A real estate office manages an apartment complex with 50 units. When the rent is $780 per month, all 50 units are occupied. However, when the rent is $825, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent p and the demand x is linear (Note:The term demand refers to thenumber of occupied units.)
(a) Write a linear equation giving the demand x in terms of the rent p. (b) Linear extrapolation - Use a graphing utility to graph the demand equation and use the trace feature to predict the
number of units occupied when the rent is raised to $855. (c) Linear interpolation - Predict the number of units occupied when the rent is lowered to $795.
Answers
Answer:
A) The linear equation is [tex]x=\frac{-1}{15}p+102[/tex]
B) When the rent is raised to $855 the number of units occupied is 45.
C) When the rent is lowered to $795 the number of units occupied is 49.
Step-by-step explanation:
A) A linear equation for the demand is written as [tex]x=mp+p_{0}[/tex], where [tex]m[/tex] is the slope, [tex]x[/tex] is the number of occupied units, [tex]p[/tex] is the rent.
[tex]m[/tex] is calculated using the problem information. When the rent is [tex]p=$780[/tex] then [tex]x=50[/tex] and when the rent is [tex]p=$825[/tex] then [tex]x=47[/tex].
Using the slope equation we have:
[tex]m=\frac{50-47}{780-825}=\frac{-3}{45}=\frac{-1}{15}[/tex]
Thus the linear equation is:
[tex]x=\frac{-1}{15}p+p_{0}[/tex]
In order to calculate [tex]p_{0}[/tex] we use the problem information, When the rent is [tex]p=$780[/tex] then number of occupied units is [tex]x=50[/tex], thus:
[tex]50=\frac{-1}{15}780+p_{0} \\\\50=-52+p_{0} \\\\p_{0}=102 \\[/tex]
Finally, the linear equation is:
[tex]x=\frac{-1}{15}p+102[/tex]
B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.
C) In order to predict the number of occupied units lets use the equation:
[tex]x=\frac{-1}{15}p+102[/tex]
where [tex]p=$795[/tex], then:
[tex]x=\frac{-1}{15}795+102\\ \\x=-53+102\\\\x=49[/tex]
Thus, when the rent is lowered to $795 the number of units occupied is 49.
Related Questions
A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study?
Answers
Answer: 11
Step-by-step explanation:
We know that the degree of freedom for a t-distribution is given by :-
[tex]df=n-1[/tex], where n is the sample size.
Given : A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.
Then, the number of individuals participated in each study = [tex]df+1=10+1=11[/tex]
Hence, the number of individuals participated in each study =11.
Evaluate the radical
Answers
Answer:
5 1/2
Step-by-step explanation:
Your calculator can give you the correct answer.
___
[tex]\sqrt[3]{343}+\dfrac{3}{4}\sqrt[3]{-8}=7+\dfrac{3}{4}(-2)=7-\dfrac{3}{2}=5\frac{1}{2}[/tex]
Pelomyxa palustris is an amoeba with a length of 4.9 mm.Amoeba proteus has a length of 0.7 mm.How many amoeba proteus would you have to line up to equal the length of three pelomyxa palustris?
Answers
Answer:
21
Step-by-step explanation:
Let n represent the number we're looking for. Then ...
n × (proteus length) = 3 × (palustris length)
n × 0.7 mm = 3 × 4.9 mm
n = (3 × 4.9 mm)/(0.7 mm) = 3 × 49/7 = 3 × 7
n = 21
You would have to line up 21 amoeba proteus to equal the length of three pelomyxa palustris.
Answer:
21
Step-by-step explanation:
1. 49
x 3 1
14.7.
21 _=period move
2. 0.7./14.7.
-14
07
-7
0
check your answer:
21
x0.7. 1
14.7.
Which is the graph of f(x)=1/4(4)^x
Answers
Answer: the 3rd one
Step-by-step explanation: you can type it into a graphing calculator and get the answer
Suppose in a society where there are equal numbers of men and women. There is a 50% chance for each child that a couple gives birth to is a girl and the genders of their children are mutually independent. Suppose in this strange and primitive society every couple prefers a girl and they will continue to have more children until they get a girl and once they have a girl they will stop having more children, what will eventually happen to the gender ratio of population in this society?
