Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.
Answers
82.9 score should be assigned for A’s and 74.4 should be assigned for B’s
In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.
It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.
We need to find what scores should be assigned A’s and B’s.
μ = 70, σ = 10
Using standard normal table,
P(X > x) = 10%
P(X > x) = 0.10
1 - P(X ≤ x) = 0.10
P(X ≤ x) =1−0.10
=0.90
Using standard normal z table,
(x - 70)/10 = 1.29
x = 82.9 (score for A’s)
Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)
P(X>x) = 0.33
1 - P(X ≤ x) = 0.33
P(X ≤ x) = 1 - 0.33
= 0.67
Using standard normal z table,
(x - 70)/10 = 0.44
x = 74.4 (score for B’s)
Therefore, the score for A = 82.9 and the score for B = 74.4
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Which of the following lines has a slope of -1?
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Answer:
I do not see any lines
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have a great day!
Step-by-step explanation:
Ejemplo: catalina compro una piscina para
ponerla en el jardín de su casa.
-Piscina cilíndrica 206cm de diámetro y 60cm
de profundidad además construirá una zona de
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puede contener la piscina? (considere T=3)
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The length of the fence must be 618cm
The volume that it can hold is 1,909,620 cm³
How to find the volume and the length of the fence?First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:
C = П*D
Here we use П = 3, then:
C = П*206cm
C = 3*206cm = 618cm
Now the volume, for a cylinder of diameter D and height H, the volume is:
V = П*(D/2)²*H
Replacing the values that we know we will get:
V = 3*(206cm/2)²*60cm = 1,909,620 cm³
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10 1/2 gal = __ qt
brainliest will be given
Answers
Answer:
10 1/2 gallons = 42 quarts:)
(1 - cos ß)(1 + cos ß) =1/cosec^2(ß)
Answers
Step-by-step explanation:
L.H.S=(1-cosB)(1+cosB)
=(1-cos^2B). {using (a+b) (a-b)=(a^2-b^2)in second step}
=sin^2B
=1/cosec^2B
Therefore,L.H.S=R.H.S proved
Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3
Answers
Answer:
O c. y-int y = 4 and No x-int
Step-by-step explanation:
In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.
There is no x-intercept present in a slope-intercept equation.
But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).
Hence, the answer is C. Y-intercept = 4 and No x-intercept.
Convert 2/3 hours to minutes
Answers
Answer:
Ur ans is 40 minutes.
Step-by-step explanation:
I hope it helps u dear! ^_^
What is the inverse of f(x) = 1/3x + 2 ?
A. h(x) = 1/3x + 2
B. h(x) = 1/3x - 2
C. h(x) = 3x - 2
D. h(x) = 3x - 6
Pls provide an explanation. I need help, and I will mark the person who helps me understand this Brainliest.
Answers
Answer:
D
Step-by-step explanation:
We are given the function:
\(\displaystyle f(x) = \frac{1}{3} x + 2\)
And we want to find its inverse h.
To find the inverse of a function, we can switch the y and x variables and solve for the new y. This will be our inverse.
We begin with:
\(\displaystyle f(x) = y = \frac{1}{3} x+ 2\)
Switching the variables yield:
\(\displaystyle x = \frac{1}{3}y + 2\)
And solving for y yields that:
\(\displaystyle y = h(x) = 3x - 6\)
In conclusion, the inverse function to f is 3x - 6. Our answer is D.
To understand why we switch the variables, recall that by the definition of inverse functions, if f(a) = b, then f⁻¹(b) = a. So, by switching the variables, we are essentially solving for f⁻¹(x).
maria , an experienced shipping clerk, can fill a certain order in 12 hours. , a new clerk, needs 13 hours to do the same job. Working together, how long will it take them to fill the order
Answers
It would take them approximately 6.24 hours (or 6 hours and 14 minutes) to complete the order if they work together.
To solve this problem, we can use the formula:
Time = Work ÷ Rate
Time is the time it takes to complete the job, Work is the amount of work to be done, and Rate is the rate of work.
Let's assume that the amount of work to be done is 1 (it doesn't matter what unit we use as long as we are consistent).
Then, Maria's rate of work is 1/12 (she can do 1 job in 12 hours) and the new clerk's rate of work is 1/13 (he can do 1 job in 13 hours).
If they work together, their combined rate of work is the sum of their individual rates:
Rate = Maria's rate + New clerk's rate
Rate = 1/12 + 1/13
Rate = (13 + 12) / (12 x 13)
Rate = 25 / 156
So, their combined rate of work is 25/156 jobs per hour.
