(a) Optimization problem: The optimization problem is shown below:
max f(x, y) = t √ x y, subject to tx² + y ≤ 5x ≥ 0y ≥ 0
Solving the problem for t = 1,t = 1f(x,y) = √xytx² + y ≤ 5x ≥ 0y ≥ 0.
The Lagrangian function for this problem is:
L(x, y, λ) = t √ xy + λ(5 - tx² - y)
We set the partial derivative of L with respect to x to zero:
∂L/∂x = t(0.5√y)/√x + (-2λtx) = 0
We then obtain:
(1) 0.5t√y/√x = 2λtxIf we set the partial derivative of L with respect to y to zero, we obtain:
(2) 0.5t√x/√y + λ(-1) = 0
Multiplying both sides by (-1), we obtain:
(3) -0.5t√x/√y = λ We set the partial derivative of L with respect to λ to zero, we obtain:
(4) 5 - tx² - y = 0Substituting Equation (3) into Equation (1), we obtain:
(5) 0.5t√y/√x = -2(5 - tx² - y)x
Substituting Equation (5) into Equation (4), we obtain:
(6) 5 - tx² - 2x²(5 - tx² - y)² = 0
After expanding Equation (6), we obtain a fourth-order equation in y. Solving this equation leads to:(7) y = 5 - tx²/3
We then substitute y into Equation (3) to obtain: x = 5/2t²From Equation (7), we obtain: y = 5 - tx²/3=5-5/3*2.5=2.7778
(b) Envelope theorem
According to the Envelope Theorem, the marginal effect of a parameter on an optimal solution is equal to the partial derivative of the optimal value with respect to that parameter. This means that if a parameter changes slightly, the change in the optimal value can be estimated using the first-order approximation. (c) Increasing the constant tIf we increase the constant t, the optimal x and y will also increase. This is because an increase in t will lead to a higher value of f(x, y).
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The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3. A. What proportion of students consume more than 13 pizzas per month? Probability = = B. What is the probability that in a random sample of size 10, a total of more than 110 pizzas are consumed? Probability = Note: You can earn partial credit on this problem.
The probability to consume more than 13 pizzas per month is 0.3707 and more than 110 pizzas in a random sample of size 10 is 0.9646.
The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 3.
A. Probability that more than 13 pizzas consumed by students:
For finding the probability, we need to find the Z-score first.
z = (x - μ) / σz = (13 - 12) / 3z = 0.3333
Now, we have to use the z-table to find the probability associated with the z-score 0.3333.
The area under the normal distribution curve to the right of 0.3333 is 0.3707 (rounded off to 4 decimal places).
Thus, the probability that a student consumes more than 13 pizzas per month is 0.3707.
B. Probability that more than 110 pizzas consumed in a random sample of size 10:
Let x be the number of pizzas consumed in the random sample of size 10.
Then, the distribution of x is a normal distribution with the mean = 10 × 12 = 120 and standard deviation = √(10 × 3²) = 5.4772
We have to find the probability that the total number of pizzas consumed is greater than 110. i.e. P(x > 110).
For finding the probability, we need to find the Z-score first.z = (110 - 120) / 5.4772z = -1.8257
The area under the normal distribution curve to the right of -1.8257 is 0.9646 (rounded off to 4 decimal places).
Thus, the probability that more than 110 pizzas are consumed in a random sample of size 10 is 0.9646.
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Find the area of the shaded region.
Answer:嘿，我不知道答案，但這段文字很酷
6. Markets with elastic supply and demand curves: a) Have demand and supply curves that never intersect. B) Are very sensitive to a change in price. C) Have greater movements in quantity than prices. D) Are very sensitive to a change in quantity. E) Are only theoretical and do not exist in the real world.
Answer:
The correct statement is B (are very sensitive to change in price)
Step-by-step explanation:
Option B is correct because of the following reason -:
The degree to which a rise in price affects the quantity demanded or supplied is known as elasticity. In the case of elastic demand and supply, as the price rises, the quantity demanded falls and the quantity supplied rises more than proportionally. Inelastic price elasticity of demand and supply, on the other hand, induces a less than proportional change in quantity as prices change.
Hence , the correct option is B .
1/(x+6)+(×+1)/x=13/(x+6)
Answer:
x = 3, 2
Step-by-step explanation:
Answer: x = 3, 2
Step-by-step explanation:
The perimeter of a square (perimeter = 4 times one side) is less than 16 inches. One side of the square measures x. what are the viable solutions for the value of x?
Answer:
C
Step-by-step explanation:
The perimeter of the square has to be only positive values, and so there has to be restrictions on the values. We can rule out answers A and B. Because the perimeter the values of x have to be less than 4. If they were greater than 4, then 4x>16. So we can rule out answer d. The correct answer is C.
