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Serjik [45]
3 years ago
7

Which could be the dimensions of a rectangular prism to service area is less than 160 ft.² check all that apply

Mathematics
2 answers:
Dovator [93]3 years ago
6 0

Area of a rectangular prism: 2(wl+hl+hw), given w=width, l=length, and h=height.

Plug the answer choices into this formula to find which one(s) are less than 160 sq. feet.

A. 136 sq. feet

B. 188 sq. feet

C. 202 sq. feet

D. 162 sq. feet

E. 142 sq. feet

So, the only ones that are less than 160 sq. feet are A (8 feet by 4 feet by 3 feet) and E (3 feet by 5 feet by 7 feet).

Your answers are A and E.

I hope this helps :)

raketka [301]3 years ago
3 0

Area of rectangular prism is given by:

A=2(wl+hl+lw)

where w=width h=height, l=length

checking for given options

1. 8 ft, by 4ft by 3ft

Area = 136 square feet

5. 3 feet by 5 feet by 7 feet

Area =142 square feet

so our first and last option matches the requirement of area less than 160 square feet.

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Plant B is 6 2/3 inches tall. and C is 4 4/15 inches tall. Complete the sentences and show your reasoning
artcher [175]

Answer:

Plant C is <u>0.64</u> times as tall as Plant B

Plant C is <u>2.4 inches</u> shorter than Plant B

Step-by-step explanation:

Plant B is 6 2/3 inches tall. Plant B is 20/3 inches tall.

Plant C 4 4/15 inches tall. Plant C is 64/15 inches tall.

a.) Plant C is shorter than Plant B = \frac{64}{15} \times \frac{1}{\frac{20}{3} }  = \frac{64}{15} \times\frac{3}{20}  = \frac{16}{25} = 0.64 times.

b.) Plant C is shorter than Plant B by = \frac{20}{3}  - \frac{64}{15}  = \frac{100}{15}  - \frac{64}{15}  = \frac{100 -64}{15}  = \frac{36}{15} = 2\frac{2}{5} = 2.4 inches

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Step-by-step explanation:

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What is the smallest integer $n$, greater than $1$, such that $n^{-1}\pmod{130}$ and $n^{-1}\pmod{231}$ are both defined?
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First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.

We have

130 = 2 • 5 • 13

231 = 3 • 7 • 11

so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.

To verify the claim, we try to solve the system of congruences

\begin{cases} 17x \equiv 1 \pmod{130} \\ 17y \equiv 1 \pmod{231} \end{cases}

Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:

130 = 7 • 17 + 11

17 = 1 • 11 + 6

11 = 1 • 6 + 5

6 = 1 • 5 + 1

⇒   1 = 23 • 17 - 3 • 130

Then

23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)

so that x = 23.

Repeat for 231 and 17:

231 = 13 • 17 + 10

17 = 1 • 10 + 7

10 = 1 • 7 + 3

7 = 2 • 3 + 1

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Then

68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)

so that y = 68.

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3 years ago
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