Question

29 nicole had a collection of 60 stuffed animals. she gave away 5 stuffed animals per month until all her stuffed animals were gone.
which graph best represents this situation?
a.
stuffed animal collection
number of stuffed animals
60
50
40
30
20
10
0
2 4 6 8 10 12
number of months
b.
stuffed animal collection
number of stuffed animals
140
120
100
80
60
40
20
0
2 4 6 8 10 12
number of months
c.
stuffed animal collection
number of stuffed animals
780
720
660
600
540
480
420
360
300
240
180
120
60
0
2 4 6 8 10 12
number of months
d.
stuffed animal collection
number of stuffed animals
600
540
480
420
360
300
240
180
120
60
0
2 4 6 8 10 12
number of months
30 nicholas is buying shirts for his baseball team.
he will pay $9.50 for each shirt plus a one - time fee of $22.50 for the design.
which equation can be used to find y, the total cost to buy x shirts?
a. $y = 9.5x + 22.5$
b. $y = 22.5x + 9.5$
c. $y = 9.5x - 22.5$
d. $y = 22.5x - 9.5$
31 the diameter of circle x is 15 centimeters. the diameter of circle y is 20 centimeters.
which measurement is closest to the difference between the circumference of circle x and the circumference of circle y in centimeters?
a. 15.7 cm
b. 7.85 cm
c. 137 cm
d. 31.4 cm

Explanation:

Question 29

Step1: Analyze the situation

Nicole starts with 60 stuffed animals and gives away 5 per month, so the number of stuffed animals decreases over time. The graph should have a y - intercept of 60 (initial number) and a negative slope (since the number is decreasing).

Step2: Evaluate each graph

• Graph A: Y - intercept is 60, slope is negative (decreasing), and when \(x = 12\) (months), \(y=0\) (since \(60\div5 = 12\) months to give away all 60).
• Graph B: Y - intercept is 60 but it is increasing, which is wrong as the number of stuffed animals should decrease.
• Graph C: Y - intercept is 0 and it is increasing, wrong.
• Graph D: Y - intercept is 600, which is wrong as initial number is 60.

Step1: Identify cost components

The cost per shirt is $9.50, so for LXI0 shirts, the cost for shirts is LXI1. There is a one - time design fee of $22.50.

Step2: Form the equation

Total cost \(y=\) cost of shirts+design fee. So \(y = 9.5x+22.5\).

Step1: Recall circumference formula

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter.

Step2: Calculate circumferences

• Circumference of circle X: \(C_X=\pi\times15 = 15\pi\)
• Circumference of circle Y: \(C_Y=\pi\times20=20\pi\)

Step3: Find the difference

Difference \(=\vert C_Y - C_X\vert=\vert20\pi - 15\pi\vert = 5\pi\approx5\times3.14 = 15.7\) cm? Wait, no, wait: Wait, \(C_Y - C_X=20\pi-15\pi = 5\pi\approx15.7\)? Wait, no, wait the question is difference between circumference of X and Y? Wait, diameter of X is 15, Y is 20. So \(C_X=\pi d_X = 15\pi\), \(C_Y = 20\pi\). The difference is \(C_Y - C_X=5\pi\approx15.7\)? Wait, but let's recalculate: \(\pi\approx3.14\), \(20\pi-15\pi = 5\pi\approx5\times3.14 = 15.7\). But wait, maybe I mixed up X and Y. Wait, diameter of X is 15, Y is 20. So \(C_X = 15\pi\), \(C_Y=20\pi\). The difference is \(20\pi - 15\pi=5\pi\approx15.7\) cm. But wait, option A is 15.7, option B is 7.85. Wait, maybe I made a mistake. Wait, no: Wait, the problem says "difference between the circumference of circle X and the circumference of circle Y". So if \(C_Y>C_X\), then \(C_Y - C_X=20\pi - 15\pi = 5\pi\approx15.7\) cm. But let's check the options. Option A is 15.7 cm.

Wait, wait, no: Wait, \(C=\pi d\), so \(C_X=\pi\times15 = 15\pi\approx47.1\) cm, \(C_Y=\pi\times20 = 62.8\) cm. The difference is \(62.8 - 47.1=15.7\) cm.

Answer:

A. The graph labeled A (Stuffed Animal Collection with y - intercept 60, decreasing line, x from 0 - 12, y from 0 - 60)

Question 30