Answer:
p = 2.7x - 20
p(90) = $223
Step-by-step explanation:
revenue → f(x) = 3x ,where x is the number of downloads.
the statement “Your profit p is $20 less than 90% of the revenue for x downloads”
<u><em>means</em></u>
![p=90\% f\left( x\right) -20](https://tex.z-dn.net/?f=p%3D90%5C%25%20f%5Cleft%28%20x%5Cright%29%20%20-20)
<u><em>means</em></u>
<u><em></em></u>![p=\frac{90}{100} \times f\left( x\right) -20](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B90%7D%7B100%7D%20%5Ctimes%20f%5Cleft%28%20x%5Cright%29%20%20-20)
<u><em>means</em></u>
![p=\frac{9}{10} \times (3x) -20](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B9%7D%7B10%7D%20%5Ctimes%20%283x%29%20%20-20)
<u><em>means</em></u>
![p=\frac{9}{10} \times (3x) -20](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B9%7D%7B10%7D%20%5Ctimes%20%283x%29%20%20-20)
<u><em>means</em></u>
![p=2.7x -20](https://tex.z-dn.net/?f=p%3D2.7x%20-20)
………………………………
the profit for 90 downloads :
= p(90)
= 2.7×(90) - 20
= $223
Answer:
Caleb arrived first 2 hours before Alyssa
Step-by-step explanation:
To solve the situation, find the speed per hour they were driving by dividing the distance they drove by the time it took.
Alyssa drove 105 miles in 3.5 hours or 105/3.5 = 30 miles per hour.
Caleb drove 168 miles in 4 hours or 168/4 = 42 miles per hour.
Since they both left at the same time and drove the same 210 miles to the beach, Caleb arrived first since he was driving faster.
He arrived in 210/42 = 5 hours.
Alyssa arrived in 210/30 = 7 hours.
He arrived 2 hours before her.
Answer:
750 < p < 1500
Step-by-step explanation:
The total cost of the affair for p attendees is ...
750 +2.25p
The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...
2.75 < (750 +2.25p)/p < 3.25
2.75 < 750/p + 2.25 < 3.25 . . . . . . . . separating the fraction parts
0.50 < 750/p < 1.00 . . . . . . . . . . . . . . subtract 2.25
2 > p/750 > 1 . . . . . . . . . . . . . . . . . . . . . take the reciprocal*
1500 > p > 750 . . . . . . . . matches choice 4
_____
* Taking the reciprocals of numbers with the same sign reverses their order:
2 < 3 but 1/2 > 1/3
__
An alternate approach to the solution would be to multiply by p:
0.50p < 750 < 1.00p
To solve this requires it be made into two inequalities:
0.50p < 750 ⇒ p < 1500
and
750 < 1.00p ⇒ 750 < p
Then these would need to be recombined to form the answer:
750 < p < 1500
Slope of f(x)
Slope of g(x)
PART A)
The slopes of f(x) and g(x) are the same.
PART B)
The equation for line f(x)
y = 4x + b
-1 = 4(0) + b
-1 = b
y = 4x - 1
The function G(x) has a bigger y-intercept. The y-intercept of g(x) is 3, while the y-intercept of f(x) is -1.