One class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.one class of 75 students has an average midterm score of 67 and an sd of 12. another class of 325 students has an average of 72 and an sd of 15. find the average and the sd of the combined list of 400 students. hint: this uses the sd of a long list formula.

Answers

Answer 1

Answer:

- average: 71.0625
- standard deviation:

Explanation:

Let

a = average score of 325 students = 72
b = average score of 75 students = 67
S = total score of 325 students
T = total score of 75 students
u = standard deviation of the score of 325 students = 15
v = standard deviation of the score of 75 students = 12
C = average of the squares of the scores of 325 students
D = average of the squares of the scores of 75 students

The total score of 325 students is calculated as:

S = 325a
= 325(72)
S = 23,400

While the total score of 75 students is calculated in similar manner:

T = 75b
= 75(67)
T = 5,025

To get the total score of 400 students, we just add the total score of 325 students and the total score of 75 students. So, the total score of 400 students is given by

S + T = 23,400 + 5,025
S + T = 28,425

To get the average score of 400 students, we just divide the total score of 400 students by the number of students, which is 400. In terms of equation,

[tex]\text{average score of 400 students} = \frac{S + T }{400} \\ = \frac{28,425}{400} \\ \boxed{\text{average score of 400 students} = 71.0625}[/tex]

To calculate the standard deviation of the scores of 400 students, we use the following formula:

[tex]\sigma_{400} = \sqrt{\left( C + D \right) - \left( \frac{S + T}{400} \right)^2}[/tex]

where

[tex]\sigma_{400}[/tex] = standard deviation of the scores of 400 students
[tex] C + D [/tex] = average of the squares of the scores of 400 students
[tex]\frac{S + T}{400}[/tex] = average of the scores of 400 students = 71.0625

Because

C = average of the squares of the scores of 325 students
D = average of the squares of the scores of 75 students
u = standard deviation of the score of 325 students = 15
v = standard deviation of the score of 75 students = 12
a = average score of 325 students = 72
b = average score of 75 students = 67

We have the following

[tex]u^2 = C - a^2 \\ \Rightarrow \boxed{C = a^2 + u^2} [/tex] (1)

[tex]v^2 = D - b^2 \\ \Rightarrow \boxed{D = v^2 + b^2}[/tex] (2)

So, using equations (1) and (2),

[tex]C + D = (a^2 + u^2) + (v^2 + b^2) \\ = (72^2 + 15^2) + (12^2 + 67^2) \\ \boxed{C + D = 10,042}[/tex]

Hence, the standard deviation of the scores of 400 students is calculated as

[tex]\sigma_{400} = \sqrt{\left( C + D \right) - \left( \frac{S + T}{400} \right)^2} \\ = \sqrt{\left( 10,042 \right) - \left(71.0625 \right)^2} \\ \boxed{\sigma_{400} \approx 70.65 }[/tex]

Answer 2

Final answer:

The average of the combined list of 400 students is 71.9 and the standard deviation is 13.1.

Explanation:

To find the average and standard deviation of the combined list of 400 students, you can use the following formulas:

Average of combined list = (Average of one class * Number of students in one class + Average of another class * Number of students in another class) / Total number of students

Standard deviation of combined list = sqrt(((SD of one class)^2 * (Number of students in one class - 1) + (SD of another class)^2 * (Number of students in another class - 1) + ((Average of one class - Average of another class)^2 * Number of students in one class * Number of students in another class)) / Total number of students)

Applying the values from the given information:

Average of combined list = (67 * 75 + 72 * 325) / 400 = 71.9

Standard deviation of combined list

= sqrt(((12^2 * 74) + (15^2 * 324) + ((67 - 72)^2 * 75 * 325)) / 400)

= 13.1

Related Questions

Drives 1,212 miles from there home to the park if they drive the same number of miles each day for 4 days how many miles will the drive each day.
A.303
B.330
C.403
D.3,030
Please Help me find the answer thank you

Answers

They drive 1212 miles each day
There are 4 days.
1212/4 = 303 miles per day <<<<<====== answer
Oops
A <<<<====

Which decimal is the equivalent of 6/11 Repeated

Answers

6/11 = 0.54_54 . . . . . the digits 54 are repeated indefinitely You can arrive at the digits 54 by multiplying the numerator (6) by 9. This will be the case for any proper fraction with 11 as a denominator.

Find two positive numbers whose difference is 2828 and whose product is 39003900.

Answers

If the question is:
"Find two positive numbers whose difference is 28 and whose product is 3900"

If the larger number is x, then
x-3900/x=28
multiply by x and transpose
x^2-28x-3900=0
Factor
(x+78)(x-50)=0
Using the zero product property,
x=-78 or x=50, ie. x=50, y=-78

NOTE: if question requires both numbers be positive, there is no solution.

