.
Z
(3a + b-2) in.
Part A
What is the perimeter of triangle WXY?
A 5a + 2b 5 in.
B 8a + 3b - 5 in.
O Houghton Mifflin Harcourt Publishing Com
9a3b- 2 in.
D 9a5b+ 2 in.
Part B
If triangle WYZ has a perimeter of 4a + 5b - 2
inches, what is the polynomial that represents the
perimeter in inches of polygon WXYZ?

15. A Polygon Has The Dimensions Shown.(2b + A) In.WX(4a-3) In.Z(3a + B-2) In.Part AWhat Is The Perimeter

Answers

Answer 1

The perimeter of triangle WXY is (8a + 3b - 5) in

the perimeter of the polygon is (4a + 8b -1) in.

How to find the perimeter of triangle WXY

The perimeter of triangle WXY is solved using addition of sides

perimeter of triangle = (2b + a) in + (4a - 3) in. +  (3a + b - 2) in.

perimeter of triangle = 8a + 3b - 5 in

perimeter of polygon = perimeter  of triangle WYZ - (4a - 3) in + (2b + a) in + (3a + b - 2) in.

perimeter of polygon = (4a + 5b - 2) in - (4a - 3) in + (2b + a) in + (3a + b - 2) in.

perimeter of polygon = (4a + 8b -1) in.

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Related Questions

find the probability that a randomly selected person from this sample believed the true headline or believed the false headline.

Answers

The probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

What is Probability?

Probability is a measure of the likelihood or chance that a specific event will occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain to occur.

The probability that a randomly selected person from this sample believed the true headline or believed the false headline can be calculated by adding the number of people who believed the true headline to the number of people who believed the false headline and dividing by the total sample size.

In this case, the number of people who believed the true headline is 120, and the number of people who believed the false headline is 80. Therefore, the total number of people who believed either headline is 120 + 80 = 200.

The total sample size is also 200, so the probability that a randomly selected person from this sample believed the true headline or believed the false headline is:

(120 + 80) / 200 = 200 / 200 = 1

Therefore, the probability is 1, or 100%, that a randomly selected person from this sample believed either the true headline or the false headline.

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Complete Question:

In a sample of 200 people, 120 believed a true headline and 80 believed a false headline. What is the probability that a randomly selected person from this sample believed the true headline or believed the false headline?

a tank contains 90 liters of fluid in which 50 grams of salt is dissolved. brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 l/min; the well-mixed solution is pumped out at the same rate. find the number a(t) of grams of salt in the tank at time t.

Answers

The answer is 50 grams of salt in the tank at all times.

To find the number of grams of salt in the tank at time t, we need to use the formula:

a(t) = a(0) + (r - p) * t

where a(0) is the initial amount of salt in the tank, r is the rate at which brine is being pumped into the tank, p is the rate at which the solution is being pumped out of the tank, and t is the time elapsed.

In this case, a(0) = 50 grams, r = 3 grams per minute (since the brine contains 1 gram of salt per liter and 3 liters are being pumped in per minute, so 3 grams of salt are being added per minute), and p = 3 grams per minute (since the solution is being pumped out at the same rate as it is being pumped in). Therefore, we can simplify the formula to:

a(t) = 50 + 0 * t
a(t) = 50 grams

This means that the amount of salt in the tank remains constant over time, since the rate at which it is being pumped in and out is equal. Therefore, the answer is 50 grams of salt in the tank at all times.

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Dana buys a plant that is 4 inches tall. After one week the plant is 7 inches tall. After a second week the plant is 10 inches tall. At this rate, how tall will the plant be after the fifth week?
a
22 inches tall
b
3 inches tall
c
14 inches tall
d
19 inches tall

Answers

Answer:

We know that the plant grows by 3 inches each week (7 inches - 4 inches = 3 inches, and 10 inches - 7 inches = 3 inches). Therefore, after 5 weeks, the plant will be 4 inches + (3 inches × 5) = 19 inches tall.

Step-by-step explanation:

- The plant is 4 inches tall when Dana buys it.

- After one week, the plant grows by 3 inches to reach a height of 7 inches.

- After a second week, the plant grows by another 3 inches to reach a height of 10 inches.

