Mathematics High School

Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about the acceleration due to gravity. The program reports a mean of 31.5 and a standard deviation of 2.5.

What is the variance of the data? Round to the nearest tenth.

1.6
2.5
5.6
6.3

Answers

Answer 1

Since the variance is the square of the standard deviation, the variance here is 6.3.

What is variance?

In statistics, the variance shows how much the values spread out around the mean. The standard deviation is obtained as the square root of the variance of a given value.

Now;

[tex]s = \sqrt{v}[/tex]

s = 2.5

[tex]v = s^2[/tex]

[tex]s = (2.5)^2 =[/tex]6.3

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Related Questions

Is 3.4 a rational or irrational number? Please explain why, thanks.

Answers

Rational, 3.4 can be written as a fraction and is noncontinuous
"An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point."

Answer:

Yes it is a rational number

I just did it and I passed

What is the missing number in the synthetic-division array?

Answers

The correct answer for this would be 7. The missing number in the synthetic division array is 7. So how did we get 7. Here is the step by step process.
-1 in the left most part is the coefficient of (x+1= 0) which makes it -1. Now, bring down 3, then multiply it by -1, and this given you -3 on the second row. -4 + -3 would be -7. Continue with the same step. -7 x -1 would be 7. And this is how we got the answer for the part with the question mark. Hope this answer helps.

The first digit in the quotient of 6523÷7

Answers

931.857143 is ur answer. Ok

A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides wont require fencing) She has decided to create a rectangular shape for the area and will use barbed wire to create the enclosure there are 600 feet of wire availible for this project and she will use all the wire. what is the maximum area enclosed by the fence then find the maximum of the function. ...?

Answers

The area enclosed is (2x)(600-2x).(2x)(600−2x)=1200x−4x2
In order to maximize we need the derivative to be equal to 0.y′=1200−8x=0
1200=8x
x=150
Therefore the sides for maximum area are 150*300.
The area is: 45000

Answer:

Area is 45000 square feet.

Step-by-step explanation:

Let x be the length of fenced side parallel to the river side.

Let y be the length of other two sides.

Then,

[tex]x+ 2y 600[/tex]

So, we get [tex]x=600-2y[/tex]

Area of this rectangle = xy

= [tex]y(600-2y)[/tex]

[tex]x=-2y^{2}+600y[/tex]

Now attached is the graph of the area function, which is a parabola opening downward.

We can see ta the maximum area occurs when y=[tex]-600/[2(-2)][/tex] = 150

And [tex]x = 600-2(150)[/tex]

x =[tex]600-300=300[/tex]

Therefore, to maximize the area, the side parallel to the river is to be 300 feet long, and the other two fenced sides should be 150 feet long.

The area is = [tex]300\times150= 45000[/tex] square feet.

160 percent of 1,825 is? Rounded to nearest tenth
...?

Answers

2920 is 160 percent of 1825

A liquid-filled glass pyramid is being erected as part of a museum attraction. The pyramid is designed to be 15 feet tall with a rectangular base that is 10 feet long and 6 feet wide. What is the total amount of liquid that the pyramid can hold?

Answers

First we calculate surface of base.

10 * 6 = 60 feet^2

The Volume of pyramid is calculated by formula:
V = B*H/3

H- height of pyramid
B- surface of base of pyramid

We have both of those so all we have to do is to finish calculation:

V = 60*15/3 = 300 feet^3

Answer is 300 qubic feets

Answer:

300 cubic feet

Step-by-step explanation:

A store is having a clearance sale where merchandise on the sales rack is reduced by 80% from the original price. If a jacket was originally priced at $76, what is the sale price.

Answers

76 - 80% = 15.2 
$15.20 is your answer :)

Find the slope of the line that passed through points a and d
A) -7/2
B) -2/7
C) 0
D) 2/7

Answers

Simple...

you have: Find the slope of the line that passed through points A and D.

A is located at: (-3,-2)

B is located at (4,0)

Using [tex] \frac{ y_{1}- y_{2} }{ x_{1}- x_{2} } [/tex] to find slope-->>>

[tex] \frac{-2-0}{-3-4} = \frac{-2}{-7} = \frac{2}{7} [/tex]

m=[tex] \frac{2}{7} [/tex]

Thus, your answer.

