What is a atom? Help me out guys!

Please Help !!! its a math problem What is the range of the quadratic equation whose graph contains the following points?

dolphi86 [110]

<h2>Range of a Quadratic Function</h2>

The range tells us the possible <em>y</em>-values that occur in the function.

When describing the range, we can write an inequality using <em>y</em>.

Examples: y > 6, y ≤ 10

When describing the range of a quadratic function, we typically use the ≥ or ≤ symbols when writing the inequality.

To write the range of a quadratic function,

Find the vertex
Determine whether the parabola opens up or down
Set <em>y</em> ≥ or ≤ the y-coordinate of the vertex

<h2>Solving the Question</h2>

We're given:

Vertex at (0,4)
Other points on the graph: (-2,0), (-1,3), (1,3), (2,0)

Because we're directly given the vertex, we just have to determine now whether the parabola opens up or down.

If the other points on the graph always have a lower <em>y-</em>coordinate value, then the graph opens down
If the other points on the graph always have a greater <em>y-</em>coordinate value, then the graph opens up

The other points that fall on the graph that we're given all have a lower y-coordinate value than 4, that means this parabola opens down.

Therefore, all other y-values for the function will be less than 4.

Therefore, y ≤ 4.

<h2>Answer</h2>

y ≤ 4

4 0

2 years ago

A company plans to ship 2,000 packages of chocolate. The company randomly selecta

a_sh-v [17]

Answer:

100 packages

Step-by-step explanation:

If 5 packages out of 100 are incorrect , then there's a 1/20 chance that a package has an incorrect weight

Therefore out of 2000

it's

$\frac{1}{20} \times 2000 = 100$

Hope it helps

Sorry I'm not really good at explaining

7 0

1 year ago

Are these all correct ? If not please let me know

Licemer1 [7]

They are all correct except in 5), 4+8 is 12, not 13.

8 0

3 years ago

Read 2 more answers

A reporter for a student newspaper is writing an article on the cost of off-campus housing. A sample was selected of 10 one-bedr

olga55 [171]

Answer:

(507.05, 592.95)

Step-by-step explanation:

Given data:

sample mean = $550, sample standard deviation S = $60.05

95% confidence interval , n = 10

For 95% confidence interval for the mean

mean ± M.E.

where M.E. is margin of error = $t_{n-1}, \alpha/2\times\frac{S}{\sqrt{n} }$

Substituting the values in above equation

$=t_{10-1}, 0.05/2\times\frac{60.05}{\sqrt{10} }$

= 2.62×18.99

=42.955

= 550±42.95

=(507.05, 592.95)

6 0

3 years ago

A counselor at a community college claims that the mean GPA for students who have transferred to State University is more than 3

Lena [83]

Answer:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=3.25$ represent the sample mean

$s=0.3$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =3.1$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is more than 3.1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.1$

Alternative hypothesis: $\mu > 3.1$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=36-1=35$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(35)}>3)=0.00247$

Conclusion

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

5 0

3 years ago