Question

a hot air balloon holds 2,200 cubic meters of helium. the density of helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, rounded to the nearest tenth of a kilogram? 392.1 kg 2,199.8 kg 2,200.2 kg 11,190.9 kg question 15 multiple choice worth 1 points (07.09 lc) circle a has center of (-2, 4) and a radius of 4; and circle b has a center of (3, 9) and a radius of 8. what steps will help show that circle a is similar to circle b? translate circle a using the rule (x - 5, y - 5) dilate circle a by a scale factor of 2 reflect circle a over the axis rotate circle a 90° clockwise about the center question 16 multiple choice worth 1 points (06.09 mc) a large diamond with a mass of 712.04 grams was recently discovered in a mine. if the density of the diamond is 3.51 (g)/(cm³), what is the volume? round your answer to the nearest hundredth. 202.86 cm³ 507.30 cm³ 177.00 cm³ 1014.44 cm³

Explanation:

First Problem (Helium Mass Calculation)

Step1: Recall density formula

Density formula: $\text{Mass} = \text{Density} \times \text{Volume}$

Step2: Substitute given values

$\text{Mass} = 0.1785 \times 2200$

Step3: Calculate and round to tenth

$0.1785 \times 2200 = 392.7$

All circles are similar, and scaling one circle by a factor equal to the ratio of the radii of the two circles maps one to the other. The ratio of circle B's radius to circle A's radius is $\frac{8}{4}=2$, so scaling circle A by 2 will make it congruent to circle B, proving similarity.

Step1: Rearrange density formula

$\text{Volume} = \frac{\text{Mass}}{\text{Density}}$

Step2: Substitute given values

$\text{Volume} = \frac{712.04}{3.51}$

Step3: Calculate and round to hundredth

$\frac{712.04}{3.51} \approx 202.86$

Answer:

392.7 kg

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Question 15 (Circle Similarity)