Listed below are measured amounts of caffeine​ obtained in one can from each of 14 brands. Find the variance, for the given sample data and leave the answer to the nearest hundredths.

57, 34, 30, 44, 33, 41, 60, 47, 56, 41, 31, 22, 12, 40.

The permutation illustrates that if no one has been cast yet, the different ways that are there to cast Jean Valjean from the 22 men is 22.

The ways to cast Jean will be:

= 22!/(22 - 1)!

= 22!/21!

= 22

When Jean Valjean has already been cast, the different ways that are there to cast Inspector Javert from the remaining men will be:

= 21!/(21 - 1)!

= 21!/20!

= 21

When Jean Valjean and Inspector Javert have already been cast, the different ways that are there to cast Marius from the remaining men will be:

= 20!/(20 - 1)!

= 20!/19!

= 20

Learn more about permutations on:

brainly.com/question/4658834

#SPJ1

Answer:

WHAT IS THE LINEAR EQUATION?

          y=2-3x     and y=x/3+2

WHY IS THAT THE LINEAR EQUATION

Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y

WHAT IS THE NONLINEAR EQUATION

Y = x(3x+2)

WHY IS THAT THE LINEAR EQUATION

A nonlinear function has more than one independent variable. The independent variable is x.

y= x(3x-2) is non linear equation.

y= x/3 + 2  is linear equation.

y= 3 -2x  is linear equation.

Linear equations are the equations of degree 1.

It is the equation for the straight line.

The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

We know that the linear equation have highest degree 1.

First, y= x(3x-2)

y= 3x² -2x

Here, the highest degree is 2 which is non linear equation.

Now, y= x/3 + 2 have highest degree 1 which is linear equation.

and, y= 3 -2x have highest degree 1 which is linear equation.

Learn more about Linear Equation here:

https://brainly.com/question/29739212

#SPJ2

Answer:

Length equals to 75 ft

Step-by-step explanation:

A=l x w           Area of a rectangle formula.

A/w=l              Solve for length

300=l x 4      

300=l x 4

4           4

300/4=l

75=l

The system of equations represented by the graph is the one in option b.

We can see that the graph is:

A solid line with a positive slope, such that the region above the line is shaded.

This is represented by:

y ≥ line.

And we can see a horizontal line at y = 4, the line is dashed and the region below the line is shaded, then we have:

y < 4

Then the system is of the form:

y ≥ line.

y < 4

The only option that has that form is option B, so that is the correct one.

If you want to learn more about systems of inequalities:

https://brainly.com/question/9774970

#SPJ1

The equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100

The complete question is in the attached image

The given parameters are:

Area = 24

Legs = x and x + 2

The area of the triangle is calculated as:

Area = 0.5 * Base * Height

This gives

0.5 * x * (x + 2) = 24

So, we have:

0.5(x)(x + 2) = 24

Divide through by 0.5

(x)(x + 2) = 48

Expand

x^2 + 2x = 48

Subtract 48 from both side

x^2 + 2x - 48 = 0

Hence, the equations to calculate the legs are 0.5(x)(x + 2) = 24, x^2 + 2x - 48 = 0 and x^2 + (x + 2)^2 = 100

Read more about area at:

https://brainly.com/question/24487155

#SPJ1

Answer:

59 degrees

Step-by-step explanation:

Supplemental means that the angles add to 180.

x + y + z = 180

x + y = 2z + 3

Replace x + y  in the top equation with 2z + 3

2z + 3 = z = 180

3x + 3 = 180 Combine the z's.

3x = 177 subtract 3 from both sides

x = 59

Answer:

3  1/2  pints

Step-by-step explanation:

A pint is two cups

7 cups  /  2cups/pint =   7/2 pint = 3  1/2 pints

Vertical angles are congruent, so:

[tex]4x+50=150\\\\4x=100\\\\x=\boxed{25}[/tex]

Answer:

2,4,9,16

Step-by-step explanation:

2

4

9

16

are range because they are exactly opposite of domain

Answer:

22.44 ft

Step-by-step explanation:

The radius is equal to half of the diameter or 1.75 ft (in this case).

