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balandron [24]
3 years ago
8

A sphere has a volume of V=1296in^3. Find its surface area

Mathematics
1 answer:
klio [65]3 years ago
5 0

Answer:

574.85 in² (approx.)

Step-by-step explanation:

The sphere's volume equation is V = (4/3) * π * r³, which we can set equal to the given volume of 1296 in³:

1296 = (4/3) * π * r³

Now solve for r to get r ≈ 6.7635 in.

The surface area of a sphere is SA = 4 * π * r². Now substitute r into that equation to get:

SA = 4 * π * (6.7635)² ≈ 574.85 in²

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Suppose a bag contains many marbles, 54% of which are purple. You draw 5 marbles from the bag with replacement.
dolphi86 [110]

Part A

Use the binomial probability distribution formula.

p = 0.54 = probability of getting a purple marble

n = 5 = sample size

x = 2 = number of purple we want to get

P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}\\\\P(2) = \frac{5!}{2!(5-2)!}*0.54^2*(1-0.54)^{5-2}\\\\P(2) = 10*0.54^2*0.46^3\\\\P(2) = 0.283831776\\\\

The \frac{n!}{x!(n-x)!} portion is from the nCr combination formula. The exclamation marks indicate a factorial.

Alternatively, you could use Pascal's Triangle for that portion.

<h3>Answer: 0.283831776</h3>

This decimal value is exact. Round it however you need to.

============================================================

Part B

To find the expected value, aka the mean, we multiply the sample size and probability of getting a purple marble on any single selection.

n*p = 5*0.54 = 2.7

<h3>Answer: 2.7</h3>
6 0
2 years ago
2 3/4 written as fraction greater than one
sladkih [1.3K]
2 3/4 = 11/4 <=== written as an improper fraction
3 0
3 years ago
Read 2 more answers
Please Help, I can't figure out this problem
Otrada [13]

Answer:

<h2>The answer is 5 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d  =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question

The points are (9,-7) and (5, -4)

The distance between them is

d =  \sqrt{ ({9 - 5})^{2} +  ({ - 7 + 4})^{2}  }  \\  =  \sqrt{ {4}^{2}  +  ({ - 3})^{2} }  \\  =  \sqrt{16 + 9}  \\  =  \sqrt{25}

We have the final answer as

<h3>5 units</h3>

Hope this helps you

3 0
3 years ago
In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-s
Radda [10]

Answer:

68%

Step-by-step explanation:

The Standard Deviation Rule = Empirical rule formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question,

Step 1

We have to find the number of Standard deviation from the mean. This is represented as x in the formula

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σ = Standard Deviation = 8

For x = 53

μ - xσ

53 = 61 - 8x

8x = 61 - 53

8x = 8

x = 8/8

x = 1

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This falls within 1 standard deviation of the mean where: 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

Therefore, according to the Standard Deviation Rule, the approximate percentage of daily phone calls numbering between 53 and 69 is 68%

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2 years ago
A coordinate grid with 2 lines. The first line is labeled g(x) and passes through the points (negative 3, 0) and (0, 2). The sec
Snezhnost [94]

The correct answer is option c i.e. (0, 2)

<h3>What is Linear Equation?</h3>

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Here, The solution to this Linear System is already shown by the graph. This is also called the Graph Method. The Solution of this Linear System is this common point in this case, (0,2).

Since each equation is represented by a line. So We have  g(x) for the red line, and f(x) for the blue one. Each line is a set of points, We know that from the Euclidean Geometry and its common point (0,2) solves this system.

Thus, the correct answer is option c i.e. (0, 2)

Learn more about linear equation from:

brainly.com/question/11897796

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