Answer:
(a) The probability that all the hotel's rooms will be rented is 0.1587.
(b) The probability that 50 or more rooms will not be rented is 0.2514.
Step-by-step explanation:
We are given that the Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List.
Suppose Broadmoor's marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30.
Let X = demand for rooms in the hotel
So, X ~ Normal([tex]\mu=670,\sigma^{2} =30^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean demand for the rooms = 670
[tex]\sigma[/tex] = standard deviation = 30
(a) The probability that all the hotel's rooms will be rented means that the demand is at least 700 = P(X [tex]\geq[/tex] 700)
P(X [tex]\geq[/tex] 700) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{700-670}{30}[/tex] ) = P(Z [tex]\geq[/tex] 1) = 1 - P(Z < 1)
= 1 - 0.8413 = 0.1587
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.
(b) The probability that 50 or more rooms will not be rented is given by = P(X [tex]\leq[/tex] 650)
P(X [tex]\leq[/tex] 650) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{650-670}{30}[/tex] ) = P(Z [tex]\leq[/tex] -0.67) = 1 - P(Z < 0.67)
= 1 - 0.7486 = 0.2514
The above probability is calculated by looking at the value of x = 0.67 in the z table which has an area of 0.7486.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
Answer:
3lbs
Step-by-step explanation:
What is the simplified value of this expression pls help
Answer:
7
Step-by-step explanation:
Remove parentheses.
[tex]\frac{-8+4(4.5)}{6.25-8.25} \\[/tex]
Add −8 and 4.5.
[tex]\frac{4(-3.5)}{6.25 - 8.25} \\\\[/tex]
Subtract 8.25 from 6.25.
[tex]\frac{4*-3.5}{-2}[/tex]
Multiply 4 by −3.5.
[tex]\frac{-14}{-2}[/tex]
Divide −14 by −2.
= 7
Hunter is 9 years older than 3 times the age of his nephew. Hunter is 33 years old. How old is his nephew?
Answer:
8 years old.
(3x+9)
(3(8)+9)=33
Toby cuts a pizza into 6 equal slices. He eats half a slice. What fraction of the pizza has he eaten?
The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.
He at 1/2 of a slice:
1/6 x 1/2 = 1/12 of the pizza
Select the correct answer from each drop-down menu. Gino is buying wood screws at the corner hardware store. The table shows different numbers of bags of screws and their corresponding prices. Bags of Screws Price ($) 2 10 4 20 7 35 According to the table, the relationship between the number of bags and the price is proportional or not proportional
find the value of x if (1.1)^x=100
Answer:
x ≈ 48.3177
Step-by-step explanation:
This is what logarithms are for (among other things).
log(1.1^x) = log(100)
x·log(1.1) = 2
x = 2/log(1.1) ≈ 48.3177
The equation x2 − 6x − 27 = 0 when solved is:
Answer:
-3 , 9
Step-by-step explanation:
Sum = - 6
Product = -27
Factors = 3, -9
x² - 6x-27 = 0
x² + 3x - 9x - 9*3 = 0
x(x + 3) - 9(x + 3) = 0
(x + 3) (x - 9) = 0
x +3 = 0 ; x - 9 = 0
x = - 3 ; x = 9
Solution: x = -3 , 9
Write an equation that expresses the following relationship. w varies directly with u and inversely with d In your equation, use k as the constant of proportionality.
Step-by-step explanation:
solution.
if variable d increases then w reduces
w=k.u ×1/d
=ku/d
therefore w=k.u/d
Which of the following shows the intersection of the sets? {1, 5, 10, 15} {1, 3, 5, 7}
Answer:
{1,5}
Step-by-step explanation:
The intersection of the sets are all of the numbers that appear in both sets. In this case, the only numbers that appear in both are 1 and 5.