- So, the plant grows by 3 inches each week.

- After 3 weeks, the plant will be 10 inches + 3 inches = 13 inches tall.

- After 4 weeks, the plant will be 13 inches + 3 inches = 16 inches tall.

- After 5 weeks, the plant will be 16 inches + 3 inches = 19 inches tall.

Therefore, the correct answer is d) 19 inches tall.

If the r = + 0.8, we would say: As X scores increase, the Y scores increase; and
the magnitude is strong. Explain what each of the following correlation coefficients indicates about the
direction and magnitude in which Y scores change as X scores increase.
a. -1.0
b. +0.32
c. -0.10
d. -0.71

Answers

If the correlation coefficient r is -1.0, it means that there is a perfect negative linear relationship between X and Y.

a) As X scores increase, Y scores decrease in a perfectly consistent manner. The magnitude is strong.

b) If the correlation coefficient r is +0.32, it means that there is a positive linear relationship between X and Y, but it is a weak relationship. As X scores increase, Y scores tend to increase, but not in a perfectly consistent manner. The magnitude is weak.

c) If the correlation coefficient r is -0.10, it means that there is a weak negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease, but not in a consistent manner. The magnitude is weak.

d) If the correlation coefficient r is -0.71, it means that there is a strong negative linear relationship between X and Y. As X scores increase, Y scores tend to decrease in a consistent manner. The magnitude is strong.

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Three mutually tangential circles with radii located at A, B, and C, have radii of 20 ft, 28 ft, and 41 ft, respectively. Find the measures of angles A, B, and C. Round to the nearest tenth of a degree. B А С A) A = 70. 3° B = 60. 7° C = 49° B) A = 77. 50 B = 59. 7° C = 42. 8° C) A-66. 3° B = 61. 5° C = 52. 2° D) A-102. 5° B = 47. 2° C = 30. 3° Determine the perimeter of a triangle with vertices defined by the given points to the nearest tenth. 6) A(1,1), B(2,5), C(5,1) 6) A) 9. 8 B) 13. 1 C) 16 D) 8

Answers

Problem 1: Three mutually tangential circles with radii located at A, B, and C, have radii of 20 ft, 28 ft, and 41 ft, respectively. Find the measures of angles A, B, and C. Round to the nearest tenth of a degree.

To solve this problem, we can use a result from Euclidean geometry that states that the angle between two tangents drawn from an external point to a circle is equal to half the difference of the measures of the intercepted arcs. We can apply this result to the three circles and the external point where they are tangential to each other.

Let O be the external point of tangency, and let D, E, and F be the points of tangency of the circles with radii 20 ft, 28 ft, and 41 ft, respectively. Then, we can form the triangle DEF, where the angles at D, E, and F are 90 degrees, and the sides are the radii of the circles.

Let x, y, and z be the measures of the arcs intercepted by the tangents at D, E, and F, respectively. Then, we have:

x + y = 180 - A

y + z = 180 - B

x + z = 180 - C

Also, using the fact that the sum of the angles in a triangle is 180 degrees, we have:

A + B + C = 180

Substituting the first three equations into the last one, we obtain:

2x + 2y + 2z = 360

x + y + z = 180

Adding these two equations, we get:

3(x + y + z) = 540

x + y + z = 180

Therefore, Option A) x = 70.3 degrees, y = 60.7 degrees, and z = 49 degrees. Thus, the measures of angles A, B, and C are approximately 70.3 degrees, 59.7 degrees, and 42.8 degrees, respectively (rounded to the nearest tenth).

Problem 2: Determine the perimeter of a triangle with vertices defined by the given points to the nearest tenth. A(1,1), B(2,5), C(5,1)

To solve this problem, we can use the distance formula, which gives the distance between two points in a plane. Let d(P,Q) be the distance between points P and Q. Then, we have:

d(A,B) = [tex]\sqrt{((2-1)^2 + (5-1)^2)}[/tex] = √17

d(B,C) = [tex]\sqrt{(5-2)^2 + (1-1)^2)}[/tex] = 3

d(C,A) = [tex]\sqrt{(1-5)^2 + (1-1)^2)}[/tex] = 4

Therefore, the perimeter of triangle ABC is approximately 9.8 units Option A) 9.8 units is the correct perimeter of triangle ABC.