Answer:

The answer is m=2/7 or answer choice D

Step-by-step explanation:

I need help with subtracting polynomials: (m^2 + 6m - 5) - (7m² - 5m + 1)
A.8m² + m - 4
B.-8m⁴ + 11m - 4
C.-7m² + m - 6
D.-6m² + 11m - 6

Answers

It is D. -6m^2 + 11m - 6
Hope this helps you

To subtract the polynomials, change the signs of the second polynomial and combine like terms. The result is -6m² + 11m - 6, which is option D.

To subtract the given polynomials, we need to subtract the second polynomial from the first one. We do this by changing the signs of the second polynomial and then combining like terms with the first.

(m² + 6m - 5) - (7m² - 5m + 1) becomes (m² + 6m - 5) + (-7m² + 5m - 1).

Now, combine the like terms:

m² - 7m² = -6m²,6m + 5m = 11m,-5 + (-1) = -6.

So, the simplified form of the polynomial after subtraction is -6m² + 11m - 6, which corresponds to option D.

Solve the inequality 6x - 8 > 4x + 26

x < 9

x < 17

x > 9

x > 17

Answers

6x > 4x+26+8
2x > 34

so,
x > 17 

Answer:

The Answer is D.  x > 17

Hope This Helps!

To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 62 numbers (1 through 62). The order in which the selection is made does not matter. How many different selections are possible? ...?

Answers

Final answer:

The number of different selections possible when picking 6 numbers from a collection of 62 numbers for a LOTTO game is 62,891,499.

Explanation:

The question asks how many different selections are possible when picking 6 numbers from a collection of 62 numbers for a LOTTO game. Since the order of the selection does not matter, we can use the concept of combinations to solve this problem. The formula for combinations is given by C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items selected. Plugging in the values, we have C(62, 6) = 62! / (6! * (62-6)!), which simplifies to 62! / (6! * 56!). Using a calculator or computer program to calculate the factorial, we find that C(62, 6) is equal to 62,891,499.

Final answer:

To find the number of different selections possible in a lotto where 6 numbers are chosen from 62, we use the combination formula: C(62, 6). This yields 45,057,474 possible selections.

Explanation:

Calculation of Different Selections in Lotto

To calculate the number of different selections possible when choosing 6 numbers from a set of 62 without regard to the order of selection, we use the combination formula:

The combination formula is C(n, r) = n! / (r! * (n-r)!), where C(n, r) is the number of combinations, n is the total number of items to choose from, r is the number of items to be chosen, and ! denotes factorial.

In this case, n = 62 and r = 6:

C(62, 6) = 62! / (6! * (62-6)!) = 62! / (6! * 56!)

Calculating the factorials and the division, we find that there are 45,057,474 possible selections.

Therefore, the probability of winning by correctly selecting all 6 numbers is 1 in 45,057,474, making lottery tickets a game of very low probability for individual success.

Jen and Heather went to lunch. When the bill came Jen discovered that she had only 8.00 dollars, luckly Heather had enough money to pay the other part or 3/5 of the bill. ...?

Answers

To answer this question, let's analyze the given problem above.
Given that Heather paid the other part of the bill which is 3/5 of the bill, then this means that, Jen paid only 2/5 of the bill. Now that Jen has only 8 dollars, this 8 dollars is equivalent to 2/5 of the bill. The next thing we are going to find out is how much did Heather pay which is 3/5 of the bill. 
So 2/5 = 8 dollars
     3/5 = ?dollars
Therefore, the answer would be $12. The amount that Heather paid is $12. Hope this answer helps.

At the grocery store, you buy a carton of milk for $1.95, a loaf of bread for $0.85, and a box of cereal for $2.05. Use mental math to find the total cost of the groceries

Answers

total cost is 4.85 dollars to do this simply add them together

Which arrangement shows 4.09,4 2/3 ,21/4 and 4.7 in order from least to greatest?

Answers

4.09 < 4 2/3 < 4.7 < 21/4

What are the constant terms in the expression? 8m−5n+2+m−148m−5n+2+m−14 Drag and drop the constant terms into the box.

Answers

2

Is is the only integer that is alone.
2, 2, and -14 are the constant terms. They never change. The other terms change when 'm' and 'n' change.

