Answer:
n≅376
So sample size is 376.
Step-by-step explanation:
The formula we are going to use is:
[tex]n=pq(\frac{z_{\alpha/2}}{E})^{2}[/tex]
where:
n is the sample size
p is the probability of favor
q is the probability of not in favor
E is the Margin of error
z is the distribution
α=1-0.98=0.02
α/2=0.01
From cumulative standard Normal Distribution
[tex]z_{\alpha/2}=2.326[/tex]
p is taken 0.5 for least biased estimate, q=1-p=0.5
[tex]n=0.5*0.5(\frac{2.326}{0.06})^{2}\\n=375.71[/tex]
n≅376
So sample size is 376
What is the length of segment AC?
Answer:
The answer to your question is dAC = 10 units
Step-by-step explanation:
Data
From the graph, take the coordinates of the points A and C.
A (3, - 1)
C (-5, 5)
Process
Use the formula of the distance between two points to find the length
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
x1 = 3 y1 = -1
x2 = -5 y2 = 5
Substitution
dAC = [tex]\sqrt{(-5 - 3)^{2} + (5 + 1)^{2}}[/tex]
Simplification
dAC = [tex]\sqrt{(-8)^{2} + (6)^{2}}[/tex]
dAC = [tex]\sqrt{64 + 36}[/tex]
dAC = [tex]\sqrt{100}[/tex]
dAC = 10 units
Bella has 3 red marbles, 7 blue marbles, and 7 yellow marbles in a bag. Without looking in the bag what is the probability that sure would pick a blue?
K is the midpoint of JL. Given that JK=2x+7 and KL=4x+1, find x, JK, KL, and JL.
Answer:
x = 3
JK = 13
KL = 13
JL = 26
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsMidpoints - separates a line segment into 2 equal partitionsStep-by-step explanation:
Step 1: Define
K is midpoint JL. Use midpoint definition.
JK = 2x + 7
KL = 4x + 1
JK = KL
2x + 7 = 4x + 1
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 2x on both sides: 7 = 2x + 1[Subtraction Property of Equality] Subtract 1 on both sides: 6 = 2x[Division Property of Equality] Divide 2 on both sides: 3 = xRewrite/Rearrange: x = 3Step 3: Find
JK
Substitute in x: JK = 2(3) + 7Multiply: JK = 6 + 7Add: JK = 13KL
Substitute in x: KL = 4(3) + 1Multiply: KL = 12 + 1Add: KL = 13JL
Define: JL = JK + KLSubstitute in variables: JL = 13 + 13Add: JK = 26The variable x is found to equal 3. Substituting x=3 into the expressions for JK and KL, both are found to equal 13. The entire line segment JL is then found to equal 26.
Explanation:In this mathematics problem, we are given that K is the midpoint of JL. This implies that the segments JK and KL are of equal length, thus JK=KL.
So, we can set the two given expressions equal to each other: 2x+7=4x+1. Solving this equation for x, we get that x=3.
Substituting x=3 into the expressions for JK and KL: JK=2x+7=2(3)+7=13, and KL=4x+1=4(3)+1=13.
To find JL, we simply add JK and KL together, since JKL is a line segment with K being the midpoint. Hence, JL=JK+KL=13+13=26.
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Andre has been practicing his math facts.He can now complete 135multiplication facts in 90 seconds if andre is answering questions at a constant rate,how many facts can he answer per second?
Answer:
Andre can answer 1.5 multiplication facts in each second.
Step-by-step explanation:
Given:
Number of multiplication facts completed = 135
Number of second took to complete multiplication facts = 90 seconds.
We need to find the Number of facts answered per second.
Solution;
Now we know that;
In 90 seconds = 135 multiplication facts.
So in 1 second = Number of fact answered in 1 second
By Using Unitary method we get;
Number of fact answered in 1 second = [tex]\frac{135}{90}=1.5[/tex]
Hence Andre can answer 1.5 multiplication facts in each second.
A tourist in France wants to visit 8 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?
Answer:
Probability p( selecting 8 cities alphabetically) = 2.48×10^-5
Step-by-step explanation:
Number of possible ways of choosing 8 cities=Permutation P(n,k) = n!/(n-k)!
P(8,8)= 8!/(8-8)! = 8! = 40,320
Probability (selecting 8 cities alphabetically) = 1/40320 = 2.48×10^-5
Answer:
The answer is 0.00002480
Step-by-step explanation:
From the question stated let us recall the following statement.
The number of cities the tourist wants to visit is =8
Now,
If the route is selected randomly, what is the probability that the cities she visits are in alphabetical order.
Therefore,
The probability that she visits the cities in alphabetical order = 1/8!
There are 8! = 40320 ways in which these cities can be visited
P(Visiting in alphabetical order) = 1/40320 = 0.00002480
Joans candy emporium is having a sale.Three pounds of gummy bunnies are selling for $4.00. How much will two pounds cost? What is the unit rate for gummy bears
Two pounds of gummy bears will cost $2.67. The unit rate for each pounds of gummy bears is measured in dollars.
What are word problems?Word problems in mathematics involve the use of mathematical concepts and arithmetic operations to solve real-life cases. It involves a careful understanding of the problem you want to solve.
From the parameters given:
3 pounds costs = $4.002 pounds will costs = $xBy cross multiplying, we have:
[tex]\mathbf{x = \dfrac{2 \ pounds \times \$4.00}{\$3.00}}[/tex]
x = $2.67
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Final answer:
The cost for two pounds of gummy bunnies is $2.66, with the unit rate being $1.33 per pound after rounding to two decimal places.
Explanation:
To determine how much two pounds of gummy bunnies will cost at Joan's candy emporium, we first need to calculate the unit rate of the gummy bunnies that are selling for $4.00 per three pounds. The unit rate is found by dividing the total cost by the number of pounds:
Unit Rate = Total Cost / Number of Pounds
Unit Rate = $4.00 / 3 pounds = $1.33 per pound (rounded to two decimal places)
Now that we have the unit rate, we can determine the cost for two pounds of gummy bunnies:
Cost for Two Pounds = Unit Rate x Number of Pounds
Cost for Two Pounds = $1.33 per pound x 2 pounds = $2.66 (rounded to two decimal places)
Bob and Meena play a two-person game which is won by the first person to accumulate at least 10 points. On each turn, there is a $\frac{2}{5}$ probability that Bob will get two points and Meena will lose one point. If that doesn't happen, then Meena gets two points and Bob loses a point. Meena is now ahead 9 to 6. What is the probability that Meena will win?
Answer:
The probability that Meena wins is 21/25
Step-by-step explanation:
In order for Meena to win, she needs to win the next turn or the following one, otherwise, she loses. The probability for that is equal to substract from 1 the probability of the complementary event: bob wins in the next 2 turns. Since each turn is independent from the other, we can obtain the probability of Bob winning the next 2 turns by taking the square of the probability of him winning on one turn, hence it is
[tex] {\frac{2}{5}}^2 = \frac{4}{25} [/tex]
Thus, the probability for Meena to win is 1-4/25 = 21/25.
Meena only needs one more point to win, and with a ⅘ or 60% probability in her favor for the next turn, she will win the game.
The question asks for the probability that Meena will win a game where she is currently ahead 9 to 6, and the game is won by the first person to reach 10 points. In each turn, there is a ⅗ chance that Bob will get 2 points and Meena will lose 1 point, and a ⅘ chance that Meena will get 2 points and Bob will lose 1 point.
To find the probability of Meena winning, we only need to look at the next round because Meena is already at 9 points and she needs only 1 point to win. Two scenarios can occur:
Bob gets 2 points, and Meena loses 1 point. This outcome is not possible because Meena cannot have 8 points; she's already at 9 points. So, this situation doesn't count.
Meena gets 2 points (which will put her at or above 10 points) and Bob loses 1 point. This is the winning scenario for Meena. The probability of this happening is ⅘ or 0.6 (since only this outcome will end the game with Meena as the winner).