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In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three groups: gastric bypass surgery; participation in a diet and exercise program; or both gastric bypass surgery and participation in the diet and exercise program. Researchers carefully observed the amount of weight lost five years after the study began. Reference: Ref 9-1 This study uses the principles of A. randomization. B. confounding. C. blocking. D. All of the above Which of the following are principles of experimental design?
A. randomization B. replication C. blinding D. All of the above

Answers

Since all three principles of experimental design are likely to have been used in the study described, Therefore option D is correct.

All of the above are principles of experimental design. Randomization helps to ensure that groups are similar in all aspects except for the treatment received, reducing the effects of confounding variables. Replication allows for assessing the variability and consistency of results. Blinding reduces the risk of bias by preventing participants or researchers from knowing which treatment was received. The study described in the question uses all of these principles of experimental design.

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A grocer mixes trail mix that costs $3.00 per pound with trail mix that costs $1.50 per pound. He makes 15 lb of trail mix that costs $2.50 per pound. How much of each trail mix did the grocer use?

HELP ASAP ITS DUE IN LIKE 10 MINS !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The grocer used 10 lbs of trail mix that costs $3.00 per pound and 5 lbs of trail mix that costs $1.50 per pound.

What is the number of each mix?

The number of each trail mix used by the grocer is calculated as follows

Let the trail mix that costs $3.00 per pound = x

Let the trail mix that costs $1.50 per pound = y

x + y = 15  ---- (1)

3x + 1.5y = 2.5(15)

3x + 1.5y = 37.5 ------- (2)

From equation (1), y = 15 - x

Substitute the value of x as follows;

3x + 1.5(15 - x) = 37.5

3x + 22.5 - 1.5x = 37.5

1.5x = 15

x = 15/1.5

x = 10

Substituting x = 10 in equation 1, we get:

10 + y = 15

y = 15 - 10

y = 5

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You are constructing a 90% confidence interval for the difference of means from simple random samples from two independent populations. The sample sizes are = 6 and = 14. You draw dot plots of the samples to check the normality condition for two-sample t-procedures. Which of the following descriptions of those dot plots would suggest that it is safe to use t-procedures?
I. The dot plot of sample 1 is roughly symmetric, while the dot plot of sample 2 is moderately skewed left. There are no outliers.
II. Both dot plots are roughly symmetric. Sample 2 has an outlier.
III. Both dot plots are strongly skewed to the right. There are no outliers.
A) I only
B) II only
C) I and II
D) I, II, and III
E) t-procedures are not recommended in any of these cases.

Answers

A) I only . In order to use t-procedures for constructing a confidence interval, the samples should be approximately normally distributed.

Option I suggests that one sample is roughly symmetric and the other is moderately skewed left, but there are no outliers. This suggests that the normality condition may be met and t-procedures can be used. Option II indicates that both samples are roughly symmetric, but one sample has an outlier. This may violate the assumption of normality and t-procedures may not be appropriate.

Option III suggests that both samples are strongly skewed to the right, which also violates the normality assumption and t-procedures are not recommended.

Therefore, the correct answer is A) I only.

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2. Closing costs are calculated based on
Odown payment made
Oselling price of the house
O loan amount minus down payment
Oselling price of the house minus down payment
(1 point)

Answers

Closing costs are calculated based on d) selling price of the house minus down payment.

Closing costs are the additional charges that buyers and sellers incur in order to finalize a real estate transaction. Loan origination fees, discount points, appraisal fees, title searches, title insurance, surveys, taxes, deed recording fees, and credit report charges are examples of these expenditures.

Lenders are required by law to give buyers with a closing disclosure three business days before the planned closing date. Closing fees are incurred when the title to the property is transferred from the seller to the buyer.

Closing costs vary depending on location and property value. Closing fees are typically between 3-6% of the purchase price. At settlement, a $300,000 mortgage will cost between $9,000 and $18,000.

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Correct question:

Closing costs are calculated based on

a) down payment made

b) selling price of the house

c)  loan amount minus down payment

d) selling price of the house minus down payment

Adam buys a chair in a sale for 540.60£, this is a reduction of 15% on the original price. claculate the original price of the chair.

