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Nuetrik [128]
3 years ago
12

A product code consists of a one-or two-digit number (including 0) followed by 5 not necessarily distinct letters. How many prod

uct codes are possiable?
Mathematics
1 answer:
Dafna1 [17]3 years ago
5 0

Answer: 1,306,951,360

Step-by-step explanation:

Number of digits in Number system = 10

Number of letters in English Alphabet= 26

Number of ways to product code consists of a one digit number (including 0) followed by 5 not necessarily distinct (repetition is allowed) letters will be:-

10\times26^5   (1)

Number of ways to product code consists of a two-digit number (including 0) followed by 5 not necessarily distinct (repetition is allowed) letters will be:-

10^2\times26^5    (2)

Now, total product codes are possible:         [Adding (1) and (2)] 10\times26^5+10^2\times26^5

=26^5(10+10^2)\\\\=(11881376)(10+100)\\\\=11881376(110)\\\\=1306951360

Hence, the number of product codes are possible = 1,306,951,360

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Repeating decimals are parts of decimals that have repetitive digits; terminating decimals are decimals whose digits end.

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Answer:

See attachment

Step-by-step explanation:

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<h3>Given:</h3><h3>Large cone:</h3>
  • r= 8 cm
  • h= 20 cm
<h3>Small cone:</h3>
  • r= 4 cm
  • h= 10cm
<h3>Note that:</h3>
  • r: radius
  • h: height
<h3>To find:</h3>
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<h3>Solution:</h3>
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\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

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V= \frac{1}{3}×\pi×{4}^{2}×10

V= 167.5516082 \: {cm}^{3}

Now, we can round off to the nearest hundredth.

The value in the thousandths place is smaller than 5 so we won't have to round up.

\boxed{V= 167.55 \: {cm}^{3}}

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.

V= \frac{1}{3}×\pi×{8}^{2}×20

V= 1340.412866 \: {cm}^{3}

Now, we can round off to the nearest hundredth.

The value in thousandths place is smaller than 5 so we won't have to round up.

\boxed{V=1340.41 \: {cm}^{3}}

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.

V= 1340.41-167.55

\large\boxed{V= 1172.86 \: {cm}^{3}}

<u>Hence, the volume of the frustum is 1172.86 cubic centimeters.</u>



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