At x = 1000 we get the c(1000) = 2000,000. Second statement 'one thousand units have the maximum cost of $200,000' is true.
It is given that the function [tex]\rm c(x)=400x-0.2x^2[/tex] represents the total costs for a company to produce a product, where c is the total cost in dollars and x is the number of units sold.
It is required to find which statement is true, mentioned in the question.
What are the maxima and minima of a function?Maxima and minima of a function are the extrema within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a function:
[tex]\rm c(x)=400x-0.2x^2[/tex]
To find the maxima and minima of any function we differentiate the function with respect to [tex]\rm x[/tex] and equate to zero.
[tex]\rm \frac{d \ c(x)}{dx} =\frac{d}{dx} (400x-0.2x^2)[/tex]
[tex]\rm \frac{d \ c(x)}{dx} =\frac{d}{dx} (400x)-\frac{d}{dx} (0.2x^2)\\\rm \frac{d \ c(x)}{dx} =400-(0.2\times2x)\\\rm \frac{d \ c(x)}{dx} =400-0.4x[/tex]
For maxima and minima [tex]\rm \frac{d \ c(x)}{dx} =0[/tex]
[tex]\rm 400-0.4x=0\\\rm x=\frac{400}{0.4} \\\rm x=1000[/tex]
If we find the seconnd differentiate, we get
c''(x) = -0.4 < 0
It means at x = 1000 we will get the maximum value of a function.
[tex]\\\\\rm c(1000) = 400(1000) - 0.2(1000)^2\\\rm c(1000)= 200,000[/tex]
Thus, at x = 1000 we get the c(1000) = 2000,000. Second statement is true.
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Answer:
B
Step-by-step explanation:
To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0. C(x) = 400x - 0.2x² dC(x) / dt = 400 - 0.4 x = 0 The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation, C(x) = (400)(1000) - 0.2(1000²) = $ 200,000Thus, the answer is letter B.
Make a scatter plot of the data pairs, (year, revenue). Draw a trend line and write its equation. Predict the revenue of US theme parks in 2012. Someone help me please.
i think its 9.9 but if its not that its 8.7
The revenue of US theme parks in 2012 is 14.5 in dollars.
What is scatter plot?Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.
From the given table, (1990, 5.7), (1992, 6.5), (1994, 7.0), (1996, 7.9), (1998, 8.7), (2000, 9.6), (2002, 9.9), (2004, 10.8), (2006, 11.5).
Using the coordinates (1990, 5.7) and (1992, 6.5), we get
Slope m=(6.5-5.7)/(1992-1990)
= 0.8/2
= 0.4
Substitute m=0.4 and (x, y)=(1990, 5.7) in y=mx+c, we get
5.7=0.4×1990+c
c=5.7-796
c=790.3
Substitute m=0.4 and c=-790.3 in y=mx+c, we get
y=0.4x-790.3
Substitute x=2012, we get
y=0.4×2012-790.3
y=804.8-790.3
y=14.5
Therefore, the revenue of US theme parks in 2012 is 14.5 in dollars.
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using the spinner above, what is the probability that you land on red or blue?
Answer:
75%
Step-by-step explanation:
red is 50 and the blue is 25
evaluate the following expression
(a+b)^0
Sunny earns $12 per hour delivering cakes. She worked for x hour this week. Unfortunately, she was charged $15 for late delivery on Tuesday. How much money did sunny earn this week? Write your answer as an expression.
The expression that can be used to represent the total money earned is $12x - $15.
What expression represents the total amount earned?
The first step is to determine the total amount earned this wek. This can be determined by multiplying the earnings per hour by the total hours/
Total earnings = $12 ×x = $12x
Now subtract the late delivry charge = $12x - $15
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Answer:
12x-15
Step-by-step explanation:
khan
The beginning balance in a checking account is $64.98.
After a deposit of $73.87 and two withdrawals of $51.00 and $23.50, what is the balance?