Answers
Answer:
eventually the gender ratio of population in this society will be 50% male and 50% female.
Step-by-step explanation:
For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.
As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.
This girl would be the n-th child with a probability [tex](0.5)^n[/tex].We will denote for P(Bₙ) the probability of a couple to have exactly n boys.
Observe that statement 1 implies that:
[tex]P(B_{n-1})=(0.5)^{n}[/tex].
Then, the average number of boys per couple is given by
[tex]\sum^{\infty}_{n=1}(n-1)P(B_{n-1})=\sum^{\infty}_{n=1}(n-1)(\frac{1}{2} )^n=\sum^{\infty}_{n=2}n(\frac{1}{2} )^n=\\\\=\sum^{\infty}_{m=2}\sum^{\infty}_{n=m}(\frac{1}{2} )^n=\sum^{\infty}_{m=2}(\frac{1}{2} )^{m-1}=\sum^{\infty}_{m=1}(\frac{1}{2} )^{m}=1.\\[/tex]
This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.
Can someone help me with the ones that aren’t done
Answers
5:
C = 5/9(F - 32)
C = 5/9(F) - 17.777
-5/9(F) + C = -17.777
-5/9(F) = -C - 17.777
F = 5/9(C) + 32.0306
Answer:
[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]
Step-by-step explanation:
We need to solve following equations in terms of indicated variable:
[tex]5.C=\frac{5}{9}\left ( F-32 \right ):F\\6.ax+by=c;y\\7.\frac{m}{n}=\frac{p}{q};p\\8.A=P+Prt;t\\9.6x+5y=12;y\\10.3y+2=9x-4;y\\12.6x-5y=9;x\\13.C=\pi d\\14.R=\frac{s^2}{A};A\\15.P=2l+2w;w\\16.3x-5y=2;y\\17.2ax+3by=6;x\\18.V=lwh;w[/tex]
Solution:
[tex]5.\, F=\frac{9C}{5}+32\\6.\,y=\frac{c-ax}{b}\\7.\,p=\frac{mq}{n}\\8.\,t=\frac{A-P}{Pr}\\9.\,y=\frac{12-6x}{5}\\10.\,y=\frac{9x-6}{3}\\12. x=\frac{9+5y}{6}\\13.\,\pi=\frac{c}{d}\\14.\,A=\frac{s^2}{R}\\15.\,w=\frac{P-2l}{2}\\16.\,y=\frac{3x-2}{5}\\17.,x=\frac{6-3by}{2a}\\18.\,w=\frac{V}{lh}[/tex]
Please please help me out! :)
Answers
Answer:
x = 24
Step-by-step explanation:
Given that y varies directly with x the the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 10 when x = 8, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{8}[/tex] = 1.25, thus
y = 1.25x ← equation of variation
When y = 30, then
30 = 1.25x ( divide both sides by 1.25 )
x = 24
Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?
Answers
Answer:
If the mean of the sample standard deviations is equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called an unbiased estimator.
If the mean of the sample standard deviations is not equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called a biased estimator.
A biased estimator regularly underestimates or overestimates the parameter.
An unbiased sample statistics are good estimators A biased sample statistics are not good estimators.Final answer:
Sample standard deviations do not target the population standard deviation but serve as estimators. The accuracy of the estimation depends on the sample size.
Explanation:
The sample standard deviations do not target the exact value of the population standard deviation. Instead, they serve as estimators of the population standard deviation. In general, sample standard deviations can be good estimators of population standard deviations, but the accuracy of the estimation depends on the sample size. When the sample size is large, the sample standard deviation tends to be close to the population standard deviation. However, when the sample size is small, the sample standard deviation may not accurately estimate the population standard deviation.
When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 54s to walk from your gate to the baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 83s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding of the moving sidewalk?
Answers
Answer:
Your travel time will be 32.71 secs.
