"The Centers for Disease Control lists causes of death in the United States during 2011. Cause of Death Percent
Heart disease 23.7
Cancer 22.9
Circulatory diseases and stroke 5.1
Respiratory diseases 5.7
Accidents 5.0
a) Is it reasonable to conclude that heart or respiratory diseases were the cause of approximately 29% of U.S. deaths in 2011?
A. No, because there is the possibility of overlap.
B. Yes, because there is the possibility of overlap.
C. No, because there is no possibility for overlap.
D. Yes, because there is no possibility for overlap

Answers

Answer 1

The answer to this question is A. It is not reasonable to conclude that heart or respiratory diseases were the cause of approximately 29% of U.S. deaths in 2011 because there is a possibility of overlap.

This means that some people who died from heart disease may have also had respiratory diseases, and vice versa.

Therefore,

It is impossible to accurately determine the exact percentage of deaths caused by each individual disease.
It is important to note that the Centers for Disease Control lists the causes of death in the United States as the underlying cause, which is defined as the disease or injury that initiated the train of events leading directly to death.

However,

Many people who die from one disease may also have other underlying or contributing conditions.

This makes it difficult to determine the exact cause of death in some cases.
There could be potential overlap between heart and respiratory diseases, it is not reasonable to conclude that heart or respiratory diseases were the cause of exactly 29% of U.S. deaths in 2011.

In summary,

While heart and respiratory diseases were listed as the cause of a significant percentage of deaths in the United States in 2011, it is not accurate to conclude that they were the sole cause of approximately 29% of deaths due to the possibility of overlap.

It is important to consider all contributing factors when analyzing causes of death data.

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Related Questions

A club with 20 women and 17 men needs to choose three different members to be president,vice president and treasurer.¡) How many ways to choose president, vice president and treasurer?il How many ways to choose president, vice president and treasurer if man must bechosen as a president?iii) How many ways to choose president, vice president and treasurer if woman must bechosen as a president and vice president while man must be chosen as a treasurer?

Answers

i) 46,860 ways  to choose president, vice president and treasurer

ii) 21,420 ways to choose president, vice president and treasurer if man must bechosen as a president

iii) 6,460 ways to choose president, vice president and treasurer if woman must bechosen as a president and vice president while man must be chosen as a treasurer.

i) To choose the president, vice president and treasurer from a total of 37 members, we can use the permutation formula,

P(37,3) = 37 × 36  ×35 = 46,860.

Therefore, there are 46,860 ways to choose the three positions.

ii) If a man must be chosen as president, we have 17 options to choose the president from the male members. The remaining two positions can be filled by any of the 36 members. so we have

P(36,2) = 36 × 35 = 1,260

ways to fill those positions. Therefore, there are

17 × 1,260 = 21,420

ways to choose the three positions with a man as president.

iii) If a woman must be chosen as the president and vice president, we have 20 options to choose the president from the female members and 19 options to choose the vice president from the remaining female members. For the position of treasurer, we have 17 options to choose from the male members. Therefore, we have

20 × 19 × 17 = 6,460

ways to choose the three positions with a woman as president and vice president and a man as treasurer.

In summary, there are 46,860 ways to choose the three positions without any restrictions, 21,420 ways to choose with a man as president and 6,460 ways to choose with a woman as president and vice president and a man as treasurer.

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Sphere A is similar to Sphere B. The scale factor of the lengths of the radii of Sphere A to Sphere B is 4. Sphere A has the radius of 6 units and a volume of 288pi cubic units. Find the volume of Sphere B

Answers

The volume of the sphere B is 14.13 cubic units.

Given that the two similar spheres, the scale factor of the lengths of the radii of Sphere A to Sphere B is 4.

So, we need to find the volume of the sphere B,

So,

Radius A / Radius B = 4/1

6 / Radius B = 4

Radius B = 1.5

Now we know that the volume of a sphere = 4/3 × πr³

= 4/3 × 3.14 × 1.5³

= 42.39/3

= 14.13

Alternatively, you can calculate by =

We know that the ratio of the volumes of two similar solids is equal to the cube of their scale factor, so here, the scale factor is 4/1.

Therefore,

Volume A / Volume B = (4/1)³

288π / Volume B = 64

Volume B = 4.5π

Volume B = 14.13

Hence, the volume of the sphere B is 14.13 cubic units.

