Question

Question 9(Multiple Choice Worth 5 points)

Answer 1

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%