The total profit made by an engineering firm is given by the function p=x^2 - 24x +5000 where x is the number of clients the firm has and p is the profit.
1. Find the maximum profit made by the company.
2. How many clients are necessary to reach the profit outlined in part one?
Answer:
[tex]5144[/tex]
[tex]12[/tex]
Step-by-step explanation:
The function [tex]p=x^2-24x+5000[/tex] is incorrect as its roots are imaginary [tex]b^2-4ac=576-4\times 5000=-19424<0[/tex].
So, the correct function is
[tex]p=-x^2+24x+5000[/tex]
Differentiating with respect to [tex]x[/tex] we get
[tex]p'=-2x+24[/tex]
Equating with zero
[tex]0=-2x+24\\\Rightarrow x=\dfrac{24}{2}\\\Rightarrow x=12[/tex]
Double derivative of the function
[tex]p''=-2<0[/tex]
So, the function is maximum at [tex]x=12[/tex]
Maximum profit is
[tex]p=-x^2+24x+5000=-12^2+24\times 12+5000\\\Rightarrow p=5144[/tex]
The maximum profit made by the company is [tex]5144[/tex]
The number of clients required to make the maximum profit is [tex]12[/tex].
first down, a football team lost 16 yd. After two
downs, the team had an overall gain of 5 yd. How
many yards were gained on second down?
Answer: +21
Step-by-step explanation:
Based on the information given, we are informed that at first down, a football team lost 16 yd and they after two downs, the team had an overall gain of 5 yd.
The number of yards that were gained on second down can be represented by x. We can then form the question as an equation as:
x - 16 = 5
x = 5 + 16
x = 21
The team gained 21 yards.
-5(3u + 1) + 10u
please helpoo
This is just a guess from doing the math, but I think the answer is -1u. Sorry if its wrong
Answer:
-5(u+1)
Step-by-step explanation:
hopefully the answer helps
For each statement below, determine whether the statement is a decision variable or not.
* Number of Aqua-Spa Produced.
* Number of Hydro-Lux Produced.
* Number of Pumps Purchased.
* Amount of Available Labor Hours.
* Amount of Available Tubing Available.
* Profit of Aqua-Spa.
* Profit of Hydro-Lux.
Answer and explanation:
Decision variables are variables that are independent(indeoendent variables) and can be controlled by the decision maker. Decision variables influence outcome or result of a solution, usually denoted x in linear programming.
Decision variables above include:
Number of Aqua-Spa Produced.
* Number of Hydro-Lux Produced.
* Number of Pumps Purchased.
* Amount of Available Labor Hours.
* Amount of Available Tubing Available
A small pump can drain a pool in 9 hours. A large pump could drain the same pool in 3 hours. How long (to the nearest minute) will it take to drain the pool if both pumps are used simultaneously?
Answer: 22.5 hours
Step-by-step explanation:
Let t be the time taken by both of the pumps to drain the pool.
Given: Time taken by pump 1 to drain the pool alone= 9 hours.
Time taken by pump 2 to drain the pool alone= 3 hours.
If both pumps are used simultaneously, then
[tex]\dfrac1t=\dfrac19+\dfrac13\\\\\Rightarrow\ \dfrac1t=\dfrac{1+3}{9}\\\\\Rightarrow\ \dfrac1t=\dfrac49\\\\\Rightarrow\ t=\dfrac94\\\\\Rightarrow\ t=2.25[/tex]
Hence, it will take 22.5 hours to drain the pool if both pumps are used simultaneously.
2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of
Step-by-step explanation:
if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):
3²+4²=5²; ⇔ 9+16=25.
PLEASE HELP THIS IS DUE TODAY How do you use proportions to calculate missing dimensions in scale drawings?
Answer:irst, write the scale factor. Next, write ratios to represent the unknown actual length and width of the display to the scale length and width of the display. Then, write two proportions by setting the two length ratios equal to one another and the two width ratios equal to one another. The given unit is feet
Step-by-step explanation:
what time will it be in 3/4 hour
Answer:
45 minutes
Step-by-step explanation:
so 1 hr= 60 minutes so you do 3/4 x 60min which is 45 minutes. Feel Free to mark Brainliest and have a great day!
3/4 of an hour is equal to 45 minutes.
To find 3/4 of an hour, we need to multiply the value of one hour by 3/4.
One hour is equal to 60 minutes.
To calculate 3/4 of an hour:
= 3/4 x 60 minutes
= (3/4) x 60
= 45 minutes.
Therefore, 3/4 of an hour is equal to 45 minutes.
Learn more about Fraction here:
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A school has 764 students of the students 189 and third grade which equation can be used to find s the total number of students in all of the other grades.
Answer:
A. 118 + s = 764
Step-by-step explanation:
I hope this could help :)
If EH = 18 and FG 1 EH, solve for the measure of EG.
Answer:
9
Step-by-step explanation:
If its perpendicular, it probably bisects EH, so just split it in half.
527856 \ 8
How do I solve this with long division to find my quotient?
Answer:
65,982
Step-by-step explanation:
Look at the attached image for the step by step solution
Round to the nearest thousand.
88,651
6th grade mafs
Answer: 89,000
Step-by-step explanation:
Answer:
90,000
Step-by-step explanation:
88 = 90
Two students on roller skates stand face-toface, then push each other away. Which student will always have the fastest speed
Answer:
The student with lower weight will move faster than the one with higher weight.