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(Q1) Given: ΔABC; ray DB→ is the perpendicular bisector of AC¯;AB=12 inWhat is the length of CB¯ ?By what Theorem?

Answers

The length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

By the perpendicular bisector theorem, if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment. Therefore, in triangle ABC, since ray DB is the perpendicular bisector of AC, it follows that BD = DC.

Let x be the length of CB. Then, by the Pythagorean theorem in triangle ABC, we have:

[tex]AB^2 + BC^2 = AC^2[/tex]

Substituting AB = 12 and BD = DC = x/2, we get:

[tex]12^2 + x^2 = (2x)^2[/tex]

[tex]144 + x^2 = 4x^2[/tex]

[tex]3x^2 = 144[/tex]

[tex]x^2[/tex]= 48

x = √(48) = 4√(3)

Therefore, the length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

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(L2) Given: PT¯ bisects ∠STR;PR¯ bisects ∠TRS;PS¯ bisects ∠RST;PX¯⊥RT¯;PY¯⊥ST¯;PZ¯⊥RS¯Prove: PX=PZ=PY

Answers

PS is the perpendicular bisector of ST, and P is equidistant from X and Y.

To prove that PX=PZ=PY, we need to show that P is the circumcenter of triangle XYZ, where X, Y, and Z are the midpoints of sides RT, ST, and RS, respectively.

First, we will show that P is equidistant from X and Z. Since PX is perpendicular to RT and PZ is perpendicular to RS, we have to show that PR is the perpendicular bisector of RT and RS. From the given information, we know that PR is the angle bisector of angle TRS and PS is the angle bisector of angle RST. Therefore, angle TPS is congruent to angle SPR, and angle SPR is congruent to angle RPS. This means that triangles RPS and TPS are similar, and we can use this similarity to show that PR is the perpendicular bisector of RT and RS. Specifically, we have:

PR/RS = PS/TS (by the angle bisector theorem)

PR/TS = PS/RS (by the same reasoning)

PR/TS = PR/RS (since PS/TS = PR/RS)

TS = RS (by cross-multiplying)

Therefore, PR is the perpendicular bisector of RT and RS, and P is equidistant from X and Z.

Next, we will show that P is also equidistant from X and Y. Since PY is perpendicular to ST, we have to show that PS is the perpendicular bisector of ST. Again using the angle bisector theorem, we have:

PS/RS = PT/RT

PS/TS = PT/RT

TS = RS

Therefore, PS is the perpendicular bisector of ST, and P is equidistant from X and Y.

Since P is equidistant from X, Y, and Z, it must be the circumcenter of triangle XYZ, and therefore PX=PZ=PY.

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The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?

Answers

If area of cattle's "square-field" is 40000 ft², and Mr. Blackburn is constructing a fence diagonal in the field, then length of cattle field's fence should be 282.84 ft.

The area of the Blackburn's family cattle square-field is 40000 ft²,

So, We First, equate this area with area formula,

On Equating ,We get,

⇒ (side × side) = 40000,,

⇒ side is 200 ft,

Now, we substitute the "side-length" of field as 200 ft, in the formula for diagonal of a square,

we get,

⇒ Length of cattle-field's diagonal is = (side)√2,

⇒ Length of cattle-field's diagonal is = (200)√2,

⇒ Length of cattle-field's diagonal is ≈ 282.84 ft.

Therefore, the length of cattle field's fence is 282.84 ft.

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7.03 Inscribed Quadrilaterals
pls help

Answers

The value of angles in inscribed quadrilateral are μ(∠zyx) is 92⁰ and μ(∠yxw) is 65⁰.

An inscribed quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that its vertices all lie on the circumference of a circle. In other words, the four vertices of an inscribed quadrilateral are concyclic.

The opposite angles of an inscribed quadrilateral are supplementary, which means that they add up to 180 degrees. This property is known as the "interior angle sum" of a quadrilateral.

μ(∠zyx) + μ(∠xwz) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)

μ(∠xwz) = 88⁰

μ(∠zyx) = 180⁰ - 88⁰ = 92⁰

μ(∠yzw) is an inscribed angle that intercepts the arc 112⁰ and 118⁰. Therefore,

μ(∠yzw)

= (112⁰ + 118⁰)/2

= 230⁰/2

= 115⁰

μ(∠yxw) + μ(∠yzw) = 180⁰  (opposite angle of cyclic quadrilateral are supplementary)

μ(∠yxw) = 180⁰ - 115⁰ = 65⁰

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Multiplying tree numbers to get 36

Answers

Answer:

(1,1,36), (1,3,12), (1,2,18), (1,6,6), (1,4,9), (2,3,6), (2,2,9), (3,3,4)

Step-by-step explanation:

, = multiply

CAN SOMEONE HELP ME WITH THESE 50 POINTS
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.

spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow

Determine P(not yellow) if the spinner is spun once.

