Solution :
Let x = number of coach class tickets sold per day on $ 10 reduced price
y = number of the business class tickets sold per day on $ 50 reduced per price.
Number of the coach class tickets sold = 20 per day at a price of $ 250
Number of the business class tickets sold = 10 per day at a price of $ 750
Decrease in the price of coach class tickets by $ 10 increases the number of tickets sold by 4 per day
Decrease in the price of business class tickets by $ 50 increases the number of tickets sold by 2 per day.
Therefore, the coach price, p(x) = 250 - 10x
Business class price, p(y) = 750 - 50y
Coach tickets, q(x) = 2 + 4x
Business class tickets, q(y) = 6 + 2y
Revenue R(x, y) = p(x) q(x) + q(y) q(y)
R(x, y) = (250-10x)(20+4x)+(750-50y)(6+2y)
R(x) = (250-10x)(0.4)+(20+4x)(-10)+0 = 0
1000-40x-200-40x=0
80x = 800
x = 10
R(y) = 0 + (750 - 50y)(0.2) + (6+2y)(-50) = 0
1500 - 100y+(-300-100y) = 0
200 y = 1200
y = 6
P(x) = 250 - 10(10) = $ 150
P(y) = 780-50(6) = $450
q(x) = 20 + 4(10) = 60
q(y) = 6 + 2(6) = 18
Maximum revenue = 150 x 60 + 450 x 18
= 9000 + 8100
= $ 17100
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
Answer:
a) SAT score = 1075
b) ACT score = 19.2.
c) ACT score = 27.9.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score
SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]
51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 1070}{204}[/tex]
[tex]X - 1070 = 0.025*204[/tex]
[tex]X = 1075[/tex]
SAT score = 1075.
(B) What would be the equivalent ACT score for this student?
ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 0.025*5.2[/tex]
[tex]X = 19.2[/tex]
ACT score = 19.2.
(C) If a student gets an SAT score of 1417, find the equivalent ACT score.
Z-score for the SAT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1417 - 1070}{204}[/tex]
[tex]Z = 1.7[/tex]
Equivalent score on the ACT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 1.7*5.2[/tex]
[tex]X = 27.9[/tex]
ACT score = 27.9.
Fun question: Which Disney character is your favorite?
Make sure it’s detailed!! Will give out Brainlist!!
Answer:
Belle is my fav.
Step-by-step explanation:
She loves to read books like me and I hate people who always go out there and try to impress me with something.
Trying to finish this test at 3:30 am plz help
Given:
The given sum is:
[tex]\sum _{k=4}^9(5k+3)[/tex]
To find:
The expanded form and find the sum.
Solution:
We have,
[tex]\sum _{k=4}^9(5k+3)[/tex]
The expanded form of given sum is:
[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]
[tex]\sum _{k=4}^9(5k+3)=213[/tex]
Therefore, the correct option is C.
The following two-way table describes student's
after school activities. Find the probability that a
randomly selected student works, given that it's a
senior.
Grade
Sports
Music/Drama
Work
Sophomore
20
7
3
Junior
20
13
2
Senior
25
5
5
P( Work | Senior) = [?]
Round to the nearest hundredth.
Answer:
[tex]P(Work | Senior) = 0.14[/tex]
Step-by-step explanation:
Given
The attached table
Required
[tex]P(Work | Senior)[/tex]
This is calculated using:
[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]
This gives:
[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]
From the table:
[tex]n(Work \ n\ Senior) = 5[/tex]
[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]
So:
[tex]P(Work | Senior) = \frac{5}{35}[/tex]
[tex]P(Work | Senior) = 0.14[/tex]
Answer:
14%
Step-by-step explanation:
add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. Construct a 95% condence interval for the proportion of water specimens that contain detectable levels of lead
Answer:
The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.
This means that [tex]n = 42, \pi = \frac{26}{42} = 0.619[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 - 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.472[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 + 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.766[/tex]
The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).
Please help me solve this problem
Answer:
90°
Step-by-step explanation:
It's simple, the angle of a line is 180°
∠EFG=90°
Line GD-∠EFG=180°-90°=90°
Please mark brainliest!
Use the quadratic formula to solve x2 – 3x - 2 = 0.
