Given:
The cost function is:
[tex]C(x)=0.28x^2-0.7x+1[/tex]
where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands.
To find:
The minimum production cost.
Solution:
We have,
[tex]C(x)=0.28x^2-0.7x+1[/tex]
It is a quadratic function with positive leading efficient. It means it is an upward parabola and its vertex is the point of minima.
If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the parabola is:
[tex]\text{Vertex}=\left(-\dfrac{b}{2a},f(-\dfrac{b}{2a})\right)[/tex]
In the given function, [tex]a=0.28, b=-0.7, c=1[/tex]. So,
[tex]-\dfrac{b}{2a}=-\dfrac{-0.7}{2(0.28)}[/tex]
[tex]-\dfrac{b}{2a}=1.25[/tex]
Putting [tex]x=1.25[/tex] in the given function to find the minimum production cost.
[tex]C(x)=0.28(1.25)^2-0.7(1.25)+1[/tex]
[tex]C(x)=0.28(1.5625)-0.875+1[/tex]
[tex]C(x)=0.4375+0.125[/tex]
[tex]C(x)=0.5625[/tex]
Therefore, the minimum production cost is 0.5625 million dollars.
Answer:
The minimum cost is 0.5625.
Step-by-step explanation:
The cost function is
C(x) = 0.28x^2 - 0.7 x + 1
Differentiate with respect to x.
[tex]C = 0.28x^2 - 0.7 x + 1\\\\\frac{dC}{dt} = 0.56 x - 0.7\\\\\frac{dC}{dt} = 0\\\\0.56 x - 0.7 = 0\\\\x = 1.25[/tex]
The minimum value is
c = 0.28 x 1.25 x 1.25 - 0.7 x 1.25 + 1
C = 0.4375 - 0.875 + 1
C = 0.5625
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
What balance will be in an account that has an initial deposit of $4600 with an APR of
1.8%? The money is compounded quarterly for 30 years.
How much interest has been earned for the entire time period?
Answer:
100$or 20.4 that is the answer
Can someone help please
9514 1404 393
Answer:
(b) f(x) = (-x)^(1/2)
Step-by-step explanation:
The square root is only defined for argument values that are non-negative. Hence the domain of ...
f(x) = (-x)^(1/2)
is all values of x less than or equal to zero. This is not "all values of x."
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
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 that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Alonzo finish history assignment and 5/8 hours then he completed his math assignment and 1/3 hours what was the total amount of time allowed to spend doing these two assignments
Step-by-step explanation:
The answer is 5/8 + 1/3
Answer = 5*3 /(8*3) +8/24 =23/24
Answer = 23/24
A number is multiplied by 5 and the answer when divided by 3 gives 1315 . what is the number ?
Answer:
5×789/3
Step-by-step explanation:
According to the question you could simplify the above numbers .
Answer:
789
Step-by-step explanation:
let the number=x
[tex]\frac{5x}{3}=1315\\5x=1315 \times 3=3945\\x=\frac{3945}{5}=789[/tex]
Need the answer plz.
Suppose 180 randomly selected people are surveyed to determine whether or not they plan on voting to reelect the current president. Of the 180 surveyed, 36 reported they will not vote to reelect the current president. Identify the values needed to calculate a confidence interval for the proportion that will not vote to reelect the current president at the 99% confidence level. Then find the confidence interval.
Answer:
(0.123 ; 0.277)
Step-by-step explanation:
Given :
Sample size, n = 180
x = 36
Proportion, p = x / n = 36/180 = 0.2
Confidence interval for sample proportion :
Confidence interval :
p ± Zcritical * √p(1 - p) / n
Zcritical at 99% = 2.576
0.2 ± 2.576 * √0.2(1 - 0.2) / 180
0.2 ± 2.576 * 0.0298142
0.2 ± 0.0768013792
(0.123 ; 0.277)
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Step-by-step explanation:
An arithmetic sequence is of the form:
[tex]A_n = A_{n-1} + d[/tex]
While a geometric sequence is of the form:
[tex]A_n = A_{n-1}*r[/tex]
notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.
In fact, the pattern is kinda easy to see.
The first term is:
A₁ = 2
the second term is:
A₂ = -10
notice that:
A₂/A₍ = r = -10/2 = -5
The third term is:
A₃ = 50
the quotient between the third term and the second term is:
A₃/A₂ = 50/-10 = -5
Whit this we can already conclude that the n-th term of our sequence will be:
[tex]A_n = A_{n-1}*(-5)[/tex]
Then the summation will be something like:
[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]
We can write:
[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]
Then the summation is just:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Which expression is equivalent to this polynomial? 9x^2 + 4
A. (3x+2i)(3x-2i)
B. (3x+2)(3x-2)
C. (3x+2i)^2
D. (3x+2)^2
Plz help, fill in the blanks in order
Please Help!! much appreciated! :D
Find the value of y.