Therefore, the probability that Meena will win on the next turn (and win the game) is 0.6 or 60%
There is a population of 50 bacteria in a colony. If the number of bacteria doubles every 300 minutes, what will the population be 600 minutes from now?
Answer:
200
Step-by-step explanation:
50 doubles to 100 and then doubles again to 200.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠W.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠W = °
Answer:
Step-by-step explanation:
Triangle WXY is a right angle triangle.
From the given right angle triangle,
WX represents the hypotenuse of the right angle triangle.
With m∠W as the reference angle,
WY represents the adjacent side of the right angle triangle.
XY represents the opposite side of the right angle triangle.
To determine m∠W, we would apply
the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos W = 5/7 = 0.7143
W = Cos^-1(0.7143)
W = 44.1° to the nearest tenth.
Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2.5 when y = 100. k = 250, y = 250x k = 0.025, y = 0.025x
Answer:
[tex]k=250[/tex]
Step-by-step explanation:
If y varies inversely with x, then
[tex]y=\dfrac{k}{x},[/tex]
where k is the constant of variation or the constant of inverse proportionality.
Since [tex]x=2.5[/tex] when [tex]y=100,[/tex] you have that
[tex]100=\dfrac{k}{2.5}[/tex]
Evaluate k:
[tex]k=100\cdot 2.5\\ \\k=250[/tex]
and
[tex]y=\dfrac{250}{x}[/tex]
Nik, a social worker for a county, helps county residents who are struggling with different issues. Nik logs the following hours meeting with clients (c) or doing other work (o):_______
Mon: 6 c, 4 o
Tue: 8 c, 2 o
Wed: 9 c, 1 o
Thu: 7 c, 3 o
Fri: Off
What percent of time did Nik spend with clients on Thursday?
a. 10%
b. 70%
c. 30 %
d. 80%
Answer: b. 70%
Step-by-step explanation:
Given : Nik logs the following hours meeting with clients (c) or doing other work (o) :
Mon: 6 c, 4 o
Tue: 8 c, 2 o
Wed: 9 c, 1 o
Thu: 7 c, 3 o
Fri: Off
The number of hours Nik spend with clients on Thursday = 7 [Number of corresponding to c is 7 in the table]
Total hours he spend in work on Thursday = 7+3 = 10
The percent of time Nik spent with clients on Thursday :
[tex]\dfrac{\text{Number of hours he spent with clients}}{\text{Total works he work on Thursday}}\times100\\\\=\dfrac{7}{10}\times100=7\times10\%=70\%[/tex]
Hence, the Nik spent 70% of his time with clients on Thursday.
Thus , the correct option is b. 70%.
Need help doing this, show steps if you could.
Answer:
option 1
Step-by-step explanation:
first we have to find the slopes of the lines
D(1, -2) E(3, 4)
y = m*x + b
m1: slope
m1 = (y2-y1) / (x2-x1)
m1 = (4 - (-2)) / (3 - 1)
m1 = 4+2 / 3-1
m1 = 6 / 2
m1 = 3
we do the same with the other 2 points
D(-1, 2) E(4, 0)
y = m*x + b
m2: slope
m2 = (y2-y1) / (x2-x1)
m2 = (0 - 2) / (4 - (-1))
m2 = -2 / 4 + 1
m2 = -2 / 5
m1 = 3 m2 = -2/5
for 2 lines to be perpendicular it must be met
m1 * m2 = -1
we check if they are perpendicular
3 * -2/5 = -1
-6/5 = -1 <-- no perpendicular
You are dealt 13 cards from a shuffled deck of 52 cards. Compute the probability that (a) your hand lacks at least one suit, (b) you get the both Ace and King of at least one suit, (c) you get all four cards of at least one denomination (all Aces, or all Kings, or all Queens, . . . , or all Twos).
Answer:
Attached is the image of the solution . cheers
In her garden Pam plants the seed 5 and one fourth in. Below the ground. After one month the tomato plant has grown a total of 11 and one half in. How many inches is the plant above the ground?
