A man has $290,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $27,600 and the amount invested at 8% is twice that invested at 12%. (a) How much is invested in each property?

12% property $

10% property $

8% property $

(b) What is the annual income from each property?

12% property $

10% property $

8% property $

Step-by-step explanation:

let amount invested at 12%=x

amount invested in 10 %=y

amount invested in 8 %=z

z=2x

x+y+z=290,000

x+y+2x=290,000

3x+y=290,000  

multiply by 5

15x+5y=1,450,000  ... (1)

12/100 x+10/100 y+8/100 z=27,600

12x+10 y+8z=2,760,000

6x+5y+4z=1,380,000

6x+5y+4(2x)=1,380,000

14x+5y=1,380,000   ... (2)

(1)-(2) gives

x=1,450,000-1,380,000=70,000

z=2(70,000)=140,000

70,000+y+140,000=290,000

y+210,000=290,000

y=290,000-210,000=80,000

invested in 12 %=$ 70,000

invested in 10 %=$ 80,000

invested in 8 %=$ 140,000

(b)

annual income from 12 %=12/100 ×70,000= $8,400

annual income from 10 % =10/100×80,000=$ 9,600

annual income from 8 %=8/100×140,000= $11,200

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation: