A class of 17 students took a math test and all had different scores. The median score was 70, the highest score was 95 and the lowest score was 33. Later, it was discovered that the highest and the lowest scores, should respectively increase by 7 points and decrease by 4 points. Let denote the old mean and denote the new mean. Find a mathematical relation that connects these two. Show your work. You can use x_new and x_old to represent the two variables.
Answers
The mathematical relation that connects the old mean (x_old) and the new mean (x_new) is x_new = x_old. This means that the old mean and the new mean are equal.
Let's denote the old mean as x_old and the new mean as x_new.
The total sum of scores is equal to the number of students (17) multiplied by the mean score. Therefore, we can write:
x_old * 17 = (sum of the old scores)
After adjusting the highest and lowest scores, the new sum of scores would be:
(x_old + 7 + x_old - 4 + sum of the other 15 scores)
The new sum of scores can be simplified as:
2x_old + 3 + (sum of the other 15 scores)
Since the number of students and the other 15 scores remain the same, the new sum of scores can also be written as:
x_new * 17
Therefore, we have:
x_new * 17 = 2x_old + 3 + (sum of the other 15 scores)
Since the sum of the other 15 scores remains the same, we can rewrite it as:
x_new * 17 = 2x_old + 3 + (sum of the other 15 scores) = x_old * 17
Simplifying the equation:
x_new * 17 = x_old * 17
Dividing both sides by 17:
x_new = x_old
Therefore, the mathematical relation that connects the old mean (x_old) and the new mean (x_new) is x_new = x_old. This means that the old mean and the new mean are equal.
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Related Questions
A small town wants to compare the number of students enrolled in public and
private schools. The polynomials below show the enrollment for each:
Public School: –19c2 + 980c + 48,989
Private School: 40c + 4046
Write a polynomial for how many more students are enrolled in public school
than private school.
Answers
Answer:
-19c(squared) + 980c + 940c + 44943
Step-by-step explanation:
Hey! I got this answer off of someone else ages ago and i hope this is what youre looking for
How can we determine whether equation are equivalent
Answers
Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. Take a look at examples of equivalent equations, how to solve them for one or more variables, and how you might use this skill outside a classroom. Putting these rules into practice, determine whether these two equations are equivalent: 1. x + 2 = 7 2. 2x + 1 = 11 To solve this, you need to find "x" for each equation. If "x" is the same for both equations, then they are equivalent.
what is 12 divided by 4
Answers
Answer:
It is 3
Step-by-step explanation:
The equation 12 divided by 4 is 3
To make sure this is true 4 times 3 is 12
Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models (this is the product mix). The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.’s sales product mix for a week is?
Answers
Each model should be produced on a weekly basis to maximize net profit is $75,900.
What is Net profit?
In both business and accounting, net income or profit is an entity's revenue less cost of goods sold, costs, depreciation and amortisation, interest, and taxes for a certain accounting period.
As given,
Number of products sold:
T ≥ 1.5G
Maximize Profit Z = 150T + 130G
Labor Constraint:
Labor hours Available:
Production Department:
Number of labor hours available per day = 58 × 7 = 406
Number of days in a week = 5
Number of lobor ours available per week = 406 × 5 = 2030
Assembly Department:
Number of labor hours available per day = 25 × 7 = 175
Number of days in a week = 5
Number of labor hours available per week = 175 × 5 = 875.
Labor hours Required:
Labor hours required for G1 model:
Labor hours required at Production department = 3.5G
Labor hours required at assembly department = 2G
Labor hours required for T1 model:
Labor hours required at Production department = 4T
Labor hours required at Assembly department = 1.5T
Total labor hours required at Production department = 3.5G + 4T
Total labor hours required at Assembly department = 2G + 1.5T.
Constraint:
Labor hours required ≤ Labor hours Available.
Production department Labor constraint
3.5G + 4T ≤ 2030
Assembly department Labor constraint:
2G + 1.5T ≤ 875
The function:
Maximum Profit Z = 150T +130G
Constraint:
3.5G +4T ≤ 2030
2G + 1.5T ≤ 875
T ≥ 1.5G
Suppose that for example:
10.5G +12T = 6090
16G + 12T = 7000
Solve both equations simultaneously,
5.5G = 7000 - 6090
5.5G = 910
G = 910/5.5
G = 363
Since, T > G
Hence,
T = 363,
G = 165
Calculate Profit:
150T + 130G = 150 × 363 + 130 × 165
= 54450 + 21450
= 75900
Hence, each model should be produced on a weekly basis to maximize net profit is $75,900.
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Eliza cannot decide which of two bicycles to buy. The original price of each is $380. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Part A: Find the sale price of each bicycle. Part B: Which bicycle should Eliza buy if the bicycles are the same except for the selling price?
Answers
Answer:
First Bike = $190 Second Bike = $212.80
Eliza should buy the first bike
Step-by-step explanation:
Which expression has a value of −9?
(−12)−3
12−(−3)
(−12)−(−3)
3−(−6)
Answers
An airline claims that it rarely loses a passenger's checked luggage, and, if checked luggage is lost, 90% of the luggage is recovered and returned to the owner within 24 hours. A consumer group believes the 24-hour recovery rate of lost luggage is actually lower (worse) than the airline's claim. They surveyed a large random sample of the airline's customers and found that 103 of 122 people who had lost luggage were reunited with the missing items within 24 hours. Is this enough evidence to claim the proportion of people who lost luggage with this airline a
Answers
The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
What is a null hypothesis?Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.
It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.
The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.
In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
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A train travelled 300 kilometres in 5 hours. Find it's rate of speed
Answers
Answer:
The train traveled 60 kilometers per hour.
Step-by-step explanation:
300/5=60
Answer:
60 km/hours
Step-by-step explanation:
in the picture above.
(2+2+2+2 = 8 points) Use Little's formula to answer the following two questions. Little's formula: WIP = Flow rate x Flow time. a) A campus deli serves 300 customers over its busy lunch period from 11:30 am to 1:30 pm. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 10 customers are in process at any point in time. What is the average amount of time that a customer spends in process? b) Madesimo is a famous resort in Italy. All of its rooms are always booked in the winter season and there are, on average, 120 skiers coming to the resort every day. On average, skiers stay in Madesimo for 10 days. What is on average the number of skiers staying in Madesimo? c) Walmart sells jeans for $40 a pair that it purchases for $20 a pair. Its annual holding cost percentage is 20% and these jeans turn 10 times per year. What holding cost does it incur for each pair of jeans? d) Home Depot's inventory turns are 4.7 turns per year, its cost of goods sold is $44.7 Billion per year. What is the average inventory it holds in $ Billion?
Answers
a) The average amount of time a customer spends in process at the campus deli is approximately 2 minutes, and b) the average number of skiers staying in Madesimo is 1,200 skiers.
a) The average amount of time that a customer spends in process can be determined using Little's formula. According to the formula, the work-in-process (WIP) is equal to the flow rate multiplied by the flow time. In this case, the flow rate is the number of customers served over the lunch period, which is 300. The WIP is the average number of customers in process at any point in time, which is 10. By rearranging the formula, we can solve for the flow time, which represents the average time a customer spends in process.
Thus, the flow time is equal to WIP divided by the flow rate. Therefore, the average amount of time that a customer spends in process is 10/300, or approximately 0.0333 hours (or 2 minutes).
b) To determine the average number of skiers staying in Madesimo, we can again apply Little's formula. The flow rate in this case is the average number of skiers coming to the resort per day, which is 120. The flow time represents the average duration of stay for skiers, which is given as 10 days. Using Little's formula, we can calculate the work-in-process (WIP), which represents the average number of skiers staying in Madesimo.
WIP is equal to the flow rate multiplied by the flow time. Therefore, the average number of skiers staying in Madesimo is 120 skiers/day multiplied by 10 days, resulting in 1,200 skiers on average.
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Orthogonal complement to S has dimension 0 when ____.
Answers
The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.
We have,
The orthogonal complement to a subspace S of a vector space is the set of all vectors in the vector space that are orthogonal (perpendicular) to every vector in S.
The dimension of the orthogonal complement is given by the difference between the dimension of the vector space and The dimension of S.
If S spans the entire vector space, then its orthogonal complement consists only of the zero vector and therefore has dimension 0.
Thus,
The orthogonal complement to S has dimension 0 when the dimension of the vector space is equal to the dimension of S.
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5. Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he
assembled 137 toys. He noticed that since he started, every day he assembled 3 more
toys than the day before. How many toys did Jamal assemble altogether during his first
20 days?
(Arithmetic sequence)——
Answers
2170 toys Jamal assemble altogether during his first 20 days.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given: Jamal got a job working on an assembly line in a toy factory. On the 20th day of work, he assembled 137 toys. He noticed that since he started, every day he assembled 3 more toys than the day before.
We have to find how many toys did Jamal assemble altogether during his first 20 days.
We apply the arithmetic sequence formula and we get
tₙ = t₁ + (n-1)d
137 = t₁ + (20-1)(3)
t₁ = 80
To calculate the total number of toys that Jamal assemble in his first 20 days,
S₂₀ = (20/2)(2×80 + (20-1)(3))
S₂₀ = 2170
Hence, 2170 toys Jamal assemble altogether during his first 20 days.
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Rearrange the equation below to identify the variables a, b and c.
0 = 4x – 5x2
Answers
Answer:
a = -5x
b = 4
c = 0
Step-by-step explanation:
binomial equation is written in form of
\(ax^2 + bx + c = 0\)
given equation
\(0 = 4x - 5x^2\)
rearranging it we have
\(0 = - 5x^2 + 4x + 0\)
comparing this equation with \(ax^2 + bx + c = 0\)
comparing coefficient of variables with same power.
a = -5x
b = 4
c = 0
f(x)= lx+3l-7
What will the function be if it has been:
1. Reflected across the x-axis
2. Translated left 4 units
3. Translated down 3 units
Please type answer with no spaces. The absolute value key should be located directly above the "Enter/Return" key on your keyboard.
Answers
The function after each transformation is given as follows:
1. Reflected across the x-axis: f(x) = -|x + 3| + 7.
2. Translated left 4 units: f(x) = |x + 7| - 7.
3. Translated down 3 units: f(x) = |x + 3| - 10
How to define the functions?The function for this problem is defined as follows:
f(x) = |x + 3| - 7.
When the function is reflected across the x-axis, we have that the entire function is multiplied by -1, hence:
f(x) = -(|x + 3| - 7)
f(x) = -|x + 3| + 7.
When the function is translated left 4 units, we have that x -> x + 4, hence:
f(x) = |x + 4 + 3| - 7
f(x) = |x + 7| - 7.
When the function is translated down 3 units, we have that f(x) -> f(x) - 3, hence:
f(x) = |x + 3| - 7 - 3
f(x) = |x + 3| - 10
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A research marketer for an online retail store was interested in the number of times per month stay-at-home moms bought items from online retail stores. She found the mean is 15 items and the standard deviation is 3 items purchased from online retail stores each month.
Using the empirical rule, approximately what percent of stay-at-home moms bought more than 21 items from online retail stores each month?
2.50%
5.0%
10.0%
16.0%
95.0%
Answers
Mean = 15
SD = 3
P(X >21) = ?
21 is equal to the mean plus 2 x the SD ( 15 + 2x3 = 15 +6 = 21)
2 times the SD would be 95% ( Empirical rule)
For 95%, that means that 5% is above and below it.
5%/2 = 2.5% is below and 2.5% is above.
The answer is 2.5%
Determine c such that f(c) is the average value of the function
on the interval [0, 2].
![Determine c such that f(c) is the average value of the function on the interval [0, 2].](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/UlTIrmCLruBm9kDN9OuFOc9wuen2LY3M.png)
Answers
The c is equal to half of the definite integral of the function over the interval [0, 2].
To determine c such that f(c) is the average value of the function on the interval [0, 2], we can use the formula for the average value of a function:
avg = 1/(b-a) * ∫(a to b) f(x) dx
In this case, a = 0 and b = 2, so the formula becomes:
avg = 1/2 * ∫(0 to 2) f(x) dx
We want to find the value of c such that f(c) = avg, so we can set these two expressions equal to each other and solve for c:
f(c) = avg
f(c) = 1/2 * ∫(0 to 2) f(x) dx
We can then use calculus to solve for c by finding the derivative of both sides with respect to c and setting them equal to each other:
f'(c) = 1/2 * (f(2) - f(0))
Solving for c gives us:
c = (1/2) * ∫(0 to 2) f(x) dx
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A bag contains 4 green marbles and 6 purple marbles. A marble is drawn and then replaced. This experiment is repeated 50 times. What is the probability that a green marble is drawn between 17 and 25 times, inclusive
Answers
P(17 ≤ X ≤ 25) = 0.8556 - 0.1862 = 0.6694Answer: 0.6694 The given bag has 4 green marbles and 6 purple marbles. A marble is drawn and then replaced. This experiment is repeated 50 times. We are required to determine the probability that a green marble is drawn between 17 and 25 times, inclusive.We can use the binomial distribution to solve this problem.