Final answer:

To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations and solve them using substitution or elimination.

Explanation:

To find two positive numbers whose difference is 2828 and whose product is 39003900, we can set up a system of equations. Let's assume the two numbers are x and y. From the given information, we have the following equations:

x - y = 2828

xy = 39003900

We can solve this system of equations by substitution or elimination. Let's use the substitution method:

From the first equation, we can express x as y + 2828. Substituting this into the second equation, we get (y + 2828)y = 39003900. Simplifying, we get y^2 + 2828y - 39003900 = 0.

Now we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula. Once we find the value of y, we can substitute it back into the first equation to solve for x. This will give us the two positive numbers.

Find the maximum and minimum values of f(x,y,z)=5x+4y+1z on the sphere x2+y2+z2=1.

Answers

Use Lagrange multipliers. The Lagrangian is

[tex]L(x,y,z,\lambda)=5x+4y+z+\lambda(x^2+y^2+z^2-1)[/tex]

with partial derivatives (set equal to 0)

[tex]L_x=5+2\lambda x=0\implies x=-\dfrac5{2\lambda}[/tex]
[tex]L_y=4+2\lambda y=0\implies y=-\dfrac4{2\lambda}[/tex]
[tex]L_z=1+2\lambda z=0\implies z=-\dfrac1{2\lambda}[/tex]
[tex]L_\lambda=x^2+y^2+z^2-1=0[/tex]

We can substitute the first three equations into the fourth to solve for [tex]\lambda[/tex]:

[tex]\dfrac{25}{4\lambda^2}+\dfrac{16}{4\lambda^2}+\dfrac1{4\lambda^2}=1[/tex]
[tex]\implies 42=4\lambda^2\implies\lambda=\pm\sqrt{\dfrac{21}2}[/tex]

Now use these values of [tex]\lambda[/tex] to solve for [tex]x,y,z[/tex], which should give you two critical points at [tex]\pm\left(\dfrac5{\sqrt{42}},\dfrac4{\sqrt{42}},\dfrac1{\sqrt{42}}\right)[/tex], which would respectively give a maximum and minimum value of [tex]\pm\sqrt{42}[/tex].

In January, you deposit $16 in your checking account. Each month, you deposit $15 more than you did the month before. How much money do you deposit in October? A) $151 B) $166 C) $356 D) $835

Answers

Sorry I mis-read the question, your answer is 151; Here is how I solved it:
January: $16
Febuary: 16 + 15 =31
March :31+15=46
April : 46+15=61
May: 61+15=76
June: 76+15= 91
July: 91+15= 106
August: 106+15= 121
September: 121+15= 136
October:136+15= 151

The amount we deposited in the month of october is $151, option A is correct.

What is Sequence?

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

We need to find the total amount deposited in 10 months, starting with $16 in January and increasing by $15 each month.

The first term is $16 and the common difference is $15.

The nth term can be found using the formula for the nth term of an arithmetic sequence:

an=a+(n-1)d

a=16, d=15

Now plug in n as 10, (10th month is october)

a₁₀=16+(10-1)15

=16+9(15)

=151

Hence, the amount we deposited in the month of october is $151, option A is correct.

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which of the columns above represent numerical data?
check all that apply

Answers

For this case, what you should do is see which columns of the ones shown in the image provide an important numerical value.
We have that in the image there are three possible columns.
ColumnA: Price
Column B: Type of cover.
Column C: Weight
The columns that provide numerical value are two:
ColumnA: Price
Column C: Weight
Answer:
Column A
Column C

Find the markup on the following item. A candy bar costing $0.52 and selling for $0.79. 0.27 0.41 0.66 1.31

Answers

0.27 is the answer....

Just do 0.79 - 0.52 which equals 0.27

What is the probability of not drawing a blue marble?

A: 1/4
B: 2/3
C: 1/3
D: 3/4

Answers

The probability is 9/12 which can simplify to D: 3/4

plz help ill give you brainlist

Answers

h= # hours rented

EQUATION:
$13.25>$1.75h + $8 fee

subtract 8 from both sides

5.25>1.75h
divide both sides by 1.75

3>h

He can rent the bike for 3 hours and not spend more than $13.25

Hope this helps! :)

standard linear equation:
y=mx+b

Initial cost=initial value = b = 8 (Q did not say $8 is for any rental time).
additional cost per hour = m = 1.75

Equation becomes
y=1.75x+8

If the maximum charge is y=13.25, then we can solve for x, the maximum number of hours to be rented,

13.25=1.75x+8
Subtract 8 from each side
13.25-8=1.75x
5.25=1.75x
divide by 1.75
5.25/1.75=x
x=3

Connor can rent the bike for at most 3 hours.

