The cost to manufacture a product is proportional to the quantity produced, with a cost of $35000 dollars per day when 700 items are produced. The cost to store n items is proportional to the square of n, with a daily storage cost of $3430 dollars when 700 items are stored. In addition, there is a fixed daily cost of $7000. The total daily cost, T when producing and storing n items is the sum of production, storage and fixed costs.
Write a formula for T as a function of n.
Solution :
[tex]$T_1$[/tex] = k.n (cost proportional to quantity)
35000 = k . 700
k = [tex]$\frac{35000}{700}$[/tex]
= 50
So [tex]$T_1$[/tex] = 50 n
Now [tex]$T_2=Pn^2$[/tex] (cost proportional to square of n)
[tex]$3430= P(700)^2$[/tex]
3430 = 490000 P
[tex]$P = \frac{3430}{490000}$[/tex]
[tex]$P = \frac{7}{1000}$[/tex]
[tex]$T_2=\frac{7}{1000}n^2$[/tex]
Now, [tex]$T_3= 7000$[/tex] (fixed)
Therefore,
Total, [tex]$T=T_1+T_2+T_3$[/tex]
[tex]$T=50n+\frac{7}{1000}n^2+7000$[/tex]
[tex]$T=0.007n^2+50n+7000$[/tex]
The required formula in terms of T and n is T = 0.000[tex]n^{2}[/tex] + 50 n +7000.
Given that ,
The total daily cost = T
When producing and storing n items is the sum of production, storage and fixed costs.
The manufacturing cost of a product when 700 items produced = $35000 dollars per day.
Daily storage cost of when 700 items are stored = $3430 dollars
We have write the formula in terms of total daily cost T and n stored items.
According to the question,
The cost to manufacture a product is proportional to the quantity produced, with a cost of $35000 dollars per day when 700 items are produced.
Where ,total daily cost T and n stored items.
[tex]T_1 = k . n[/tex]
$35000 = k.700
[tex]k = \frac{35000}{700}[/tex]
k = $50
The cost to store n items is proportional to the square of n, with a daily storage cost of $3430 dollars when 700 items are stored.
[tex]T_2 = pn^{2}[/tex]
$3430 = P [tex](700)^{2}[/tex]
$3430 = P 490000
[tex]P = \frac{3430}{490000} \\\\P = \frac{7}{1000}[/tex]
There is a fixed daily cost of $7000.
[tex]T_3 = 7000[/tex]
Combine all the equation ,
Where T = [tex]T_1 = T_2 = T_3[/tex] and p = k =n
T = 0.000[tex]n^{2}[/tex] + 50 n +7000
Hence, The required formula in terms of T and n is T = 0.000[tex]n^{2}[/tex] + 50 n +7000.
For the more information about System of equations click the link given below.https://brainly.com/question/14418346
Write the equation of a line in slope- intercept form passing through these two points (-1,-2) and (1,4)
Answer:
y=3x+1
Step-by-step explanation:
4--2=6
1--1=2
6/2=3
slope is 3
4=3(1)+b
4=3+b
4-3=3-3+b
1=b
1 is the y intercept
Answer:
y = 3x + 1
Step-by-step explanation:
(x₁, y₁) = (-1, -2) & (x₂ , y₂) = (1, 4)
[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]= \frac{4-[-2]}{1-[-1]}\\\\= \frac{4+2}{1+1}\\\\= \frac{6}{2}\\\\= 3[/tex]
m = 3
y -y₁ = m(x - x₁)
y - [-2] = 3(x - [-1])
y + 2 = 3(x +1)
y + 2 = 3x + 3
y = 3x + 3 -2
y = 3x + 1
Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are at least 59? Please do not round your answer.
Answer:
1.35%
Step-by-step explanation:
Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical rule, what ? Please do not round your answer.
Empirical rule formula states that:
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
We don't know the number of Standard deviation yet , hence:
Mean = 104
Standard deviation = 15.
