Answer:
9 ft × 7 ft × 1 ft and 21 ft × 3 ft × 1 ft
Step-by-step explanation:
The formula for the volume of a rectangular prism is
V = lwh
The prime factors of 63 are
3, 3, and 7.
Most raised garden beds are 1 ft deep, so two combinations that would work are
(3 × 3) × 7 × 1 = 9 ft × 7 ft × 1 ft = 63 ft³
3 × (3 × 7) × 1 = 21 ft × 3 ft × 1 ft = 63 ft³
The number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through the production line has either 3, 7, or 12 defects, for which of theses values does the mean number of defects per car for the first six cars equal the median?
I. 3
II. 7
III. 12
A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III
Answer:
D
Step-by-step explanation:
Depending on the number of defects in 6th car, we have 3 cases:
3,4,6,7,9,10 (median 13/2 =6.5) 4,6,7,7,9,10 (median 14/2 = 7) 4,6,7,9,10,12 (median 16/2 = 8)To find mean we can use the sum of numbers given (= 36) and add either 3, 7, or 12 to it and then divide by 6 (number of cars).
(36 + 3) /6 = 39/6 = 6.5 (== median above)
(36 + 7) /6 = 43/6 = 7.1 (does not equal median above)
(36 + 12) /6 = 48/6 = 8 (== median above)
Answer: D (I and III only).
Select the TRUE statements.
For the function 48(1.25)x, the parameter for the growth factor is 1.25.
For the function f(x) = 75x + 250, the parameter for the beginning value is 75.
For the function 28(0.5)x, the parameter for the decay factor is 50%.
For the function y = 18x + 72, the parameter for the average rate of change is 18.
Answer:
a) For the function [tex]48(1.25)^x[/tex], the parameter for the growth factor is 1.25
c) For the function [tex]28(0.5)^x[/tex], the parameter for the decay factor is 50%.
d) For the function y = 18x + 72, the parameter for the average rate of change is 18.
Step-by-step explanation:
We are given the following in the question:
a) the parameter for the growth factor is 1.25.
[tex]f(x) = 48(1.25)^x[/tex]
Comparing it to
[tex]y(x) = a(1+r)^x[/tex]
The growth factor is
[tex]1+r = 1.25[/tex]
Thus, the given statement is true
b) the parameter for the beginning value is 75.
We are given the equation
[tex]f(x) = 75x + 250[/tex]
The beginning value is given when x = 0. Putting value, we get
[tex]f(0) = 75(0) + 250 = 250[/tex]
Thus, the beginning value is 250.
Hence, the given statement is false.
c) the parameter for the decay factor is 50%.
[tex]f(x) = 28(0.5)^x[/tex]
Comparing it to
[tex]y(x) = a(1-r)^x[/tex]
The growth factor is
[tex]1-r = 0.5 = 50\%[/tex]
Thus, the given statement is true
d) the parameter for the average rate of change is 18.
[tex]y = 18x + 72[/tex]
Comparing to general form of equation:
[tex]y = mx + c[/tex]
where m is the slope and gives the average rate of change.
Thus, the average rate of change is 18.
Hence, the given statement is true.
A rectangular prism with the surface area of 336 and width of 4 is similar to a rectangular prism with the width of 6, what is the surface area of the larger prism
Answer:
The larger surface area would be 756 [tex]Unit^2[/tex]
Step-by-step explanation:
Given the surface area of rectangular prism is 336 [tex]Unit^2[/tex] when its width is 4 [tex]Unit[/tex].
We need to compute the surface area when its width is 6 [tex]Unit[/tex].
Also, it was given that prisms are similar to each other.
Let us assume the [tex]l[/tex] is length [tex]b[/tex] is width and [tex]h[/tex] is the height of the prism.
So, the surface area would be
[tex]S=2(lb)+2(bh)+2(hl)[/tex]
[tex]336=2(4l)+2(4h)+2(hl)[/tex] Equation (1)
Now, the new width is 6 [tex]Unit[/tex]. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.
We can write
[tex]b'=1.5\times b=1.5\times 4=6\\l'=1.5\times l\\h'=1.5\times h[/tex]
So, the new surface area would be
[tex]S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5\times l\times 1.5\times 4)+2(1.5\times4 \times 1.5\times h)+2(1.5\times h\times 1.5\times l)\\S'=2.25\times 2(l4)+2.25\times 2(h)+2.5\times 2(hl)[/tex]
[tex]S'=2.25[2(4l)+2(4h)+2(hl)][/tex]
From Equation (1) we can plug [tex]336=2(4l)+2(4h)+2(hl)[/tex]
[tex]S'=2.25\times 336=756\ Unit^2[/tex]
So, the larger surface area would be 756 [tex]Unit^2[/tex]
PLEASE i need help ASAP i beg of you!! due today!!! 50 points! and brainliest!!!!!!!
