To find the maximum value of a and the minimum value of b, we need to solve the equation 9+9x-x²-x³ = k for x and then determine the range of values for k where the equation has only one solution.
First, we can rearrange the equation to get:
x³ + x² - 9x - (k - 9) = 0
We can then use the rational root theorem to find the possible rational roots of this polynomial equation. The possible rational roots are of the form p/q, where p is a factor of the constant term (k - 9) and q is a factor of the leading coefficient (1). The factors of (k - 9) are ±1, ±3, ±(k-9), and the factors of 1 are ±1. So the possible rational roots are:
±1, ±3, ±(k-9), ±(k-9)/3
We can test each of these possible roots by plugging them into the equation and checking if the result is zero. After testing each possible root, we find that the only root that works is x = 3. Therefore, the equation has only one solution when x = 3.
To determine the range of values for k where the equation has only one solution, we can substitute x = 3 into the equation:
9 + 9(3) - 3² - 3³ = k
Simplifying this, we get:
k = -9
So the equation has only one solution when k = -9. Now, we need to find the maximum value of a and the minimum value of b for this value of k.
For k < -9, the equation has no real solutions, since the equation is a cubic polynomial with a negative leading coefficient, which means it has a local maximum and a local minimum. Therefore, the maximum value of a is -9.
For k > -9, the equation has three real solutions, since the equation is a cubic polynomial with a negative leading coefficient, which means it has a local maximum and a local minimum, and crosses the x-axis three times. Therefore, the minimum value of b is -9.
So the maximum value of a is -9 and the minimum value of b is -9.
using a .05 level of significance, conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts. what is the p-value and what is your conclusion?
To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.
The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.
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20% of a population of tree frogs are brightly-colored. One hundred of the frogs are sampled randomly; let X represent the number of them that are brightly colored. In which of the following cases would the standard deviation of X be smaller? A)The sampling is without replacement B)The sampling is with replacement C)Not enough information given
The standard deviation of X would be smaller if the sampling is with replacement (option B). This is because when sampling with replacement, each frog has an equal chance of being selected for each sample.
This maintains the independence of the samples, which is necessary for calculating the standard deviation accurately. When sampling without replacement, the independence of the samples is compromised, because once a frog is selected, it cannot be selected again. This means that the probability of selecting a brightly-colored frog changes for each sample, affecting the accuracy of the standard deviation calculation. Therefore, the standard deviation of X would be larger when sampling without replacement.
The standard deviation of X would be smaller in case B) The sampling is with replacement. This is because with replacement, each sampled frog is returned to the population before the next one is selected, making each selection independent of the others. Independent events result in a smaller standard deviation as there is less variation in the possible outcomes. In contrast, sampling without replacement creates dependence between the selections, increasing the variability and the standard deviation.
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Last spring, the average amount of rent paid for apartments in Greenpoint was $1,460. This spring, it is 0% less. What is the current average?
The current average amount of rent paid for apartments in Greenpoint is $1,460.
What are the current average?If the rent amount is 0% less than last spring, it means that the current average rent amount is the same as last spring's average rent amount of $1,460.
current average = (100% - 0%) x $1,460
current average = 100% x $1,460
current average = 1 x $1,460
current average = $1,460
So the current average amount of rent paid for apartments in Greenpoint is $1,460.
Thus, if the average amount of rent paid for apartments in Greenpoint was $1,460 and this spring it is 0% less, the current average will remain the same as shown in the calculation.
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a regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation below. one student in the sample was 73 inches tall with a foot length of 29 cm. what is the predicted foot length for this student? give your answer to two decimal places.
The provided regression equation can be used to predict the foot length for the given student:
Foot length = 5.00 + 0.51(Height)
Substituting the student's height of 73 inches into the equation, we get:
Foot length = 5.00 + 0.51(73) = 41.83 cm
Therefore, the predicted foot length for this student is 41.83 cm.