Answers

The original price of the chair was £636.

To calculate the original price of the chair, we can use the formula:

Original price = Sale price / (1 - Discount rate)

where the discount rate is expressed as a decimal. In this case, the sale price is £540.60 and the discount rate is 15%, or 0.15 as a decimal.

So, plugging in the numbers we get:

Original price = £540.60 / (1 - 0.15)Original price = £540.60 / 0.85Original price = £636

Therefore, the original price of the chair was £636.

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The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.01 level that the medicine relieves pain in more than 328 seconds. For a sample of 39 patients, the mean time in which the medicine relieved pain was 333 seconds. Assume the population standard deviation is 22. Find the P-value of the test statistic.

Answers

The P-value of the test statistic is 0.0294.

To determine the P-value, we need to calculate the test statistic first. Here, the sample size (n) is 39, sample mean (x) is 333 seconds, population standard deviation (σ) is 22, and the null hypothesis is that the medicine relieves pain in 328 seconds or less (μ ≤ 328).

The test statistic can be calculated using the formula:

t = (x - μ) / (σ / sqrt(n))

Substituting the values, we get:

t = (333 - 328) / (22 / sqrt(39))t = 1.8469

To find the P-value of the test statistic, we need to use a t-distribution table with degrees of freedom (df) equal to n - 1 = 38. At a significance level of 0.01 and df = 38, we find the critical value to be 2.704.

Since the calculated t-value (1.8469) is less than the critical value (2.704), we fail to reject the null hypothesis. However, to find the P-value, we need to calculate the area under the t-distribution curve to the right of the calculated t-value.

Using a t-distribution calculator or software, we can find that the P-value is 0.0294. Since this value is less than the significance level of 0.01, we can conclude that there is sufficient evidence to reject the null hypothesis and conclude that the medicine relieves pain in more than 328 seconds.

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Find the measures of the interior angles of a triangle when one of the angles is x the other angle is x-24 and the other angle is 68

Answers

Answer:

X = 68

x - 24 = 44

and the last angle is given as 68

Step-by-step explanation:

Hope this helps! Pls give brainliest!

In a class of 35 pupils, 15 are girls how many are boys

Answers

Answer: 20 boys

Step-by-step explanation:

35 - 15 = 20

(L7) A Pythagorean Triple is a set of three nonzero positive _____ numbers, a,b, and c, such that a²+b²=c².

Answers

A Pythagorean Triple is a set of three integers that are positive whole numbers, namely a, b, and c, such that a²+b²=c².

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle

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Determine the total time spent outside by all the children

Answers

The total time spent outside by all the children is 5 hours.

Assuming that the school boy's schedule is representative of the average student's schedule, we can use the proportion of time spent on each activity to estimate the average amount of time spent on each activity by all the children.

7 hours on school

4 hours on homework

2 hours on play

8 hours on sleep

3 hours on other activities

Adding these up, we get a total of 24 hours, which is the same as the total number of hours in a day.

Therefore, we can estimate that the average student does spend any time outside, since all 24 hours of the day are accounted for by these activities is

=> Play + others

=> 2 + 3 = 5

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Complete Question:

The data given below shows number of hours spent by a school boy on different activities on a working day.

Activity        School         Homework         Play         Sleep       Other       Total

Number of hours 7           4                          2              8               3              24

Determine the total time spent outside by all the children

How to find the area of a rhombus with one diagonal and perimeter?.

Answers

The area of rhombus can be found using the formula A = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals. Using area formula, we get A = (24 x 18)/2 the area of the rhombus is 24√(119) square meters.

Let's start by finding the other diagonal of the rhombus.

We know that the perimeter of a rhombus is four times the length of one of its sides. So, if the perimeter is 80 m, then each side has a length of 80/4 = 20 m.

We also know that the diagonals of a rhombus are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Therefore, each leg of one of these right triangles is half of one of the diagonals of the rhombus.

Let's call the other diagonal of the rhombus d. Then, using the Pythagorean theorem in one of the right triangles, we have

(20/2)² + (d/2)² = 24²

100 + d²/4 = 576

d²/4 = 476

d = 2√(119)

Now that we have both diagonals, we can find the area of the rhombus by multiplying them and dividing by 2

Area = (24 * 2√(119))/2

Area = 24√(119)

Therefore, the area of the rhombus is 24√(119) square meters.