Step-by-step explanation:
Let the total distance be x feet.
Speed while walking = [tex]\frac{x}{54}[/tex] feet per second
Speed on the sidewalk = [tex]\frac{x}{83}[/tex] feet per second
Therefore, total speed while walking on moving sidewalk =
[tex]\frac{x}{54} +\frac{x}{83y}[/tex]
= [tex]\frac{83x+54x}{54\times83}[/tex]
= [tex]\frac{137x}{4482}[/tex]
= [tex]\frac{x}{32.71}[/tex]
Hence, your travel time will be 32.71 secs.
You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination.
Answers
Answer:
3 hours
Step-by-step explanation:
275+55 t=440
55 t=440-275
or 55 t=165
t=165/55=3
wants the perimeter of his rectangular garden to be, at most, 60 feet. He plans on making the length 19 feet. what is the maximum width of his garden , Solving Equations Word problems geometry and angles
Answers
Answer:
width = 11 feet
Step-by-step explanation:
The perimeter of a rectangle is 2 times length + width.
He already decided that the perimeter is at most 60 feet and the length is 19 feet. Then replacing in the formula for perimeter you have:
60 = 2 ( 19 + width)
30 = 19 + width
11 = width
Therefore the maximum width is 11 feet
Blossom Company began the year with retained earnings of $390000. During the year, the company recorded revenues of $489000, expenses of $379000, and paid dividends of $44500. What was Blossom retained earnings at the end of the year?
a) 489000
b) 455500
c) 533500
d) 833500
Answers
Answer:
b) $455,500
Step-by-step explanation:
We have been given that Blossom Company began the year with retained earnings of $390000. During the year, the company recorded revenues of $489000, expenses of $379000, and paid dividends of $44500.
To find the retained earnings, we will use following formula.
[tex]\text{Retained earnings}=\text{Retained earnings (Previous)+Revenue}-\text{Expenses}-\text{Dividends}[/tex]
Upon substituting our given values, we will get:
[tex]\text{Retained earnings}=\$390,000+\$489,000-\$379,000-\$44,500[/tex]
[tex]\text{Retained earnings}=\$879000-\$423,500[/tex]
[tex]\text{Retained earnings}=\$455,500[/tex]
Therefore, the retained earnings at the end of the year was $455,500.
You are going to make three shelves for your father and have one piece of lumber 14 feet long. Your plan is to make the top shelf a foot shorter than then middle shelf and to have the bottom shelf a foot shorter then twice the length of the top shelf. How long is each shelf?
Answers
Answer:
The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- There are 3 shelves
- You have one piece of lumber 14 feet long
- Your plane is:
# The top shelf is 1 foot shorter than the middle shelf
# The Bottom shelf a foot shorter than twice the length of the top shelf
* Assume that the length of the middle shelf is x feet
∵ The length of the middle shelf = x
∵ The top shelf is shorter by 1 foot
∴ The length of the top shelf = x - 1
∵ The length of the bottom shelf is 1 less than twice the length of
the top shelf
- That means multiply the length of the top shelf by 2 and subtract
1 from the product
∵ The length of the top shelf is x - 1
∴ The length of the bottom shelf = 2(x - 1) - 1
- Simplify it by multiplying the bracket by 2 and add like terms
∴ The length of the bottom shelf = 2x - 2 - 1
∴ The length of the bottom shelf = 2x - 3
* The sum of the lengths of the 3 shelves equal the length of lumber
∵ The length of the lumber is 14 feet
∵ The length of the 3 shelves are x - 1 , x , 2x - 3
∴ x - 1 + x + 2x - 3 = 14
- Add like terms in the left hand sides
∴ 4x - 4 = 14
- Add 4 for both sides
∴ 4x = 18
- Divide both by 4
∴ x = 4.5
- Lets find the length of each shelf
∵ The length of the top shelf is x - 1
∴ The length of the top shelf = 4.5 - 1 = 3.5 feet
∵ The length of the middle shelf is x
∴ The length of the middle shelf = 4.5 feet
∵ The length of the bottom shelf is 2x - 3
∴ The length of the bottom shelf = 2(4.5) - 3 = 9 - 3 = 6 feet
* The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet
Final answer:
To find the length of each shelf, a system of equations is created based on the conditions given. Solving this system shows the middle shelf to be 4.5 feet, the top shelf to be 3.5 feet, and the bottom shelf to be 6 feet long.