Let X be the number of times a green marble is drawn in 50 trials of the experiment. Then X ~ B(50, 0.4) where p = 0.4 is the probability of drawing a green marble in one trial.P(X = x) = (50Cx)(0.4)x(1 - 0.4)50 - xThe probability that a green marble is drawn between 17 and 25 times, inclusiveP(17 ≤ X ≤ 25) = P(X ≤ 25) - P(X < 17)We haveP(X < 17) = P(X ≤ 16)P(X ≤ 16) = ∑P(X = x) from x = 0 to x = 16Now using the binomial distribution, we getP(X ≤ 16) = 0.1862P(X ≤ 25) = ∑P(X = x) from x = 0 to x = 25Now using the binomial distribution, we getP(X ≤ 25) = 0.
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Asolve this system of equations using a matrix inverse. if a is the coefficient matrix of the above system of equations and , then the elements of are , the elements of are , and the elements are . the solution of this system is (x, y, z) = .
Answers
The solution of this system is represented by the values of (x, y, z).
To solve the system of equations using a matrix inverse, we first need to find the inverse of the coefficient matrix, denoted as "A". Let's assume that "A" is a 3x3 matrix.
Find the determinant of matrix A:
det(A) = ad - bc
Check if the determinant is non-zero. If det(A) ≠ 0, then A has an inverse.
Calculate the matrix of minors:
M = |d -b a |
|-f e -c|
|i -h g |
Calculate the matrix of cofactors:
C = |d -b a |
|-f e -c|
|i -h g |
Calculate the adjugate matrix:
Adj(A) = C^T (transpose of C)
Find the inverse of A:
A^-1 = (1/det(A)) * Adj(A)
Multiply the inverse matrix by the constant matrix:
X = A^-1 * B
The solution of this system is represented by the values of (x, y, z).
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Which expression is a monomial
Answers
second one for sure
Find the measure of the angle in red.
Answers
Answer:
Sin 7pie/12 would be the answer
What are the correct answers for the other problems?
Answers
Answer:
3/5 = 0.6
1/4 = 0.25
7/8 = 0.875
Step-by-step explanation:
Hope this helps!
\(\\ \sf\longmapsto \dfrac{3}{5}\)
\(\\ \sf\longmapsto \dfrac{3(2)}{5(2)}\)
\(\\ \sf\longmapsto \dfrac{6}{10}\)
\(\\ \sf\longmapsto 0.6\)
#2
\(\\ \sf\longmapsto \dfrac{1}{4}\)
\(\\ \sf\longmapsto \dfrac{1(25)}{4(25)}\)
\(\\ \sf\longmapsto \dfrac{25}{100}\)
\(\\ \sf\longmapsto 0.25\)
#3
\(\\ \sf\longmapsto \dfrac{7}{8}\)
\(\\ \sf\longmapsto \dfrac{7(125)}{8(125)}\)
\(\\ \sf\longmapsto \dfrac{875}{1000}\)
\(\\ \sf\longmapsto 0.875\)
Mario paid $44.25 in taxi fare from the hotel to
the airport. The cab charged $2.25 for the first
mile plus $3.50 for each additional mile. How
many miles was it from the hotel to the airport?
A. 10
B. 11
C. 12
D. 13
Answers
Answer:
C. 12
hope they help
first mile $2.25 plus $3.50 ×12= $42.00+2.25=44.25
Factoriser 100 - 40x ²
Answers
Answer: 20(5-2x^2)
Step-by-step explanation:
Verified the answer with my math powers
Can someone help me on this?
Answers
5s + 10a = 3000
x = students
y = adults
5x + 10y = 3000
follow the instructions to find x/y intercept;
for example;
5(0) + 10y = 3000
10y = 3000
y = 300;
you would then want to solve for “x” by plugging “y” for 0.
I can explain further if you’d like;
Consider a line process with 3 processing stages. The production requires each unit to go through Stage A through Stage C in sequence. The characteristics of the Stages are given below: Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100% Determine the system capacity. Which stage is the bottleneck? What is the utilization of Stage 3.