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--The given question is incomplete, the complete question is given

"  The area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m is ..........."--

a study reported that in a sample of 100 people who watch television news, 41 had elevated diastolic blood pressure levels (in millimeters of mercury, or mmhg). in a sample of 60 people who do not watch television news, 15 had elevated diastolic blood pressure levels. at the 5% level of significance, can you conclude that the proportion of people with elevated diastolic blood pressure levels differs between news-watchers and those who do not watch news? compute the p-value of the test. use at least five decimal places for the denominator during your computations. pick a closest value among the choices.

Answers

the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the proportion of people with elevated diastolic blood pressure levels differs between news-watchers and non-watchers. the correct answer is: 0.03120.

To determine whether the proportion of people with elevated diastolic blood pressure levels differs between news-watchers and non-watchers, we can conduct a hypothesis test using a two-sample proportion test.

Let p1 be the proportion of news-watchers with elevated diastolic blood pressure levels and p2 be the proportion of non-watchers with elevated diastolic blood pressure levels. The null hypothesis is that there is no difference in proportions:

H0: p1 = p2

Ha: p1 ≠ p2

We can calculate the sample proportions as:

p1 = 41/100 = 0.41

p2 = 15/60 = 0.25

The pooled proportion is:

p = (41 + 15)/(100 + 60) = 0.33

The test statistic is:

z = (p1 - p2) / sqrt(p * (1 - p) * (1/100 + 1/60))

= (0.41 - 0.25) / sqrt(0.33 * 0.67 * (1/100 + 1/60))

= 2.156

Using a standard normal distribution table, the p-value for a two-tailed test at the 5% level of significance is:

p-value = 2 * (1 - P(Z < 2.156))

= 2 * (1 - 0.9842)

= 0.0312

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7.03 Inscribed Quadrilaterals
pls help

Answers

The measures of the angles of cyclic quadrilaterals will be -

Blank 1: 98 degrees

Blank 2: 82 degrees

The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.

Given that, the angles of the cyclic quadrilateral are

angle BAD = 14x

angle ADC = 10x + 5

angle ABC = 15x

Clearly angle ABC and angle ADC are opposite angles of a cyclic quadrilateral. So,

angle ABC + angle ADC = 180

15x + 10x + 5 = 180

25x = 180 - 5

25x = 175

x = 175/25

x = 7

So angle BAD = 14x = 14*7 = 98 degrees

angle ABC = 15x = 15*7 = 105 degrees

angle ADC = 10x + 5 = 10*7 + 5 = 75 degrees

Since we know that the sum of all angles of a quadrilateral is 360 degrees. So, the angle BCD = 360 - (98 + 105 + 75) = 82 degrees.

So Blank 1 will be '98 degrees' and Blank 2 will be '82 degrees'.

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Solve this question please because I don’t get it at all.

Answers

Answer:

20,908

Step-by-step explanation:

We can represent the amount of people after each year as 103% of the amount from the previous year. Using this logic, we can multiply the town's original population (its principal value) by 103% 7 times, because the increase happens every year. We can represent this in the equation:

P = (og. population) × 103%⁷

We can use an exponent of 7 to indicate repeated multiplication, and when plugging a percentage into a calculator, we have to represent it as a decimal (103% => 1.03).

P = 17,000 × 1.03⁷

P ≈ 20,907.86

P ≈ 20,908

Note that we rounded the population to the nearest whole number as instructed instead of performing a more realistic truncation of the partial person.

Anthony purchased a $213 stereo system at Wrigley's Department Store. He paid $47 down and agreed to pay the balance in 12 equal monthly payments. The finance charge was 8. 1% simple annual interest. What was the amount of each payment?​

Answers

Each monthly payment will be approximately $20.50, which includes the principal amount of $166 and the finance charge of 8.1% simple annual interest.

To find the amount of each monthly payment for the stereo system, we need to take into account the finance charge of 8.1% simple annual interest. Since the payments are made monthly, we need to convert this to a monthly interest rate by dividing by 12, which gives us an interest rate of 0.675% per month (8.1%/12).

