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3 years ago

Use the quadratic function f(x) = 2x2 + 4x +3 to answer the following questions.

1 answer:

8 0

The vertex is (-1,1)

Explanation

The vertex formula to find the x coordinate of the formula is -b/2a

So we plug in the values into the formula which is

-4/2(2)

Simplify it

-4/4
=-1
-1 is now the x cord of the vertex.

So now we will plug in the x into the quadratic equation which is 2x^2+4x+3

2(-1)^2 + 4(-1) + 3 = 2 -4 +3

Simplify it

5 - 4= 1

Y=1
So the Coordinates of the vertex is (-1,1)

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Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

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".

Solution to the problem

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:

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

Part a

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 $ME =\pm 0.02$ 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)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

3 years ago

24>-3r>-9 Can someone help me its an example plz help me understand this for my algebra 2 class.

harkovskaia [24]

I hope this helps you

7 0

3 years ago

En un salon de clases cuando se colocan cuatro alumnos en cada banca, 3 de ellos quedan sin puesto y cuando se colocan de a 5 en

Harlamova29_29 [7]

Answer: 5 benches and 23 students

Step-by-step explanation:

I will answer in English.

We have E students and B benches.

If we sit 4 students per bench, we have 3 students left.

then:

E = 4*B + 3

And if we sit 5 students per bench, there are two places with no students sited.

E = 5*B - 2

now we can replace the E in the second equation with the right part in the first equation:

4*B + 3 = 5*B - 2

3 + 2 = 5*B - 4*B

5 = B

So we have 5 benches, and:

E = 4*5 + 3 = 23 students.

5 0

3 years ago

How many thousands make 30 million? (just curious)

fenix001 [56]

Answer:

30,000 thousands make 30 million

Step-by-step explanation:

Solve by dividing 30 million by 1,000

8 0

3 years ago

Which of the following in equalities matches the graph?

Natalka [10]

I believe it is D)3x+2y<7
Hope I helped

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3 years ago

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