The volume of a sphere is defined as the equation:

V = 4/3 * pi * radius ^ 3

V = 4/3 * 3.14 * 1.75 ^ 3

V = 4/3 * 3.14 * 5.36

V = 22.44 ft

Answer: 0.01225%

Step-by-step explanation:

[tex]\frac{8}{20} *\frac{8}{20} *\frac{8}{20} *\frac{7}{20} *\frac{7}{20} *\frac{5}{20} *\frac{5}{20} *\frac{5}{20} = \frac{49}{400000} =0.0001225=0.01225[/tex]%

Based on the calculations, the amount of money she invested is equal to $3,520.

First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:

Since Lydia invested the same amount of money in both stocks, we have:

x = y     ....equation 1.

At the two interest rates, the total amount Lydia gets is given by:

0.11x + 0.14y = 440     ....equation 2.

Solving the equations simultaneously, we have:

0.11y + 0.14y = 440

0.25y = 440

y = 440/0.25

y = $1,760.

Thus, the total investment is given by:

Total investment = 1760 + 1760

Total investment = $3,520.

Read more on interest rates here: https://brainly.com/question/16793428

#SPJ1

[tex]f(3) = 1 \: \: \: \: \: \: \: \: f(7) = 3[/tex]

[tex] \frac{f(7) - f(3)}{7 - 3} = \frac{3 - 1}{4} = \frac{2}{4} = 0.5[/tex]

Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.

En esta pregunta tenemos una torta de cumpleaños, que asumimos de forma circular. Si leemos con cuidado el enunciado, encontramos que la proporción del pastel correspondiente al cumplimentado mediante la siguiente sustracción de fracciones:

x = 1 - 1/7 - 3/14 - 2/7

x = 6/7 - 3/14 - 2/7

x = 4/7 - 3/14

x = 8/14 - 3/14

x = 5/14

Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.

Para aprender más sobre los números fraccionarios: https://brainly.com/question/24249348

#SPJ1

Answer:

Step-by-step explanation:

[tex]\frac{19}{x}[/tex] = tan 29°

x = [tex]\frac{19}{tan29^o}[/tex] ≈ 34.28

medians of a triangle is triangle 4

Answer:

16 pieces

Step-by-step explanation:

(100*100)-(25*25)=16

[tex]\large\displaystyle\text{$\begin{gathered}\sf 7+5y=-13 \end{gathered}$}[/tex]

Subtract 7 from both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-13-7 \end{gathered}$}[/tex]

Subtract 7 from −13 to get −20.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-20 \end{gathered}$}[/tex]

Divide both sides by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf y=\frac{-20}{5} \end{gathered}$}[/tex]

Divide −20 by 5 to get −4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf y=-4 \end{gathered}$} }\large\displaystyle\text{$\begin{gathered}\sf \ \ \to \ \ \ Answer \end{gathered}$}[/tex]

We let y = -4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7+5\times-4=-13 \ \ \to \ \ [ Multiply] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7-20 \ \ \to \ \ [Subtract] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-13=-13 \ \ \to \ \ [ Equality \ holds ]} \end{gathered}$}[/tex]

Answer:

5y= -13-7

5y=-20

5y = -20

5 = 5

y = -4

Answer:

544 words

Step-by-step explanation:

The number of 4 letter words can be constructed from ABCDE would be 5^4 = 625

The number of  4 letter words can be constructed using BCD would be 3^4 = 81

So the number of words that use at least one vowel would be  5^4 - 3^4  =  625-81 = 544

Answer:

[tex]\sqrt[10]{4}[/tex]

Step-by-step explanation:

Apply power to power rule on the exponents, [tex]\frac{2}{5}*\frac{1}{4} = \frac{1}{10}[/tex] when simplified

[tex]4^\frac{1}{10}[/tex] is also the same as [tex]\sqrt[10]{4}[/tex]

Answer:

[tex]\sqrt[10]{4}[/tex]

Step-by-step explanation:

We know that,

[tex](a^{x} )^y=a^x^y\\\sqrt{x} =x^{\frac{1}{2} } \\x^\frac{1}{y} =\sqrt[y]{x}[/tex]

By following those, let us solve the given expression.

