9 times 10 to the fourth power

Which equation represents the graph? (y-1)^2/49-x^2/81=1 (y-1)^2/7-x^2/9=1

Anon25 [30]

Answer: A, (y-1)^2/49-x^2/81=1

7 0

3 years ago

In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a s

Oksi-84 [34.3K]

Answer:

a) $\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

b) From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

c) $P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

$P(Z\geq2.070)=1-P(Z$

Step-by-step explanation:

Let X the random variable the represent the scores for the test analyzed. We know that:

$\mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4$

And we select a sample size of 64.

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Part a

For this case the mean and standard error for the sample mean would be given by:

$\mu_{\bar x} =\mu = 276.1$

$\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3$

Part b

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)$

Part c

For this case we want this probability:

$P(\bar X \geq 285)$

And we can use the z score defined as:

$z=\frac{\bar x -\mu}{\sigma_{\bar x}}$

And using this we got:

$P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)$

And using a calculator, excel or the normal standard table we have that:

$P(Z\geq2.070)=1-P(Z$

8 0

3 years ago

Three times a number n plus 16

HACTEHA [7]

Answer:

3n+16

Step-by-step explanation:

three times: (3) a number n +16

(3)n+16 or 3xn+16

3n+16

4 0

3 years ago

The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be

erik [133]

Answer: 3000 gallon

Step-by-step explanation:

Here, The total quantity of 15% alcohol content = 3000 gallon

And, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.

Let the total quantity of 9% alcohol content = x

In which quantity of alcohol = 9% of x gallon= 9x/100 gallon

Now, according to the question, The wine with a 9% alcohol content will be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content.

Thus, the total quantity of mixture of 12% alcohol content = The total quantity of 15% alcohol content + total quantity of 9% alcohol content

= 3000 + x

In which quantity of alcohol = 12 % of ( 3000+x) = (360 + 12x/100) gallon ---(1)

But, the quantity of alcohol in 12 % of alcohol content = quantity of alcohol in 15% of alcohol content + quantity of alcohol in 9% of alcohol content

The quantity of alcohol in 12 % of alcohol content = (450 + 9x/100) gallon ---(2)

On equating equation (1) and (2)

We get, 360 + 12x/100 = 450 + 9x/100

⇒ 3x/100 = 90

⇒ x = 3000

Therefore, The total quantity of the mixture of 9% alcohol content = 3000

6 0

4 years ago

Please help! I’m very confused on this question. I’m not very good at geometry.

Ahat [919]

Well, to find the perimeter we have to add all of the side lengths, so let's do that:

2x+3 +2x+3 +2x

And we know that this equals 36 so let's solve for x

2x+3+2x+3+2x = 36

6x+6 = 36

6x = 30

x = 5

So we know know that x = 5.

Now all you have to do is plug in the values of x into the lengths

2(5) + 3

= 10+3

= 13 is the length of two of the sides.

2x

= 2(5)

= 10

And 10 is the length of the last side.

8 0

3 years ago

Read 2 more answers