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3 years ago

Choose the correct simplification of the expression (3x)^4.

Mathematics

2 answers:

Kazeer [188]3 years ago

8 0

Answer: $81x^4$

Step-by-step explanation:

The given expression: $(3x)^4$

The law of exponent says that

$(ab)^n=a^nb^n$

Therefore by applying the above law we get the given expression as:

$(3x)^4=3^4x^4=$

Since, $3^4=3\times3\times3\times3=81$

Therefore, $3^4x^4=81x^4$

Hence, the correct simplification of the expression $(3x)^4=81x^4$

Y_Kistochka [10]3 years ago

6 0

The exponent 4 needs to be applied to both 3 and x, so we would have:
3 * 3 * 3 * 3 * x^4.
9 * 9 * x^4.
81x^4

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I have 100 items of product in stock. The probability mass function for the product's demand D is P(D=90)=P(D=100)=P(D=110)=1/3.

masya89 [10]

Answer:

The probability mass function for the items sold is

$P_X(k) = \left \{ {\frac{1}{3} \, \, \, {k=90} \atop \, \frac{2}{3} \, \, \, {k=100}} \right.$

The mean is 96.667

The variance is 22.222

b) The probability mass function for the unfilled demand due to lack of stock is

$P_Y(k) = \left \{ {\frac{2}{3} \, \, \, {k=0} \atop \, \frac{1}{3} \, \, \, {k=10}} \right.$

The mean is 3.333

The variance is 33.333

Step-by-step explanation:

If the demand is higher than 100, then you will sell 100 items only. Thus, there is a probability of 1/3+1/3 = 2/3 that you will sell 100 items, while there is a probability of 1/3 that you will sell 90.

The probability mass function for the items sold is

$P_X(k) = \left \{ {\frac{1}{3} \, \, \, {k=90} \atop \, \frac{2}{3} \, \, \, {k=100}} \right.$

The mean is 1/3 * 90 + 2/3 * 100 = 290/3 = 96.667

The variance is V(X) = E(X²)-E(X)² = (1/3*90² + 2/3*100²) - (290/3)² = 200/9 = 22.222

b) If order to be unfilled demand, you need to have a demand of 110, which happens with probability 1/3. In that case, the value of the variable, lets call it Y, that counts the amount of unfilled demand due to lack of stock is 110-100 = 10. In any other case, the value of Y is 0, which would happen with probability 1-1/3 = 2/3. Thus

$P_Y(k) = \left \{ {\frac{2}{3} \, \, \, {k=0} \atop \, \frac{1}{3} \, \, \, {k=10}} \right.$

The mean is 2/3 * 0 + 1/3 * 10 = 10/3 = 3.333

The variance is 2/3*0² + 1/3*10² = 100/3 = 33.333

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3 years ago

Complete this pattern 3400000, 34000,______3.4,______

Ira Lisetskai [31]

Well the pattern is moving 2 decimal places to the left to make it smaller so it starts off with 3,400,000. 34,000. Then 340. 3.4 and then .034.
ANSWER: 1) 340 2) .034

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3 years ago

A wheel has 10 equally sized slices numbered from 1 to 10.

Ksenya-84 [330]

The random probability of event X, wheel stopping on a white slice is 0.9 while the probability of not X, wheel stopping on Grey slice is 0.1

Total numbers on wheel = total possible outcomes = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Grey colored portion = {3}

White colored portion = {1, 2, 4, 5, 6, 7, 8, 9, 10}

X = Event that wheel stops on a white slice

P(X) = number of white slices ÷ total number of slices

P(X) = 9 / 10 = 0.9

P(not X) = 1 - P(X)

P(not X) = 1 - 0.9 = 0.1

Therefore, the probability that wheel stops on a white slice is 0.9 while, the probability that wheel does not stop on a white slice is 0.1

Learn more :brainly.com/question/18153040

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3 years ago

If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 year

saveliy_v [14]

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Total = 4,500 * 2.718281828459^(.08)
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Total = 4,874.79 
calculator for checking the answer:
http://www.1728.org/compint.htm

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Ostrovityanka [42]

Answer:

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Step-by-step explanation:

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