Answer:
{ 1,5}
Step-by-step explanation:
The intersection is what the two sets have in common
{1, 5, 10, 15}∩ {1, 3, 5, 7}
= { 1,5}
Jeff worked 4 and 2/3 hours in the morning and 3 and 3/4 hours in the afternoon. How many total hours did he work
1. 8 and 1/2 hours
2.7 and 5/7 hours
3.7 and 5/12 hours
4.8 and 5/12 hours
Answer:
4. 8 5/12
Step-by-step explanation:
4 2/3 + 3 3/4 =
= 4 + 2/3 + 3 + 3/4
= 4 + 3 + 8/12 + 9/12
= 7 + 17/12
= 7 + 12/12 + 5/12
= 7 + 1 + 5/12
= 8 5/12
3.
A passenger jet can fly 1,290 mil
in 3 hours with a tailwind bi
1,230 miles in 3 hours
headwind. Find the speed
the Jet in Still air and the
of the wind.
Answer:
Jet= 420 mph Wind = 10mph
Step-by-step explanation:
The speed of the plane in a tailwind can be modeled by x+y where x is the speed of the plane and y is the speed of the wind. Dividing 1290 by 3 gets you the average speed of the jet in a tailwind, which is 430.
The speed of the plane in a headwind can be modeled by x-y where x is the speed of the plane and y is the speed of the wind. Dividing 1230 by 3 gets you the average speed of the jet in a tailwind, which is 410.
This can be modeled by a system of equations, where x+y=430 and x-y=410. Solving the equation you get x=420 and y=10.
So, the speed of the jet is 420 mph and the speed of the wind is 10 mph.
Which of the following relations is a function?
a{(1, 3), (2, 3), (4,3), (9,3)}
b{(1, 2), (1, 3), (1, 4), (1,5)}
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
d{(6,-1), (1,4), (2, 3), (6, 1)}
Answer:
a{(1, 3), (2, 3), (4,3), (9,3)}
Step-by-step explanation:
For the relation to be a function, each x can only go to 1 y
a{(1, 3), (2, 3), (4,3), (9,3)}
function
b{(1, 2), (1, 3), (1, 4), (1,5)}
x=1 goes to 4 different y's so not a function
c{(5, 4), (-6, 5), (4, 5), (4, 0)}
x=4 goes to 2 different y's so not a function
d{(6,-1), (1,4), (2, 3), (6, 1)}
x = 6 goes to 2 different y's so not a function
The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.a. To perform this study, we should form a null hypothesis stating that the average is ______________ 100,000. (Please fill in only one of the following: "less than", "less than or equal to", "equal to", "greater than", "greater than or equal to". Please do not use symbols.)b. At the 10% significant level, the p-value/statistics is _____________________ (Please keep three decimal points) so we should __________________ the null hypothesis (Please only fill in "reject" or "not reject".).c. Hence, we may conclude that the average _________________ increased (Please only fill in "has" or "has not") and the probability that our conclusion is correct is at least _________________ percent.
Answer:
Step-by-step explanation:
a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ equal to 100000
For the alternative hypothesis,
H1: µ greater than 100000
This is a right tailed test
Since the population standard deviation is nit given, the distribution is a student's t.
Since n = 200
Degrees of freedom, df = n - 1 = 200 - 1 = 199
t = (x - µ)/(s/√n)
Where
x = sample mean = 103157
µ = population mean = 100000
s = samples standard deviation = 27498
t = (103157 - 100000)/(27498/√200) = 1.62
We would determine the p value using the t test calculator.
p = 0.053
Alpha = 10% = 0.1
Since alpha, 0.1 > than the p value, 0.053, then
b) At the 10% significant level, the p-value/statistics is 0.053, so we should not reject the null hypothesis.
c) Hence, we may conclude that the average has not increased and the probability that our conclusion is correct is at least 90 percent.
. A box contains four red, three yellow, and seven green balls. Three balls are randomly selected from the box without replacement. (a) What is the probability that all three balls are the same colo
Answer:
10/91
Step-by-step explanation:
Number of Red balls = 4
Number of Yellow balls = 3
Number of green balls=7
Total=4+3+7=14
If we pick three balls of the same color, there are three possibilities: (All Red, All Green Or all Yellow).
