Bob has a concession at Yankee Stadium. He can sell 500 umbrellas at $10 each if it rains. (The umbrellas cost him $5 each.) If it shines, he can sell only 100 umbrellas at $10 each and 1000 sunglasses at $5 each. (The sunglasses cost him $2 each.) He has $2500 to invest in one day, but everything that isn’t sold is trampled by the fans and is a total loss. This is a game against nature. Nature has two strategies: rain and shine. Bob also has two strategies: buy for rain or buy for shine. Find the optimal strategy for Bob assuming that the probability for rain is 50%.

Answers

Answer 1

Answer:

Answer:

The optimal strategy for Bob is buying for shine (unless he can watch a forecast to know the next day weather).

Step-by-step explanation:

This is a typical problem of hopes to win vs hopes to lose. Let's analyze each of the strategies Bob can adopt in both kinds of weather.

Bob buy for rain:

Bob will buy 500 umbrellas for a cost of $5 each. This is a total cost of $2500.

If it rain, Bob can sell all umbrellas for $10 each. This gives a maximum revenue of $5000. Therefore the maximum profit is $2500. Remember that:

Profit= Revenue - Cost

If it's a sunny day, Bob can only sell 100 umbrellas for $10 each. This gives a maximum revenue of $1000. Therefore the maximum profit is -$1500. That means that in this case, the minimum loss is $1500.

Bob buy for Shine:

Bob will buy 100 umbrellas for a cost of $5 each and 1000 sunglasses for a cost of $2 each. This is a total cost of $2500.

If it's a sunny day, Bob can only sell all umbrellas for $10 each and all sunglasses for $5. This gives a maximum revenue of $6000. Therefore the maximum profit is $3500.

If it rains, Bob can sell only sell all the 100 umbrellas for $10 each but none of the sunglasses. Therefore the maximum profit is $1000. Therefore the maximum profit is -$1500. That means that in this case, the minimum loss is $1500.

In both cases, the worst-case scenario is the same: a loss of $1500.

Nevertheless in the best case scenario buying to shine gives a bigger profit. Therefore if the risk is the same, is better to go for the strategy with better profits.

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Translate the English phrase into an algebraic expression: the sum of 17y² and 19.

Suppose a regional computer center wants to evaluate the performance of its memory system. One measure of performance is the average time between failures of its disk drive. To estimate the value, the center recorded the time between failures for a random sample of 45 drive failures. The sample mean has been computed to be 1,762 hours and the sample standard deviation is 215. Estimate the true mean time between failures with a 90% confidence interval? Interpret the confidence interval.

Answers

Answer:

The 90% confidence interval is (1408.325 hours, 2115.675 hours).

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1-0.9)/(2) = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find M as such

$M = z*s$

In which s is the standard deviation of the sample. So

$M = 1.645*215 = 353.675$

The lower end of the interval is the mean subtracted by M. So it is 1762 - 353.675 = 1408.325 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 2115.675 hours.

The 90% confidence interval is (1408.325 hours, 2115.675 hours).

What value of x would make KM ∥ JN?Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.

Complete the statements to solve for x.

By the converse of the side-splitter theorem, if JK/KL = , then KM ∥ JN.

Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.

Cross-multiply: (x – 5)() = x(x – 3).

Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).

Multiply and simplify: x2 – x – = x2 – 3x.

Solve for x: x = .

Answers

Answer:

x = 10

Step-by-step explanation:

By the converse of the side-splitter theorem, if $(JK)/(KL)= (NM)/(ML)$ , then KM ∥ JN.

Substitute the expressions into the proportion:

$(x-5)/(x)= (x-3)/(x+4)$

Cross-multiply:

(x – 5)(x+4) = x(x – 3).

Distribute:

$x(x) + x(4) - 5(x) - 5(4) = x(x) + x(-3).$

Multiply and simplify:

$x^2 +4x- 5x - 20 = x^2-3x\n-x-20=-3x\n$Collect like terms$\n-x+3x=20\n2x=20\n$Divide both sides by 2\nx=10$

Solve for x: x = 10

Therefore, the value of x that would make KM parallel to JN is 10.

Answer:

What value of x would make KM ∥ JN?