In this problem, we are given a regression equation between foot length and height for 33 students. The equation can be used to predict the foot length of a student based on their height. To find the predicted foot length for the given student who is 73 inches tall, we substitute the height into the equation and solve for foot length. The predicted foot length is obtained as 41.83 cm, which is rounded to two decimal places.
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Fifteen elves made some identical cakes for a
party. Each elf ate half of a cake, one-fifth of a
cake, and a third piece, which was six times
smaller than the second piece. Three cakes
were left untouched. How many cakes did the
elves make?
To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.
Now we can set up an equation:
7.5x + 0.3x + 6(0.3x) + 3 = x
Simplifying and solving for x, we get:
8.1x + 3 = x
7.1x = 3
x ≈ 0.42
However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.
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To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.
Now we can set up an equation:
7.5x + 0.3x + 6(0.3x) + 3 = x
Simplifying and solving for x, we get:
8.1x + 3 = x
7.1x = 3
x ≈ 0.42
However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.
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The spinner shown is spun once. find each probability p(6), p(prime number), p(odd or unshaded)
use the spinner below to help u solve this
The probabilities for this problem are given as follows:
p(6) = 1/12.p(prime number) = 1/2.p(odd or unshaded) = 3/4.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of regions is given as follows:
12.
One of these 12 regions is a six, hence:
p(6) = 1/12.
Six of these numbers are prime numbers, hence:
p(prime number) = 6/12 = 1/2.
Six of the numbers are odd, while 4, 6 and 9 are unshaded even numbers, hence:
p(odd or unshaded) = 9/12 = 3/4.
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a vet-med researcher carries out a hypothesis test to evaluate the claim that, in a population of dogs, 85% are good dogs. she obtains an independent sample of 120 dogs, and finds that 94 of these are good dogs. what is closest to the p-value for this result?
The closest answer to the p-value for this result is 0.0124.The p-value for this result, we need to first calculate the test statistic. Since we are testing a proportion, we will use the z-test.
The formula for the z-test is:
z = (p - P) / sqrt(P * (1 - P) / n)
where p is the sample proportion, P is the hypothesized population proportion, n is the sample size, and sqrt is the square root function. In this case, our sample size is n = 120, and our hypothesized population proportion is P = 0.85. Our sample proportion is p = 94/120 = 0.783.
Plugging in these values, we get:
z = (0.783 - 0.85) / sqrt(0.85 * 0.15 / 120) = -2.24
The p-value, we need to look up the area to the left of this value on the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0124.
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The perimeter of the trapezium, in millimeters (mm) is
The perimeter of trapezium, is 0.92 meters. And 0.92 meters in millimeters is 920 mm. Therefore, option B is the answer.
Let's name the trapezium as ABCD.
AB= 0.41m
BD= 0.21m
CD= 0.18m
AC= 0.12m
∴ AB and CD are parallel sides and AC and BD are oblique sides.
The perimeter of trapezium = Sum of parallel sides + Sum of oblique sides
The perimeter of trapezium = (AB+CD) + (AC+BD)
= (0.41+0.18) + (0.12+0.21)
= 0.59 + 0.33
∴ The perimeter of trapezium ABCD = 0.92 meters.
Converting 0.92 meters into millimeters (mm)
0.92 × 1000 = 920 millimeters (mm)
Therefore, the perimeter of trapezium in millimeters is 920 mm.
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The average of a class 21 student is 14 years 3 months. If the oldest student is not counted in the average drops to the 14 years 2 months. Calculate the age of the oldest student
The age of the oldest student is 13 years.
Let the age of the oldest student be x years.
The sum of ages of all 21 students is (21 × 14 years 3 months)
= (21 × 14) + (21 × 3/12) years
= 297 years
When the oldest student is not counted, the sum of ages is (20 × 14 years 2 months)
= (20 × 14) + (20 × 2/12) years
= 284 years
we have the equation:
297 - x = 284
Solving for x, we get:
x = 13 years
Therefore, the age of the oldest student is 13 years.