At least 59
Hence:
104 - 15x = 59
104 - 59 = 15x
45 = 15x
x = 45/15
x = 3
Hence, At least 59 is 3 standard deviations away from the mean on one side of the distribution thus,
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
100% - 99.7%
= 0.003
Since it is on one side of the distribution:
= 1.5% - 0.3%
= 0.015 - 0.0015
= 0.00135
Converting to percentage
= 1.35%
The percentage of IQ scores that are at least 59 is 1.35%
Jeremy buys a value pack of cheese crackers that contains 42 1/2 ounces of crackers. He divides this into servings of 1 1/4 ounces each. What is the total number of servings Jeremy can make from the value pack?
A. 34 servings
B. 44 servings
C. 53 servings
D. 85 servings
Answer:34
Step-by-step explanation:
(8j + 1) + (6j + 8)
...
Answer:
Step-by-step explanation:
creo que es 14j+9
Answer:
14j + 9
Step-by-step explanation:
(8j + 1) + (6j + 8)
8j + 1 + 6j + 8
14j + 9
Which equation illustrates the additive inverse property?
Answer:
A.
Step-by-step explanation:
A negative of the same value added to positive always gives you 0
negative is inverse of positive
What is 1/3 of 1/9 of a ton?
Make sure your answer is fully reduced
Answer:
0.03703703703
Step-by-step explanation:
Evaluate the function f (x) = 4x^2 - 10x + 2 find f (-7)
Answer:
268
Step-by-step explanation:
Substitute -7 where x is in the equation which would be 4(-7)^2 -10 (-7) +2
simplify the equation and you should get 268
This is confusing if you can help me with this ASAP if your able to
Answer:
Step-by-step explanation:
5^2-3^2= 16
25-9=16
On a coordinate plane, a line goes through (negative 4, 0) and (0, 2).
The graph of the equation y = 1
2
x + 2 is displayed. Which equations would intersect the orange line at the y-intercept? Check all that apply.
y = 7x + 2
y = 3x + 5
y = 2 minus StartFraction 7 Over 3 EndFraction x
y – 2 = 4x
3y = –9x – 6
Answer:
y – 2 = 4x
3y = –9x – 6
Step-by-step explanation:
Answer:
a, c, d
Step-by-step explanation:
(2/3x+2) - (1/3x - 4)
Answer:
simplified: 6 + x/3
Step-by-step explanation:
(2/3x+2) - (1/3x - 4)
= 6 + x/3 .
Hope this helps !
A number is ten less than four times another number”?
Answer:
14
Step-by-step explanation:
4y-10 + y = 20
5y - 10 = 20
5y = 30
y = 6
and then
x = 14
Kit made contributions to a Roth IRA over the course of 30 working years. contations average $2.000 in the exact she
on the account was 6. Upon retirement, stopped working and making Roth IRA Contributions stead been on trommet
tax bracket. Factoring in taxes, what is the effective value of Roth IRA a brement assume annual compounding (3)
O $287.432.74
$305.432.74
$240 335.88
O $298 232.74
Answer: the third i think
I don't know how to do that
Answer:
[tex] \frac{x}{ - 6} \geqslant - 20[/tex]
[tex]x \geqslant - 20 \times ( - 6)[/tex]
[tex]x \geqslant 120[/tex]
Is there a proportional relationship between x and y? Explain.
Answer:
Where's the question?
Step-by-step explanation:
Plz help me
Clark made four of his truck payments late and was fined four late fees. The total change to his savings from late fees was -$40. How much was one late fee?
Answer:
-10
Step-by-step explanation:
If he has four trucks and the total was -40 then one is 10
Divide 40÷10 =10
Answer: the answer is 10
Step-by-step explanation:
Find the x- and y-intercepts from the table.
Answer:
x-intercept = 5
y-intercept = 350
Step-by-step explanation:
Assuming that h=x and m=y, when x is at 0 the y is at it's intercept giving you a y-intercept of 350. When y is at 0 the x is at it's intercept giving you an x-intercept of 5.
