Profit, revenue and cost are related, and can be calculated from one another.
The profit function is [tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]The domain of the profit function is x > 0The profit when producing 60 items is 1650The profit when producing 70 items is 1600The cost function is given as:
[tex]\mathbf{C(x) =30x + 150}[/tex]
The revenue function is given as:
[tex]\mathbf{R(x) =-0.5(x -90)^2 + 4050}[/tex]
(a) Calculate the profit function
This is calculated using:
[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]
So, we have:
[tex]\mathbf{P(x) =-0.5(x -90)^2 + 4050 - 30x - 150}[/tex]
Evaluate like terms
[tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]
(b) The domain of the profit function
When profit is 0 or less, then it becomes no profit.
Hence, the domain of the profit function is x > 0
(c) The profit for 60 and 70 items
Substitute 60 and 70 for x in P(x)
[tex]\mathbf{P(60) =-0.5(60 -90)^2 - 30 \times 60 + 3900}[/tex]
[tex]\mathbf{P(60) =1650}[/tex]
The profit when producing 60 items is 1650
[tex]\mathbf{P(70) =-0.5(70 -90)^2 - 30 \times 70 + 3900}[/tex]
[tex]\mathbf{P(70) = 1500}[/tex]
The profit when producing 70 items is 1600
(d) Why producing 10 more units less profit
When a function reaches the optimal value, the value of the function begins to reduce.
This means that, producing 10 more units takes the profit function beyond its maximum point.
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For all horizontal lines the range is
When you have a function where y equals a constant, your graph is a truly horizontal line,
In that case, the range is just that one and only value. No other possible values can come out of that function! Many other functions have limited ranges.
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate).
4 sin(2θ) − 2 sin(θ) = 0
Answer:
θ = πk, 1.318+2πk, 4.965+2πk
Step-by-step explanation:
4sin(2θ) − 2sin(θ) = 0
8sin(θ)cos(θ) - 2sin(θ) = 0
2sin(θ)[4cos(θ)-1] = 0
2sin(θ) = 0
sin(θ) = 0
θ = πk
4cos(θ)-1 = 0
4cos(θ) = 1
cos(θ) = 1/4
θ ≈ 1.318+2πk, 4.965+2πk
Therefore, θ = πk, 1.318+2πk, 4.965+2πk
I will give brainlist to the most helpful answer
Answer:
1. 4
2. 6
3. 10
4. 30
5. 48
6. 55
7. 68
8. 148
9. 102
10. 38
The perimeter of a regular heptagon is 21 m. How long is each side?
5 m
2 m
3 m
4 m
Answer:
3m
Step-by-step explanation:
A heptagon has 7 sides so 21÷7=3m
Answer:
3m
Step-by-step explanation:
3m X 7 is 21m
make me brainlist.
work out the area of this quarter circle take p2b 3.14 to and read and other digits given by a calculator
Answer:
Step-by-step explanation:
area of a full circle is A = πr²
so a quarter of a circle area is A = πr²/4
A = 3.142(7²)/4
A = 38.4895 cm² picture answer
Using π = 3.14 results in
A = 3.14(7²)/4
A = 38.465 cm² written question answer
For comparison purposes,
Carrying the precision of π into many more significant digits results in
A = 38.484510006474...cm²
Which claim supports this graph?
A- There is a huge difference in the number of times students use social media.
B- There is a small difference in the number of times students use social media.
C- Students mostly use social media 0 times per day.
D- Students mostly use social media 10 times per day.
Answer:
I would say A. it makes the most sense.
A 9 in the thousandths place has 10 times the value of a 9 in the ? Place.
Answer:
10,000th place
Step-by-step explanation:
Solve for k.
k + 4.9 = 12.28
Answer:
k=7.38
Step-by-step explanation:
12.28-4.9=7.38
Answer:
7.38Step-by-step explanation:
= > x + 4.9 = 12.28
= > x = 12.28 - 4.9
= > x = 7.38
Hope it helps!!
If you start with 65 milligrams of Chromium 51, used to track red blood cells, which has a half-life of 27.7 days. How long will it take for 80% of the material to decay?
Answer:
Half-Life uses the formula N () = Noe # No = Initial Amount time h = length of half-life. Ifyou start with 65 milligrams of Chromium 51,used to track red blood cells, which has half-life of 27.7 days: How long will it take for 80% ofthe material to decay? t= (27.7) h5 (65) (h3) 4= (27.7) h; (05)
Step-by-step explanation:
For the given data it will take 8.69 days for 80% of the material to decay.
What is half-life?A radioactive substance's half-life is typically described as the amount of time it takes for one-half of its atoms to disintegrate or change into another substance.
It is given that, If you start with 65 milligrams of Chromium 51, used to track red blood cells, which has a half-life of 27.7 days.