O $189.85
O $138.85
O $87.85
O $64.35
Answer:
D) 64.35
Step-by-step explanation:
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Bill wants to order new jerseys for his baseball team. He has found two different companies and needs to determine which one is the better deal for his team. PRINT IT sells jerseys for $21.0 each. TOP PRINT a onetime set up cost of $45.0 and jerseys for $18.0 each. A. Write a system of equations for this situation.
Answer:
[tex]Cost = 21.0j[/tex] --- PRINT IT
[tex]Cost = 45.0 +18.0j[/tex] --- TOP PRINT
Step-by-step explanation:
Given
Print IT & Top Print
Represent the number of jerseys with j.
For PRINT IT.
[tex]Cost=\$21.0[/tex] per jersey
For Top Print
[tex]Base\ Amount = \$45.0[/tex]
[tex]Cost = \$18.0[/tex] per jersey.
j jerseys with PRINT IT will cost: [tex]21.0 * j[/tex]
[tex]Cost = 21.0 * j[/tex]
[tex]Cost = 21.0j[/tex]
j jerseys with TOP PRINT will cost: [tex]45.0 +18.0 * j[/tex]
[tex]Cost = 45.0 +18.0j[/tex]
A triangle has two sides of length 11 and 12. What is the smallest possible whole-number length for the third side?
Answer: 2
To maximize the length of the third side, which I'll call x, it needs to be one of the two shorter sides.
So by the triangle inequality theorem, 11+x>12 meaning the minimum whole number value of x is 2.
n - Are x = 4 and y = 8 solutions of the equation: y = x² - 2x + 1? Circle: Yes or No
Answer:
No
Step-by-step explanation:
put 4 where x is and 8 where y is
y = x² - 2x + 1
does
8 = 4^2 -2(4) + 1
8 = 16 -8 + 1
8 = 9
Does 8 = 9 ?
No
Select the correct answer from each drop-down menu. To find the average grades scored by students in science and math, the principal of a school sends a questionnaire to the top five students in each grade of the high school. Is the sample used by the principal random? Will a generalization from this sample be valid? The sample used by the principal is. A generalization made from this sample is.
Answer:
a) This is not a random sample
b) The generalization from this sample would not be valid
Step-by-step explanation:
No the sample is not random. If the questionnaire would had been send to any five students in a class irrespective of whether they are among the top five, then the sample could be referred as random sample.
The marks of top five students in any grade would give an average value that will be an outlier to the average of marks of all students with in a grade.
Hence, the generalization from this sample would not be valid
Simplify
I don’t get this subject
Answer: 3
You're going to multiply 3 by 2 which gives you 6. you then have 6 over 2. Next find a number that goes into both of them which is 2 in this case. So now you divide the top and bottom by 2, so now you have 3 because two divided by two is zero, that is as small as it gets.
Geometry help!!!!!!!
Answer:
[tex]\huge\boxed{\text{The polygons are NOT similar}}[/tex]
Step-by-step explanation:
Because triangle DBC has an angle of measure 49°, and triangle IHJ does not, the polygons are not similar.
Hope it helps :) and let me know if you want me to elaborate.
Serenity is moving and must rent a truck. There is an initial charge for the rental plus
a fee per mile driven. The total cost of renting the truck can be modeled by the
equation C = 50 +2.75m, where m is the number of miles driven. What is the y-
intercept of the equation and what is its interpretation in the context of the problem?
