An equilateral triangle forms a semi-regular tessellation with which of the following regular polygons

Among freshman at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 10

lina2011 [118]

Answer:

a) 6.68th percentile

b) 617.5 points

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 550, \sigma = 100$

a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.

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

$Z = \frac{400 - 550}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

So this student is in the 6.68th percentile.

b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.

He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.

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

$0.675 = \frac{X - 550}{100}$

$X - 550 = 0.675*100$

$X = 617.5$

6 0

3 years ago

The length of a rectangle is 5 inches shorter than double its width. The perimeter of the rectangle is 192 inches. Write a two-s

alukav5142 [94]

Answer:

Step-by-step explanation:

Givens

Let the width = x

Let the length = x + 5

Equation

2w + 2W = P

Solution

2x + 2(x + 5) = 192 Remove the brackets <=== Answer

2x + 2x + 10 = 192 Combine like terms

4x + 10 = 192 Subtract 10 from both sides

4x = 192 - 10

4x = 182 Divide by 4

4x/4 = 182/4

x = 45.5

8 0

3 years ago

Kaynard's first step in solving this rational equation is to simplify it by multiplying both sides by a common denominator. Whic

bulgar [2K]

x^2 - 9 = (x + 3)(x -3)

3x - 9 = 3(x - 3)

and

6

Common denominator would be 6(x+3)(x - 3)

Answer: 6(x+3)(x - 3)

5 0

3 years ago

Chloe and tino have a combined age of 48. three years ago chloe was double the age tino is now. find tinos age

jeka94

As given Chole and Tinos age , the present age of Tino is equal to 15 years.

As given,

Let x and y be the present age of Chole and Tino. respectively.

Combined age = 48

Given condition,

x + y = 48 _______(1)

Three years ago

x - 3 = 2y

⇒x =2y +3 _______(2)

Substitute the value of x in (1),

2y+3 +y =48

⇒ 3y = 45

⇒ y = 15years

Therefore , as given Chole and Tinos age , the present age of Tino is equal to 15 years.

Learn more about age here

brainly.com/question/3023145

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5 0

2 years ago

What is the basic difference between liability insurance and collision insurance?

tia_tia [17]

Liability insurance only covers incidents that youre liable for... so if you hit a car, your insurance pays for damages on other persons car and not your own car. Collision is usually covered in a collision with another vehicle.. so like not if you hit a tree or something

4 0

3 years ago