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work out an estimate for the value of 83 x 1.72
Answer:142.76
Step-by-step explanation:
Answer:
One method for calculating 83 x 1.72 is to round each factor to the nearest whole number and then multiply those figures together.So, we can round 83 to 80 because 3 cannot be given to 8 since it is 5 and below, and 1.72 to 2, because 7 is above 5 so i can +1 to 2.
80 x 1.7 = 136
So an estimate for 83 x 1.72 is approximately 136.
27 25 28 29 25 a. determine the mean and the standard deviation. b. at the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. assume the population is normally distributed. c. repeat the test using the
a. mean = 27, standard deviation 1.673
b. The calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.
c. The p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.
a. To determine the mean and standard deviation of the given data, calculate the following:
Mean:
(28 + 27 + 25 + 28 + 29 + 25) / 6
= 162 / 6 = 27 miles (mean)
Standard Deviation:
First, calculate the deviation from the mean for each data point:
(28 - 27) = 1
(27 - 27) = 0
(25 - 27) = -2
(28 - 27) = 1
(29 - 27) = 2
(25 - 27) = -2
Then, square each deviation:
1² = 1
0² = 0
(-2)² = 4
1² = 1
2² = 4
(-2)² = 4
Calculate the variance by summing the squared deviations and dividing by (n-1):
(1 + 0 + 4 + 1 + 4 + 4) / (6-1)
= 14 / 5 = 2.8
Finally, take the square root of the variance to get the standard deviation:
√2.8 ≈ 1.673 (standard deviation)
b. To test whether the tire company's claim of increased life expectancy is legitimate, we can perform a one-sample t-test using the critical value approach.
Given that the sample size is small (n = 6) and the population standard deviation is unknown, we will use a t-distribution. The null and alternative hypotheses are as follows:
Null Hypothesis (H0): The average life expectancy of the new tires is equal to the previous average of 26,000 miles.
Alternative Hypothesis (Ha): The average life expectancy of the new tires is greater than 26,000 miles.
Using the critical value approach at the 0.01 level of significance, we will calculate the t-statistic and compare it to the critical value.
Degrees of freedom (df) = n - 1 = 6 - 1 = 5
Calculate the t-statistic:
t = (sample mean - population mean) / (sample standard deviation / √(n))
t = (27 - 26) / (1.673 / √(6))
t ≈ 1.21
Using a t-table, find the critical value for a one-tailed test with 5 degrees of freedom at the 0.01 level of significance. For this example, let's assume the critical value is 2.571.
Since the calculated t-statistic (1.21) is not greater than the critical value (2.571), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.
c. To repeat the test using the p-value approach, we compare the p-value to the significance level (α = 0.01).
Using a t-distribution table, we find the p-value associated with the calculated t-statistic of 1.21. For this example, let's assume the p-value is 0.274.
Since the p-value (0.274) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the average life expectancy of the new tires is significantly greater than 26,000 miles.
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Given question is incomplete, the complete question is below
A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires life expectancy has increased. In order to test the legitimacy of its advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data.
Life expectancy (In thousands of miles)
28
27
25
28
29
25
a. Determine the mean and the standard deviation
b. at the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.
c. Repeat the test using the p-value approach.
1|G9_ IGCSE1 - Chapter 14 Linear inequalities - Question 1 Solve the inequality. 3n-5> 17+8n Math
Answer:
n < -22/5
Step-by-step explanation:
3n - 5 > 17 + 8n
-5n - 5 > 17
-5n > 22
n < -22/5
A train travelled 200 mi.in 5 hrs. At that rate how far would it travel in 8 hrs.