The intensity I of light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 250 w/m^2 when the distance is 5 m. How much farther would it be to a point where the intensity is 40 w/m^2? ...?

Answers

Final answer:

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. To find the distance where the intensity is 40 w/m², use the inverse square law formula to solve for the distance.

Explanation:

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. This means that as the distance increases, the intensity decreases.

If the intensity is 250 w/m² at a distance of 5 m, and we want to find the distance where the intensity is 40 w/m², we can use the inverse square law formula:

I₁d₁² = I₂d₂²

Plugging in the values, we get:

250 × (5)² = 40 × (d₂)²

Simplifying, we find that d₂² = 250 × (5)² / 40

d₂² = 312.5

Therefore, d₂ = √312.5 ≈ 17.68

So, it would be approximately 17.68 - 5 = 12.68 meters farther to a point where the intensity is 40 w/m².

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Sure, let's solve it step by step.

First, we know that the initial intensity (I1) is 250 w/m^2 and the initial distance (d1) is 5 m. We are asked to find a distance where the intensity is 40 w/m^2, which would be our final intensity (I2).

According to the inverse square law, the intensity of light is inversely proportional to the square of the distance from the source, i.e., I ∝ 1/d². Therefore, we can say that I1 * d1² = I2 * d2². This equation allows us to find the distance at which the intensity is I2.

So, substituting the given values in the equation, we have 250 * (5)² = 40 * d2².

Now, we can solve for d2. Rearranging terms, d2 = √((250 * (5)²) / 40), which will give us d2 = 12.5 m.

So, the distance at which the intensity of light is 40 w/m^2 is 12.5 m.

However, we have been asked to find the additional distance that needs to be traveled to reach a point where the intensity is 40 w/m^2. This additional distance is the difference between the final distance (d2) and the initial distance (d1), that is, distance_travelled = d2 - d1 = 12.5 - 5 = 7.5 m.

Therefore, you would need to travel an additional 7.5 m to reach a point with an intensity of 40 w/m^2.

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What value(s) of x make the equation x2 - 18x + 81 = 0 true?

Answers

1. x =(18-√648)/2=9-9√ 2 = -3.728
2.  x =(18+√648)/2=9+9√ 2 = 21.728
To solve for the values of X that will make the equation true, all you have to do is factor this trinomial. Basically find 2 numbers that multiply to give you 81 and also add to give you -18, in this case the numbers would be -9 and -9. Since -9 + -9 = -18 and -9 • -9 = 81. Thus the factored expression would be like this:

(X-9)(X-9) = 0
X - 9 = 0 and X - 9 = 0
In both cases the solutions for X is that X is equal to 9.

The value of X that will make this equation true, is if X is equal to 9.

what is a term without a variable

Answers

A term without a variable is called a constant term, and the degree of that term is 0 Hope that helps you I knew this was 0 beciase i study this a long time ago

A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0N . What would the tension be if the ball went around in only half a second?

Answers

The tension in the string balances out, and thus equals the centripetal force of the ball 

T = mv^2/r 

if it only takes half the time to finish one orbit it has to be moving at twice the original speed. 

And since v is squared T will increase by 4 

T' = m(2v)^2/r 

T' = 4mv^/r = 4T 

T' = 24.0 N

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
Final answer:

If the ball went around in half a second, the tension in the string would be 24.0 N.

Explanation:

To find the tension in the string if the ball went around in half a second, we can use the equation for centripetal force. The tension T in the string provides the centripetal force, which is equal to the mass of the ball times the square of its velocity divided by the radius of the circle:

T = (m * v^2) / r

In this case, the mass of the ball and the radius of the circle remain the same, but the velocity changes. Since the ball takes half the time to complete the circle, the velocity is twice as fast. Therefore, the tension in the string would be four times greater:

Tension = 4 * 6.0 = 24.0 N

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Erica went shopping for new clothes for school. She bought a pair of jeans for $70.19 and several shirts for $8.63 each. If x represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's shopping trip? Explain your choice.


plzzzz helpppp

Answers

it's at least y=$8.63x+$70.19
Y=70.19+(8.63*X)

To find the total she spent all you have to do is add everything together. The cost of the pants was $70.19, to find how much she spent on shirts you take the amount each shirt was, which in this case is $8.63, and multiply it by how many shirts she bought. We don't know how many shirts she bought so we use the varriable of X to represent that number.