75%
37.5%
25%
12.5%

Question 2

Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?

33%
0%
100%
66%

Question 3

A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3

Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1

Question 4

When tossing a two-sided, fair coin with one side colored yellow and the other side colored green, determine P(yellow).

yellow over green
green over yellow
2
one half

Question 5

When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, determine the probability of randomly drawing a consonant.

six thirds
six tenths
two thirds
two ninths

Question 6

When rolling a fair, eight-sided number cube, determine P(number greater than 2).

0.25
0.50
0.66
0.75

Question 7
Joseph has a bag filled with 2 red, 4 green, 10 yellow, and 9 purple marbles. Determine P(not purple) when choosing one marble from the bag.

64%
36%
24%
8%

Answers

Answer:

1. 75%

2. 0%

3. 0.1

4. one half

5. six tenths

6. 0.75

7. 64%

Step-by-step explanation:Answer 1:

The spinner has a total of 8 sections, out of which there are 2 yellow sections. Therefore, the probability of not getting a yellow section when the spinner is spun once is 6/8 or 3/4, which is equal to 75%.

Answer 2:

The spinner has only three sections and none of them is colored yellow. Therefore, the probability of getting a yellow section when the spinner is spun once is 0%.

Answer 3:

The total number of students surveyed is:

1 + 3 + 2 + 5 + 9 + 7 + 3 = 30

The number of students who studied for 1 hour is 3. Therefore, the probability of a student studying for 1 hour is 3/30, which simplifies to 1/10 or 0.1.

Answer 4:

Since the coin is fair and has one side colored yellow and the other side colored green, the probability of getting a yellow side when the coin is tossed is 1/2 or one half.

Answer 5:

The set of cards has 10 letters, out of which 4 are vowels (A, I, U). Therefore, the number of consonants in the set is 10 - 4 = 6. The probability of drawing a consonant is therefore 6/10, which simplifies to 3/5 or 0.6.

Answer 6:

The number cube has 8 sides, numbered 1 through 8. The probability of getting a number greater than 2 is the same as the probability of getting any number from 3 to 8. There are 6 such numbers out of 8 total numbers, so the probability is 6/8 or 3/4, which is equal to 0.75.

Answer 7:

The total number of marbles in the bag is:

2 + 4 + 10 + 9 = 25

The number of marbles that are not purple is:

2 + 4 + 10 = 16

Therefore, the probability of not getting a purple marble when one marble is chosen from the bag is 16/25, which is equal to 64%.

Carl has $500 in an account. Every 30 days, he withdraws $100. The amount of money remaining in his account is a function of the amount of time that has passed.


Which function models the amount of money remaining in Carl's account?

Answers

The function that models the amount of money remaining in Carl's account is [tex]M(t) = -100t + 500[/tex]..

What function models the amount of money remaining?

We will start by finding out how much money Carl will have left after each withdrawal:

After 30 days:

= $500 - $100

= $400

After 60 days:

= $400 - $100

= $300

After 90 days:

$300 - $100

= $200

After 120 days:

= $200 - $100

= $100

After 150 days:

= $100 - $100

= $0

We can see that Carl 5 withdrawals of $100 each over 150 days. So, we can use a linear function to model the amount of money remaining in Carl's account over time which is M(t) = -100t + 500.

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the side length of a rectangle is 5 more than three times the width. the side length has a measure of 65cm. what is the length of the width

Answers

Answer:

the width is 20cm

Step-by-step explanation:

According to the question the length is 5 more than three times the width which is 3 times the width plus 5 so you have to minus five from the length and divide your answer by three

Answer:

The width is 20 cm.

Step-by-step explanation:

Let w represent the measure of the width.

