Answer:
9000 A and 7000 B should be producedp = 100, q = 170$350,000 is the maximum profitStep-by-step explanation:
We assume that "p" and "q" are given in dollars, so that the profit function (in thousands of dollars) can be written:
P = xp +yq -C(x, y)
Profit will be maximized when the partial derivatives of P with respect to x and y are both zero:
∂P/∂x = p +x(∂p/∂x) +y(∂q/∂x) -∂C/∂x = 0
(120 -3x +y) +x(-3) +y(1) -80 = 0
-6x +2y +40 = 0
3x -y = 20 . . . . put in standard form
and ...
∂P/∂y = x(∂p/∂y) +q +y(∂q/∂y) -∂C/∂y = 0
x(1) +(210 +x -7y) +y(-7) -(130) = 0
2x -14y +80 = 0
x -7y = -40 . . . . put in standard form
__
The solution to these simultaneous equations can be found a variety of ways. Using Cramer's Rule, we have ...
x = ((-1)(-40) -(-7)(20))/(-1·1-(-7)(3)) = 180/20 = 9
y = (20(1) -(-40)(3))/20 = 140/20 = 7
9000 type A and 7000 type B earphones should be produced.
__
The corresponding selling prices are ...
p = 120 -3(9) +7 = 100
q = 210 +9 -7(7) = 170
The selling prices should be ...
p = $100, q = $170
__
The maximum profit is ...
P = xp +yq -C(x, y) = (9)(100) +(7)(170) -(110 +80(9) +130(7))
P = 9(100 -180) +7(170 -130) -110 = 180 +280 -110
P = 350
The maximum profit is $350,000.
a man received a salary of 4920 in two years what is his monthly salary?
Answer:
$205 per month
Step-by-step explanation:
Answer:
$205
Step-by-step explanation:
there are 24 months in 2 years
4920/24= 205
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = 1 2 x4 − 4x2 + 5 (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection points.
Answer:
Please, read the answer below.
Step-by-step explanation:
You have the following function:
[tex]f(x)=12x^4-4x^2+5[/tex]
(a) To find the intervals of increase or decrease of f(x) you first calculate the derivative of f(x):
[tex]\frac{df}{dx}=\frac{d}{dx}[12x^4-4x^2+5]\\\\\frac{df}{dx}=12(4)x^3-4(2)x=48x^3-8x[/tex] (2)
Next, you equal the derivative to zero and obtain the roots of the obtained polynomial:
[tex]48x^3-8x=0\\\\6x^3-x=0\\\\x(6x^2-1)=0[/tex]
Then, you have the following roots for x:
[tex]x_1=0\\\\x_{2,3}=\pm \sqrt{\frac{1}{6}}[/tex] = ±0.40
Hence, there are three special points.
Next, you evaluate the derivative (expression (2)) for the x values close to the x1, x2 and x3. The values of the derivative give to us the value of the slope of a tangent line in that point, and so, if the function increases or decreases:
First interval, for a number lower than -0.40
[tex]48(-0.41)^3-8(-0.41)=-0.02<0[/tex]
The function decreases in the interval:
[tex](-\inft,-\frac{1}{\sqrt{6}})[/tex]
It is necessary that after x=-0.40 the function increases until the next special point, that is x=0. Then, the interval in which the function increases is:
[tex](-\frac{1}{\sqrt{6}},0)[/tex]
By symmetry, from the point x=0 until x=0.40 the function decreases.
[tex](0,\frac{1}{\sqrt{6}})[/tex]
Next, you evaluate the expression (2) for a number higher than 0.40:
[tex]48(0.41)^3-8(0.41)=0.02>0[/tex]
Then, the function increases for the following interval:
[tex](\frac{1}{\sqrt{6}},+\infty)[/tex]
(b) Due to the results obtained in the previous step you can conclude that the local minimum are:
[tex]x_{min}=-\frac{1}{\sqrt{6}}\\\\x_{min}=\frac{1}{\sqrt{6}}[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},f(-\frac{1}{\sqrt{6}}))=P_1(-\frac{1}{\sqrt{6}},4.66)\\\\P_2(\frac{1}{\sqrt{6}},f(\frac{1}{\sqrt{6}}))=P_2(\frac{1}{\sqrt{6}},4.66)[/tex]
[tex]P_1(-\frac{1}{\sqrt{6}},0)\\\\P_2(\frac{1}{\sqrt{6}},0)[/tex]
(these are the point in which the function change of a decrease to an increase)
The same reason as before. There in one local maximum:
[tex]x_{max}=0[/tex]
[tex]P(0,f(0))=P(0,5)[/tex]
(c) The inflection points are calculated by using the second derivative:
[tex]\frac{d^2f}{dx^2}=144x^2-8=0\\\\x^2=\frac{8}{144}=\frac{1}{18}\\\\x=\pm \frac{1}{\sqrt{18}}[/tex]
Then , there are two inflection points , given by:
[tex]P_1(-\frac{1}{\sqrt{18}},f(-\frac{1}{\sqrt{18}}))=P_1(-\frac{1}{\sqrt{18}},4.82)\\\\P_2(\frac{1}{\sqrt{18}},f(\frac{1}{\sqrt{18}}))=P_2(\frac{1}{\sqrt{18}},4.82)[/tex]
148, 139, 109, 146, 141, 179, 187, 131, 149, 141 What is the mean absolute deviation of the data set
Answer:
The mean absolute deviation is 15
Step-by-step explanation:
First you have to find the mean, which in this case is 147.
