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3 years ago

What is the diameter of a hemisphere with a volume of 257 m^3

Mathematics

1 answer:

Alex73 [517]3 years ago

4 0

Answer:

9.9

Step-by-step explanation:

\text{Volume of Hemisphere}\text{:}

Volume of Hemisphere:

\,\,257

257

\text{Volume of Sphere}\text{:}

Volume of Sphere:

\,\,514

514

Double volume of hemisphere to get volume of the entire sphere

\text{Volume of a Sphere:}

Volume of a Sphere:

V=\frac{4}{3}\pi r^3

πr

514=

\,\,\left(\frac{4}{3}\pi\right) r^3

(

π)r

514=

\,\,(4.1887902)r^3

(4.1887902)r

Evaluate 4/3pi in calc

\frac{514}{4.1887902}=

4.1887902

514

\,\,\frac{(4.1887902)r^3}{4.1887902}

4.1887902

(4.1887902)r

Evaluate \frac{4}{3}\pi

π in calc

122.7084611=

\,\,r^3

\sqrt[3]{122.7084611}=

122.7084611

\,\,\sqrt[3]{r^3}

Cube root both sides

4.9692575=

\,\,r

\text{Then the diameter equals }9.938515

Then the diameter equals 9.938515

diameter is radius times 2

\text{Final Answer:}

Final Answer:

d\approx 9.9\text{ m}

d≈9.9 m

Round to nearest tenth

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Weights of American adults are normally distributed with a mean of 180 pounds and a standard deviation of 8 pounds. What is the

ahrayia [7]

Answer:

15.87% probability that a randomly selected individual will be between 185 and 190 pounds

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 180, \sigma = 8$

What is the probability that a randomly selected individual will be between 185 and 190 pounds?

This probability is the pvalue of Z when X = 190 subtracted by the pvalue of Z when X = 185. So

X = 190

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

$Z = \frac{190 - 180}{8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 185

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

$Z = \frac{185 - 180}{8}$

$Z = 0.63$

$Z = 0.63$ has a pvalue of 0.7357

0.8944 - 0.7357 = 0.1587

15.87% probability that a randomly selected individual will be between 185 and 190 pounds

3 0

2 years ago

Need help solving pleaseee!!!

natta225 [31]

Answer:

Step-by-step explanation:

50.

line AB that has the points (2,5) and (9,2) hhas the slope

m= (y2-y1) / (x2-x1)= 5-2 / 2-9 = 3/-7 = -3/7

Parallel line have the same slope so m= -3/7 for the line that has the point (-3,4).

Point-slope equation is y-y1 = m (x-x1), y -4 = -3/4 (x+3) or

you can writte it as y= (-3/4)x - 9/4 +16/4 so y = (-3/4)x + 7/4

51.

line PQ has slope m= -6+1 / 4-6 = -5/-2 = 5/2

Perpendicular lines have their slope negative reciprocal of eachother so the line that goes trough the point (1,3) has the slope m= -2/5

y-3 = -2/5 (x-1)

5 0

2 years ago

Write the standard equation for the hyperbola with the following conditions: vertices: (-2, -3) and (6, -3) foci: (-4, -3) and (

STALIN [3.7K]

Hello,

Vertices are on a line parallele at ox (y=-3)

The hyperbola is horizontal.

Equation is (x-h)²/a²- (y-k)²/b²=1

Center =middle of the vertices=((-2+6)/2,-3)=(2,-3)
(h+a,k) = (6,-3)
(h-a,k)=(-2,-3)
==>k=-3 and 2h=4 ==>h=2
==>a=6-h=6-2=4 (semi-transverse axis)

Foci: (h+c,k) ,(h-c,k)
h=2 ==>c=8-2=6

c²=a²+b²==>b²=36-4²=20

Equation is:
$\boxed{ \dfrac{(x-2)^2}{16} - \dfrac{(y+3)^2}{20} =1}

$

8 0

2 years ago

Identify all the sets to which the number belongs choose from rational number whole number or integer 1.256 I think irrational c

VLD [36.1K]

Answer:

Rational

Step-by-step explanation:

1.256 is not a whole #, and it's also not an integer. An integer is basically whole #s and their opposites. The # is not irrational. 1.256 is a terminating decimal, and can be turned into a fraction. 1.256 = 1 32/125.

4 0

2 years ago

Simplify the equation

pashok25 [27]

Answer:

I think that the answer is C. 9^24

6 0

3 years ago