Answers
The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.
A line process has three processing stages with the characteristics given below:
Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%
To determine the system capacity and the bottleneck stage and utilization of Stage 3:
The system capacity is calculated by the product of the processing capacity of each stage:
1 x 1 x 2 = 2 units per minute
The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:
Process time per unit = 1 + 2 + 3 = 6 minutes per unit
Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit
The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.
However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.
Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.
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Don't need it answered immediately.
Answers
Answer:
ºC = (ºF - 32) / (9/5)
Step-by-step explanation:
Take the formula that you already have:
ºF = (ºC × 9/5) + 32
Flip the ºF and ºC:
ºC = (ºF × 9/5) + 32
Move the whole number to the right side of the equation and change it's sign:
ºC = (ºF - 32) / (9/5)
(This will also force the fraction to move to the right hand side of the equation, but for that you keep the value of the number the same)
Hope this helped!
The school store earned $625.32 one week, and then $98.36, $145.98, and $304.09 during the next three weeks. How much did the school store earn in the four weeks?
Answers
Answer:
The store earned $1173.75 in the 4 weeks
Step-by-step explanation:
To calculate the amount earned by the school in the 4 weeks, we are going to add all what had been earned in the previous weeks;
Mathematically that would be;
$625.32 + $98.36 + $145.98 + $304.09 = $1,173.75
g The hourly wage of some automobile plant workers went from $ 6.10 6.10 to $ 8.58 8.58 in 7 years (annual raises). If their wages are growing exponentially what will be their hourly wage in 10 more years
Answers
The hourly wage in 10 years = $12.37, In this scenario, automobile plant workers' hourly wages increased from $6.10 to $8.58 over a period of 7 years, with the wages growing exponentially.
To calculate their hourly wage in 10 more years, we will use the exponential growth formula:
Final Amount = Initial Amount * (1 + Growth Rate)^Years
First, we need to find the annual growth rate. To do this, we can rearrange the formula as follows:
Growth Rate = [(Final Amount / Initial Amount)^(1 / Years)] - 1
Plugging in the given values:
Growth Rate = [(8.58 / 6.10)^(1 / 7)] - 1
Growth Rate ≈ 0.0476
Now that we have the annual growth rate, we can calculate their hourly wage in 10 more years:
Hourly Wage in 10 Years = 8.58 * (1 + 0.0476)^10
Hourly Wage in 10 Years ≈ $12.79
Therefore, the automobile plant workers' hourly wage will be approximately $12.79 in 10 more years, assuming their wages continue to grow exponentially at the same rate.
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please help !!! its math problem i give brainlist What type of function is represented in the table below?
Answers
Answer:
linear is correct
Step-by-step explanation:
Question 5 of 10
You find a mutual fund that offers approximately 5% APR compounded
monthly. You will invest enough each month so that you will have $1000 at
the end of the year. How much money will you have invested in total after 1
year?
OA. $1053.65
OB. $977.28
OC. $912.43
D. $753.90
Answers
After 1 year, you have invested $977.28. The Option B
How much money will you have invested?To find the total amount, we have to determine monthly investment required.
Let's represent monthly investment as M.
After 12 months of compounding, the final amount will be $1000. We will use formula for compound interest \(A = P(1 + r/n)^{nt}\)
To solve for monthly investment (M), we rearrange the formula as follows: \(A = M * ((1 + r/n)^{nt} - 1) / (r/n)\)
\(1000 = M * ((1 + 0.05/12)^{12*1} - 1) / (0.05/12)\\M = $1000 * (0.05/12) / ((1 + 0.05/12)^{12*1} - 1)\\M = $81.4408151 \\M = $81.44\)
To get total amount invested after 1 year, we will multiply investment by 12 months:
= $81.44 * 12
= $977.28.
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Fill in the blank to complete the equation below. 99 + 33 = 11(?+3)
Answers
Answer:
? = 9
Step-by-step explanation:
you know 99 + 33 = 132 so you can substitute that: 132 = 11 (? + 3). im going to change ? into x for now: 132 = 11 (x + 3). then distribute the 11 so 132 = 11x + 33. then subtract 33 from both sides (99 = 11x) and divide both side by 11 (x = 9) and you get 9!
hope this helps!