1. Anthony has a sink that is shaped like a half-sphere. The sink has a volume of
660 pi in^3. One day, his sink clogged. He has to use one of two
cylindrical cups to scoop the water out of the sink. The sink is completely full
when Anthony begins scooping.
(a) One cup has a diameter of 5 in, and a height of 8 in. How many cups of
water must Anthony scoop out of the sink with this cup to empty it?
Round the number of scoops to the nearest whole number.
(b)One cup has a diameter of 10 in, and a height of 8 in. How many cups of
water must he scoop out of the sink with this cup to empty it? Round the
number of scoops to the nearest whole number.
THE ANSWER FOR CUP A IS 660 divided by 157
the answer to cup b is 660 divided by 628.319
brainliest plz
As a business person you need to visit each of the following cities once. You need to start in Atlanta and end in Atlanta. Use the "Nearest Neighbor" Algorithm to find one of the cheaper routes to visit each city and return home again.
Group of answer choices
A
B
C
D
Answer:
it was B
Step-by-step explanation:
The algorithm employing "Nearest Neighbour" to determine one of the cheaper routes to visit every city and get back home again would be:
B). ATL-CHI-BOS-DEN-ATL
Algorithm is described as the compilation of sequenced steps that assist in resolving a mathematical problem. This involves a step-by-step organization that assists in determining the final value post following the steps. In the given scenario, the cheaper route to visit all the given cities once and returning home again would be beginning from Atlanta via Chicago, Boston, Denver, and returning back to Atlanta.
Thus, option B is the correct answer.
Learn more about "Algorithm" here
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We have two fair three-sided dice, indexed by i = 1, 2. Each die has sides labeled 1, 2, and 3. We roll the two dice independently, one roll for each die. For i = 1, 2, let the random variable Xi represent the result of the i-th die, so that Xi is uniformly distributed over the set {1, 2, 3}. Define X = X2 − X1. 1. Calculate the numerical values of following probabilities:____________. (a) P(X = 0) = (b) P(X = 1) = (c) P(X = −2) = (d) P(X = 3) = Let Y = X2 . Calculate the following probabilities:_________. (a) P(Y = 0) =(b) P(Y = 1) = (c) P(Y = 2) =
Answer:
(a) P(X = 0) = 1/3
(b) P(X = 1) = 2/9
(c) P(X = −2) = 1/9
(d) P(X = 3) = 0
(a) P(Y = 0) = 0
(b) P(Y = 1) = 1/3
(c) P(Y = 2) = 1/3
Step-by-step explanation:
Given:
- Two 3-sided fair die.
- Random Variable X_1 : Result on 1st die.
- Random Variable X_2: Result on 2nd die.
- Random Variable X = X_2 - X_1.
Solution:
- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }
- The corresponding probabilities for each outcome are:
( X = -2 ): { X_2 = 1 , X_1 = 3 }
P ( X = -2 ): P ( X_2 = 1 ) * P ( X_1 = 3 )
: ( 1 / 3 ) * ( 1 / 3 )
: ( 1 / 9 )
( X = -1 ): { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }
P ( X = -1 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)
: ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )
: ( 2 / 9 )
( X = 0 ): { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } + { X_2 = 3 , X_1 = 3 }
P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )
: 3*( 1 / 3 ) * ( 1 / 3 )
: ( 3 / 9 ) = ( 1 / 3 )
( X = 1 ): { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }
P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )
: 2* ( 1 / 3 ) * ( 1 / 3 )
: ( 2 / 9 )
( X = 2 ): { X_2 = 1 , X_1 = 3 }
P ( X = 2 ): P ( X_2 = 3 ) * P ( X_1 = 1 )
: ( 1 / 3 ) * ( 1 / 3 )
: ( 1 / 9 )
- The distribution Y = X_2,
P(Y=0) = 0
P(Y=1) = 1/3
P(Y=2) = 1/ 3
- The probability for each number of 3 sided die is same = 1 / 3.