Therefore:
The probability that all three balls are the same color (note that the selections are without replacement)
=P(RRR)+P(GGG)+P(YYY)
[tex]=(\frac{4}{14} \times \frac{3}{13} \times \frac{2}{12})+(\frac{3}{14} \times \frac{2}{13} \times \frac{1}{12})+(\frac{7}{14} \times \frac{6}{13} \times \frac{5}{12})\\\\=\frac{1}{91} + \frac{1}{364}+ \frac{5}{52}\\\\=\frac{10}{91}[/tex]
The probability that all three balls are the same color is 10/91.
Jason has bought a new pool and has already measured some of the sides. Using the figure below and your knowledge of quadrilaterals, solve for x and y.
Answer:
x = 12
y = 12
Step-by-step explanation:
Each triangle is a right angle triangle
5² + x² = 13²
x² = 169 - 25
x = √144
x = 12
The shape is a parallelogram
Therefore
x = y
y = 12
PLEASE HELP ASAP DUE IN 10 MINUTES PLEASE!!!!!!!!!!!!!The president of the United States produces a new national plan to reduce water pollution which of these would most likely provide the revenue to pay for this new public service
Answer
i think its federal income tax increase. 2nd one i believe
Step-by-step explanation:
The President of the United States proposes a new national plan to reduce water pollution.
Which of these would most likely provide the revenue to pay for this new public service?
Step-by-step explanation:
answer is :
the united states senate passes a bill that increases the federal income tax rate , which then pays for the service read it b4 yhu answer your question.have a good day!!and DM meh if yhu need a question answer here for 24/7pls if yhu want to mark meh as brainlist.....PLSS GUYS I NEED HELP
Answer:
Option B. is the right choice.
Step-by-step explanation:
f(-3) = 3 and f(3) = 5 (First and the last column of table B)
Best Regards!
Which point is a solution to the inequality shown in this graph?
5
(3,-1)
(-3,-3)
O A. (5,-5)
O B. (1,5)
C. (-3,-3)
D. (3, -1)
Hey there!
To find the answer, we just need to see which point falls in this blue, which represents the inequality.
We see that the point (5,-5) is not on the blue.
We see that the point (1,5) is on the blue.
(-3,-3) is on the dotted line but not a solution of the inequality. The dotted line is excluded from the inequality. If it were a bold line, then it would be a solution of the inequality.
(3,-1) is also on the dotted line so it is not a solution.
Therefore, the answer is B. (1,5)
I hope that this helps!
We want to see which point is a solution for the graphed inequality.
We will find that the correct option is B, (1, 5)
Notice that the line that defines the inequality contains the points (-3, -3) and (3, -1)
Then the slope of that line is:
[tex]a = \frac{-1 -(-3)}{3 - (1)} = 1/2[/tex]
Then the line is something like:
y = (1/2)*x + b
To find the value of b, we use the fact that this line passes through the point (3, -1), then we have:
-1 = (1/2)*3 + b
-1 - 3/2 + b
-5/2 = b
So the line is:
y = (1/2)*x - 5/2
And we can see that the line is slashed, and the shaded area is above the line, then we have:
y > (1/2)*x - 5/2
Now that we have the inequality, we can just input the values of the points in the inequality and see if this is true.
First, options C and D can be discarded because these points are on the line, and the points on the line are not solutions.
So we only try with A and B.
A) x = 5
y = -5
then we have:
-5 > (1/2)*5 - 5/2
-5 > 0
Which clearly is false.
B) x = 1
y = 5
Then we have:
5 > (1/2)*1 - 5/2 = -4/2
5 > -4/2
This is true, then the point (1, 5) is a solution.
Thus the correct option is B.
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Calculate the slope of a line passing through point A at (2, 1) and point B at (4, 2). Calculate to one decimal place.
Answer: 0.5
Step-by-step explanation:
To find the slope of a line with two given points, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
[tex]m=\frac{2-1}{4-2}=\frac{1}{2}=0.5[/tex]
The slope is 0.5.
