<h2>
Answer:6 ways</h2>
Step-by-step explanation:
The number of ways in which
distinct objects can be arranged in a row is
.
![n!](https://tex.z-dn.net/?f=n%21)
![=n\times (n-1)\times (n-2).......\times 2\times 1](https://tex.z-dn.net/?f=%3Dn%5Ctimes%20%28n-1%29%5Ctimes%20%28n-2%29.......%5Ctimes%202%5Ctimes%201)
Given that we have
distinct blocks and each block can be used only once.
We need four block patterns which means we need all all the four blocks available to creating one pattern.
Given that every pattern starts with a red block.
So,three blocks can be arranged after the red block in
ways.
So,the number of patterns that can be made is
.
You can draw the area bounded by the unequality
![y\ \textgreater \ \frac{3}{4} x-2](https://tex.z-dn.net/?f=y%5C%20%5Ctextgreater%20%5C%20%20%5Cfrac%7B3%7D%7B4%7D%20x-2)
in following way:
1. Draw a dashed line
![y=\frac{3}{4} x-2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B4%7D%20x-2)
with a slope
![\frac{3}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B4%7D%20)
(a dashed, because all points from this line, for example when x=0, y=-2 do not belong to the area);
2. Define which part (under the line or over the line) is suitable by substituting values. For example, when x=0 and y=0 you obtain that
![0\ \textgreater \ \frac{3}{4} \cdot 0-2](https://tex.z-dn.net/?f=0%5C%20%5Ctextgreater%20%5C%20%20%5Cfrac%7B3%7D%7B4%7D%20%5Ccdot%200-2)
is a right unequality, that means that the point (0,0) is a solution and belongs to the area;
3. Shade that part of the plane to which point (0,0) belongs, you receive the area over the line (see image).
From the done steps you can see that only fourth statement is true.
Answer: 13 whole pieces of wire can be cut from that spool and
of wire is left over.
Step-by-step explanation:
Convert from mixed number to improper fraction. To do it you must multiply the whole numbe part by the denominator of the fraction and then add the product to the numerator. The denominator does not change. Then:
![7\frac{3}{8}in=\frac{(7*8)+3}{8}in=\frac{59}{8}in](https://tex.z-dn.net/?f=7%5Cfrac%7B3%7D%7B8%7Din%3D%5Cfrac%7B%287%2A8%29%2B3%7D%7B8%7Din%3D%5Cfrac%7B59%7D%7B8%7Din)
Since the spool contains 100 inches of wire, you must divide this lenght by
:
![\frac{100in}{\frac{59}{8}in}=\frac{800}{59}](https://tex.z-dn.net/?f=%5Cfrac%7B100in%7D%7B%5Cfrac%7B59%7D%7B8%7Din%7D%3D%5Cfrac%7B800%7D%7B59%7D)
Convert from improper fraction to mixed number:
- When you divide the numerator 800 by the denominator 59, the quotient is 13 (this is the whole number part)
- The remainder is 33 (This is the numerator of the fraction).
- The denominator does not change.
Then:
![13\frac{33}{59}](https://tex.z-dn.net/?f=13%5Cfrac%7B33%7D%7B59%7D)
Therefore 13 whole pieces can be cut from that spool.
The amount of wire left over is:
![100in-(\frac{59}{8}in)(13)=4.125in](https://tex.z-dn.net/?f=100in-%28%5Cfrac%7B59%7D%7B8%7Din%29%2813%29%3D4.125in)
Answer:
discount=109.5
sale price=$255.50
Step-by-step explanation:
365×30%=109.5
365-109.5=255.5
Answer:
(5x + 4)(3x+2)
Step-by-step explanation:
15x² + 22x + 8
First, you find two, when added equals 22 and when multiplied together equals 15*8
You then replace 22x with the two numbers
15x² + 10x + 12x + 8
You then group the above expression in 2s
(15x²+10x) + (12x + 8)
Find common factors in each group
5x(3x + 2) + 4(3x + 2)
(5x + 4)(3x+2)