The profit equation is:
p(x) = -0.5*x^2 + 70x - 200
The domain is:
x ∈ [0, 140], such that x ∈ Z
and the profit is larger for 70 items.
We know that:
Cost equation:
c(x) = 50*x + 200
revenue equation:
r(x) = -0.5*(x - 120)^2 + 7,200
The maximum capacity is 140
Then x can be any value in the range [0, 140]
We want to find the profit equation, remember that:
profit = revenue - cost
Then the profit equation is:
p(x) = r(x) - c(x)
p(x) = ( -0.5*(x - 120)^2 + 7,200) - ( 50*x + 200)
Now we can simplify this:
p(x) = -0.5*(x - 120)^2 + 7,200 - 50x - 200
p(x) = -0.5*(x - 120)^2 + 7,000 - 50x
p(x) = -0.5*(x^2 - 2*120*x + 120^2) + 7,000 - 50x
p(x) = -0.5*x^2 + 120x - 7,200 + 7,000 - 50x
p(x) = -0.5*x^2 + 70x - 200
Now we want to answer, what is the domain of p(x)?
The domain is the set of the possible inputs of the function.
Remember that x is in the range [0, 140], such that x should be a whole number, so we also need to add x ∈ Z
then:
x ∈ Z ∧ x ∈ [0, 140]
Then that is the domain of the profit function.
Now we want to see the profit for 70 and 80 items, to do it, just evaluate p(x) in these values:
70 items:
p(70) = -0.5*70^2 + 70*70 - 200 = 2,250
p(80) = -0.5*80^2 + 70*80 - 200 = 2,200
So the profit is smaller for the larger number of items, why does this happen?
You can see that the profit equation is a quadratic equation with a negative leading coefficient, so, as the value of x increases after a given point (the vertex of the quadratic) the profit will start to decrease.
If you want to learn more about quadratic functions, you can read:
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Can someone help me pls?
Answer:
x = 17.2
Step-by-step explanation:
cos 35 = x/21
0.8192(21) = x
x = 17.2
Consider the probability that no less than 95 out of 152 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 61%. Approximate the probability using the normal distribution. Round your answer to four decimal places.
Answer:
0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume the probability that a given registered voter will vote in the presidential election is 61%.
This means that [tex]p = 0.61[/tex]
152 registed voters:
This means that [tex]n = 152[/tex]
Mean and Standard deviation:
[tex]\mu = E(X) = 152*0.61 = 92.72[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{152*0.61*0.39} = 6.01[/tex]
Probability that no less than 95 out of 152 registered voters will vote in the presidential election.
This is, using continuity correction, [tex]P(X \geq 95 - 0.5) = P(X \geq 94.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 94.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{94.5 - 92.72}{6.01}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a pvalue of 0.6179
1 - 0.6179 = 0.3821
0.3821 = 38.21% probability that no less than 95 out of 152 registered voters will vote in the presidential election.
An environmentalist wants to find out the fraction of oil tankers that have spills each month. Step 1 of 2: Suppose a sample of 211 tankers is drawn. Of these ships, 146 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate of the proportion of oil tankers that had spills is 65/211 = 0.308.
Step-by-step explanation:
Proportion of oil tankers that had spills.
Number of tankers with spills divided by the total number of tankers.
In this question:
211 tankers
146 did not have spills, so 211 - 146 = 65 had
Proportion:
[tex]p = \frac{65}{211} = 0.308[/tex]
The estimate of the proportion of oil tankers that had spills is 65/211 = 0.308.
33x + 55 > 17 solution
Answer:
Step-by-step explanation:
33x > -38
x > -38/33
Which is the equation of a line perpendiculat to the line with the equation 3x + 4y = 7?
Answer:
What do you need to know?
Step-by-step explanation:
Answer:
Step-by-step explanation:
At Yogurtland, the scale says that Brooke has 9 ounces of chocolate yogurt in her cup. Brielle's yogurt weighs 13 ounces. How many pounds of frozen yogurt did they buy altogether? Express your answer as a mixed number.
Answer:
1.375 pounds
Step-by-step explanation:
have a nice night mate
:)
mark brainliest please :)
help me answer this question please
Answer:
x = 12 ft, y = 24 ft
12 ft x 24 ft
Step-by-step explanation:
12 x 24 = 288 ft²
2(12) + 24 = 48 ft fencing
Caroline misses 25% of the free throws she attempts in a season. How many total free throws did she attempt if she missed 39?
