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Yuki888 [10]
3 years ago
9

A church building fund has invested some money in two ways: part of the money at 7% interest and four times as much at 11%. Find

the amount invested at each rate if the total annual income from interest is 7650.
Mathematics
1 answer:
aliya0001 [1]3 years ago
4 0

Answer: he invested $15000 in part 1 and $60000 in part 2

Step-by-step explanation:

Let x represent the amount of money invested in part one.

Let 4x represent the amount of money invested in part 2 .

Total amount of money invested in part 1 and part 2 is

x + 4x = 5x

The formula for simple interest is expressed as

I = PRT/100

Where

P is the principal or initial amount.

T is the duration in years

R is the number rate.

For part 1

R = 7%

T = 1 year

P = x

I = (x × 7 × 1)/100 = 0.07x

For part 2,

R = 11%

T = 1 year

P = 4x

I = (4x × 11 × 1)/100 = 0.44x

if the total annual income from interest is 7650. This means that

0.44x + 0.07x = 7650 - - - - - - - -2

0.51x = 7650

x = 7650/0.51

x = 15000

Amount invested in part 1 is $15000

Amount invested in part 2 is 4×15000 = $60000

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Determine if the table shows a linear or an exponential function​
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Answer:

<em>The table shows an exponential function</em>

Step-by-step explanation:

<u>Linear vs Exponential Functions</u>

A linear function is written as:

y=mx+b

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

An exponential function is written as:

y=y_o.r^x

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}

Calculate the slope for (0,4) and (1,2):

\displaystyle m=\frac{2-4}{1-0}=-2

Calculate the slope for (1,2) and (2,1):

\displaystyle m=\frac{1-2}{2-1}=-1

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

\displaystyle r=\sqrt[1-0]{\frac{1}{2}}

The radical of index 1 is simply equal to its argument:

\displaystyle r=\frac{1}{2}

Now calculate the ratio for (0,4) and (2,1)

\displaystyle r=\sqrt[2-0]{\frac{1}{4}}

\displaystyle r=\sqrt{\frac{1}{4}}

\displaystyle r=\frac{1}{2}

Testing other points we'll find the same ratio, thus the table is an exponential function

4 0
3 years ago
Read 2 more answers
Y=23x+5 and<br><br> y=x+3<br><br> what is the solution
kondor19780726 [428]

Answer:

I solved this like you would a system of equations - if that is not the answer you need LMK

Point form:

(- 1/11, 32/11)

Equation Form:

x = -1/11, y = 32/11

Step-by-step explanation:

8 0
3 years ago
A local car dealership sells Buicks and Hondas. The following data shows the number of buyers this month according to the brand
Lina20 [59]

Answer:

16%

Step-by-step explanation:

The data provided on brand purchased by age group is.

\begin{array}{ccc}Age&Buick&Honda\\Under\ 40&6&17\\40\ or\ older&19&8\end{array}

A total of 50 cars were sold this month.

Since the number of buyers 40 years or older that purchased a ​Honda is 8, the percentage is:

P=\frac{8}{50}=0.16=16\%

16% of buyers were 40 years or older and purchased a​ Honda.

8 0
3 years ago
PLEASE HELP!!!!
LekaFEV [45]

Answer:

500

Step-by-step explanation:

It's a box with a square base, so let's say the width and length are x and the height is y.

The surface area of the box without the top is:

A = x² + 4xy

300 = x² + 4xy

The volume of the box is:

V = x²y

Solve for y in the first equation and substitute into the second:

y = (300 − x²) / 4x

V = x² (300 − x²) / 4x

V = x (300 − x²) / 4

V = 75x − ¼ x³

To optimize V, find dV/dx and set to 0:

dV/dx = 75 − ¾ x²

0 = 75 − ¾ x²

x = 10

So the volume of the box is:

V = 75x − ¼ x³

V = 500

The maximum volume is 500 cm³.

4 0
3 years ago
jacobi bought 7 1/2 pounds of meatballs. he decided to cook 1 i/4 pounds and freeze the rest. how many pounds did he freeze?
horsena [70]
Did You Mean 1 1/4??
8 0
3 years ago
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