MATHEMATICS COLLEGE

(G1) The distance from Flagstaff Arizona toTucson Arizona is 260 miles. Express this
distance in meters.
A. 418,418 meters
B. 419,000 meters
C. 126,200 meters
D. 260,000 meters

Answers

Answer 1

Answer:

Answer:

A. 418, 418

Step-by-step explanation:

The formula to convert miles to meters is the following:

1 = 1,609.34

so for every 1 mile, you have 1,609.34 meters

so you take your distance in miles and multiply it by 1,609.34

d= 260 x 1,609.34

d = 418, 428.4

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A number, n, is multiplied by -3/8. The product is -0.5 What is the value of n?

Answers

Answer:

n=4/3

Step-by-step explanation:

n*(-3/8)=-0.5

n=0.5/3/8

n=1/2 / 3/8

n=4/3

Check:

4/3*-3/8=-0.5

4/3*-3/8=-1/2

-1/2=-0/5

CORRECT!

According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,999. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $574. (Round your z-score computation to 2 decimal places and final answers to 2 decimal places.) What percent of the adults spend more than $2,550 per year on reading and entertainment?

Answers

Answer:

The probability is $P(X > x ) = 0.19215$

Step-by-step explanation:

From the question we are told that

Th The population mean $\mu = \$ 1,999$

The standard deviation is $\sigma = \$ 574$

The values considered is $x = \$ 2,500$

Given that the distribution of the amounts spent follows the normal distribution then the percent of the adults spend more than $2,550 per year on reading and entertainment is mathematically represented as

$P(X > x ) = P(( X - \mu)/(\sigma ) > ( x - \mu)/(\sigma ) )$

Generally

$X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X )$

$P(X > x ) = P(Z > ( x - \mu)/(\sigma ) )$

substituting values

$P(X > 2500 ) = P(Z > ( 2500 - 1999)/(574 ) )$

$P(X > 2500 ) = P(Z >0.87 )$

From the normal distribution table the value of $P(Z >0.87 )$ is

$P(Z >0.87 ) = 0.19215$

Thus

$P(X > x ) = 0.19215$

Final answer:

We calculate the z-score for the amount $2,550 using the given mean and standard deviation. The z-table gives us the percentage of people who spend less than this, which we subtract from 1 to find the percentage who spend more. Approximately 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Explanation:

To compute the percentage of adults spending more than $2,550 per year, we must first find the z-score associated with this value. The z-score is a measurement of how many standard deviations a particular data point is from the mean.

The formula for calculating the z-score is: Z = (X - μ) / σ.

Where:
- X is the value we are interested in.
- μ is the mean.
- σ is the standard deviation.

Using this formula, the z-score for $2,550 is:
Z = ($2,550 - $1,999) / $574 = 0.96.

Next, we need to use a z-table or a standard normal distribution table to find out the probability that lies below the calculated z-score. Looking this up on a z-table, we get a value of 0.8315, meaning that 83.15% of the population will spend $2,550 or less per year on reading and entertainment. Since we want to know the percentage spending more than $2,550, we subtract this value from 1: 1 - 0.8315 = 0.1685.

Therefore, based on the given mean and standard deviation, about 16.85% of adults in the 25- to 34-year age group spend more than $2,550 on reading and entertainment each year.

Learn more about Z-Score here:

brainly.com/question/31613365

#SPJ3

11 The net force on a vehicle that is accelerating at a rate of 1.5 m/s² is 2,800 newtons. What isthe mass of the vehicle to the nearest kilogram?

Answers

Answer:

$Mass = 1867kg$

Step-by-step explanation:

Given

$Force = 2800N$

$Acceleration = 1.5m/s^2$

Required

Determine the mass of the vehicle

This question will be answered using Newton's second law

$Force = Mass * Acceleration$

Substitute values for Force and Acceleration

$2800 = Mass * 1.5m/s^2$

Make Mass the subject

$Mass = (2800N)/(1.5m/s^2)$

$Mass = 1866.6667kg$

$Mass = 1867kg$ ---- approximated

Hence, the mass of the vehicle is 1867kg

Find each percent increase. Round to the nearest percent

Answers

Answer:

1. 15 to 21 = 21 - 15 / 15 = 0.4*100% = 40%

2. 12 teachers to 48 teachers = 48 - 12/48 = 0.75 * 100% = 75%

3. 80 pencil to 120 pencil = 120 - 80 / 80 = 0.5*100% = 50%

4. 40 cans to 70 cans = 70 - 40 / 70 = 0.43 * 100% = 43%

Solve system by Substitution
method, provide steps.
y = 8x + 12
3.x – 3y = 6

Answers

Step-by-step explanation:

y = 8x + 12 _____(1)

3x - 3y = 6 ______(2)

Substituting the.the expression for y in eqn (1)

into eqn (2).

3x - 3(8x + 12) = 6

3x - 24x - 36 = 6

-21x = 42

x = -2.

y = 8(-2) + 12 = -4.

hence x = -2 and y = -4.

Answer:

Step-by-step explanation:

Statistics can help decide the authorship of literary works. Sonnets by a certain Elizabethan poet are known to contain an average of μ = 8.9 new words (words not used in the poet’s other works). The standard deviation of the number of new words is σ = 2.5. Now a manuscript with six new sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain an average of x~ = 10.2 words not used in the poet’s known works. We expect poems by another author to contain more new words, so to see if we have evidence that the new sonnets are not by our poet we test the following hypotheses.H0 : µ = 8.88 vs Ha : µ > 8.88
Give the z test statistic and its P-value. What do you conclude about the authorship of the new poems? (Let a = .05.)
Use 2 decimal places for the z-score and 4 for the p-value.
a. What is z?
b.The p-value is greater than?
c.What is the conclusion? A)The sonnets were written by another poet or b) There is not enough evidence to reject the null.

Answers

Answer:

We conclude that the sonnets were written by by a certain Elizabethan poet.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 8.9

Sample mean, $\bar{x}$ =10.2

Sample size, n = 6

Alpha, α = 0.05

Population standard deviation, σ = 2.5

First, we design the null and the alternate hypothesis

$H_(0): \mu = 8.88\nH_A: \mu > 8.88$

We use One-tailed z test to perform this hypothesis.

a) Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(10.2 - 8.9)/((2.5)/(√(6)) ) = 1.28$

Now, $z_(critical) \text{ at 0.05 level of significance } = 1.64$

b) We calculate the p value with the help of z-table.

P-value = 0.1003

The p-value is greater than the significance level which is 0.05

c) Since the p-value is greater than the significance level, there is not enough evidence to reject the null hypothesis and accept the null hypothesis.

Thus, we conclude that the sonnets were written by by a certain Elizabethan poet.

Final answer:

The z-score is 1.86 and the p-value is 0.0314. As the p-value is less than the level of significance α (0.05), we reject the null hypothesis and conclude that the new sonnets were likely written by another author.

Explanation:

In this statistical testing scenario for authorship of literary works, we need to find out the z-score or z test statistic and then determine the p-value to check if the new sonnets could be the works of the known Elizabethan poet or not.

For calculating the z score, you use the formula z = (x~ - μ) / (σ / √n) = (10.2 - 8.9) / (2.5/ √6) = 1.86 to two decimal places. The p-value is determined from the standard normal distribution table which for a z-score of 1.86 is 0.0314.

Given that α = 0.05, since the p-value is less than α, we reject the null hypothesis H0 (that the works were by the Elizabethan poet). Therefore, we accept the alternative hypothesis Ha (the sonnets were written by another author).