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3 years ago

(Y^3 - 125) divided (y -5)

Mathematics

1 answer:

dimaraw [331]3 years ago

5 0

Answer:

(y^2+5y+25)

Step-by-step explanation:

(y^3 - 125) ÷ (y -5)

Factor the first term. This is the difference of cubes

a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Let a=y and b = 5 (5^3 =125)

(y^3-125) = (y-5) (y^2+5y+25)

Substitute this back into the original equation

(y-5) (y^2+5y+25)

----------------------------

(y-5)

The y-5 term cancels

(y^2+5y+25)

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What square root is closest to 5

nikklg [1K]

Answer: 2.236

Step-by-step explanation: The square root of 5 is expressed as √5 in the radical form and as (5)½ or (5)0.5 in the exponent form. The square root of 5 rounded up to 5 decimal places is 2.23607. It is the positive solution of the equation x2 = 5.

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2 years ago

According to a 2018 survey by Bankrate, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose t

nalin [4]

Answer:

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they save nothing for retirement, or they save something. The probability of an adult saving nothing for retirement is independent of any other adult. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

20% of adults in the United States save nothing for retirement (CNBC website).

This means that $p = 0.2$

Suppose that sixteen adults in the United States are selected randomly.

This means that $n = 16$

What is the probability that three or less of the selected adults have saved nothing for retirement?

This is:

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{16,0}.(0.2)^{0}.(0.8)^{16} = 0.0281$

$P(X = 1) = C_{16,1}.(0.2)^{1}.(0.8)^{15} = 0.1126$

$P(X = 2) = C_{16,2}.(0.2)^{2}.(0.8)^{14} = 0.2111$

$P(X = 3) = C_{16,3}.(0.2)^{3}.(0.8)^{13} = 0.2463$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0281 + 0.1126 + 0.2111 + 0.2463 = 0.5981$

0.5981 = 59.81% probability that three or less of the selected adults have saved nothing for retirement

4 0

3 years ago

On a bicycle trail, the city is painting arrows like the one shown below: Upper pointing arrow with height of 15 and length of 1

Luden [163]

Answer:

229.5 $cm^{2}$

Step-by-step explanation:

In order to calculate the area of the arrow we need to calculate the area of the body of the arrow, and then the head of the arrow. The body of the arrow is a rectangle meaning that the area (Ar) can be calculated by multiplying the length by the height like so...

Ar = l * h

Ar = 11cm * 12cm

Ar = 132 $cm^{2}$

Now we need to find the area of the head of the arrow, which is a triangle and therefore we can use the formula for the area of a triangle (At) which is height times base divided by 2...

At = $\frac{h * b}{2}$