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
I’m in summer school can y’all plz help me
Answer: Choice A. [tex]-x^2+2x+8[/tex]
Work Shown:
[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\[/tex]
which shows the answer is choice A.
Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.
Answer:
hope it helps u plz mark me brainliest mate
Step-by-step explanation:
(f-g)(x)=2x+1-(x^2-7)
(f-g)(x)=2x+1-x^2+7
(f-g)(x)= -x^2+2x+8
this is the correct answer
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
What is the cardinal number of the set {-1,3,7,52,36,19,-6}
Answer:
can you please send me another one
HELP ME PLS!!!!!
Which of the following is | 5-12i |?
A) -√119
B) √119
C) −13
D)13
Answer:
D) 13
[tex]\sqrt{169} = 13[/tex]
Step-by-step explanation:
Consider the following data representing the price of refrigerators (in dollars).14051405, 11211121, 13391339, 10961096, 12991299, 14011401, 11381138, 11491149, 12231223, 10711071, 13991399, 14001400, 12421242, 13181318, 11011101, 10651065, 14281428, 12251225, 13501350, 13581358, 13121312Copy DataPrice of Refrigerators (in Dollars)Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency1049–1118 1119–1188 1189–1258 1259–1328 1329–1398 1399–1468 Step 2 of 7 : Determine the frequency of the fifth class.
Answer:
3
Step-by-step explanation:
Given the data:
1405, 1121, 1339, 1096, 1299, 1401, 1138, 1149, 1223, 1071, 1399, 1400, 1242, 1318, 1101, 1065, 1428, 1225, 1350, 1358, 1312
Using the intervals:
Class interval ___ Frequency
1049–1118 ________ 4
1119–1188 ________ 3
1189–1258 ________3
1259–1328 _______ 3
1329–1398 _______ 3
1399–1468 _______ 5
From the table ; the fifth class is the interval :
1329 - 1398 and it has a frequency of 3
f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
Answer true or false and explain your answer. If it is important not to reject a true null hypothesis, the hypothesis test should be performed at a small significance level.
Answer: No, The goal when testing a hypothesis is to to guess a large significant level to possibly have the answer correct based upon evidence. False. It needs to be a large significant level
Step-by-step explanation:
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker plz simple for class 5 pleeease
Answer:
$150
Step-by-step explanation:
discount=60%
let the price=x
(100-60)% of x=$60
40% of x=60
x=60×(100/40)=150
Is the answer right?
Answer:
one solution.. your answer is correct
Step-by-step explanation:
discriminate = 900 - (4*9*25) = 0
thus only one solution
Need answers please offering 30 points
Answer:
yefeihuerijohiftv3ugrhoerfujfy
Step-by-step explanation:
A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]
Step-by-step explanation:
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value =[tex]t\alpha /2,[/tex] df = 1.771
Margin of error
[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,
[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]
What is 10+2
Please I need help
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Check the picture below
f(x)=-2x^2+x-5 find f(5)
f(5) = -50
Hope it helps you...
What is the length of Line segment A C? Round to the nearest tenth.
Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters.
10.5 m
12.3 m
18.3 m
21.4 m
Answer:
10.5
Step-by-step explanation:
In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.
Answer:
A) 10.5
Step-by-step explanation:
REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:
Please explain this! Thank you!
Supplementary angles are those angles which make a sum of 180°.
Complementary angles are those angles which make a sum of 90°.
The supplementary angles are given by the straight lines making angles of 180°.
There are two straight lines CB and DE
The angles DAF and FAE are the two angles making a straight line DE
The angles CAF and FAB are the two angles making a straight line CB
The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.
Angle BAF is formed by angle BAE and angle AEF
Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.
Complementary Angle BAF is formed by angle BAE and angle AEF.
https://brainly.com/question/12919120
Two vectors m and n are defined by 3i+4j and n=2i-j. find the angle between m and n
Answer:
[tex]{ \tt{m.n = |m| |n| \cos( \theta) }} \\ { \tt{ (3 \times 2) + (4 \times - 1) = (5)( \sqrt{5}) \cos( \theta) }} \\ { \tt{ \cos( \theta) = \frac{0.4}{ \sqrt{5} } }} \\ \theta = 79.7 \degree[/tex]
Find the intersection of the line and the circle given below
2x+y=-5
x^2+y^2=10
Answer:
There are two intersections.
(-3,1) and (-1,-3)
Step-by-step explanation:
Answer:
They intersect at (-3,1), and also (-1,-3)
Step-by-step explanation:
Graph:
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=530x−9240 where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt. what is the slope of the line represent?
A. the GDP per capita of the country with the lowest corruption score
B. the corruption score needed for a GDP per capita of zero
C. the average GDP per capita for every point in the corruption score
D. the increase in GDP per capita for every increase of one in corruption score
Step-by-step explanation:
pandemic times: Potential ... - CAF
have shown evidence that the effect of corruption on real GDP per capita is more pronounced in countries with low levels of8
