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lakkis [162]
3 years ago
12

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, th

en its volume is:
A) 36
B) 12sqrt3
C)18sqrt3
D)24sqrt3
E)36sqrt3

The correct answer was E. Hoping someone could explain how that is.
Mathematics
1 answer:
almond37 [142]3 years ago
5 0
Letter E is correct.
Area of equilateral trianlge= (1/2) tiime a^2 square root 3
Equation for the base is = x^2+y^2 =9

at x ,
y= square root (9-x^2)
Side of triangle a= 2y

d times Volume = (1/2)a^2 square root 3 dx

d times V= (square root 3) (9-x^2) dx

V= square root 3 INT (9-x^2) dx
-3V= 2square root INT (9-x^2) dx
0
V= 2 square root 3 ( 9x-x^3/3)

V=2 square root 3 ( 27-9)
V= 36 square root 3

The answer is E.
You might be interested in
If the measure of ZB is 40°, what measures can ZA and
lubasha [3.4K]

Answer: 30° and 110°

55° and 85°

70° and 70°

The sum of angles in a triangle is 180°. Therefore, since an angle has been given as 40°, the remaining angles will be:

= 180° - 40°

= 140°

Therefore,

30° + 110° = 140°

55° + 85° = 140°

70° + 70° = 140°

5 0
2 years ago
Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame
lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{207.9 - 208}{0.1678}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0
3 years ago
PLZZZ NEED HELP!!!!!!
Nuetrik [128]
Uhh thats a test...... a or b
4 0
3 years ago
Read 2 more answers
HELP!!!!:(<br>2.) WHAT'S THE RESULT?​
Juli2301 [7.4K]

-1+5x

You combine like terms:

Here there are two different ones.

the number without the variable (the 1s) and the one with the variable (5x)

All you have to do is combine them:

1+(-1)+(-1) = 1-1-1 = -1

5x = 5x

So, the answer would be -1+5x

Hope this helps :D

6 0
3 years ago
I need this done today whoever gets this correct gets brainliest!!! PLZZ HELPP MEE!!!
Stella [2.4K]

Answer:

B Survey a random sample of eighth-grade students

Step-by-step explanation:

In order to reach the best conclusion without biased data, the best sampling method would be B because not only does it survey 8th graders, but it also surveys a random group, ensuring that not all of the students are potentially excelling in and/or having trouble with homework.

7 0
3 years ago
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