The mean mark of a group of 10 boys is 58. If the mean of 7 of them is 61, what is the mean of the remaining 3 boys

Answers

Answer 1

Answer:

The mean of the remaining 3 boys is 51.

Step-by-step explanation:

The mean mark of the entire group ([tex]p_{10}[/tex]), dimensionless, is:

[tex]p_{10} = \frac{1}{10}\cdot \Sigma_{i = 1}^{10} x_{i}[/tex] (Eq. 1)

([tex]p_{10} = 58[/tex])

[tex]\frac{1}{10}\cdot \Sigma_{i=1}^{10} x_{i} = 58[/tex] (Eq. 1b)

Where [tex]x_{i}[/tex] is the mark of the i-th boy, dimensionless.

In addition, we know the following mean marks from statement:

[tex]p_{7} = \frac{1}{7} \cdot \Sigma_{i = 1}^{7} x_{i}[/tex] (Eq. 2)

([tex]p_{7} = 61[/tex])

[tex]\frac{1}{7}\cdot \Sigma_{i=1}^{7} x_{i} = 61[/tex] (Eq. 2b)

[tex]p_{3} = \frac{1}{3}\cdot \Sigma_{i=8}^{10}x_{i}[/tex] (Eq. 3)

Where:

[tex]p_{7}[/tex] - Mean mark of the first 7 boys, dimensionless.

[tex]p_{3}[/tex] - Mean mark of the remaining 3 boys, dimensionless.

By applying sum properties in (Eq. 1b) and using (Eq. 2b) and (Eq. 3), we obtain the mean of the remaining 3 boys:

[tex]\frac{1}{10}\cdot [\Sigma_{i = 1}^{7}x_{i}+\Sigma_{i=8}^{10}x_{i}] = 58[/tex]

[tex]\frac{1}{10}\cdot [7\cdot (61)+3\cdot p_{3}] = 58[/tex]

[tex]7\cdot (61) + 3\cdot p_{3} = 580[/tex]

[tex]3\cdot p_{3} = 153[/tex]

[tex]p_{3} = \frac{153}{3}[/tex]

[tex]p_{3} = 51[/tex]

The mean of the remaining 3 boys is 51.


Related Questions

HELPPPPPPPPPPPPPPPPPPP

Answers

Answer:

15

Step-by-step explanation:

Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50 monthly maintenance fee. Jill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. What is the mean number of checks Jill wrote per month during the last four months? Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. Estimate the total monthly fees Jill will pay each month for the new checking account.

Answers

Step-by-step explanation:

 Kindly find attached a summary of the checks she has written from May to August.

A. What is the mean number of checks Jill wrote per month during the last four months

mean= (14+19+23+24)/4

mean= 80/4

mean= 20 checks

B.  Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account.

the expression for the total is given as

y=12.50+0.2x

y=12.50+0.2(20)

y=12.50+4

y=16.5

=$16.5

C. Estimate the total monthly fees Jill will pay each month for the new checking account.

May= 12.50+0.2(14)

May=12.5+2.8= 15.3

June= 12.50+0.2(19)

June=12.5+3.8= 16.3

July= 12.50+0.2(23)

July=12.5+4.6= 17.1

August= 12.50+0.2(24)

August=12.5+4.8= 17.3

total will be = 15.3+16.3+17.1+17.3= $66

A:20

B:$4.00

C:$16.50

A: 14+19+23+24/4 = 20

B: 20/.2 = 4

C: 12.50+4= 16.50

Mike has at least 250 in his savings account.Which inequality represents this situation

Answers

What is the situation??

A cougar jumped a distance of 13 yards. How many inches did this cougar jump?​

Answers

Answer:

468 in

Step-by-step explanation:

Step 1: Define conversions

3 feet = 1 yard

1 foot = 12 inches

Step 2: Use dimensional analysis

[tex]13 \hspace{3} yards(\frac{3 \hspace{3} feet}{1 \hspace{3} yard} )(\frac{12 \hspace{3} inches}{1 \hspace{3} feet} )[/tex] = 468 inches

how to find the area figure of square inches​

Answers

It is length times width in^3

1.) 4x+2y-z=21
2.) -x-2y+2z=13
3.) 3x-2y+5z=70

Answers

Answer:

Step by Step Solution:

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): Dot was discarded near "2.-".

(2): "133.3" was replaced by "(1333/10)".

Too Many Equal Signs

Step-by-step explanation:

At a sale this week, a suit is being sold for $306 . This is a 15% discount from the original price.
What is the original price?

Answers

Answer:

260.1

Step-by-step explanation:15% of 306=45.9

306-45.9=260.1

Answer:

351.9

Step-by-step explanation:

x/306=15/100. then I cross multiplied. And when I do I get 100x/100=4590/100.

