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A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round you

marta [7]

Volume of cone formula: V = PI x r^2 x h/3

Volume of sphere formula: 4/3 x PI x r^3

Cone: 3.14 x 9^2 x 9/3 = 763.02 cubic inches

1/2 sphere: 1/2 x 4/3 x 3.14 x 9^3 = 1526.04 cubic inches.

Total volume : 1526.04 + 763.02 = 2289.1 cubic inches

4 0

3 years ago

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Evaluate the cosine if the angle of rotation which contains the point (9, -3) on its terminal side

Liono4ka [1.6K]

so we know the terminal point is at (9, -3), now, let's notice that's the IV Quadrant

$\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill$

$\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}$

6 0

2 years ago

A rectangular prism has a base that is 1.5 meters by 2 meters and the prsim is 4 meters high,What is the surface area

daser333 [38]

Answer:

34

Step-by-step explanation:

the equation is 2(lw+lh+wh)

2( 1.5 x 2 + 1.5 x 4 + 2 x 4)

8 0

3 years ago

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A certain brand of automobile tire has a mean life span of 35,000 miles, with a standard deviation of 2250 miles. Assume the lif

yawa3891 [41]

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

$z = \dfrac{x - \mu}{\sigma}$

For x = 34000

$z = \dfrac{34000 - 35000}{2250}$

$z = \dfrac{-1000}{2250}$

z = −0.4444

For x = 37000

$z = \dfrac{37000 - 35000}{2250}$

$z = \dfrac{2000}{2250}$

z = 0.8889

For x = 3000

$z = \dfrac{30000 - 35000}{2250}$

$z = \dfrac{-5000}{2250}$

z = -2.222

From the above z- score that corresponds to their life span; it is glaring that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

$z = \dfrac{30500 - 35000}{2250}$