N₀ = 65 milligrams
t1/2=27.7 days
N(t)=0.8(65 milligrams)=52 milligrams
[tex]N(t) = N_0(1/2)^ {\frac{t}{t_{1/2}} }[/tex]
Here,
N(t) is the amount of the substance remaining
N₀ is the initial substance amount
t is the time elapsed
t1/2 is the half-life
Substitute the given values,
[tex]N(t) = N_0(1/2)^ {\frac{t}{t_{1/2}} } \\\\ 52 = 65(1/2)^\frac{t}{27.7} \\\\ 52=65\left(\frac{1}{2}\right)^{\frac{t}{27.7}} \\\\ \frac{65\left(\frac{1}{2}\right)^{\frac{t}{27.7}}}{65}=\frac{52}{65} \\\\ \left(\frac{1}{2}\right)^{\frac{t}{27.7}}=\frac{4}{5} \\\\ \frac{t}{27.7}\ln \left(\frac{1}{2}\right)=\ln \left(\frac{4}{5}\right) \\\\ t =-\frac{27.7\ln \left(\frac{4}{5}\right)}{\ln \left(2\right)}[/tex]
[tex]t = 8.69 \ days[/tex]
Thus, for the given data it will take 8.69 days for 80% of the material to decay.
Learn more about half-life here,
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What is 68×4-43..? XP I really need help with this one.
A square is inscribed in a circle as shown below. The radius of the circle is
decreasing at a constant rate of ½ centimeter per second. When the
radius of the circle is 4√2 centimeters, what is the rate of change of the
area of the shaded region found outside the square but inside the circle.
Answer:
3
Step-by-step explanation:
Plz help I need help
Which lines are parallel? Why?
A) a || b by same side interior angles
B) c || d by same side interior angles
C) c || d by converse of corresponding angles
D) a || b by converse of same side interior angles
E) a || b by converse of corresponding angles
F) a || b by corresponding angles
G) c || d by converse of same side interior angles
H) c || d corresponding angles
9514 1404 393
Answer:
C) c || d by converse of corresponding angles
Step-by-step explanation:
Only corresponding angles where transversal b crosses lines c and d are shown. All answer choices involving a||b or interior angles can be eliminated from consideration.
The "corresponding angle" theorem tells you corresponding angles are congruent if the lines are parallel.
The converse of that theorem tells you the lines are parallel if the corresponding angles are congruent. Here, the angles are shown congruent, so the "converse" theorem applies.
He has a new 0.85-ounce tube of toothpaste that’s supposed to last him the whole trip. The amount of toothpaste Ken squeezes out of the tube each time he brushes varies according to a Normal distribution with mean 0.13 ounces and standard deviation 0.02 ounces.
Using the normal distribution, it is found that there is a 0.8888 = 88.88% probability that his tube last the whole trip.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]In this problem:
For each time he brushes his teeth, the mean is of 0.13 ounces and the standard deviation is of 0.02 ounces, hence [tex]\mu = 0.13, \sigma = 0.2[/tex]He will brush his teeth 6 times, hence [tex]n = 6, n\mu = 6(0.13) = 0.79, s = 0.2\sqrt{6}[/tex]The probability that his tube last the whole trip is the p-value of Z when X = 0.85, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Considering the n instances
[tex]Z = \frac{X - n\mu}{s}[/tex]
[tex]Z = \frac{0.85 - 0.79}{0.2\sqrt{6}}[/tex]
[tex]Z = 1.22[/tex]
[tex]Z = 1.22[/tex] has a p-value of 0.8888.
0.8888 = 88.88% probability that his tube last the whole trip.
A similar problem is given at https://brainly.com/question/24663213
hey I need someone to help me
Answer:
A and F
Step-by-step explanation:
You plug in each one and see which ever one gets 20.
12Q. Sweeti covered 2/7 of the running track by walking and rest by running and the length of the track is 630 m. Find the distance covered by running ?
Step-by-step explanation:
Given that :
Total length of the track = 630 m
Distance covered by Sweeti by walking = 2/7 of the running track
2/7 of 630 m
⇛ (2/7)×630
⇛ (2×630)/7
⇛ 1260/7
⇛ 180 m
Distance covered by walking = 180 m
Remaining distance =
Total distance - Distance covered by walking
⇛630 m - 180 m
⇛ 450 m
The total distance covered by running by Sweeti is 450 m.
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You can burn about 450 calories if you run 5 miles. How many miles will you need to run to burn 630 calories? Justify your reasoning.....
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Use Definition 7.1.1,
DEFINITION 7.1.1 Laplace Transform
Let f be a function defined for
t ≥ 0.
Then the integral
ℒ{f(t)} =
∞
e−stf(t) dt
0
is said to be the Laplace transform of f, provided that the integral converges.
to find
ℒ{f(t)}.
(Write your answer as a function of s.)
Answer:
1q1231564rr54drdfgy6
Yesterday, Chris had m baseball cards. Today, he gave 18 away. Using m, write an expression for the number of cards Chris has left.
m-18
(MARK ME BRAINLIEST PLS I WILL GET NEW RANK(ACE) Pls))A research question is a declarative statement which can be tested to determine the probability of it being true or false.
Answer:
Step-by-step explanation:
Yes the answer is true.
