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Nezavi [6.7K]
3 years ago
10

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 48 centimeters cubed. A sphere with heigh

t h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? Centimeters cubed
Mathematics
1 answer:
Burka [1]3 years ago
8 0

Answer:

The answer is 64 cm3.

Step-by-step explanation:

We would use the formula V=4/3 pi r subscript3.

Substitude the numbers in.

V=4/3 pi 48

so, 4 times 48= 192

192 divide by 3=64

So the answer is 64.!

You might be interested in
Given J(1, 1), K(3, 1), L(3, -4), and M(1, -4) and that J'(-1, 5), K'(1, 5), L'(1, 0), and M'(-1, 0). What is the rule that tran
anastassius [24]
(x; y) -> (x - 2; y + 4)

J(1; 1) ⇒ J'(1 - 2; 1 + 4) = (-1; 5)

K(3; 1) ⇒ K'(3 - 2; 1 + 4) = (1; 5)

L(3;-4) ⇒ L'(3 - 2; -4 + 4) = (1; 0)

M(1;-4) ⇒ M'(1 - 2;-4 + 4) = (-1; 0)


5 0
3 years ago
Ali hops on his 3 wheeler and heads off at 12 mph. Two hours later, Fatimah chases after him on a moped at 18 mph. How far will
mash [69]

Answer: 72 miles.

Step-by-step explanation:

We know the relationship:

Distance = speed*time.

Then we can write the equation for distance as a function of time for Ali as:

A(t) = 12mph*t

where t is time in hours.

Fatimah's equation will be:

F(t) = 18mph*(t - 2h)

where the -2h appears because she starts two hours after Ali.

Fatimah will overtake Ali when F(t) = A(t) (their positions are the same)

Then we need to solve:

12mph*t = 18mph*(t - 2h)

12mph*t = 18mph*t - 18mph*2h

12mph*t = 18mph*t - 36 mi

36 mi = (18mph - 12mph)*t

36mi = 6mph*t

36mi/6mph = t

6h = t

So Ali travels for 6 hours before he gets overtaken, then the total distance that Ali travels is:

A(6h) = 12mph*6h = 72 mi

3 0
2 years ago
Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale
nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) Z = 1.05

e) Z = -1.10

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

\mu = 515, \sigma = 100

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 620. So

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

Z = \frac{620 - 515}{100}

Z = 1.05

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

\mu = 515, \sigma = 100

This is Z when X = 405. So

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

Z = \frac{405 - 515}{100}

Z = -1.10

3 0
3 years ago
Im giving 30 points pls help
gayaneshka [121]

Step-by-step explanation:

Pathagory and Theorem

a^2+b^2=c^2

(x-3)^2+(x-4)^2=6^2

expand:

2x^2-14x+25=36

2x^2-14x-11=0

x=(\sqrt{71}+7)/2

perimeter=(x-3)+(x-4)+6=2x-1

insert the value for x into 2x-1

\sqrt{71}+6=perimeter

Hope that helps :)

7 0
3 years ago
Read 2 more answers
Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?
vazorg [7]

Answer:

x = 4 ± \sqrt{19}

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± \sqrt{19} ( add 4 to both sides )

x = 4 ± \sqrt{19}

8 0
2 years ago
Read 2 more answers
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