Then you need to find the difference between each individual number and the mean. Once you have all the diffences written down, you need to add all the differences together. If you take the sum of the differences and divide them by the mean, you'll get your answer!
Let me know if that makes sense! :)
There were 208 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper box tickets cost $10.00. The total amount of money spent was $2187.50. How many of each kind of ticket were purchased?
Answer:
so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold
Step-by-step explanation:
lets take "x" as the # of lower box tickets
and "y" as the number of upper box tickets
so in total the number of tickets sold was 208
so x+y=208
next, we know that each lower box ticket costs 12.50 and each upper box tickets costs 10 and the total amount of money spent was $2187.50 so:
12.5x+10y=2187.50
lets subtract "x" from both sides in first equation to find value of y
y=208-x
now substitute y in equation number 2:
12.5x-10(208-x)=2187.5
12.5x-2080+10x=2187.5
22.5x-2080=2187.5
22.5x=4267.5
x=189.666
so 189 tickets lower box tickets were purchased now, substitute 190 in equation 1 to find value of "y"
y=208-190
y=18
so 189(from 189.66) lower box tickets are sold and 18 upper box tickets are sold
What is the quotient
x24 - x18 + x12 ÷ x6
Answer:
Simplified expression: x^18 - x^12 + x^6
Step-by-step explanation:
1. Let us write down the question at hand, firstly: x^24 - x^18 + x^12/ x^6
2. Let us factor equation x^24 - x^18 + x^12/ x^6 ⇒ x^12(x^12 - x^6 + 1)/ x^6
3. Now apply exponential rules to get x^6 to the numerator:
x^12 - 6(x^12 - x^6 + 1)
4. Simplify this expression to be ⇒ x^6(x^12 - x^6 + 1)
5. And further simplify this expression by distributing the x^6:
Answer: x^18 - x^12 + x^6
A tire manufacturer has 1000 units of raw rubber to use in producing radial tires for passenger cars and tractor tires. Each radial tire requires 5 units of rubber; each tractor tire requires 20 units. Labor costs are $80 for a radial tire and $120 for a tractor tire. Suppose the manufacturer does not wish to pay more than $15,000 in labor costs and wishes to make a profit of $100 per radial tire and $250 per tractor tire. How many of each kind of tire should be made in order to maximize profit
Answer:
180 Passenger Car Tires and 5 Tractor Tires should be produced in order to maximize profit.
Step-by-step explanation:
Here, we can form two equations from the given situation.
First, we are given that the total raw tube units are 1000. And 5 units are required for passenger car tire, while 20 units are required for tractor tire. So, the equation becomes:
5 x + 20 y = 1000 -------- eqn (1)
where,
x = no. of passenger car tires produced
y = no. of tractor tires produced
Another condition is given that, maximum labor cost should be $ 15,000. Since, the labor cost is $80 for a passenger tire and $120 for a tractor tie. Thus, the equation becomes:
80 x + 120 y = 15000 -------- eqn (2)
Solving eqn (1) and eqn (2), simultaneously, we get:
x = 180
y = 5
Therefore,
No. of Passenger Car Tires Produced = x = 180
No. of Tractor Tires Produced = y = 5
Help !!! I got -15 & it’s wrong !
Answer:
-11
Step-by-step explanation:
I substitute x in ( put parenthesis around x so it makes it clear)
-9-6-18+9+4+9
simplify
-33+22
-11
Answer: -11
Step-by-step explanation:
That polynomial simplifies to -2x^2-x+4
If we plug in -3 for x, we get -2(-3)^2-(-3)+4 and thats -11
The product of two consecutive natural numbers is 19 greater than their sum. Find thee numbers.
Answer:
The numbers are suppose to be natural numbers that is positive integers form 1 upward. So the numbers will be 5 and 6.
Step-by-step explanation:
The product of 2 consecutive natural numbers is 19 greater than their sum . We need to understand important terms in this question like consecutive and natural numbers.