The profit, in thousands of dollars, from the sale of x thousand candles can be estimated by P(x) = 5 x - 0.7 x ln x.
1) Find the marginal profit, P'(x).
2) Find P'(10), and explain what this number represents. What does P'(10) represent?
A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
B. The additional profit, in thousands of dollars, when 10,000 candles are sold.
C. The additional cost, in thousands of dollars, to produce a thousand candles once 10,000 candles have already been sold.
D The additional cost, in thousands of dollars, to produce 10,000 candles.
C. How many thousands of candles should be sold to maximize profit?
1) The marginal profit is [tex]4.3 - 0.7 ln(x)[/tex].
2) The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) To maximize profit 462,481 thousands of candles should be sold.
Given: [tex]P(x) = 5 x - 0.7 x[/tex] [tex]{\text}ln x.[/tex]
1) Take the derivative of the profit function P(x) with respect to x.
P(x) = 5x - 0.7x ln(x)
To find P'(x), differentiate each term separately using the power rule and the derivative of ln(x):
[tex]P'(x) = 5 - 0.7(1 + ln(x))[/tex]
= [tex]5 - 0.7 - 0.7 ln(x)[/tex]
= [tex]4.3 - 0.7 ln(x)[/tex]
2) Substitute x = 10 into the derivative:
P'(10) = 4.3 - 0.7 ln(10)
= 4.3 - 0.7(2.30259)
= 4.3 - 1.61181
= 2.68819
Therefore, the additional profit for selling a thousand candles once 10,000 candles have already been sold.
Thus, option (A) is correct.
C) Set P'(x) = 0 and solve for x:
[tex]4.3 - 0.7 ln(x) = 0[/tex]
[tex]0.7 ln(x) = 4.3[/tex]
[tex]{\text} ln(x) = 4.3 / 0.7[/tex]
[tex]{\text} ln(x) = 6.14286[/tex]
[tex]x = e^{6.14286[/tex]
[tex]x = 462.481[/tex]
Therefore, 462,481 thousands of candles should be sold.
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1) The marginal profit, P'(x), is -0.7ln(x) + 4.3.
2) The number of thousands of candles that should be sold to maximize profit is approximately 466.9.
1) To find the marginal profit, P'(x), we need to take the derivative of the profit function, P(x), with respect to x. Using the power rule and the chain rule, we can differentiate the function:
P(x) = 5x - 0.7x ln(x)
Taking the derivative with respect to x:
P'(x) = 5 - 0.7(ln(x) + 1)
Simplifying:
P'(x) = 5 - 0.7ln(x) - 0.7
P'(x) = -0.7ln(x) + 4.3
2) To find P'(10), we substitute x = 10 into the marginal profit function:
P'(10) = -0.7ln(10) + 4.3
Using a calculator, we can evaluate this expression:
P'(10) ≈ -0.7(2.3026) + 4.3 ≈ -1.6118 + 4.3 ≈ 2.6882
The value of P'(10) is approximately 2.6882.
Now, let's interpret what P'(10) represents:
The correct interpretation is A. The additional profit, in thousands of dollars, for selling a thousand candles once 10,000 candles have already been sold.
P'(10) represents the rate at which the profit is changing with respect to the number of candles sold when 10,000 candles have already been sold. In other words, it measures the additional profit (in thousands of dollars) for each additional thousand candles sold once 10,000 candles have already been sold.
Lastly, to determine the number of thousands of candles that should be sold to maximize profit, we need to find the critical points of the profit function P(x). This can be done by setting the derivative P'(x) equal to zero and solving for x.
-0.7ln(x) + 4.3 = 0
-0.7ln(x) = -4.3
ln(x) = 4.3 / 0.7
Using properties of logarithms:
x = e^(4.3 / 0.7)
Using a calculator, we can evaluate this expression:
x ≈ e^(6.1429) ≈ 466.9
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Which of the following functions is graphed below?
