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3 years ago

11

If the entire school had 720 students can use this data to estimate how many of them would say that it takes them more than 10 m

inutes to get to school

1 answer:

Law Incorporation [45]3 years ago

7 0

Answer:

I don't know but this question feels incomplete

You might be interested in

Jeremiah plans on building a 5 meter long garden walkway that is paved with square stones that measure LaTeX: \frac{5}{6}5 6 met

yan [13]

Answer:

Example 1

A backyard farmer wants to enclose a rectangular space for a new garden. She has purchased 80 feet of wire fencing to enclose 3 sides, and will put the 4th side against the backyard fence. Find a formula for the area enclosed by the fence if the sides of fencing perpendicular to the existing fence have length

L.

In a scenario like this involving geometry, it is often helpful to draw a picture. It might also be helpful to introduce a temporary variable,

W, to represent the side of fencing parallel to the 4th side or backyard fence.

Since we know we only have 80 feet of fence available, we know that

L + W + L = 80, or more simply, 2L + W = 80. This allows us to represent the width, W, in terms of L: W = 80 – 2L

Now we are ready to write an equation for the area the fence encloses. We know the area of a rectangle is length multiplied by width, so

A = LW = L(80 – 2L)

A(L) = 80L – 2L2

This formula represents the area of the fence in terms of the variable length

L.

Example 2

Returning to our backyard farmer from the beginning of the section, what dimensions should she make her garden to maximize the enclosed area?

Earlier we determined the area she could enclose with 80 feet of fencing on three sides was given by the equation

A(L) = 80L – 2L2. Notice that quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

In finding the vertex, we take care since the equation is not written in standard polynomial form with decreasing powers. But we know that

a is the coefficient on the squared term, so a = -2, b = 80, and c = 0.

Finding the vertex:

h

=

−

80

2

(

−

2

)

=

20

,

k

=

A

(

20

)

=

80

(

20

)

−

2

(

20

)

2

=

800

The maximum value of the function is an area of 800 square feet, which occurs when

L = 20 feet. When the shorter sides are 20 feet, that leaves 40 feet of fencing for the longer side. To maximize the area, she should enclose the garden so the two shorter sides have length 20 feet, and the longer side parallel to the existing fence has length 40 feet.

Example 3

A ball is thrown upwards from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation

H(t) = –16t2 + 80t + 40.

What is the maximum height of the ball?

When does the ball hit the ground?

To find the maximum height of the ball, we would need to know the vertex of the quadratic.

h

=

−

80

2

(

−

16

)

=

80

32

=

5

2

,

k

=

H

(

5

2

)

=

−

16

(

5

2

)

2

+

80

(

5

2

)

+

40

=

140

The ball reaches a maximum height of 140 feet after 2.5 seconds.

To find when the ball hits the ground, we need to determine when the height is zero—when

H(t) = 0. While we could do this using the transformation form of the quadratic, we can also use the quadratic formula:

t

=

−

80

±

√

80

2

−

4

(

−

16

)

(

40

)

2

(

−

16

)

=

−

80

s

q

r

t

8960

−

32

Since the square root does not simplify nicely, we can use a calculator to approximate the values of the solutions:

t

=

−

80

−

s

q

r

t

8960

−

32

a

p

p

r

o

x

5.458

The second answer is outside the reasonable domain of our model, so we conclude the ball will hit the ground after about 5.458 seconds.Step-by-step explanation:

8 0

3 years ago

A national survey conducted in 2011 among a simple random sample of 1,507 adults shows that 56% of Americans think the Civil War

Drupady [299]

Answer:

a) $z=4.658$

$p_v =P(z>4.65)=1-P(z$

b) Using the significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is higher than 50%.

c) The 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

Step-by-step explanation:

I )Part a

1) Data given and notation

n=1507 represent the random sample taken

X represent the Americans who thinks that the Civil War is still relevant to American politics and political life

$\hat p$ estimated proportion of Americans who thinks that the Civil War is still relevant to American politics and political life in the sample

$p_o=0.5$ is the value that we want to test since the problem says majority

$\alpha=0.05$ represent the significance level (no given, but is assumed)

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= population proportion of Americans who thinks that the Civil War is still relevant to American politics and political life

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life exceeds 50%(Majority). :

Null Hypothesis: $p \leq 0.5$

Alternative Hypothesis: $p >0.5$

We assume that the proportion follows a normal distribution.

This is a one tail upper test for the proportion of union membership.

The One-Sample Proportion Test is "used to assess whether a population proportion $\hat p$ is significantly (different,higher or less) from a hypothesized value $p_o$ ".

Check for the assumptions that he sample must satisfy in order to apply the test

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

$np_o =1507*0.5=753.5>10$

$n(1-p_o)=1507*(1-0.5)=753.5>10$

3) Calculate the statistic

The statistic is calculated with the following formula:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}$

On this case the value of $p_o=0.5$ is the value that we are testing and n = 1507.

$z=\frac{0.56 -0.5}{\sqrt{\frac{0.5(1-0.5)}{1507}}}=4.658$

The p value for the test would be:

$p_v =P(z>4.65)=1-P(z$

II) Part b

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

Based on the alternative hypothesis the p value would be given by:

$p_v =P(z>4.65)=1-P(z$

Using the significance level assumed $\alpha=0.05$ we see that $p_v$ so we have enough evidence at this significance level to reject the null hypothesis. And on this case makes sense the claim that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life is higher than 50%.

III) Part c

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.56 - 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.527$

$0.56 + 2.58 \sqrt{\frac{0.56(1-0.56)}{1507}}=0.593$

And the 90% confidence interval would be given (0.527;0.593).

We are confident that about 54% to 59% of all Americans think the Civil War is relevant.

And this result agrees with the result of part b, since the interval not contains the value of 0.5 we can conclude that the proportion of Americans who thinks that the Civil War is still relevant to American politics and political life it's higher than 0.5 at 90% of confidence.

7 0

3 years ago

Which undefined terms are needed to define parallel lines

Alexandra [31]

Parallel lines<span> are coplanar </span>lines<span> that do not intersect</span>

6 0

3 years ago

Maddi has a bin shaped like a right prism. She knows that the area of the base of the bin is 14 in² and the volume of the bin is

Oksana_A [137]

Answer:

The answer is 28 in

Step-by-step explanation:

I divided 392/14=28

hopefully it helps.

please mark brainliest.

8 0

2 years ago

Read 2 more answers

PLS I need help with this,

Over [174]

Answer:

5

Step-by-step explanation:

2:16-2:18=3

180ft-185ft=5

6 0

3 years ago