Answer:
x = 2 , 1
Step-by-step explanation:
Answer:
2.5 or 3.5
Step-by-step explanation:
The quadratic formula is [tex]x = -b +/- \frac{\sqrt{b^2 + 4ac}}{2a}[/tex] .
a, b, and c are determined by the terms in the formula ax^2 + bx + c
They gave you the equation x^2 - 3x - 2, which fits that formula. a is 1, b is -3, and c is -2. So plug those values into the equation:
[tex]x = -(-3) +/- \frac{\sqrt{(-3)^2 + 4(1)(-2)}}{2(1)}[/tex]
[tex]x = 3 +/- \frac{\sqrt{9 -8}}{2}[/tex]
[tex]x = 3 +/- \frac{\sqrt{1}}{2}[/tex]
[tex]x = 3 +/- \frac{1}{2}[/tex]
So x is 3 plus or minus -1/2. 3 plus -1/2 is 2.5
3 minus -1/2 is 3.5
So the 2 possible x values are 2.5 and 3.5.
Ms. Lin’s son likes to lift weights. He was lifting 125 pounds last year. This year he can lift 35 more pounds. How much weight can he lift this year?
Answer:
He can lift 160 pounds
Step-by-step explanation:
125 (from last year) + 35 (more pounds) = 160 (total pounds)
125 + 35 = 160
What is the mean ? 50, 55, 58, 58, 90, 92, 99
sum of observations
mean =..........................no. of observations
50+55+58+90+58+92+99 502
....................................... = .........= 71.77 7
awnser is 71.7
hope this helpedPLEASE HELP I DONT KNOW
Answer:
28 in.
Step-by-step explanation:
Since the right portion of the figure is a square, the unlabeled bottom must be the same as the top or 6 in., therefore just add up the pieces starting on the right side. (5 + 6 + 2 + 5 + 4 + 6 = 28)
whats 7 times 8 divided by 2 i think the answer s 6 am i right or ring please tell me
Answer:
28Step-by-step explanation:
First,
7 times 8 = 7 × 8 = 56
Then,
The product divided by 2 = 56 ÷ 2 = 28
Hence,
The required answer is 28
What is the speed if the distance is 234 MI and time is 3 hrs
Answer:
speed = 78 miles per hour
Step-by-step explanation:
Speed is distance divided by time
speed = 234 miles / 3 hours
speed = 78 miles per hour
Is the equation a linear function?
y = -x + 3
Answer:
x=3
Step-by-step explanation:
y=-x+3
0=-x+3
x=3
will give brainliest
Answer:
Step-by-step explanation:
1/48 + 5/6
The LCD of 48 and 6 is 48 so we have:
1/48 + 40/48
= 41/38
Answer:
41/48
Step-by-step explanation:
Given that the triangles shown below are similar, what is the value of x? 32 20 H 48M P A. 96 B. 10.7 C. 24 D. 20
Answer:
I DONT SEE TRIANGLES
Step-by-step explanation:
Between which x-values and y-values does the cluster lie?
Answer:
Here is the picture
Step-by-step explanation:
The number lies between x-values 4 and 6 and y-values 6 and 9.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given that scatter plot lies in quadrant 1 of a coordinate plane, and the 14 points are plotted in the first quadrant.
We need to find the range of x and y values for this scatter plot.
The x values of the 14 points are given as;
2, 4, 4,1, 5, 5, 5, 5, 6, 6, 7, 8, 9.5, 9.5
The y values of the 14 points are given as;
5, 6, 9, 7.2, 6, 6.8, 8, 9, 7, 8.5, 10, 10.5, 9.5, 11.4
We can conclude that that most of the points are clustered between x-values 4 and 6 and y-values 6 and 9.
Therefore, the points are clustered between the x-values 4 and 6 and y-values 6 and 9.
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The complete question is
Select the correct answer. Scatter plot in quadrant 1 of a coordinate plane. 14 points are plotted at (2, 5), (4, 6), (4, 9), (4.1, 7.2), (5, 6), (5, 6.8), (5, 8), (5, 9), (6, 7), (6, 8.5), (7, 10), (8, 10.5), (9.5, 9.5), and (9.5, 11.4). Between which x-values and y-values does the cluster in this scatter plot lie? A. It lies between x-values 2 and 4 and y-values 4 and 6. B. It lies between x-values 4 and 6 and y-values 9 and 10. C. It lies between x-values 4 and 6 and y-values 6 and 9. D. It lies between x-values 7 and 9 and y-values 10 and 11.
