Answer:
A. 7,348
Step-by-step explanation:
P = le^kt
intitial population = 500
time = 4 hrs
end population = 3,000
So we have all these variables and we need to solve for what the end population will be if we change the time to 6 hours. First, we need to find the rate of the growth(k) so we can plug it back in. The given formula shows a exponencial growth formula. (A = Pe^rt) A is end amount, P is start amount, e is a constant that you can probably find on your graphing calculator, r is the rate, and t is time.
A = Pe^rt
3,000 = 500e^r4
now we can solve for r
divide both sides by 500
6 = e^r4
now because the variable is in the exponent, we have to use a log
ln(6) = 4r
we can plug the log into a calculator to get
1.79 = 4r
divide both sides by 4
r = .448
now lets plug it back in
A = 500e^(.448)(6 hrs)
A = 7351.12
This is closest to answer A. 7,348
Answer:
a = 38⁰
b = 54⁰
c = 54⁰
Step-by-step explanation:
a + 142⁰ = 180⁰ because a straight line = 180⁰
b + 38⁰ + 88⁰ = 180⁰ because the angles of a triangle equal 180⁰, and the missing measurement = 38⁰ because it is a vertical angle to angle a
c + 88⁰ = 142⁰ because the angles are corresponding angles
Answer:
A, B, F
Step-by-step explanation:
2/3 - x + 1/6 = 6x
Collect like terms
2/3 + 1/6 = 6x + x
(4+1) / 6 = 7x
5/6 = 7x
x = 5/6 ÷ 7
= 5/6 × 1/7
x = 5/42
a) 4 - 6x + 1 = 36x
4 + 1 = 36x + 6x
5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
b) 5/6 - x = 6x
5/6 = 6x + x
5/6 = 7x
This is equivalent to the third step of the simplification
c) 4 - x + 1 = 6x
4 + 1 = 6x + x
5 = 7x
x = 5/7
Not equivalent to any of the steps in the simplification above
d) 5/6 + x = 6x
5/6 = 6x - x
5/6 = 5x
x = 5/6 ÷ 5
= 5/6 × 1/5
x = 5/30
Not equivalent to any of the steps in the simplification above
e) 5 = 30x
x = 5/30
Not equivalent to any of the steps in the simplification above
f) 5 = 42x
x = 5/42
Equivalent to the last step of the simplification above
Answer:
20
30
Step-by-step explanation:
Do 5 times ten.
5 times -6
Gives you 20
Then do 6 times 4, 6 times 10, to get the final answer of 30.
<h3>
Part A:</h3>
The area A of a rectangle is A = bh, where b is the base of the rectangle and h is the height. The area of each rectangle with side lengths 1.5 ft and 2 ft is 1.5 × 2 = 3ft2. Since there are two rectangles with these dimensions, the combined area is 2 × 3 = 6 ft2. The area of each rectangle with side lengths 1.5 ft and 2.5 ft is 1.5 × 2.5 = 3.75 ft2. The area of each rectangle with side lengths 2 ft and 2.5 ft is 2 × 2.5 = 5 ft2. Since there are two rectangles of each type, the combined area is 2 × 3.75 + 2 × 5 =17.5 ft2. <u><em>So, the total surface area of the box is 6 ft2+ 17.5 ft2 = 23.5 ft2</em></u>
<u><em></em></u>
<h3>Part B:</h3>
The employee needs to wrap 8 boxes, each with a surface area of 23.5 ft2. So, the combined surface area needing to be wrapped is 8 × 23.5 = 188 ft2. Since there is only 160 square feet of wrapping paper left, the employee will not be able to wrap all of the gifts