Consecutive numbers are numbers that follows each other continuously from smallest to largest. Natural numbers are numbers that includes all the positive numbers from 1 to infinity example 1, 2, 3, 4............infinity.
Let the consecutive number be a and a+1.
The product of this 2 numbers are when you multiply them. Therefore,
a(a + 1) = a² + a
The sum of the 2 numbers are their addition. Therefore,
a + (a + 1) = 2a + 1
The product is 19 greater than the sum. This means the product of this numbers minus the sum of this numbers is equals to 19.
a² + a - (2a + 1) = 19
a²+ a - 2a - 1 = 19
a²- a - 20 = 0
Find the numbers that can be multiplied to get -20 and added together to get -1. The numbers are 4 and -5
a² + 4a - 5a - 20 = 0
a(a + 4) - 5(a + 4) = 0
(a + 4)(a - 5) = 0
a = - 4 and a = 5
The numbers are suppose to be natural numbers that is positive integers from 1 upward. So the numbers will be 5 and 6.
To prove it
5 × 6 = 30(products)
5 + 6 = 11(sum)
30 - 11 = 19
PLEASE HELP WITH THIS EASY QUESTION!! EXPLANATION NEEDED!!
Answer:
100
Step-by-step explanation:
(b/2)^2
b= -20
(-20/2)^2
(-10)^2
100
The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4, and 5 to represent the outcome "the pass is completed" and the digits 6, 7, 8, and 9 to represent the outcome "the pass is not completed." To be confident that our simulation is accurate, one needs to :
A. Repeat the simulation several more times
B. Assign new digits to represent outcomes
C. Take the average of the results of Line 134 and Line 101
Answer:
A. Repeat the simulation several more times
Step-by-step explanation:
The purpose of the simulation model is to represent the effectivity of the passes.
The proportion of successful passes is 60%.
As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.
But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.
Step-by-step explanation:
C
Answer:
The answer is C
Step-by-step explanation:
I took the test and got it right :)
hopefully this helps you :)
pls mark brainlest ;)
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. It can be described with the equation -4h=-14. What value of h makes the equation true?
The equation is -4h = -14
To find h, divide both sides of the equation by -4:
H = -14 / -4
H = 3.5 hours.
Given f(x)=2x^2-8x+6 and g(x)=3x-1, what is f(x)+g(x) ?
Answer:
2x^2 -5x +5
Step-by-step explanation:
f(x)=2x^2-8x+6 and g(x)=3x-1
f(x)+g(x) = 2x^2-8x+6 +3x-1
Combine like terms
= 2x^2 -5x +5
Answer:
2x^2 -5x +5
Step-by-step explanation:
Drag the item from the item bank to its corresponding match.
Match the prism or cylinder with its volume.
Answer:
i cant help you because i cant see the things on the picture if u get a better picture i can help
Step-by-step explanation:
Which description matches finding the volume of the solid ?
Square prism + Triangular prism. Hope it helps.
She used 25 equally sized stones to make a path that is 12 feet long. How long is each stone
Answer:
The length of each stone is
L = 12/25 = 0.48 ft
Hope this helps!
:)
Each stone measures 0.48 feet.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here, the number of stones is 25 and it is used to construct 12 feet long then measure of each stone =12/25
=0.48 feet
Hence, Each stone measures 0.48 feet.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ2
Mark wants a new car that costs $30000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he chose
Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.
Step-by-step explanation:
what is the area of the figure below
Answer:
58
Step-by-step explanation:
Answer: 58 in.^2
Step-by-step explanation:
Use the diagram to find the indicated angle measures.
m<1= degrees
m<2= degrees
m<3= degrees
Please help !
Answer:
Step-by-step explanation:
its m<2=degrees
Answer:
m∠1 = 131
m∠2 = 49
m∠2 = 112
Step-by-step explanation:
Hotel 3 provides a 6 hour booking for 120 delegates in one room (including tea and lunch).how much would this cost?
Answer:
$3840
Step-by-step explanation:
The total cost is ...
(6 hr)(cost per hr) +(120 persons)(food cost per person)
= 6($190) +120($15 +7.50)
= $3840
The booking at Hotel 3 would cost $3840.
Which of these expressions is equivalent to log (9^2)?
A. log (2) - log (9)
B. 2 * log (9)
C. log (2) + log (9)
D. log (2) * log (9)
Answer:
B. 2 * log (9)
Step-by-step explanation:
I put them both into my calculator and got the same answer both times.
The expression that is equivalent to log(9^2) is 2log89. Option B is correct.
According to the law of logarithm,
log (a^b) = blog a
Note that the power of the function is taken to the back of the logarithmic function.