The balance of the stereo system after the down payment is $213 - $47 = $166. This is the amount that Anthony will be paying off in 12 equal monthly payments.

To find the amount of each payment, we can use the formula for the present value of an annuity:

PV = P * (1 - (1 + r)⁻ⁿ) / r

where PV is the present value of the annuity (the amount Anthony owes), P is the payment amount, r is the monthly interest rate (0.675%), and n is the number of payments (12).

Substituting the values we have, we get:

166 = P * (1 - (1 + 0.00675)⁻¹²) / 0.00675

Simplifying this equation, we get:

166 = P * 8.0951

Dividing both sides by 8.0951, we get:

P = 166 / 8.0951

P ≈ $20.50

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from a group of six people, two individuals are to be selected at random. how many selections are possible? group of answer choices 12 36 15 8

Answers

There are a total of six people in the group. To select two individuals at random, we can use the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of individuals in the group and r is the number of individuals to be selected. Therefore, the number of selections possible is:

6C2 = 6!/(2!(6-2)!) = 15

The formula for combinations is used to calculate the number of ways we can select r individuals from a total of n individuals. This formula is nCr = n!/r!(n-r)!. In this case, n is 6 (the total number of individuals in the group) and r is 2 (the number of individuals to be selected). Therefore, we substitute n=6 and r=2 into the formula to obtain the number of selections possible.

The number of selections possible from a group of six people, where two individuals are to be selected at random, is 15. This is obtained by using the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of individuals in the group and r is the number of individuals to be selected.

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For each combination of sample size and sample proportion, find the approximate margin of error for the 95% confidence level. (Round the answers to three decimal places.)
(a) n = 200, pÌ = 0.52. (b) n = 800, pÌ = 0.52. (c) n = 800, pÌ = 0.10. (d) n = 800, pÌ = 0.70. (e) n = 1200, pÌ = 0.60.

Answers

The margin of error is:

a) 0.069

b) 0.035

c)  0.021

d) 0.032

e) 0.028

What is confidence level?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Given,

Here at 95% CI, the z value is 1.96

a) sample n = 200, p = 0.52

Now, we find the margin of error and we get

Margin of error = z×√(p(1-p)/n)

Now, substitute values of p, n, and z and we get

= 1.96×√(0.52(1-0.52)/200)

= 0.069

b) n = 800 , p = 0.52

Margin of error = z×√(p(1-p)/n)

Now, we substitute values of n, p, and z and we get

= 1.96×√(0.52(1-0.52)/800)

= 0.035

c) n = 800 , p = 0.1

First,  we find the margin of error and we get

Margin of error = z×√(p(1-p)/n)

Now, we substitute values and we get

= 1.96×√(0.1(1-0.1)/800)

= 0.021

d) n = 800 , p = 0.7

Margin of error = z×√(p(1-p)/n)

Now, we substitute values and we get

= 1.96×√(0.7(1-0.7)/800)

= 0.032

e) n = 1200 , p = 0.60

First, we find the margin of error and we get

Margin of error = z×√(p(1-p)/n)

After substituting values we get

= 1.96×√(0.6(1-0.6)/1200)

= 0.028

Hence,

The margin of error is:

a) 0.069

b) 0.035

c)  0.021

d) 0.032

e) 0.028

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Problem 1: Healthcare for all American A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage. What is the sample in this study? What is the population of interest? What is the variable of interest in this study?

Answers

The sample in this study refers to the 1050.

The population of interest is all adult Americans.

The variable of interest in this study is the belief of adult Americans regarding the responsibility of the federal government to ensure healthcare coverage for all Americans.

As it is given in the question that Healthcare for all American A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government. So, the sample in this study refers to the 1050 adult Americans who participated in the Gallup poll.

The population of interest is all adult Americans, which means the Gallup poll results aimed to provide insights into the beliefs of all adult Americans regarding the responsibility of the federal government must secure universal healthcare coverage.

The variable of interest in this study is the belief of adult Americans regarding the responsibility of the federal government to ensure healthcare coverage for all Americans. The variable can be expressed in binary form, where 1 represents those who believe that the federal government has a responsibility to ensure healthcare coverage for all Americans, and 0 represents those who do not believe that the federal government has this responsibility. In the given poll, 493 out of 1050 respondents believed that the federal government has a responsibility to ensure healthcare coverage for all Americans.

