Consider the following null and alternative hypotheses.

<img src="https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%20%2B3" id="TexFormula1" title="y=x^{2} +3" alt="y=x^{2} +3" align="absmiddle"

Katena32 [7]

Answer:

The domain is (negative infinity, infinity) the range is [3. Infinity) y>=3

Step-by-step explanation:

The domain for all quadratic functions are (Negative infinity, infinity)

The range is the output values of the function 3, to infinity

6 0

3 years ago

A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at

hodyreva [135]

Answer:

There is an 8.38% probability that the anchor will be fired.

Step-by-step explanation:

For each resident, there is only two possible outcomes. Either they can name the news anchor on the evening news at their station, or they cannot.

This means that the binomial probability distribution will be used in our solution.

However, we are working with samples that are considerably big. So i am going to aaproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X), \sigma = \sqrt{V(X)}$ .

In this problem, we have that:

400 city residents are going to be asked. So $n = 400$ .

Suppose that in fact 12% of city residents could name the anchor if asked. This means that $p = 0.12$ .

So,

$\mu = E(X) = 400*0.12 = 48$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{400*0.12*0.88} = 6.5$ .

They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so.

What is the approximate probability that the anchor will be fired?

10% of the residents is 0.10*400 = 40 residents.

Fewer than 10% is 39 residents. So the probability that the anchor will be fired is the pvalue of Z when $X = 39$ .

So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39 - 48}{6.5}$

$Z = -1.38$

$Z = -1.38$ has a pvalue of 0.0838. This means that there is an 8.38% probability that the anchor will be fired.

5 0

3 years ago

Aisha needs to be at least 48 inches tall to ride the colossal coaster at the amusement park. If she grows 5 inches during the n

Anni [7]

X < 43, implies that the height of Aisha is less than 43 and can't be equal to 43 ( as there is no equal operator)

A is wrong as the inequality does not imply that Aisha is 0 tall , but any height height from 0 to 42.99999...

B) Correct , Aisha is not 43 and less she is less than that.

C) no, she may just need to grow 1 or 2 inches who knows.

D) nope, Aisha is at most 43 ( at least = 43 or taller)

at most 43 or less

4 0

3 years ago

Read 2 more answers

What is the volume of the right rectangular prism?

Vlad1618 [11]

Answer:

216 cubic inches

Step-by-step explanation:

The volume of a right rectangular prism is given by the area of the base rectangle multiplied by the height.

Now, see the given figures with the question.

The base of the prism is a rectangle, and its area is (6 × 12) = 72 square inches.

Now, the volume of the prism will be (72 × 3) = 216 cubic inches (Answer)

6 0

3 years ago

Which trigonometric function is equivalent to sec(-270) ? a. sec(-120) c. sec(-30) b. sec(60) d. sec(90)

BARSIC [14]

The equivalent of sec (-270) will be found as follows:
we add our angle to 360°
-270+360
=90
But sec(-270) is a positive value, this implies that the angle that will give us the same answer as sec (-270) should also give us the positive value. This means that 90 is our answer since it will give us the positive sec value.
The answer is d. sec(90)

8 0

3 years ago