Select all points that are on the line through 0,5and 2,8.


4,11
5,10
6,14
30,50
40,60​

Answer:

a) Nothing, beause the distribution of the monthly rental prices are not normal.

b) 1.43% probability that the sample mean rent price will be greater than $900

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , the sample means with size n of at least 30 can be approximated to a normal distribution with mean and standard deviation

(a) Suppose a one-bedroom rental listing in this large city is selected at random. What can be said about the probability that the listed rent price will be at least $930?

Nothing, beause the distribution of the monthly rental prices are not normal.

(b) Suppose a random sample 30 one-bedroom rental listing in this large city will be selected, the rent price will be recorded for each listing, and the sample mean rent price will be computed. What can be said about the probability that the sample mean rent price will be greater than $900?

Now we can apply the Central Limit Theorem.

This probability is 1 subtracted by the pvalue of Z when X = 900.

By the Central Limit Theorem

has a pvalue of 0.9857

1 - 0.9857 = 0.0143

1.43% probability that the sample mean rent price will be greater than $900

Answer:

Speed of a= 21 miles/hr

r = Speed of b= 7 miles/hr

Speed of a = 3r

Step-by-step explanation:

The cyclist are 112 miles apart

Time traveled by two = 4 hours

Speed of a = 3 * speed of b

If a cylcles 3 times More than b, then a will cover 3*distance of b

But speed = distance/time

Time = 4hours

Total distance=112

a = 3b

3b + b = 112

4b = 112

b = 112/4

b = 28 miles

a = 3b

a = 3*28

a = 84 Miles

They bought traveled 4 hours

Speed of a = 84miles/4 hours

Speed of a= 21 miles/hr

Speed of b = 28miles/4 hours

Speed of b = 7 miles/hr

Final answer:

The slower cyclist is traveling at a speed of 7 mph, while the faster cyclist is traveling at 21 mph.

Explanation:

We first need to recognize that the sum of the distances travelled by each cyclist is equal to the total 112 miles. We can let r represent the speed of the slower cyclist, and since the faster cyclist is traveling 3 times the speed of the slower, we can call his speed 3r.

As they each traveled for 4 hours, the slower cyclist traveled a distance of 4r miles, and the faster cyclist traveled a distance of 4 × 3r = 12r miles. Their combined distances should equal the total distance between them, 112 miles. This forms the equation 4r + 12r = 112.

To solve for r, we combine the like terms on the left side of the equation to get 16r = 112. Dividing both sides by 16, we find r = 7 miles per hour. Therefore, the slower cyclist is traveling at 7 mph, and the faster cyclist is traveling 3 times that speed, giving us 21 mph.

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The two solutions of the equation 2|3x - 1| = 10 are x = 2 and

x = -4/3.

We have the following equation -

2|3x -1| = 10

We have to solve the equation to find the solutions.

What is modulus function ?

The modulus function is as follows -

for x > 0 , |x| = x

for x < 0 , |x| = - x

According to the question, we have -

2|3x - 1| = 10

|3x -1| = 5

Now, using the modulus property -

3x - 1 = 5       and       3x - 1 = -5

3x = 6        and       3x = -4

x = 2          and        x = -4/3

Hence, the two solutions of the equation 2|3x - 1| = 10 are x = 2 and

x = -4/3.

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a.The expression for temperature change in City A is 9 + (-8)

b.The amount the temperature changes for City A = 1°F

c.The expression for temperature change in City B is -1 + (-3) = -4°F

d.The amount the temperature changes for City B = -4°F

What is temperature?

The degree of hotness or coldness of an object is called as temperature.

Now it is given that,

In City A,

rise in temperature from 8 am to  9 am = 9°F

drop in temperature from 9 am to  10 am = 8°F

In City B,

drop in temperature from 8 am to  9 am = 1°F

drop in temperature from 9 am to  10 am = 3°F

a.The expression for temperature change in City A

rise in temperature =  +9°F

drop in temperature = -8°F  

∴the expression for change in temperature for City A = 9 + (-8)

b.The amount the temperature changes for City A = 9 + (-8)= 1°F

c.The expression for temperature change in City B

drop in temperature = -1°F

drop in temperature = -3°F  

∴the expression for change in temperature for City A = -1 + (-3)

d.The amount the temperature changes for City B = -1 + (-3)= -4°F

Hence,the required answers are,

a.The expression for temperature change in City A is 9 + (-8)

b.The amount the temperature changes for City A = 1°F

c.The expression for temperature change in City B is -1 + (-3) = -4°F

d.The amount the temperature changes for City B = -4°F

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We are given number in words " two hundred fifty three thousandths".

Let us write it in number form: First we would write the number form of "two hundred fifty".

Two hundred fifty = 253.

Now, we need to write three thousandths.

Three thousandths =  .003

Now, we need to combine 253 and 0.003.

On combining we get 253.003.

Therefore, two hundred fifty three thousandths in standard form is 253.003.