A declarative statement is one that
makes a statementprovides a factoffers an explanationconveys informationThat being said, it can make a statement that is testable. It is testable, it can be assigned a probability.
pleasle help with math problem
Answer: 12
I am not sure what you need help with exactly but
3 ÷ 1/4 = 12
Reason: 3 ×4/1 = 12 3×4= 12/1 take off the 1 and the answer is 12
why 4/1 you would find the reciprocal of 1/4 and the reciprocal of 1/4 is 4/1 or just 4 you dont need the 1 but if you cant handle your math problem without the 1 you can use it but always remember to take out the 1 in your final answer.
I really hopes this helps you.
Which inequality correctly compares 2/5, 1/8, and 5/7
• 1/8 < 2/5 < 5/7
• 1/8 < 5/7 < 2/5
• 2/5 < 5/7 < 1/8
• 2/5 < 1/8 < 5/7
Plz be quick I’m being timed
Answer:
second or last
Step-by-step explanation:
Answer: 1/8 < 2/5 < 5/7
Step-by-step explanation:
bill planted 4 pecan trees and 2 apple trees what fraction of that is pecan
Answer:
4 / 6 or 2/3
pecan total tree
Answer:
2/3
Step-by-step explanation:
So, Bill planted -
Pecan trees = 4
Apple trees = 2
Total trees = 6
We want the fraction of Pecan trees. Thus,
4/6
Where 4 is Pecan trees, (What we want)
And 6 is the total.
4/6 in its simplest form is 2/3.
I hope it helps.
help please ill give the person who answeres honstly a biranly and 25 points ofc ofc
Answer:
Alright I’ll go in order
Well first things first I’m gonna make the numbers in order first to make life easier
22, 36, 39, 39, 40, 40, 41, 42, 45, 46, 46, 49
#1: Is asking for the median of the data
The median is basically the center of the data in order
In this case the middle number here is 40 and 41, we jsut find the average between those 2 to find it. 40+41= 81 81/2= 40.5
Median :40.5
#2: Is asking for the mode
The mode is the number that comes up or repeats the most.
in this case it’s 39, 40, and 46
Mode: 39, 40, 46
#3: Is asking for the mean
The mean is basically the average, you add up all the given numbers and divide it by the amount of numbers there are. In this case it goes something like
22+36+39+39+40+40+41+42+45+46+46+49
you would get 446
Now theres 12 numbered so we divide that by 12
446/12 you’d get 37 1/6 as ther average or 37.166666666666…
#4: Is asking for the range
You just find the difference ebetween the greatest number and llowest number. In this case it’s 49-22 so you got 27
Range: 27
I think you can figur the rest out on your own!
PLEASE NO LINKS DONT WASTE YOUR TIME IM NOT GONNA CLICK. Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
Answer:
B.
Step-by-step explanation:
factored form actually contains the x intercepts right in it. Basically whatever sets the whole equation equal to zero.
On the graph you can see that it passes through both positive and negative 4. so (x+4)(x-4) is the answer because plugging in 4 for x will make it zero. Same for plugging in negative 4
Hope this helps!
Similar Triangles
In the figure below, AB has length 6 feet, BC has length 8 feet and CD has length 7 feet.
If angles B and D are right angles, what is the length of DE rounded to the nearest tenth foot?
Answer:
5.3 ft
Step-by-step explanation:
Because CD corresponds to BC, the scale factor from triangle ABC to triangle CDE, is 7/8. Now, DE corresponds to AB, so to get DE, we must multiply the value of AB by 7/8. 6 times 7/8 is 5.25, and rounding to the nearest tenth of a foot, the value of DE is 5.3.
The two numbers are in the ratio of 4:5 and the sum of these numbers in981 find the numbers
Answer:
Step-by-step explanation:
let x be the larger number
x + (4/5)x = 981
(9/5)x = 981
x = 981(5/9)
x = 545
(4/5)(545) = 436
ADD the given the polynomials: (x + 2) + (8x + 4)
CHOOSE THE RIGHT ANSWER:
A] 9x + 6
B] 8x + 6
C] 7x + 6
D] 9x + 8
NEED SOLUTION PLS!
Answer:
the answer is 9x + 6 ......
Answer:
[tex] = > (x + 2) + (8x + 4)[/tex]
[tex] = > x + 2 + 8x + 4[/tex]
[tex] = > x + 8x + 2 + 4[/tex]
[tex] = > 9x + 6[/tex]
In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?
Given that
In a Parallelogram CARS ,∠C = (5x-20)°
∠A = (3x+20)°
angle C and angle A are adjacent angles
We know that
In a Parallelogram the adjacent angles are supplementary.
⇛∠C + ∠A = 180°
⇛ (5x-20)°+(3x+20)° = 180°
⇛5x°-20°+3x°+20° = 180°
⇛(5x°+3x°)+(20°-20°) = 180°
⇛8x°+0 = 180°
⇛8x° = 180°
⇛ x° = 180°/8
⇛ x° = 22.5°
Answer:-The value of x = 22.5°
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how is 7 square root 2 is equal to 49?
Answer:
Square root is how many times your multiply the number by itself. So 7 square root 2 is 7x7 which is 49.
