Math / Data & Statistics

QuestionAn archeologist recorded the masses of four artifacts in the table below. Masses of Artifacts \begin{tabular}{|c|c|} \hline Artifact & Mass (grams) \\ \hline A & $2.4 \times 10^{-2}$ \\ \hline B & 14.4 \\ \hline C & $7.01 \times 10^{4}$ \\ \hline D & $8.4 \times 10^{5}$ \\ \hline \end{tabular}
Part A. How many times greater is the mass of artifact B than the mass of artifact A? Part B. What is the combined mass of artifact C and artifact D in grams? Enter the correct answers in the boxes. A. $\square$ times greater B. $\square$ grams

Studdy Solution

STEP 1

1. We are given the masses of four artifacts A, B, C, and D.
2. We need to calculate how many times the mass of artifact B is greater than the mass of artifact A.
3. We need to find the combined mass of artifacts C and D.

STEP 2

1. Calculate the ratio of the mass of artifact B to the mass of artifact A.
2. Calculate the combined mass of artifacts C and D.

STEP 3

Write down the masses of artifacts A and B in grams.
$\text{Mass of A} = 2.4 \times 10^{-2} \text{ grams}$ $\text{Mass of B} = 14.4 \text{ grams}$

STEP 4

Calculate the ratio of the mass of artifact B to the mass of artifact A.
$\frac{\text{Mass of B}}{\text{Mass of A}} = \frac{14.4}{2.4 \times 10^{-2}}$

STEP 5

Simplify the ratio.
$\frac{14.4}{2.4 \times 10^{-2}} = \frac{14.4}{0.024}$

STEP 6

Perform the division to find the ratio.
$\frac{14.4}{0.024} = 600$

STEP 7

Write down the masses of artifacts C and D in grams.
$\text{Mass of C} = 7.01 \times 10^{4} \text{ grams}$ $\text{Mass of D} = 8.4 \times 10^{5} \text{ grams}$

STEP 8

Calculate the combined mass of artifacts C and D.
$\text{Combined Mass} = \text{Mass of C} + \text{Mass of D}$ $\text{Combined Mass} = 7.01 \times 10^{4} + 8.4 \times 10^{5}$

STEP 9

Simplify the combined mass.
$7.01 \times 10^{4} = 70100$ $8.4 \times 10^{5} = 840000$ $\text{Combined Mass} = 70100 + 840000 = 910100 \text{ grams}$
Solution: Part A: The mass of artifact B is 600 times greater than the mass of artifact A. Part B: The combined mass of artifacts C and D is 910100 grams.

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Studdy Solution

STEP 1

1. We are given the masses of four artifacts A, B, C, and D.
2. We need to calculate how many times the mass of artifact B is greater than the mass of artifact A.
3. We need to find the combined mass of artifacts C and D.

STEP 2

1. Calculate the ratio of the mass of artifact B to the mass of artifact A.
2. Calculate the combined mass of artifacts C and D.

STEP 3

Write down the masses of artifacts A and B in grams.
$\text{Mass of A} = 2.4 \times 10^{-2} \text{ grams}$ $\text{Mass of B} = 14.4 \text{ grams}$

STEP 4

Calculate the ratio of the mass of artifact B to the mass of artifact A.
$\frac{\text{Mass of B}}{\text{Mass of A}} = \frac{14.4}{2.4 \times 10^{-2}}$

STEP 5

Simplify the ratio.
$\frac{14.4}{2.4 \times 10^{-2}} = \frac{14.4}{0.024}$

STEP 6

Perform the division to find the ratio.
$\frac{14.4}{0.024} = 600$

STEP 7

Write down the masses of artifacts C and D in grams.
$\text{Mass of C} = 7.01 \times 10^{4} \text{ grams}$ $\text{Mass of D} = 8.4 \times 10^{5} \text{ grams}$

STEP 8

Calculate the combined mass of artifacts C and D.
$\text{Combined Mass} = \text{Mass of C} + \text{Mass of D}$ $\text{Combined Mass} = 7.01 \times 10^{4} + 8.4 \times 10^{5}$

STEP 9

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Studdy Solution

STEP 1

1. We are given the masses of four artifacts A, B, C, and D.2. We need to calculate how many times the mass of artifact B is greater than the mass of artifact A.3. We need to find the combined mass of artifacts C and D.

STEP 2

1. Calculate the ratio of the mass of artifact B to the mass of artifact A.2. Calculate the combined mass of artifacts C and D.

STEP 3

Write down the masses of artifacts A and B in grams.Mass of A=2.4×10−2 grams \text{Mass of A} = 2.4 \times 10^{-2} \text{ grams} Mass of A=2.4×10−2 grams Mass of B=14.4 grams \text{Mass of B} = 14.4 \text{ grams} Mass of B=14.4 grams

STEP 4

Calculate the ratio of the mass of artifact B to the mass of artifact A.Mass of BMass of A=14.42.4×10−2 \frac{\text{Mass of B}}{\text{Mass of A}} = \frac{14.4}{2.4 \times 10^{-2}} Mass of AMass of B​=2.4×10−214.4​

STEP 5

Simplify the ratio.14.42.4×10−2=14.40.024 \frac{14.4}{2.4 \times 10^{-2}} = \frac{14.4}{0.024} 2.4×10−214.4​=0.02414.4​

STEP 6

Perform the division to find the ratio.14.40.024=600 \frac{14.4}{0.024} = 600 0.02414.4​=600

STEP 7

Write down the masses of artifacts C and D in grams.Mass of C=7.01×104 grams \text{Mass of C} = 7.01 \times 10^{4} \text{ grams} Mass of C=7.01×104 grams Mass of D=8.4×105 grams \text{Mass of D} = 8.4 \times 10^{5} \text{ grams} Mass of D=8.4×105 grams

STEP 8

STEP 9

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1. We are given the masses of four artifacts A, B, C, and D.
2. We need to calculate how many times the mass of artifact B is greater than the mass of artifact A.
3. We need to find the combined mass of artifacts C and D.

1. Calculate the ratio of the mass of artifact B to the mass of artifact A.
2. Calculate the combined mass of artifacts C and D.

Write down the masses of artifacts A and B in grams.
$\text{Mass of A} = 2.4 \times 10^{-2} \text{ grams}$ $\text{Mass of B} = 14.4 \text{ grams}$

Calculate the ratio of the mass of artifact B to the mass of artifact A.
$\frac{\text{Mass of B}}{\text{Mass of A}} = \frac{14.4}{2.4 \times 10^{-2}}$

Simplify the ratio.
$\frac{14.4}{2.4 \times 10^{-2}} = \frac{14.4}{0.024}$

Perform the division to find the ratio.
$\frac{14.4}{0.024} = 600$

Write down the masses of artifacts C and D in grams.
$\text{Mass of C} = 7.01 \times 10^{4} \text{ grams}$ $\text{Mass of D} = 8.4 \times 10^{5} \text{ grams}$