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3 years ago

Determine if x+2 is a factor of p(x) = x4 + 3x3 +4x2 -8

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Hello,

Yes it is.

p(-2)=(-2)^4+3*(-2)^3+4*(-2)^2-8
=16-24+16-8=0

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

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8 (-7x + 6) = -56x + 49

inysia [295]

Answer: 1.02

Step-by-step explanation:

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3 years ago

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The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $50

Natali5045456 [20]

Answer:

(a) See Explanation

(b) $\bar x =50$ and $\sigma_x = 0.8944$

(d) $P(\bar x > 55) = 0$

Step-by-step explanation:

Given

$\mu = \$50$ -- mean

$\sigma = \$20$ --- standard deviation

$n=500$ --- sample size

Solving (a): The reason we can't determine the probability that an amount to access internet by a household will exceed $55.

The question says that a lot of households pay low rates, but the percentage of the households in this category is not given. This means that it is impossible to determine the shape of the distribution.

Hence, the probability cannot be calculated.

Solving (b): Sample mean and Sample standard deviation

The sample mean estimates the population mean

So:

$\bar x =\mu$

$\bar x =50$

The sample standard deviation is calculated as thus:

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{20}{\sqrt{500}}$

$\sigma_x = \frac{20}{22.36}$

$\sigma_x = 0.8944$

Solving (c): The shape of the distribution.

We have:

$n = 500$ --- The sample size

According to Central limit theorem, When the sample size is greater than 30, then the shape of the distribution is normal.

Hence, the shape is normal

Solving (d): $P(\bar x \ge 55)$

Calculate the test statistic (t)

$t = \frac{\bar x - \mu}{\sigma}$

$t = \frac{55 - 50}{0.8945}$

$t = \frac{5}{0.8945}$

$t = 5.590$

So:

$P(\bar x > 55) = P(t > 5.590)$

Referencing the z table, we have:

$P(t > 5.590) = 0$

Hence:

$P(\bar x > 55) = 0$

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3 years ago

If a rectangle is inscribed in a circle, each diagonal also serves another function. What is this function?

Kipish [7]

Answer:

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle.

Step-by-step explanation:

A rectangle is made of two right triangles then a rectangle inscribed in a circle must have its diagonal as the diameter of the circle. Hope this helps

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2 years ago

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Basile [38]

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2 years ago

How would I solve the problem: e^4x=120

borishaifa [10]

Answer: x = 1.1968729357 ; or, round to: 1.2 .
____________________________________________ You would take the "ln" (that is, "natural logarithm") of EACH side of the equation:

ln (e^4x) = ln (120);
______________________
Then continue:

4x ln e = ln 120

4x = ln 120 ; (since "ln e = 1")

then divide EACH side of the equation by "4", to isolate "x" on one side of the equation; and to solve for "x" ;
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4x / 4 = (ln 120) / 4 ;
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x = (ln 120) / 4 ;
______________________________
Using a calculator:
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x = (ln 120) / 4 = (4.78749174278) / 4 = 1.1968729357
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3 years ago