Answer:
8
Step-by-step explanation:
The given expression is "three less than the quotient of ten and a number, increased by six”
The quotient of ten and a number increased by six is translated into mathematical expression as:
![\frac{10}{n}+6](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7Bn%7D%2B6)
Three less than the quotient of ten and a number, increased by six is
![(\frac{10}{n}+6)-3](https://tex.z-dn.net/?f=%28%5Cfrac%7B10%7D%7Bn%7D%2B6%29-3)
When we substitute n=2, we get:
![(\frac{10}{2}+6)-3](https://tex.z-dn.net/?f=%28%5Cfrac%7B10%7D%7B2%7D%2B6%29-3)
Divide to get:
![(5+6)-3](https://tex.z-dn.net/?f=%285%2B6%29-3)
Add to get:
![11-3](https://tex.z-dn.net/?f=11-3)
Subtract
![8](https://tex.z-dn.net/?f=8)
Six and a half hours at a speed of 45 mph. 45 mph is forty five miles per hour. since there are six full hours, multiply six (time) by speed (45) to get the distance within the six full hours, which is 270 miles. you also have an additional half hour at a 45 mph speed, so rather than going 45 miles in one hour, you for half an hour, meaning you go 22.5 miles. add these two together (270 + 22.5) to get 292.5 miles. a faster way to get to this would be to multiply 6.5 * 45. hole this helps!
Answer: ![D'(-14,1);\ E'(4,7);\ F'(4,1)](https://tex.z-dn.net/?f=D%27%28-14%2C1%29%3B%5C%20E%27%284%2C7%29%3B%5C%20F%27%284%2C1%29)
Step-by-step explanation:
Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':
![D_{O,k}(x,y)=(k(x-a)+a, k(y-b)+b)](https://tex.z-dn.net/?f=D_%7BO%2Ck%7D%28x%2Cy%29%3D%28k%28x-a%29%2Ba%2C%20k%28y-b%29%2Bb%29)
Where "O" is the center of dilation at (a,b) and "k" is the scale factor.
In this case you can identify that:
![(a,b)=(1,1)\\k=3](https://tex.z-dn.net/?f=%28a%2Cb%29%3D%281%2C1%29%5C%5Ck%3D3)
Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:
Vertex D' → ![(3(-4-1)+1,\ 3(1-1)+1)=(-14,1)](https://tex.z-dn.net/?f=%283%28-4-1%29%2B1%2C%5C%203%281-1%29%2B1%29%3D%28-14%2C1%29)
Vertex E' → ![(3(2-1)+1,\ 3(3-1)+1)=(4,7)](https://tex.z-dn.net/?f=%283%282-1%29%2B1%2C%5C%203%283-1%29%2B1%29%3D%284%2C7%29)
Vertex F' → ![(3(2-1)+1,\ 3(1-1)+1)=(4,1)](https://tex.z-dn.net/?f=%283%282-1%29%2B1%2C%5C%203%281-1%29%2B1%29%3D%284%2C1%29)
Answer:
P(yellow or red) =8/15
Step-by-step explanation:
There are 15 marbles, 3 green, 4 blue, and 5 red marbles.
3+4+5 = 12
That means there are 15-12 = 3 3 yellow marbles.
3 green,
4 blue
5 red
3 yellow
To find the probability of yellow or red, we add the number of yellow and red marbles together over the total number of marbles
P(yellow or red) = (yellow +red)/ total
= (3+5)/ 15
=8/15