(I used the asterisk * to indicate the multiplication)

tinku is fond of collecting spiders and insects. He knows spiders have 8 legs and insects have 6 legs. he counted 36 legs. How many of each does he have in hi collection?

Answers

Let, number of spiders = x
number of insects = y

6x + 8y = 36

remember, legs can't be in fraction or decimal.

So, only (3, 2) fits with that.

So, there are 3 spiders & 2 insects in his collection.

Hope this helps!

An organic farm uses 3/7 of the land to grow potatoes and 2/5 of the land to grow spinach. The remaining land is used to grow tomato plants. What fraction of the land is used to grow tomato plants?

Answers

Fraction of the land is used to grow tomato plants=1-(fraction of the land to grow potatoes + fraction of the land to grow spinach)


Land used for to grow tomato plants=1-(3/7 + 2/5)
=1-(15+14)35
=1-29/35
=(35-29)/35
=6/35

Answer: this organic far uses 6/35 of the land to grow tomato plants.

Thirteen and eight tenths

Answers

13 8/10

hope this helps you

Solve the following equation for B
y=mx+b

Answers

The answer is:
__________
b = y − mx .
__________
Explanation:
__________
Given:
__________
y = mx + b ; 
_________
We want to isolate "b" on one side of the equation to solve for "b".
_______________________
→ y = mx + b ; Subtract "mx" from BOTH sides of the equation; to isolate "b" one side of the equation; and solve for "b":
____________________________________
y = mx + b → y − mx = mx + b − mx ;
____________________________________
                  → y − mx = b ; ↔ b = y − mx
____________________________________
                  → b = y − mx .
____________________________________
In the slope intercept form, or y = mx + b, m represents the slope, and b represents the y-intercept.

To solve for b, you just have to replace x and y in the formula with the given coordinates and replace m with the calculated value.

For example, you have to find the equation of a line with the coordinate points (1, -2) and (6, 5). Replace one set of ordered pairs in the slope intercept formula.

Graph both of the coordinate points in a coordinate plane, or a graph, to find it's slope. Use rise over run. Simply count how many points it takes to go the other ordered pair.

The slope of (1, -2) and (6, 5) is 7/5.

If you found the slope, plug those numbers in.

I used (1, -2). I plugged in the slope.
-2 = 7/5(1) + b

You just have to solve for b by simplifying the equation.

John has 15 more music cds than micheal together they have a total of 55 cds

Answers

Michael has 40 CDs. 40+15=55. 

Simplify 659/8. What is the answer rounded to the nearest whole number?

Answers

659/8 to the nearest whole number is 82.
i got 82 3/8 but percentage is 82.375 so the 3 is less then 5 so the answer is 82

It takes for three gardeners 90 minutes to weed a garden. If the job is to be done in only 15 minutes, how many more gardeners need to be put on the jobs?

Answers

3 gardeners :90 minutes
? Gardeners : 15 minutes
1 gardener : 270 minutes
? Gardeners : 270/15
18 gardeners
The answer is 15 gardeners.
Thus, 15 gardeners would be needed if the job is to be done in only 15 minutes.

license plates in a particular state display two letters followed by three numbers, such as AT-887 or BB-013. How many different license plates can be manufactured for this state?

Answers

10^3*26^2
10 values 0-9 which can repeat
26 letters which can repeat

HELP!!!
what is the value of x in the following equation:
1/4 x + 1/4 x = 4/5 ?
A. 8/5
B.5/8
C.2/5
D.3/5

Answers

the value of x in this equation is 2/5

Farmer tom’s chickens and sheep are all in a jumble. he counts 48 heads and 134 legs, how many sheep does he have?

Answers

Chickens have 2 legs and sheep have 4 legs. If x is the number of chickens and y is the number of sheep, then we have the system of equations: x + y = 48, 2 x + 4 y = 134. We can solve this system : x = 48 - y, then we will put it into the 2nd equation: 2 * ( 48 - y ) + 4 y = 134, 96 - 2 y + 4 y = 134, 2 y = 134 - 96, 2 y = 38, y = 38 : 2, y = 19. Answer: Farmer Tom has 19 sheep.
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