Three years ago the sum of the ages of father and his son was
48 years and three years hence father's age will be three times
that of his son. Find the present ages of the father and his son.
Answer:
The father is 42 years old and the son is 12 years old.
Step-by-step explanation:
Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:
F + S = 48
F + 6 + S + 6 = 3S
34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)
38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)
40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)
39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)
39 + 3 = 42
9 + 3 = 12
Therefore, the father is 42 years old and the son is 12 years old.
ANSWER IT HOW THE QUESTIONS ARE ASKED!! Thank you so much!!
Answer:
[tex](a)\ Pr = \frac{2}{5}[/tex]
[tex](b)\ Pr = \frac{9}{20}[/tex]
[tex](c)\ E(Orange) = 100[/tex]
[tex](d)\ E(Orange) = 62.5[/tex]
Step-by-step explanation:
Solving (a): Theoretical probability of green or yellow
Here, we consider the spinner itself
From the attached image, we have:
[tex]n= 5[/tex] --- i.e. 5 sections
[tex]Yellow = 1[/tex]
[tex]Green = 1[/tex]
So, the probability is:
[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]
[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]
[tex]Pr = \frac{1}{5} + \frac{1}{5}[/tex]
Take LCM
[tex]Pr = \frac{1+1}{5}[/tex]
[tex]Pr = \frac{2}{5}[/tex]
Solving (b): Experimental probability of green or yellow
Here, we consider the result of the experiment
From the attached image, we have:
[tex]n= 40[/tex] --- i.e. 40 spins
[tex]Yellow = 12[/tex]
[tex]Green = 6[/tex]
So, the probability is:
[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]
[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]
[tex]Pr = \frac{12}{40} + \frac{6}{40}[/tex]
Take LCM
[tex]Pr = \frac{12+6}{40}[/tex]
[tex]Pr = \frac{18}{40}[/tex]
Simplify
[tex]Pr = \frac{9}{20}[/tex]
Solving (c): Expectation of orange outcomes in a spin of 500 times, theoretically.
Here, we consider the spinner itself
From the attached image, we have:
[tex]n= 5[/tex] --- i.e. 5 sections
[tex]Orange = 1[/tex]
So, the probability of having an outcome of orange in 1 spin is:
[tex]Pr = P(Orange)[/tex]
[tex]Pr = \frac{Orange}{n}[/tex]
[tex]Pr = \frac{1}{5}[/tex]
In 500 spins, the expectation is:
[tex]E(Orange) = Pr * 500[/tex]
[tex]E(Orange) = \frac{1}{5} * 500[/tex]
[tex]E(Orange) = 100[/tex]
Solving (c): Expectation of orange outcomes in a spin of 500 times, base on experiments.
Here, we consider the spinner itself
From the attached image, we have:
[tex]n= 40[/tex] --- i.e. 40 spins
[tex]Orange = 5[/tex]
So, the probability of having an outcome of orange is:
[tex]Pr = P(Orange)[/tex]
[tex]Pr = \frac{Orange}{n}[/tex]
[tex]Pr = \frac{5}{40}[/tex]
[tex]Pr = \frac{1}{8}[/tex]
In 500 spins, the expectation is:
[tex]E(Orange) = Pr * 500[/tex]
[tex]E(Orange) = \frac{1}{8} * 500[/tex]
[tex]E(Orange) = 62.5[/tex]
Bert measured a swimming pool and made a scale drawing. The scale of the drawing was
1 centimeter = 1 meter. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Submit
An additional amount of money added to borrowed money only on principal is what kind
of interest?
-Interest rate
-Terms
-Simple Interest
-Compound interest
Answer:
simple interest
Step-by-step explanation:
An additional amount of money added to borrowed money only on the principal could be simple interest.
How to calculate a simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Since, the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, it is left for T unit of time for that compound interest.
we can conclude that the additional amount of money added to borrowed money only on principal is simple interest.
Learn more about simple interest here:
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Plz help this is due today NO LINKS OR GROSS PICTURES OR I Will REPORT And please show work
Answer:
the volume is 600
Step-by-step explanation:
15*8*5=600
v=w*h*l
William went to play basketball. He wondered what the area of
the court was. He measured the length and width and found
that they were 28m and 15 m respectively. What is the area of
the court in cm"?
there's a width of 8 in., a length of 20 in., and a height of 12 in.
a) what is the longest poster you could fit in the box? express your answer to the nearest tenth of an inch.
b) explain why you can fit only one maximum-length poster in the box, but you can fit multiple 21.5-inch posters in the same box.