Coffee is ordered weekly in bulk, and you must specify the number of pounds to order. You
must also choose coffee quality: good quality, high quality, or organic. Small cups use 1 shot of
espresso, medium use 2 shots, and large cups use 3 shots. It is estimated that each shot of
espresso requires approximately 7 grams of coffee, or about 1/64 of a pound—but you may
want to allow a bit extra in case your servers spill some. Thus, a large size would use
approximately 3/64 of a pound of coffee. Fresh coffee grounds are discarded immediately after
use. Any coffee left at the end of the week is discarded for quality and freshness reasons. If you
run short, local purchases are made at a higher cost than when ordering in bulk.
Given estimated sales of 2,000 cups of coffee per week, how many pounds of coffee should you buy? Explain in detail.
Based on estimated sales of 2,000 cups of coffee per week and the amount of coffee required for each cup size, it is recommended to purchase approximately 46.875 pounds of coffee.
To determine the amount of coffee needed for 2,000 cups of coffee per week, we need to consider the size of each cup and the amount of coffee required for each size.
According to the information provided, small cups use 1 shot of espresso, medium cups use 2 shots, and large cups use 3 shots.
Since each shot requires approximately 7 grams of coffee (or about 1/64 of a pound), a small cup would require approximately 1/64 of a pound, a medium cup would require approximately 2/64 (or 1/32) of a pound, and a large cup would require approximately 3/64 of a pound.
Let's calculate the total amount of coffee required for 2,000 cups based on these proportions. Assuming a certain distribution of cup sizes, we can estimate the average number of shots per cup.
Let's assume that 40% of the cups are small, 40% are medium, and 20% are large.
With these proportions, we can calculate the total amount of coffee required.
(0.4 * 2,000 * 1/64) + (0.4 * 2,000 * 2/64) + (0.2 * 2,000 * 3/64) = 62.5 + 125 + 46.875 = 234.375
Therefore, to meet the estimated sales of 2,000 cups of coffee per week, it is recommended to purchase approximately 46.875 pounds of coffee.
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Which transformation carries the parallelogram onto itself?
Answer: D) a rotation of 180 degrees Clockwise about the center of the parallelogram
Step-by-step explanation:
Plot the x-intercepts, the y-intercept, and the vertex of the graph (Must use Desmos!)
Answer:
x-intercept: (-1,0)
y-intercept: (0,3)
Vertex: (-2,-1)
Step-by-step explanation:
Which expression is equivalent to the expression shown below? --8x – 2(5 + 4x)
-8x-2(5+4x)
Step-by-step explanation:
-8x-10-8x -8x-8x-10 -16x-10
Find the unit rate for each, then compare. Which is faster?
8 laps in 70 seconds
12 laps in 98 seconds.
Answer:
8 laps in 70 seconds is faster.
Step-by-step explanation:
If we divide 70/8 and 98/12 we get the following:
70/8= 8.75
98/12=8.16
8.75>8.16
The unit rate is 1 lap in 8.75 seconds and 1 lap in 8.16 seconds
The ratio of boys to girls at the play was 4 to 3. If there were 15 girls, how many boys were there?
Answer:
20 boys
Step-by-step explanation:
If there are 4 boys for every 3 girls, multiply both numbers by 5 (3*5 = 15) to find the number of boys.
Answer:
20
Step-by-step explanation:
4/3 = ?/15
multiply both sides by 15
15*4/3 = ?
? = 20
If the ratio of boys to girls is 1:4 and there are 20 girls in your class, how many boys are there?
Answer:
Step-by-step explanation:
5 boys
Answer:
me
Step-by-step explanation:
beceaus im the best Guy
Suppose that A and B are mutually exclusive events Select the correct answer below, O A. Since A and B are mutually exclusive events, then the probability that A or Boccur is 1. That is, P(A)*P(B)-1 OB. Since A and B are mutually exclusive events, then the probability that both A and B occur is O. That is, PA}{B} = 0, OC. Since A and B are mutually exclusive events, then the probability that A or B occur is 1. That is, PIA & B)=1, OD. Since A and B are mutually exclusive events, then the probability that both A and B occur is O. That is, P(A&B)=0
The correct answer is option D. Since A and B are mutually exclusive events, the probability that both A and B occur is 0. In other words, P(A&B) = 0.
When two events, A and B, are mutually exclusive, it means that they cannot occur simultaneously. If one event happens, the other event cannot happen at the same time. In this scenario, the correct answer is option D, which states that the probability of both events A and B occurring together is 0, i.e., P(A&B) = 0.
