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Posted in Mathematics

The following data values represent a population. What is the variance of the values? 8, 10, 14, 12 A.22 B.11 C.5 D.10


 Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. We do as follows:

Mean = 8+10+14+12 / 4 = 11

Variance = (8-11)^2 + 
(10-11)^2 + (12-11)^2 + (14-11)^2 / 4
Variance = 5 <-------OPTION C

Related Questions

Posted in Mathematics

The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken

Since there are 20 members in the soccer team. Then six members voted to eat pizza and 10 member voted to eat chicken and the rest is hotdog

Member voted for hotdog = 20 – 10 – 6 = 4

Ratio for hotdog to chicken is 10 : 4 or 5:2

Posted in Mathematics

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞)

The solution to the problem is as follows:

solve for x :

−3(6−2x)≥4x+12

−18+6x≥4x+12

2x≥30

x≥15

So the answer is D ) 15 to +infinity


I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Identify the expression as a numerical expression or a variable expression. For a variable expression, name the variable. 1 × 12 A. numerical expression B. variable expression; a is the variable. C. variable expression; there is no variable. D. variable expression; l is the variable.

The best and most correct answer among the choices provided by the first question is the first choice or letter A.

The expression above is an example of a numerical expression.


I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data? About 160 people weigh more than 165 pounds. About 320 people weigh more than 165 pounds. About 320 people weigh less than 165 pounds. About 640 people weigh less than 165 pounds.

Z = (X-Mean)/SD 
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16% 

Therefore, 

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160

Posted in Mathematics

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b. A. –7 B. 7 C. 14 D. 32

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.


I hope my answer has come to your help. God bless and have a nice day ahead!

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Posted in Mathematics

Each set of ordered pairs represents a function. Write a rule that represents the function. 1. (0,0),(1,4),(2,16),(3,36),(4,64) 2. (0,0),(1,0.5),(2,2),(3,4.5),(4,8)

My answer to the question is as follows:

First one looks like you are squaring the number, then multiplying the result by 4, i.e.

y=4x2

second one is similar, but instead of squaring and multiplying by 4, you are squaring and then dividing by 2

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Which polynomial expression represents the area of the outermost square tile, shown below? A square shaped tile with length x plus three is shown x2 + 6x + 6 x2 + 9x + 6 x2 + 6x + 9 x2 − 6x + 9

I believe the correct answer from the choices listed above is the third option. The polynomial expression that represents the area of the outermost square tile would be x^2 + 6x + 9. The area of a square is calculated by the square of its side and the side of this square is given as x+3.

A = (x+3)^2 = x^2+6x+9

Posted in Mathematics

You can buy an 8 pack of paper towels for $7.92 or 12 pack for $11.64, which is a better buy?

Divide $7.92 by 8 and then divide $11.64 by 12 and see which has the lowest answer.

The first option has a price of $0.99 for one paper towel, and the second option has a price of $0.97 for one paper towel.

The second option is the better buy.

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The public library has fewer than 4,000 books. Let b represent the number of books in the library. Which inequality describes the number of books? b < 4,000 b > 4,000 b ≤ 4,000 b ≥ 4,000

Answer:  The correct option is (A) b < 4000.

Step-by-step explanation:  Given that the public library has fewer than 4,000 books.

We are to select the inequality that describes the number of books in the library.

The number of books in the library is represented by b.

According to the given information, the inequality hat describes the number of books in the library is given by

b<4000.

Thus, (A) is the correct option.

Posted in Mathematics

Solve for x. round to nearest tenth if needed. 1. 7r-7=2r+18 a.r=-5 b.r=5 c.r=2.2 d.r=1.2 2. 2x+12=18-x a.x=3 b.x=10 c.x=6 d.x=2 3. 8x-3=15x+18 a.x=-3 b.x=3 c.x=2.1 d.x=0.9 4. 6y-6=4y+16 a.y=2.2 b.y=-2.2 c.y=11 d.y=5 5. 3(x-4)=5(x+2) a.x=11 b.x=-11 c.x=1 d.x=-1

