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2 months ago

Find the annual rate of growth (interest rate) on an account that was worth $200 in 1975 and $415.79 in 1990

2 answers:

8 0

To find the percent change over time, use the following formula: PR = Percent Rate, VPresent = Present or Future Value, VPast = Past or Present Value. The annual percentage growth rate is calculated by dividing the percent growth by N, which is the number of years. The calculation (415.79 - 200) / 200 * 100 results in 107.89. The annual percentage growth rate is then 107.89 divided by 15, which equals 7.193.

PIT_PIT [12.4K]2 months ago

5 0

For compound interest, the model used is: A = P (1+r)^5, where A represents the total amount, P is the initial principal, r is the annual interest rate expressed as a decimal, and t indicates the number of years. Setting 1975 as year 0 (t=0) and 1990 as year 15 (15 years later), we find that for year 0: $200 = P(1+r)^0, leading to P being $200. In year 15, we have $415.79 = $200 (1+r)^15. Solve this for r as a decimal.

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Eric is studying people's typing habits. He surveyed 525 people and asked whether they leave one space or two spaces after a per

lawyer [12517]

Response: (0.8115, 0.8645)

Step-by-step outline:

Define p as the proportion of individuals who leave one space after a sentence.

Provided: Sample size: n= 525

Number of respondents indicating they leave one space: 440

Thus, the sample proportion is: $\hat{p}=\dfrac{440}{525}\approx0.838$

The z-score for a 90% confidence interval is: 1.645

The formula for determining the confidence interval:

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)$

Consequently, a 90% confidence interval for the proportion of people who leave one space after a period is: (0.8115, 0.8645)

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2 months ago

Points H and F lie on circle C. Circle C is shown. Line segments E C, F C, and D C are radii. Tangents E G and D G intersect at

PIT_PIT [12445]

The answer in education is 6 units.

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2 months ago

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555 grams of wool were needed to knit a sweater, a hat, and a scarf. The hat required 5 times less wool than the sweater and 5 g

Zina [12379]

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.

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3 months ago

Nina can stitch 2/3 of a dress in 4 hours. If d represents the number of dresses and h represents the number of hours, which equ

tester [12383]

Response:

D=4 hours

Detailed explanation:

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2 months ago

In a box of marbles, the ratio of red marbles to total marbles is 2:5. the ratio of green marbles to total marbles is 3:10. if t

Inessa [12570]

Ratio: Red: Total 2: 5 (x2) 4: 10. Green: Total 3: 10. The aggregate of red and green marbles is 4 + 3 = 7. Therefore, Blue marbles = 10 - 7 = 3. This gives us a breakdown of 10 parts equating to 40 marbles and consequently, 1 part = 40 ÷ 10 = 4 leading to 3 parts = 4 x 3 = 12. Final answer: There are 12 blue marbles.

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1 month ago