Step-by-step explanation:
The students are on roller skates and it is assumed that their wheels are identical. They are on a frictionless flat horizontal ground. According to Newton's Law F=ma
Mass of student 1 is 97 kg
Mass of student 2 is 61 kg
The force magnitude is assumed to be equal and acceleration is same. The student with higher weight will have lesser force exerted than the student with lighter weight.
Evaluation 6ab when a = 1/2 and b = 7
Answer:
21
Step-by-step explanation:
6x1/2x7
6 x 1/2=3, 3 x 7=21
I hope this helps and have a nice day!
what is the value of the y coordinate of point A
Answer:
E on Edge
Step-by-step explanation:
Part A:
In the statement for step 2, ∠A is congruent to which angle? Which angle is ∠B congruent to?
Part B:
What is the missing statement in step 3?
Answer:
Step-by-step explanation:
What would be 82% of 50
Answer:
82% of 50 is 41
Step-by-step explanation:
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PLEASE HELP!!!!
f(x)= {____for____
{____for____
9514 1404 393
Answer:
[tex]f(x)=\left\{\begin{array}{ccc}3&\text{for}&-5\le x < 0\\1-x&\text{for}&0<x \le 5\end{array}\right.[/tex]
Step-by-step explanation:
The left section is defined at x = -5, but not at x = 0, so the interval for that definition is -5 ≤ x < 0. The function value on that interval is constant: 3.
The right section is defined a x = 5, but not at x = 0, so the interval for that definition is 0 < x ≤ 5. That section is a straight line with a slope of -1 and a y-intercept of 1. The function value on that interval can be written -x+1.
Then the piecewise definition is ...
f(x) = {3, for -5 ≤ x < 0; -x+1, for 0 < x ≤ 5}
which expression is equivalent to 7a-8-12a+4
Answer:
-5a-4
Step-by-step explanation:
7a-8-12a+4
7a-12a-8+4
=-5a-4
Can someone help me? Thank you!
Answer:
It's C
Step-by-step explanation:
A water mill grinds corn to make cornmeal. The water wheel has a radius of 18 feet. The wheel is rotating at 8 revolutions per minute. Find the linear speed, in feet per minute, of the water.
Answer:
904.9 feet per minute
Step-by-step explanation:
The Angular distance can be calculated using below expression
S= r θ ..............eqn(1)
Where
θ = angular distance travelled
r= Radius= radius of 18 feet
But angular distance can also be expressed as
θ = wt...................eqn(2)
w= angular speed= 8 rev per minute= (8 × 2π)
t= time
Velocity can also be expressed as
V= s/t............eqn(3)
Where
V= velocity
s= distance
t= time
Substitute eqn(2) into eqn(3)
V=( r θ)/ t................eqn(4)
Substitute eqn(2) into eqn(4)
V=( r w t)/ t
V= r w ..............eqn(5)
V= 18×(8 ×2π)
=288π
= 904.9 feet per minute
Hence, the linear speed, in feet per minute, of the water. is 904.9 feet per minute
which expression is NOT equivalent to the other three
a. 2x-2.5 + 3x-3
b. 5(x-1.1)
c. 5 (x-5.5)
d. 5x-5.5
Step-by-step explanation:
it either b or c hope this help
what is the answer? ;3
While selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come in five sizes, while packets of licorice nibs come in two. If he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos. If he chooses licorice nibs, he must choose between red and black. How many choices does he have
Answer and explanation:
First Prof. Murphy has to choose between two alternatives: gummy candy or licorice nibs
To find total choices, we only need to multiply number of sizes for each alternative and then add totals for each alternative together
So if Prof Murphy chooses gummy candy. He has sizes= 5 choices and types =3 choices, therefore he has 5×3= 15 choices for gummy candy
If he chooses licorice nibs, he has sizes = 2 choices and types= 2 choices, therefore he has 2×2= 4 choices for licorice nibs
Total choices: 15+4=19
He has 19 different options for selecting candy.
Since while selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs, and gummy candy packets come in five sizes, while packets of licorice nibs come in two, and if he chooses gummy candy, he must select gummy bears, gummy worms, or gummy dinos, while if he chooses licorice nibs, he must choose between red and black, to determine how many choices does he have, the following calculation must be performed:
Number of sizes x number of options = X Gummy candy = 5 x 3 = 15 Licorice nibs = 2 x 2 = 4 15 + 4 = 19
Therefore, he has 19 different options for selecting candy.
Learn more in https://brainly.com/question/238045
A unit vector lies in the xy plane, at an angle of 153 degrees from the x axis, with a positive y component. What is the unit vector
Answer:
unit vector = -0.891i + 0.454j
Step-by-step explanation:
Given that;
magnitude of unit vector =
angle of 153° degrees from the x axis, with a positive y component
{ second quadrant }
so, x and y components of the vector are;
x component = 1 × cos(153°) = - 0.891
y component = 1 × sin(153°) = 0.454
⇒ -0.891i + 0.454j
Therefore, unit vector = -0.891i + 0.454j
What number must be added to the expression below to complete the
square?
x² -200
A. 100
B. 10
C. -100
D. -10
Which expression is equivalent to 4x - (3x2 + x) + 5 - (2x2 + 1)?
Solve the equation3/5G - 1/3= -10/3
G=
Answer:
g = 5/59
Step-by-step explanation:
Please help, I will give brainliest, I am struggling badly.
Answer:
y= -3/5 x
Step-by-step explanation:
I hope this helps!!!
When Michael was 10 years old, Sam was 14. Sam is now 28 and Michael is 24.
Answer:
4 years difference
Step-by-step explanation: