Please help me! Math

A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest

nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate you need to divide by 100 to get it in decimal form

t = time, in years if you are given a partial year, divide the months by 12

P = $12,000

r = 7.5% = .075

t = 1

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075 Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0

3 years ago

Are all equilateral triangles acute?

Anvisha [2.4K]

Answer:

Yes, all equilateral triangles are acute.

Step-by-step explanation:

yea

hope this helps :)))

8 0

3 years ago

(x - 4/6) = (x + 2/12) what is x please show your work.

Alex17521 [72]

-4/6 times 2 is -8/12

x - 8/12= x + 2/12

0=10/12
0=5/6

but since 0 does not equal 5/6, this will be no solution

3 0

3 years ago

Miss Lim bought some puzzles for her pupils in the Maths Club. She bought a total

xxMikexx [17]

Answer:

She bought 24 Tangram puzzles

Step-by-step explanation:

Let the number of Tangram puzzles be t and the number of IQ puzzles be i

The sum of all the puzzles is 40;

i + t = 40 ••••••(i)

Cost of all Tangram puzzles at a cost of $4 per one will be;

4 * t = $4t

cost of all Iq puzzles at a cost of $2 per one is

2 * i = $2i

Sum

paid for all is $128

so;

4t + 2i = 128 •••••••(ii)

From equation i;

i = 40-t

Substitute into ii

4t + 2(40-t) = 128

4t + 80 - 2t = 128

2t = 128-80

2t = 48

t = 48/2

t = 24

6 0

3 years ago

A quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain bra

tensa zangetsu [6.8K]

Answer:

We conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

Step-by-step explanation:

We are given that a quality-control manager for a company that produces a certain soft drink wants to determine if a 12-ounce can of a certain brand of soft drink contains 120 calories as the labeling indicates.

Using a random sample of 10 cans, the manager determined that the average calories per can is 124 with a standard deviation of 6 calories.

Let $\mu$ = average calorie content of a 12-ounce can.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 120 calories {means that the average calorie content of a 12-ounce can is less than or equal to 120 calories}

Alternate Hypothesis, $H_A$ : $\mu$ > 120 calories {means that the average calorie content of a 12-ounce can is greater than 120 calories}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average calories per can = 124 calories

s = sample standard deviation = 6 calories

n = sample of cans = 10

So, test statistics = $\frac{124-120}{\frac{6}{\sqrt{10} } }$ ~ $t_9$

= 2.108

The value of t test statistics is 2.108.

Now, at 0.05 significance level the t table gives critical value of 1.833 at 9 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 2.108 > 1.833, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average calorie content of a 12-ounce can is greater than 120 calories.

7 0

3 years ago