Answer:
156
Step-by-step explanation:
39 * 4 = 156
There 25 pieces what is the probability of 1st pulling out a circle putting it back then pulling out a square
Answer:
3.6
Step-by-step explanation:
In which step did the student make the first error?
step 1
step 2
step 3
step 4
Answer:
there is no picture for us to see so we can't answer it.
Step-by-step explanation:
sorry
Answer:
C: step 2 (Took the test on edge got 100%)
Step-by-step explanation:
Your question was incomplete you have forgotten to include the graph necessary to answer.
can u tell me is this test important or not
Answer:
Yes, indeed it is one of the most important examinations.
determine the difference of the place value of 7s
in 3701 4472
Answer:
Place value of 1st digit=7,000,000
,,. ,,,. ,,,. of 2nd digit= 70
Difference= 7,000,000-7
You get 6,999,930
This is your answer. If I'm right so,
Please mark me as brainliest. thanks!!!
Find the missing measure
In 1995, there were 20 wolves in Yellowstone. In 2005 there were 120. Find the percent of change.
Answer:
500% increase
Step-by-step explanation:
A rectangle measures 2 1/2 meters by 1 3/4 meters. What is its area?
Answer:
4 3/8
Step-by-step explanation:
1. We can use the formula
Area = L (length) x W (width)
2. The area is unknown so we can substitute it for a
The length and width are both known, so we can plug them in.
a= 2 1/2 x 1 3/4
3. Solve by multiplying
a=4 3/8
Area of the rectangle is [tex]4\frac{3}{8}[/tex] meter square
What is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface
What is rectangle?Rectangle is a quadrilateral with four right angles
Area of the rectangle = Length × Width
Length of the rectangle = [tex]2\frac{1}{2} =\frac{5}{2}[/tex]
Width of the rectangle = [tex]1\frac{3}{4}=\frac{7}{4}[/tex]
Area of the rectangle = [tex](\frac{5}{2}).(\frac{7}{4})=\frac{35}{8}=4\frac{3}{8}[/tex] meter square
Hence, the area of the rectangle is [tex]4\frac{3}{8}[/tex] meter square
Learn more about Area and rectangle here
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Help please I’ll give the brainliest
Answer:
Step-by-step explanation:
a)
5.75x + 3.25y ≤ 625
b)
55 youth shirts
5.75x + 3.25 (55) ≤ 625
5.75x + 178.75 ≤ 625
5.75x ≤ 446.25
x ≤ 77.6086....
so 77 adult t-shirts
Name
Week 5 Test Taking Skills, Page 1
1
7
The weight of a box of rice is
8
pound. If Mrs. Ortega buys 6 boxes of rice, how many pounds of rice is she
buying?
Rice
Rice
Rice Rice Rice Rice
Weight Weight Weight? Weight |
Weight? Weight?
A
5 1 / 2
1b
B
Ib
8
с
4 - lb
D
5 lb
Answer: D - 5 1/4
Step-by-step explanation:
7/8 x 6 = 5.25
5.25 = 21/4
21/4 = 5 1/4
Answer:
D) 5 1/4
Step-by-step explanation:
what is the length of x ??
Which of the following statements is NOT true for figures and their dilation when the origin is the center of dilation?
Answer:
Here are two ways to help with dilation as cm counting can help and so can division.
Step-by-step explanation:
1. Image of a Button enlarged 5 times and shows it is 6cm image is divided by 5 and shows a decimal 1.2 etc. so you write 1.2cm
2. Coordinates shown of A : B : C can be found from their cm measurement we measure the AB and BC measure being; Adjacent (m1) and Hypotenuse (m2) in cm and include any decimals. alternately if they are difficult to count then we take coordinates of AB BC or any adjacent and hypotenuse coordinates to suit y2-y1 / x2-x1 and enter those as our measure and just ensure they are turned positive to enter into calculator.
Note m = measure here found after the above is done.
Then Calculate Adjacent / Hypotenuse = m1/m2 = multiplier
Then input the multiplier to cos-1 found on your shift button.
5. Consider the contexts the follow.
a. Create a table for each context.
b. Graph the data in each table.
c. Determine a recursive rule then an explicit equation that fits each context.
Context D: The Rowing Team is selling cookies for $1 each. A friend is selling the cookies and allows you to pay later for cookies you buy beyond the $3 you have in your pocket. How much will you pay your friend if you buy C cookies? (Negative dollars are dollars you pay your friend after the sale).
