Answer:
−4(3n+5)
the answer is the third one
Maximum profit. A university student center sells 2,000 cups of coffee per day at a price of $4.0. A market survey shows that for every $0.1 reduction in price, 100 more cups of coffee will be sold. The cost of making one cup of coffee is $1.0. a) how much should the student center charge for a cup of coffee in order to maximize the profit? b) how many cups of coffee is the student center selling per day with this price? c) what is the maximum profit?
Answer:
a) $3.50
b) 2,500 cups
c) $6,250
Step-by-step explanation:
a) The number of cups of coffee the student sells, n = 2,000 cups
The price at which the student sells the coffee, P = $4.0
The number of extra cups sold for every $0.1 reduction in price = 100 cups
The cost of making one cup of coffee, C = $1.0
Let 'x' represent the set charge for a cup of coffee, we get;
The number of cups, nₙ = 2,000 + 100 × (4.0 - x)/0.1 = 6,000 - 1,000·x
Therefore, the revenue is given as follows;
Revenue, R = x × (6,000 - 1,000·x) = 6000·x - 1,000·x² = 1,000·(6·x - x²)
The cost, C = 1 × 6,000 - 1,000·x = 6,000 - 1,000·x
The profit, P = Revenue - Cost
∴ Profit = 6000·x - 1,000·x² - (6,000 - 1,000·x) = 7,000·x - 1,000·x² - 6,000
Profit, P = 7,000·x - 1,000·x² - 6,000 = 1,000 × (7·x - x² - 6)
At the maximum profit, we have; , we have;
dP/dx = 0
∴ dP/dx = d(1,000 × (7·x - x² - 6))/d
dR/dx = 1,000·d(7·x - x² - 6)/dx = 1,000 × (7 - 2·x) = 0
x = 7/2 = 3.5
The price that gives the maximum profit, x = $3.50
Therefore, the amount the student center should charge for a cup of coffee to maximize profit, x = $3.50
b) We have;
The number of cups, n = 6,000 - 1,000 × 3.5 = 2,500
The number of cups of coffee the student center sells at the price that gives the maximum profit, n = 2,500 cups
c) The maximum profit, [tex]P_{max}[/tex] = 1,000 × (7 × 3.5 - 3.5² - 6) = 6,250
The maximum profit, [tex]P_{max}[/tex] = $6,250.
HELP PLEASE BRAINLEST FOR ANSWER Which sample is biased?
Which is not baised
A.
A book store owner surveys 50 customers to find out if they like to read.
B.
Two students survey 100 people on the street asking for their favorite soda.
C.
A phone system randomly calls people living in a city asking for their favorite store.
D.
A computer program randomly emails a survey to customers to see if they are satisfied with the service.
Answer:
I think A and B are biased and C and D aren't.
Step-by-step explanation:
A and B are surveying a certain amount of people while C and D are surveying people at random
Find the surface area of a rectangular prism that has the following dimensions:
length: 4.5 In.
width: 6 in.
height: 12 In.
surface area = in2?
ASAP
Answer:
324in2
Step-by-step explanation:
A=bxwxh (basexwidthxheight)
A=4.5x6x12=324
A=324in2
Answer:
306
Step-by-step explanation:
hope this helps
An author works on a new book and after writing a few chapters, begins a new plan to write 600 words per day. On the fifth day of working on this plan, 4,500 words have been written. If the equation y = 600x + b represents the total number of words the author has written, y, based on the number of days, x, since the new plan was started, what is the value of b?
Someone, Please help asap! :)
work out angle ‘a’
angles - OW
first we will find angle BED = 180 - 49 = 131 degrees
then find angle BDE = 90 - 64 = 26
then subtract the sum of both from 180
180-26+131=23 degrees
Simplify negative 3 and 1 over 9 − negative 8 and 1 over 3.
Answer:
-11 4/9
Step-by-step explanation:
-3 1/9 minus 8 1/3 with common denominators would be -3 1/9 minus 8 3/9, and that would be -11 4/9.
A spinner has A-H on it.
What is the probability of spinning a vowel?
a
2/7
b
1/3
c
1/4
d
3/8
Answer:
C
Step-by-step explanation:
there are 2 vowels in the 8 letters
so
2/8 but simplify it and 1/4
help me please thank you
Answer:A
Step-by-step explanation:
1/5 x 5 1/2 =
Can someone help me ?
Answer:
1/2
Step-by-step explanation:
reduce the numbers with the greatest common factor 5
1/5×5 1/2
1/2
Answer:
this is the answer hope it helps
In rhombus ABCD shown below, AB=17 and AC=16 determine the length of BD without (hint , not with trigonometry)
Answer:
[tex]BD = 30[/tex]
Step-by-step explanation:
Given
[tex]AB = 17[/tex]
[tex]AC = 16[/tex]
See attachment
Required
Find BD
If AC = 16, then:
[tex]AO = 16/2[/tex] i.e. half the diagonal AC
[tex]AO = 8[/tex]
The diagonals of a rhombus are perpendicular.
This implies that we can apply Pythagoras theorem.
