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Name: 
qquad
, Afigure is shown, where lines 
AB and 
CD intersect at point 
E
What is the measure, in degrees, of angle AEC?

110.

Which number represents the probability of an event that is very likely to occur?
A. 0.10
B. 1.75
C. 0.93
D. 0.06
Jerry draws a circle with a diameter of 9 inches. What is the area of the circle? 
qquad square inches
At a store, a hat has a regular price of 
x dollars. During a sale, the price of the hat is discounted by 
15%. The expression 
0.85 x describes the discounted price, in dollars, of the hat. Which expression also describes the discounted price, in dollars, of the hat?
A. 
0.15 x
B. 
x-15
C. 
x-0.15
D. 
x-0.15 x
The ratio of boys to girls in the 
7^("th ") grade is 
4:5. There are 64 boys in the 
7^("th ") grade class. How many girls are in the 
7^("th ") grade class? 
qquad girls

Name: \qquad \newline, Afigure is shown, where lines AB A B and CD C D intersect at point E \mathrm{E} \newlineWhat is the measure, in degrees, of angle AEC?\newline110. 110 . \newline22. Which number represents the probability of an event that is very likely to occur?\newlineA. 00.1010\newlineB. 11.7575\newlineC. 00.9393\newlineD. 00.0606\newline33. Jerry draws a circle with a diameter of 99 inches. What is the area of the circle? \qquad square inches\newline44. At a store, a hat has a regular price of x x dollars. During a sale, the price of the hat is discounted by 15% 15 \% . The expression 0.85x 0.85 x describes the discounted price, in dollars, of the hat. Which expression also describes the discounted price, in dollars, of the hat?\newlineA. 0.15x 0.15 x \newlineB. x15 x-15 \newlineC. AB A B 00\newlineD. AB A B 11\newline55. The ratio of boys to girls in the AB A B 22 grade is AB A B 33. There are 6464 boys in the AB A B 22 grade class. How many girls are in the AB A B 22 grade class? \qquad girls

Full solution

Q. Name: \qquad \newline, Afigure is shown, where lines AB A B and CD C D intersect at point E \mathrm{E} \newlineWhat is the measure, in degrees, of angle AEC?\newline110. 110 . \newline22. Which number represents the probability of an event that is very likely to occur?\newlineA. 00.1010\newlineB. 11.7575\newlineC. 00.9393\newlineD. 00.0606\newline33. Jerry draws a circle with a diameter of 99 inches. What is the area of the circle? \qquad square inches\newline44. At a store, a hat has a regular price of x x dollars. During a sale, the price of the hat is discounted by 15% 15 \% . The expression 0.85x 0.85 x describes the discounted price, in dollars, of the hat. Which expression also describes the discounted price, in dollars, of the hat?\newlineA. 0.15x 0.15 x \newlineB. x15 x-15 \newlineC. AB A B 00\newlineD. AB A B 11\newline55. The ratio of boys to girls in the AB A B 22 grade is AB A B 33. There are 6464 boys in the AB A B 22 grade class. How many girls are in the AB A B 22 grade class? \qquad girls
  1. Angle AEC Measurement: For the angle AECAEC, since it's given as 110110 degrees, the measure of angle AECAEC is directly provided.
  2. Probability of Event: For the probability of an event that is very likely to occur, the options are A. 0.100.10, B. 1.751.75, C. 0.930.93, D. 0.060.06. The correct answer is C. 0.930.93, as probabilities range from 00 to 11 and 0.930.93 is close to 11, indicating high likelihood.
  3. Area of Circle Calculation: To find the area of a circle with a diameter of 99 inches, use the formula A=πr2A = \pi r^2. The radius rr is half of the diameter, so r=92=4.5r = \frac{9}{2} = 4.5 inches. Then, A=π(4.5)2=π(20.25)63.62A = \pi(4.5)^2 = \pi(20.25) \approx 63.62 square inches.
  4. Discounted Price Expression: For the discounted price of the hat, the expression 0.85x0.85x is given. The correct expression that also describes this is D.x0.15xD. x - 0.15x, which simplifies to 0.85x0.85x.
  5. Number of Girls Calculation: To find the number of girls in the 7th7^{th} grade class with a boy to girl ratio of 4:54:5 and 6464 boys, set up the proportion 45=64g\frac{4}{5} = \frac{64}{g}, where gg is the number of girls. Solving for gg gives g=(54)64=80g = \left(\frac{5}{4}\right) * 64 = 80 girls.

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