spiral review\n1. what property is shown?\na. 19 + 0 and 0 + 19\nb. 9 + 7 + 3 and 9 + 3 + 7\n2. thomas…

spiral review\n1. what property is shown?\na. 19 + 0 and 0 + 19\nb. 9 + 7 + 3 and 9 + 3 + 7\n2. thomas flipped two quarters 80 times. he tails on both quarters 8 times. would you expect this result? why or why not?\n3. willy, abby, and maddy are playing golf. willy ends with a score of -9. abby’s score is -10. maddy scores +6. what is the difference between the scores of maddy and abby?\n4. beth’s golf ball has a circumference of 4.71 in. what is the radius of her golf ball?\nbidziil is examining a scale drawing of the national park near his home. he wants to hike from the park entrance to a hot spring. on the map, the entrance and hot spring are 2.5 inches apart. there is a scale map: 1 in = 2.5 mi. how far will he have to hike?

spiral review\n1. what property is shown?\na. 19 + 0 and 0 + 19\nb. 9 + 7 + 3 and 9 + 3 + 7\n2. thomas flipped two quarters 80 times. he tails on both quarters 8 times. would you expect this result? why or why not?\n3. willy, abby, and maddy are playing golf. willy ends with a score of -9. abby’s score is -10. maddy scores +6. what is the difference between the scores of maddy and abby?\n4. beth’s golf ball has a circumference of 4.71 in. what is the radius of her golf ball?\nbidziil is examining a scale drawing of the national park near his home. he wants to hike from the park entrance to a hot spring. on the map, the entrance and hot spring are 2.5 inches apart. there is a scale map: 1 in = 2.5 mi. how far will he have to hike?

Answer

Explanation:

1a.

The expressions (19 + 0) and (0+19) show the commutative - property of addition. The commutative property of addition states that for any two numbers (a) and (b), (a + b=b + a). Here (a = 19) and (b = 0).

1b.

The expressions (9 + 7+3) and (9 + 3+7) show the commutative property of addition. The order of the addends (7) and (3) is changed while the sum remains the same.

2.

The probability of getting tails on one quarter is (\frac{1}{2}), and the probability of getting tails on two independent quarters is (\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}). If the experiment is repeated (n = 80) times, the expected number of times to get tails on both quarters is (E=n\times p), where (p=\frac{1}{4}). So (E = 80\times\frac{1}{4}=20). Since (8) is less than (20), this result is lower than expected, but still possible due to random - variation.

3.

To find the difference between Maddy's score ((+ 6)) and Abby's score ((-10)), we use the formula (a - b), where (a = 6) and (b=-10).

Step1: Write the subtraction formula

(6-(-10))

Step2: Apply the rule (a-(-b)=a + b)

(6 + 10=16)

4.

The formula for the circumference of a circle is (C = 2\pi r). Given (C = 4.71) inches and (\pi\approx3.14).

Step1: Solve the formula for (r)

(r=\frac{C}{2\pi})

Step2: Substitute (C = 4.71) and (\pi = 3.14)

(r=\frac{4.71}{2\times3.14}=\frac{4.71}{6.28}=0.75) inches

5.

The scale is (1) inch ( = 2.5) miles. The distance on the map is (d_{map}=2.5) inches.

Step1: Use the scale to find the actual distance (d_{actual})

(d_{actual}=d_{map}\times2.5)

Step2: Substitute (d_{map}=2.5) inches

(d_{actual}=2.5\times2.5 = 6.25) miles

Answer:

1a. Commutative property of addition 1b. Commutative property of addition 2. The result is lower than expected (expected 20 times), but possible due to random - variation. 3. 16 4. 0.75 inches 5. 6.25 miles