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1 year ago

A cube has a volume of 64. What is the length of one side of the cube?

Mathematics

1 answer:

Sauron [17]1 year ago

8 0

We will solve this using volume of cube formula. Since, It is a cube all the sides are equal in length. Let's find the length with volume... ~

$\boxed{ \sf \: volume = a^{3} }$

Where A is the side of cube

We have, Volume = 64

Let's solve for a

$\sf\to64 = {a}^{3}$

Swap the sides of the equation

$\sf \to \: a^{3} = 64$

Take the cube root of 64

$\sf \to \: a = \sqrt[3]{64}$

Solve for root

$\sf \to \: a = 4$

<em>Thus, Each side of the cube measures 4 unit..!</em>

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The heights of 1000 students at a local school were recorded and found to be approximated by the normal curve below. Which answe

Vlada [557]

Answer:

The mean of the distribution of heights of students at a local school is 63 inches and the standard deviation is 4 inches.

Step-by-step explanation:

The normal curve approximating the distribution of the heights of 1000 students at a local school is shown below.

For a normal curve, the mean, median and mode are the same and represents the center of the distribution.

The center of the normal curve below is at the height 63 inches.

Thus, the mean of the distribution of heights of students at a local school is 63 inches.

The standard deviation represents the spread or dispersion of the data.

From the normal curve it can be seen that values are equally distributed, i.e. the difference between two values is of 4 inches.

So, the standard deviation is 4 inches.

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2 years ago

Select the pair of equations whose graphs are perpendicular.

viktelen [127]

$k:\ y=m_1x+b_1\ \ \ \ and\ \ \ \ l:\ y=m_2x+b_2\\ \\the\ line\k\ is\ perpendicular\ to\ the\ line\ l\ \ \ \Leftrightarrow\ \ \ m_1\cdot m_2=-1\\----------------------------\\\\A.\\2y=-3x+5\ \ \Rightarrow\ \ \ y=- \frac{3}{2} x+2.5\ \ \Rightarrow\ \ m_1=- \frac{3}{2} \\\\2x+3y=4\ \ \Rightarrow\ \ 3y=-2x+4\ \ \Rightarrow\ \ y=- \frac{2}{3}x+1 \frac{1}{3} \ \ \Rightarrow\ \ m_2=- \frac{2}{3} \\\\m_1\cdot m_2=- \frac{3}{2} \cdot (- \frac{2}{3})=1 \neq -1$

$B.\\5x-8y=9\ \ \Rightarrow\ \ -8y=-5x+9\ \ \Rightarrow\ \ \ y= \frac{5}{8} x-1 \frac{1}{8} \ \Rightarrow\ \ m_1= \frac{5}{8} \\\\12x-5y=7\ \Rightarrow\ \ -5y=-12x+7\ \ \Rightarrow\ \ y= \frac{12}{5}x-1 \frac{2}{5} \ \ \Rightarrow\ \ m_2= \frac{12}{5} \\\\m_1\cdot m_2= \frac{5}{8} \cdot \frac{12}{5}= \frac{3}{2} \neq -1$

$C.\\y=2x-7\ \ \Rightarrow\ \ m_1=2 \\\\x+2y=3\ \Rightarrow\ \ 2y=-x+3\ \ \Rightarrow\ \ y= -\frac{1}{2}x+1 \frac{1}{2}\ \ \Rightarrow\ \ m_2=- \frac{1}{2} \\\\m_1\cdot m_2= 2 \cdot (- \frac{1}{2})= -1\ \ \Rightarrow\ \ y=2x-7\ \ \ \ \perp\ \ \ \ x+2y=3$

$
D.\\x+6y=8\ \ \Rightarrow\ \ 6y=-x+8\ \ \Rightarrow\ \ \ y=- \frac{1}{6} x+1 \frac{1}{3}\ \ \Rightarrow\ \ m_1= -\frac{1}{6} \\\\y=2x-8\ \Rightarrow\ \ m_2= 2 \\\\m_1\cdot m_2= -\frac{1}{6} \cdot2=- \frac{1}{3} \neq -1$

7 0

2 years ago

Someone plz help (20 points)

lbvjy [14]

Answer:

The answer is A

Step-by-step explanation:

4 0

2 years ago

The dinner bill came to $72.48, and Julio tipped the waiter 15%. What is the total price of dinner?

balu736 [363]

Answer:

It is 83.35 Unless your rounding up then it is 84 dollars

Step-by-step explanation:

5 0

2 years ago

How much higher is 500 than 400 m?

AnnyKZ [126]

Answer:

100m?

Step-by-step explanation:

Uh 100? is the 500m or something else I am assuming 500m perhaps.

3 0

2 years ago

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