The mean of 11 numbers is 49. Removing one of the numbers causes the mean to decrease to 45. What number was removed?

Answers

Answer 1

Answer:

89

Step-by-step explanation:

The mean:

[tex]\overline{x}=\dfrac{a_1+a_2+a_3+...+a_n}{n}[/tex]

We have:

[tex]\overline{x}=49;\ n=11[/tex]

Then we have

[tex]\dfrac{11\cdot49}{11}=49[/tex]

[tex]n[/tex] - the number

new mean is equal 45.

Therefore we have the equation:

[tex]\dfrac{11\cdot49-n}{11-1}=45\\\\\dfrac{539-n}{10}=45\qquad|\text{multiply both sides by 10}\\\\539-n=450\qquad|\text{subtact 539 from both sides}\\\\-n=-89\qquad|\text{change the signs}\\\\n=89[/tex]

Answer 2

Step-by-step explanation:

(x1 + x2 + ... + x11)/11 = 49

x1 + x2 + ... + x11= 49×11 = 539

(x1 + x2 + ... + x10)/10 = 45

x1 + x2 + ... + x10 = 45×10 = 450

so, the difference in both sums is

539 - 450 = 89

89 was the removed number.


Related Questions

All of the license plates in a particular state feature three letters followed by three digits (e.g. ABC 123). How many different license plate numbers are available to the state's Department of Motor Vehicles?

Answers

Step-by-step explanation:

for each letter position there are 26 choices.

and each of these 26 choices can be combined with the next 26 choices.

so, they alone are 26×26×26 = 26³ = 17,576

then we have the three number positions.

each has 10 options.

so, they are 10×10×10 = 10³ = 1000

and both combined are

26³×10³ = 17,576,000 different number plates

The number of different license plate numbers are available to the state's Department of Motor Vehicles is 17,575,000.

What is fundamental counting principle?

The fundamental counting principle or basic principle of counting is a method or a rule used to calculate the total number of outcomes when two or more events are occurring together.

This principle states that the total number of outcomes of two or more independent events is the product of the number of outcomes of each individual event.

For each letter position there are 26 choices, and each of these 26 choices can be combined with the next 26 choices.

so, they alone are 26×26×26 = 26³ = 17,576

then we have the three number positions, each has 10 options.

so, they are 10×10×10 = 10³ = 1000

and both combined are;

26³×10³ = 17,576,000 different number plates.

Hence the number of different license plate numbers are available to the state's Department of Motor Vehicles is 17,575,000.

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Eighteen greater than a number is 159. Find the number. Check your solution

The number is___

Answers

Answer:

let the number be x.

[tex]x + 18 = 159 \\ x = 159 - 18 = 141[/tex]

the number is 141

hope helpful <3

-4/15x =1.44 Enter your answer as a mixed number in simplest form.

Answers

Answer:

[tex]\frac{ - 4}{15x} = 1.44 \\ - 4 = 15x \times 1.44 \\ 15x = \frac{1.44}{ - 4} \\ 15x = \frac{144}{ - 4 \times 100} \\ 15x = 0.36 \\ x = \frac{36}{100 \times 15 } \\ x = 0.024[/tex]

Answer:

-5 2/5

Step-by-step explanation:

i took the test from k12

Una chompa cuesta 112 bs ¿a como debo venderla para tener una ganancia de 15%?

Answers

Answer:

746

Step-by-step explanation:

112 dividir 15

Y por el resultado lo multiplicas x 100

y esas va ser tu respuesta

What is the gradient of the graph shown ? Give your answer in its simplest form

Answers

Answer:

-2

Step-by-step explanation:

choose any point on the graph

Answer:

Step-by-step explanation:

Yo you man its 3

What is the probability that you will be able to draw all of the cards in the deck without being forced to stop because you have $0 in your pocket?

Answers

Step-by-step explanation:

Probability will be 0 According to me!!

Mark me BRAINLIEST

Find the equation of the line with slope m = 2 that contains the point (8,19).

Answers

Answer:

y = 2x + 1

Step-by-step explanation:

Pls mark as brainliest

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Slope:

m = 2

Point = (8, 19) = (x, y) _____(A)

Now,

The equation of a line is given as,

y = mx + c ______(B)

Substitute (A) into (B)

From (A) we get,

19 = 2 x 8 + c

19 = 16 + c

c = 19 - 16

c = 3

Now,

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

Thus,

The equation of the line with slope m = 2 and point (8, 19) is

y = 2x + 3

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i need help asap plss

Answers

Answer:

12

Step-by-step explanation:

20% is 20/100 = 0.2

60% is 60/100 = 0.6

So 20% of 60%= 0.2*0.6=0.12

0.12 in % = 0.12*100 = 12%

Yes i know… Math sucks

Anyways have a great day and if its correct please give brainliest

Stay Safe And Healthy

Thank you

joey enter a hot dog eating competition. He ate 30 1/2 hot dogs in 3/4 minutes. How many hot dogs did he eat in one min.

Answers

8 and 2/15

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT

                                                                                 

thanks in advance ill mark brainliest ​

Answers

the answer is the first one

Answer:

i

Step-by-step explanation:

i think it is a. ..........

9
10
11
12
13
An international company has 21.100 employees in one country. If this represents 23.9% of the company's employees, how many employees does it have in
total?

Answers

ok then I don't understand well but I think its 45.10.00

Need help with thissss!!