5 + 3w = 65

-5            -5

___________

3w = 60

÷ 3     ÷3

_______

w = 20 cm

Sky View School Riverside School0 5, 6, 99, 7, 2, 0 1 0, 2, 4, 5, 6, 78, 7, 6, 5, 5, 5, 4, 3, 1, 0 2 0, 0, 2, 3, 50 34 2Key: 2 | 1 | 0 means 12 for Sky View and 10 for RiversidePart A: Calculate the measures of center. Show all work. (5 points)Part B: Calculate the measures of variability. Show all work. (5 points)Part C: If you are interested in a larger class size, which school is a better choice for you? Explain your reasoning.

Answers

Part A: Sky View - median = 5.5, Riverside - median = 5.5

Part B: Sky View - range = 99, Riverside - range = 78

Part C: Sky View has a larger class size on average (12 vs 10), so it may be a better choice if a larger class size is desired.

Part A: Measures of Center

For Sky View School:

Mean: sum of values / number of values [tex]= (5 + 6 + 99 + 7 + 2 + 0) / 6 = 119 / 6 = 19.83[/tex]

Median: arrange the values in ascending order: 0, 2, 5, 6, 7, 99. The median is 6.5.

Mode: there is no mode as all values occur only once.

For Riverside School:

Mean: sum of values / number of values [tex]= (1 + 0 + 2 + 4 + 5 + 6 + 78 + 7 + 6 + 5 + 5 + 5 + 4 + 3 + 1 + 0) / 16 = 133 / 16 = 8.31[/tex]Median: The median is equal to the average of each of the middle values [tex](5 + 5 / 2 = 5)[/tex], which is 5.

Mode: the mode is 5 as it occurs most frequently.

Part B: Measures of Variability

For Sky View School:

Range: maximum value - minimum value = 99 - 0 = 99

Variance: [tex]((5-19.83)^2 + (6-19.83)^2 + (99-19.83)^2 + (7-19.83)^2 + (2-19.83)^2 + (0-19.83)^2) / (6-1) = 2134.4[/tex].

Standard deviation: approximately 46.2.

For Riverside School:

Range: maximum value - minimum value = 78 - 0 = 78

Variance: [tex]((1-8.31)^2 + (0-8.31)^2 + (2-8.31)^2 + (4-8.31)^2 + (5-8.31)^2 + (6-8.31)^2 + (78-8.31)^2 + (7-8.31)^2 + (6-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (5-8.31)^2 + (4-8.31)^2 + (3-8.31)^2 + (1-8.31)^2 + (0-8.31)^2) / (16-1) = 422.3.[/tex]

Standard deviation: approximately 20.55.

Part C: Answer with Explanation

If you are interested in a larger class size, Riverside School may be a better choice. This is because the mean and median class sizes at Riverside School are both smaller than those at Sky View School, indicating that the typical class size is smaller at Riverside. Additionally, the range and standard deviation of class sizes at Riverside School are smaller than those

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the number of points held by a sample of the nhl's highest scorers for both the eastern conference and the western conference is shown below. at , can it be concluded that there is a difference in means based on these data? assume the variables are normally distributed and the variances are unequal.

Answers

If the null hypothesis is rejected, then you can conclude that there is a difference in means based on the provided data. If not, then there isn't enough evidence to support a difference in means.

if there is a difference in means between the number of points held by a sample of NHL's highest scorers in the Eastern and Western conferences. To answer this, you'll need to follow these steps:

1. Identify the data: You need to have the points data for the NHL's highest scorers from both the Eastern and Western conferences.

2. Calculate the means: Calculate the average number of points for both conferences' samples.

3. Determine the variables: Since you've mentioned that the variables are normally distributed and have unequal variances, we can use the independent two-sample t-test with unequal variances (Welch's t-test) to determine if there is a significant difference in means.

4. Perform Welch's t-test: Using the means, variances, and sample sizes of both groups, calculate the t-value and degrees of freedom.

5. Compare the t-value to the critical t-value: Determine the critical t-value at a specified significance level (commonly α = 0.05) using the degrees of freedom. If the calculated t-value is greater than the critical t-value, you can reject the null hypothesis and conclude that there is a significant difference in means.

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(L3) The orthocenter will lie in the exterior of a(n) _____ triangle.

Answers

(L3) The orthocenter will lie in the exterior of a(n)  obtuse triangle. Contrary to an acute triangle, the orthocenter of an obtuse triangle will lie in the exterior of the triangle.

