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3 years ago

Bases are squares with sides that measure 27 inches. The height is 12 inches.

Mathematics

1 answer:

Elan Coil [88]3 years ago

3 0

Answer:

Part 1) $V=8,748\ in^3$

Part 2) $SA=2,754\ in^2$

Step-by-step explanation:

The correct question is

Find the volume and the surface area of a rectangular prism. Bases are squares with sides that measure 27 inches. The height is 12 inches.

Part 1) Find the volume of the prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base

h is the height of the prism

Find the area of the base B

$B=27^2=729\ in^2$ ---> the base is a square

we have

$h=12\ in$

substitute

$V=(729)(12)=8,748\ in^3$

Part 2) Find the surface area of the prism

The surface area of the prism is equal to

$SA=2B+Ph$

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the perimeter of the base P

$P=4(27)=108\ in$

substitute the values in the formula

$SA=2(729)+108(12)=2,754\ in^2$

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Andrej [43]

Answer:

If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

Step-by-step explanation:

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2 years ago

Seattle, wa and san francisco, ca lie on the same longitudinal line. san francisco is at 38° latitude and seattle is at 47° lati

Varvara68 [4.7K]

Step 1.

Calculate measure of angle α:

$47^o-38^o=9^o$

Step 2.

Calculate what fraction of the angle 360° is the angle α:

$\dfrac{9^o}{360^o}=\dfrac{1}{40}$

Step 3.

Calculate the circumference of the Earth (circle):

$C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi$

Step 4.

The length of arc is equal 1/40 of the circumference:

$\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi$

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3 years ago

Assume that the function f is a one-to-one function, (a) f(8) = 9, find f ^ -1 (9)

Annette [7]

(a) since we are given that f(8) = 9, the inverse of 9 is simply 8. Therefore, f^-1(9) = 8.

(b) Again, f is the inverse of f^-1, therefore, you simply switch numbers, and you get that f(-3) = -7.

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3 years ago

To graduate this semester, you must pass Statistics 314; and you estimate that you have an 85% chance of passing. You need to pa

Nitella [24]

Answer:

Probability of graduating this semester is 0.7344

Step-by-step explanation:

Given the data in the question;

let A represent passing STAT-314

B represent passing at least in MATH-272 or MATH-444

M1 represent passing in MATH-272

M2 represent passing in MATH-444

C represent passing GERMAN-32

now

P( A ) = 0.85, P( C ) = 90, P( M1 ) = P( M2 ) = 0.8

P( B ) = P( pass at least one of either MATH-272 or MATH-444 ) = P( pass in MATH-272 but not MATH-444 ) + ( pass in MATH-444 but not in MATH 272) + P( pass both )

P( B ) = P( M1 ) × ( 1 - P( M2 ) ) + ( 1 - P( M1 ) ) × P( M2 ) + P( M1 ) × P( M2 )

we substitute

⇒ 0.8×0.2 + 0.2×0.8 + 0.8×0.8 = 0.16 + 0.16 + 0.64 = 0.96

∴ the probability of graduating this semester will be;

⇒ P( A ) × P( B ) × P( C )

we substitute

⇒ 0.85 × 0.96 × 90

⇒ 0.7344

Probability of graduating this semester is 0.7344

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2 years ago

Which is the dependent variable when 3x = y?

Andrej [43]

Answer:

A dependent variable is a variable (often denoted by y ) whose value depends on that of another. so it is the variable that changes depending on the numbers beside it.

I hope this helps if not check out Khan academy

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-dependent-independent/v/dependent-and-independent-variables-exercise-example-3

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