1)  The answer is: [B]: r = 5 .
__________________________
Explanation:
__________________________ 
Given: 7r − 7 = 2r + 18 ; Round your answer to the nearest tenth, if necessary.
____________________________
Since "r" is the only variable given, let us assume we want to solve for "r" (instead of "x").
___________________________
→ Subtract "2r" from EACH SIDE of the equation; and & add "7" to EACH SIDE of the equation:
_____________
→ 7r − 7 − 2r + 7 = 2r + 18 − 2r + 7 ;  to get: → 5r = 25 ;
_____________
→ Now, divide EACH SIDE of the equation by "5"; to isolate "r" on one side of the equation; and to solve for "r" :
______________
→ 5r / 5 = 25 / 5 → r = 5 → which is: "Answer choice: [B]".
_________________
Let us check our answer, by plugging in "5" for "r" in the original equation:
_________________
 → 7r − 7 = 2r + 18 ;  →  7(5) − 7 =? 2(5) + 18? ;
______________________
→ 35 − 7 =? 10 + 18 ?;     → 28 =? 28? Yes!
______________________
 2) The answer is: [D]: x = 2 .
_____________
Explanation: 
_____________
Given: 2x + 12 = 18 − x ; Solve for "x" (round to nearest tenth, if necessary).
_______________
→ Add "x" to EACH SIDE of the equation, & subtract "12" from EACH SIDE of the equation:  → 2x + 12 + x − 12 = 18 − x + x − 12 ; 
______________
→ To get: 3x = 6 ;  → Divide EACH SIDE of the equation by "3";
to isolate "x" on one side of the equation; and to solve for "x":
_____________
→ 3x / 3 = 6 / 3 ; → x = 2 ; which is: "Answer choice: [D]".
______________
Let us check our answer, by plugging in "2" for "x" in the original equation:
________________
→ 2x + 12 = 18 − x ; → 2(2) + 12 =? 18 − 2 ?
________________
→ 4 + 12 =? 18 − 2 ? ;   → 16 =? 16?  Yes!
________________________________
3)  The answer is: [A]: x = -3 . 
_____________
Explanation:
________________
Given:  8x − 3 = 15x + 18 ; Solve for "x". Round your answer to the nearest tenth, if necessary.
_________________
→ Subtract "8x" from EACH SIDE of the equation, & add "3" to EACH SIDE of the equation:
_______________
→ 8x − 3 − 8x + 3 = 15x + 18 − 8x + 3 ; to get:
_______________
→ 0 = 7x + 21 ; → Subtract "21" from EACH SIDE of the equation;
_______________
→ 0 − 21 = 7x + 21 − 21 ; to get:
_______________
→  -21 = 7x ; Now divide EACH SIDE of the equation by "7";
    to isolate "x" on one side of the equation; & to solve for "x":
_______________
→ = -21 / 7 = 7x / 7 ; →  -3 = x ; which is "Answer choice: [A]."
_________________
Let us check our answer, by plugging in "-3" for "x" in the original equation:
________________
→  8x − 3 = 15x + 18 ;  → 8(-3) − 3 =?  15(-3) + 18 ?;
________________________
→ -24 − 3 =?  -45 + 18 ? ;   →  -27 =? -27?  Yes!
___________________________
4)  The answer is: [C]: y = 11 .
_____________
Explanation:
____________
Given: 6y − 6 = 4y + 16 ; Solve for "y"; Round to the nearest tenth, if necessary.
____________
(Note: Since "y" is the only variable given; assume we are to solve for "y" instead of "x").
____________
→ Subtract "4y" from EACH SIDE of the equation, & add "6" to EACH SIDE of the equation; → 6y − 6 − 4y + 6 = 4y + 16 − 4y + 6 ; to get:
_______________
→ 2y  = 22 ; Now, divide EACH SIDE of the equation by "2"; to isolate "y" one side of the equation; and to solve for "y" ;
_______________
→ 2y / 2 = 22 / 2 ; →  y = 11 → which is "Answer choice: [C]".
_______________________________
Let us check our answer, by plugging in "11" for "y" in the original equation:
___________________
→  6y − 6 = 4y + 16 ; → 6(11) − 6 =? 4(11) + 16 ?
_______________________
→ 66 − 6  =? 44 + 16 ?  → 60 =? 60 ?  Yes!
__________________
5)  The answer is: [B]: x = -11 .
_____________________
Explanation:
_________________
Given: 3(x − 4) = 5(x + 2) ; Solve for "x". Round to the nearest tenth, if necessary.
___________
→Note the "distributive property of multiplication": 
_____________
a*(b + c) = ab + ac ;  and: a*(b − c) = ab − ac ;
_______________
→ Let us expand EACH SIDE of our given equation.
→Start with the "left-hand side":
____________
3(x − 4) = (3*x)  − (3*4) = 3x − 12;
______________________________
→Now let us expand the "right-hand side" of the given equation:
____________
→  5(x + 2) = (5*x) + (5*2) = 5x + 10 ;
______________
→Now, we can rewrite the original equation:
_______________
→ 3(x − 4) = 5(x + 2) ; by substituting the expanded values for EACH SIDE of the question:   →  3x − 12 = 5x + 10 ;
__________________
→ Subtract "3x" from EACH SIDE of the equation; and add "12" to EACH SIDE of the equation: →  3x − 12 − 3x + 12 = 5x + 10 − 3x + 12 ; to get:
________________
→  0 = 2x + 22;  → Now subtract "22" from EACH SIDE of the equation:
______________
→  0 − 22 = 2x + 22 − 22 ; to get:  →  -22 = 2x ;
__________
→ Divide EACH SIDE of the equation by "2"; to isolate "x" on one side of the equation; & to solve for "x" ;
_____________
→  -22 / 2 = 2x /2 ;  →  -11 = x ; which is "Answer choice: [B]".
______________
Let us check our answer, by plugging in "-11" for "x" in the original equation:
___________
→ 3(x − 4) = 5(x + 2) ; →  3(-11 − 4) =? 5(-11 + 2) ? ; 
_______________________
→3(-15) =? 5(-9) ? ; → -45 =? -45 ?  Yes!
_____________________________________________
Hope these answers and explanations are helpful. Best of luck!

