in a sample of 62 swim instructors, 37 said that the butterfly stroke is the most difficult to teach. find the critical value used to test a claim that a majority of swim instructors think that the butterfly is the most difficult stroke to teach at the 1% significance level.

2034.72ft³ is the required cylinder volume.

The capacity of a cylinder determines how much material it can carry, or we may say that the volume of a cylinder is the total number of unit cubes that can fit inside of it.

The volume of a cylinder is r²h, and its surface area is 2πrh+2πr².

The volume of cylinder Formula: V = A × h

We will assume the cylinder is a right circular cylinder.

Then, we have the formula:

V = πr²h

We already know:

Radius = 6ft

Height = 18ft

Now, calculate the volume as follows:
(V) = π× 6² × 18

(V) = 2034.72ft³

Therefore, 2034.72ft³ is the required cylinder volume.

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The probability they will get a full scholarship and an internship Is 0.2

What is Probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

However, if two coins are tossed, four outcomes might occur: (H, H), (H, T), (T, H), and (T, T).

For instance, when we flip a coin, there are just two potential results: Head OR Tail (H, T).

Given that these two events are independent. Hence,

P(Full scholarship and an internship)

= P(Full scholarship) * P(Internship)

= 0.50 * 0.40

= 0.20

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Answer:

-10 = x

Step-by-step explanation:

2x = 3x + 10  Is this what you meant to write?  Subtract 2x from both sides

0 = x + 10  Subtract 10 from both sides

-10 = x

or are you combining like terms?

2x + 3x + 10

5x + 10

The equation y=0.75x is the relationship between x, the length of the chain in feet, and y, the price of the chain.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that hardware store sells many different sizes of chains.

The price of each chain is determined by its length.

From the table we need to find the equation  best represents the relationship between x, the length of the chain in feet, and y, the price of the chain.

Let us find this by taking 0.75 as x and multiplying with lengths to get the price.

1.8×0.75=1.35

3×0.75=2.25

3.4×0.75=2.55

6.2×0.75=4.65

y=0.75x.

Hence, y=0.75x is equation best represents the relationship between x, the length of the chain in feet, and y, the price of the chain.

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In this instance, a sample size of 393 adults who live in homes without landlines and use cell phones would be required.

Picking the number of observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study whose objective is to draw conclusions about a population from a sample must take into account the sample size. In reality, a study's sample size is typically chosen based on the expense, convenience, or time required to collect the data as well as the requirement that the sample size have a high enough statistical power. There could be a variety of sample sizes used in complex studies; for instance, there might be different sample sizes for each stratum in a stratified survey. The intended sample size for a census is equal to the population because the entire population's data is being sought.

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The option B "The trials are done without replacement" is not a requirement for constructing a confidence interval for estimating the population​ proportion.

In the given question we have to check which of the following is not a requirement for constructing a confidence interval for estimating the population​ proportion?

The given options are:

a. There are at least 5 successes and 5 failures.

b. The trials are done without replacement.

c. The sample is a simple random sample.

d. There is fixed number of trials.

As we know that, an estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.

As given that we have to find which of the following is not a requirement for constructing a confidence interval for estimating the population​ proportion. So for constructing a confidence interval for estimating the population​ proportion, we can find the trials without replacement.

So the option B "The trials are done without replacement" is correct.

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the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Given inequality is

[tex]\frac{15}{8} < \frac{n+k}{k} < \frac{13}{7}[/tex]

[tex]\frac{8}{15} < \frac{n}{n+k} < \frac{7}{13}[/tex]

[tex]n\frac{6}{7} < k < n\frac{7}{8}[/tex]

[tex]n\frac{7}{8}-n\frac{6}{7}[/tex] > 2

n[tex]\leq[/tex]112

Hence, the largest positive integer n[tex]\leq[/tex]112 for which there is a unique integer k

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Answer:

6cm

Step-by-step explanation:

30 divded by 5 times 1

Answer:

Step-by-step explanation:

5cm

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

Given,

What is the weight at birth?

