Answer:
reflect over the x-axis and shift down 5
Step-by-step explanation:
Assuming the transformed graph has equation.
and the parent function is
Then the transformed function is obtained by reflecting the parent function in the x-axis and then shifting it down by 5 units.
The coy option is reflect over the x-axis and shift down 5 units.
Answer:
If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams
Step-by-step explanation:
Mean =
Standard deviation =
We are supposed to find If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams i.e.P(X>x)=0.02
The mean weight is in the highest 2%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.98.
n = 27
Refer the z -table
P(Z>x)=2.06
So, If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams
Answer:
18. compound interest
19. simple interest
20. simple interest
Step-by-step explanation:
For these problems, the initial balance is irrelevant. All that matters is the multiplier of that balance. For simple interest at rate r for t years, the multiplier is ...
simple interest multiplier = (1 +rt)
For interest compounded annually, the multiplier of the initial balance is ...
compound interest multiplier = (1 +r)^t
A spreadsheet can do the computations for you.
___
As an example of the computations involved, consider problem 19:
simple interest multiplier = 1 + 0.13·6 = 1.78
compound interest multiplier = 1.10^6 = 1.771561
The latter is less than the former, so the simple interest account will have the (slightly) greater balance at the end of 6 years.
Answer:
height = 14.5 ft
width = length = 3.2 ft
Step-by-step explanation:
Let the side of the square base is a and the height of the box is h.
The material required to make the box is equal to the total surface area of the box.
Area of base = a²
Cost of square base is $ 2 per ft²
So, the cost of making base = 2a²
Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah
Cost of making walls and the top is $ 1 per ft²
So, the cost of making walls and the top = 1 x ( 3a² + 2ah)
Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah
According to the question
144 = 5a² + 2ah
.... (1)
The volume of the box is V = length x width x height
V = a x a x h
V = 72 a - 2.5 a³ from equation (1)
Differentiate both sides with respect to a.
dV/da = 72 - 7.5 a²
Put, it equal to zero for maxima and minima
7.5 a² = 72
a = 3.2 ft
Put in equation (1)
h = 14.5 ft
So, the dimensions of the box are
height = 14.5 ft
width = length = 3.2 ft