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agasfer [191]
2 years ago
9

Gary won $70,000 in the lottery after all tax deductions. He invested part of the money at 11% and deposited the remainder in ta

x-free bonds at 12%. His total annual income from the investments was $7900. Find the amount invested at 11%. Find the amount invested at 12%.
Mathematics
1 answer:
Paraphin [41]2 years ago
6 0
Let x represent the amount of money he invested at 11% and y money he invested at 12%. Now we write system of equations:

x*1.11 + y*1.12 = 70 000 + 7900
x + y = 70 000

We will multiply second equation with 1.11
x*1.11 + y*1.11 = 77700
and subtract if from first:
0.01*y =  200
y = 20000

x = 70000 - 20000 = 50000
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This question was not written properly

Complete Question

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. Use the empirical rule (68-95-99.7\%)(68−95−99.7%) to estimate the probability of a lion living between 5.3 to 10. 1 years.

Answer:

Thehe probability of a lion living between 5.3 to 10. 1 years is 0.1585

Step-by-step explanation:

The empirical rule formula states that:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

3) 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Mean is given in the question as: 12.5

Standard deviation : 2.4 years

We start by applying the first rule

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

μ - σ

12.5 -2.4

= 10.1

We apply the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

We apply the third rule

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

From the above calculation , we can see that

5.3 years corresponds to one side of 99.7%

Hence,

100 - 99.7%/2 = 0.3%/2

= 0.15%

And 10.1 years corresponds to one side of 68%

Hence

100 - 68%/2 = 32%/2 = 16%

So,the percentage of a lion living between 5.3 to 10. 1 years is calculated as 16% - 0.15%

= 15.85%

Therefore, the probability of a lion living between 5.3 to 10. 1 years

is converted to decimal =

= 15.85/ 100

= 0.1585

8 0
2 years ago
Rachel created 215 pairs of earrings. Material for the earrings were $0.25 a pair. At a craft fair rachel sells all 215 pairs of
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Answer: 14.97 per pair of earrings

Step-by-step explanation:

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2 years ago
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Peter wants to fence the park in front of his home on three sides which measure 152m 40cm, 205m 10cm, 310m 39cm. What is the tot
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One centimenter is 0.01 meters. So, you can write the measures as

152.40\text{m},\quad 205.10\text{m},\quad 310.39\text{m}

Once this rewriting is done, getting the total length T is quite trivial, since all measurements are in the same unit, and we can simply sum everything:

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2 years ago
Jesus wants to start saving for college. His parents started an account for him that currently holds $325. Jesus adds $50 each m
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Answer:

y-intercept, c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

Step-by-step explanation:

We are given the following in the question:

A saving account currently holds $325. Jesus adds $50 each month.

Let x be the number of months and y be the total money n the saving account.

Then, we can use a linear function to represent the money in the account.

y(x) = 325 + 50x

Comparing to general linear function,

y = mx + c

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Comparing we get:

m = 50

c = 325

y-intercept = c = 325

Slope, m = 50

The x-axis represents the number of months and y-axis represents the total amount in saving accounts.

The attached image shows a graph for the same.

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X is sugar
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