Problem 1
<h3>Answer:
104 cubic inches</h3>
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Explanation:
The prisms are similar so they have the same shape, but different sizes.
The linear scale factor from small to large is:
large/small = 10/4 = 2.5
Meaning that we multiply each dimension of the smaller prism by 2.5 to get the corresponding side length of the larger prism
4*2.5 = 10
This linear scale factor is then cubed to get the volume scale factor
(2.5)^3 = 15.625
Which tells us:
larger volume = 15.625*(smaller volume)
smaller volume = (larger volume)/15.625
smaller volume = (1625)/15.625
smaller volume = 104 cubic inches
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Problem 2
<h3>Answer: 650 square inches</h3>
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Explanation:
We will go back to the linear scale factor of 2.5
This time, we square it to get (2.5)^2 = 6.25
This is the surface area scale factor.
larger surface area = 6.25*(smaller surface area)
larger surface area = 6.25*(104)
larger surface area = 650 square inches
Answer:
6
Step-by-step explanation:
3 ⋅ 2^t
Let t=1
3 ⋅ 2^1
Exponents first
3 * 2
6
Answer:
°¥°•°¥÷€° ¥÷¥℅• ¥÷• °€°¥™•°€°¥ ¥÷€^¥°
L-5l+l9l=
5+9=14
and done :P
Answer:
The average total cost per hour of training is $70.5
Step-by-step explanation:
The form of the linear function is f(x) = m x + b, where
- m is the average rate
- b is the initial value
∵ The gym charges a $615 yearly fee for membership plus
$50 for each hour of personal training
- That means the initial amount is 615 and the average rate is 50
∴ m = 50 dollars per hour
∴ b = 615 ⇒ fixed fee
- Substitute m and b in the form of the linear function
∴ c(x) = 50 x + 615, where c(x) is the cost per year for x
training hours
∵ A member works with a personal trainer for 30 hours in a year
- That means x = 30
∴ x = 30
- Find the total cost of this year by substituting x by 30
∴ c(30) = 50(30) + 615
∴ c(30) = 1500 + 615
∴ c(30) = 2115
∴ The total cost of this year is $2115
To find the average cost per hour divide the total cost by the number of the training hours
∵ Average cost per hour = 2115 ÷ 30
∴ The average cost per hour = 70.5 dollars
∴ The average total cost per hour of training is $70.5