To understand this concept, consider a simple example. Let's say event A represents flipping a coin and getting heads, while event B represents flipping a coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, it is impossible for both events A and B to occur simultaneously. Therefore, the probability of both A and B occurring together is 0. In summary, when events A and B are mutually exclusive, the correct answer is option D, which states that the probability of both A and B occurring together is 0, i.e., P(A&B) = 0.
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Giving away 30 points, have a good day
Answer:
For real???
Step-by-step explanation:
Tysm!! <3 you deserve so much!
Answer:thanks
Step-by-step explanation:
help me find the answer please
Answer:
A x<1125
Step-by-step explanation:
What is the midpoint of DC with endpoints C (6,−1) and D (−7,8)?
Answer:
Fraction form: (-1/2, 7/2) Decimal form: -.5, 3.5)
Step-by-step explanation:
use the midpoint formula of: (x1 + x2/2 , y1 + y2/2) in order to get (x,y) coordinates.
Let's call endpoint C x1 and y1. So 6=x1 and -1=y1.
This makes endpoint D x2 and y2. So -7=x2 and 8=y2.
Now plug it in and simplify!
x-coordinates: (6+-7)/2 = (6-7)/2 = -1/2 or -.5
y-coordinates: (-1+8)/2 = (8-1)/2 = 7/2 or 3.5
the midpoint of endpoints C and D is (-1/2, 7/2)
**decimal form: (-.5, 3.5)
write the number thirty three in figures
Answer:
3x10 15x2 5x6
Step-by-step explanation:
what is the answer to
-6x+4(-2+8y)- 2y+ 4
Answer:
− 6 + 3 0 − 4
Answer:
do you mean simplify the expression?
-6x+4(-2+8y)- 2y+ 4
-6x - 8 + 32y - 2y + 4
-6x + 30y + 4 - 8
-6x + 30y - 4
3 feet
5 feet
4 feet
Answer:
Post the question along with this
PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!
Answer:
it is A
Step-by-step explanation:
i remember doing this in middle school.
HELP PLS ITS ALMOST DUE PLS PLS PLS
Answer:
19. B
20. C
Step-by-step explanation:
Can you please help me
Answer:
7. 7.1+5.4+2.9=15.7
10.3+5.4=15.7
8. 373.4 - 152.9 = 220.5
373.4 - 153 = 220.4
220.4 - 0.1 = 220.5
9. 18.25 + 7.99 + 4.75 = 30.99
10. 1.05 + 3 + 4.28 + .95 = 9.28
11. 302.504
12 50.5
Find the lateral area of this square
based pyramid.
10 in
5 in
[ ? ] in
Answer:
100in
Step-by-step explanation:
1/2 *10*5=25
4(25)=100
Florida Immigration 9 Points 910 randomly sampled registered voters in Tampa, FL were asked if they thought workers who have illegally entered the US should be allowed to keep their jobs and apply for US citizenship. (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, (iii) lose their jobs and have to leave the country, or (iv) not sure. These voters were also asked about their political ideology, to which they responded one of the following: conservative, liberal, or moderate. Q4.4 Type I Error 3 Points Describe what it would mean if we made a Type I Error on this test. (You must discuss what decision we made, and what the actual truth about the population is.)
Type I Error: A Type I error is the first kind of error that can occur when testing a hypothesis. A Type I error occurs when a null hypothesis is rejected even when it is accurate.
If we make a Type I Error on this test, it would mean that we reject a null hypothesis that is true. This mistake would be made if we made a decision to reject the null hypothesis when there is no significant evidence to support that decision. The null hypothesis is the hypothesis that claims no change or no difference between the groups being compared. Null hypothesis is the opposite of the alternative hypothesis which is the hypothesis that claims that there is a difference between groups being compared.
In this context, making a Type I Error would mean that we reject the null hypothesis which is that all groups of voters would agree that workers who have illegally entered the US should be allowed to keep their jobs and apply for US citizenship. Making this error would mean we have come to the conclusion that they do not agree, which would be incorrect.
