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Inga [223]
2 years ago
7

Dana is holding a bottle of shampoo, which is cylindrical in shape with a radius of about 2 in. and a height of about 7 in. She

is wondering how many bottles of this shampoo she can fit in a suitcase that is shaped like a rectangular prism and is about 3 ft long, 2 ft wide, and 1 ft tall. Her reasoning, shown here, contains an error.
The shampoo bottle has a volume of about 88 in³, or about 8×101 in³.
The suitcase has a volume of about 10,368 in³, or about 1×105 in³.
1×1058×101=18×104 , so about 1250 bottles of shampoo could fit in the suitcase.

What is Dana's error?

A. The value 88 should have been rounded to 8×102 .
B. The volume of the shampoo bottle is not 88 in³.
C. The volume of the suitcase is not about 10,368 in³.
D. The value 10,368 should have been rounded to 1×104 .
Mathematics
1 answer:
Margarita [4]2 years ago
5 0
Volume of the shampoo bottle
                                    V = πr²h
Substituting,
                                      V = π(2 in)²(7 in) = 87.9 in³  ≈ 88 in³

Volume of the suitcase,
         Convert all dimensions to inches by multiplying by 12.
                              length = 36 in  ;  width = 24 in   ; height = 12 in

Multiply the given dimensions,
                                  V = (36 in)(24 in)(12 in) = 10,368 in³

Dividing the two calculated values will give us an answer of 117.82 or approximately 117 bottles. 

The mistake done is described in letter A because as much as possible we want to overestimate the volume of the shampoo as its value becomes the divisor. 
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Answer:

The ratios are not equal.

Step-by-step explanation:

To justify the answer we will assume the dimes and quarters.

Let number of dimes be denoted by 'x'.

Let number of quarters denoted by 'y'.

In Siri's coin purse

Number of dimes (x) = 6

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Therefore ratio of quarter to dimes we get;

\frac{x}{y}=\frac{6}{4} ⇒ equation 1.

In Martha Coin purse.

Number of dimes (x) = 5

Number of quarters (y) = 3

Therefore ratio of quarter to dimes we get;

\frac{x}{y}=\frac{5}{3} ⇒ equation 2.

Now we will check if both have the same ratios.

We will check by making both equation 1 and equation 2 equal.

\frac{6}{4}=\frac{5}{3}

By cross multiplication we get;

18\neq 20

Hence the ratios are not equal.

4 0
2 years ago
Richard bought 3 slices of cheese pizza and 2 sodas for $8.75. Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50. How
Alex17521 [72]
Let
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y------------> the cost of one soda

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</span>

5 0
2 years ago
A restaurant serves custom-made omelets, where guests select meat, cheese, and vegetables to be added to their omelet. There are
kondor19780726 [428]

Answer: The number of different combinations of 2 vegetables are possible = 15 .

Step-by-step explanation:

In Mathematics , the number of combinations of selecting r values out of n values = ^nC_r=\dfrac{n!}{r!(n-r)!}

Given : Number of available vegetables = 6

Then, the number of different combinations of 2 vegetables are possible will be :

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5 0
2 years ago
The volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width
liraira [26]
Let the width be w, length = 3w and height = 2w

Volume = length x width x height = w x 3w x 2w = 6w^3
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8 0
2 years ago
Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20
Aleksandr-060686 [28]

Answer:

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

Step-by-step explanation:

we have

-3x-7

Solve for x

Adds 7 both sides

-3x

-3x

Divide by -3 both sides

Remember that

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

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x> 27/(-3)\\x>-9

The solution is the interval (-9,∞)

therefore

A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10.

6 0
2 years ago
Read 2 more answers
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