Question

Please help me! Don't answer unless you are SURE that the answer is right, please! Will give 25 points.

Question One:

A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive, and the zoo only has room for a maximum of 20 male birds. Let x represent the number of male birds and y represent the number of female birds. Write the constraints to represent a thriving population of birds at the zoo.

A. x > 0 and y > 0
B. 0 < x ≤ 20 and y > 60
C. x > 0 and y < 20
D. 0 < x ≤ 20 and 0 < y ≤ 60

Question Two
A motorcycle can travel 60 miles per gallon. Approximately how many gallons of fuel will the motorcycle need to travel 40 km?

[1 mile = 1.6 km]

A. 0.04
B. 0.08
C. 0.20
D. 0.42


Question Three
A contractor can spend at most $425 a day on operating costs and payroll. It costs $80 each day to operate the forklift and $65 a day for each crew member. Write an inequality to represent the contractor's budget for the day.

A. 80x − 65 ≤ 425
B. 80x − 65 ≥ 425
C. 80 + 65x ≤ 425
D. 80 + 65x ≥ 425

Question Four
The total cost f(x), in dollars, for renting a bowling lane for x hours is shown:

f(x) = 2x + 12

What does f(14) represent?

A. The number of dollars it costs to rent the bowling lane for 14 hours
B. The number of games you can bowl for a cost of $14
C. The number of games you can bowl in 14 hours
D. The number of hours the bowling lane can be rented for a cost of $14

Question Five
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget:

2,020 − 22m

What does the coefficient of the expression represent?

A. The number of months Megan will wait to sell the gadget
B. The monthly depreciation value of the gadget
C. The amount of money Megan will get when she sells the gadget
D. The original value of the gadget

Question Six
Solve for x: 4x − 2 > 6x + 8.

A. x > −5
B. x < −5
C. x > 5
D. x < 5

Question Seven
Which equation is equivalent to the formula m = ca?

A. a = cm
B. a = m over c
C. c = am
D. c = a over m

Question Eight
Solve the equation 6(3x + 4) = 4x − 4.

A. x = negative 10 over 7
B. x = negative 4 over 7
C. x = -2
D. x = 2

Question Nine
A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 10 minutes. Air traffic control approved a new flight plan that will allow her to arrive three times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.

A. y = 1 over 3 x + 5
B. y = 3x +10
C. y = 1 over 3 x - 10
D. y = 3x - 10

Thank you so much for taking some of your time on this!!

Answer 1

the first thing to note is since one gallon= 60 miles then 1/2 gallon= 30 miles, now I know 1/2 is not an answer but it is easiest to decrease in moderate amounts. 1/2 gallon= 48 Km so we are close, and 1/2=0.5 so if we brought it down to 0.42 we would have 25.2 miles and 25.2 miles = 40.32. The question wants to know the approximate number and 40.32 is the closest we are going to get so the answer is 0.42

question 3

Answer:

80 + 65x ≤ 425

Explanation:

First of all we know that the 425 must be greater than or equal to the other side, so the symbol to show that would be ≤. We also know that the forklift is a fixed price by the words 'each day'. And the to hire a single crew member would be $65 unless there are more crew workers, which would be multiplied with the 65.

question 4

Jimthompson5910Expert

Part A

Yes y is a function of x. Specifically the equation is y = x^5

For any given input, there is exactly one output

Notice how if x = 1 then y = x^5 = (1)^5 = 1

Notice how if x = -1 then y = x^5 = (-1)^5 = -1

Notice how if x = -2 then y = x^5 = (-2)^5 = -32

Notice how if x = 2 then y = x^5 = (2)^5 = 32

In general,

x^5 = x*x*x*x*x

there are five copies of x multiplied

A more specific example

3^5 = 3*3*3*3*3

there are five copies of '3' multiplied

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Part B

All we do is replace x with 4 and use PEMDAS to simplify

f(x) = 2x+12

f(4) = 2(4)+12

f(4) = 8+12

f(4) = 20

The value of f(4) is 20

What does it mean? It is the total cost of renting the bowling lane for 4 hours. If you rent it for four hours, then you'll pay a total of $20.

The portion 2x = 2*4 = 8 is the variable cost which depends on how long you play. The more hours, the more the variable cost goes up

The fixed cost is 12. This is always fixed as this is the price to get in the door. If you play for 0 hours, but somehow got in the door, then you still pay $12

In total, variableCost+fixedCost = 8+12 = 20 = totalCost