Explanation:
The question involves using a piece of lumber that is 14 feet long to make three shelves with specific relative lengths. We can let the length of the middle shelf be x feet. Therefore, the top shelf will be x - 1 feet long, and the bottom shelf will be 2(x - 1) - 1 feet long, which simplifies to 2x - 3 feet. Adding together the lengths of the three shelves gives us the total length of the lumber:
x (middle shelf)x - 1 (top shelf)2x - 3 (bottom shelf)So: x + (x - 1) + (2x - 3) = 14.
Solving the equation:
x + x - 1 + 2x - 3 = 144x - 4 = 144x = 18x = 4.5Therefore, the middle shelf is 4.5 feet long, the top shelf is 3.5 feet (4.5 - 1), and the bottom shelf is 6 feet (2(3.5) - 1).
Find the area of this irregular polygon.
Answers
Answer:
970m^{2}
Step-by-step explanation:
This polygon can be divided in two figures: one is a triangle, an the other one is a square.
We'll begin calculating the triangle's area, using the following formula:
[tex]At= \frac{b.h}{2}[/tex]
Where:
[tex]H= height = 30 m[/tex]
[tex]B = 9 m + 9 m + 20 m = 38 m[/tex]
As you can see, I added both sides of the triangle that measure 9 m and also the lenght of the square that measures 20 m! This added up is what the base of the triangle measures on total.
[tex]At= \frac{38 m .30 m}{2}[/tex]
[tex]At= \frac{1140 m^{2} }{2}[/tex]
[tex]At= 570 m^{2} [/tex]
Now we are going to calculate the square's area, that is much more simple:
[tex]As= L^{2} [/tex]
Where:
[tex]L=20 m [/tex]
[tex]As= (20 m)^{2} = 400m^{2} [/tex]
To know the whole figure's area, we add up both areas:
[tex]A = At+As = 570m^{2} +400m^{2}=970m^{2} [/tex]
I don't know how to solve this:
In a pair of complementary angles, one angle measures 18* less than three times the other angle. Find the measure of each angle.
Answers
Answer:
18, 72
Step-by-step explanation:
Two angles are complementary if they sum up to 90°. Call them [tex] x, (90-x) [/tex]. From the second part,
[tex]
3 x = 90-x+18 \\
4x = 72 \\
x= 18 [/tex]
The second angle is [tex] 90-18 = 72 [/tex]
Use the formula to estimate the temperature when n = 52 chirps/min. Round to the nearest whole number, if necessary. The formula F equals n divided by 4 plus 37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. A. 58°F B. 52°F C. 53°F D. 50°F
Answers
Answer:
The answer to your question is: d) 50°F
Step-by-step explanation:
Data
n = 52 chirps/min
Formula
F = n/4 + 37
Substitution
F = 52/4 + 37
F = 13 + 37 simplifying
F = 50 °F result
Upon joining the Girl Scouts a member receives 4 patches. Karen has been in the girls scouts for quite awhile and has a total of 70 patches. If Karen earns 3 patches each month,how many months has Karen been a member of the girls scouts?
Answers
Answer:
Karen has been a member of Girl Scouts for 22 months
Step-by-step explanation:
Let
x -----> the time in months
we know that
The total number of patches must be equal to the number of months multiplied by 3 patches each month plus 4 patches
so
[tex]70=3x+4[/tex]
Solve for x
Subtract 4 both sides
[tex]70-4=3x\\66=3x[/tex]
Divide by 3 both sides
[tex]22=x[/tex]
Rewrite
[tex]x=22\ months[/tex]
therefore
Karen has been a member of Girl Scouts for 22 months
Karen has been a member of the Girl Scouts for 22 months.