Answer: the plant is 6 1/4 inches above the ground.
Step-by-step explanation:
In her garden Pam plants the seed 5 and one fourth inches below the ground. Converting 5 and one fourth inches to improper fraction, it becomes 21/4 inches.
After one month the tomato plant has grown a total of 11 and one half inches. Converting 11 and one half inches to improper fraction, it becomes 23/2 inches.
The height of the the plant above the ground would be
23/2 - 21/4 = (46 - 21)/4 = 25/4
Converting to mixed fraction, it becomes
6 1/4 inches
Isosceles triangle $ABE$ of area 100 square inches is cut by $\overline{CD}$ into an isosceles trapezoid and a smaller isosceles triangle. The area of the trapezoid is 75 square inches. If the altitude of triangle $ABE$ from $A$ is 20 inches, what is the number of inches in the length of $\overline{CD}$ ?
Answer:
5 inches
Step-by-step explanation:
See attachment for explanation.
In order to investigate treatments for morbid obesity, obese subjects satisfying fairly strict requirements were randomly assigned to one of three groups: gastric bypass surgery; participation in a diet and exercise program; or both gastric bypass surgery and participation in the diet and exercise program. Researchers carefully observed the amount of weight lost five years after the study began. This study uses the principles of A. randomization. B. confounding. C. blocking. D. All of the above
Answer:A randomization
Step-by-step explanation:Randomization in scientific experiments is a sampling method in which the participants or researchers are chosen randomly and assigned a treatment.
Here the participants or researchers do not know for sure which treatment is better.
Randomization reduces any possible bias responses to a minimal.
Reggie is going to make a scale model of a tyrannosaurus rex dinosaur. Tyrannosaurus was 20 ft high, if you use a scale of 2. : 5ft how tall will the model be?
A. 10in
B. 6in
C. 4in
D. 8in
Answer:
D) 8 inches
Step-by-step explanation:
Since the ratio is 2:60 inches, therefore the model should be:
2/60 X 240=8 inches tall, or 8/12=2/3 foot tall.
1. Joy wants to find the distance, AB, across a creek. She starts at point B and walks along the edge of the river 105 ft and marks point C. Then she walks 85 ft further and marks point D. She turns 90° and walks until her final location and marks point E. Point E, point A, and point C are co-linear.
Answer:
The answer to your question is below
Step-by-step explanation:
a) Yes, Joy can conclude that ΔABC is similar to ΔEDC because
∠ACB ≅ ∠ECD they are vertical angles and,
∠ABC ≅ ∠EDC they are right angles
We conclude that ΔABC is similar to ΔEDC because of the AA postulate.
b) [tex]\frac{AB}{BC} = \frac{DE}{CD}[/tex]
Solve for AB
AB = (BC)(DE) / (CD)
Substitution
AB = 105 (90) / 85
Simplification
AB = 105(1.06)
Result
AB = 111.2 ft
please help i will give brainlist
Answer:
7.5
Step-by-step explanation:
For function f(x), the average rate of change between x=a and x=b is given by ...
average rate of change = (f(b) -f(a))/(b -a)
For your function, this will be ...
average rate of change = ((2^5 +3) -(2^1 +3))/(5 -1) = (35 -5)/4
average rate of change = 7.5
Oliver makes blueberry jam every year the number of pints of jam he makes this can be represented by the expression 4p - 9= where p is the number of pints of jam he made last year oliver made 8 pints of jam.Last year how many pints dose he make this year
Answer: He makes 23 pints this year .
Step-by-step explanation:
Given : Oliver makes blueberry jam every year the number of pints of jam he makes this can be represented by the expression
[tex]4p - 9[/tex] , where p = the number of pints of jam he made last year.
if Oliver made 8 pints of jam last year , then p = 8
Substitute value p= 8 in the given expression , we get
Then, the number of pints he make this year = [tex]4(8)-9 = 32-9=23[/tex]
Hence, the number of pints Oliver make this year = 23
If Rachel were to paint her living room alone it would take five hours her sister Barbara could do the job in eight hours how many hours would it take them working together express your answer as a fraction reduced to lowest terms if needed
Answer:
40/13 hours
Step-by-step explanation:
Let 1 represent the room being painted.