Answer:
The y-intercept of the equation is 50
Its interpretation in the context is " the initial charge for the rental "
Step-by-step explanation:
The linear relationship can be represented by the equation
y = a x + b, where
a is the slope ( the rate of change)b is the y-intercept (initial amount, or fixed amount, or the amount of y at x = 0)∵ Serenity is moving and must rent a truck
∵ There is an initial charge for the rental
∴ b represents the initial charge for the rental
∵ There is a fee per mile driven
∴ a represents the fee per mile driven
∵ The equation represents this situation is C = 50 + 2.75 m
∵ C is the total cost
∵ m is the number of miles driven
→ Compare it with the form of the equation above
∴ a = 2.75
∴ b = 50
∵ b is the y-intercept
∴ The y-intercept of the equation is 50
∵ b represents the initial charge for the rental
∴ The initial charge for the rental is $50
∴ Its interpretation in the context is " the initial charge for the rental "
A restaurant sends customers in their loyalty program a coupon for a free birthday dessert. Suppose that 8\%8%8, percent of the children and 12\%12%12, percent of the adults redeem their coupons. The restaurant takes separate random samples of 100100100 children and 909090 adults from their loyalty program to see the difference between the sample proportions (\hat{p}_\text{C}-\hat{p}_\text{A})( p ^ C − p ^ A )left parenthesis, p, with, hat, on top, start subscript, start text, C, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, A, end text, end subscript, right parenthesis. What will be the shape of the sampling distribution of \hat{p}_\text{C}-\hat{p}_\text{A} p ^ C − p ^ A p, with, hat, on top, start subscript, start text, C, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, A, end text, end subscript, and why?
Using the Central Limit Theorem, it is found that the sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]It also states that when two variables are subtracted, the mean is the subtraction of the means, and the standard deviation is the square root of the sum of the variances.In this problem, for each sample, the mean and the standard error are given by:
[tex]p_C = 0.08, s_C = \sqrt{\frac{0.08(0.92)}{100}} = 0.0271[/tex]
[tex]p_A = 0.12, s_A = \sqrt{\frac{0.12(0.88)}{100}} = 0.0325[/tex]
Then, for the distribution of differences, we have that:
[tex]p = p_C - p_A = 0.08 - 0.12 = -0.04[/tex]
[tex]s = \sqrt{s_C^2 + s_A^2} = \sqrt{0.0271^2 + 0.0325^2} = 0.0423[/tex]
The sampling distribution will be approximately normal, with mean of -0.04 and standard error of 0.0423.
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PLease help me!!!! (:
You' ll get brainliest!!!!
Answer:
The last one
Step-by-step explanation:
The last one is the only one in standard form.
Which of the numbers below could be terms in the sequence an=7n +4?
24
46
32
36
Answer:
46
Step-by-step explanation:
46 - 4 = 42
42/7 = 6
Answer:46 and 32 just did the quiz
Step-by-step explanation:
8.55 l=_______ml ?
Help
Answer:
8550
Step-by-step explanation:
Find the total surface area of this triangular prism.
10 cm
6 cm
4 cm
8 cm
Answer:
144cm^2
Step-by-step explanation:
0.5x8x6x2=48cm^2
8x4=32cm^2
10x4=40cm^2
6x4=24cm^2
=(48+32+40+24)cm^2
=144cm^2
Which of the following represents the fastest speed in miles per hour?
a. 8 miles in ⅙ hour b. 10 miles in ⅕ hour c. 6 miles in ⅐ hour
Answer:
b,
Step-by-step explanation:
8 miles in 1/6 hour 8*6=48 mph
10 miles in 1/5 hour 10*5=50 mph
6 miles in 1/7 hour 6*7 = 42 mph
PLEASE HELP!!! Find the equation of this line. All three answers please!!!
Answer:
[tex]y=-\frac{3}{4}x+3[/tex]
Step-by-step explanation:
formula for the gradient is [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}}[/tex]
we insert our intercepts to get [tex]\frac{0-3}{4-0}=\frac{-3}{4}[/tex]
and our y-intercept (where the line crosses the y-axis) is 3
If I have $6600 after investing $6000 for 5 years, what was the rate? (Write as a percent.)
Answer:
10%
Step-by-step explanation:
6600-6000=600
You've earned $600
600/6000 = 1/10 or 10%
Answer:
1.925%
Step-by-step explanation:
to check, use the equation [tex]6000(1+.01925)^5[/tex]
this gives us the value of 6600.16.
