Pupils Per Teacher The frequency distribution shows the average number of pupils per teacher in some states of the United States. Find the variance and standard deviation for the data. Use a TI-83 Plus/TI-84 Plus calculator. Round your answers to at least one decimal place.
Answers
The variance and standard deviation for the frequency of pupils per teacher in some states of US is; Variance= 4.62 = 4.6 and Standard Deviation = 2.14 = 2.1
What is variance?Variance(σ²) is a measure of dispersion. A measure of dispersion is a quantity that is used to check the variability of data about an average value. Data can be of two types - grouped and ungrouped. When data is expressed in the form of class intervals it is known as grouped data.
The standard deviation(σ) of a random variable, is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
That means;
Standard Deviation = √variance.
For the given data the sum of frequencies = 1+16+11+7+1+2= 38.
Midpoint is 12,15,18,21,24,27.
ni x mi = 12,240,198,147,24,54.
Sum of ni + mi = 675.
Mean (u) = 17.76
mi - u is -5.76,-2.76,0.24,3.24,6.24,9.24.
(mi - u)² is 33.17,7.61,0.057,10.49,38.93,85.37.
Sum of (mi - u)² = 175.62.
Variance = Sum of (mi - u)² / sum of frequencies
= 175.62/38
= 4.62 = 4.6.
Standard deviation = √variance.
= √4.62
= 2.14 = 2.1.
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Related Questions
A total of 491 tickets were sold for the school play. They were either adult tickets or student tickets. There
were 60 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answers
Answer:
Adult tickets = 276
Step-by-step explanation:
a + s = 491 Eq. 1
a = s + 61 Eq. 2
a = adult tickets
s = student ticket
Replacing Eq. 2 in Eq. 1:
(s+61) + s = 491
2s + 61 = 491
2s = 491 - 61
2s = 430
s = 430/2
s = 215
from the Eq. 2
a = s + 61
a = 215 + 61
a = 276
Check:
from Eq. 1:
a + s = 491
276 + 215 = 491
Which of the following is a whole number? Select all correct answers.
Select all that apply:
15
0
439
−9
−10
5
Answers
Answer:
15, 0, 439, 5
Step-by-step explanation:
-9 and -10 are negative integers. Whole numbers can't be negative.
Answer:
15,0,439,5 are whole numbers. eg: when we count the number of students we use 1,2,3 etc we won't use any decimal or fractions or negative values. like that whole numbers are like the numbers we count number of students
72/45 in simplest form
Answers
A patient is limited to 2000 milliliters (mL) of liquid intake per day. If the patient has 300 mL of juice for breakfast and 500 mL of milk for lunch, how much liquid can the patient have for the rest of the day?
Answers
Answer: 300mL + 500mL = 800 mL
2000 mL - 800 mL = 1200mL
The patient can have 1200 milliliters of liquid for the rest of the day.
Find the sum of 2.54 x 1019 and 3.218 x 1017.
3.2434 x 1036
2.57218 x 1036
3.2434 x 1019
2.57218 x 1019
Answers
Answer:
Option 4
Step-by-step explanation:
[tex]2.54 \times 10^{19}+3.218 \times 10^{17} \\ \\ =(254+3.218) \times 10^{17} \\ \\ =257.218 \times 10^{17} \\ \\ =2.57218 \times 10^{19}[/tex]
Answer:
2.57218*1019
Step-by-step explanation:
Layla has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $319.28.
She buys 3 bicycle reflectors for $4.90 each and a pair of bike gloves for $37.94.
She plans to spend some or all of the money she has left to buy new biking outfits for $77.02 each.
Use the drop-down menu below to write an inequality representing oo, the number of outfits she can buy while staying within her budget.
Answers
Layla should by not more than 4 outfits in order not to exceed her budget
The inequality expression is n ≤ 4
Given data
price of a new bicycles = $319.28
3 bicycle reflectors = $4.90
a pair of bike gloves = $37.94.
new biking outfits = $77.02 each
Layla's total money to spend at a bicycle store = $680
How to write the required inequality equationLayla's expenses will not be more than her total amount to spend at the bicycle store therefore will use less than or equal to sign, before the sum of the other items
The expression is written as follows
$680 ≤ $319.28 + 3 * $4.90 + $37.94 + n * $77.02
where n represents the number of the new biking outfits
$680 - ( $319.28 + 3 * $4.90 + $37.94 ) ≤. + n * $77.02
( $680 - ( $319.28 + 3 * $4.90 + $37.94 ) ) / $77.02 ≥ n
( $680 - $371.64 ) / $77.02 ≥ n
( $308.36) / $77.02 ≥ n
4 ≥ n
Layla should by not more than 4 outfits in order not to exceed her budget
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the function f multiplies it’s input by 2 and then subtracts 17 to produce its output. What is the symbolic representation of this operation
Answers
Answer:
f(x)= 2x-17
Step-by-step explanation:
Let, input be x,
Multiplying input by 2: 2x
then subtracting it by 17: 2x-17
Therefore, Symbolic representation required is : f(x)= 2x-17
The symbolic representation of the function defined is f(x) = 2x-17
What is function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, the function f multiplies it’s input by 2 and then subtracts 17 to produce its output. we need to express the operation into symbolic representation.
Let the input be x, then the output will be the value of f(x).
Therefore, it is given, the input is multiplied by 2, that mean,
f(x) = 2x
Then 17 is subtracted from it, that will give,
f(x) = 2x-17
Hence, the symbolic representation of the given operation is f(x) = 2x-17
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PLEASE ANSWER THIS QUESTION QUICKLY!
Solve by factoring:
2(m-1)^2-11(m-1)+5=0
Give either of the two solutions.
Rules answering these questions:
Show your work!
Explain your answer!
Nonsense answer will be reported and delete your answer!
Do not spam answers!
Thanks!
Answers
2((m-1)(m-1))-11m+11+5=0
solve (m-1)(m-1) first then multiply the answer by 2
2(m^2-2m+1)-11m+16=0
2m^2-4m+2-11m+16
2m^2-15m+18
make factors
2m^2-3m-12m+18
m(2m-3)-6(2m-3)
(m-6)(2m-3)
there will be two answers
solve (m-6) first
m-6=0
m=6
Now (2m-3)
2m-3=0
2m=3
m=3/2
There will be two answers to this equation 6 and 3/2
Rewrite (10 + 6) + 5+ 3 using the Associative Law of Addition,
O 10+6+5+3
O 10+(6+5) + 3
O 3+5+ (10+6)
O (10+6) + 3+5
Answers
Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
How to compute the value?It should be noted that the Associative Law of Addition explains that a + (b + c) is the same as (a + b) + c.
Therefore, Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
It should be noted that this will still give same value.
Therefore, the correct option is B.
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The Lopez family buys 4 dinners at the market. The total cost is $5 above or below $50. Write an equation that models the cost x, in dollars of a single dinner?
answer: |_-_x|-_=0
Answers
==================================================
Explanation:
x = cost of one dinner
4x = cost of four dinners
50-4x = the difference in the cost of $50 vs 4x dollars
To ensure this difference is never negative, we use absolute value to form the expression |50-4x|
Set this equal to 5 since we want this distance or difference to be 5 units above or below 50
|50-4x| = 5
|50 - 4x| - 5 = 0
Answer:
l 50 - 4x l - 5 = 0
Step-by-step explanation:
If anyone can help me to solve this!!