1/5 would represent 1/5 of a room painted in 1 hour.
1/8 would represent 1/8 of a room being painted in 1 hour
But they are are working together so
(1/5)x + (1/8)x = 1
The lowest common denominator is 5 * 8 = 40
[(1/5)x * 40 + (1/8)x * 40] = 1
8x + 5x = 40
13x = 40
x = 40/13
x = 3.077 hours
But you want a fraction as your answer so it is 3 1/13 or 40/13
You should notice that 3.077 is smaller than the lowest amount of time both of them use. That always happens with these questions.
Final answer:
Rachel and Barbara would take ⅜shy hours to paint the living room together, as they have a combined work rate of 0.325 room/hour calculated from their rates of 1 room per 5 hours and 1 room per 8 hours, respectively.
Explanation:
To find out how many hours it would take Rachel and Barbara to paint the living room together, we can use the concept of work rate. Rachel's work rate is ⅑or (1 room per 5 hours), and Barbara's work rate is ⅑or (1 room per 8 hours). To find their combined work rate, we add their rates together.
Rachel's rate: ⅑or (1 room/5 hours) = 0.2 room/hour
Barbara's rate: ⅑or (1 room/8 hours) = 0.125 room/hour
Combined rate: 0.2 + 0.125 = 0.325 room/hour
To find out how long it takes them to paint the room together, we can set up the equation: 1 room = (0.325 room/hour) × (hours). Solving for 'hours' gives us:
Hours = ⅑or / 0.325
Hours = ⅑or / (⅜shy / 1)
Hours = ⅜shy × 1
Hours = ⅜shy
Therefore, it would take them ⅜shy hours to complete the painting together.
If it is exact find a function F(x,y) whose differential, dF(x,y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation: dy/dx = (-4x^(4)-3y)/(3x+2y^(4)) First rewrite as M(x,y) dx + N(x,y) dy = 0 where M(x,y)= ?
and N(x,y)= ?
The differential equation provided is transformed to M(x,y) dx + N(x,y) dy = 0 with M(x,y) = [tex]-4x^4 - 3y[/tex]and N(x,y) = 3x + [tex]2y^4[/tex], setting the stage for verifying its exactness through partial differentiation.
Explanation:To address the student's query about finding a function F(x,y) whose differential fits the given differential equation, we'll first transform the differential equation dy/dx =[tex](-4x4-3y)/(3x+2y4)[/tex] into the form M(x,y) dx + N(x,y) dy = 0.
This transformation requires us to regard the equation as a differential one, implying:
M(x,y) = -4x4 - 3yN(x,y) = 3x + 2y4This representation simplifies the process of checking for exactness, which necessitates partial differentiation and comparison of ∂M/∂y and ∂N/∂x.
Should these partial derivatives be equal, the differential is exact, enabling the determination of the function F(x, y) through integration.
In a state lottery, four digits are drawn at random one at a time with replacement from 0 to 9. Suppose that you win if any permutation of your selected inte- gers is drawn. Give the probability of winning if you select.(a) 6, 7, 8, 9. (b) 6, 7, 8, 8. (c) 7, 7, 8, 8. (d) 7, 8, 8, 8.
Answer:
(a) 0.0024
(b) 0.0012
(c) 0.0006
(d) 0.0004
Step-by-step explanation:
The total number of possible integers when any number is selected is 10 (i.e from 0 - 9). When four number integers are selected, the total number of sample sample will be;
10 × 10 × 10 × 10 = 10,000
The sample space = 10,000
To know the possible ways of selecting the given four digits, we will use permutation.
