Question

estimate the value of $8.97 \div 0.31$
30
40
50
question 4
1 pts
without using a calculator, determine which whole number $\sqrt{70}$ is closest to.
7
8
9
question 5
1 pts
a cyclist rides 27 miles in 1.5 hours.
which is the best estimate of her speed?
18 mph
17 mph
19 mph
20 mph

Explanation:

First Question (Estimate \( 8.97 \div 0.31 \))

Step1: Round the numbers

Round \( 8.97 \) to \( 9 \) and \( 0.31 \) to \( 0.3 \).

Step2: Perform the division

Calculate \( 9 \div 0.3 \). Since \( 0.3\times30 = 9 \), so \( 9\div0.3 = 30 \).

Recall the perfect squares around \( 70 \). We know that \( 8^2 = 64 \) and \( 9^2 = 81 \). Now, find the distance of \( 70 \) from \( 64 \) and \( 81 \). The distance from \( 70 \) to \( 64 \) is \( 70 - 64 = 6 \), and the distance from \( 70 \) to \( 81 \) is \( 81 - 70 = 11 \). Since \( 6 < 11 \), \( 70 \) is closer to \( 64 \) (which is \( 8^2 \))? Wait, no, wait. Wait, \( 8^2 = 64 \), \( 9^2 = 81 \). Wait, \( 70 - 64 = 6 \), \( 81 - 70 = 11 \). Wait, but actually, \( \sqrt{64}=8 \), \( \sqrt{81}=9 \). Wait, but \( 70 \) is 6 more than 64 and 11 less than 81? Wait, no, 81 - 70 is 11, 70 - 64 is 6. So 70 is closer to 64? But 64 is 8 squared, 81 is 9 squared. Wait, but 70 is 6 away from 64 and 11 away from 81? Wait, no, that can't be. Wait, 88=64, 99=81. 70 - 64 = 6, 81 - 70 = 11. So the difference between 70 and 64 is 6, between 70 and 81 is 11. So 70 is closer to 64, so \( \sqrt{70} \) is closer to 8? Wait, no, wait, 8.366... is \( \sqrt{70} \), so it's closer to 8? Wait, no, wait, 8^2=64, 9^2=81. 70 - 64 = 6, 81 - 70 = 11. So 70 is 6 units from 64 and 11 units from 81. So since 6 < 11, \( \sqrt{70} \) is closer to 8? Wait, but wait, 8.366 is closer to 8 or 9? 8.366 - 8 = 0.366, 9 - 8.366 = 0.634. So 0.366 < 0.634, so it's closer to 8? Wait, but the options are 7,8,9. Wait, 7^2=49, 8^2=64, 9^2=81. So 70 is between 64 and 81, so between 8 and 9. The distance from 70 to 64 is 6, to 81 is 11. So since 6 is less than 11, 70 is closer to 64, so \( \sqrt{70} \) is closer to 8? Wait, but let's calculate the decimal. \( \sqrt{70} \approx 8.366 \), which is closer to 8 or 9? 8.366 - 8 = 0.366, 9 - 8.366 = 0.634. So 0.366 < 0.634, so closer to 8. Wait, but the options are 7,8,9. So the answer is 8? Wait, but wait, maybe I made a mistake. Wait, 8^2=64, 9^2=81. 70-64=6, 81-70=11. So 6 is less than 11, so 70 is closer to 64, so square root of 70 is closer to 8. So the answer is 8? Wait, but let's check again. \( \sqrt{64}=8 \), \( \sqrt{81}=9 \). The number 70 is 6 above 64 and 11 below 81. So the square root of 70 is 8.366..., which is 0.366 above 8 and 0.634 below 9. So it's closer to 8. So the answer is 8.

Step1: Recall the speed formula

Speed \( = \frac{\text{Distance}}{\text{Time}} \).

Step2: Substitute the values

Distance is 27 miles, Time is 1.5 hours. So speed \( = \frac{27}{1.5} \).

Step3: Perform the division

\( 27 \div 1.5 = 18 \) (since \( 1.5\times18 = 27 \)).

Answer:

30

Question 4 (Determine which whole number \( \sqrt{70} \) is closest to)