Using Pythagoras theorem on triangle AOB, we have:
[tex]AB^2 = AO^2 + OB^2[/tex]
[tex]17^2 = 8^2 + OB^2[/tex]
[tex]289 = 64 + OB^2[/tex]
Collect like terms
[tex]OB^2 = 289 - 64[/tex]
[tex]OB^2 = 225[/tex]
Take positive square roots of both sides
[tex]OB = 15[/tex]
To solve for BD, we use:
[tex]OB = \frac{BD}{2}[/tex] --- i.e. half the diagonal BD
[tex]BD = 2 * OB[/tex]
[tex]BD = 2 * 15[/tex]
[tex]BD = 30[/tex]
Add the following expressions: 3r - 7 and -10r + 2
-13r-9
13-5
O -7r - 9
-7r -5
Answer:
Step-by-step explanation:
-7r - 5
Hope that helps! :)
-Aphrodite
Answer:
-7r - 5
Step-by-step explanation:
3r - 7 and -10r + 2
*remember that you can only combine the like terms
3r - 10r = - 7r
-7 + 2 = -5
Final Answer: -7r - 5
A triangle has sides of lengths 5, 7 and 13. Is it a right triangle? Explain.
Which of the following are identities? Check all that apply.
Answer: The correct identities are: 1 + tan^2x = sec^2x 1 + cot^2x = csc^2x sin^2x + cos^2x = 1 which correspond to B and D
Step-by-step explanation:
T////T
im ok at math if its wrong im sorry T^T
Answer:
A, B, C, and D.
Yeah, I bet you didn't see this one coming.
Hope this helps!
HELP URGENT
Mal and Priya each played 10 games of bowling and recorded the scores, Mai's median score was 120, and her
IQR was 5. Priya's median score was 118, and her IQR was 15. Whose scores probably had less variability?
Explain how you know
Answer:
Mai has less variability as compared to that of Priya
Step-by-step explanation:
IQR is the Inter quartile range and is the difference between upper and lower quartiles. It measures the variability as in terms it depicts the middle 50% of values when the values are arranged in ascending order
In case of Priya's median score was 118, and her IQR was 15. IQR = 15 means that there is a difference of 15 between the upper and lower quartiles
While in case of Mai, the IQR is 5 only.
Hence, Mai has less variability as compared to that of Priya
8 points !!! I will mark brainiest if your correct !!!!
the number cube shown is rolled and the spinner shown is spun. find P(an odd number and yellow)
the spinner has 2 yellow squares, 1 blue square and 1 green
A: 1/4
B: 3/4
C: 3/5
D: 3/20
Answer:
A
Step-by-step explanation:
1/4 is the required answer.
hope it helps u and keep smiling :)
Select all the solutions to
( x - 2) to the power of 2 = -16
what is the area of the triangle in square inches?
Answer:
22in.^2
Step-by-step explanation:
Area of a triangle formula is A= b*h* 1/2
(b= base h= height)
the base is 8
the height is 5 1/2
8*5 1/2
----------
2
5 1/2 = 5.5
8* 5.5 = 44
44/2 = 22
Need help please don’t understand could use any help will help me.
I LOVE SUDUKO
okay so basically, each row, and square has to have one of each number
Devon is buying 3 greeting cards that cost $0.97 each. How can rounding be used to estimate the total cost of the cards?
Since each card is about $1, the total cost is approximately 3 + 1 = $4.
Since each card is about $1, the total cost is approximately 3 × 1 = $3.
Since he is buying about 10 cards, the total cost is approximately 10 × 0.97 = $9.70.
Since he is buying about 10 cards, the total cost is approximately 10 + 0.97 = $10.97.
Answer:
Since each card is about $1, the total cost is approximately 3 × 1 = $3.
Step-by-step explanation:
So 3 x 1 = 3
1 > 0.97
0.97 x 3 ≈ 2.91 which if rounded to the nearest WHOLE number it would be approximately 3$
Hope this helps!
2.
Abus drove 70 miles in 2 hours. What is the unit rate?
d
b
70 miles
35 miles
140 miles
140 miles
1 hour
2 hours
1 hour
4 hours
No
Answer:
The unit rate is 35 miles per hour
Step-by-step explanation:
HELP PLZ ASAP AND I GIVE BRAINILST
Answer:
F
Step-by-step explanation:
Answer:
G its simple
Step-by-step explanation:
verify the following identity: sinx+cosx×cotx=cscx
What is the equation of the line that includes points (25, 100) and (15, 120)
Answer:
y = -2x + 150
Step-by-step explanation:
y2 - y1 / x2 - x1
120 - 100 / 15 - 25
20 / -10
= -2
y = -2x + b
100 = -2(25) + b
100 = -50 + b
150 = b
What is volume? USE YOUR WORDS NOT G00GLE"S. (if answer is in a folder or link please dont answer) thank uu
Answer:
Typically, volume is used to measure the capacity of a container/bottle/etc. It is used alongside measurements for liquids, like mL or L.
Step-by-step explanation:
Someone please help me I’ll give out brainliest please dont answer if you don’t know
Answer:
[tex]12.5(x + 20) = 460 \\ x + 20 = 460 \div 12.5 \\ x + 20 = 36.8 \\ x = 36.8 - 20 \\ x = 16.8[/tex]
Hence, 16.8 miles is your answer
solve for x: 2x-y=3 if you can show work thanks.
Answer:
x = 3/2 + y/2
Step-by-step explanation:
:)
Can anyone explain how to do this?
Step-by-step explanation:
Using the equation [tex]a^{2} + b^{2} = c^{2}[/tex]
so [tex]a^{2} = 35[/tex] and [tex]b^{2} =50[/tex]
[tex]a^{2} + b^{2} = 85^{2}[/tex]
Answer:
85 units²
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
The hypotenuse is the side opposite the right angle ( third side ) , then
area = 35 + 50 = 85 units²
Help me please!!!!!!!!
Answer:
You can find 0.5% of a number by multiplying the number by
Step-by-step explanation:
Go bad b go bad b go, bad b, ah fat, 40 inch hair yours came in a pack.