To find how far the train would travel in 8 hours at the same rate, we can use the formula:
distance = rate x time
We know that the train traveled 200 miles in 5 hours, so we can find its rate as:
rate = distance / time = 200 miles / 5 hours = 40 miles per hour
Now we can use this rate to find how far the train would travel in 8 hours:
distance = rate x time = 40 miles per hour x 8 hours = 320 miles
Therefore, the train would travel 320 miles in 8 hours at the same rate.
y= x square + 14x -9
what is the probability that Aakesh will select a blue marble from each other
Aakash will choose a blue stone from each bag is ,
⇒ 2/27.
Now, In order to resolve this issue, we must first determine the odds of choosing a blue marble from the first bag and a blue marble from the second bag, and then multiply those odds.
Hence, When choosing a blue marble from the first bag, there is a chance of:
P(blue from first bag) = 5/15
The likelihood of drawing a blue marble from the second bag is as follows:
Blue from the second bag: P(blue) = 2/9
Hence, The chances of drawing a blue marble from each bag are as follows:
Blue from the first bag, P Blue from the second bag:
⇒ P(1/3) (2/9) = 2/27
Hence, The probability to choose a blue stone from each bag is ,
⇒ 2/27.
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Complete question is,
Aakesh has two bags of marbles. The first bag contains 6 red marbles, 5 blue marbles, and 4 green marbles. The second bag contains 3 red marbles, 2 blue marbles, and 4 green marbles. Aakesh will randomly select one marble from each bag,
What is the probability that Aakesh will select a blue marble from each bag?
Assume ABC= ADEF. If AB = 18, BC = 10, and AC - 25, what is the length
of DF?
• A. 25
• B. Cannot be determined
• c. 10
• D. 18
"The correct answer is B. Cannot be determined." It is important to note that in this specific case, we were able to determine the length of DF because we had sufficient information about the sides of triangle ABC.
Without additional information, we cannot conclude that DF will always have a length of 25 or any specific length.
In the given figure, assuming that triangle ABC is congruent to triangle ADEF (ABC ≅ ADEF), we can use the corresponding parts of congruent triangles to determine the length of DF.
From the information provided, we know that AB = 18, BC = 10, and AC = 25.
Since ABC ≅ ADEF, the corresponding sides are congruent. Therefore, we can conclude that DE = 18, EF = 10, and AD = 25.
To find the length of DF, we need to sum up the lengths of DE and EF:
DF = DE + EF = 18 + 10 = 28
The length of DF is 28.
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agencia de viajes quiere incrementar el turismo nacional por carretera, para ello genera una estrategia
publicitaria, cuyos resultados exitosos se verían reflejados cuando
A. se mantengan los porcentajes de respuesta a la pregunta 2
B. se aumente el porcentaje de personas que prefieren viajar a lugares cercanos a su residencia, en la
pregunta 3
C. los porcentajes de respuesta a la pregunta 1 quedan intercambiados y se mantengan los porcentajes en
las otras preguntas
D. se disminuyan los porcentajes de los que no prefieren viajar por carretera, en la pregunta
Options B and D are the most relevant to the Objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.
A travel agency's goal is to increase national tourism by road, and they have developed an advertising strategy to achieve this. The success of this strategy will be reflected in certain criteria. Let's examine the options:
A. Maintaining the response rates to question 2.
This option does not directly indicate how it relates to the objective of increasing national tourism by road. It does not specify how the response rates to question 2 contribute to achieving the goal.
B. Increasing the percentage of people who prefer to travel to places close to their residence, as mentioned in question 3.
This option aligns with the objective of promoting national tourism by road. By encouraging people to choose destinations that are closer to their residences, the travel agency aims to promote road travel within the country. Therefore, this option is relevant to the goal of increasing national tourism by road.
C. Exchanging the percentages of answers to question 1 and maintaining the percentages in the other questions.
This option does not provide clear information on how it relates to the objective of increasing national tourism by road. Swapping the percentages of answers to question 1 alone may not directly contribute to the goal unless the specific content of the question is known.
D. Reducing the percentages of those who do not prefer to travel by road, as mentioned in the question.
This option is directly aligned with the objective of increasing national tourism by road. By reducing the percentage of people who do not prefer road travel, the travel agency aims to attract more travelers to choose road transportation for their trips.
In conclusion, options B and D are the most relevant to the objective of increasing national tourism by road. By increasing the percentage of people who prefer to travel to nearby destinations and reducing the percentage of those who do not prefer road travel, the travel agency can effectively promote road tourism within the country.
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Tarek has 72 feet of plastic fencing to make a flower garden in his backyard. The garden shape can either be circular or square. If he uses all of the fencing, what is the difference between the area of the circular garden and the square garden? Use 3. 14 for π. Round to the nearest hundredth if necessary
Let's calculate the difference between the area of the circular garden and the square garden using the given information.
For the circular garden:
The circumference of a circle is given by the formula: C = 2πr, where r is the radius.
Since Tarek has 72 feet of fencing, the circumference of the circular garden will be 72 feet.
So, we have: 2πr = 72.
Dividing both sides by 2π, we get: r = 72 / (2π) ≈ 11.46 feet (rounded to two decimal places).
The area of a circle is given by the formula: A = πr².
Substituting the value of r, we get: A = π(11.46)² ≈ 412.49 square feet (rounded to two decimal places).For the square garden:
The perimeter of a square is given by the formula: P = 4s, where s is the length of each side.
Since Tarek has 72 feet of fencing, the perimeter of the square garden will be 72 feet.
So, we have: 4s = 72.
Dividing both sides by 4, we get: s = 72 / 4 = 18 feet.
The area of a square is given by the formula: A = s².
Substituting the value of s, we get: A = (18)² = 324 square feet.
Now, let's calculate the difference between the areas:
Difference = Area of circular garden - Area of square garden
Difference ≈ 412.49 square feet - 324 square feet
Difference ≈ 88.49 square feet (rounded to two decimal places).
Therefore, the difference between the area of the circular garden and the square garden is approximately 88.49 square feet.
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8. Assume 'a' and 'b' are positive integers. Decide whether each statement is true or false
a!(b!c!) = (a!b!)c!
True
False
Answer: False
Step-by-step explanation: The order of multiplication matters, and in this case, the two sides of the equation are not equal.
Variable costs are the costs incurred for treating each patient. Normally it consists of supplies such as gloves, needles, syringes, gowns, or other items used in the practice. Different methods exist to assign variable costs. For the Capstone Project, the hospital system will cover variable costs by assigning (or taking) 10% of total reimbursement of each patient visit
Net reimbursement per patient will be [tex]90[/tex]% of the total reimbursement per patient.
What is the net reimbursement per patient?Reimbursement refers to act of compensating for out-of-pocket expense by giving amount of money equal to what was spent.
Let R be the total reimbursement per patient.
Now, the net reimbursement per patient can be calculated as follows:
Net Reimbursement = Total Reimbursement - Variable Costs
Net Reimbursement = R - (0.10 * R)
Net Reimbursement = R * 0.9
Net Reimbursement = 0.9R
So, the net reimbursement per patient will be 90% of the total reimbursement per patient.
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Use the table to answer the question.
Preferences Mountains Seaside Island
Hiking 45 20 12
Swimming 12 53 40
Given the data in the table, what is the relative frequency that the people who prefer hiking also prefer mountains? Round the percentage to the nearest tenth.
(1 point)
%
The relative frequency that the people who prefer hiking also prefer mountains is 58.4%.
Based on the table, there are 45 people who prefer both hiking and mountains. To find the relative frequency, we will calculate the total number of people who prefer hiking, which is 45 (mountains) + 20 (seaside) + 12 (island) = 77.
To find the percentage, divide the number of people who prefer both hiking and mountains by the total number of people who prefer hiking:
45 / 77 ≈ 0.5844
Now, multiply this result by 100 to get the percentage and round to the nearest tenth:
0.5844 * 100 ≈ 58.4%
So, the relative frequency that people who prefer hiking also prefer mountains is approximately 58.4%.