Answer:
a.
Approximately [tex]24.7\; \rm in[/tex].
b.
While there are three diagonals in a box (a rectangular prism,) all three diagonals goes through the same point- the centroid of this box.
For a maximum-length poster to fit in this box, it would have to be on one of the main diagonals of this box. Hence, any maximum-length poster that fits in this box would go through the centroid of this box.
It's not possible to force more than one posters to go through the same point (i.e., the centroid) in space. Hence, it would not be possible to fit a second maximum-length poster into this box.
This argument does not apply to [tex]21.5\; \rm in[/tex] posters. These posters are shorter than the diagonal of this box; they could fit inside the box without having to go through a particular point in space.
Step-by-step explanation:
The longest poster that could be fit into this box (a rectangular prism) would be as long as the longest line segment in this box. That line segment would be one of the three diagonals of this box.
Apply the Pythagorean theorem twice to find the length of that diagonal.
Start by finding calculating the diagonal of the base of this box. The base of this box is a rectangle with width [tex]8\; \rm in[/tex] and length [tex]10\; \rm in[/tex]. The length of its diagonal would be [tex]\sqrt{8^2 + 10^2}[/tex] inches.
Combine that with the height of this box to find the length of the diagonal of this box.
[tex]\begin{aligned}& \sqrt{{\left(\sqrt{8^2 + 10^2}\right)}^2 + 12^2 \\ &= \sqrt{8^2 + 10^2 + 12^2} \\ &\approx 24.7 \end{aligned}[/tex].
Chile I’m struggling
Answer:
the answer is c
Step-by-step explanation:
Help please
(Worth 10 points)
Please respond with a actual answer
*No robots no bad links*
The makers of MaxGrow want to ensure customers that their product will work under a wide variety of conditions such as a variety of watering conditions (no added water or watering daily) and how much fertilizer was used (no fertilizer, half fertilizer, or full fertilizer). The researchers randomly choose which group each tomato plant will be assigned to. At the end of the experiment, the number of tomatoes picked from each tomato plant is recorded.
a. Identify the subjects.
b. Explanatory variables
c. Treatments
d. Response variable
Answer:
Subject : Tomato plant
Explanatory variables : Watering condition ; Fertilizer addition
Treatment : daily watering ; half fertilizer ; full fertilizer
Response variable = Number of tomato picked
Step-by-step explanation:
Subjects are the individuals, animals or plants upon which treatment is applied. The subject here are the tomato plants
The Explanatory variables are the independent variables upon which we want base the variation of the dependent variable. The Independent variables are the watering condition a d the amount of fertilizer added.
Treatment : These are the actual changes made or applied on the subject, they include, daily watering, full or half fertilizer application.
Response variable : The number of tomatoes picked. This is also called the dependent variable, it is the outcome which may be due to the effect of the independent variable.
A manufacturer has 5,634 pens to divide into packs of 4 pens. The manufacturer makes as many packs as possible.
How many packs of pens does the manufacturer make, and how many pens are left over?
Answer:
1,408 packs can be made, and 2 pens will be left out.
Step-by-step explanation:
Given that a manufacturer has 5,634 pens to divide into packs of 4 pens, and the manufacturer makes as many packs as possible, to determine how many packs of pens does the manufacturer make, and how many pens are left over, the following must be done calculation:
5.634 / 4 = X
1,408.5 = X
5,634 - (1,408 x 4) = X
5.634 - 5.632 = X
2 = X
Therefore, 1,408 packs can be made, and 2 pens will be left out.
Answer: 1,408 packs can be made and 2 will be left out
Step-by-step explanation:
Five friends are sharing 4 fruit bars. Each friend gets the same amount.
How much fruit bar does each friend get?
Answer:
4/5 of a fruit bar
Step-by-step explanation:
Simplify.
4^3•4^-6
A. 1/4^3
B. 1/4^9
C. 1/4^18
D. 4^3
Answer:
A
Step-by-step explanation:
This can be rearranged as 4^3 * 1/(4^6)
or (4^3)/(4^6)
This can be changed to:
(4^3)/((4^3)*(4^3)
Which is equal to 1/(4^3)
or
4^(-3)
what is the value of the expression ? 11.263 ÷ 11.21
Answer:
1.004728
Step-by-step explanation:
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