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considerthedata(wines2012)datatable.thesedataareexpertratingsof20differentfrench and american wines by 9 different french and american judges. your goal is to model score, the subjective rating assigned by each judge to each wine. i recommend standardizing it. in this problem, consider only variation among judges and wines. construct index variables of judge and wine and then use these index variables to construct a linear regression model. justify your priors. you should end up with 9 judge parameters and 20 wine parameters. how do you interpret the variation among individual judges and individual wines? do you notice any patterns, just by plotting the differences? which judges gave the highest/lowest ratings? which wines were rated worst/best on average?

Answers

The goal of this problem is to create a model for the subjective ratings assigned to 20 different French and American wines by 9 different judges. To start, it is recommended to standardize the scores. For this problem, we only consider the variation among judges and wines. To construct the index variables of judge and wine, we can assign a number to each judge and each wine. Using these index variables, we can construct a linear regression model.

The priors for this problem should be that each judge and wine has a unique effect on the subjective rating. This means that we expect each judge to rate the wines differently and each wine to have its own unique characteristics that affect the rating.

By plotting the differences, we may notice patterns in the data. For example, some judges may consistently give higher or lower ratings compared to the other judges. Some wines may consistently receive higher or lower ratings compared to the other wines.

Based on the model, we can interpret the variation among individual judges and individual wines as the unique effect that each judge and wine has on the subjective rating. This means that the rating assigned by a particular judge may be influenced by their personal preferences and biases, and the rating assigned to a particular wine may be influenced by its unique characteristics.

By analyzing the model, we can identify which judges gave the highest and lowest ratings, and which wines were rated the worst and best on average. This information can be useful for understanding the preferences of the judges and the characteristics of the wines.

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find the first five non-zero terms of power series representation centered at for the function below : f(x) = ln (4-x). what is the radius of convergence?

Answers

The first five non-zero terms of power series representation centered at for the function below : f(x) = ln (4-x): The radius of convergence is (4-2)/2 = 1.

To find the first five non-zero terms of the power series representation centered at 0 for the function f(x) = ln(4-x), we'll first rewrite the function using a Maclaurin series. We know that ln(1+z) can be expressed as the following Maclaurin series:

ln(1+z) = z - (z^2)/2 + (z^3)/3 - (z^4)/4 + ...

Now, let z = 4 - x - 1 = 3 - x. Then, f(x) = ln(1+(3-x)) and the series becomes:

f(x) = (3-x) - ((3-x)^2)/2 + ((3-x)^3)/3 - ((3-x)^4)/4 + ...

Now, we can find the first five non-zero terms of the series:

1st term: (3-x)
2nd term: -(1/2)(3-x)^2
3rd term: (1/3)(3-x)^3
4th term: -(1/4)(3-x)^4
5th term: (1/5)(3-x)^5

For the radius of convergence, we can use the Ratio Test on the series representation of ln(1+z):

|z^(n+1)/(n+1) * n/z^n| = |n/(n+1) * z|

Take the limit as n approaches infinity:

lim (n→∞) |n/(n+1) * z| = |z|

For the series to converge, the absolute value of z must be less than 1. In our case, z = 3-x, so:

|3-x| < 1

Solve for x:

-1 < (3-x) < 1
2 < x < 4

The radius of convergence is (4-2)/2 = 1.

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on a coordinate plane, mariana's house is at (1,2) and her grandparent's house is at (7,10) what is the shortest distance, in units, between the two houses?

Answers

The shortest distance, in units, between the two houses is 10 units.

How to find the distance?

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

distance = √( (x₂ - x₁)² + (y₂ - y₁)²)

Here we want to find the distance between the points (1,2) and (7, 10), using the formula we will get:

distance = √( (7 - 1)² + (10 - 2)²)

distance = 10 units.

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Harley-davidson motorcycles reportedly make up 32% of all motorcycles registered in the united states. you think that is an understatement. you interview a random sample of 600 motorcycle owners and find that 33.8% of them own harleys.the hypotheses are: a. h0: p less or equal than 0.338 h1: p greater than 0.338 b. h0: p with hat on top less or equal than 0.32 h1: p with hat on top greater than 0.32 c. h0: p equals 0.32 h1: p not equal to 0.32 d. h0: p less or equal than 0.32 h1: p greater than 0.32

Answers

The correct option is option d). The hypothesis that fits the scenario is option d).

