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Alja [10]
3 years ago
15

Write an equation of each parabola in vertex form vertex : (-4,-24) point: (-5,-25)

Mathematics
1 answer:
kati45 [8]3 years ago
6 0
The equation for this parabola would be y=-(x+4)^2-24
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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
Find the equation of the plane that goes through three points:
frosja888 [35]

The equation of the plane that goes through these points is:

6x + 2y + z = 10.

<h3>How to find the equation of a plane given three points?</h3>

The equation of the plane is found replacing the points into the following equation:

ax + by + c = z.

For point A, we have that:

3b + c = 4.

For point B, we have that:

a + 2b + c = 0.

For point C, we have that:

-a + 6b + c = 4.

Hence the system is:

  • 3b + c = 4.
  • a + 2b + c = 0.
  • -a + 6b + c = 4.

From the first equation, we have that:

c = 4 - 3b.

Replacing in the second, we have that:

a + 2b + 4 - 3b = 0

a - b = -4.

Replacing in the third, we have that:

-a + 6b + 4 - 3b = 4.

-a + 3b = 0.

a = 3b.

We have that a - b = -4, hence:

3b - b = -4

2b = -4

b = -2.

a = 3b, hence a = -6.

c = 4 - 3b -> c = 10.

Hence the equation is:

ax + by + c = z.

z = -6x - 2y + 10

6x + 2y + z = 10.

More can be learned about the equation of a plane at brainly.com/question/13854649

#SPJ1

7 0
1 year ago
On Tuesday the dollar worth of merchandise was sold on Wednesday ​
____ [38]

Answer:

and?

Step-by-step explanation:

3 0
3 years ago
Hana buys a new dress for $40. how much does she pay if there is a 7% tax
Rzqust [24]

Answer:

$42.80

Step-by-step explanation:

We can set up an equation to solve this as such

40*1.07=42.80

6 0
3 years ago
Can someone please help me I will be forever grateful
Dominik [7]

Answer:

66 feet

Step-by-step explanation:

30+30=30 feet

6+6=12 yards

1 yard=3 feet

12*3=36

30+36=66

5 0
3 years ago
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