Question

mad math
5 which value of x makes the inequality -11.8 < x < -√20 true?
a. -√100; taking a nap
b. -360%; watching tiktok videos
c. \\(\frac{-20}{5}\\); eating lunch
d. -4π; walking the dogs
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mad math
6 which of the following numbers best represents m on the number line?
a. \\(\frac{-4}{5}\\); tons of beetles
b. -0.7 ; old leaves
c. -21%; ants
d. -√1; pollen
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mad math
7 if the following numbers were ordered greatest to least, which number would be 2nd in the list?
4.5%, \\(\frac{1}{7}\\), 0.2, √0.12
a. 4.5%; dish soap
b. √0.12; molasses
c. \\(\frac{1}{7}\\); food coloring
d. 0.2; nail polish
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mad math
8 which symbol makes the statement \\(\frac{-11}{24} \bigcirc \frac{-6}{15}\\) true?
a. > ; 5 minutes
b. = ; 30 seconds
c. < ; 2 hours
d. none of the above; 12 minutes
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Explanation:

Problem 5: Which value of \( x \) makes the inequality \( -11.8 < x < -\sqrt{20} \) true?

Step 1: Calculate \( -\sqrt{20} \)

We know that \( \sqrt{16} = 4 \) and \( \sqrt{25} = 5 \), so \( \sqrt{20} \) is between 4 and 5. More precisely, \( \sqrt{20} \approx 4.472 \), so \( -\sqrt{20} \approx -4.472 \).

Step 2: Analyze each option

• Option A: \( -\sqrt{100} = -10 \). We check if \( -11.8 < -10 < -4.472 \). \( -11.8 < -10 \) is true, and \( -10 < -4.472 \) is also true. But let's check other options.
• Option B: \( -360\% = -3.6 \). We check if \( -11.8 < -3.6 < -4.472 \). But \( -3.6 > -4.472 \), so this is false.
• Option C: \( \frac{-20}{5} = -4 \). Check \( -11.8 < -4 < -4.472 \). \( -4 > -4.472 \), so false.
• Option D: \( -4\pi \approx -12.566 \). Check \( -11.8 < -12.566 < -4.472 \). \( -12.566 < -11.8 \), so false.

Wait, there was a miscalculation earlier. Wait, \( -\sqrt{20} \approx -4.472 \), so the upper bound is approximately -4.472. Let's re - evaluate Option A: \( -\sqrt{100}=-10 \). \( -11.8 < -10 \) (since -10 is to the right of -11.8 on the number line) and \( -10 < - 4.472\) (since -10 is to the left of -4.472 on the number line). But let's check the other options again. Wait, maybe I made a mistake in the sign for Option B. \( -360\%=-3.6 \), and \( -3.6 > - 4.472\), so it's not in the interval. Option C: \( \frac{-20}{5}=-4 \), \( -4 > - 4.472\), not in the interval. Option D: \( -4\pi\approx - 12.566\), \( -12.566 < -11.8\), so not in the interval. So Option A is the only one that satisfies \( -11.8 < x < -\sqrt{20} \) because \( -11.8 < - 10\) and \( -10<-\sqrt{20}\approx - 4.472\).

Step 1: Analyze the number line

The number line has - 0.5, 0, and \( M \) is between - 0.5 and 0, closer to 0.

Step 2: Analyze each option

• Option A: \( \frac{-4}{5}=-0.8 \). - 0.8 is less than - 0.5, so not between - 0.5 and 0.
• Option B: \( - 0.7\). - 0.7 is less than - 0.5, so not between - 0.5 and 0.
• Option C: \( -21\%=-0.21 \). - 0.21 is between - 0.5 and 0.
• Option D: \( -\sqrt{1}=-1 \). - 1 is less than - 0.5, so not between - 0.5 and 0.

So the number that best represents \( M \) is - 21% (Option C).

Step 1: Convert all numbers to decimals

• \( 4.5\% = 0.045 \)
• \( \frac{1}{7}\approx0.1429 \)
• \( 0.2 = 0.2 \)
• \( \sqrt{0.12}\approx0.3464 \)

Step 2: Order the numbers from greatest to least

Ordering the decimals: \( \sqrt{0.12}\approx0.3464>0.2 >\frac{1}{7}\approx0.1429 > 4.5\% = 0.045 \)
So the order from greatest to least is \( \sqrt{0.12}, 0.2,\frac{1}{7},4.5\% \). The second number in the list is \( 0.2 \).

Answer:

A. \( -\sqrt{100} \); taking a nap

Problem 6: Which of the following numbers best represents \( M \) on the number line?