Answer:
d
Step-by-step explanation:
1+3=4
I need help if you awnser right I will mark you
Answer:
300
Step-by-step explanation:
I think like 70 precent sure
) Cars are parked in line as they come off the assembly lines. There are three models: red cars which take up 2 spaces, blue cars which also take up 2 spaces, and green cars which take up only 1 space. Let an be the number of ways of filling the first n parking spaces with red, blue and green cars.
Answer:
Hello your question has some missing information below is the complete question
answer :
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
Step-by-step explanation:
Red car and Blue car take up 2 spaces each
Green cars take up 1 space
lets determine the number of ways of filling up the parking spaces
i) First lets assume the last space is filled by Green car then there will be [tex]n^{th}[/tex] space occupied hence there will be ( n - 1 ) spaces left to be filled in [tex]a_{n-1}[/tex] ways
ii) lets assume the last space is filled by either a Red car or a Blue car then there will be [tex]n^{th} + ( n -1 )^{st}[/tex] parking space occupied hence there will be
( n - 2 ) spaces left to be filled in [tex]a_{n-2}[/tex] ways
Hence A closed formula for [tex]a_{n}[/tex]
[tex]a_{n} = a_{n-2} + a_{n-2} + a_{n-1}[/tex]
where : a1 = 1 way , a2 = 3 ways
Easy question look at the photo.
Answer:
SSS
Step-by-step explanation:
Answer:
Step-by-step explanation:
sss
A cube is a rectangular prism with the same measurement for length, width, and height. If a cube is 4 inches tall, what is it’s volume?
1/2 + (- 3/4)
1. 1
2. -1
3. -1/4
4. 1/4
Answer:
3. -1/4
Step-by-step explanation:
Similar to doing 0.5-0.75 which ends up as -0.25 which is equal to -1/4
A machine used to fill beverage cans is supposed to put exactly 12 ounces of beverage in each can, but the actual amount varies. The standard deviation of fill volumes is 0.05 ounce. How large a sample of cans must be selected to estimate the population mean fill volume with a 95% confidence interval that has a margin of error of 0.008 ounce? Round your answer UP to the nearest integer.
Answer:
A sample of 151 cans must be selected.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation of fill volumes is 0.05 ounce.
This means that [tex]\sigma = 0.05[/tex]
How large a sample of cans must be selected to estimate the population mean fill volume with a 95% confidence interval that has a margin of error of 0.008 ounce?
We need a sample of n.
n is found when M = 0.008. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.008 = 1.96\frac{0.05}{\sqrt{n}}[/tex]
[tex]0.008\sqrt{n} = 1.96*0.05[/tex]
[tex]\sqrt{n} = \frac{1.96*0.05}{0.008}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.05}{0.008})^2[/tex]
[tex]n = 150.1[/tex]
Rounding up:
A sample of 151 cans must be selected.
5
Given volume of rectangular prism is 432 m.
h
12 m
4 m
Find height?
Answer:
9m
Step-by-step explanation:
volume = length x width x height so
432 / 12 / 4 = 9
Lola purchases music from two online services. Company A charges Lola a $10
subscription fee plus 89 cents for each song. Company B charges no subscription fee but
$1.19 per song. What is the minimum number of songs Lola would have to purchase for
Company A to be the cheaper option?
9514 1404 393
Answer:
8. (c) 34
9. 38 women
Step-by-step explanation:
8. The price for s songs is ...
A = 10 +0.89s
B = 1.19s
We want A < B, so ...
10 +0.89s < 1.19s
10 < 0.30s
33.33... < s
Lola would have to purchase 34 songs for Company A to be the cheaper option.
__
9. Let m represent the number of men. Then the number of women (w) is ...
w = 4m+2
The total of men and women is 47, so we have ...
m + w = 47
m + (4m +2) = 47
5m = 45 . . . . . . . . . subtract 2
m = 9 . . . . . . . . . . . .divide by 5
4m +2 = 4(9) +2 = 38 . . . . find the number of women
The PTA has 38 women in it.
HURRY IM TIMED ON EDGE Which is the best estimate for the percent equivalent to 3/8?
26%
279%
37%
38%
Answer:
C.) 37%
Step-by-step explanation:
[tex]\frac{3}{8}[/tex] as a percentage is 37.5%
[tex] \purple{ \huge{\mathtt{✨Answer✨}}}[/tex]
C. 37%
which statement about this triangle is true?
tan 0= 4/5
sin 0 = 3/5
cos 0 = 3/5
sin 0 = 3/4
Answer:
I'm not sure but I believe it is than 0=4/5