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in how many ways can three different integers be selected from 1 - 10 such that no two integers chosen are consecutive
There are 56 different ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive.
To determine the number of ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive, we can use combinatorics principles.
First, let's consider the total number of ways to choose three integers without any restrictions. This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
In this case, we have 10 integers to choose from, and we want to choose 3. Therefore, the total number of ways to choose three integers without any restrictions is:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = 120
Now, let's consider the restricted condition that no two chosen integers can be consecutive. We can approach this by selecting three non-consecutive integers from the available set.
To do this, we can start by choosing any integer, then excluding its two adjacent integers. For example, if we choose 1, we cannot choose 2 or 3. Similarly, if we choose 10, we cannot choose 9 or 8.
Since there are two adjacent integers to exclude for each choice, we have 8 integers remaining to choose from. Therefore, the number of ways to select three non-consecutive integers is:
C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = 56
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Write an equation in point-slope form of the line that passes through the point (2, 1)
and has a slope of m=2
.
Answer:
y - 1 = 2(x - 2)-----------------------
Point-slope form is:
y - y₁ = m(x - x₁), where, m is the slope and (x₁, y₁) is the point on the lineSubstitute the given into equation:
y - 1 = 2(x - 2)Using Pythagoras' theorem, calculate the length of XY. Give your answer in centimetres (cm) to 1 d.p. 15 cm Z X 7 cm Y Not drawn accurately
Answer:
13.3cm
Step-by-step explanation:
The Pythagorean theorem is [tex]a^{2} +b^{2} =c^{2}[/tex].
Plug the values into the equation.
[tex]7^{2} +b^{2} =15^{2}[/tex]
Simplify.
[tex]49+b^{2} =225[/tex]
Subtract 49 from both sides.
[tex]b^{2} =176[/tex]
Take the square root of both sides.
[tex]\sqrt{b^{2}} =\sqrt{176[/tex]
b=13.266
b=13.3cm
segment jk has coordinates j(3 -6) and k(-3 2). Find the coordinates of the midpoint M. Find the distance between the endpoints of JK.
The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.
To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).
To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.
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a factory has two machines A and B producing 300 and 720 bulbs per day respectively. machine A produces 1% defective bulbs and machine B produces 1.5% defective bulbs. One bulb is chosen at random at the end of a day and found. what is the probability that machine B produce defective bulb ?
The Probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.
To find the probability that the defective bulb was produced by machine B, we can use Bayes' theorem.
Let event A be the defective bulb being chosen, and event B be the bulb being produced by machine B. We want to find P(B|A), the probability that the bulb was produced by machine B given that it is defective.
From the information given, we know that machine A produces 300 bulbs per day, of which 1% (3 bulbs) are defective, while machine B produces 720 bulbs per day, of which 1.5% (10.8 bulbs) are defective.
Thus, the total number of defective bulbs produced per day is 3 + 10.8 = 13.8.
The probability of choosing a defective bulb is equal to the total number of defective bulbs divided by the total number of bulbs produced per day:
P(A) = 13.8 / (300 + 720) = 0.016
The probability of machine B producing a bulb is equal to the number of bulbs produced by machine B divided by the total number of bulbs produced per day:
P(B) = 720 / (300 + 720) = 0.706
The probability of a bulb being defective given that it was produced by machine B is equal to the number of defective bulbs produced by machine B divided by the total number of bulbs produced by machine B:
P(A|B) = 10.8 / 720 = 0.015
Now, we can use Bayes' theorem to find P(B|A):
P(B|A) = P(A|B) * P(B) / P(A)
Substituting in the values we have calculated, we get:
P(B|A) = 0.015 * 0.706 / 0.016
Simplifying the equation, we get:
P(B|A) = 0.664
Therefore, the probability that the defective bulb was produced by machine B is approximately 0.664 or 66.4%.