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Rewrite in simplest term: 3(-7h-4)+4(h-6)
Answer:
-17h-36
Step-by-step explanation:
mutiply 3 by each terms inside the parenteses
you will get:
-21h-12+4h-24
-17h-36
Two girls scout troops are completing a wilderness campout. Use the information to answer the questions. The Blue Tripp hikes 2/3 mile every 1/2 hour. The Yellow Troop hikes 3/4 mile every 1/3 hour. How long does it take each troop to walk 1 1/2 miles, 1/2 mile, and 3/4 mile?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Blue tripp:
Hikes 2/3 miles every 1/2 hour
Yellow troop:
Hikes 3/4 miles every 1/3 hour
How long does it take each troop to walk 1 1/2 miles, 1/2 mile, and 3/4 mile?
To hike 1 1/2 miles
Blue troop:
2/3 miles = 1/2 hours
3/2 miles = x
2/3x = 3/4
x = 3/4 * 3/2
x = 9/8 = 1 1/8 hours
Yellow troop:
3/4 = 1/3 hours
3/2 = x
3/4x = 3/6
x = 3/6 * 4/3
x = 12/18 = 2/3 hours
To hike 1/2 mile :
Blue troop:
2/3 miles = 1/2 hours
1/2 miles = x
2/3x = 1/4
x = 1/4 * 3/2
x = 3/8 hours
Yellow troop:
3/4 = 1/3 hours
1/2 = x
3/4x = 1/6
x = 1/6 * 4/3
x = 4/18 = 2/9 hours
To hike 3/4 miles :
Blue troop:
2/3 miles = 1/2 hours
3/4 miles = x
2/3x = 3/8
x = 3/8 * 3/2
x = 9/16 hours
Yellow troop:
3/4 = 1/3 hours
3/4 = x
3/4x = 3/12
x = 1/4 * 4/3
x = 4/12
x = 1/3 hours
Evaluate the expression shown for x=12 -5/6x +7
Answer:-3
Step-by-step explanation:
Look at the photo.
find c! please explain the steps and help me find the answer.
Answer:
34.78
Step-by-step explanation:
using cosine rule
AB^2 = CB^2 + AC^2 -2(CB × AC × COS C)
18^2 = 17^2 + 27^2 -2(27×17×COS C)
324= 289+729- 918COSC
324-289-789= -918COSC
-754= -918COSC
COS C = 754/918
COS C = 0.82135076253
C= arccos(0.82135076253)
C= 34.78(2 dp)
Express as a sum
1) a-5
2) m-n
Express as a difference
1) 7+3
2) a+5
Answer:
I think it would be
Sums
1) a + -5
2) m + -n
Differences
1) 7 - -3
2) a - -5
Step-by-step explanation:
Point s is between points R and T on RT. RS=7 and ST = 11. What is the length of RT?
Answer:
18
Step-by-step explanation:
Because you have to add 11 to 7 and the equals 18. I hope that helped! :)
I need the awnser for number 16 I will brainlist who ever can provide the awnser
Answer:
Not rounded: 1602.342
Rounded: 1602.3
Step-by-step explanation:
Volume of cone : 3.14(r^2)h/3
3.14(9^2) 19/3
3.14(81)19/3
(254.34)19/3
(254.34)6.3
1602.342
Have an amazing day!!!
Please rate and mark brainliest!!
Please help me asap if can!!!
Answer:
Step-by-step explanation:
2m in height : 11m in length
300m in length: 1650m in length
This is because you multiply each side by 150.
The horizontal length will be 1650m.
b) I'm so sorry. I'm in year 9 so I don't think I've learnt this. I think it might be tan. :)
Price is $20.00 Sales Tax is 4% What is the total cost?
Answer:
your answer is correct
Step-by-step explanation:
i don't know why i it didn't work
If the price of an item is $20.00 with a sales tax of 4%, the total cost of the item is $20.80.
How the total cost is determined using the sales tax:The total cost involves adding the price and the sales tax amount.
We can compute the total cost by determining the sales tax factor using the sales tax rate as follows:
The price of the item = $20.00
Sales tax = 4% = 0.04 (4/100)
The sales tax factor = 1.04 (1 + 0.04)
Thus, the total cost, including the price and the sales tax, is $20.80 ($20 x 1.04).
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x-y=1 solve by substitution
Answer:
2-1
Step-by-step explanation: