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3 years ago

John has 4 dimes and 8 quarters in a box. Find the probability of drawing a dime.

1 answer:

8 0

The probability that an event occurs is the number of times it could occur compared to the total number of possible events, assuming the probability of each event occurring is equal.

John has $4+8=12$ coins total. If 4 of the coins are dimes, the probability that he draws a dime is $\frac{4}{12}=\frac{1}{3}\approx 33\% \approx 0.33$ .

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1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the a

Rudik [331]

Answer:

Part A) $\$42,888.48$

Part B) $A=\$22,304$

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12$

substitute in the formula above

$A=8,500(1+\frac{0.0812}{12})^{12*20}$

$A=8,500(1.0068)^{240}$

$A=\$42,888.48$

Part B) What if the deposit were compounded monthly with simple interest?

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=20\ years\\ P=\$8,500\\r=0.0812$

substitute in the formula above

$A=8,500(1+0.0812*20)$

$A=\$22,304$

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

$A(t)=8,500(1.0068)^{12t}$ ------> equation A

$A(t)=8,500(1+0.0812t)$ -----> equation B

using a graphing tool

see the attached figure

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

5 0

3 years ago

A flower shop acquired 80 new customers last year. Costs in the marketing and sales areas were the following:

icang [17]

Using proportions, it is found that the Customer Acquisition Cost was of $1,215.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount.

In this problem, the customer acquisition cost is the spending in sales divided by the number of customers added.

80 customers were added, considering costs of 1200 + 9000 + 87000 = $97,200, hence:

97200/80 = $1,215.

More can be learned about proportions at brainly.com/question/24372153

5 0

2 years ago

Two angles with measures (6x + 60) and (90) are supplementary. What is the value of x?

marshall27 [118]

Supplementary angles add up to 180, so
6x+60+90 = 180 and solve for x
6x= 30
x=5

5 0

3 years ago

Read 2 more answers

A water wheel has a radius measuring between 13 feet and 24 feet. The wheel is able to turn 7π9 radians from its starting positi

madam [21]

Answer:

31.76 ft and 58.64 ft

Step-by-step explanation:

The radius measures between 13 feet and 24 feet.

The wheel is able to turn 7π/9 radians before getting stuck.

We need to find the range of distances that the wheel could spin before getting stuck. That is, the length of arc.

Length of an arc is given as:

$L = \frac{\theta}{2\pi} * 2\pi r$

where θ = central angle = 7π/9 radians

r = radius of the circle

Therefore, for 13 feet:

$L = \frac{7\pi}{18 \pi} * 2 * \pi * 13\\\\L = 31.76 ft$

For 24 feet:

$L = \frac{7\pi}{18 \pi} * 2 * \pi * 24\\\\L = 58.64 ft$

The wheel could spin between 31.76 ft and 58.64 ft before getting stuck.

4 0

3 years ago

In quadrilateral ABCD, if AB = BC = CD = DA, the quadrilateral can be classified as a __________.

yaroslaw [1]

It could be parallelogram but square is always true

4 0

3 years ago