In this exercise we have to use the knowledge of probability to calculate the chance of an event to occur, so:
A) P(X = 0) = 1/3
B) P(X = 1) = 2/9
C) P(X = −2) = 1/9
D) P(X = 3) = 0
A) P(Y = 0) = 0
B) P(Y = 1) = 1/3
C) P(Y = 2) = 1/3
organizing the following information given in the text we have that:
Two 3-sided fair die.Random Variable X_1 : Result on 1st dieRandom Variable X_2: Result on 2nd die.Random Variable X = X_2 - X_1.Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }Then calculating the probability we find that:
A) For P(X = 0) we have
[tex]( X = -2 ): { X_2 = 1 , X_1 = 3 } \\P ( X = -2 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]
B) For P(X = 1) er have:
[tex]( X = -1 ): { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }\\ P ( X = -1 ): P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)\\ : ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )[/tex]
C) For P(X = −2) we have:
[tex]( X = 0 ): { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } + { X_2 = 3 , X_1 = 3 }\\ P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )\\ : 3*( 1 / 3 ) * ( 1 / 3 )\\ : ( 3 / 9 ) = ( 1 / 3 )[/tex]
D) For P(X = 3), we have:
[tex]( X = 1 ): { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }\\ P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )\\ : 2* ( 1 / 3 ) * ( 1 / 3 )\\ : ( 2 / 9 )\\ ( X = 2 ): { X_2 = 1 , X_1 = 3 }\\ P ( X = 2 ): P ( X_2 = 3 ) * P ( X_1 = 1 ) \\ : ( 1 / 3 ) * ( 1 / 3 ) \\ : ( 1 / 9 )[/tex]
In this next case we have to take into account that the number will be the probability of falling 3, that is:
A) P(Y=0) = 0
B) P(Y=1) = 1/3
C) P(Y=2) = 1/ 3
See more about probability at brainly.com/question/795909
5. Richard is flying a kite. The kite string makes an angle of 57 with the ground. If
Richard is standing 100 feet from the point on the ground directly below the kite, find
the length of the kite string
So
Answer: the length of the kite string is 183.6 feet
Step-by-step explanation:
The string of the kite forms an angle of 57° with the ground thus, a right angle triangle is formed. Richard's distance from the point on the ground directly below the kite represents the adjacent side of the right angle triangle. The length of the kite, h represents the hypotenuse of the right angle triangle. To determine h, we would apply the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 57 = 100/h
h = 100/Cos57
h = 100 /0.5446
h = 183.6 feet
We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. 1. How many people would you expect to have consumed alcoholic beverages? (round to one decimal place) 2. What is the standard deviation? (round to two decimal places) 3. Would you be surprised, if there were 45 or more people who have consumed alcoholic beverages? _
Answer:
(1) The expected number of people who would have consumed alcoholic beverages is 34.9.
(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.
(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.
Step-by-step explanation:
Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.
The probability of the random variable X is, p = 0.697.
A random sample of n = 50 adults in the age group 18 - 20 years is selected.
An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.
The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.
The probability mass function of a Binomial random variable X is:
[tex]P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...[/tex]
(1)
Compute the expected value of X as follows:
[tex]E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9[/tex]
Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.
(2)
Compute the standard deviation of X as follows:
[tex]SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56[/tex]
Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.
(3)
Compute the probability of X ≥ 45 as follows:
P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)
[tex]=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006[/tex]
The probability that 45 or more have consumed alcoholic beverages is 0.0006.
An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.
The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.
Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.
Oak pollen sent 21,000 people to U.S. emergency rooms for asthma in 2010. By 2090 the rate could climb another 5 or 10 percent. If true, what would the numbers then be Show your work.
The probable number of prople sent to US emergency rooms by 2090 can be between 22,050 and 23,100
Step-by-step explanation:
Total sent to US emergency room by 2010= 21000
The estimated increase in the rise of cases = 5 to 10% by 2090
Final numbers in 2090
Hence the final numbers in 2090 would be 5 to 10% more than the total cases in 2010
Lower limit= 5% of 21000= 1050
Hence lower limit of cases in 2090= 21000+1050= 22050
Upper limit of cases in 2090= 10% of 21000= 21000+2100= 23,100
The number would lie anywhere between 22050 and 23,100 in 2090
Factor the expression. 48g2 – 22gh – 15h2
A. (6g – 5h)(8g + 3h)
B. (6g – 5)(8g + 3)
C. (6g + 5)(8g + 3h2)
D. (6g + 5h)(8g – 3h)
Answer:
A
Step-by-step explanation:
FOIL:First,Inner,Outer,Last
After the polynomial operations are done we can see that A is the answer.