Triangle J L N is cut by line segment K M. Line segment K M goes from side J L to side L N. The length of J K is x minus 5, the length of K L is x, the length of L M is x + 4, and the length of M N is x minus 3.

Complete the statements to solve for x.

By the converse of the side-splitter theorem, if JK/KL =

✔ NM/ML

, then KM ∥ JN.

Substitute the expressions into the proportion: StartFraction x minus 5 Over x EndFraction = StartFraction x minus 3 Over x + 4 EndFraction.

Cross-multiply: (x – 5)(

✔ x + 4

) = x(x – 3).

Distribute: x(x) + x(4) – 5(x) – 5(4) = x(x) + x(–3).

Multiply and simplify: x2 – x –

✔ 20

= x2 – 3x.

Solve for x: x =

✔ 10

.Step-by-step explanation:

The solution to 8x = 32 is x = __.

Answers

$\huge\text{Hey there!}$ !

$\large\text{8x = 32}$

$\large\text{DIVIDE 8 to BOTH SIDES}$

$\mathsf{(8x)/(8) = (32)/(8)}$

$\large\text{Cancel out: } \mathsf{(8)/(8)}\large\text{ because that gives you } \mathsf{1}$

$\large\text{Keep: }\mathsf{(32)/(8)}\large\text{ because it helps us solve for }\mathsf{x}$

$\mathsf{(32)/(2)\ = x \ or\ x = (32)/(8)}$

$\mathsf{(32)/(8) = 32/ 8 \rightarrow \bf 4}$

$\boxed{\boxed{\large\text{Answer: \bf x = 4}}}\huge\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

Find the distance between (-8, -2)
and 6, -1)

Answers

The distance between the given coordinate points is $√(197)$ units.

The given coordinate points are (-8, -2) and (6, -1).

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On $2D$ plane the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is Distance $= √((x_2-x_1)^2+(y_2-y_1)^2)$ .

Substitute $(x_1, y_1)=(-8, -2)$ and $(x_2, y_2)=(6, -1)$ in distance formula, we get

Distance $= √((6+8)^2+(-1+2)^2)$

Distance $= √((14)^2+(1)^2)$

Distance $= √(196+1)$

Distance $= √(197)$ units

Therefore, the distance between the given coordinate points is $√(197)$ units.

To learn more about the distance formula visit:

brainly.com/question/27262878.

#SPJ3

Answer:

-8,-2= 6

6,-1=7

Step-by-step explanation:

get a number line and use that to it and look up how to use a number line with negative numbers it’s not hard once you see how it’s done

Suppose the correlation coefficient between a predictor variable (a person’s height, measured in centimeters) and a response variable (a person’s weight, measured in kilograms) is 0.72.Suppose that we change the units used to measure height from centimeters to inches and the units used to measure weight from kilograms to pounds, and then we recompute the correlation coefficient. Which of the following would be true?Select one:a. The new correlation coefficient should be the same: R = 0.72.b. The new correlation coefficient should be R = 0.72 × (2.54/2.2) ≈ 0.83.c. The new correlation coefficient should be R = 0.72 × (2.2/2.54) ≈ 0.62.d. The new correlation coefficient should be something other than the options given here.

Answers

Answer:

a) The new correlation coefficient should be the same: R = 0.72

Step-by-step explanation:

The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables.

It is a relative dimensionless measure, so it does not depend on the units of measurement of the variables involved.

If the variables are correlated in centimeters and kilograms, they will also be correlated in inches and pounds, and with the same relative magnitude.

So the answer is

a) The new correlation coefficient should be the same: R = 0.72

The ratio of the heights of two similar cylinders is 1:3. If the volume of the smaller cylinder is 67cm cubed, find the volume of the larger cylinder.

Answers

Answer:

volume = 1809 cm³

Step-by-step explanation:

The ratio of the height of two similar cylinder is 1:3 . The volume of the smaller cylinder is 67 cm³. The volume of the larger cylinder can be computed below:

If 2 object are similar and the ratio of the corresponding sides is x ,then the ratio of their volume is x³.

ratio of height = 1/3

ratio of volume = (1/3)³ = 1/27

volume of smaller cylinder/volume of larger cylinder = 1/27 = 67/x

where

x = volume of the larger cylinder

x = 27 × 67

x = 1809 cm³

volume = 1809 cm³

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