Let x represent amount invested in the higher-yielding account.
We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be 
.
We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.
, where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
We are told that interest rates are 6% and 10%.
Amount of interest earned from lower-yielding account: 
.
Amount of interest earned from higher-yielding account: 
.
Let us solve for x.
Therefore, the man invested $30,000 at 10%.
Amount invested in the lower-yielding account would be 
.
Therefore, the man invested $60,000 at 6%.
Answer:
<em>The shaded region has an area of 1400 square units</em>
Step-by-step explanation:
<u>Area of Compound Shapes</u>
We are given a shape and it's required to calculate its area. The shape can be divided into three rectangles as shown in the figure attached below.
The lengths of these rectangles are x, y, and z.
The value of x can be calculated as:
x = 60 - 15 - 10 = 35
Similarly:
y = 60 - 15 = 45
z = y = 45
The first rectangle has dimensions of x by 10, thus its area is:
A1 = 35*10 = 350
The second rectangle has dimensions of 60 by 10:
A2 = 60*10 = 600
The third rectangle has dimensions y by 10:
A3 = 55*10 = 450
The shaded area is:
A = 350 + 600 + 450 = 1400
The shaded region has an area of 1400 square units
Answer:
36 cubic inches.
Step-by-step explanation:
Let the length, width and height of the rectangular prism are a, b, c respectively.
So, surface area, 2(ab + bc + ca) = 32 {Given} ............ (1)
Volume, abc = 12 {Given} ............ (2)
And, the sum of all the edges, 4(a + b + c) = 28 {Given} .......... (3)
Now, if the length width and height are increased by 1 inch, then the volume of the prism will be = (a + 1)(b + 1)(c + 1)
= abc + (ab + bc + ca) + (a + b + c) + 1
= 12 + 16 + 7 + 1 {From equations (1), (2) and (3)}
= 36 cubic inches. (Answer)
Answer:
4x -12
Step-by-step explanation:
Your question answers itself: you use the distributive property to remove the parentheses.
4(x -3) = 4(x) +4(-3) = 4x -12
Answer:
Rayshawn originally had $30.
Step-by-step explanation:
i) Rayshawn has a certain amount of money. Let us say this amount is $x.
ii) Rayshawn spends $20 which means that he is left with $(x - 20)
iii) it is also given that amount of money left after spending $20 is 
of the original amount, $x, the amount remaining is 
.
iv) from the information given in ii) and iii) we get
$(x - 20) = , Therefore we get 3x - 60 = x , therefore 2x = 60,
Therefore x = $30. Rayshawn originally had $30.