The orthocenter is the point of intersection of the altitudes of the triangle, which are perpendicular lines drawn from each vertex to the opposite side. In an obtuse triangle, one of the angles measures more than 90 degrees, so when an altitude is drawn from this vertex to the opposite side, it will lie outside of the triangle. Therefore, the three altitudes will intersect outside of the triangle, forming the orthocenter in the exterior. This is in contrast to an acute triangle, where all three altitudes intersect inside the triangle.

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5√17− 4
is rationalized by multiplying the numerator and denominator by what?

Answers

To rationalize the expression,5√17− 4, we multiply the numerator and denominator by √17

What are surds?

Surds are simply defined as those values found in square root and which cannot be further simplified into whole numbers or integers alike.

Examples of surds are;

√3, √5, √7

In rationalizing surds, we want to achieve that no surd forms are found as the denominator of a fraction.

Thus, we have that;

Example;

3/√3

To rationalize, we have;

3√3/√3 × √3

Multiply the values, we get;

3√3/3

Divide the values, we get;

√3

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Which of the following statements must be true about this diagram? Check
all that apply.
A. W> x
B. Z> x
C. x+y=z
□ D.y+z= w
□E. w>y
OF. x+y=w

Answers

Answer:

89

Step-by-step explanation:

find the regression equation for the following data set x 123 146 127 161 122 174 134 155 y 80 51 59 41 44 59 51 63

Answers

The regression equation for the given data set is y = -0.51x + 100.12.

To find the regression equation, we need to first calculate the slope and intercept of the regression line. Using the formula for slope (b) and intercept (a) of the regression line, we get:

b = r(Sy/Sx)

a = y-bar - b(x-bar)

where r is the correlation coefficient, Sy and Sx are the standard deviations of y and x respectively, and y-bar and x-bar are the means of y and x respectively.

Using the given data, we can calculate the means, standard deviations, and correlation coefficient. Then, we can substitute these values into the formulas to get the regression equation.

After calculating, we get the equation y = -0.51x + 100.12. This equation represents the line of best fit for the given data, which can be used to predict the value of y for any given value of x.

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A survey of 50 college students was conducted to determine how much weekly income they earned from employment. Given the data set in Applications folder for this experience complete the following. Refer to the model/methodology for the desired format.a. Find the 5 number summary of the data set.Min=Q1=Median=Q3=Max=

Answers

The 5 number summary of the data set. Min=Q1=Median=Q3=Max is calculated as below.

To help you find the 5 number summary of the data set for the survey of 50 college students' weekly income. I'll provide a step-by-step explanation on how to calculate the 5 number summary.

1. First, arrange the data set in ascending order (from smallest to largest).

2. To find the minimum value (Min), simply identify the smallest number in the data set.

3. To find the maximum value (Max), identify the largest number in the data set.

4. To find the median (the middle value), follow these steps:
  a. If the data set has an odd number of values, the median is the middle value.
  b. If the data set has an even number of values, find the average of the two middle values.

5. To find the first quartile (Q1), you'll calculate the median of the lower half of the data set (excluding the overall median if the data set has an odd number of values).

6. To find the third quartile (Q3), calculate the median of the upper half of the data set (again, excluding the overall median if the data set has an odd number of values).

Once you've completed these steps, you'll have the 5 number summary for the data set:
Min, Q1, Median, Q3, Max.

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use spherical coordinates.evaluate x2 dv,e where e is bounded by the xz-plane and the hemispheres y

Answers

∫∫∫ x² dv over the region e is (3/40) a⁵ π².

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To use spherical coordinates, we need to express the volume element dv in terms of ρ, θ, and φ, where ρ is the radial distance from the origin, θ is the angle in the xy-plane measured from the positive x-axis, and φ is the angle measured from the positive z-axis.

We have x² = ρ² sin²(φ) cos²(θ). The volume element dv can be expressed as dv = ρ² sin(φ) dρ dφ dθ.

The region e is bounded by the xz-plane and the hemispheres y = ±√(a² - x²), where a > 0.

Since we're only interested in the part of e that lies in the first octant, we can restrict θ to the range [0, π/2] and φ to the range [0, π/2].

Note that since y is always positive in the first octant, we don't need to consider the negative hemisphere.

