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IgorC [24]
2 years ago
11

Judy Clark went to Reel Bank. She borrowed $7,800 at a rate of 6 1/2%. The date of the loan was September 2. Judy hoped to repay

the loan on January 20. Assuming the loan is based on ordinary interest, Judy will pay back on January 20: ____________
Mathematics
1 answer:
abruzzese [7]2 years ago
8 0

Answer:

$7995.85

Step-by-step explanation:

We will use simple interest formula to solve our given problem.

A=P(1+rt), where,

A = Amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

r=6.5\%=\frac{6.5}{100}=0.065

t=\text{141 days}=\frac{141}{365}\text{ year}

A=\$78001+0.065\times \frac{141}{365})

A=\$7800(1+0.065\times 0.38630136986)

A=\$7800(1+0.025109589041)

A=\$7800(1.025109589041)

A=\$7995.85479

A\approx \$7995.85

Therefore, Judy will will pay back on January 20: <u>$7995.85</u>.

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Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole
Art [367]

Answer:

a = 5 and b = 12

Step-by-step explanation:

<u>Step 1: Find angle B</u>

<em>Angle C = 90°</em>

<em>Angle A = 22.6°</em>

<em>Angle B = B</em>

<em>All angles in a triangle are equal to 180°.</em>

Angle A + Angle B + Angle C = 180°

22.6 + 90 + B = 180°

B = 180 - 112.6

B = 67.4°

<u>Step 2: Find the value of side AC 'b'</u>

<em>Hypotenuse = 13</em>

<em>Adjacent = b</em>

<em>Angle A = 22.6°</em>

Cos (Angle) = Adjacent/Hypotenuse

Cos (22.6) = b/13

b = 12

<u>Step 3: Find the value of side CB 'a'</u>

<em>Hypotenuse = 13</em>

<em>Opposite = a</em>

<em>Angle A = 22.6°</em>

Sin (angle) = Opposite/Hypotenuse

Sin (22.6°) = a/13

a = 4.99 rounded off to 5

Therefore, the value of a=5 and b=12.

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8 0
2 years ago
Read 2 more answers
Rectangle ABCD with coordinates A(1,1), B(4,1), C(4,2) and D(1,2) dilates with respect to the origin to give rectangle A’B’C’D’.
Delvig [45]

Answer: Option C.

Step-by-step explanation:

You need to find the distance AB with the formula for calculate the distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:

AB=\sqrt{(4-1)^2+(1-1)^2}=3

You know that A'B'=6, then the scale factor of dilation can be calculated with:

k=\frac{A'B'}{AB}

Substituting values, you get:

k=\frac{6}{3}\\\\k=2

This matches with the option C.

8 0
2 years ago
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An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the A
Ksivusya [100]

Answer:

0.7 ; 0.65 ; 0.115

Step-by-step explanation:

Step-by-step explanation:

P(A) = 0.5 ; P(B) = 0.3

P(not successful) = P(B') = 1 - 0.3 = 0.7 ; P(A') = 1 - 0.5 = 0.5

1.)

Both events are independent events, hence the outcome of one does not depend on the other. That is the failure of the Asian project has nothing to do with the European project.

Probability that European project isn't successful;

P(B') = 1 - P(B) = 1 - 0.3 = 0.7

2.)

Probability that atleast one of the 2 projects is successful :

P(AUB) = P(A) + P(B) - P(AnB)

P(AnB) = P(A) * P(B) = 0.5 * 0.3 = 0.15

P(AUB) = 0.5 + 0.3 - 0.15 = 0.65

3.)

Probability that only the Asian project is successful, given that atleast one of the two projects is successful :

[P(A) - P(AnB)] ÷ P(AuB)

[0.5 * 0.15] ÷ 0.65

= 0.075 ÷ 0.65

= 0.1153846

= 0.115

6 0
2 years ago
Oscar has received a $4,000 gift and is looking for a bank to start a savings account. Which option
kirza4 [7]

Answer:

The best option for him would be a real interest rate of 5%.

Step-by-step explanation:

The nominal interest rate is the one that represents the percentage of increase of the money that is in a certain investment, without discounting the depreciation due to inflation or the payment of taxes.

On the other hand, the real interest rate is the one that represents the real increase in the money invested, after discounting inflation and any taxes to be paid.

Therefore, the best option for Oscar would be to invest his $ 4,000 in a savings account with a real interest rate of 5% per year.

7 0
2 years ago
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the ta
Evgen [1.6K]

Answer:

1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2) He did not multiply the numerator and denominator by the correct number to equal 1,500.

5) He should have multiplied the numerator and denominator by 75, not 30,  because 20 x 75 = 1,500.

Step-by-step explanation:

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2 years ago
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