Now, we can use the formula to find the time it takes for them to complete the job together:
Time = Work ÷ Rate
Time = 1 ÷ (25/156)
Time = 156/25
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5. Look at the two grids below How many squares can you count in each one?
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You did not copy the image with the question. Sometimes you have to screenshot or use the Snip-it app to get the image.
A group of students stand at the door of the school and asked every 10th student who they would vote for in the upcoming class elections and why?
Answers
This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.
This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.
However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.
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Your grandmother will be giving you $10,000 every year for the next five years, the first payment beginning at the end of the first year
A) If you invest these receivables in a bank at 6%, what is the total value at the end of 10 years if you make withdrawals of $3,000 in years 9 and 10?
B) An investor expects to receive $3,000 in year 2, $5,000 in year 5, and $7,000 in year 7. What is the present value of these payments if the interest rate is 8%?
Please also write the Excel formulas.
Answers
Answer:
a. The present value of these receivables is $42,123.64
b. The total value at the end of 10 years is $69,257.02
c. The present value of these payments is $10,059.37
Step-by-step explanation:
Which inequality represents the values of x for which triangle ABC exists
Answers
After considering all the given options we come to the conclusion that the inequality that represents the values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.
Here, the sides of a triangle should gradually satisfy the triangle inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x
Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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Use a calculator to solve for x in the equation 2e3x = 400. Round your answer to three decimals.
Question 8 options:
A)
6.397
B)
1.766
C)
5.991
D)
5.298
Answers
The value of the expression is 1.766.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given the expression,
2\(e^{3x}\) = 400
divide by 2 into both sides
\(e^{3x}\) = 400/2
\(e^{3x}\) = 200
converting the expression in form of a log,
ln(\(e^{3x}\))= ln(200)
log(aⁿ) = n log(a)
3x ln(e) = ln(200) [ln(e) = 1 and ln(200) = 5.2931]
3x = 5.2931
x = 1.766
Hence Option B is correct.
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an air traffic controller is tracking two planes. to start plane A is at the altitude of 4000 feet and plane B is at an altitude of 3146 feet. plane A is gaining altitude at 33.5 feet per second and plane B is gaining altitude at 50.75 feet per second
Answers
the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.
What is plane?A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.
Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:
altitude of plane A = 4000 + 33.5t
altitude of plane B = 3146 + 50.75t
where t represents time in seconds.
To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:
4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:
854 + 33.5t = 50.75t
Subtracting 33.5t from both sides, we get:
854 = 17.25t
Dividing both sides by 17.25, we get:
t = 49.45 seconds
Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:
altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet
Using the equation for plane B, we get:
altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet
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Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
I NEED HELP WITH THIS ASAP I WILL MARK YOU THE BRAINLIEST NO LINKS!!!
Answers
Answer:
0.08x
Step-by-step explanation:
0.08 is read as 8 hundredths. This can also be written as 8/100. Percent means out of 100; this means 8/100 is 8%. This means 0.08x is taking 8% of the original amount; this would represent the sales tax that is paid.
what is 1\10 in semplis form
Answers
Answer:
1/10 is the simplest form of the fraction
1.2 divided by 0.3 asp asp
Answers
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
Simplify. Express the answers using positive exponents
Answers
Answer:
C
Step-by-step explanation:
The simplified expression of the given expression -5\(w^2y^{-2\) / -15\(w^{-6}y^2\) is \(w^{16\).
The expression -5\(w^2y^{-2\) / -15\(w^{-6}y^2\) can be simplified as follows:
= -5 * \(w^{2 - (-6)\) * \(y^{-2 - 2\) / -15 * \(w^{-6 - 2\) * \(y^{2 - (-2)\)
= -5 * \(w^8\) * \(y^{-4\) / -15 * \(w^{-8\) * \(y^4\)
= (-5 / -15) * (\(w^8\) / \(w^{-8\)) * (\(y^{-4\) / \(y^4\))
= 1 * \(w^{16\) * \(y^0\)
= \(w^{16\)
Therefore, the simplified expression is w^16.
Here is a breakdown of the steps involved in the simplification:
The powers of w and y are combined using the distributive property of exponents.
The negative exponents are changed to positive exponents by dividing by the same base raised to the power of the negative exponent.
The factors of 5 and 15 are simplified.
The common factors of w and y are simplified.
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a surfer is stranded on an island in the shape of an equilateral triangle. the surfer wants to build a hut where the sum of the distances to the sides of the island is a minimum, because she surfs on each of the three beaches and equal amount of time. Where should she build her hut
Answers
Which choice is equivalent to the quotient shown here for acceptable
values of X?
square root 30(x - 1)/square root15(x - 1)^2?
