Solve for x<br><img src="https://tex.z-dn.net/?f=x%20%2B%2015%20%3D%208" id="TexFormula1" title="x + 15 = 8" alt="x + 15 = 8" al

How many permutations exist of the letters a, b, c, d taken two at a time?

Fittoniya [83]

The number of permutations of the 4 different letters, taken two at a time, is given by:
$4P2=\frac{4!}{2!}=12$

3 0

4 years ago

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Elmer has a collection of 300 fossils. Of these, 21 percent are fossilized snail shells.

chubhunter [2.5K]

In order to figure out the number of fossilized snail shell, multiply 21% by 300. first change 21% into a decimal, in order to do that, move the percent symbol two spaces to the left, and replace the "%" symbol to a decimal. 0.21 X 300= 63
so 21% of 300 is 63

5 0

3 years ago

Zack flips a coin a rolls a number cube with sides labeled 1 to 6. What is the probability that he gets heads and a number great

Nitella [24]

To get heads: 1/2 because there are two sides to a coin.

There are 6 sides on a cube and 2 numbers are greater than 4 (5 and 6) so 2/6

Now multiply: 1/2 * 2/6 = 2/12 = 1/6

1/6 is the final answer.

7 0

4 years ago

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The square based pyramid is cut horizontally at a height of 15cm to leave this frustum. Calulate the volume of the frustum.

allsm [11]

Answer:

The answer is given below

Step-by-step explanation:

The question is not complete. The correct question is:

A square based pyramid have a height of 30 cm and base of 10 cm. The The square based pyramid is cut horizontally at a height of 15cm to leave this frustum.

Answer:

The frustum would have a base of 10 cm and height of 15 cm. The lower base has a length of 10 cm. to calculate the upper base, we use the formula:

$\frac{height\ of\ frustum}{height\ of \ pyramid}=\frac{base \of\ upper\ edge}{base \of\ lower\ edge}$

Substituting:

$\frac{30}{15}=\frac{10}{b} \\ b=15*10/30=5$

The volume of the frustum is given by the formula:

$V=\frac{h}{3}(A_1+A_2+\sqrt{A_1A_2} )$

Where h is the height of the frustum = 15 cm, A1 is the area of the lower base = 10 * 10 = 100 cm², A1 is the area of the upper base = 5 * 5 = 25 cm²

Substituting gives:

$V=\frac{h}{3}(A_1+A_2+\sqrt{A_1A_2} )=\frac{15}{3}(100+25+\sqrt{100*25} )= 875\ cm^3$

7 0

3 years ago

One morning a bagel shop sold 3 plain bagels, 6 raisin bagels, and 6 sesame seed bagels. If the shop sells 20 bagels the next mo

notka56 [123]

you cant really predict how many bagels will be sold the next morning because of different scenarios but mathematically speaking if you compare plain bagels to total bagels you get 3/15 so if you multiply the denominator by 1 1/4 to get twenty as the denominator then you have to do the same to the numerator to get a fraction of 3.75/20 or roughly 3-4 plain bagels sold

3 0

3 years ago

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