Mathematics High School

Alan invests a total of ​$16,500 in three different ways. He invests one part in a mutual fund which in the first year has a return of​ 11%. He invests the second part in a government bond at​ 7% per year. The third part he puts in the bank at​ 5% per year. He invests twice as much in the mutual fund as in the bank. The first year​ Alan's investments bring a total return of ​$1,425. How much did he invest in each​ way?

Answers

Answer 1

Answer:

>> $9000 invested in mutual fund

>> $3000 invested in government bond

>> $4500 put in the bank

Step-by-step explanation:

Let us denote the money invested in each case by a letter. Thus;

a = the money that he invested in a mutual fund

b = the money that he invested in a government bond

c = the money that he put in the bank

We are told that he invested a total of ​$16,500. Thus;

a + b + c = 16500 - - - (eq 1)

He invested twice as much in the mutual fund as he did in the bank. Thus;

a = 2c - - - (eq 2)

From the percentage given and the return of ​$1,425 from the first year investments, we have;

0.11a + 0.07b + 0.05c = 1425 - - - (eq 3)

Let's put 2c for a in eq (1) and eq (3)

Thus;

2c + b + c = 16500

b + 3c = 16500 - - - (eq 4)

Also,

0.11(2c) + 0.07b + 0.05c = 1425

0.07b + 0.27c = 1425 - - - (eq 5)

From eq 4, b = 16500 - 3c

Putting this in eq(5) gives;

0.07(16500 - 3c) + 0.27c = 1425

1155 - 0.21c + 0.27c = 1425

0.06c = 1425 - 1155

0.06c = 270

c = 270/0.06

c = $4500

b = 16500 - 3(4500)

b = 16500 - 13500

b = $3000

Since a = 2c, then;

a = 2(4500)

a = $9000

Related Questions

will give brainliest if you help me

Answers

Answer:

1120 in³

Step-by-step explanation:

The volume (V) of a cuboid is calculated as

V = area of base × height , then

V = 80 × 14 = 1120 in³

What is the combined height for 3 nickels, 2 nickels, and 1 nickel? The thickness of one nickel is 1/16 inch.

Answers

Answer:

3/8 of an inch

Step-by-step explanation:

3/16 + 2/16 + 1/16 = 6/16 = 3/8 inch

Answer:

3/8 inch

Step-by-step explanation:

So we know there are 6 nickels and we know the height of one nickel: 1/16

So 6*1/16 = 6/16 = 3/8

just help me again for 2 times

Answers

Answer:

A. 86.7

first, the base. length x width.

it's square, so

5.1 x 5.1= 26.01

then the sides. formula for a triangle is base times height divided by 2.

5.1 x 5.95= 30.345 divided by 2 is 15.1725

there are 4 sides, so multiply times 4

4 x 15.1725= 60.69

now, add the base to the sides

26.01 + 60.69= 86.7

Angle a in angle B are complementary angle E equals 3X +4 angle B equals 5X +6 what is the measure of angle a

Answers

(3x+4)+(5x+6)=90
8x+10=90
8x=80
X=10

3(10)+4= A
30+4=A
24° is the measure of angle a.

Students in Ms. Singh’s class had the following scores on their last quiz. What was the median score of Ms. Singh’s 20 students?

85, 83, 68, 77, 72, 95, 87, 75, 73, 55,
82, 85, 91, 86, 92, 78, 85, 86, 79, 82

Answers

Answer:

Median score = 82.5

Step-by-step explanation:

First, arrange the given data in an ordered manner. Thus:

55, 68, 72, 73, 75, 77, 78, 79, 82, 82, 83, 85, 85, 85, 86, 86, 87, 91, 92, 95

The median = the average of the 10th and 11th data

Median = (82 + 83) ÷ 2

Median = 165 ÷ 2

Medina = 82.5

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Answers

Answer: Quora. It will help, trust me or search it up

If y = -2x + 3, find y when x = -3

Answers

Y= -2(-3) + 3

-2 multiplied by -3 is 6 and 6+3 is 9, meaning y= 9 when x= -3

The school band gets $5 for each T-Shirt they sell at a fundraiser. They have a goal of raising $150. If $45 has been raised do far, how many more T-Shirts do they have to sell to reach or exceed the goal?