Explanation:To determine the number of months Karen has been a member of the Girl Scouts, we can set up an equation using the information given.
Let's assume that Karen has been a member for x months.
Since she earns 3 patches each month, the total number of patches she has earned is 3x.
Adding the initial 4 patches she received upon joining, we have the equation 3x + 4 = 70.
To solve for x, we can subtract 4 from both sides of the equation: 3x + 4 - 4 = 70 - 4, which simplifies to 3x = 66.
Finally, we can divide both sides of the equation by 3 to solve for x: x = 66 ÷ 3 = 22.
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20 POINTS AND BRAINLIEST PLZ HELP
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.
A. −5
B. -1/5
C. 1/5
D. 5
Answers
Answer:
Step-by-step explanation:
B or C is your answer
A local Computer City sells batteries ($3) and small boxes of pens ($5). In August, total sales were $960. Customers bought 5 times as many batteries as boxes of pens. How many of each did Computer City sell?
Answers
Answer:
The number of batteries sold was 240 and the number of small boxes of pens sold was 48
Step-by-step explanation:
Let
x -----> the number of batteries sold
y ----> the number of small boxes of pens sold
we know that
[tex]3x+5y=960[/tex] -----> equation A
[tex]x=5y[/tex] ----> equation B
substitute equation B in equation A
[tex]3(5y)+5y=960\\15y+5y=960\\20y=960\\y=48\ boxes\ of \ pens[/tex]
Find the value of x
[tex]x=5(48)=240\ batteries[/tex]
therefore
The number of batteries sold was 240 and the number of small boxes of pens sold was 48
You are adding air to a tire the air pressure in the tire should be 32 27/200 pounds per square inch. What decimal should you watch for not the digital pressure gauge
Answers
Answer:
24
Step-by-step explanation:
The air pressure in tire should be 32.135 pounds per square inch. Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The air pressure in the tire should be pounds per square inch. This pressure is in the form of a mixed fraction. It is required to convert this pressure into a decimal form. We can convert it as follows;
The air pressure in tire =32 27/200
It is given in the form of a mixed fraction.
32 27/200 = ( 32 x 200) 27/200
First we, convert this mixed fraction into unlike fraction and then convert it into a decimal number;
32 27/200 = ( 32 x 200) 27/200
= 6427 /200
= 32.135
Therefore, the air pressure in tire should be 32.135 pounds per square inch.
Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.
Learn more about the unitary method;
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The process of manipulating one or more independent variables and measuring their effect on one or more dependent variables while controlling for the extraneous variables is called an experiment. a. True b. False
Answers
Answer: Ok, let's think our dependent variable like the position of a car with velocity of 50km/h, and our independent variable the time.
so, you can choose any time you want, and for each time, the car will be in a different position, so the position is a variable dependent of the time.
let's suppose you don't know the velocity of the car.
first you see the position at a time t₁ and the position is r₁.
then you see the position at time t₂, and the result is r₂.
here you changed the independent variable and observed how the dependent variable changed. And in this case, with the 4 numbers you observed you can obtain the velocity of the car.
So yes, you can call it an experiment.
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.
Answers
Answer:
Step-by-step explanation:
$3x6=18 the six represents the apples and the 3 is the cost of each apple, 18 is the cost.
$2x9=$18 the nine is the oranges and the two is the money spent on each one. The total would be $36 in total for all the fruit.
So (9x2)+(3x6)=$36
Answer with Step-by-step explanation:
Susan needs to buy apples and oranges to make fruit salad.
She needs 15 fruits in all.
Let m represent the number of apples.
Number of oranges= 15-m
Apples cost $3 per piece, and oranges cost $2 per piece.
Amount spent= $ (3m+2(15-m))
= $ (3m + 2×15 - 2m)
= $ (m+30)
If she bought 6 apples.
i.e. m=6
Amount spent =$ (6+30)
= $ 36
Hence,
Expression that represents the amount Susan spent on the fruits is:
m+30
The amount Susan spent if she bought 6 apples is:
$ 36
In the equation left parenthesis x squared plus 14 x right parenthesis plus left parenthesis y squared minus 18 y right parenthesisequals5, complete the square on x by adding _______ to both sides. Complete the square on y by adding _______ to both sides.
