Winston earns $140.00 by selling 56 hot dogs at the concession stand at school. Using the same rate for

What is the equation of the graph below? On a coordinate plane, a curve goes through (0, 0). It has a maximum of 1 and a minimum

bogdanovich [222]

Answer:

y=cos(x+π)

Step-by-step explanation:

Known that the cosine function has a period of 2π.

Now, the parental function is y = cosx, which has y-intercept at y = 1, and x-intercept at π/2.

Notice that the function showed in the graph attached has y-intercept at y = -1 and x-intercept at π/2. This indicates that the function has been moved leftwards π units.

Therefore, the function that belongs to this graph is

$y=cos(x + \pi)$

6 0

2 years ago

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.96})^2}=425.22$

And rounded up we have that n=426

3 0

2 years ago

A jewelry artist is selling necklaces at an art fair. It costs $135 to rent a booth at the fair. The cost of materials for each

mash [69]

Answer: No

Step-by-step explanation:

$12-$4.50= $7.50

$7.50*15= $112.50

The Total cost is $135 She will only be making $112.50 in profits.

3 0

1 year ago

∠C and ∠D are vertical angles with m∠C=−x+26 and m∠D=2x−10 . What is m∠D ?

Valentin [98]

Vertical angles are made by two intersecting lines .and they are always equal
<span>∠C and ∠D are equal.
so </span><span>−x+26 =2x-10
-3x=-36
x=36/3
x=12</span>°

∠D= 2x-10
put value of x here
∠D=24-10
∠D=14°

3 0

2 years ago

Read 2 more answers

You and a group of friends are going to a five-day outdoor music festival during spring break. You hope it does not rain during

KIM [24]

Answer:

The probability of not rain during the entire festival is 0.19

Step-by-step explanation:

The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

In this case we have the probability of raining of each day, we need the probability of NOT raining.

First day= 45% chance of rain, the complement is 55%

Second day 55% chance of rain, the complement is 45%

Third day a 10% chance of rain, the complement is 90%

Fourth day a 10% chance of rain, the complement is 90%

Fifth day 5% chance of rain, the complement is 95%

To get the probability of NOT raining in the entire festival is the multiplication of all the complements.

P(not raining) = 0.55 x 0.45 x 0.90 x 0.90 x 0.95= 0.19

4 0

2 years ago