Given the log function log(9^2), to get the equivalent expression, we will simply take the power which is 2 to the back of the log function to have 2log9
Learn more here: https://brainly.com/question/23882267
1.(09.05
Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Approximately what percent of pizzas are delivered between 24 and 30 minutes? (2 points)
32%
689
09
99.75
Answer:
About 68% (is that an answer choice?)
Step-by-step explanation:
In a normal distribution (a bell curve), about 68 percent of the data is in the range between one standard deviation below the mean to one standard deviation above. If your mean is 27, and the standard deviation is 3, then one deviation below to one above would be 27 - 3 to 27 + 3, or 24 - 30.
Length of rectangle is three times bigger than the width. Area of rectangle is 27. A) find width of rectangle B) find length of rectangle C) find perimeter of rectangle.
What is the answer? I need help to solve it.
Answer:
Length: 9
Width: 3
Perimeter: 24
Step-by-step explanation:
First you can set up a few equations. You know that L x W is your area, or 27.
L * W = 27
Then you also know that your length is equal to three times the width.
L = 3W
So you can substitute L into the first equation to solve for W.
3W * W = 27
3W^2 = 27
W^2 = 9
W = 3
Then you can plug 3 into either equation to solve for your length.
L = 3(3)
L = 9
Then your perimeter is just 2L + 2W
2(9) + 2(3) = 24
Answer:
Step-by-step explanation:
Let the dimensions of the rectangle be length = L and width = W. Then P = perimeter = 2L + 2W. A = area of rectangle = L * W. Finally, L = 3W.
Here A = 27 units^2 = W*(3W) = (3*W^2), or 3W^2 = 27 units^2, or
W^2 = 9 units^2, or W = 3 units. Then L = 3W = 3(3 units) = 9 units.
The length of the rectangle is 9 units. See above.
The perimeter of the rectangle is 2(9 units) + 2(3 units) = 24 units.
A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likelyto come to rest in any of the slots. One of the simplest wagerschooses red or black. A bet of $1 on red returns $2 if the balllands in a red slot. Otherwise, the player loses his dollar. Whengamblers bet on red or black, the two green slots belong to thehouse. Because the probability of winning $2 is18/38, the meanpayoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numberstells us about what will happen if a gambler makes very many betson red.
Answer:
Step-by-step explanation:
The question says,
A roulette wheel has 38 slots, of which 18 are black, 18 are red,and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many betson red.
The law of large numbers tells us that as the gambler makes many bets, they will have an average payoff of which is equivalent to 0.947.
Therefore, if the gambler makes n bets of $1, and as the n grows/increase large, they will have only $0.947*n out of the original $n.
That is as n increases the gamblers will get $0.947 in n places
More generally, as the gambler makes a large number of bets on red, they will lose money.
some help?I don't know how to solve it
Farmer Smith Jr is putting together fruit baskets. He has 240 oranges and 150 grapefruits. What is the largest number of baskets he can put together so that he can have the same number of oranges in each basket and the same number of grapefruits in each basket?
Answer:
why does it say college even tho this is a question on my homework
Step-by-step explanation:
and i'm in 7th grade.
In a bowl of marbles, there are 5 red ones, 6 green ones, and 4 blue ones. If two marbles are chosen at random with replacement If two marbles are chosen at random with replacement, find P(red and a blue).
Answer:
4/45.
Step-by-step explanation:
There are a total of 15 marbles in the bowl, so:
P(red) = 5/15 = 1/3
P(blue) = 4/15
Required probability = 1/3 * 4/15
= 4/45
Answer:
P(red, blue) = (5/15)*(4/15) = 4/45
what happens to the value of the expression 5/x + 5 as x decreases froma large positive number to a small positive number
Answer:
The value increases
Step-by-step explanation:
the smaller the divisor, the larger the quotient.
An assembly line is operating satisfactorily if fewer than 2 % of the phones produced per day are defective. To check the quality of a day's production, the company randomly samples 5 0 phones from a day's production to test for defects. Define the population of interest to the manufacturer. all the phones produced during the day in question the 50 phones sampled and tested the 2% of the phones that are defective the 50 responses: defective or not defective
Answer:
all the phones produced during the day in question.
Step-by-step explanation:
Okay, we are given the following data or information or parameters in the question above and they are; 2 % of the phones produced per day are defective, the quality of a day's production was checked by sampling 50 samples randomly.
Therefore, the best option or Explanation that best Define the population of interest to the manufacturer is; ''all the phones produced during the day in question''.
Also, the 50 phones that are sampled randomly and 2% which are defective is a condition that the manufacturer should be interested in.
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
f is the correct option pls mark me as the brainliset
Answer:
D, E, F
Step-by-step explanation:
because you need to do this when you are gathering resources