The necklace charm shown has two parts, each shaped like a trapezoid with identical dimensions.

What is the total area, in square millimeters, of the charm?

Answers

883 is the answer......

Solve the equation using square roots. 7x2 + 6 = 13

Answers

7x² +6=13
7x²=7
x²=1
x=1 or -1

Given the equation is 7x² + 6 = 13.

Solving the quadratic equation using square roots :-

7x² + 6 = 13

Step 1 :- subtracting 6 from both sides

7x² + 6 - 6 = 13 - 6

7x² = 7

Step 2 :- Dividing by 7 on both sides

[tex] \frac{7x^{2}}{7} = \frac{7}{7} \\\\
x^{2} = 1 [/tex]

Step 3 :- Taking square root on both sides

[tex] \sqrt{x^{2}} = \sqrt{1} \\\\
x = -1 \;\;OR\;\; x=1 [/tex]

So, x = -1 or x = 1 is the final answer.

Divide and simplify. 32x9y2 2xy-2

Answers

Is it one problem or 2?

The radius of a sphere is 6 inches. Find the length of a chord connecting two perpendicular radii. x = inches

Answers

Answer:

6√2 ≈ 8.485 inches

Step-by-step explanation:

The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.

_____

Comment on isosceles right triangle

It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:

... c² = a² + b²

... c² = 1² + 1² = 2 . . . . for legs of length 1

... c = √2 . . . . . . . . . . take the square root.

Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.

simplify the expression using the distributive property 42 + 7a

Answers

42+7a= 7(6+a)
By noticing they both have a factor of 7, I was able to find the equation.

Angel draws a circle with a radius of 5 cm. What is the area of Angel's circle? Use 3.14 for pi

Answers

The area of a circle is
A = pi r^2
r = 5
pi = 3/14

A = 3.14 * (5)^2
A = 3.14 * 25
A = 78.5

Hope this helps!

Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off. The original price is $4.73. How much does she need to pay for the cereal?

Answers

4.73 - 0.35 = 4.38. Mrs Applebaum needs to pay $4.38

Answer:

She needs to pay $4.38

Step-by-step explanation:

Mrs. Applebaum goes to the supermarket to buy a box of cereal. She has a coupon for 35 cents off.

The original price is $4.73. 35 cents off

35 cents can be converted into dollars when we divide by 100

35 divide by 100=0.35

to find the amount she need to pay, we subtract 0.35 from original price

Amount to pay=[tex]4.73-0.35=4.38[/tex]

You bought a new shirt for $15.95 and 5 pairs of socks. Your friend bought 10 pairs of socks and spent $4.20 less then you. How much did each pair is socks cost
Answer with an equation with variable. Make the variable the cost of socks.

Answers

Let s represent the cost of a pair of socks.
.. 15.95 +5s -4.20 = 10s
.. 11.75 = 5s
.. 2.35 = s

Any of the above equations will get you to the cost of a pair of socks, which is
$2.35.

At a certain point in time, each dimension of a cube of ice is 30 cm and is decreasing at the rate of 2 cm/hr. How fast is the ice melting (losing volume)?

Answers

recall that for a cube, all dimensions, length, width and height, are the same in value.

so, if say length = width = height = x, then the volume of the cube is V = x³, therefore

[tex]\bf V=x^3\implies \cfrac{dV}{dt}=\stackrel{chain~rule}{3x^2\cfrac{dx}{dt}}\quad \begin{cases} x=30\\ \frac{dx}{dt}=\stackrel{cm/hr}{2} \end{cases}\implies \cfrac{dV}{dt}=3(30)^2(2) \\\\\\ \cfrac{dV}{dt}=5400[/tex]

In the diagram, MQ = QP = PO = ON.

If NP is greater than MP, which must be true?

Segment OP is longer than segment MQ.
Segment MN has the same length as segment MP.
The measure of angle Q equals the measure of angle O.
Angle O is larger than angle Q.

Answers

MQ = QP = PO = ON

If NP is greater than MP

answer
Angle O is larger than angle Q.

Answer:The measurement of angle O is greater than angle Q is the correct statement.

Explanation: Since, According to the question, MQ = QP = PO = ON and MP is greater than NP.

Then, In first option, segment OP is longer than segment MQ is false because OP=MQ.

In second option, MN=MP can not be possible because NP is greater than MP.

