A circle has a diameter of 46 cm. What is its radius?

An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i

natita [175]

Answer:

$70,000 at 7%
$304,000 at 8%

Step-by-step explanation:

Given:

Total interest earned on two investments is $29,220.

An amount is invested at 7%.

$24,000 more than 4 times that amount is invested at 8%.

Find:

The amount invested at each rate.

Solution:

Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

interest on 7% account + interest on 8% account = total interest

0.07x + 0.08(24000+4x) = 29220

0.39x + 1920 = 29220 . . . . . . . . . . . simplify

0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

7% interest + 8% interest = 29,220

0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

Comment on 6-step method

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Identify the given information (Given)
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6 0

3 years ago

In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts Co

Vera_Pavlovna [14]

B. 0.75 is the answer for this equation

7 0

3 years ago

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her liste

Paraphin [41]

Complete Question:

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 46 listeners from age 22-39 and 57 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded in the file attached below.

1. At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age?

2. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?

Answer:

1) There is no significant difference in the proportion of listeners based on age

2) No, there is no evidence

Step-by-step explanation:

Sample size of group 1, $n_1 = 46$

Sample size of group 2, $n_2 = 57$

Number of Yes in group 1, $X_1 = 32$

Number of Yes in group 2, $X_2 = 47$

Proportion of Yes in group 1:

$\hat{p_1} = \frac{X_1}{n_1} \\\hat{p_1} = \frac{32}{46}\\\hat{p_1} = 0.6957$

Proportion of Yes in group 2:

$\hat{p_2} = \frac{X_2}{n_2} \\\hat{p_2} = \frac{47}{57}\\\hat{p_2} = 0.8246$

Null Hypothesis, $H_0: p_1 = p_2$

Alternate Hypothesis, $H_a: p_1 \neq p_2$

$\hat{p} = \frac{X_1 + X_2}{n_1 + n_2} \\\\\hat{p} = \frac{ 32+47}{46+57} \\\\\hat{p}= 0.767$

Significance level,

Calculate the test statistic

$z = (\hat{p_1} - \hat{p_2})/\sqrt{(\hat{p} * (1-\hat{p}) * (\frac{1}{N_1} + \frac{1}{N_2})}\\\\z = (0.6957-0.8246)/ \sqrt{(0.767*(1-0.767)*(1/46 + 1/57))}\\\\z = -1.54$

Get the P-value from the probability distribution table:

At z = -1.54, P-value = 0.1236

Since (P-value = 0.1236) > (α = 0.05), we will accept the null hypothesis. This means that there is no evidence to suggest that there is difference in the proportion of listeners based on age.

7 0

2 years ago

Chris made $378 for 18 hours of work.

andre [41]

Answer:

$147

Step-by-step explanation:

378 / 18 = 21

1 hour of work = $21

7 hours of work = $21 * 7 = $147

5 0

3 years ago

PLEASE HELP!!!! I HAVE TO SUBMIT THIS IN AND I DONT KNOW!!

masya89 [10]

Answer:

your answer is clearly luke skywalker banana toungue

Step-by-step explanation:

because i felt like it

8 0

3 years ago