Birth weight is the term used to describe a newborn's body weight. Typically, newborns of European heritage weigh between 2.5 and 4.5 kilos, on average 3.5 kilograms, at delivery. Babies from South Asia and China typically weigh 3.26 kg.

Here,

Babies of nonsmokers frequently ranged in weight from 1,000 to 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

The usual ranges of birth weights between the two groups do show some notable differences, though. Nearly half of neonates among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grams since there are fewer babies in the lower weight ranges. Fewer babies are in the bigger weight groups, with 40 of 74, or 54%, of the newborns delivered to smokers having birth weights between 2,000 and 3,000 grams.

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Answer:

see pic

Step-by-step explanation:

see pic

The correct option is the third one, the function is neither odd nor even.

A function y = f(x) is an odd function if for all values of x in its domain:

f(x) = f(-x)

The graph of these functions have an axis of symmetry at the y-axis.

And it is an odd function is for all values of x in its domain:

f(x) = -f(x)

These functions "invert" at the y-axis,

Now let's look at the graph.

When x = 5, we can see that:

f(x) = 9

And when x = -5, the function is:

f(-5) = -0.5

Neither of the conditions is meet.

Then the function is neither odd nor even.

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Answer:

Step-by-step explanation:

45 different choices of pens you have with this band.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

A popular brand of the pen is available in 15 colors and 3 writing tips.

Choosing from one of 15 colors and one of 3 writing tips.

Each color could have one of two different writing tips.

To find the total different pens available multiply the number of colors by the number of tips: 15*3=45

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Answer:

Step-by-step explanation:

go to school

Answer: 24%

Step-by-step explanation: First find the percentage of the stereo.

190/250 = 0.76 of 76%

Then subtract 76% from 100% or subtract 190 from 250.

250 - 190 = 60 then 60/250 = 0.24 or 24%

Duke spent 24% of his earnings on his bike.

By using the concept of testing of hypothesis, the null and alternative hypothesis is given by

[tex]H_0 :p_i = \frac{1}{5}[/tex]

[tex]H_a : p_i \neq \frac{1}{5}[/tex] for atleast one day

What is testing of hypothesis?

Suppose there is a hypothesis and there is a data at hand. Testing of Hypothesis determines whether a particular hypothesis is supported by the data at hand.

The null and alternative hypothesis can be written are as follows-

Null hypothesis: [tex]H_0[/tex] : There is no difference in the number of swimmers from day to day.

Alternative hypothesis: [tex]H_a[/tex] : There is a difference in the number of swimmers from day to day.

[tex]H_0 :p_i = \frac{1}{5}[/tex]

[tex]H_a : p_i \neq \frac{1}{5}[/tex] for atleast one day

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Complete Question

The manager of the city pool has scheduled extra lifeguards to be on staff for Saturdays. However, he suspects that Fridays may be more popular than the other weekdays as well. If so, he will hire extra lifeguards for Fridays, too. In order to test his theory that the daily number of swimmers varies on weekdays, he records the number of swimmers each day for the first week of summer. Test the manager’s theory at the 0.10 level of significance.

Swimmers at the City Pool

Monday Tuesday Wednesday Thursday Friday

Number 46 68 43 51 70

Step 1 of 4 :

State the null and alternative hypotheses in terms of the expected proportion for each day. Enter your answer as a fraction or a decimal rounded to six decimal places, if necessary.

H0: pi=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Ha: There is a difference in the number of swimmers from day to day.

Answer:

k=-1

Step-by-step explanation:

Please look at the attachment, hope this helps, have a great day! :D

The number of men on the sight-seeing tour was 22.

What is the proportion?

A unique class of ratio called a percentage has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women (i.e. the total population).

We have,

w/c = 5/2

w/c = 5/2

w = 5x  

and c=2x

for some integer x. Q : m =?