The null hypothesis (H0) is that the proportion of Harley-Davidson motorcycle owners is less than or equal to 0.32, while the alternative hypothesis (H1) is that the proportion is greater than 0.32.

This is because the initial claim is that Harley-Davidson motorcycles make up 32% of all motorcycles registered in the United States, but the researcher believes that this is an understatement. When conducting a random sample of 600 motorcycle owners, 33.8% of them owned Harley-Davidson motorcycles, which supports the alternative hypothesis that the proportion is greater than 0.32.

Therefore, the hypothesis testing is focused on rejecting the null hypothesis in favor of the alternative hypothesis, which is d. H0: p ≤ 0.32 and H1: p > 0.32.

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Sara is studying how quickly adults tire after eating turkey. She splits a group of 20 adults into 2 groups. One group is given turkey to eat and the other group is not given anything to eat. Sara asks the adults to start exercising at the same, and to stop when they tire, measuring the time each adult stops exercising. She finds that the adults who did not eat turkey exercised 2 minutes longer than those who did eat turkey. Sara rerandomizes the data, calculates the difference between the means, and creates the dot plot shown below. Based on the data, can sara conclude the difference is significant?.

Answers

Yes, Sara can conclude the difference is significant because a 2-minute difference is not likely to happen by chance.

Given, that Sara is studying how quickly adults tire after eating turkey. She splits a group of 20 adults into 2 groups.

One group is given a turkey to eat and the other group is not given anything to eat.

Sara asks the adults to start exercising at the same and to stop when they tire, measuring the time each adult stops exercising.

She finds that the adults who did not eat turkey exercised 2 minutes longer than those who did eat turkey.

We have to determine Sara rerandomizes the data, calculates the difference between the means, and creates the dot plot shown below.

Level of significance measures the unlikeliness of a hypothesis's against the measured reading.

0.05 is a common level of significance which depicts that there are 5% chances of a  type I error thereby rejecting a true null hypothesis in a one-way test.

In two way test, it depicts that there are 2.5% chances of a  type I error thereby rejecting a true null hypothesis.

It is the probability of rejecting a null hypothesis with a probability of test suffering an error of type based on the data, Sara can conclude that the difference is significant because when we are analyzing data and reach a statistically significant result then nothing or no event happens by chance.

Sara can conclude that the difference is significant because a two minutes difference is not likely to happen by chance.

In analyzing data, a statistically significant result is one that is not attributed to chance, that is, there is no way the event could have occurred by chance.

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what is the answser?

Answers

The volume of the cylinder in the diagram is  226.08 m²

How to find the volume of the prism?

The volume of a cylinder of diameter D and height H is:

V = pi*(D/2)²*H

wher pi = 3.14

In the diagram we can see that the cylinder has a diameter of 6 meters and a height of 8 meters, replacing that in the formula above, we can get:

V = 3.14*(6m/2)²*8m

V = 226.08 m²

That is the volume of the cylinder.

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Answer:

V = 72π m³ (exact)

V = 226.19 m³ (approximate)

SA = 66π m² (exact)

SA = 207.34 m² (approximate)

Step-by-step explanation:

Since you don't specify what you are looking for, here are the volume and surface area.

Volume:

V = πr²h

Total Surface Area

SA = 2πr² + 2πrh

r = d/2 = 6 m / 2 = 3 m

V = πr²h
V = π × (3 m)² × 8 m

V = 72π m³ (exact)

V = 226.19 m³ (approximate)

SA = 2πr² + 2πrh

SA = 2 × π × (3 m)² + 2 × π × 3 m × 8 m

SA = (18π + 48 π) m²

SA = 66π m² (exact)

SA = 207.34 m² (approximate)

find the limit if is exists. if it exists, enter the value of the limit. if it does not exist enter dne. y sin(x-y)

Answers

The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: [tex]\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)[/tex]

We have to find the limit of the given function.

=  [tex]\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)[/tex]

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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