Answers

$45 ÷ 5 = 9 (T-shirts sold so far)
$150 ÷ 5 = 30 (t-shirts they want to sell in order to have a goal of $150)
30-9= 21 more t-shirts
Ans: 21

29,58,116,... find the 71st term

Answers

Answer:

sorry it doesn't make sense to me either but here is a link to another one of the 71st things hopefully it helps :)

Step-by-step explanation:

https://brainly.com/question/15779922

find the area

length=x+10 width=2x+5

explain/show your steps

Answers

2x^2 + 25x + 50 not sure about the steps

c) Jasper and Emma are training for a marathon. Jasper runs 6 kilometers at a
time while Emma prefers to run in blocks of 3 kilometers. At the end of a
month, they realize that they have run same total number of kilometers. What
is the smallest number of kilometers that each must have run?

Answers

Answer:

The smallest number of kilometers that each must have ran is 6 km

Step-by-step explanation:

The distance Jasper prefers to run at a time = 6 km

The distance Emma prefers to run at a time = 3 km

The distance ran by Jasper at month end = The distance ran by Emma at the end of the month

The smallest number of kilometers that each must have ran is given by the lowest common multiple, LCM of 6 and 3 as follows;

The multiples of 6 are;

6 × 1 = 6, 6 × 2 = 12...

The multiples of 2 are;

3 × 1 = 3, 3 × 2 = 6...

∴ The LCM of which = 6

Therefore, the smallest number of kilometers that each must have ran = 6 km

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Answers

for the page that starts with problems 13 and 14, it is mostly all the pythagorean therom which is a² + b² = c² (all you have to do is plug the numbers in)
in order to do this make sure you remember the longest side or the side directory across from the 90 degree angle is always c! a and b can be any of the other two sides (the legs) they just cannot be the longest side. Here’s problem 13:

a² + b² = c²
now we plug in all the numbers we have
a² + 3² = 5²
in this case i made the missing side “a”
now we must square the numbers
a² + 9 = 25
we can’t square a since we don’t have a number for it
a² + 9 = 25
-9 -9
——————
a² = 16
since we can’t add to get to the missing side like usual, we must subtract the other leg (b in this case) from c
now we must get rid of the square on the a, and because we can’t square it, the only that gets rid of a square is a square root (remember what you do to one side you must do to the other)

√a² = √16
if you don’t know how to square root on a regular calculator i suggest looking up a square root calculated (calculator soup is a pretty good reasource)
you only have to do actual math for the 16, so once you square root the 16, just cross out the square root and square on the a and you’ll get your answer
a = 4

A color printer prints 25 pages in 8 minutes.
How many pages does it print per minute?

(round to the nearest hundredth)

Answers

Answer: 0.13

Step-by-step explanation:

50.6 is what percent of 55?
50.6 is % of 55.

Answers

Answer:

50.6 is 92% of 55

Step-by-step explanation:

50.6:55*100 =

(50.6*100):55 =

5060:55 = 92

Now we have: 50.6 is what percent of 55 = 92

Hope this helped!

What number is 80% of 80?

Answers

Answer:

64 IS THE ANSWER........

I need help please, I will give brainliest to the first 2 people

Answers

Answer: that should be B !! so sorry if wrong..

Step-by-step explanation:

The answers is A if it’s asking for the mid section point ,

Kim's baby sister weighed 9 pounds when she was born. How many ounces are in 9 pounds?

Answers

144 ounces
Explanation: 1 pound is 16 ounces 16x9=144

Factor 60y - 90 - 20x to identify equivalent expressions

Answers

Answer:

10(6y−9−2x) and 5(12y−18−4x)

Answer: 10(60y/10 - 90/10 +-20x/10)

Diana is working on a painting for school. She needs 1 1/5 ounces of yellow paint and 2 1/2 ounces of orange paint. How much less yellow paint does she need than the orange paint?

