Given right triangle DEF, what is the value of tan(F) 9/41 40/41 40/9 41/9

Holly is taking out a loan in the amount of $10,000. Her choices for the loan are a 4-year loan at 4% simple interest and a 6-ye

notsponge [240]

Answer:

The difference in the amount of interest she would have to pay for the two loans is $1,400

Step-by-step explanation:

The amount of loan Holly is taking out, P = $10,000

The choices available for the loan are;

1) Loan duration, T₁ = 4-year

Interest rate, R₁ = 4%

2) Loan duration, T₂ = 6-year

Interest rate, R₂ = 5%

For the first choice, we have;

The simple interest, I, given by the formula;

$I_1 = \dfrac{P \times R_1 \times T_1 }{100} = \dfrac{10,000 \times 4 \times 4 }{100} = \$ 1,600$

For the second choice, we have;

The simple interest, I, given by the formula;

$I_2 = \dfrac{P \times R_2 \times T_2 }{100} = \dfrac{10,000 \times 5 \times 6 }{100} = \$ 3,000$

The difference, D, in the amount of interest she would have to pay for the two loans is therefore;

D = I₂ - I₁ = $3,000 - $1,600 = $1,400

The difference in the amount of interest she would have to pay for the two loans = D = $1,400.

7 0

3 years ago

Read 2 more answers

Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

rusak2 [61]

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that $\sigma = 2$

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when $M = 0.5$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.5 = 1.96\frac{2}{\sqrt{n}}$

$0.5\sqrt{n} = 2*1.96$

Dividing both sides by 0.5

$\sqrt{n} = 4*1.96$

$(\sqrt{n})^2 = (4*1.96)^2$

$n = 61.5$

Rounding up

We would have to take a sample of 62 to achieve this result.

8 0

3 years ago

Which of the following is true?

Ratling [72]

In this question, we're trying to find the inequality that is true.

To find your answer, we can convert the numbers in the absolute value:

|−5| < 4:

5 < 4 false

|−4| < |−5|:

4 < 5 true

|−5| < |4|

5 < 4 false

|−4| < −5

4 < -5 false

The only true inequality here would be |−4| < |−5|, since it works with the inequality sign.

Answer:

|−4| < |−5|

4 0

3 years ago

From the sum of 2 and -11, subtract the sum of 2 and -6

jolli1 [7]

Answer: -5

Step-by-step explanation: 2 + -11 = -9 and subtract -4 from it since it’s the sum of 2 + -6. -9 - -4 is -9 + 4 so -5

7 0

3 years ago

Read 2 more answers

Is 2 yards greater less than equivalent to 5 ft

Setler79 [48]

Hi there.

3 feet = 1 yard;
2 yards = 6 ft; therefore, 2 yards is greater than 5 ft.

I hope this helps!

3 0

3 years ago