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2 years ago

A conveyor belt dumps gravel into conical piles. Kevin measured the height of one pile of gravel. It was 10 1/2

Mathematics

1 answer:

Eddi Din [679]2 years ago

8 0

Answer:

189

Step-by-step explanation:

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If Michael drove 135 miles on 6 gallons of gas, how far can he drive on 15 gallons of gas?

laiz [17]

Answer:337.5 miles

Step-by-step explanation:

Find the unit rate 135/6 = 22.5/1

He can drive 22.5 miles on 1 gallon of gas

Then multiply by 15

22.5x15= 337.5

6 0

2 years ago

Please answer fast The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5),

hammer [34]

Answer:

See below ~

Step-by-step explanation:

Drawing the rectangle (Refer attachment)

Horizontal sides

There are two x-values present : 1 and 6
Find the difference
6 - 1 = 5
The horizontal sides of the rectangle are 5 units long

Vertical sides

Two y-values are present : 4 and 5
Find the difference
5 - 4 = 1
The vertical sides of the rectangle are 1 unit long

Perimeter

2(Horizontal side + Vertical side)
2(5 + 1)
2(6)
12
The perimeter of the rectangle is 12 units

3 0

1 year ago

Find out the number of combinations and the number of permutations for 8 objects taken 6 at a time. Express your answer in exact

umka2103 [35]

Solution:

The permutation formula is expressed as

$\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}$

The combination formula is expressed as

$\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}$

where

$\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}$

Given that 6 objects are taken at a time from 8, this implies that

$\begin{gathered} n=8 \\ r=6 \end{gathered}$

Thus,

Number of permuations:

$\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}$

Number of combinations:

$\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}$

Hence, there are 28 combinations and 20160 permutations.

7 0

8 months ago

THe product of three numbers is 3150. Two of the number are 14 and 15. Find the third number

Sholpan [36]

Answer:

Step-by-step explanation:

Let's call the mystery number x.

$14\cdot 15\cdot x=3150 \\\\210x=3150 \\\\x=3150/210=15$