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2 years ago

(08.01 MC)

Mathematics

1 answer:

Brilliant_brown [7]2 years ago

3 0

Answer:

d. 72 in³

Step-by-step explanation:

To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:

From the question volume of the cone = 24 cubic inches

volume of a cone = $\frac{1}{3}$ πr²h

and volume of a cylinder = πr²h

This implies

volume of a cone = $\frac{1}{3}$ πr²h

= $\frac{1}{3}$ (volume of a cylinder)

volume of a cone = $\frac{1}{3}$ (volume of a cylinder)

24 = $\frac{1}{3}$ (volume of a cylinder)

multiply both-side of the equation by 3

24×3 = $\frac{1}{3}$ (volume of a cylinder)

72 =volume of a cylinder

Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches

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Beau's recipe for granola bars calls for 3 1/2 cups of oatmeal. He only has a 1/6 cup scoop. How many scoops of oatmeal will he

Drupady [299]

There will be $\boxed{\bf 21}$ scoops of oatmeal to complete the recipe.

Further explanation:

Given that Beau’s recipe of granola bars contains $3\frac{1}{2}$ cups of oatmeal.

Beau’s has only $\frac{1}{6}$ cup scoop.

Our aim is to find the number of scoops of oatmeal Beau’s needed to complete the recipe for granola bars.

Total cups of oatmeal are $3\frac{1}{2}$ .

First we have to convert the total cups of oat meal to proper fraction.

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There is only $\frac{1}{6}$ cup scoop.

Since there are $\frac{7}{2}$ cups of oatmeal and $\frac{1}{6}$ cup scoop, therefore, number of scoops required to complete the meal are calculated as follows:

$\begin{aligned}\text{Number of scoops required}&=\dfrac{\frac{7}{2}}{\frac{1}{6}}\\&=\dfrac{7}{2}\cdot 6\\&=7\cdot 3\\&=21\end{aligned}$

The total number of scoops is obtained in whole number; therefore, this is our final answer.

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Learn more:

1. Learn more about simplified form brainly.com/question/1602237

2. Learn more about equations brainly.com/question/1473992

3. Learn more about fractions brainly.com/question/1648978

4. Learn more about composite function brainly.com/question/2723982

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Fractions

Keywords: Beau’s, recipe, granola, bars, cups, oatmeal, scoop, 3 1/2 ,1/6 cup scoop, complete, cups of oatmeal, fractions, whole number.

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Step-by-step explanation:

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If a positive integer is equal to the following product: 25b3c425b3c4, where b and c are distinct prime numbers greater than 2,

Vlad [161]

Answer: 64 distinct even factors

Step-by-step explanation:

let the 2 distinct numbers be b and c and the integer is expected to be 25b3c425b3c4

since b, c > 2 and prime numbers,

potential options include 3, 5, and 7

hence the likelihoods are (b = 3, c = 5), (b = 5, c = 3), (b = 3, c = 7), (b = 7, c = 3), (b = 5, c = 7), (b = 7, c = 5)

Possibility 1 (b = 3, c = 5)

integer is now 253354253354

the distinct even factors = 2, 202, 262, 1934, 19802, 26462, 195334, 253354, 2000002, 2594062, 19148534, 25588754, 262000262, 1934001934, 2508457954, 253354253354

number of distinct even factors = 16

Possibility 2 (b = 5, c = 3)

integer is now 255334255334

the distinct even factors = 2, 86, 202, 5938, 8686, 19802, 253354, 599738, 851486, 2000002, 25788734, 58792138, 25588754, 86000086, 2528061934, 1934001934, 5938005938, 253354253354

number of distinct even factors = 18

Possibility 3 (b = 3, c = 7)

integer is now 253374253374

the distinct even factors = 2, 6, 22, 66, 202, 242, 606, 698, 726, 2094, 2222, 6666, 7678, 19802, 23034, 24442, 59406, 70498, 73326, 84458, 211494, 217822, 253374, 653466, 775478, 2000002, 2326434, 2396042, 6000006, 6910898, 7188126, 8530258, 20732694, 22000022, 25590774, 66000066, 76019878, 228059634, 242000242, 698000698, 726000726, 836218658, 2094002094, 2508655974, 7678007678, 23034023034, 84458084458,253354253354

number of distinct even factors = 48

Possibility 4 (b = 7, c = 3)

integer is now 257334257334

the distinct even factors = 2, 6, 14, 22, 42, 66, 154, 202, 462, 606, 1114, 1414, 2222, 3342, 4242, 6666, 7798, 12254, 15554, 19802, 23394, 36762, 46662, 59406, 85778, 112514, 138614, 217822, 257334, 337542, 415842, 653466, 787598, 1237654, 1524754, 2000002, 2362794, 3712962, 4574262, 6000006, 8663578, 11029714, 14000014, 22000022, 25990734, 33089142, 42000042, 66000066, 77207998, 121326854, 154000154, 231623994, 363980562, 462000462, 849287978, 1114001114, 2547863934, 3342003342, 7798007798, 12254012254, 23394023394, 36762036762, 85778085778, 257334257334

number of distinct even factors = 64

Possibility 5 (b = 5, c = 7)

integer is now 255374255374

the distinct even factors = 2, 14, 34, 58, 74, 202, 238, 406, 518, 986, 1258, 1414, 2146, 3434, 5858, 6902, 7474, 8806, 15022, 19802, 24038, 36482, 41006, 52318, 99586, 127058, 138614, 216746, 255374, 336634, 574258, 697102, 732674, 889406, 1517222, 2000002, 2356438, 3684682, 4019806, 5128718, 9762386, 12455458, 14000014, 21247546, 25792774, 34000034, 58000058, 68336702, 74000074, 87188206, 148732822, 238000238, 361208282, 406000406, 518000518, 986000986, 1258001258, 2146002146, 2528457974, 6902006902, 8806008806, 15022015022, 36482036482, 255374255374

number of distinct even factors = 64

Possibility 6 (b = 7, c = 5)

integer is now 257354257354

the distinct even factors = 2, 202, 19802, 257354, 2000002, 25992754, 2548061954, 257354257354

number of distinct even factors = 8

From the six possibilities, the highest number of likely distinct even factors is 64

7 0

2 years ago