MATHEMATICS COLLEGE

To obtain the graph of y = x2 - 6, shift the graph of y = x2
units.

Answers

Answer 1
Answer:

Answer: down 6 units

Step-by-step explanation:

Edge 20
Answer 2
Answer:

Answer:

Down 6 Units

Step-by-step explanation:

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Scores on a college entrance exam are normally distributed with a mean of 550 and a standard deviation of 100. Find the value that represents the 90th percentile of scores. Answer with a whole number.

Answers

Answer:

The value that represents the 90th percentile of scores is 678.

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 = (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

Find the value that represents the 90th percentile of scores.

This is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.

Z = (X - \mu)/(\sigma)

1.28 = (X - 550)/(100)

X - 550 = 100*1.28

X = 678

The value that represents the 90th percentile of scores is 678.

Based on the graph of the function shown, identify the Range of the function.A. All real numbers between -6 and +2
B. All real numbers
C. All real numbers between -6 and -1 & -1 and 2
D. All real numbers between -8 and 4

Answers

I think that it's D because the y-values go from 4 and end at -8

What sample size would be required to estimate the true proportion of American female business executives who prefer the title "Ms.," with an error of ±0.025 and 98 percent confidence? (Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.) Sample size

Answers

Answer:

n=(0.5(1-0.5))/(((0.05)/(2.326))^2)=2164.1104

And rounded up we have that n=2165

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".

p represent the real population proportion of interest

\hat p represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

The population proportion have the following distribution  

p \sim N(p,\sqrt{(\hat p(1-\hat p))/(n)})  

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 98% of confidence, our significance level would be given by \alpha=1-0.98=0.02 and \alpha/2 =0.01. And the critical value would be given by:  

z_(\alpha/2)=-2.326, z_(1-\alpha/2)=2.326

The margin of error for the proportion interval is given by this formula:  

ME=z_(\alpha/2)\sqrt{(\hat p (1-\hat p))/(n)} (a)  

And on this case we have that ME =\pm 0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

(b)

We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:  

n=(0.5(1-0.5))/(((0.05)/(2.326))^2)=2164.1104

And rounded up we have that n=2165

The three perpendicular bisectors of a triangle intersect at the _______.Question 12 options:

a)

circumcenter

b)

incenter

c)

centroid

d)

orthocenter

Answers

Answer:

  a)  circumcenter

Step-by-step explanation:

You want to know the name of the point of intersection of the three perpendicular bisectors of the sides of a triangle.

Circumcircle

Each side of a triangle is a chord of the circumscribed circle. The perpendicular bisector of a chord is a line through the center of the circle. Hence the point of concurrency of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.

The name of the center of the circle circumscribing a triangle is "circumcenter."

__

Additional comment

When the triangle is a right triangle, the circumcenter is the midpoint of the hypotenuse, which is a diameter of the circle.

Check Your Understanding!1. A Ford Escape has a 14-gallon fuel tank and can travel approximately 26 miles with one gallon of
gas, Write a function d(x), that gives the distance the Escape can travel with x gallons of gas in
the tank.

Answers

Given :

Maximum capacity of fuel tank , M = 14 gallon .

It can travel approximately 26 miles with one gallon of  gas.

To Find :

A function d(x), that gives the distance the Escape can travel with x gallons of gas in  the tank.

Solution :

Car can travel 26 miles in one gallon of gas.

So , distance covered in x gallon of gas :

D(x)=26x

( Here,  0 ≤ x ≤ 14 ) or x ∈ [ 0 , 14 ] .

Hence , this is the required solution.

Factor the trinomial.
The factors of m2 + 12m + 35

Answers

Answer:

(m + 7)(m + 5)

Step-by-step explanation:

Factor, find factors of m² & 35 that, when combined, will give 12m:

m² + 12m + 35

m                 7

m                 5

(m + 7)(m + 5) is your answer.

Check: Use the FOIL method to check.

(m)(m) = m²

(m)(5) = 5m

(7)(m) = 7m

(7)(5) = 35

Combine like terms:

m² + (5m + 7m) + 35 = m² + 12m + 35 √.

Answer:

(m+7) and (m+5)

Step-by-step explanation:

Just had this on a test
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