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3 years ago

What is the smallest positive perfect cube that is a multiple of 180?

Mathematics

1 answer:

Lelechka [254]3 years ago

5 0

Answer:Factor it into its prime factors:

180 / 2 = 90

90 / 2 = 45

45 / 3 = 15

15 / 3 = 5

5 / 5 = 1

2 x 2 x 3 x 3 x 5

All of those factors pair should pair up in 3 members to make cube

2 x 2 x 2 x 3 x3 x 3 x 5 x 5 x 5 = (30)^3 = 27000

Smallest no. = 2 x 3 x 5 x 5 = 150

Step-by-step explanation:

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Wingspans of adult horses have approximate normal distribution with mean 125 cm and standard deviation 12 cm. What are the rst a

blagie [28]

Answer:

The first and third quartile of the wingspans are 116.9 cm and 133.1 cm respectively.

Step-by-step explanation:

The first and third quartile of a normal distribution are:

$Q_{1}=\mu-0.675\sigma\\\\Q_{3}=\mu+0.675\sigma$

The information provided is as follows:

$\mu=125\\\sigma=12$

Compute the first and third quartile of the wingspans as follows:

$Q_{1}=\mu-0.675\sigma=125-(0.675\times 12)=116.9\\\\Q_{3}=\mu+0.675\sigma=125+(0.675\times 12)=133.1$

Thus, the first and third quartile of the wingspans are 116.9 cm and 133.1 cm respectively.

7 0

3 years ago

19. The midpoint of JK is M(0, 1). One endpoint is /(-6, 3). Find the coordinates of

S_A_V [24]

Answer:

(6,-1)

Step-by-step explanation:

let coordinates of K be (x,y) then

$0=\frac{-6+x}{2}\\or~-6+x=0\\x=6\\1=\frac{3+y}{2}\\y+3=2\\y=2-3=-1\\so ~K~is ~(6,-1)$

3 0

3 years ago

The relationship between ttt and rrr is expressed by the equation 2t+3r+6=02t+3r+6=02, t, plus, 3, r, plus, 6, equals, 0. If rrr

Greeley [361]

Question:

The relationship between t and r is expressed by the equation 2t+3r+6 = 0. If r increases by 4, which of the following statements about t must be true?

Answer:

The value of t is reduced by 6 when the value of r is increased by 4

Step-by-step explanation:

Given

$2t + 3r + 6 = 0$

Required

What happens when r is increased by 4

$2t + 3r + 6 = 0$ -------- Equation 1

Subtract 2t from both sides

$2t + 3r + 6 - 2t = 0 - 2t$

$3r + 6 = - 2t$ --- Equation 2

When r is increased by 4, equation 1 becomes

$2T + 3(r+4) + 6 = 0$

Note that the increment of r also affects the value of t; hence, the new value of t is represented by T

Open bracket

$2T + 3r+12 + 6 = 0$

Rearrange

$2T + 3r+6 +12 = 0$

Substitutr -2t for 3r + 6 [From equation 2]

$2T -2t +12 = 0$

Make T the subject of formula

$2T = 2t - 12$

Divide both sides by 2

$\frac{2T}{2} = \frac{2t - 12}{2}$

$T = t - 6$

This means that the value of t is reduced by 6 when the value of r is increased by 4

3 0

3 years ago

What is the answer to 90x144?

I am Lyosha [343]

The Answer Is 12,960.

4 0

3 years ago

To solve a system of equations, you can replace a ____________with an equal value or expression.

Ludmilka [50]

Answer:

Variable

Step-by-step explanation:

If you can substitute a unknown variable with another expression that is equal, you can then solve for another variable, and with that equal expression, solve for the first variable.

4 0

3 years ago