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a forester measured 40 of the trees in a large woods that is up for sale. he found that their mean diameter was 187 inches and their standard deviation 20.4 inches. suppose that these trees provide an accurate description of the whole forest and that the diameter of the tree follows a normal distribution. answer the following: a) what percentage of trees would be below 191 inches in diameter? b) what percentage of trees would be between 176 and 196 inches? c) what size diameter represents the bottom 35% of the trees? d) what size diameter represents the top 35% of the trees?
Approximately 57.83% of trees would be below 191 inches in diameter.
Approximately 37.48% of trees would be between 176 and 196 inches in diameter.
A diameter of approximately 194.83 inches represents the top 35% of the trees.
To find the percentage of trees below 191 inches in diameter, we need to calculate the cumulative probability below that value.
Using the mean and standard deviation given:
Mean (μ) = 187 inches
Standard Deviation (σ) = 20.4 inches
We can standardize the value 191 inches using the z-score formula:
z = (x - μ) / σ
z = (191 - 187) / 20.4 ≈ 0.1961
Next, we find the cumulative probability using the z-score:
P(Z < 0.1961)
Using a standard normal distribution table or calculator, we find that P(Z < 0.1961) ≈ 0.5783.
b) To find the percentage of trees between 176 and 196 inches in diameter, we need to find the cumulative probability between these values.
First, we calculate the z-scores for both values:
z1 = (176 - 187) / 20.4 ≈ -0.5392
z2 = (196 - 187) / 20.4 ≈ 0.4412
Next, we find the cumulative probabilities for each z-score:
P(Z < -0.5392) ≈ 0.2946
P(Z < 0.4412) ≈ 0.6694
To find the probability between these two values, we subtract the smaller probability from the larger probability:
P(-0.5392 < Z < 0.4412) = 0.6694 - 0.2946 ≈ 0.3748
c) To find the diameter that represents the bottom 35% of the trees, we need to find the z-score corresponding to that percentile.
Using a standard normal distribution table or calculator, we find the z-score that corresponds to the bottom 35% is approximately -0.3853.
Next, we can solve for the diameter using the z-score formula:
-0.3853 = (x - 187) / 20.4
Solving for x, we get:
x ≈ 179.17 inches
So, a diameter of approximately 179.17 inches represents the bottom 35% of the trees.
d) To find the diameter that represents the top 35% of the trees, we can use the same approach as in part c) but with the z-score corresponding to the top 35% (which is the same as the bottom 65%).
Using a standard normal distribution table or calculator, we find the z-score that corresponds to the top 35% (bottom 65%) is approximately 0.3853.
Using the z-score formula:
0.3853 = (x - 187) / 20.4
Solving for x, we get:
x ≈ 194.83 inches
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Given the semi-circle shown, find the values of both x and y .
Check the picture below.
Solve for x
Geometry
Answer:
x = 11 degrees
Step-by-step explanation:
Those 2 angles would add up to 180.
So (11x+16) + 43 = 180
11x + 59 = 180
11x = 121
Divide both sides by 11
x = 121/11
x = 11
x = 11 degrees
Step-by-step explanation:
11x + 16 and 43 are supplementary ....they sum to 180 degrees
11x+ 16 + 43 = 180
11x = 121
x= 11
A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. With all conditions for inference met, the test produced a test statistic of t = -2.073 and a p- value of 0.042. Based on the p-value and a significance level of a = 0.05, which of the following is a correct conclusion? There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke. B There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. С There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is greater than the average time to swim a lap with the butterfly stroke. D There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. E There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.
A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.
With all conditions for inference met, the test produced a test statistic of t = -2.073 and a p- value of 0.042. Based on the p-value and a significance level of a = 0.05, which of the following is a correct conclusion? There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke. B There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. С There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is greater than the average time to swim a lap with the butterfly stroke. D There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. E There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.
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