6g*8g=48g^2
6g*3h=18gh
8g*-5h=-40gh
-5h*3h=-15h
After combining like terms we get :
48g^2-22gh-15h^2
Amanda spent a total of 70 minutes competing her chores this week. Write and solve an equation to represent the number of minutes Amanda spent washing the dishes
Answer:
28 minutes spent in washing the dishes.
Step-by-step explanation:
Given the table
Chore time in minutes
Sweeping 42
Dishes ?
Amanda spent a total of 70 minutes competing her chores this week
Total of 70 minutes spent
42 minutes spent in sweeping . to find the number of minutes Amanda spent in washing the dishes , subtract 42 minutes from the total time spent
let x be the number of minutes spent washing the dishes
[tex]42+x=70[/tex]
To solve for x , subtract 42 from both sides
[tex]42+x=70\\x= 70-42\\x=28[/tex]
28 minutes spent in washing the dishes.
HELP PLEASE 98 points
Given: BD¯¯¯¯¯ is an altitude of △ABC .
Prove: sinAa=sinCc
Triangle A B C with an altitude B D where D is on side A C. side A C is also labeled as small b. Side A B is also labeled as small c. Side B C is also labeled as small a. Altitude B D is labeled as small h.
Select from the drop-down menus to correctly complete the proof.
Statement Reason
BD¯¯¯¯¯ is an altitude of △ABC . Given
△ABD and △CBD are right triangles. Definition of right triangle
sinA=hc and sinC=ha
csinA=h and asinC=h
csinA=asinC
csinAac=asinCac Division Property of Equality
sinAa=sinCc Simplify.
Answer:
Given: BD is an altitude of △ABC .
Prove: sinA/a=sinC/c
Triangle ABC with an altitude BD where D is on side AC. Side AC is also labeled as small b. Side AB is also labeled as small c. Side BC is also labeled as small a. Altitude BD is labeled as small h.
Statement Reason
BD is an altitude of △ABC .
Given △ABD and △CBD are right triangles. (Definition of right triangle)
sinA=h/c and sinC=h/a
Cross multiplying, we have
csinA=h and asinC=h
(If a=b and a=c, then b=c)
csinA=asinC
csinA/ac=asinC/ac (Division Property of Equality)
sinA/a=sinC/c
This rule is known as the Sine Rule.
Answer:
For the people on Edge the answers are:
a/f
cf
c/b
cf + ec
c
If f(x) = 2x - 4 and g(x) = x^2+3, find each value.
19. (f - g)(x)
20. (f • g)(x)
Step-by-step explanation:
[tex](f - g)(x) = f(x) - g(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2x - 4) - ( {x}^{2} + 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x - 4 - {x}^{2} - 3 \\ \red{ \boxed{\therefore (f - g)(x) = - {x}^{2} + 2x - 7}}[/tex]
Find the angle of the rotations for the graphs below. The center of rotation is the origin, and the darker image is the preimage. Your answer will be 90°, 270 degrees, or 180 degrees.
Answer:
a. 90°
b. 180°
c. 180°
Step-by-step explanation:
For these problems there is a bit of a shortcut you can take. Each figure is entirely within one quadrant, and the rotation is said to be by 90° (one quadrant), 180° (two quadrants), or 270° (three quadrants) clockwise.
a. The image is in the adjacent clockwise quadrant, so rotation is 90°.
b, c. The image is in the diagonally opposite quadrant, so rotation is 180°.
Cole has 4 regular dice and 1 unique dice that has the value 1 on each of the 6 faces. He picks one at random and rolls 3 ones in a row. What is the probability he picked the unique dice
Answer:
0.008
Step-by-step explanation:
The probability of having chosen the unique dice three times in a row would be the multiplication of the probability of each event.
The event is always repeated. Take the single dice of 5 dice in total. Therefore the probability is 1/5.
Then the final probability would be:
(1/5) * (1/5) * (1/5), and that is equal to 0.008.
The probability that Cole picked the unique die given that he rolled three ones in a row is approximately 49.1%. This is calculated using Bayes' Theorem with the probabilities of rolling three ones with both the unique and regular dice.
Cole has 4 regular dice and 1 unique die that always rolls a 1. Let's calculate the probability that he picked the unique die given that he rolled three ones in a row.
