MATHEMATICS COLLEGE

After writing a $800 check to pay a bill, a student had a balance of $350 in his account. How muchdid he have in the account before he wrote the check?
a) Let X = his balance before writing the check. Write the equation you would use to solve this
problem.

Answers

Answer 1
Answer:

The equation to solve the problem is X  - $800 = $350. And the amount in his account before he wrote the check is $1150.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that after writing an $800 check to pay a bill, a student had a balance of $350in his account.

We need to find out how much did he have in the account before he wrote the check.

The amount of the check = $800

The amount the student has in balance = $350

The amount the student had before he wrote the check.

Let X be the amount the student had before the check.

Now,

X  - $800 = $350

X - 800 = 350 is our equation to find the amount the student has before the check.

The value of X can be written as,

We have,

X  - $800 = $350

Add $800 on both sides

X = $350 + $800

X = $1150

Hence, the equation to solve the problem is X  - $800 = $350. And the amount in his account before he wrote the check is $1150

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Answer 2
Answer:

Answer:

x=800+350

Step-by-step explanation:

The money spent plus the money he has left would equal the money he had in the first place.

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The probability that the first production line stops is 0.5 while the probability that the second production line stops is 0.22 . If the production lines work independently of each other what is the probability that both lines are working at any given time ?

Answers

Answer:

0.11

Step-by-step explanation:

The events are independent, so:

P(A and B) = P(A) × P(B)

P = 0.5 × 0.22

P = 0.11

The Richter Scale gives a mathematical model for the magnitude of an earthquake in terms of the ratio of the amplitude of an earthquake wave (also known as the intensity of an earthquake) to the amplitude of the smallest detectable wave. If we denote the magnitude of the earthquake by R, the intensity (also known as the amplitude of the earthquake wave) of the earthquake by A, and the amplitude of the smallest detectable wave by S, then we can model these values by the formula R=log(AS)
In 1906, San Francisco felt the impact of an earthquake with a magnitude of 7.8. Many pundits claim that the worst is yet to come, with an earthquake 748,180 times as intense as the 1906 earthquake ready to hit San Francisco. If the pundits ability to predict such earthquakes were correct, what would be the magnitude of their claimed earthquake? Round your answer to the nearest tenth.

Answers

Answer:

The magnitude of the claimed earthquake would be 13.67.

Step-by-step explanation:

The 1906 earthquake had a intensity of A and a magnitude of 7.8.

S is going to have the same value, so i am going to write as 1. So:

\log{A} = 7.8

A = 10^(7.8)

A = 63095734.448

Many pundits claim that the worst is yet to come, with an earthquake 748,180 times as intense as the 1906 earthquake ready to hit San Francisco.

So A = 748180*63095734.448

So

R = \log{A} = \log{748180*63095734.448} = 13.67

The magnitude of the claimed earthquake would be 13.67.

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).

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Which of the following statements are equivalent to the ratio 10:3? Choose all that apply-(5 points)
A. 28 days to 6 days
B. 120 meters to 8,000 meters
C. 2,000 pounds to 600 pounds
D. 300 seconds to 20 seconds
E. 250 cents to 75 cents
Need answer ASAP please

Answers

Answer:
C and E would be your answers
Explanation:
C is correct because If you multiple 10 by 200 you get 2,000 and then do 3 times 200 gets 600.
E is correct because if you do 10 x 25 it become 250 and if you do 3 x 25 it equals 75!!
—————
So sorry if I am wrong!!

A washer and a dryer cost $857 combined. The washer costs $93 less than the dryer. What is the cost of the dryer?

Answers

The cost of the dryer is $475 and the cost of the washer is $382.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a washer and a dryer cost $857 combined.

Let the cost of dryer be x.

The washer costs $93 less than the dryer.

Then, the cost of washer will be x-93

So, x+x-93=857

2x=857+93

2x=950

x=$475

x-93=475-93

= $382

Hence, the cost of the dryer is $475.

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Answer:

Dryer cost $475;  Washer cost $382

Step-by-step explanation:

For this problem, we will simply set up a system of equations to find the value of each the washer (variable x) and the dryer (variable y).

We are given the washer and dryer cost $857 together.

x + y = 857

We are also given that the washer cost $93 less than the dryer.

x = y - 93

So to find the cost of the dryer, we simply need to find the value of y.

x + y = 857

x = y - 93

( y - 93 ) + y = 857

2y - 93 = 857

2y = 950

y = 475

So now we have the value of the dry to be $475.  We can check this by simply plugging in the value and see if it makes sense.

x + y = 857

x + 475 = 857

x = 382

And check this value:

x = y - 93

382 ?= 475 - 93

382 == 382

Therefore, we have found the values of both the washer and the dryer.

Cheers.

18% of the cars in the parking lot are blue.If there are 150 cars in the parking lot,how many cars are blue

Answers

Answer:

Step-by-step explanation:

14

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