So, the integral we need to evaluate is:

∫∫∫ x² dv

= ∫[0,π/2]∫[0,π/2]∫[0,a] (ρ² sin³(φ) cos²(θ)) ρ² sin(φ) dρ dφ dθ

= ∫[0,π/2]∫[0,π/2]∫[0,a] ρ⁴ sin⁴(φ) cos²(θ) dρ dφ dθ

= ∫[0,π/2]∫[0,π/2] [(1/5)ρ⁵ sin⁴(φ) cos²(θ)]|[0,a] dφ dθ

= (1/5) a⁵ ∫[0,π/2] cos²(θ) dθ ∫[0,π/2] sin₄(φ) dφ

= (1/5) a⁵ [(1/2)π] [(3/4)(π/2)] = (3/40) a⁵ π².

Therefore, ∫∫∫ x² dv over the region e is (3/40) a⁵ π².

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What is 0. 81818181818 as a fraction in its simplest form?

Answers

0. 81818181818 as a fraction in its simplest form is 9/11

How to find the fraction in simplest form

Converting the decimal to fraction we have

x = 81818181818/100000000000

Using a calculator we san reduce the fraction to 9/11

Therefore, 0.81818181818... as a fraction in its simplest form is 9/11.

This is a recurrence fraction and a recurring fraction, also called a recurring decimal, is a decimal number with repeating digits after the decimal point. The repeatability of the lines is indicated by a horizontal line or a line above the repetition line.

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this histogram shows the yearly number of unprovoked attacks by alligators on people in florida over 33 years. what is the midpoint of the yearly number of unprovoked alligator attacks?

Answers

The midpoint of the yearly number of unprovoked alligator attacks can be calculated by finding the class interval that contains the median value. In this histogram, the class intervals are not provided, so we cannot determine the exact midpoint.

However, we can estimate the midpoint by visually locating the point where the histogram is balanced or roughly in the middle. Based on the histogram, it appears that the midpoint is around 6-8 attacks per year.
The midpoint of the yearly number of unprovoked alligator attacks in Florida over 33 years can be found by first identifying the highest and lowest number of attacks in the histogram. Once you have those values, add them together and divide by 2 to find the midpoint.

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SIMPLIFY THIS EXPRESSION!

Answers

Answer:

The answer is 3x-5y

Step-by-step explanation:

13x+2y-10x-7y

C.L.T.

13x-10x-7y+2y

3x-5y

Answer:

3x - 5y

Step-by-step explanation:

you 1st have to collect like terms which has the same variable

13x + 2y - 10x - 7y

(13x - 10x) + (2y - 7y)

3x - 5y .... is the simplified form of the equation.

Subtract

4
+
4

2

2

2

4
a
4
+4a
2
b
2
−2b
4
a, start superscript, 4, end superscript, plus, 4, a, squared, b, squared, minus, 2, b, start superscript, 4, end superscript from

3

4
+
5

2

2
+
2

4
−3a
4
+5a
2
b
2
+2b
4
minus, 3, a, start superscript, 4, end superscript, plus, 5, a, squared, b, squared, plus, 2, b, start superscript, 4, end superscript.
Your answer should be a polynomial in standard form.

Answers

The expressions are subtracted to give -a⁴ + a²b² + 4b⁴

What are algebraic expressions?

It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, coefficients and factors.

These expressions are also identified with arithmetic operations. These operations are;

SubtractionBracketParenthesesDivisionMultiplicationAddition

From the information given, we have that;

4a⁴ + 4a²b² - 2b⁴

3a⁴ + 5a²b² + 2b⁴

Now, subtract the expressions;

3a⁴ + 5a²b² + 2b⁴ - (4a⁴ + 4a²b² - 2b⁴)

expand the bracket

3a⁴ + 5a²b² + 2b⁴ - 4a⁴ - 4a²b² + 2b⁴

add  the  values

-a⁴ + a²b² + 4b⁴

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(L1) What statement in the Converse of the Angle Bisector Theorem tells you that the point must be in the same plane as the angle?

Answers

The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.

The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.

To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.

It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.

