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Question 9(Multiple Choice Worth 5 points)
(05.05 MC)

The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 6 inches?

4 inches
8 inches
18 inches
20 inches
Question 10(Multiple Choice Worth 5 points)
(05.01 LC)

The current size of an image on Sandy's computer is shown below:

A rectangle is shown. The length of the rectangle is labeled as length equal to 4 inches and the width is labeled as width equal to 6 inches.

What are the dimensions of the image at fraction 1 over 2 times its current size?

Length = 8 inches, width = 12 inches
Length = 6 inches, width = 8 inches
Length = 2 inches, width = 4 inches
Length = 2 inches, width = 3 inches
Question 11(Multiple Choice Worth 5 points)
(05.04 LC)

The image below is a triangle drawn inside a circle with center O:

A triangle is shown inscribed inside a circle. The leg of the triangle labeled 8 inches passes through the center of the circle, O. The other two legs are labeled as 4 inches and 5 inches.

Which of the following expressions shows the area, in square inches, of the circle?

(π = 3.14)

3.14 ⋅ 42
3.14 ⋅ 52
3.14 ⋅ 5
3.14 ⋅ 22
Question 12(Multiple Choice Worth 5 points)
(05.02 MC)

Based on the figure below, what is the value of x?

A right angle is shown divided in two parts. The measure of the angle of one part is 20 degrees and the measure of the other part is 5x plus 15 degrees.

1
9
11
15
Question 13(Multiple Choice Worth 5 points)
(06.02 LC)

A coin is flipped 70 times and lands on tails 28 times. What is the relative frequency of the coin landing on tails?

20%
30%
40%
50%
Question 14(Multiple Choice Worth 5 points)
(06.01 LC)

During the grand opening of an electronics store, any customer has a 17% chance of winning a free laptop. What is the chance that a customer does not win a free laptop?

81%
83%
51%
37%
Question 15(Multiple Choice Worth 5 points)
(06.04 MC)

The figure below shows a shaded circular region inside a larger circle:

A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 3 inches and below r equal to 3 inches is written R equal to 5 inches.

What is the probability that a point chosen inside the larger circle is not in the shaded region?

24%
36%
50%
64%

Respuesta :

calculista

Answer:

Part 9) 8 inches

Part 10) Length = 2 inches, width = 3 inches

Part 11) 3.14(4)²

Part 12) x=11°  

Part 13) 40%

Part 14) 83%

Part 15) 64%

Step-by-step explanation:

Part 9) we know that

The area of a triangle is equal to

A=(1/2)bh

we have

A=24 in²

b=6 in

substitute and solve for h

24=(1/2)(6)h

48=6h

h=8 in

Part 10) we know that

The scale factor is 1/2

To find the new dimensions, multiply the original dimensions by the scale factor

Length=4*(1/2)=2 in

width=6*(1/2)=3 in

Part 11) we know that

If the leg of the triangle labeled 8 inches passes through the center of the circle

then

the diameter of the circle is 8 inches

the radius is

r=8/2=4 in ----> the radius is half the diameter

The area of the circle is equal to

A=πr²

substitute the values

A=3.14(4)²

Part 12) we know that

20°+(5x+15)°=90°  ----> by complementary angles

so

Solve for x

(5x+15)°=90-20°

5x=70°-15°

x=55°/5=11°  

Part 13) we know that

70 times represent the 100%

using proportion

100%/70=x/28

x=28*100%/70

x=40%

Part 14) we know that

Any customer has a 17% chance of winning a free laptop

so

the chance that a customer does not win a free laptop is equal to

100%-17%=83%

Part 15)

step 1

Find the area of the larger circle minus the smaller circle

A=π(5²-3²)=16π in²

step 2

Find the area of the larger circle

   A=π(5²)=25π in²

step 3

Find the probability  that a point chosen inside the larger circle is not in the shaded region

Divided the area of of the larger circle minus the smaller circle by the area of the larger circle

16π/25π=0.64=64%

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