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svetlana [45]
1 year ago
8

PLEASE HELP 100 POINTS!

Mathematics
1 answer:
krok68 [10]1 year ago
8 0

Answer:

800%

Step-by-step explanation:

<u>Volume of a square based pyramid</u>

\sf V=\dfrac{1}{3}a^2h

where:

  • a = base side length
  • h = height

<u>Given values</u> for Pyramid A:

  • a = 14 inches
  • h = 6 inches

Substitute the given values into the formula to find the volume of <u>Pyramid A</u>:

\begin{aligned}\textsf{Volume of Pyramid A} & = \sf \dfrac{1}{3}(14)^2(6)\\\\& = \sf \dfrac{1176}{3}\\\\& = \sf 392\:\: in^3 \end{aligned}

Given:

  • Volume of Pyramid B = 3136 in³

To find how many times bigger Pyramid B is than Pyramid A, divide the <u>volume of Pyramid B</u> by the <u>volume of Pyramid A</u>:

\implies \sf \dfrac{3136}{392}=8

Therefore, the volume of Pyramid B is 8 times bigger than the volume of Pyramid A.

8 as a percentage is 800%, since 800/100 = 8.

Therefore, the volume of Pyramid B is 800% the volume of Pyramid A.

To verify this, find 800% of the volume of Pyramid A:

⇒ 800% of 392

= 800/100 × 392

= 8 × 392

= 3136

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Callie bought a bag of dried fruit: cherries, pears, and apples.In the bag,1/4 of the dried fruit is cherries and 2/3 of the rem
goldenfox [79]

Answer:

There 24 pieces of Apples in the bag of dry fruit.

Step-by-step explanation:

Let the total number of dried fruit bought be 'x'.

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1/4 of the dried fruit is cherries.

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Also Given:

2/3 of the remainder is pears.

Hence we can say Number of pears is equal to 2/3 times Total number of dried fruit minus Number of cherries.

Framing the equation we get;

Number of Pears = \frac{2}{3} (x-\frac{1}{4}x) = \frac{2}{3} x- \frac{2}{12}x= \frac{2}{3} x- \frac{1}{6}x

But Given:

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Substituting the values we get;

\frac{2}{3} x- \frac{1}{6}x= 48\\

By taking L.C.M we get;

\frac{2\times2}{3\times 2} x- \frac{1\times1}{6\times1}x= 48\\\\\frac{4}{6} x- \frac{1}{6}x= 48\\\\\frac{4x-x}{6}=48\\\\\frac{3x}{6}=48\\\\\frac{x}{2}=48\\\\x= 48\times2= 96

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Number of cherries = \frac{1}{4}x=\frac{1}{4} \times 96 = 24

Now We need to find the Number of Pieces of Apples.

We know that Total Number of Pieces of dried fruit is equal to sum of Number of cherries and Number of Pears and Number of Apples.

Framing Equation we get

Number of Pieces of Apples= Total Number of Pieces of dried fruit - Number of cherries - Number of Pears = 96-48-24 =24 pieces

Hence There 24 pieces of Apples in the bag of dry fruit.

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