Posted in Mathematics

Solve for w. 2w=12-4w Simplify your answer as much as possible.

So we have an equation:
2w=12-4w
Firstly, let's simplify, and divide all terms by 2:
w=6-2w
Now, we add 2w over to the other side:
3w=6
And finally, we divide both sides by 3:
w=2
Hope this helps!

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Posted in Mathematics

Which rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I'? (x, y)→(x - 8, y - 7) (x, y)→(x - 7, x - 8) (x, y)→(x - 4, x - 5) (x, y)→(x - 5, y - 4)

Correct answer is A.

Each vertex of the hexagon is translated 8 units left and 7 units down. So, the x-coordinate is 8 units smaller (x - 8), and the y-coordinate is 7 units smaller (y - 7).

Therefore (x, y) → (x - 8, y -7)

Posted in Mathematics

12 meters into centimeters

We Know, 1 m = 100 cm
hen, 12 m = 100 * 12 = 1200 cm

So, your final answer is 1200 cm

Hope this helps!

Posted in Mathematics

Which expression represents the sum of 2/3m - 1 1/6 and 5/6 - 1 1/3?a. 1 1/2m + 2 1/2b.1/6m - 1/3c.1 1/2m - 2 1/2d.1/6m + 1/3

The answer to "which expression represents the sum of 2/3m - 1 1/6 and 5/6 - 1 1/3?a. 1 1/2m + 2 1/2b.1/6m - 1/3c.1 1/2m - 2 1/2d.1/6m + 1/3" is B.

Posted in Mathematics

Which answer describes the type of sequence? −99, −88, −66, −55, ... A. arithmetic B. neither arithmetic nor geometric C. geometric

Here, Geometric ratio, r = -88/-99 or -66/-88 which is 8/9 or 6/8. As they are not equal, it is not a geometric.

Now, Arithmetic difference, d = -88-(-99) or -66-(-88) which is 11 or 22. As they are not equal, it is not a Arithmetic.

So, it's neither an Arithmetic nor a Geometric.

Option B is your answer!

Hope this helps!

Posted in Mathematics

What number is in the tenths place? 123.456

The 2 because starting from left to right it is hundreds hundreds, ten's, ones

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What is the common difference d of the sequence? 9, −8, −25, −42, −59, ... d =

Common difference, d = -8-9 or -25-(-8) which is equal to -17

So, your final answer is -17

Hope this helps!

Posted in Mathematics

0x6+12 divided by 3-1 answer

(0x6) = 0 
0+12 = 12
3-1 = 2
12 divided by 2 =6.

Posted in Mathematics

What is 125 in exponential form?

Number = 125
Here, ∛125 = 5
so, in exponential form, it would be: 5³

So, your final answer is 5³

Hope this helps!

Posted in Mathematics

5x-3y=12 what is the x-intercept

Your x-intercept is (12/5,0) and your y-intercept is (0,-4)

Posted in Mathematics

Membership in the fishing club went from 120 members last year to 87 members this year. What was the percent of decrease in membership?

It would be: 87/120 * 100 = 72.5

Percentage decrease = 100 - 22.5 = 27.5

So, your final answer is 27.5%

Hope this helps!

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Posted in Mathematics

125% of what number is 264

Let, the number = x
x * 125 / 100 = 264
x = 264*100 / 125
x = 26400/125
x = 211.2

So, that number & your final answer is 211.2

Hope this helps!

Posted in Mathematics

What is 1626 divided by 12 as a mixed number

It would be: 1626 / 12 = 135.5 = 135 1/2

So, your final answer is 135 1/2

Hope this helps!

Posted in Mathematics

Is 3/4 equivalent to 12/15

For this, you have to reduce the larger fraction, which is 12/15
After reduction, it would be: 4/5 which is not equivalent to 3/4

4/5 ≠ 3/4

So, your final answer is "NO", it's not equivalent 

Hope this helps!

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