A. sr30(x - 1) - 5(x - 1)?
B. sr6(x - 1)
C. sr 6/(x - 1)
D. sr150(x - 1)^3
Answers
Eric has 4 lb of blueberries to make into pie. How many pies can Eric make if each pie needs the given amount of blueberries.
Answers
Answer:
2 pies because you need 2 lb for each pie
Step-by-step explanation:
What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
Answers
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
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In the figure below, two secants are drawn to a circle from exterior point V.
Suppose that VZ=30, VW=45, and VX=22.5. Find XY.
Answers
The value of secant XY is 37.5 units.
How to find the value of secant XY?The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".
Using the theorem above, we can say:
VZ * VW = VX * VY
30 * 45 = 22.5 * VY
22.5VY = 1350
VY = 1350/22.5
VY = 60 units
Since VY = VX + XY. We have:
60 = 22.5 + XY
XY = 60 - 22.5
XY = 37.5 units
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A sidewalk will be put in around the block. The sidewalk will cover an area of 67,500 square feet and the length will be three times the width. The area is represented by the equation: w(3w) = 67, 500. Solve for w.
Answers
Explanation
Given that the area of the side block is represented by
\(w\mleft(3w\mright)=67,500\)The value of w can be found below;
\(\begin{gathered} w(3w)=67,500 \\ 3w^2=67500 \\ \text{Divide both side by 3} \\ w^2=\frac{67500}{3} \\ w^2=22500 \\ w=\sqrt[]{22500} \\ w=150 \end{gathered}\)Answer: 150
Answer:
Step-by-step explanation:
This question is part of a quiz for a cyber school in Pennsylvania. Please remove the question and its solution. Signed, the teacher
5x-y=1/4 write in slope-intercept form
Answers
The slope intercept form of the given equation is,
y = 5x - 1/4
Given an equation of a line as,
5x - y = 1/4
We have to write the equation of the line in slope intercept form.
Equation of the line in slope intercept form is,
y = mx + c
Here m is the slope and c is the y intercept.
Rearranging the given equation,
5x = y + 1/4
5x - 1/4 = y
or,
y = 5x - 1/4
Hence the slope intercept form is y = 5x - 1/4.
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Johnathan is using a hose to fill his pool with water. The pool already had 2,000 gallons of water in it before he started, and the hose puts water into the pool at a rate of 360 gallons per hour. Let g represent the number of gallons that the hose has put into the pool after a given number of hours. Let h represent the number of hours that the hose has put water into the pool. Let w represent the total number of gallons of water in the pool. Complete the equations so that: Equation 1 shows the relationship between g and h. Equation 2 shows the relationship between g and w.
Answers
The problem states that Jonathan is using a hose to fill his pool with water. Initially, the pool already had 2,000 gallons of water in it before he started.
By doing step by step process we can get both equations solution:
The hose puts water into the pool at a rate of 360 gallons per hour.
Equation 1: g = 360h
Explanation: The number of gallons that the hose has put into the pool (g) is directly proportional to the number of hours that the hose has put water into the pool (h) at a constant rate of 360 gallons per hour. Therefore, we can express this relationship as g = 360h.
Equation 2: w = g + 2,000
Explanation: The total number of gallons of water in the pool (w) is equal to the number of gallons that the hose has put into the pool (g) plus the initial 2,000 gallons of water that were already in the pool. Therefore, we can express this relationship as w = g + 2,000.
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Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
Answers
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do we explain?When an account is found to be uncollectible, the direct write-off method records the expense for uncollected accounts receivable. This approach involves simply writing off the uncollectible account as a bad debt expense and deducting the outstanding quantity from the accounts receivable total.
Despite being quite easy to understand and basic, this method does not adhere to generally accepted accounting principles (GAAP) because it does not match expenses to the time period during which income was generated.
In contrast, the allowance approach establishes an allowance for doubtful accounts contra-asset account and estimates the amount of uncollectible accounts before recognizing the expense for uncollected accounts receivable.
This allowance account is used to lower the balance of accounts receivable to the anticipated amount of collection. Instead of when the account is found to be uncollectible, the expense is recognized at the time the estimate is made. Because it matches the expense to the time period in which the revenue was received, this method is thought to be more accurate than the direct write-off method.
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12. After 2 hours, Morgan had earned $12.75 at her lemonade stand. After 5
hours, she had earned $44.25. Assuming a linear function, write an
equation in the form y=mx+b that shows the profit earned from selling
lemonade for x hours.
Answers
Answer:
y = 10.5x - 8.25
Step-by-step explanation:
m = (44.25 - 12.75)/(5 - 2) = 10.5
y = mx + b
y = 10.5x + b
12.75 = 10.5 × 2 + b
b = -8.25
y = 10.5x - 8.25