In third option, The measure of angle Q equals the measure of angle O also can not be possible because MN is not parallel to QO.

But, In fourth option, Since MP is greater than NP thus NO makes larger angle than MQ.

Thus, fourth option is correct.

If it takes 6.7 lb of seed to plant one acre of grass how many acres can be planted with 8.04 pounds of seed?

Answers

This is a proportion problem. 6.7lbs to one acre as 8.04 lbs is to x acres.

x= # lbs of seed to cover 8.04 acres

6.7/1=8.04/x
cross multiply

(6.7*x) =(1*8.04)
6.7x=8.04
divide both sides by 6.7

x= 1.2 pounds needed to cover 8.04 acres

Hope this helps! :)

Answer:

1.2 acres of grass

Step-by-step explanation:

It takes 6.7 lb of seed to plant one acre of grass. The ratio of interest is 6.7 lb seed:1 acre of grass. We can find the acres of grass that can be planted with 8.04 pounds of seed using a conversion fraction.

8.04 lb × (1 acre/6.7 lb) = 1.2 acre

We can plant 1.2 acres of grass with 8.04 pounds of seed.

A given line has the equation 10x+2y=-2. What is the equation , in slope intercept form, of the line that is parallel to the given line that passes through the point (0,12)

Answers

2y = - 10x - 2
y = - 10x / 2 - 2/2
y = - 5x - 1

The new line is y = -5x + b
Use (0,12) to get b
12 = -5(0) + b
b = 12
y = - 5x + 12 <<<<<<===== Answer

Answer:

y = -5x + 12

Step-by-step explanation:

Slope intercept form of a line is,

y = mx + c

Where, m is the slope of the line,

Here, the given equation of line,

10x+2y=-2,

2y = - 10x - 2

y = -5x - 1,

By comparing,

m = -5,

So, the slope of line 10x+2y=-2 is -5,

We know that the two parallel line have same slope,

Let the equation of the parallel line of the 10x+2y=-2 is,

y = -5x + c

According to the question,

It passes through the point (0,12),

That is (0, 12) must satisfy this line,

12 = -5(0) + c ⇒ c = 12,

Hence, the equation of the parallel line is,

y = -5x + 12

WILL GIVE BRAINLIEST / 5 STARS FOR CORRECT ANSWER

Find the sum of the arithmetic sequence.

-4, -1, 2, 5, 8, 11, 14

A) 42
B) 35
C) -28
D) 17

Answers

Hello!

When you add a negative to a negative, it will result in a negative.

(-4) + (-1) = -5

The rest of the numbers are positive. When you add a positive to a negative, it will result in a positive -- which means we just need to add the rest of them up.

(-5) + 2 + 5 + 8 + 11 + 14 = 35

ANSWER:

The sum of the arithmetic sequence is B) 35.

Distribute and simplify these radicals. 12 x(-1+ √5)

Answers

Answer is B. -2√3+2√15

By using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

What is distributive property?

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given

12 × (-1 + [tex]\sqrt{5}[/tex])

Apply distributive property

= 12 × (-1) + 12 × [tex]\sqrt{5}[/tex]

= -12 + 12[tex]\sqrt{5}[/tex]

≅ 14.832

Hence by using distributive property, 12 × (-1 + [tex]\sqrt{5}[/tex]) = 14.832.

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Help ASAP please!

Which set of numbers could represent the lengths of the sides of a right triangle?

16, 32, 36

8, 12, 16

3, 4, 5

9, 10, 11

Answers

The numbers 3, 4, 5 should jump out at you as the correct choice.

_____
{3, 4, 5} is the set of smallest integers that will satisfy the Pythagorean theorem. They are also the only "Pythagorean triple" that forms an arithmetic sequence. Many folks remember these numbers for their simplicity and utility. They show up in many algebra problems and can be useful in real life.

William bought Wiggit stock at 15.125 and sold it for 18. What was the percent of increase?

Answers

so from 18 to 15.125 is 2.875, namely their difference.