[tex]^{n}P_{r} = \frac{n!}{(n-r)!}[/tex]
To get the probability,
[tex]Probability \ of \ winning (Selected \ numbers) = \frac{number\ of\ possible\ outcomes\ of\ selected\ numbers}{sample\ space}[/tex]
(a) When 6,7,8,9 are selected, n = 4 , r = 4
The possible ways of selecting 6,7,8,9 is;
[tex]^{4}P_{4} = \frac{4!}{(4-4)!}[/tex]
[tex]= \frac{4!}{(0)!}[/tex]
but 0! = 1
[tex]^{4}P_{4} = 4![/tex]
= 4 × 3 × 2 × 1 = 24
[tex]Prob (6,7,8,9) = \frac{24}{10000} = 0.0024[/tex]
(b) When 6, 7, 8, 8 are selected,
The possible ways of selecting 6,7,8,8 is;
[tex]= \frac{4!}{1! \ 1! \ 2!}[/tex]
[tex]= \frac{4!}{2!}[/tex]
[tex]=\frac{4 * 3 * 2 * 1}{2 * 1}[/tex]
= 12
[tex]Prob (6,7,8,8) = \frac{12}{10000} = 0.0012[/tex]
(c) When 7, 7, 8, 8 are selected,
The possible ways of selecting 7,7,8,8 is;
[tex]= \frac{4!}{2! \ 2!}[/tex]
[tex]=\frac{4 * 3 * 2 * 1}{(2 * 1)(2 * 1)}[/tex]
= 6
[tex]Prob (7,7,8,8) = \frac{6}{10000} = 0.0006[/tex]
(d) When 7, 8, 8, 8 are selected,
The possible ways of selecting 7,8,8,8 is;
[tex]= \frac{4!}{1! \ 3!}[/tex]
[tex]=\frac{4 * 3 * 2 * 1}{3 * 2 * 1}[/tex]
= 4
[tex]Prob (7,8,8,8) = \frac{4}{10000} = 0.0004[/tex]
You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $7 per guest and averaged 79 guests per night. The next week you charged $16 per guest and averaged 43 guests per night.(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.q(p) = (b) Find the nightly revenue R as a function of the cover charge p.R(p) = (c) When you set the admission to p dollars, the club's nightly costs, including rent, salaries, and two free non-alcoholic drinks for each guest, amounts toC(p) =−26.75p +939Find the profit in terms of the cover charge p.P(p) = (d) Determine entrance fees that allow Swing Haven to break even. Enter the lower fee first, and round your answer to two decimal places.When the entrance fee is p = or dollars per guest, then Swing Haven breaks even.
Answer:
a) The demand function is
[tex]q(p) = -4 p + 107[/tex]
b) The nightly revenue is
[tex] R(p) = -4 p^2 + 107 p [/tex]
c) The profit function is
[tex]P(p) = -4 p^2 + 133.75 p - 939 [/tex]
d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
Step-by-step explanation:
a) Lets find the slope s of the demand:
[tex] s = \frac{79-43}{7-16} = \frac{36}{-9} = -4 [/tex]
Since the demand takes the value 79 in 7, then
[tex]q(p) = -4 (p-7) + 79 = -4 p + 107[/tex]
b) The nightly revenue can be found by multiplying q by p
[tex]R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p[/tex]
c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)
[tex]P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939[/tex]
d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P
[tex]r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41[/tex]
Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
We found the linear demand equation as q(p) = -4p + 107. The nightly revenue R(p) is R(p) = -4p^2 + 107p, and the profit P(p) is P(p) = -4p^2 + 133.75p - 939. Setting the profit equal to zero, we found the club breaks even at entrance fees $5.32 and $44.31.
Explanation:In this question, we're asked to formulate linear demand, revenue, and profit equations, and find the entrance fees for break even. First, let's find the linear demand equation.
To obtain this demand equation, we can use the two given points ($7, 79) and ($16, 43) and find the slope (rate of change) equals (43-79) / (16-7) = -4. Hence the demand equation will be q(p) = -4p + b. To find b, substitute one of the points into the equation, for example ($7, 79), we get b=107, hence q(p) = -4p + 107.
Next, let's find the nightly revenue R (p), which is simply the product of the entrance fee and the number of guests, hence R(p) = p * q(p) = p (-4p + 107) = -4p^2 + 107p.