First, find the probability of rolling three ones in a row using a regular die:
Probability of rolling a 1 on a regular die = 1/6Probability of rolling three ones in a row = (1/6) × (1/6) × (1/6) = 1/216Second, since the unique die always rolls a 1, the probability of rolling three ones in a row with it is 1.
Using Bayes' Theorem, we calculate the probability that Cole picked the unique die:
Let A be the event that Cole picked the unique die.
Let B be the event that Cole rolled three ones in a row.
P(A) = 1/5 (since there's 1 unique die out of 5 dice)P(B|A) = 1 (probability of B given A)P(B|A') = 1/216 (probability of B given not A)P(A') = 4/5 (probability of not picking the unique die)P(B) = P(B|A)P(A) + P(B|A')P(A') = 1 × (1/5) + (1/216) × (4/5)P(B) = 1/5 + 4/1080 = 0.2 + 0.0037 = 0.2037Finally, P(A|B) = (P(B|A)P(A)) / P(B) = (1 × 1/5) / 0.2037 ≈ 0.491Thus, the probability that Cole picked the unique die is approximately 0.491 or 49.1%.
Wu rolls two fair, six-sided dice. You are not told what the rolls were, but you are told that the sum of the two rolls is a prime. What is the probability that the sum of the two rolls is $5$?
The probability of rolling a sum of 5 when rolling two fair, six-sided dice is 1/18.
Explanation:The probability that the sum of the two rolls is 5 can be found by considering the possible outcomes. There are a total of 36 equally likely outcomes when rolling two fair, six-sided dice.
Out of these, the prime sums are 5, 7, 11, and 17. The sum of 5 can only be obtained by rolling a 1 and a 4 or a 2 and
a 3. Since each die has 6 sides, the probability of rolling a 1 and a 4 is 1/6 × 1/6 = 1/36.
Similarly, the probability of rolling a 2 and a 3 is also 1/36. Therefore, the overall probability of rolling a sum of 5 is
1/36 + 1/36 = 2/36 = 1/18.
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There is a sale on computers at your local Comp2u. The gaming system that you are interested in has the latest Intel Quad core processor and duel NVIDIA GeForce 9800S graphics card. The sale price on the computer is $1,500.00 plus 5.1% sales tax. Your monthly gross salary is $2,500. How much will you have saved over a two month period and will you be able to afford the computer, given your monthly expenses total $1,250, Social Security is 6.2% of your biweekly income, Medicare is 1.45% of your biweekly income, and you pay State and Federal taxes in the amount of $45.00 and $89.51 biweekly respectively?
Answer:
$1,579.44; yes
Step-by-step explanation:
The student will have saved $2500 over the two month period and will be able to afford the computer.
Explanation:In order to calculate the amount saved over a two month period, we need to calculate the monthly savings. To do this, we subtract the monthly expenses from the monthly gross salary:
$2,500 - $1,250 = $1,250
So the monthly savings is $1,250. To find the savings over a two month period, we multiply the monthly savings by 2:
$1,250 x 2 = $2,500
The cost of the computer is $1,500 plus 5.1% sales tax. To find the total cost, we multiply $1,500 by 1.051:
$1,500 x 1.051 = $1,576.50
Since the savings over a two month period is $2,500, and the total cost of the computer is $1,576.50, the student will be able to afford the computer and have savings left over.
two integers whose product is 90 and whose sum is 21
Answer:
6 and 15
Step-by-step explanation:
Answer:
6 and 15
Step-by-step explanation:
the factors of 90 are:
1 90
2 45
3 30
5 18
6 15
9 10
find the factors that =21
6+15=21 and 6 x 15=21
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 73,000 + 70 x and [tex]p(x) = 250 - (\frac{x}{20}), 0 \leq x \leq 5000[/tex].(A) Find the maximum revenue.
(B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
(C) If the government decides to tax the company $55 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
(A) The maximum revenue is $_________.
(B) The maximum profit is when sets are manufactured and sold for each.
(C) When each set is taxed at $55, the maximum profit is when sets are manufactured and sold for each.
Answer:
a) The maximum revenue is $312500
b) The maximum profit is $89000, the production level that will realize the maximum profit is 1800, and the price the company should charge for each television set is $160.
