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Delvig [45]
3 years ago
12

a sphere has a radius of 3x+2. which polynomial in standard form. best describes the total surface area of the sphere

Mathematics
1 answer:
Semenov [28]3 years ago
3 0
The answer is 36πx² + 48πx + 16π.

The surface area of the sphere with radius r is:
A = 4 π r²

r = 3x+2
A = 4 π (3x+2)²

Since (a+b)² = a² + 2ab + b², then (3x+2)² = (3x)² + 2 * 3x * 2 + 2² = 9x² + 12x + 4

A = 4π*(3x+2)² =
    = 4π*(9x² + 12x + 4) = 
    = 4π*9x² + 4π*12x + 4π*4 = 
    = 36πx² + 48πx + 16π
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Alison does 8 math problems in 2 minutes. How long will it take her to do a set of 160 problems?
erastovalidia [21]

Answer:

40 min

Step-by-step explanation:

find unit rateeee  p=problems

8 p= 2 min

8/2=4

so Alison can do 4 math problems per minute

so 160/4= 40 minutes

hope this helps

5 0
3 years ago
Read 2 more answers
Donatello Co. has identified an activity cost pool to which it has allocated estimated overhead of $9,600,000. It has determined
ahrayia [7]

Answer:

option (a) Widgets $2,400,000, Gadgets $1,800,000, Targets $5,400,000

Step-by-step explanation:

Data provided in the question:

Allocated estimated overhead = $9,600,000

Expected use of cost drivers for the activity = 800,000 inspections.

Inspections required by Widgets = 200,000

Inspections required by Gadgets = 150,000

Inspections required by Targets = 450,000

Therefore,

Total overhead per activity = \frac{\textup{estimated overhead}}{\textup{Total activity}}

= \frac{\textup{9,600,000}}{\textup{800,000 }}

= $12 per activity

Thus,

Overhead allocated to Widgets = 200,000 × 12 = $2,400,000

Overhead allocated to Gadgets = 150,000 × 12 = $1,800,000

Overhead allocated to Target = 450,000 × 12 = $5,400,000

Hence, The correct answer is option (a)

8 0
3 years ago
The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal dist
Veseljchak [2.6K]
<span>P(Z≥z)=p<span>% may help out... (:
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4 0
3 years ago
Read 2 more answers
726 estimated <br><br><br><br><br> thank you , <br><br> vicky
malfutka [58]
726 to the hundred's is 700
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6 0
3 years ago
Q 4.19: To verify whether there are negative consequences of taking a new type of medicine, 3000 tests were conducted. Assume th
tiny-mole [99]

Answer:

The p-value obtained is less than the significance level at which the test was performed at, hence, we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Step-by-step explanation:

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the new medicine has no negative effects and the alternative hypothesis is that the new medicine is potentially harmful

Mathematically,

The null hypothesis is represented as

H₀: p = 0

The alternative hypothesis is represented as

Hₐ: p > 0

To do this test, we will use the z-distribution because although no information on the population standard deviation is known, the sample size is large enough.

So, we compute the test statistic

z = (x - μ)/σₓ

x = sample proportion = (31/3000) = 0.0103

μ = p₀ = 0

σₓ = standard error = √[p(1-p)/n]

where n = Sample size = 3000

σₓ = √[0.0103×0.9897/3000] = 0.0018462936 = 0.0018463

z = (0.0103 - 0) ÷ 0.0018463

z = 5.60

checking the tables for the p-value of this test statistic

Significance level = 1% = 0.01

The hypothesis test uses a one-tailed condition because we're testing only in one direction.

p-value (for z = 5.60, at 0.01 significance level, with a one tailed condition) = < 0.00001

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.01

p-value = < 0.00001

p-value < 0.00001 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the the new medicine is potentially harmful.

Hope this Helps!!!

6 0
3 years ago
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