now, if we take 15.125 to be the 100%, what is 2.875 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 15.125&100\\ 2.875&p \end{array}\implies \cfrac{15.125}{2.875}=\cfrac{100}{p}\implies p=\cfrac{2.875\cdot 100}{15.125}[/tex]

f (x)-x^2+6x-7 at x=2

Answers

Consider the vertex form of the parabola.y=a(x+h)2+ky=a(x+h)2+kRewrite the function in terms of xx and yy.y=x2+6x−7y=x2+6x-7Complete the square on the right side of the equation.(x+3)2−16(x+3)2-16Reorder the right side of the equation to match the vertex form of a parabola.y=(x+3)2−16y=(x+3)2-16Since 33 does not contain the variable to solve for, move it to the right side of the equation by subtracting 33 from both sides.x=−3x=-3Use the vertex form, y=a(x−h)2+ky=a(x-h)2+k, to determine the values of aa, hh, and kk.a=1a=1h=−3h=-3k=−16k=-16Since the value of aa is positive, the parabola opens up.Opens UpFind the vertex (h,k)(h,k).(−3,−16)(-3,-16)Find pp, the distance from the vertex to the focus.1414Find the focus.(−3,−634)(-3,-634)Find the axis of symmetry by finding the line that passes through the vertex and the focus.x=−3x=-3Find the directrix.y=−654y=-654Use the properties of the parabola to analyze and graph the parabola.Direction: Opens UpVertex: (−3,−16)(-3,-16)Focus: (−3,−634)(-3,-634)Axis of Symmetry: x=−3x=-3Directrix: y=−654

I sorta shortened the steps a bit if you need me to explain any more steps I will just ask.
I am sure you probably went over some of this in your class that is why I skipped a few steps so you would at least learn a little bit hehe.

I really hope this helps you.

Chen has an unlimited supply of square tiles. She has 1 cm x 1 cm tiles, 2 cm x 2 cm tiles, 3 cm x 3 cm tiles, and so on. Every tile has integer side lengths. A rectangular table top with an 84 cm x 112 cm surface is to be completely covered by identical square tiles, none of which can be cut. Chen wants to use the minimum number of identical tiles to complete the job in order to reduce her costs. Determine the minimum number of identical tiles required to completely cover the table top.

Answers

84 = 2 × 2 × 3 × 7
112 = 2 × 2 × 2 × 2 × 7
Highest Common Factor of 84 and 112 = 2 × 2 × 7 = 28

So the tiles should be 28 x 28

84 ÷ 28 = 3
112 ÷ 28 = 4

Total tiles needed = 3 x 4 = 12

Ans: 12 tiles

The minimum number of identical square tiles required to completely cover an 84 cm x 112 cm tabletop is 12 tiles, each with side lengths of 28 cm.

To determine the minimum number of identical square tiles required to completely cover a rectangular tabletop with dimensions 84 cm x 112 cm, we need to find the greatest common divisor (GCD) of the two side lengths. This is because using tiles that match the GCD will ensure that they fit perfectly across both lengths and widths without needing to cut any tiles.

The GCD of 84 and 112 is 28. Therefore, the side length of the square tile that Chen should use is 28 cm x 28 cm. To find the number of tiles needed, we then divide the area of the tabletop (which is 84 cm x 112 cm or 9408 square cm) by the area of one tile (which is 28 cm x 28 cm or 784 square cm).

The calculation is as follows: 9408 square cm / 784 square cm = 12. Therefore, Chen needs a total of 12 tiles of 28 cm x 28 cm to cover the entire tabletop.

Using the figure,
a
c
=
d
a
.

What steps need to be taken to change this to a² = cd?

Example: Multiply by 2; divide by a, etc

Answers

[tex] \frac{a}{c} = \frac{d}{a}[/tex] is changed to [tex] a^{2} = cd[/tex] by multiplying by the product of the denominators.

[tex] \frac{a}{c} \times ac = ac \times \frac{d}{a}[/tex]

Because the end result looks like the numerator on the left is multiplied by the denominator on the right, and vice versa, the process is often referred to as "cross multiplying." That is an illusion. The rules of algebra require the same thing be done to both sides of the equation. In this case, that is multiplication of both sides by the product of the denominators.

On a drawing a triangle has sides that equal 4 cm, 5 cm, and 6 cm. If the scale of the drawing is 1 cm = 10 feet, find the sides of the original large triangle.

Answers

4 * 10 = 40
5 * 10 = 50
6 * 10 = 60

The side length of the original large triangle are 40 feet, 50 feet, and 60 feet.

Answer:

A= 40 B=50 c=60

Step-by-step explanation:

The number of ways of selecting items where the order is not important, is known as a number of ________.

Answers

let's consider hmmm a group of letters, say AAABBBCCC.

now, we can combine them in groups of say 3, like ABC, or BBA, or AAB, or CBA, and so on.

notice ABC and CBA has the same letters, arranged differently, but the same, a "permutation" says, that is ok, "order IS important", meaning ABC and CBA are really two different groups, because of how they're arranged.

but a "combination" says, wait just a second here, you've got the same letters, "order is NOT important" for me, so ABC and CBA is the same cat with a different dress, come on now, you can't fool me, go get other letters you slacker.

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