Answers
Answer:
[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]
Step-by-step explanation:
Standard form of a quadratic equation:
[tex]\boxed{ax^2+bx+c=0}[/tex]
Question 1
Given:
[tex]x^2+x=20[/tex]
Rearrange to standard form by subtracting 20 from both sides:
[tex]\implies x^2+x -20=20-20[/tex]
[tex]\implies x^2+x -20=0[/tex]
Therefore:
a = 1b = 1c = -20Question 2
Given:
[tex]4x^2-2x=28[/tex]
Rearrange to standard form by subtracting 28 from both sides:
[tex]\implies 4x^2-2x-28=28-28[/tex]
[tex]\implies 4x^2-2x-28=0[/tex]
Therefore:
a = 4b = -2c = -28Question 3
Given:
[tex]5x^2=225[/tex]
Rearrange to standard form by subtracting 225 from both sides:
[tex]\implies 5x^2-225=225-225[/tex]
[tex]\implies 5x^2-225=0[/tex]
Therefore:
a = 5b = 0c = -225Question 4
Given:
[tex]x^2-x=36[/tex]
Rearrange to standard form by subtracting 36 from both sides:
[tex]\implies x^2-x-36=36-36[/tex]
[tex]\implies x^2-x-36=0[/tex]
Therefore:
a = 1b = -1c = -36Question 5
Given:
[tex]3x^2-4=7x[/tex]
Rearrange to standard form by subtracting 7x from both sides:
[tex]\implies 3x^2-4-7x=7x-7x[/tex]
[tex]\implies 3x^2-4-7x=0[/tex]
[tex]\implies 3x^2-7x-4=0[/tex]
Therefore:
a = 3b = -7c = -43. The mean of four numbers is 30. If three of the numbers are 12, 50, and 48, what is the fourth
number?
O 120
O 10
012
030
Answers
Answer:
12 10 12 30
Step-by-step explanation:
eso se devide y es 1.030
The sum of the four numbers divided by 4 is equal to the mean.
the sum/4 = mean
(12 + 50 + 48 + n)/4 = 30
(110 + n)/4 = 30
(110 + n) = 30 × 4
(110 + n) = 120
n = 120 - 110
n = 10
Acasa Insurance Company offers several plans for home insurance.
Plan A has a $700 yearly premium with a $3,000 deductible.
Plan B has a $1,200 yearly premium with a $1,000 deductible.
The average payout by the insurance company for a fire claim is $27,000. Suppose 5% of the claims were for fire damage. What would Acasa's expected value (loss or gain) be per customer who chooses plan A
Answers
Acasa's expected value loss be per customer who chooses plan A
Assumption
Fill customers choose plan A
The average payout is the same for plans A & B
Expected value = net payment in -Net payment out
⇒ 1000% × 700$ - 5% ×[27000$ - 3000$]
⇒ 700$ - 1200$
⇒ -500$
What are a profit and loss?
A profit and loss statement is a record of revenue and expenses incurred by a business in a given period of time. A profit and loss statement is also called a P&L, an income statement, a statement of profit and loss, and income and expense statement, or a statement of financial results.
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Algebra 1 > J.7 Solve linear equations: complete the solution EVP
Complete the process of solving the equation.
Fill in all missing terms and select all missing descriptions. Simplify any fractions.
11d4 14 = -7
11d 18 = -7
Submit
11d =
d =
Subtract 4 from both sides
Add 4 to both sides
Subtract 4 from both sides
Work it
Answers
1.) 11d-(18)=-7
We combined like terms, in this case the constants -4 and -14. -4-14 = -(14+4) = -18. So, first step is -4-14.
2.) 11d=11
The additive inverse of -18 is 18, so we canceled it out from the left and combined it with the content of -7 on the right to isolate 11d.
3.) d=1
We divided 11d by 11 to cancel it out, and we divided 11 by 11 on the left.
A sample of copper has a mass of 15.6 g and a volume of 1.75 cm^3. Calculate the density of copper from this sample.
this is for earth science but its math :/
Answers
Given the mass and volume of the sample, the density of the copper sample is approximately 8.91 g/cm².
What is the density of copper from the given sample?The density of a substance is simply the mass of that substance per unit of its volume.
Density is expressed mathematically as;
Density = Mass / Volume.
Given the data in the question;
Mass of copper sample = 15.6 gVolume of copper sample = 1.75 cm³Density of copper sample = ?Plug the given values into the formula above and solve for density.