The profit P(p) is the difference between revenue and costs, hence P(p) = R(p) - C(p) = -4p^2 + 107p - (-26.75p + 939) = -4p^2 + 133.75p - 939.
Finally, for Swing Haven to break even, the profit must be zero. By setting P(p) = 0 and solving the equation -4p^2 + 133.75p - 939 = 0, we get the two solutions p = 5.3216 and p = 44.3031, or roughly $5.32 and $44.31.
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The area of the rectangle is 54 units squared. Write and solve an equation to find x.
Answer: [tex]x=5[/tex]
Step-by-step explanation:
The area of a rectangle can be found with the following formula:
[tex]A=lw[/tex]
Where "l" is the length and "w" is the width.
In this case you can identify in the figure given in the exercise that:
[tex]l=4x-2\\\\w=3[/tex]
You know that the area of that rectangle is the following:
[tex]A=54[/tex]
Therefore, knowing those values, you can substitute them into the formula and then you must solve for "x" in order to find its value. You get that this is:
[tex]54=(4x-2)(3)\\\\54=12x-6\\\\54+6=12x\\\\\frac{60}{12}=x\\\\x=5[/tex]
: The world's tallest unsupported flagpole is a 282 ft. Tall steel pole in Surrey, British Columbia. The shortest shadow cast by the pole during the year is 137 ft. Long. To the nearest degree, what is the angle of elevation of the sun when casting the flagpole's shortest shadow?
Answer:
64.08
Step-by-step explanation:
To find the angle of elevation of the sun, we use the tangent function with the height of the flagpole and the length of the shadow. Calculating the arctangent of the ratio of the height to the shadow length and converting it to degrees gives us the angle of elevation.
Explanation:The question asks about the angle of elevation of the sun when casting the shortest shadow of a flagpole. We can use trigonometric functions to find this angle using the height of the flagpole and the length of the shadow. The height of the flagpole is 282 ft and the length of the shadow is 137 ft.
To find the angle of elevation (θ), we use the tangent function, which is the ratio of the opposite side (height of the flagpole) to the adjacent side (length of the shadow). So, tangent(θ) = opposite/adjacent = 282 ft / 137 ft.
Now, we will calculate the angle using the inverse of the tangent function, also known as arctangent.
θ = arctan(282/137)
To find the angle in degrees, we use a calculator to compute arctan(282/137). After computing, we round the result to the nearest whole number to find the angle of elevation to the nearest degree.
To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. The splash is seen 5.6 seconds after the stone is dropped. What is the height of the building? Use the position function s(t) = 4.9t² + v_0 t + s_0 for free falling objects.
Answer:
The height of the building is 153.664 meter.
Step-by-step explanation:
Consider the provided function.
[tex]s(t) = 4.9t^2 + v_0 t + s_0[/tex]
Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.
It is given that the splash is seen 5.6 seconds after the stone is dropped.
That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.
Substitute respective values in the above function.
[tex]0 = 4.9(5.6)^2 +5.6(0)+ s_0[/tex]
[tex]0 = 4.9(31.36)+ s_0[/tex]
[tex]s_0=-153.664[/tex]
As height can't be a negative number so the value of s₀ is 153.664.
Hence, the height of the building is 153.664 meter.
3. Find the length of MG. EGF ~ EML.
The length of MG is 56 for the given similar triangles.
Step-by-step explanation:
Let us consider EML and EGF is two similar triangles.
From the triangle,
EG=5x+2.
EM=16.
EL=28.
EF=126.
According to similar triangle property,
triangle ratio= [tex]\frac{EM}{EG} =\frac{EL}{EF} =\frac{ML}{GF} .[/tex]
[tex]\frac{16}{5x+2}=\frac{28}{126}[/tex].
126(16)=28(5x+2).
2016=140x+56.
140x=1960.
x=14.
⇒EG=5(14)+2.
EG=70+2.
EG=72.
To find the length of MG,
EG=EM+MG.
MG=EG-EM.
=72-16.
MG=56.