I cross out the 100/100 and I leave with x, then I divide 4590 with 100 and get 45.9. So x=45.9.

Then I added the price it was sold..=306+45.9=351.9

Kevin bought a used guitar at a garage sale for $150. He fixed it up and sold it for $200. What was the percent increase?
(Need explanation to show my work)

Answers

Answer:

33.3

Step-by-step explanation:

You need to divide 200  and 150 to get you 4/3. Then you will have to _____________________________

A bookshelf at a bookstore is 3 feet 9 inches wide. There are 18 copies of the same book on the shelf, which fit the shelf exactly. What is the width of 1 of the books?

Answers

Answer:

5 / 2 inches OR 2.5 in

Step-by-step explanation:

3 ft 9 in = 45 inches

45in/18 books

5 in / 2 book

is -4 greater,less than or equal to +4 ?​

Answers

Less than.

The sequential order would be -4, -3, -2, -1, 0, 1, 2, 3, 4

Help me out fast on this question.

Answers

The third one 15.5x2.3

PLZ HELP!!!!!
how can 28/8 be a decimal?

Answers

Answer:

What is 28/8 as a decimal you ask? Converting the fraction 28/8 into a decimal is very easy.

To get 28/8 converted to decimal, you simply divide 28 by 8. Don't worry. You don't need to get the calculator out, because we did this for you.

28/8 as a decimal is:

3.5

If Megan's tuition, fees, and expenditures for books this year total $19,000, what will they be during her senior year (three years from now),
assuming costs rise 7 percent annually? Round Future value of a Single
Amount in intermediate calculations to four decimal places.

Answers

Answer:

$23,275.817

Step-by-step explanation:

To get this answer, multiply 19,000 by 1.07.

$19,000 x 1.07 = 20,330 (one year later)

$20,330 x 1.07 = $21,753.10 (two years later)

$21,753.10 x 1.07= $23,275.817 (three years later)

The answer round to cents would be $23,275.82

What polyhedron can be assembled from this net? Explain how you know.

Find the surface area of this polyhedron. Show your reasoning.

Answers

Answer:

It would be a triangular prism.

Step-by-step explanation:

We know this because of the two triangles at the top and bottom of this net and the rectangle connecting them. Then, if you imagine folding the second rectangle up, it would be one of the triangle's sides. Lastly for the third rectangle, it would be folded over the two triangles to finish the shape.

I hope this helps!!

Answer:

It would be a triangular prism

Step-by-step explanation:

If they ask how you got that say since the triangles at the top and bottom are both parell and to be a prim you need to have parell sides

pls help <3 thank you sm ;)

Answers

a = 7 have a good day!

Can someone help me solve this?

Answers

Answer:

2313

Step-by-step explanation:

Find the measure of the missing angle

Answers

Answer:

M1=108° M2=72°

Step-by-step explanation:

M1 and the original 108° angle are equal, and to calculate M2, which is on the same straight line as the original 108°, we must remember that all angles on a straight line add up to 180°. So, 180-108=72, making M2 72°

The sum 51 + (-37) is equal to what? -14 88 88 14

Answers

Answer:

14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

the answer is 14 and it's postive

is 3/4 less than,greater than,or equal to -1/2 ?​

Answers

Answer: Greater than

3/4 greater than -1/2

3/4 > -1/2

Any positive number is always larger than any negative number

On a number line, stuff on the right side is always larger than stuff on the left side.

Answer:

it"s greater then

Can anyone tell me if u pass the ela state exam but u didn't pass the math state exam can u still go to 9th grade cuz im in 8th please answer and my grades are always good so does it help? and my classwork etc is always around 80-100 is it good

Answers

i think u can still go to 9th grade because overall ur a good student who does their class work . if by chance u cant can u redo the state test?

Find constants a , b, and c such that the function

y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.

Answers

Answer: a = -2, b = -2, c = 1.

Step-by-step explanation:

We know that:

y = a*x^2 + b*x + c.

Then:

y' = 2*a*x + b

y'' = 2*a.

Then we can write the equation:

y′′ + y′ − 2y = 4x^2.

as:

2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2

To solve this, the first step is moving all the terms to the same side:

2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0

Now let's group terms with the same power of x.

(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0

Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:

-4 - 2*a = 0

-2*b + 2*a = 0

-2*c + b = 0

From the first equation:

-4 - 2*a = 0

-4 = 2*a

-4/2 = a

a = -2

And from the second equation:

-2*b + 2*a = 0

2*a = 2*b

a = b

b = -2.

From the third equation we have:

-2c + b = 0

-2c = b

c = b/-2 = -2/-2 = 1.

c = 1

Then our equation is:

y = -2*x^2 - 2*x + 1.