Density = Mass / Volume
Density = 15.6 g / 1.75 cm³
Density = 8.91 g/cm²
Given the mass and volume of the sample, the density of the copper sample is approximately 8.91 g/cm².
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jack graphs how far he plans ton bike over a 3-day charity ride find the slope of the line
Answers
The slope of the line for 3-day charity ride is 30.
What is referred as the slope of the straight line?The slope of a straight line indicates the steepness of its inclination. It is also known as the gradient.
The greater the slope of a line, the steeper it is.The slope of a line remains constant throughout its length, ensuring that the line is straight.A line can be thought of as the hypotenuse of such a right-angled triangle.A slope measurement is calculated by comparing its vertical and horizontal components.The formula for the slope is;
slope = m = Δy/Δx
m = (y₂ - y₁)/(x₂ - x₁)
The given coordinators of the points (taken from Jack's graph are);
(x₁, y₁) = (2, 60)
(x₂, y₂) = (3, 90)
Put the values in the formula;
m = (90 - 60)/(3 - 2)
m = 30
Therefore, the slope of the straight line for the 3-day charity ride is 30.
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A science class has a total of 47 students. The number of males is 11 more than the number of females. How many males and how many females are in the
class?
Number of males:
Number of females:
Answers
Answer:
number of males: 29
Number of females: 18
Step-by-step explanation:
X=number of females
X+11=number of males
X+X+11=47
2X+11=47
2X=47-11
2X=36
X=36/2
X=18
So number of females = 18
X+11=18+11=29
So number of males = 29
Write the following equation in slope-intercept form. State the slope and y-intercept.
-18x-9y= 7
Answers
The slope and y-intercept of the line is 2 and -7/9 respectively
slope intercept form of an equationThe formula for calculating the slope intercept form of an equation is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Given the equation -18x-9y = 7
Write in slope intercept form
-9y = 18x + 7
y = -18/9 x - 7/9
Compare
m = -2
b = -7/9
Hence the slope and y-intercept of the line is 2 and -7/9 respectively
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Solve for x.
4x-7=3x+21
Answers
Answer: x=28
Step-by-step explanation:
4x-7=3x+21
4x-3x-7=3x-3x+21
x-7=21
x=28
Which expression is equivalent to , if y ≠ 0?
A.
B.
C.
D.
Answers
Answer:
is there more??? i don't have a enough info
Step-by-step explanation:
PLEASE ANSWERING THIS QUESTION!!!
The volume of a cone with height h and a radius r can be found using the formula [tex]\sf{V=\dfrac{1}{3}\pi r^2h[/tex]
Find the volume of a cone with radius 5 feet and height 4 feet.
(Blank) ft^3
Rules answering these questions:
Explain your answer!
Do not spam answers!
Show your work!
Nonsense answers will be reported and delete your answers.
Thanks!
Answers
Answer:
104.8cm³(1 decimal place)
Step-by-step explanation:
Volume of a cone is given by the formula
V=1/3πr²h
we are given a radius of 5 and a height of 4 so we will just substitute for the values and we will give our pie as 22/7
V=1/3× 22/7×5²×4
V=1/3 × 22/7 ×25 ×4
V=2200/21
V=104.76190476
V=104.8cm³(1decimal place)
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For a party, Ashley wants to make 12 hamburgers. If she has 2.964
pounds of meat, how much would each patty weigh? _________ pounds
Answers
Answer:
247
Step-by-step explanation:
divides 2964 entre 12 y obtienes 247
What happens to the sum of the ball’s kinetic energy and potential energy as the ball rolls from point A to point E? Assume there’s no friction between the ball and the ground. An image shows a curve that starts at point A, decreases at B, then increases at C and D, and ends at E. A. The sum decreases. B. The sum increases. C. The sum remains the same. D. The sum always equals zero
Answers
The sum of the ball's kinetic energy and potential energy remains the same. as the ball rolls from point A to E.( if there is no friction between the ball and the ground).
based on the law of mechanical energy's conservation, the sum of both kinetic and potential energies i.e. the total amount of mechanical energy remain conserved even in the absence of dissipative forces ( friction or air resistance) in a bound system.
the kinetic energy is when ball goes downward but potential energy decreases and reverse happens when ball goes up. but in these case, the sum energy would be constant one.
