Factor 18x^3+24x^2-21x-28

Pythagorean theorem round to nearest tenth .

icang [17]

Answer:

$16$

Step-by-step explanation:

In a right triangle, the Pythagorean Theorem goes as follows:

$a^2+b^2=c^2$ , where $c$ is the hypotenuse of the triangle and $a$ and $b$ are legs of the triangle.

We can set up the following equation using the information given:

Let $x$ be the missing side:

$12^2+x^2=20^2,\\144+x^2=400,\\x^2=256,\\x=\boxed{16}$

3 0

3 years ago

Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passe

Angelina_Jolie [31]

Answer:

a) $P(X=0)=(3C0)(0.8)^0 (1-0.8)^{3-0}=0.008$

$P(X=1)=(3C1)(0.8)^1 (1-0.8)^{3-1}=0.096$

$E(X) = np = 3*0.8= 2.4$

We expect 2.4 successes in a sample of three selected.

And the standard deviation is given by:

$Sd(X)= \sigma = \sqrt{np(1-p)}=\sqrt{3*0.8*(1-0.8)}= 0.693$

Represent the typical variation around the mean.

b) $Y \sim Binom(n=4, p=0.8)$

And we want this probability:

$P(Y=3)=(4C3)(0.8)^3 (1-0.8)^{4-3}=0.4096$

c) $Z \sim Binom(n=4, p=0.8)$

And we want this probability:

$P(Z=3)=(4C3)(0.8)^3 (1-0.8)^{4-3}=0.4096$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=3, p=0.8)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

And we want the following probabilities

$P(X=0)=(3C0)(0.8)^0 (1-0.8)^{3-0}=0.008$

$P(X=1)=(3C1)(0.8)^1 (1-0.8)^{3-1}=0.096$

The mean is given by:

$E(X) = np = 3*0.8= 2.4$

We expect 2.4 successes in a sample of three selected.

And the standard deviation is given by:

$Sd(X)= \sigma = \sqrt{np(1-p)}=\sqrt{3*0.8*(1-0.8)}= 0.693$

Represent the typical variation around the mean.

Part b

Let Y the random variable of interest, on this case we now that:

$Y \sim Binom(n=4, p=0.8)$

And we want this probability:

$P(Y=3)=(4C3)(0.8)^3 (1-0.8)^{4-3}=0.4096$

Part c

Let Z the random variable of interest, on this case we now that:

$Z \sim Binom(n=4, p=0.8)$

And we want this probability:

$P(Z=3)=(4C3)(0.8)^3 (1-0.8)^{4-3}=0.4096$

6 0

3 years ago

A window washer drops a brush from a scaf-

yuradex [85]

9.8 * 1.53 = 14.994 (speed/velocity)
1/2 * 9.8 * 1.53^2 = 1/2 * 9.8 * 2.3409 = 11.47041 (distance)

8 0

4 years ago

Which three measurements could be the lengths of the sides of a triangle?

natali 33 [55]

A). No. Even end-to-end, the 5 and the 3 couldn't cover the 9.

B). Technically yes, but not really. End-to-end, the 5 and the 2 would lay down
right on top of the 7. It would be a triangle with two angles of 0° and one angle
of 180°. The base would be 7, the height would be zero, and the whole thing
would just look like a piece of line.

C). No. Even end-to-end, the 2 and the other 2 couldn't cover the 5.

D). Yes. A cute little scalene triangle.

8 0

4 years ago

Read 2 more answers

HELPPP....PLEASE...........

kogti [31]

Answer:

9 1/3, 12 1/2, 14 3/4

Step-by-step explanation:

I assume the formula you’re working with is A=b*h since nothing says otherwise...

((Patio 1))

So you have your area (147) and your base (15 3/4), now you need to plug them in, which should look like this:

147= 15 3/4*h

You need to isolate your h in order to get the missing number, so you should divide both sides by 15 3/4 OR 63/4 ((15*3—>60+3=63))

Dividing by a fraction is the equivalent of multiplying by its reciprocal... so

147 * 4/63 = 588/63 which can be simplified to 84/9 once both the numerator and denominator are divided by 7

In mixed number for it is 9 3/9 which simplified becomes 9 1/3

You solve the other similarly

3 0

4 years ago