Help now plz

4/9-2/18

Answers

Answer:

The answer would be 6/18 or 3/9

Step-by-step explanation:

Answer:

if dividing...0.3

if multiplying...0

Step-by-step explanation:

A recipe calls for 18 ounces of cream cheese with 15 ounces of sugar." How many ounces of cream cheese are there per ounce of sugar?
PLEASE HELP

Answers

Answer:

1.2

Step-by-step explanation:

Just divide

Answer:

1.2

Step-by-step explanation:

Divide 18 by 15 and get the answer.

The length of a rectangle is (3x − 5) inches, and its width is 2x inches. Find the area of the rectangle.

Hint: Area of a rectangle = length × width.

Answers

Answer:

A = 6x² - 10x

General Formulas and Concepts:

Area of a Rectangle: Length × Width

To expand, use FOIL - First, Outside, Inside, Last

Step-by-step explanation:

Step 1: Define variables

l = 3x - 5

w = 2x

Step 2: Find area

Substitute:                   A = (3x - 5)(2x)Expand (FOIL):            A = 6x² - 10x

Answer: A=6x^2-10x ✅

Step-by-step explanation:

Hii, do you need to find the area of the rectangle? Let me help you out! (:

Luckily, there's a formula to find this! (:

Area

To find the area of a rectangle, multiply its length times its width. This is shown below.

[tex]\LARGE\boldsymbol{A=L W}[/tex]

Here, "A" denotes the area

"L" denotes the length

"W" denotes the width

NB : "L" and "W" are interchangeable

Next, it's just a matter of sticking in the known values...

[tex]\twoheadrightarrow\sf A=2x(3x-5)[/tex]

===> it's perfectly legal to stick in the values the other way around, because they are interchangeable

Alright, the next step is to multiply the values...

[tex]\twoheadrightarrow\sf A=(2x\cdot3x)-(2x\cdot(-5)[/tex]

Then we need to simplify...

[tex]\twoheadrightarrow\sf A=6x^2-10x[/tex]

Voila! There's the area of this rectangle! (:

Cheers! (:_______________

Hope I helped! Best wishes.

⚜ Reach far. Aim high. Dream big. ⚜

_______________

I NEED THIS ANSWER QUICK PLEASE!!!!!!!!!!
During the first hour of a snowstorm, 1 2/8 inches of snow fell. In the next hour, 4 3/8 inches fell. In the third hour, the snow stopped and 1 inch of snow melted. How much snow was on the ground at the end of the third hour?

Answers

Answer:

1 + 4 = 5

4/8 +3/8 = 7/8

5 7/8 - 7/8 = 5 inches left on the ground after 3 hours

Step-by-step explanation:

In 1980, the number of high school dropouts in a country was 5217 thousand. By 2008, this number had decreased to 3120 thousand. Find and interpret the average rate of change

per year in the number of high school dropouts.

Answers

Answer:

74893 students per year

Step-by-step explanation:

The Average rate of change is calculated as

= Difference in number of students / Difference in years

= 3120 thousand - 5217 thousands/ 2008 - 1980

= (3120000 - 5217000)/(2008 - 1980)

= -2097000/28

= -74892.857143 per year

Therefore, the average rate of change

per year in the number of high school dropouts is approximately 74893 students per year

Why do we use coordinate planes to do
transformations and dilations?

Answers

Answer: a coordinate plane is used in order to track the location of the object.

Translations are congruence transformations that move an object, without changing its size or shape

Dilations are transformations that generate an enlargement

Step-by-step explanation:

if angle 4 equals 50 degrees find the measure of angle 5 will mark brainiest​

Answers

Answer:

∠5 = 50°

Step-by-step explanation:

its alternate internal angles:

∠4 ≅ ∠5 (angle 4 is congruent or equal to alternate internal angle)

therefore,

∠5 = 50°

The measure of angle 5 should be considered as the 50 degrees when angle 4 should be equivalent to 50 degrees.

What is alternate internal angles?

Alternate interior angles should be created via intersecting the 2 parallel lines in a transversal way. It should be located that lies between the two parallel lines.

Since the given diagram shows the alternate internal angles

Since angle 4 is 50

So angle 4 should be congruent or equivalent to alternate internal angle)

So angle 5 should be 50 degrees.

learn more about an angle here: https://brainly.com/question/21103473

In 1998, Susie Maroney set a record for the longest ocean swim without flippers. She swam 122 miles from Mexico to Cuba. Use a conversion factor to find the distance in feet. 1mile=5280 feet

Answers

Answer:

it's 644160 u need to times it if she swam 122 miles and each mile is 5280 and u answer is 644160

The lines y = 3x + 4 and y = 3x - 17 are perpendicular

Answers

Answer: No

Step-by-step explanation: Here's something that I learned. Same slope different y-intercept (no solution). Same slope and same y-intercept (Infinitely many solutions). Different slope and same y-intercept (one solution). Different slope and different y-intercept (one solution).

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