C) If the government decides to tax the company $55 for each set it produces, the sets should the company manufacture each month to maximize its profit is 1250. the maximum profit is $70825 What should the company charge for each set is $187.5
Step-by-step explanation:
a) Revenue R(x)
R(x) = p(x) * x = x * [tex](250-\frac{x}{20})[/tex] = [tex](250x-\frac{x^{2} }{20})[/tex]
For maximum revenue, the first derivative of R(x) = R'(x) = 0
R'(x) = [tex](250-\frac{2x}{20}) = 0[/tex]
[tex](250-\frac{2x}{20}) = 0\\[/tex]
[tex]250=\frac{2x}{20}[/tex]
x = 2500
the second derivative of R(x)=R''(x)
R''(x) = -1/10 which is less than 0.
Maximum revenue is at x = 2500
R(2500) = [tex](250*2500-\frac{2500^{2} }{20})=312500[/tex]
b) Profit P(x)
P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+70x) = -73000+180x-\frac{x^{2} }{20}[/tex]
For maximum profit, the first derivative of P(x) = P'(x) = 0
P'(x) = [tex]180-\frac{2x }{20}=0[/tex]
[tex]180=\frac{2x }{20}[/tex]
x = 1800
the second derivative of P(x)=P''(x)
P''(x) = -1/10 which is less than 0.
For maximum profit, x = 1800
Therefore P(1800)[tex]=-73000+180*1800-\frac{1800^{2} }{20}[/tex] = 89000
The price the company should charge for each television set is p(1800) =[tex](250-\frac{1800}{20}) = 160[/tex]
c) f the government decides to tax the company $55 for each set it produces, the new cost C(x) = 73000 + 125x
Profit P(x)
P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+125x) = -73000+125x-\frac{x^{2} }{20}[/tex]
For maximum profit, the first derivative of P(x) = P'(x) = 0
P'(x) = [tex]125-\frac{2x }{20}=0[/tex]
[tex]125=\frac{2x }{20}[/tex]
x = 1250
the second derivative of P(x)=P''(x)
P''(x) = -1/10 which is less than 0.
For maximum profit, x = 1250 hence 1250 sets should the company manufacture each month to maximize its profit
Therefore P(1800) =[tex]-73000+125*1250-\frac{1250^{2} }{20}[/tex] = 70825
The price the company should charge for each television set is p(1250) =[tex](250-\frac{1250}{20}) = 187.5[/tex]
Alexandra wants to sign up for cell phone service she trying to decide which company she should choose. Telecorp has a flat rate of 7 cents per minute, America's charges 25cents per call and phone busters charges 35 cents per call and 2 cents per min
Answer:
Step-by-step explanation:
Let us assume that she makes 10 minutes of call.
Telecorp has a flat rate of 7 cents per minute. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is
0.07 × 10 = $0.7
America's charges 25cents per call. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is $0.25
Phone busters charges 35 cents per call and 2 cents per min. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is
0.35 + 10 × 0.02
= 0.35 + 0.2
= $0.55
The cheapest service is that of America's. Therefore, she should choose it.
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115. You choose an SRS of 100 students and average their SAT reading scores. If you do this many times, the mean of the average scores will be close to:_______. A. 115.
B. 115 / square root of 100 = 1.15.
C. 115 / square of 100 = 11.5.
Answer:
Option C) 115 / square of 100 = 11.5
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 496
Standard Deviation, σ = 115
Sample size, n = 100
a) Mean of scores
[tex]\bar{x} = \mu = 496[/tex]
b) The standard Deviation
[tex]s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{115}{\sqrt{100}} = \dfarc{115}{10} = 11.5[/tex]
Thus, the correct answer is
Option C) 115 / square of 100 = 11.5
Answer:
Option C. 115 / square of 100 = 11.5.
Step-by-step explanation:
We are given that Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 496 and standard deviation 115.
An SRS of 100 students is chosen and average their SAT reading scores.
The z score normal probability is given by;
Z = [tex]\frac{xbar-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
So, the mean of the average scores will be close to [tex]\frac{\sigma}{\sqrt{n} }[/tex] i.e.;
= 115 / square root of 100 = [tex]\frac{115}{\sqrt{100} }[/tex] = 115/10 = 11.5
Parents wish to have 160,000 available for a child's education. If the child is now 8 years old, how much money must be set aside at 3 % compounded semiannually to meet their financial goal when the child is 18?