Answers

Answer:

1 3/10

Step-by-step explanation:

We are to determine the difference the paint of yellow and orange paint

The equation we are to solve is

[tex]2\frac{1}{2} - 1\frac{1}{5}[/tex]

The equation can be solved by taking the following steps

Subtract the two whole numbers divide each denominator by the least common multiple of the denominator and multiply the figures by the numerator

[tex]1\frac{5 - 2}{10}[/tex] = [tex]1\frac{3}{10}[/tex]

Carlos cut StartFraction 5 Over 12 EndFraction of a yard of cloth into 5 pieces of equal length. What was the length of each piece of cloth? HELP?????????!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

1/12 yard

Step-by-step explanation:

From the above question:

5 pieces of equal length = 5/12 yards

1 piece of equal length = x yard

Cross Multiply

5 pieces × x = 1 piece × 5/12 yards

x = 1 piece × 5/12 yards/5 pieces

x = 5/12 ÷ 5

x = 5/12 × 1/5

x = 1/12 yard

The length of each piece of cloth is 1/12 yard

A cube has a volume of 64. What is the side length of one side
#15

Answers

Answer:

4

Step-by-step explanation:

volume is equal to a x a x a

This means that [tex]a^{3}[/tex] = V

Therefore, a = cube root of V, which is 4

It would be 4.

Using the formula
V=a3
Solving fora
a=V⅓=64⅓≈4

SOMEONE PLS HELP I HAVE LIKE A MINUTE LEFT!!!

Answers

Answer:

C

Step-by-step explanation:

I'll explain if you need but i'm trying to answer quick for you

Answer:

C

Step-by-step explanation:

3500(1.04)^15

6,303

so in 15 years it will be over 6,000 dollars in the account

2a + 3b = 5
b = a - 5

Answers

1st Equation:

Answer for A:

[tex]a = \frac{5 - 3b}{2} [/tex]

Answer for B:

[tex]b = \frac{5 - 2b}{3} [/tex]

2nd Equation:

Answer:

[tex]a = b + 5[/tex]

hope it helps.

I need help what is this answer Yesterday, it rained for 335 minutes. The day before that it rained for 5 hours and 10 minutes. On which day did it rain for a longer period of time?

Answers

Answer: Yesterday it rained longer

335 / 60 = Hours

335 minutes

= 5 7/12 hours

≈ 5.58333 hours

335 minutes

= 5 hours & 35 minutes

Hope it helps and have a good day! (:^w^:)

(WILL GIVE BRAINLIST) The number of phone calls received by the complaint department of a small company over a five day period is as follows:
28, 26, 33, 41, 47
Find the mean deviation for this data.
Select one:
8.9
7.2
7.9
62.8

Answers

Answer:

im not shure which one it is

Step-by-step explanation:

Please please help please please ASAP please I'm begging you please I have 10 minutes please y'all help please any ACE that can help please

Answers

Answer:

SQ

Step-by-step explanation:

NL:SQ = MN:SR = ML:RQ (corr.side, similar triangles)

Booker earned $1,200 over
the summer. He invested the money in
stocks. To his surprise, the stocks increased
in value to $1,335 in only 9 months. Find
the simple interest rate for the investment.

Answers

Answer:

15%

Step-by-step explanation:

1335-1200=135

9 months=9/12

135=1200 x r x 9/12

135=900r

divide each by 900

135/900       900r/900

0.15=r

0.15=15%

If x = 64, what is the value of x(x - 6)?

Answers

Answer:

64(64-6) = 3712

Step-by-step explanation:

64(64 -6)

64-6 = 58

64(58) = 3712

Which solid has the net shown?
A. Triangular pyramid
B. Square pyramid
C. Rectangular prism
D. Triangular prism

Answers

Answer:

D

Step-by-step explanation:

PLEASE I NEED HELP ASAP
In diagram triangle PQV and triangle WXY . What is length of XY

Answers

Answer:

:(

Step-by-step explanation:

idek

I think this is the answer
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