The question, asking for the length of a segment within a triangle, belongs to the field of Mathematics and is most likely at a High School level. However, based on the given information, an exact answer cannot be provided.
Explanation:Unfortunately, the provided information is not sufficient enough to find the length of MG. The relationship EGF ~ EML indicates that the triangles EGF and EML are similar, meaning their corresponding sides are proportional. To find the length of MG (a segment within triangle EML), we would typically use a known length from triangle EGF and the scale factor between the two triangles. However, without these additional specifics, we cannot provide an exact value for the length of MG.
Learn more about Similar Triangles here:https://brainly.com/question/34830045
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So the problem I got was "Ben is splitting 2 quarts of icecream with 9 members of the team. If the icecream is split evenly how many cups will each person get?" I know 1 qt= 2pts which #4 cups so 2 qts= 8 cups dividing the icecream among 9 people means each gets ? Cups how many cups will 9 people get?
Answer:
8/9 of a cup
Step-by-step explanation:
8 cups of icecream to be divided among 9 people, so they can't have full cups.
Each person will get 8/9 of a cup
Please Help ASAP A basketball player shoots a basketball with an initial velocity of 15 ft/sec. The ball is released from an initial height of 6.5 feet.
The function h(t) = -16t^2 + v0t + h0 models the height, in feet, of an object after t seconds. v0 is the initial velocity of the object, and h0 is the initial height of the object.
Part 1: Write a function that models the height of the basketball. Use your function to answer Parts 2-4.
Part 2: How long does it take for the basketball to hit the ground? Round your answer to the nearest hundredth. Show all of your work.
Part 3: When does the basketball reach its maximum height? Round your answer to the nearest hundredth. Show all of your work and explain your answer.
Part 4: What is the maximum height of the basketball? Round your answer to the nearest hundredth. Show all of your work and explain your answer.
Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]
Part 2: The basketball hits the ground after approximately 0.97 seconds.
Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.
Part 4: The maximum height of the basketball is approximately 11.39 feet.
Part 1: To model the height of the basketball, we use the given function [tex]\( h(t) = -16t^2 + v0t + h0 \)[/tex] with the initial velocity [tex]\( v0 = 15 \)[/tex] ft/sec and the initial height [tex]\( h0 = 6.5 \)[/tex] feet. Plugging in these values, we get the function:
[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]
Part 2: To find the time it takes for the basketball to hit the ground, we set the height function equal to zero and solve for [tex]\( t \)[/tex]:
[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]
Using the quadratic formula [tex]\( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex]where [tex]\( a = -16 \), \( b = 15 \)[/tex], and [tex]\( c = 6.5 \)[/tex], we get two solutions. We discard the negative solution because time cannot be negative, and we round the positive solution to the nearest hundredth:
[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \] \[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \] \[ t = \frac{-15 \pm \sqrt{641}}{-32} \] \[ t \approx \frac{-15 + 25.31}{-32} \] \[ t \approx 0.97 \text{ seconds} \][/tex]
Part 3: To find when the basketball reaches its maximum height, we need to find the vertex of the parabola. The time coordinate of the vertex of a parabola [tex]\( ax^2 + bx + c \)[/tex] is given by [tex]\( t = -\frac{b}{2a} \)[/tex]. For our function, [tex]\( a = -16 \)[/tex]and [tex]\( b = 15 \)[/tex], so:
[tex]\[ t = -\frac{15}{2(-16)} \] \[ t = \frac{15}{32} \] \[ t \approx 0.47 \text{ seconds} \][/tex]
Part 4: To find the maximum height, we substitute the time at which the maximum height is reached back into the height function:
[tex]\[ h(0.47) = -16(0.47)^2 + 15(0.47) + 6.5 \] \[ h(0.47) \approx -16(0.2209) + 7.05 + 6.5 \] \[ h(0.47) \approx -3.5344 + 7.05 + 6.5 \] \[ h(0.47) \approx 11.39 \text{ feet} \][/tex]
Therefore, the basketball reaches a maximum height of approximately 11.39 feet after approximately 0.47 seconds.