Answer:
$118,791.2985
Step-by-step explanation:
Given that,
A = 160,000
T = 18 - 8 = 10 years
Rate = 3%
since it is semi annual, n = 2
A = P ( 1 + R/2) ∧ 2T
160000 = P ( 1 + 3/2*100) ∧ 2 * 10
160000 = P ( 1 + 3/200) ∧20
160000 = P( 1 + 0.015) ∧20
160000 = P(1.015)∧20
P= 160000/ (1.015)∧20
P = 160000/ 1.3469
= $118,791.2985
Why do we use two supply curves in the aggregate goods and services market? What is the difference between them, and why do they have different slopes?
Answer:
Supply curve vs Aggregate Supply
Step-by-step explanation:
- Supply express a direct relationship between what producers supply and how that relationship affects the price of a specific product or service. Hence, expresses a linear increase - or a constant slope
- Aggregate supply are the total supply in an economy at a particular period of time and a particular price threshold. Aggregate supply is an economy's gross domestic product (GDP), the total amount a nation produces and sells.
- Aggregate supply convey how much firms are willing to produce at a specific price point.
- Aggregate supply is a response to increasing prices that drive firms to utilize more inputs to produce more output. The incentive is that if the price of inputs remains the same but if the price of outputs increase, the firm will generate larger profits and margins by producing and selling more. The aggregate supply curve is represented by a curve that slopes upward, which indicates that as the price per unit goes up, a firm will supply more. Increasing slope - Not constant.
- The supply curve eventually becomes vertical, indicating that at a certain price point a firm cannot produce anymore, as they are limited by certain inputs, e.g. number of employees and number of factories.
A rectangle that is x feet wide is inscribed in a circle of radius 25 feet. Express the area of the rectangle as a function of x. Give the function and state its domain.
Answer:
[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x,
and x: >0, <50 is the domain of the function.
Step-by-step explanation:
Draw an appropriate figure and then express the area of the rectangle as a function of x.
We know that the diagonal of a rectangle inscribed in a circle, will be equal to the diameter of the circle. 50 feet
let w = the width of the rectangle
therefore
[tex]x^2 + w^2 = 50^2\\w^2 = 2500 - x^2\\w = \sqrt{2500-x^{2} }[/tex]
recall
Area = x*w
replace w
[tex]A(x)=x(\sqrt{2500-x^{2} } )[/tex] is the area expressed as function of x
b)state the domain of the function
x: >0, <50
To find the area of the rectangle inscribed in a circle, we can use the Pythagorean theorem to find the length of the rectangle. Then, we can calculate the area by multiplying the width and length. The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2), and the domain is x >= 0 and x <= 50.
Explanation:To find the area of the rectangle, we need to consider that the diagonal of the rectangle is equal to the diameter of the circle, which is twice the radius. Therefore, the diagonal measures 50 feet.
We can use the Pythagorean theorem to find the length of the rectangle. Let's denote the length as y. We have:
x^2 + y^2 = 50^2
This equation represents the relationship between the width and length of the rectangle. By solving for y, we can express the length as a function of x.
Once we have the width and length of the rectangle, we can calculate the area by multiplying them:
A = x * y = x * sqrt(50^2 - x^2)
The function that represents the area of the rectangle as a function of x is A(x) = x * sqrt(2500 - x^2). The domain of this function is x >= 0 and x <= 50.
Learn more about Finding the area of a rectangle inscribed in a circle here:https://brainly.com/question/32036772
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A body of water is being drained it begins with 700 gallons of water and is draining 6.5 gallons each hour .If there are now 388 gallons then for how many hours has it been draining
Answer:
Therefore it has been draining 48 hours.
Step-by-step explanation:
Given that a water body is being drained it begins with 700 gallons of water.
Let after x hours the amount of water in the water body will 388 gallons.
The water body is draining 6.5 gallons each hour
It means
The amount of water that drain in 1 hour is 6.5 gallons.
The amount of water that drain in 2 hour is (6.5+6.5) gallons.
=(2×6.5)gallons.
The amount of water that drain in 3 hour is( 6.5+6.5+6.5) gallons.
=(3×6.5) gallons.
Therefore
The amount of water that drain = time ×6.5
The amount of water that drain in x hour is (x×6.5) gallons=6.5x gallons.