The ball would not change the energy.
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arrange the following in ascending order 1/3 , 3/4 , 5/12 ,2/8
Answers
The ascending order is: 2/8 < 1/3 < 5/12 < 3/4.
What is termed as the ascending order?The configuration of numbers or even other items in order of increasing from smallest to largest is referred to as ascending order. Ascending order is represented by numbers that show up on a number line from left to right. We generally represent it with commas or by using the 'less-than symbol (<)' between numbers. For instance, 1, 2, 3, 4, 5 or 1 < 2 < 3 < 4 < 5.The given order is;
1/3 , 3/4 , 5/12 ,2/8
Write the values in the decimal forms;
0.33, 0.75, 0.416, 0.25.
Now arrange the sequence is the ascending order;
0.25, 0.33, 0.416, 0.75
Again transform them in fraction form;
2/8 < 1/3 < 5/12 < 3/4
Thus, the ascending order is found as 2/8, 1/3, 5/12, 3/4.
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If z/4+3=-2 what is the value of z/4+7?
Put your answer in the form of [x]
Answers
Answer: x=2
Step-by-step explanation:
x=z/4+7
x=z/4+3+4
x=(z/4+3)+4
x=-2+4
x=2
What’s the length of AZ. If A is between Y and Z, Y A = 22, AZ = 16x, and Y Z = 166
A) 9
B) 22
C) 144
D)188
Answers
Answer:
c) 144
Step-by-step explanation:
Since A is between Y and Z,
[tex]YZ = YA + AZ[/tex]
[tex]116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9[/tex]
however, the question asks for [tex]the length of AZ[/tex], not the value of x.
Thus,
[tex]AZ = 16x[/tex]
[tex]AZ = 16\\[/tex] × [tex]9[/tex]
[tex]AZ = 144[/tex]
0.625+0.125+0.3125+0.0625
Answers
Answer:
the answer is = 1.125
Step-by-step explanation:
hopefully this helps!
Cesar is reading a 450 page book. He reads the first 90 pages in 3 days
continues to read at the same rate, how long will it take him to finish t
Solve on scrap paper first if you need to.
It will take Cesar
days to finish the book.
Answers
maths geometry questions
pleas help
Answers
Step-by-step explanation:
remember, a parallelogram is a quadrilateral with 2 pairs of parallel and equal sides, and 2 pairs of correspondingly equal angles. and its diagonals are intersecting each other in their midpoint.
with that in mind
(i)
because ABCD is a parallelogram, AD = BC, and AB = CD.
and angle A = angle C (and angle B = angle D).
therefore, as AE = FC, this also means that ED = BF.
via SAS (side angle side) it is clear that the triangles ABE and CDF are congruent.
therefore, EB = DF.
as ED is part of AD, and BF is part of BC, it is also clear that ED || BF.
together with ED = BF this means that EB || DF.
so, we have with BEDF 2 pairs of parallel and equal sides. and that is a parallelogram.
(j)
BCDE and ABCG are parallelograms.
so, BC = DE = AG, CD = BE, AB = CG.
due to the midpoint intersection rule of the diagonals of parallelograms, we also know
GE = CG = AB, DG = BG.
and as CG || AB, then also GE || AB.
together with AB = GE that means that AE = BG and AE || BG.
so, we have with ABGE again 2 pairs of parallel and equal sides. and that is a parallelogram.
HELP PLEASE!!!!Write two words that have a ratio of vowels to consonants of 3:2 and two words that have a ratio of the letters e and r of 2:1.
Answers
Answer:
ratio: 3 vowels; 2 consonants
media: 3 vowels; 2 consonants
letter: 2 e's; 1 r
electric: 2 e's; 1 r