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3 years ago

Multiply (x^2+x-2)(x+2)

Mathematics

2 answers:

Blababa [14]3 years ago

5 0

Answer:

The answer is x^3+3x^2-4

Have a great day!

-Seth

Dvinal [7]3 years ago

3 0

For this case we must multiply the polynomial $(x ^ 2 + x-2)$ by the monomial $(x + 2)$ , for this, we apply distributive property that states:

$(a + c) * (b + d) = ab + ad + cb + cd$

So:

$(x ^ 2 + x-2) (x + 2) = (x ^ 2 * x) + (2 * x ^ 2) + (x * x) + (x * 2) + (- 2 * x) + (-2 * 2)$

Considering that $+ * - = -$

$(x ^ 2 + x-2) (x + 2) = x ^ 3 + 2x ^ 2 + x ^ 2 + 2x-2x-4$

Adding similar terms:

$(x ^ 2 + x-2) (x + 2) = x ^ 3 + 3x ^ 2-4$

So, by multiplying $(x ^ 2 + x-2) (x + 2)$ we get $x ^ 3 + 3x ^ 2-4$

Answer:

$(x ^ 2 + x-2) (x + 2) = x ^ 3 + 3x ^ 2-4$

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We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty

maw [93]

Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable X is, p = 0.697.

A random sample of n = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.

The probability mass function of a Binomial random variable X is:

$P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...$

(1)

Compute the expected value of X as follows:

$E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9$

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56$

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of X ≥ 45 as follows:

P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

$=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006$

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

6 0

3 years ago

What the difference 7 7/8 and 3 1/2

zalisa [80]

Answer:

35/8 reduced is 4 3/8

Step-by-step explanation:

just subtract 7 7/8 and 3 1/2 to get 35/8 and reduce it to 4 3/8

8 0

3 years ago

0.1 times N = 89.5 what is the value of N?

goldenfox [79]

If you would like to know the value of N in the equation 0.1 * N = 89.5, you can calculate this using the following steps:

0.1 * N = 89.5 /0.1
N = 89.5 / 0.1
N = 895

Result: The value of N is 895.

5 0

3 years ago

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Convert the Cartesian equation x 2 + y 2 + 2y = 0 to a polar equation.

Kisachek [45]

R2(cos2ϕ−sin2ϕ)−2rcosϕ=0r2(cos2⁡ϕ−sin2⁡ϕ)−2rcos⁡ϕ=0

r2cos(2ϕ)−2rcosϕ=0r2cos⁡(2ϕ)−2rcos⁡ϕ=0

Now divide through by r≠0r≠0 and get

rcos2ϕ−2cosϕ=0rcos⁡2ϕ−2cos⁡ϕ=0

r=2cosϕcos2ϕr=2cos⁡ϕcos⁡2ϕ

3 0

3 years ago

Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade of orange. If he uses 9 pints of yellow pai

VMariaS [17]

Answer:

Henry will need 6 pints of red color.

All together he will need 15 pints.

Step-by-step explanation:

Henry needs 2 pints of red paint and 3 pints of yellow paint to get a specific shade of orange.

The ratio is 2:3

Now he uses 9 pints of yellow paint so we need to find the pins of red paint used to get the same orange.

Let the pints of red paint be x

We can relate this as:

$\frac{2}{3} =\frac{x}{9}$

Solving for x;

$3x=18$

So, x = 6

Hence, 6 pints of red color are needed.

And all together Henry needs $9+6=15$ pints of paint.

3 0

3 years ago

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