Therefore the remaining water
= initial amount of water- drainage water
=(700-6.5x)gallons
According to the problem,
700-6.5x= 388
⇒ -6.5x = 388-700
⇒ - 6.5x = - 312
[tex]\Rightarrow x=\frac{-312}{-6.5}[/tex]
⇒ x= 48
Therefore it has been draining 48 hours.
x2 + y2 – 8x + 12y- 8 = 4
Answer:
3x-7y=-6
Step-by-step explanation:
Ann works 51/2 hours, Mary works 61/3 hours, and John works 41/4 hours. How many combined hours have they worked? A. 155/12 B. 165/12 C. 161/12 D. 151/12
Answer:
C. 16 + 1/12
Step-by-step explanation:
5 + 1/2 = 11/2 = 66/12
6 + 1/3 = 19/3 = 76/12
4 + 1/4 = 17/4 = 51/12
66/12 + 76/12 + 51/12 = 193/12
193/12 = 16 + 1/12
What is the approximate value of log625?
Answer:
2.79588001734
Step-by-step explanation:
If you use the log button on your calculator
log625 or log(625)
you get 2.79588001734
Answer:
2.79588001734
Step-by-step explanation: but you can solve for the nearest ten thousand just use a scientific calculator and input the numbers with or before log. Depends what type of scientific calculator you use.
fewer students can afford to attend college. Some commentators have suggested that a heightened sense of patriotism may increase military enlistments, while others think that the existence of actual hostilities may deter young people from choosing a military path. A polling organization wants to investigate what this year’s high school seniors are planning to do after they graduate.
1) During the ‘90s about 63% of high school graduates enrolled in college. The pollsters hope to estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4%. What size sample would suffice if they want to have 90% confidence in the estimate?
The pollsters randomly select 5 cities in Upstate New York and then randomly selected on high school in each city. The guidance office at each of the chosen schools is instructed to ask 100 randomly selected seniors what their current plans are, and to report the results back to the pollsters. The data collected from the 5 schools are summarized in the following table.
Plans
Count
College
289
Employment
112
Military
26
Other (travel, parenting, etc.)
51
Undecided / No response
22
2) Determine a 90% confidence interval for the percentage of seniors planning to go to college this year. Explain in context what your interval means. Make sure you include your checks that the conditions for inference have been met.
3) During the 90’s about 4.5% of high school seniors enlisted in the military. Do these data suggest that the percentage who enlist is different this year? Test an appropriate hypothesis and state your conclusion. Make sure you state your null and alternative hypothesis, the test statistic, the P-value, your alpha level, and your conclusion.
4) A few of the seniors did not respond to the guidance queries, and others said they were undecided. Some of the people might eventually decide to enlist in the military. Suppose that half of this small group also enlist. Would that cause you to change your conclusion in Question 3? Make sure you perform another hypothesis test and make sure you state your null, alternative hypothesis, the test statistic, the P-value, your alpha level, and your conclusion.
To estimate the percentage of seniors attending college with a 4% margin of error and 90% confidence, a sample size of 424 is needed. For constructing a confidence interval and hypothesis testing about military enlistment, various statistical formulas are applied, including adjustments for undecided responses.
Explanation:To estimate the percentage of this year’s seniors planning to attend college with a margin of error no greater than 4% and 90% confidence, we use the formula for determining sample size for a proportion, which is n = (Z^2 * p * (1-p)) / E^2, where Z is the Z-score corresponding to the confidence level, p is the estimated proportion, and E is the margin of error. With a 90% confidence level, the Z-score is approximately 1.645, and assuming we don't have a preliminary estimate, we use p = 0.5 for maximum variability, thus maximizing the required sample size.
To calculate: n = (1.645^2 * 0.5 * 0.5) / 0.04^2 = 423.3. Therefore, a sample size of 424 is required to achieve the desired margin of error and confidence level.
For the second question regarding the confidence interval for the percentage of seniors planning to go to college this year, the total sample size is the sum of students from all categories, which is 500. The proportion planning to go to college is 289/500. Using a formula for constructing a confidence interval for a proportion, C.I. = p ± (Z*sqrt(p(1-p)/n)), we can find our interval.
Testing the hypothesis regarding military enlistment involves setting up a null hypothesis (H0: p = 0.045) and an alternative hypothesis (H1: p ≠ 0.045), where p is the proportion of high school seniors enlisting in the military. The test statistic is calculated using a formula, and the P-value associated with this statistic is compared against the alpha level to decide whether to reject H0.
If considering undecided or no response students as potential enlistees changes this calculation significantly, we reassess by including an adjusted number of potential enlistees.
Simplify this expression.
3^5/3^3
Answer:
3^2
Step-by-step explanation:
3^5/3^3=3^(5-3)=3^2
Answer:
[tex] \frac{ {3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9[/tex]
Step by step explanation :
When dividing two fraction we subtract the powers if the bases are same.