Answers
Answer:
Complete the square on x by adding 49 to both sides.
Complete the square on y by adding 81 to both sides.
Step-by-step explanation:
We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.
We know to complete a square, we add the half the square of coefficient of x or y term.
Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.
[tex](\frac{14}{2})^2=7^2=49[/tex]
[tex](\frac{18}{2})^2=9^2=81[/tex]
Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:
[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]
Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:
[tex](x+7)^2+(y+9)^2=135[/tex]
Therefore, We can complete the square on x by adding 49 to both sides and the square on y by adding 81 to both sides.
3. Suppose that you initially have $100 to spend on books or movie tickets. The books start off costing $25 each and the movie tickets start off costing $10 each. For each of the following situations, would the attainable set of combinations that you can afford increase or decrease?
a. Your budget increases from $100 to $150 while the prices stay the same.
b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.
c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.
Answers
Answer:
Suppose that you initially have $100 to spend on books or movie tickets.
The books start off costing $25 each and the movie tickets start off costing $10 each.
a. Your budget increases from $100 to $150 while the prices stay the same.
Increase
b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.
Decrease
c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.
Increase
A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. Compute the probability that 2 or fewer will withdraw (to 4 decimals). Compute the probability that exactly 4 will withdraw (to 4 decimals). Compute the probability that more than 3 will withdraw (to 4 decimals). Compute the expected number of withdrawals.
Answers
Step-by-step explanation:
a) Compute the probability that 2 or fewer will withdraw
First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:
[tex](0.3)^2(0.7)^{18}[/tex].
Then, we must multiply this quantity by
[tex]{20\choose2}=\frac{20!}{18!2!}=\frac{20\times19}{2}=190,[/tex]
which is the number of ways to choose 2 students from the total of 20. Therefore:
the probability that exactly 2 students withdraw is [tex]190(0.3)^2(0.7)^{18}[/tex].Following an analogous process we can determine that:
The probability that exactly 1 student withdraw is [tex]{20\choose1}(0.3)(0.7)^{19}=20(0.3)(0.7)^{19}.[/tex] The probability that exactly none students withdraw is [tex]{20\choose 0}(0.7)^{20}=(0.7)^{20}.[/tex]Finally, the probability that 2 or fewer students will withdraw is
[tex]190(0.3)^2(0.7)^{18}+20(0.3)(0.7)^{19}+(0.7)^{20}=(0.7)^{18}(190(0.3)^2+20(0.3)(0.7)+(0.7)^2)\approx0.0355[/tex]
b) Compute the probability that exactly 4 will withdraw.
Following the process explained in a), the probability that 4 student withdraw is given by
[tex]{20\choose4}(0.3)^4(0.7)^{16}=\frac{20\times19\times18\times17}{4\times3\times2} (0.3)^4(0.7)^{16}=4845(0.3)^4(0.7)^{16}\approx 0.1304.[/tex]
c) Compute the probability that more than 3 will withdraw
First we will compute the probability that exactly 3 students withdraw, which is given by
[tex]{20\choose3}(0.3)^3(0.7)^{17}=\frac{20\times19\times18}{3\times2} (0.3)^3(0.7)^{17}=1140(0.3)^3(0.7)^{17}\approx 0.0716.[/tex]
Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929
d) Compute the expected number of withdrawals.
As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
This problem involves using the binomial distribution to compute probabilities of student withdrawal and the expected number of withdrawals. Probability values are computed using the binomial probability formula and the expected number of students withdrawing from the course is given by n*p.
Explanation:To solve the probability and expected value questions, we need to use the binomial distribution since the event (a student withdraws or not) is independent and repeated a fixed number of times.
