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3 years ago

Write the prime factorization of 81

Mathematics

2 answers:

Alborosie3 years ago

6 0

Answer:

Prime factorization: 81 = 3 x 3 x 3 x 3 which can also be written 3⁴

Ann [662]3 years ago

5 0

Hey!

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Answer:

↓ ↓

9 9

↓ ↓ ↓ ↓

3 3 3 3

There are four three's! So that means 4 is the exponent.

3^4 = 81

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Explanation:

A prime factorization tree is something where when you solve the ending number you can solve with an exponent of how many of that number to get the starting result. In this case the prime number tree for 81 ends with 3, which is a prime number.

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Hope This Helped! Good Luck!

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Andreas93 [3]

Answer:

Step-by-step explanation:

Angles 3, 4, and 5 are supplementary to each other, meaning that all of them added together equal 180. Therefore, to solve for x:

x + 18 + x + 15 + 4x + 3 = 180 and

6x + 36 = 180 and

6x = 144 so

x = 24

Angles 1 and 3 are vertical angles, so they are congruent, meaning they both have the exact same angle measure. If angle 3 measures, x + 18, so does angle 1. If x = 24, then angle 1 = 24 + 18 which is 42 degrees.

That also answered part c. Angles 1 and 3 are not complementary, they are vertical.

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3 years ago

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Deffense [45]

Consider the fraction $\dfrac{k+7}{4k+28}$ .

1. You can see that the denominator 4k+28 can be simplified to expression 4(k+7), because 4k=4·k and 28=4·7, so using the distributive property you can write that 4k+28=4(k+7).

2. Then the initial fraction becomes

$\dfrac{k+7}{4k+28}= \dfrac{k+7}{4(k+7)}$ .

3. The nominator and the denominator have the common divisor k+7, then you can divide top and bottom by k+7:

$\dfrac{k+7}{4k+28}= \dfrac{k+7}{4(k+7)}=\dfrac{1}{4}$ .

Answer: $\dfrac{1}{4}$

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3 years ago

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Umnica [9.8K]

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8 0

4 years ago

A drawer contains 6 black neckties, 2 white neckties,4 red neckties,2 maroon neckties and 2 blue neckties. One necktie is picked

kogti [31]

A) The probability of picking a white tie 300 times = $(\frac{1}{8}) ^{300}$

B) The probability of picking a blue tie 300 times = $(\frac{1}{8}) ^{300}$

C) The probability of picking a red tie 300 times = $(\frac{1}{4}) ^{300}$

D) the probability of picking a black tie 300 times = $(\frac{3}{8}) ^{300}$

E ) the probability of picking a maroon tie 300 times = $(\frac{1}{8}) ^{300}$

F) the probability of NOT picking a white tie 300 times = $(\frac{7}{8}) ^{300}$

Step-by-step explanation:

Here, the total number of black neckties = 6

The total number of white neckties = 2

The total number of red neckties = 4

The total number of maroon neckties = 2

The total number of blue neckties = 2

The number of times the experiment is repeated = 300

A ) P(Picking a white tie) = $\frac{\textrm{Total number of white ties}}{\textrm{Total Bow ties}}$

= $\frac{2}{16} = \frac{1}{8}$

So, the probability of picking a white ONCE is 1/8.

Now, as the experiment is REPEATED 300 times with replacement.

So, the probability of picking a white tie 300 times = $(\frac{1}{8}) ^{300}$

B) P(Picking a BLUE tie) = $\frac{\textrm{Total number of blue ties}}{\textrm{Total Bow ties}} = \frac{2}{16} = \frac{1}{8}$

So, the probability of picking a blue ONCE is 1/8.

Hence, the probability of picking a blue tie 300 times = $(\frac{1}{8}) ^{300}$

C) P(Picking a Red tie) = $\frac{\textrm{Total number of Red ties}}{\textrm{Total Bow ties}} = \frac{4}{16} = \frac{1}{4}$

So, the probability of picking a red ONCE is 1/4.

Hence, the probability of picking a red tie 300 times = $(\frac{1}{4}) ^{300}$

D) P(Picking a Black tie) = $\frac{\textrm{Total number of black ties}}{\textrm{Total Bow ties}} = \frac{6}{16} = \frac{3}{8}$

So, the probability of picking a red ONCE is 3/8.

Hence, the probability of picking a black tie 300 times = $(\frac{3}{8}) ^{300}$

E) P(Picking a maroon tie) = $\frac{\textrm{Total number of maroon ties}}{\textrm{Total Bow ties}} = \frac{2}{16} = \frac{1}{8}$

So, the probability of picking a maroon ONCE is 1/8.

Hence, the probability of picking a maroon tie 300 times = $(\frac{1}{8}) ^{300}$

F) P(Picking a NOT whiten tie) = 1 - P( picking a white tie)

$= 1-(\frac{1}{8} ) = \frac{8-1}{8} = (\frac{7}{8} )$

So, the probability of NOT picking a white ONCE is 7/8.

Hence, the probability of NOT picking a white tie 300 times = $(\frac{7}{8}) ^{300}$

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3 years ago

Nina’s dog eats 1/6 lb of dog food twice a day. If Nina buys a 20 lb bag of dog food how many days will the bag feed her dog? Ho

sp2606 [1]

Answer:

60.6

$20 \div \frac{1}{6} \times 2$

= 60.6

6 0

3 years ago