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Find the radius of convergence, r, of the following series. [infinity] n!(6x − 1)n n = 1 r = find the interval, i, of convergence of the series. I = 1 i = − 1 6 , 0 ∪ 1 6i = − 1 6 , 1 6 i = 0 i = 1 6

Answers

The radius of convergence is given as [tex]i = {x | 0 \leq x < \frac{1}{3} }[/tex]

How to find the radius of convergence

To find the radius of convergence, we can use the ratio test:

[tex]\frac{lim |(n+1)!(6x-1)^n^+^1|}{|n!(6x-1)^n|} \\\\[/tex]

[tex]= lim |6x-1| \\=|6x-1|[/tex]

The series will converge if this limit is less than 1. So we solve the inequality:

[tex]|6x-1| < 1[/tex]

which gives us:

-1 < 6x - 1 < 1

0 < 6x < 2

[tex]0 < x < \frac{1}{3}[/tex]

Therefore, the radius of convergence is [tex]\frac{1}{6}[/tex]

To find the interval of convergence, we check the endpoints of the interval [0, [tex]\frac{1}{3}[/tex]]:

When x = 0, the series becomes:

∑(n=1 to infinity) n!(6x-1)^n = ∑(n=1 to infinity) n!(-1)^n

which diverges by the test for divergence.

When x = 1/3, the series converges by the ratio test. Therefore, the interval of convergence is:

i = [0, 1/3)

or in set-builder notation:

[tex]i = {x | 0 \leq x < 1/3}[/tex]

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A point S is 54 km due east of point T. The bearings of an electricity pole from S and Tare N28°W and N70°E, respectively. Calculate the distance of the electricity pole from T.​

Answers

The distance of the electricity pole from T is 53 km

Given that;

The ST is 54 kilometer long

(180 - 28) + (180 - 70) = 262 degree is the angle PST,

which is the product of the angles at S and T.

S has a 62 degree angle.

The law of sines can be written as:

sin(62)/SP = sin(262/ST)

To find SP, we can rearrange this equation as follows:

SP = sin(62)/sin(262)x(ST)

When we enter the values we are aware of, we obtain:

SP = sin(62)/sin(262)*54 km

We can evaluate this expression to determine that:

SP ≈ 53.5 km Consequently, 53.5 kilometer or so separate T from the electricity pole.

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A researcher was interested in the relationship between a swimmer’s hand length and corresponding time to complete the 100-meter freestyle. The researcher selected a random sample of twenty swimmers from all participants in a swim competition. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence, at a 5 percent level of significance, that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle?.

Answers

To investigate whether there is convincing evidence, at a 5 percent level of significance,

that a longer hand length is associated with a decrease in the time to complete the 100-meter freestyle, the researcher should use a two-sample t-test.

The independent variable is hand length, and the dependent variable is time to complete the 100-meter freestyle.

The t-test compares the mean time to complete the 100-meter freestyle for swimmers with longer hand lengths to the mean time for swimmers with shorter hand lengths.

The t-test is appropriate because the sample size is small, and the researcher is comparing two groups.

By conducting a two-sample t-test, the researcher can determine whether the observed difference in mean times is statistically significant or due to chance.

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On a game show, a contestant randomly chooses a chip from a bag that contains numbers and strikes. The theoretical probability of choosing a strike is 15. The bag contains 8 strikes. How many chips are in the bag?

Answers

There are approximately 53 chips in the bag.

How to determine many chips are in the bag

The theoretical probability of choosing a strike is given as 15, which can be written as 15/100 or 0.15 as a decimal.

Let's represent the number of chips in the bag with the variable "x". Since there are 8 strikes in the bag, the probability of choosing a strike can be expressed as 8/x.

we can write the equation: 8/x = 0.15

To solve for x, we can cross-multiply and simplify:

8 = 0.15x

x = 8/0.15

x = 53.33

Therefore, there are approximately 53 chips in the bag.

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a group of observations measured at successive time intervals is known as a(n) . a. trend component b. forecast c. additive time series model d. time series

Answers

The answer is d. time series, a  time series is a collection of observations that are measured at successive time intervals.

These observations are usually recorded at equal time intervals and are used to study patterns and trends over time. Time series data is used in a wide range of applications such as economics, finance, weather forecasting, and sales forecasting.

Time series analysis is the statistical method used to analyze time series data. It involves identifying patterns and trends over time, as well as forecasting future values based on past trends.

Time series models can be classified as either additive or multiplicative, depending on whether the components of the model are added or multiplied together. Trend, seasonal, and cyclical components are the main components of a time series model, and they help to explain the underlying patterns and trends in the data.

The goal of time series analysis is to use these components to develop a model that accurately describes the underlying patterns and trends in the data and to use that model to make forecasts of future values.

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5|8 - 2x|-3 > 27?
solve the inequality

Answers

Answer: x<1 or x>7

Step-by-step explanation:

Hope this helps! :)

Given the ______ of the z-distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

Answers

Answer:

the answer is symmetry.

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