1. The probability that 2 or fewer will withdraw is [tex]P(X < =2) = P(0)+P(1)+P(2) where P(x) = C(n, x) * (p^x) * (q^(n-x)). For n=20, p=0.3, q=0.7.[/tex]
2. The probability that exactly 4 withdraw is given by the binomial probability formula P(X=4). Again, use the same values of n, p, and q.
3. The probability that more than 3 will withdraw is P(X > 3) which is 1 - P(X<= 3). Compute P(X<=3) similar to the first situation and subtract it from 1.
4. The expected number of withdrawals, or the expectation of a binomial distribution, is given by n*p.
Calculations using these formulas will give you the desired probabilities to the accuracy you require.
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Which of the following is the solution to 9 | x + 4 | >= 54?
PLEASE HELP
Answers
Answer:
your selection is correct
Step-by-step explanation:
You can divide by 9 to get ...
| x+4 | ≥ 6
This resolves to two inequalities:
-6 ≥ x +4 ⇒ -10 ≥ xx +4 ≥ 6 ⇒ x ≥ 2These are disjoint intervals, so the solution set is the union of them:
x ≤ -10 or 2 ≤ x
Answer:
Step-by-step explanation: A is correct
When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel:
F=kR4(This is known as Poiseuille’s Law;) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. Show that the relative change in F is about four times the relative change in R. How will a 5% increase in the radius affect the flow of blood?
Answers
Answer:
[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]
So a 5% relative increase in R would mean a 20% relative increase in F
Step-by-step explanation:
First we need to remind the definition of relative increase of a variable.
For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].
Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].
Let's then start by deriving F with respect to R:
[tex]\frac{dF}{dR}=4kR^3[/tex]
thus
[tex]dF=4kR^3dR[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]
[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].
If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get
[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]
According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.
Explanation:Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.
To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.
By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.
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The length of a rectangle is five times its width.
If the area of the rectangle is 405 in^2, find its perimeter.
Answers
Answer:
The answer to your question is: Perimeter = 108 in
Step-by-step explanation:
Data
Length (l) = 5 width (w)
A = 405 in²
Perimeter = ?
Formula
Area = l x w
Perimeter = 2w + 2l
Process
405 = 5w x w
405 = 5w²
405/5 = w²
w = √81
w = 9 in
l = 5(9) = 45 in
Perimeter = 2(9) + 2(45)
= 18 + 90
= 108 in
Mary and tom park their cars in an empty parking lot with n ≥ 2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). mary and tom pick parking spaces at random. (all pairs of distinct parking spaces are equally likely.) what is the probability that there is at most one empty parking space between them?
Answers
Answer:
p(at most one space between) = (4n-6)/(n(n-1))
Step-by-step explanation:
There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...
(n -1) +(n -2) = 2n-3
The number of ways that 2 cars can be parked in n spaces is ...
(n)(n -1)/2
So, the probability is ...
(2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))
___
If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.
__
Check
For n=2 or 3, p=1 as you expect.
For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
We have,
To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:
Mary and Tom park their cars in adjacent spaces.
Mary and Tom park their cars in spaces with one empty space in between them.
Scenario 1: Mary and Tom park their cars in adjacent spaces.
In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.
Scenario 2: Mary and Tom park their cars with one empty space between them.
In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.
Now, we add up the probabilities of both scenarios because they are mutually exclusive:
Total Probability = Probability of Scenario 1 + Probability of Scenario 2
Total Probability = [(n - 1) / n] + [(n - 2) / n]
To make these fractions have a common denominator, we can rewrite them as:
Total Probability = [(n - 1) + (n - 2)] / n
Total Probability = [2n - 3] / n
Thus,
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
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The value of a collector's item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years. $578.81 $607.75 $1687.50 $2531.25
Answers
Answer:
$607.75
Step-by-step explanation:
As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.
The appropriate answer choice is $607.75.
_____
The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...
$500 × 1.21550625 = $607.753125 ≈ $607.75
Answer:
Answer: $607.75
Step-by-step explanation:
Answer:
$607.75
Step-by-step explanation:
As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.
The appropriate answer choice is $607.75.
_____
The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...
$500 × 1.21550625 = $607.753125 ≈ $607.75