(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11

c/m = 5/11cm

c=5y and m = 11y,

for some integer y. Not sufficient to calculate m.

(2) the number of women on the sight-seeing tour was less than 30 --> w<30. Not sufficient to calculate m.

(1) + (2)

w = 5x < 30w --> x<6x.

c=2x and as c=5y,

c is a multiple of 5 --> x=5x  

c = 10 = 5y --> y = 2

m = 11y = 22.

Hence, the number of men on the sight-seeing tour was 22.

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The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

5x-2y=12

2y = 5x - 12

y = (5/2)x - 6

The slope of the above line is 5/2

Since the slope of two perpendicular lines is the negative inverse of each other.

Thus,slope of line = -1/(5/2) = -2/5

So equation will be y = (-2/5)x + c

Hence"The slope of two perpendicular lines is the negative inverse of each other thus the equation of the perpendicular line will be y = (-2/5)x + c".

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1.The following is the 90% confidence interval for the mean difference between the park's tree heights in 2009 and 2019:

(11.59, 14.21)

2. The conditions for the confidence interval are of:

A. Large samples and no extreme outliers.

D. Independently sampled pairs.

Given,

What is a confidence interval for the t-distribution?

When the population's standard deviation is unknown, the t-distribution is utilized, and the boundaries of the confidence interval are provided using the following formula:

x ± t s/√n

When the equation's variables are laid down as follows:

The sample mean = x

The critical value = t

The sample size = n

The standard deviation for the sample = s

Using a t-distribution calculator, the critical value is t = 1.6766 for a two-tailed 90% confidence interval with 50 - 1 = 49 df.

The remaining parameters are given as follows:

x = 12.9, s = 5.52, n = 50

Then the lower bound of the interval is of:

12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.

The upper bound of the interval is of:

12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.

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Question is incomplete. Completed question is given below;

Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.

Year Mean SD n

2009 11.4 3.6 50

2019 24.3 8.8 50

Difference 12.9 5.52 50

Round all calculated values to 4 decimal places as appropriate.

1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.

2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:

A. Large samples and no extreme outliers.

B. There must be at least 3 levels of the categorical variable.

C. np^≥10 and n(1−p^)≥10

D. Independently sampled pairs.

The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters

From the question, we have

Fencing available, Perimeter = 1600 meters

Number of sections, n = 3

Represent the dimensions with x and y

So, we have:

Area = Number of sections* x * y = 3xy

Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y

Recall that

Perimeter = 1600 meters

So, we have

6x + 4y = 1600

A = 3xy

Divide 6x + 4y = 1600 by 2

3x + 2y = 800

Make y the subject

y = (800 - 3x)/2

Substitute y = (800 - 3x)/2 in A = 3xy

A = 3x(800 - 3x)/2

So, we have

A = 1200x - 4.5x²

Differentiate and set to 0

1200 - 9x = 0

So, we have

9x = 1200

Divide by 9

x = 400/3

Recall that y = (800 - 3x)/2

So, we have

y = (800 - 3 x 400/3)/2

Evaluate

y = 200

Hence, the dimensions are 200 by 400/3

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500 mph is the speed of the plane.

This creates a right triangle, with the distance between the plane and the radar station serving as the hypotenuse (s). Let y represent the plane's height and x represent its flight route.

s2 = y2 + x2

Given: the constant value of y = 6

negative since decreasing, ds/dt = -400

Trying to locate dx/dt

Taking the implicit derivative of the above equation's two sides

0 + 2xdx/dt = 2sds/dt

(S/X) ds/dt = dx/dt

When x = 8

s = √(62+82) = √100 = 10

dx/dt = (10/8)(-400) = -500 mph, or 500 mph traveling toward the radar station at a distance of 6 miles.