What are equivalent fraction to 33/48 with the numeration as 11
Answer:
11/16
Step-by-step explanation:
The first thing I would do is see 11 times what will get me 33
The answer is 3
Next I would ask myself 48 divided by 3 is what
The answer is 16
To double check my work I would do 3 x 11 = 33
3 x 16 = 48
The distance around a circular track a.circumference
b.area
Answer: Circumference
Step-by-step explanation: The distance around a circle on the other hand is called the circumference (c). Half of the diameter, or the distance from the midpoint to the circle border, is called the radius of the circle (r). Consider marking this answer as brainliest if it helped you out.
Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this?A. Set the value for a Type II error at 0.05.
B. Set the alpha level at 0.05.
C. Place the rejection region in both tails.
D. Both setting the alpha level at 0.05 and placing the rejection region in both tails.
Answer:
B. Set the alpha level at 0.05.
Step-by-step explanation:
Hypothesis testing is a procedure whereby a researcher determines if the null hypothesis is rejected or accepted, depending on the significant level or the alpha level. When a type I error is made, the null hypothesis is rejected even though it is correct. To solve this problem, the significant or alpha level is set to 5% or 0.05.
At a summer job, Maya is painting houses. She charges a $100 fee to start a job and $25 per
hour for each hour she spends on the job. Complete the table belly to show how much
money Maya makes painting one house.
Answer:
the answer would 125
Step-by-step explanation:
Answer:
I think the answer will be 225. Because 1st she got 100 for starting the job and 25 $ for per hour. She did 5 hours. So five times 25 . It will be 125 and 100 . The answer is 225
The table represents a linear function.
What is the slope of the function?
x. -2,-1,0,1,2
y.8,2,-4,-10,-16
answers. -6,-4,4,6
Answer:
the answer is a
Step-by-step explanation:
The average student college loan rate is 4%. You borrowed $18,000 per year for 4 years for tuition, room, & board. If the interest is computed as simple interest, annually, how much interest will you owe when you graduate. Assume 4 years interest on the freshman year loan, 3 years on the sophomore loan, 2 years on the junior loan, and 1 year on the senior loan.
Answer:
$7200
Step-by-step explanation:
How do you solve 3 1/2 ÷ 2 5/6
Answer:
1 4/17
Step-by-step explanation:
3 1/2 ÷ 2 5/6
= 7/2 ÷ 17/6
= 7/2 * 6/17
= 21/17
= 1 4/17
Which expression means "y more than seven"?
Answer:
7+y
Step-by-step explanation:
Hey! I just want to make sure if I'm right, if I'm not, whats the answer? I'm stuck on this but I will highly appreciate it if you can help me. if you can't see the question clearly, here it is.
Veron adds some flour to a partially filled bin by pouring it
in at a constant rate until the flour reaches the brim. He
stops pouring flour when the bin is full.
Which graph could represent this scenario?
Answer:
Step-by-step explanation:
Veron adds some flour to a partially filled bin by pouring it
in at a constant rate until the flour reaches the brim. He
stops pouring flour when the bin is full.
Which graph could represent this scenario?
How far is `50\%` of a `2,000`-kilometer trip?
How do I write "the value of y is the square of the quantity two minus the value of x"?
Answer:
(y x 2) -x
Step-by-step explanation:
Idk anything about math please I need help
Answer:
21 boys
Step-by-step explanation:
2:3=14:x you cross multiply this to find the amount of boys
2x=42
x=21
There are 21 boys in the class.
Basically, solve what you have there with cross-multiplication.
2x = 14 x 3
2x = 42
Then divide both sides by 2. (edited it bc didn't say what you actually had to do)
2x ÷ 2 = 42 ÷ 2
x = 21.
There are 21 boys in the class.
What is a fraction form of 1.80
Answer: I think it's 1 4/5
Answer:
180/10
Step-by-step explanation:
1.80=180
1/10th of 180 is 18
18 times 10 is 180