[tex](4^\frac{2}{5} )^\frac{1}{4} \\\\4^\frac{2*1}{5*4} \\\\4^\frac{2}{20} \\\\4^\frac{1}{10}\\\\\sqrt[10]{4}[/tex]

Using the combinations formula, the probability that you'll win the jackpot is given by:

A. 1/302575350.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

5 numbers are selected from a set of 70, along with one number from a set of 25, hence the number of combinations is given by:

[tex]C_{70,5}C_{25,1} = \frac{70!}{5!65!} \times \frac{25!}{1!24!} = 302575350[/tex]

Only one combination is correct, hence the probability of winning is given by:

A. 1/302575350.

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

Answer:

Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.

Answer:

full list of words from this list

factor anything that contributes causely to a result

multiply the number by which multiplicant is multiplied

multiply the number that is multiplied by a multiplier

project and refer that has been created by someone or some process

The solution to the given graph is (-√5/2, √5/2)

Given the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4

The solution will be the point of intersection of the two curves.

Equate the functions

x²-1 =  -x² + 4

Equate to zero

x²+x² - 1-  4 = 0

2x² -5 = 0

2x² = 5

x² = 5/2

x = ±√5/2

Hence the solution to the given graph is (-√5/2, √5/2)

Learn more on quadratic equation here: https://brainly.com/question/1214333

#SPJ1

Answer:

  not equivalent; signs don't match

Step-by-step explanation:

Apparently, you want to compare the expressions ...

The distributive property allows you to eliminate parentheses by multiplying each term inside parentheses by the factor outside.

When we do that to the first expression, we get ...

  -0.5(3x +5) = (-0.5)(3x) +(-0.5)(5) = -1.5x -2.5

Note that the signs of the terms inside parentheses are the same, and the signs of the terms after removing parentheses are the same. (Both terms have their signs changed by the negative factor multiplying the parentheses.)

The expanded expression -1.5x -2.5 is not equivalent to -1.5x +2.5, which has terms of different signs.

Using continuous compounding, it is found that:

a) The account will be worth $26,916.31 in 10 years.

b) It will take 42.18 years for the account to be worth $70,000.

The amount of money earned, in continuous compounding, after t years, is given by:

[tex]A(t) = Pe^{rt}[/tex]

In which:

The parameters are given as follows:

A(0) = 20000, r = 0.0297, t = 10.

Hence the worth in 10 years will be given by:

[tex]A(t) = Pe^{rt}[/tex]

[tex]A(10) = 20000e^{0.0297 \times 10}[/tex]

A(10) = $26,916.31.

Now, we find in how many years it will be worth $70,000, as follows:

[tex]A(t) = Pe^{rt}[/tex]

[tex]70000 = 20000e^{0.0297t}[/tex]

[tex]e^{0.0297t} = 3.5[/tex]

[tex]\ln{e^{0.0297t}} = \ln{3.5}[/tex]

[tex]0.0297t = \ln{3.5}[/tex]

[tex]t = \frac{\ln{3.5}}{0.0297}[/tex]

t = 42.18 years.

More can be learned about continuous compounding at https://brainly.com/question/24722580

#SPJ1

Using the expected value of a discrete distribution, the values are given as follows:

a) $250.

b) $2,500,000.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

The distribution of the company's earnings is given as follows:

Considering that the policy sells for $600, for example, a $5000 claim is a loss of $5000 - $600 = $4,400 for the company, which explains the above distribution.

Item a:

The expected value for a policy sold is given by:

E(X) = 600(0.965) - 4400(0.02) -9400(0.01) - 29400(0.005) = 250.

Item b:

Considering the value found in item a for a single policy, for 10,000 policies, the expected profit is given by:

E = 10000 x 250 = 2,500,000.

More can be learned about discrete distributions at https://brainly.com/question/24802582

#SPJ1

The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have center of the circle(h, k) = (-7, -6)

The radius of the circle r = 2

The standard form of a circle:

(x - h)² + (y - k)² = r²

(x - (-7))² + (y - (-6))² = 2²

(x + 7)² + (y + 6)² = 4

Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

Learn more about circle here:

brainly.com/question/11833983

#SPJ1

Answer:

24

Step-by-step explanation:

7x4