Graph the inequality x>2

What is the radius and center of the circle given by the equation (x-5)^{2}+(y+2)^{2} = 81/4

artcher [175]

Answer:

The center is (5, -2) and the radius is 9/2

Step-by-step explanation:

The equation of a circle can be written by

(x-h) ^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-5)^{2}+(y+2)^{2} = 81/4

( (x-5)^{2}+(y- -2)^{2} = (9/2)^2

The center is (5, -2) and the radius is 9/2

6 0

3 years ago

Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale

nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) $Z = 1.05$

e) $Z = -1.10$

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

Normal probability distribution

Problems of normally distributed samples are 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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

$\mu = 515, \sigma = 100$

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 620. So

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

$Z = \frac{620 - 515}{100}$

$Z = 1.05$

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 405. So

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

$Z = \frac{405 - 515}{100}$

$Z = -1.10$

3 0

3 years ago

Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a t

masya89 [10]

Emil starts the day with <u>16 liters</u> of lemonade if he is left with 4 liters by the end of the day. Computed using the fractional values given.

Let the initial quantity of lemonade with Emil be x liters.

Quantity sold by Emil in the morning = Half of his lemonade = (1/2)x liters, that is half fraction of x.

Quantity left with Emil = x - x/2 = x/2 liters, that is half fraction of x.

Quantity sold by Emil at lunchtime = Quarter of what was left = (1/4)(x/2) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = x/2 - x/8 = 3x/8 liters, that is the three-eight fraction of x.

Quantity sold by Emil in the afternoon = One-third of what was left = (1/3)(3x/8) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = 3x/8 - x/8 = x/4 liters, that is the quarter fraction of x.

Now, we are said that Emil closes for the day with 4 liters remaining.

Therefore, x/4 = 4, or, x = 4*4 = 16 liters.

Therefore, Emil started the day with 16 liters of lemonade.

Learn more about fractions at

brainly.com/question/11562149

#SPJ10

6 0

2 years ago

Select the correct answer. Which of the following is a solution to ? A. B. C. D. E.

Leni [432]

Answer:

the answer to your question is A

3 0

3 years ago

Read 2 more answers

The image of a parabolic mirror is sketched on a graph. The image can be represented using the function y = x2 + 2, where x repr

Nadusha1986 [10]

Answer:

The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far ...

Step-by-step explanation:

The image can be represented using the function y = x2 + 2, where x represents the horizontal distance from the maximum depth of the mirror and y represents the depth of the mirror as measured from the x-axis. How far ...

3 0

3 years ago