Answers

Answer:

f(5) = 38

Step-by-step explanation:

f(a) = 7(a + 1) - 4

f(5) = 7(5 + 1) - 4

f(5) = 7(6) - 4

f(5) = 42 - 4

f(5) = 38

Three friends each create 4 bags of starter bread dough. After ten
days, each of those four bags is then divided into four more bags of
dough. How many days pass before 192 of dough are created?
1.20
2.40
3.30

Answers

Answer:

20

Step-by-step explanation:

4x3=12

12x4=48 after 10

48x4=192 after another 10

To begin each friends have made 4 bags of dough. This gives 12 bags at the outset. After 10 days all 12 bags are made into (4*12) bags or 48 bags. After 20 days the 48 bags are made into (48*4), or the required 192 bags. After 20 days then the friends have the needed 192 bags

I DONT KNOW THIS QUESTION

Answers

**Answer**

11/4z + 6/20

**EXPLANATION**

. Which equation is linear? y=xy 3 y=-y OOO y=x2-4 3x+4y=24​

Answers

3x+4y=24 since it is a straight line

Help please write and solve the equation in the comments

Answers

Answer:

x=34

Step-by-step explanation:

2x-5=3(1/2x+4)

2x-5=3/2x+12

1/2x-5=12

1/2x=17

x=34

Answer:

x=34

Step-by-step explanation:

Is 34/18 greater or less than or equal to 1 5/6

Answers

Answer:

34/18 is greater than 1 5/6.

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

Answer:

greater than

Step-by-step explanation:

1=6/6 and 6+5=11, so 1 5/6= 11/6

Next, you want to find a common denominator, in this case 18

11/6=x/18

x=33

11/6=33/18

34/18 > 33/18

Solve for x.
100°
(2x+3)
51°

Answers

Answer:

23

Step-by-step explanation:

Exterior angle property: Exterior angle equals sum of opposite interior angles

51 + 2x +3 = 100

2x + 54 = 100

       2x = 100 - 54

      2x = 46

        x = 46/2

       x = 23

Finding the limit on Mathematica. How do I type this in Mathematica?

Answers

See the documentation for the Limit symbol for more info.

i. Limit[(t^3 + 3t^2 - 12t + 4)/(t^3 - 4t), t -> 2]

ii. For a one-sided limit, is the Direction option.

Limit[(y + 6)/(y^2 - 36), y -> 6, Direction -> -1]

The option value -1 essentially means we treat y as if it's greater than 6, so its value has to decrease in order to approach 6.

Solve this system using the substitution method: 9x – 2y = 4; 3x – 5 = y

Answers

Pick one of the equation and solve for one of the variable. I choose the first equation and solved for y. Just like the name suggest, substitute in the variable you just solved for into the second equation. For me, I substitute y into the second equation. Then, just solve it like a regular algebra equation. Once you get the answer for one of the variable, take that variable and substitute it back into one of the equation and solve for the other variable. Please mark me as the brainlest answer :)

what topics of algebra are on the shsat

Answers

Answer:

Step-by-step explanation:

Proportions.

Volume.

Scale.

Geometry (angles)

Solve for variable.

Logic.

Consecutive integers.

Unit conversion.

and much more...

41/2≤1.2x what is the answer

Answers

Answer:

i can help just meassage me

Step-by-step explanation:

ok thak u

you’ll live 100 more years if you help me answer 1 through 5 :D!!!

Answers

Answer:

You need to give me a thanks and brainliest: 1. = 16 ; 2. = 100 ; 3. = 64; 4. = 604; 5. Cant see the problem in the screen shot.

Step-by-step explanation:

log(AsqrootB) + log(A^5
) =

Answers

Answer:

log(A^8)

Step-by-step explanation:

because i learned it a bit early as a teen

Find two numbers x and y with a sum of 200 and a difference of 82

Answers

Answer:

Let x be the bigger number, and y be the smaller number.

[tex]x+y=200[/tex]

[tex]x=200-y[/tex]

Since the difference is 82,

[tex]x-y=82[/tex]

Substitute x in:

[tex](200-y)-y=82[/tex]

[tex]200-2y=82[/tex]

[tex]2y=200-82[/tex]

[tex]2y=118[/tex]

[tex]y=59[/tex]

[tex]x=200-59[/tex]

[tex]x=141[/tex]

2) How long will it take for $1300 to grow to $ 45,600 at an interest rate of 8.9% if the interest is compounded
continuously? Round the number of years to the nearest hundredth.

Answers

Answer:

  39.97 years

Step-by-step explanation:

The compound interest formula is ...

  A = Pe^(rt)

Solving for t gives ...

  ln(A/P)/r = t

  t = ln(45600/1300)/0.089 ≈ 39.97 . . . years

It will take 39.97 years for $1300 to grow to $45,600 when earning 8.9% interest compounded continuously.

Write x^2+3x-8 in the form of (x+p) ^2+q​

Answers

Answer:

(x+1.5)^2 -10.25

Step-by-step explanation:

1)first, we half 3 to give us 1.5

(x+1.5)^2

2)square 1.5=2.25

so far we have (x+1.5)^2 - 2.25 --- the negative sign from 2.25 is part of the formula

3)we subtract 8 from -2.25. the 8 comes from here shown in bold ----- x^2+3x-8

4) (x+1.5)^2 -2.25 - 8

5)simplify the last part by doing -2.25 - 8= -10.25

6)answer is (x+1.5)^2 - 10.25

Which expression has the same value as − 4 1/5 + 9 3/5?

Answers

Answer:

27 / 5

Step-by-step explanation:

− 4 1/5 + 9 3/5 = 5.4 or 5 2/5

27/5 = 5.4 or 5 2/5

What would you do if you found out that you wrote a cheque of $78 but it was recorded as $98 in check register?

Answers

Answer:

I will cryy because I only want to write 78 why it recorded as 98

Pls help need asap thx!

Answers

Answer: C

Step-by-step explanation: it has to go like this a m

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