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.16 with the 6 repeating to a fraction
1. Find
A) 35
B) 47.5
C) 67.5
D95
Answer:
find which one my guy im trying to get infinite awnseres srryyyyy
Step-by-step explanation:
A hiker is lost in the forest, but has his cell phone with a weak signal. Cell phones with GPS can give an approximate location through triangulation, which works by giving distances from two known points. Suppose the hiker is within distance of two cell phone towers that are 22.5 miles apart along a straight highway (running east to west, double-dashed line). Based on the signal delay, it can be determined that the signal from the hiker's phone is 14.2 miles from Tower A and 10.9 miles from Tower B. Assume the hiker is traveling a straight path south reach the highway quickly. How far must the hiker travel to reach the highway
Answer:
The distance the hiker must travel is approximately 5.5 miles
Step-by-step explanation:
The distance between the two cell phone towers = 22.5 miles
The distance between the hiker's phone and Tower A = 14.2 miles
The distance between the hiker's phone and Tower B = 10.9 miles
The direction of the highway along which the towers are located = East to west
The direction in which the hiker is travelling to reach the highway quickly = South
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;
a = 22.5 miles
b = 14.2 miles
c = 10.9 miles
Therefore, we have;
22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)
cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6
∠A = arccos(-0.6) ≈ 126.9°
By sine rule, we have;
a/(sin(A)) = b/(sin(B)) = c/(sin(C))
∴ sin(B) = b × sin(A)/a
∴ sin(B) = 14.2×(sin(126.9°))/22.5
∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°
∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil
The distance the hiker must travel, d = c × sin(B)
∴ d = 10.9 × sin(30.31°) ≈ 5.5
Therefore, the distance the hiker must travel, d ≈ 5.5 miles.
Each letter in the word THEORETICAL is placed on a separate piece of paper
and placed in a hat. A letter is chosen at random from the hat. What is the
probability that the letter chosen is an E?
(Give answer in format 'a/b, no spaces, use slash for fraction bar)
Answer:
The answer is 1/11
Step-by-step explanation:
Explanation is in the picture above
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If a random variable has binomial distribution with n = 150 and p = 0.6. Using normal approximation the probability; P(X≥ 95) =---
The required probability is 0.2023.
Given random variable X with binomial distribution with n=150 and p=0.6.
The binomial distribution with parameters n and p has probability mass function:
$$f(x)= \begin{cases} {n\choose x} p^x (1-p)^{n-x} & \text{for } x=0,1,2,\ldots,n, \\ 0 & \text{otherwise}. \end{cases}$$
Now the mean, μ = np = 150 × 0.6 = 90 and standard deviation, σ = √(npq) = √(150 × 0.6 × 0.4) = 6
Using the normal approximation,
we have:
$$\begin{aligned}P(X ≥ 95) &\approx P\left(Z \geq \frac{95 - \mu}{\sigma}\right)\\ &\approx P(Z \geq \frac{95 - 90}{6})\\ &\approx P(Z \geq 0.8333) \end{aligned}$$
Using the standard normal table, the area to the right of 0.83 is 0.2023.
Therefore, P(X ≥ 95) = 0.2023.
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According to the given information, the required probability is 0.2019.
The random variable has a binomial distribution with n = 150 and p = 0.6.
We can use the normal approximation to the binomial distribution to find the probability P(X ≥ 95).
Normal Approximation:
The conditions for the normal approximation to the binomial distribution are:
np ≥ 10 and n(1 - p) ≥ 10
The expected value of the binomial distribution is given by the formula E(X) = np
and the variance is given by the formula [tex]Var(X) = np(1 - p)[/tex].
Let X be the number of successes among n = 150 trials each with probability p = 0.6 of success.
The random variable X has a binomial distribution with parameters n and p, i.e., X ~ Bin(150, 0.6).
The expected value and variance of X are:
[tex]E(X) = np = 150(0.6) = 90[/tex],
[tex]Var(X) = np(1 - p) = 150(0.6)(0.4) = 36[/tex].
The probability that X takes a value greater than or equal to 95 is:
[tex]P(X ≥ 95) = P(Z > (95 - 90) / (6))[/tex]
where Z ~ N(0,1) is the standard normal distribution with mean 0 and variance 1.
[tex]P(X ≥ 95) = P(Z > 0.8333)[/tex]
We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table, we find:
[tex]P(Z > 0.8333) = 0.2019[/tex]
Thus, [tex]P(X ≥ 95) = 0.2019[/tex] (rounded to four decimal places).
Therefore, the required probability is 0.2019.
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find the remainder when f(x) = 2x3 − 12x2 11x 2 is divided by x − 5. (2 points) 7 −3 3 −7
The remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.
We can use the remainder theorem to find the remainder when a polynomial is divided by a linear factor.
The remainder theorem states that the remainder when a polynomial f(x) is divided by x - a is f(a). In this case, the polynomial is f(x) = 2x3 - 12x2 + 11x + 2 and the linear factor is x - 5. So, the remainder is f(5).
To find f(5), we can simply substitute x = 5 into the polynomial. This gives us f(5) = 2(5)3 - 12(5)2 + 11(5) + 2 = 7.
Therefore, the remainder when f(x) = 2x3 - 12x2 + 11x + 2 is divided by x - 5 is 7.
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