-12x - 0.4 > 0.2(36.5x + 80) - 55 Remove the brackets.
-12x - 0.4 > 7.3x + 16 - 55 Combine the like terms on the right
-12x - 0.4 > 7.3x - 39 Add 12x to both sides
- 0.4 > 7.3x + 12x - 39
- 0.4 > 19.3x - 39 Add 39 to both sides.
-0.4 + 39 > 19.3x Combine like terms on the left
38.6 > 19.3x Divide by 19.3
38.6 / 19.3 > x
2 > x
The answer as a fraction is 5/6
We want to figure out how many pages Charlotte can read in 1 minute. Since we know how many pages she can read in 10 minutes, in order to find out how many she reads in 1 minute, simply do 10 divided by 8 1/3. Which will give you your answer, 5/6.
Answer:
The correct option is A.
Step-by-step explanation:
If a line passes through two points
and
, then the equation of line is
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
Let y be the profit (in millions) after x years.
From the given graph it is clear that the line passes through the point (1,-100).
The company paid for these costs and made combined profits of $80 million after 4 years. It means the graph passes through the point (4,80).
The line passes through (1,-100) and (4,80). So, the equation of line is
![y-(-100)=\frac{80-(-100)}{4-1}(x-1)](https://tex.z-dn.net/?f=y-%28-100%29%3D%5Cfrac%7B80-%28-100%29%7D%7B4-1%7D%28x-1%29)
![y+100=\frac{180}{3}(x-1)](https://tex.z-dn.net/?f=y%2B100%3D%5Cfrac%7B180%7D%7B3%7D%28x-1%29)
![y+100=60(x-1)](https://tex.z-dn.net/?f=y%2B100%3D60%28x-1%29)
![y+100=60x-60](https://tex.z-dn.net/?f=y%2B100%3D60x-60)
Subtract 100 from both sides.
![y+100-100=60x-60-100](https://tex.z-dn.net/?f=y%2B100-100%3D60x-60-100)
![y=60x-160](https://tex.z-dn.net/?f=y%3D60x-160)
The function form is
![f(x)=60x-160](https://tex.z-dn.net/?f=f%28x%29%3D60x-160)
Therefore, the correct option is A.
Answer:
Mean : 95
Median : 85
Mode : 90
Part B : Impossible
Step-by-step explanation:
We can make an equation to find the mean using the first 5 history test scores.
![85=\frac{80+75+90+75+95+n}{6} \\ \\ 85=\frac{415+n}{6} \\ \\ 510=415+n \\ \\ n=95](https://tex.z-dn.net/?f=85%3D%5Cfrac%7B80%2B75%2B90%2B75%2B95%2Bn%7D%7B6%7D%20%5C%5C%20%5C%5C%2085%3D%5Cfrac%7B415%2Bn%7D%7B6%7D%20%5C%5C%20%5C%5C%20510%3D415%2Bn%20%5C%5C%20%5C%5C%20n%3D95)
So a 95 would be needed to have a mean of 85.
Next, the median.
First, we sort the first 5 history scores from least to greatest.
We get 75, 75, 80, 90, 95.
Since, 80 is the middle value, it will be used in the calculation of the median.
We can make an equation with this.
![82.5=\frac{80+n}{2} \\ \\ 165=80+n \\ \\ n=85](https://tex.z-dn.net/?f=82.5%3D%5Cfrac%7B80%2Bn%7D%7B2%7D%20%5C%5C%20%5C%5C%20165%3D80%2Bn%20%5C%5C%20%5C%5C%20n%3D85)
So a score a 85 would be needed to have a median of 82.5
Thirdly, the mode.
Since 90 is already in the set once, we can just have Maliah score another 90 to make 90 the mode (with the exception of 75 of course).
Finally, Part B.
We can use the equation we had for the first mean calculation but change 85 to 90.
![90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125](https://tex.z-dn.net/?f=90%3D%5Cfrac%7B80%2B75%2B90%2B75%2B95%2Bn%7D%7B6%7D%20%5C%5C%20%5C%5C%2090%3D%5Cfrac%7B415%2Bn%7D%7B6%7D%20%5C%5C%20%5C%5C%20540%3D415%2Bn%20%5C%5C%20%5C%5C%20n%3D125)
So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.