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zaharov [31]
3 years ago
11

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the

formula S = 4pir2 for the surface area of a sphere.
Mathematics
1 answer:
vampirchik [111]3 years ago
7 0
Answer:
area = pi * (64x² + 32x + 4)
Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Explanation:
We are given that:
area of sphere = 4 * pi * r²
radius = 4x + 1

Substitute with the radius in the given formula to get the area as follows:
area = 4 * pi * (4x+1)²
area = 4 * pi * (16x² + 8x + 1)
area = pi * (64x² + 32x + 4)

Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56

Hope this helps :)

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Answer:

One of the problems humans have made is a large amount of pollution.

And so some of the ways we can fix this is;

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Step-by-step explanation:

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2 years ago
One kind of plant has only blue flowers and white flowers. According to a genetic model, the offsprings of a certain cross have
IrinaVladis [17]

Answer:

There is not enough evidence to support the claim that the chance of this cross to be blue-flowering is significantly smaller than 0.75 (P-value = 0.11).

Test statistic z=-1.225.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the chance to be blue-flowering is significantly smaller than 0.75.

Then, the null and alternative hypothesis are:

H_0: \pi=0.75\\\\H_a:\pi

The significance level is 0.05.

The sample has a size n=200.

The sample proportion is p=0.71.

p=X/n=142/200=0.71

The standard error of the proportion is:

\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.75*0.25}{200}}\\\\\\ \sigma_p=\sqrt{0.000938}=0.031

Then, we can calculate the z-statistic as:

z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.71-0.75+0.5/200}{0.031}=\dfrac{-0.038}{0.031}=-1.225

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z

As the P-value (0.11) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the chance to be blue-flowering is significantly smaller than 0.75.

8 0
3 years ago
When two balanced dice are rolled, the sum of the dice can be 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12, giving 11 possibilities. th
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False.

There are 36 possible outcomes, corresponding to numbers 1-6 independently appearing on each of the dice. Only one of those outcomes is double-sixes, resulting in a sum of 12. The probability that the sum is 12 is 1/36.

In short, the 11 outcomes listed in your problem statement are not equally-likely.
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3 years ago
Find the formula for the nth term of these sequences:
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A child makes a pitcher of fruit punch by completely dissolving fruit- flavoured powder in water. The child drinks a glass and decides the punch needs to be sweeter, so she stirs in more powder. This time the powder does not all dissolve, but settles on the bottom of the pitcher. A) Is the fruit-flavoured powder a pure substance or a mixture? * helpme anyone?

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Which angle has a sine of -1/2 and a cosine of -√3/2
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\sin x=-\dfrac{1}{2} < 0\\\\\cos x=-\dfrac{\sqrt3}{2} < 0\\\\therefore\ x\in(180^o;\ 270^o)

\text{We know:}\ \tan x=\dfrac{\sin x}{\cos x}\\\\\text{therefore:}\ \tan x=\dfrac{-\frac{1}{2}}{-\frac{\sqrt3}{2}}=\dfrac{1}{2}\cdot\dfrac{2}{\sqrt3}=\dfrac{1}{\sqrt3}\cdot\dfrac{\sqrt3}{\sqrt3}=\dfrac{\sqrt3}{3}

\tan x=\dfrac{\sqrt3}{3}\Rightarrow x=30^o+180^o\cdot k;\ k\in\mathbb{Z}

x\in(180^o;\ 270^o)\ therefore\ \boxed{x=30^o+180^o=210^o}
8 0
3 years ago
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