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Answer: 40

Step-by-step explanation:

P = a+b+c = 10+17+13 = 40

The percentage of children aged between the ages of 8 - 12 who own phones are, in fact, lower than the 52% industry average. Of the 832 children aged 8 to 12 who were questioned by the national consumer league, 449 had cell phones.

You must use survey data to calculate the percentage of youngsters between the ages of 8 as well as 12 who own phones to ascertain whether the commercial manager's assertion is accurate. To achieve this, divide the total number of children polled (832) by the total number of kids who own phones (449), multiply the outcome by 100 to get the percentage, and so on.

This estimate gives a percentage of 53.8%, which is slightly higher than the advertising manager's stated figure.

This implies that the claim made by the management could not be genuine, and more investigation would be required to ascertain if it is real or not.

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If there are 6 circles and 10 triangles, then the simples ratio of circles to total shapes is 3 : 8

Total number of circles = 6 circles

Total number of triangles = 10 triangles

Total number of shapes = Total number of circles + Total number of triangles

Substitute the values in the equation

Total number of shapes = 6 + 10

= 16 shapes

The ratio of circles to total shapes = Total number of circles : Total number of shapes
Substitute the values

= 6 : 16

Simplify the ratio

= 3 : 8

Therefore, the simplified ratio of circles to total shapes is 3 : 8

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The function for the quadratic model that gives the average revenue in dollars where x is the price in dollars of a large one-topping pizza, with data from 9.25 ≤ x ≤ 14.25 is -105.6x² + 254.28x - 12.16.

Quadratic model

In regression, quadratic model means  mathematical model represented by a quadratic equation such as Y = aX² + bX + c, or by a system of quadratic equations.

Given,

A pizza parlor has been experimenting with lowering the price of their large one-topping pizza to promote sales. the average revenues from the sale of large one-topping pizzas on a Friday night (5 p.m. to midnight) at various prices are given below.

Here we need to find the quadratic model function with data from 9.25 ≤ x ≤ 14.25.

While we plot the given table of values in the graph then we get the graph like the following.

Through the graph we have identified that the value of

mean of x 11.75

mean of y 1,165.35

correlation coefficient r 0.9924547615

A -105.6

B 254.28

C -12.16

So, through these values the quadratic model of the function is written as,

=> -105.6x² + 254.28x - 12.16.

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It is "false" to claim that you cannot use both the present value of an explanatory variable and its delays in a regression.

A statistical method called regression links a dependent variable with one or much more independently (explanatory) variables.

Thus, it is "wrong" to claim that you cannot use both the present value of an explanatory variable and its delays in a regression.

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Answer: 89.7

Step-by-step explanation:

a) q= sin d

Angle is represented by d, and value is represented by q.

b) p = tan1 c

Angle is represented by c, and value is represented by p.

c) arccos n = ν

Angle is represented by n, and value is represented by v.

Given that,

We have to find the variables that indicate the angle and the value of the trigonometric function in each of the following equations.

In the following three equations:

(a) q = sin d;

(b) p = tan1 c; and

(c) arccos n = ν,

We know that,

a) q= sin d

Angle is represented by d, and value is represented by q.

b) p = tan1 c

Angle is represented by c, and value is represented by p.

c) arccos n = ν

Angle is represented by n, and value is represented by v.

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Tom Pedalled his bike at a pace of 6 km/h and ran at a speed of 3 km/h.

Given,

Tom went on a bike ride;

Distance covered = 6 miles

Speed of bike = x

Speed of jogging = x - 3

Jogging is one hour more than bike ride

That is,

(6/x - 3) - (6/x) = 1

6 (x - x + 3 / x(x - 3)) = 1

18 / x² - 3x = 1

x² - 3x = 18

x² - 3x - 18 = 0

x² - 6x + 3x - 18 = 0

x(x - 6) + 3(x - 6) = 0

(x + 3) (x - 6) = 0

x = 6

That is,

Tom travelled at a speed of 6 km/hr with bike and 3 km/hr by jogging.

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