Answer:
C
Step-by-step explanation:
C is the solution
Answer:
Option C
Step-by-step explanation:
The graph is a horizontal translation 4 units left and a vertical translation 2 units down ⇒ y= |x+4|-2
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide. What is the length of the fence not including the gate? m Use π = 3.14
Answer:
The length of the fence is 6.28x-150 cm.
Step-by-step explanation:
Let the circular pool has the radius (r ) = x cm.
Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.
Length of fence = Circumference of the pool – width of the gate.
Length of fence = 2 π r – 150
Length of fence = 2 × 3.14 × x – 150
Length of fence = 6.28x – 150 cm.
Mario and tabitha are calculating the probability of getting a 4 and a 2 if they roll a die twice. Who is correct?
Answer:
[tex]\frac{2}{12}[/tex] simplified to [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
4 = [tex]\frac{1}{12}[/tex]
2 = [tex]\frac{1}{12}[/tex]
[tex]\frac{1}{12}[/tex] + [tex]\frac{1}{12}[/tex] = [tex]\frac{2}{12}[/tex] ÷ 2 = [tex]\frac{1}{6}[/tex]
From a group of graduate students including 25 men and 22 women, 37 are chosen to participate in a presentation. What is the probability that exactly 19 men and 18 women are chosen
Answer:
25.02% probability that exactly 19 men and 18 women are chosen
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[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]
Desired outcomes:
19 men, from a set of 25
18 women, from a set of 22
[tex]D = C_{25,19}*C_{22,18} = \frac{25!}{19!6!}*\frac{22!}{18!4!} = 1295486500[/tex]
Total outcomes:
37 people from a set of 25 + 22 = 47. So
[tex]T = C_{47,37} = \frac{47!}{37!10!} = 5178066751[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{1295486500}{5178066751} = 0.2502[/tex]
25.02% probability that exactly 19 men and 18 women are chosen
If nine of every 11 trick-or-treaters that came to your house last Halloween were dressed as pirates what proportion of trick-or-treaters were not dressed as pirates
Answer:
11 - 9 = 2 trick-or-treaters out of 11 were not dressed as pirates so the proportion is 2/11.
Answer: Ratio is 2:11
Step-by-step explanation:
So your ratio of pirates to non-pirates would be 9:11
So you subtract number of pirates from total trick-or-treaters and get 2.
So the proportion of non-pirates would be 2:11.
WHO CAN HELP ME WITH MY ACCOUNTING HOMEWORK???
Duran Manufacturing uses a process costing system and manufactures its product in three departments. Which of the following is NOT a way in which Duran can use the cost per unit of each process?
A) Duran can look for ways to cut the costs when actual process costs are more than planned process costs.
B) Duran needs to set the selling price to cover the costs of making the product and provide a profit.
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
D) Duran needs to know the ending balances in the following accounts: Work-In-Process Inventory, Finished Goods Inventory, and Cost of Goods Sold.
Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
Andrea and Helen participated in a donut eating contest. Andrea ate six more than four times the number of donuts that Helen ate. Let d represents the number of donuts Helen ate. Write the expression that gives the number of donuts that Andrea ate.
Answer:
4d + 6
Step-by-step explanation:
Helen ate d donuts.
Andrea ate 6 more than 4 times d.
4d + 6
can anyone help me with this?
Answer: 16y² - x²
Step-by-step explanation: The - sign means a difference, so the choices with + signs are eliminated (though 64x² and 9 are squares)
10 is not a square so that one is eliminated (though the y² and the 4x² are squares)
16 is the square of 4, y² is the square of y, and x² is the square. That expression shows a difference of squares.
pls help me help me
Answer:
A
Step-by-step explanation:
A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular
customer for the past 20 months. Use the given data to answer parts (a) and (b).
325 517 424 395 494
396 351 379 408 426
523 421 434 373 456
535 394 437 403 513
(a) Determine the standard deviation and interquartile range of the data.
s=(Round to two decimal places as needed.)
Answer:
The answer is: 325 517 424 395 494
Step-by-step explanation: