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wariber [46]
2 years ago
8

Mr mojo borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20000 at what interest rate did he borro

wnthe money
Mathematics
1 answer:
sesenic [268]2 years ago
5 0

The rate of interest is 12.2 %

<em><u>Solution:</u></em>

Given that, Mr mojo borrowed $9000 for 10 years to make home improvements

He repaid a total of $ 20000

To find: Rate of interest

We can use simple interest formula to calculate the rate of interest

Total amount = Principal + simple interest

20000 = 9000 + simple interest

Simple interest = 20000 - 9000

Simple interest = 11000

<em><u>The simple interest is given as:</u></em>

I = \frac{ p \times r \times t}{100}

Where,

"I" is the simple interest

"p" is the principal

"r" is the rate of interest

"t" is the number of years

Substituting the values,

11000 = \frac{9000 \times r \times 10}{100}\\\\11000 = 900 \times r\\\\r = \frac{11000}{900} = 12.2

Thus rate of interest is 12.2 %

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Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t
svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

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 = 450, \sigma = 100

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

Z = \frac{550 - 450}{100}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 350

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

Z = \frac{350 - 450}{100}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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

1.88 = \frac{X - 450}{100}

X - 450 = 1.88*100

X = 638

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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

0.253 = \frac{X - 450}{100}

X - 450 = 0.253*100

X = 475.3

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

-0.385 = \frac{X - 450}{100}

X - 450 = -0.385*100

X = 411.5

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

0.385 = \frac{X - 450}{100}

X - 450 = 0.385*100

X = 488.5

The middle 30% of the test scores is between 411.5 and 488.5.

7 0
3 years ago
Word problem
Vlad [161]

Answer:

p=2

Step-by-step explanation:

4.05p+14.40=4.50(p+3)          < equation

4.05p+14.40=4.50p+13.50     < multiply

14.40=.45p+13.50                   < subtract

.9=.45p                                    < subtract

2=p                                          < divide

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3 years ago
Read 2 more answers
3c-2(c+10)=7c-5(c+2)
jeka94

Answer: C= -10

Step-by-step explanation: First step: simplify both sides of the equation

3c−2(c+10)=7c−5(c+2)

3c+(−2)(c)+(−2)(10)=7c+(−5)(c)+(−5)(2) (Distribute)

3c+−2c+−20=7c+−5c+−10

(3c+−2c)+(−20)=(7c+−5c)+(−10) (Combine Like Terms)

c + -20 = 2c - 10

c - 20 = 2c - 10

Step 2: Subtract 2c from both sides

c - 20 - 2c = 2c -10 - 2c

−c−20=−10

Step 3: Add 20 to both sides

−c−20+20=−10+20

−c=10

Step 4: Divide both sides by -1

-c/-1 = 10/-1

C=-10

   

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