Determine whether the events A and B are mutually exclusive. Explain your choice. A sample of 75 books is selected from a library. A: At least 10 of the authors are female: B: At least 10 of the books are fiction.

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:

3  1/2  pints

Step-by-step explanation:

A pint is two cups

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

[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]

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

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Vertical angles are congruent, so:

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

Answer:

Step-by-step explanation:

[tex]\frac{19}{x}[/tex] = tan 29°

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

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]

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.

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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

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)

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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 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.

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Answer:

-1.

Step-by-step explanation:

1) according to the DeMoivre's theorem:

[tex]1*(cos\frac{ \pi}{6} +isin\frac{ \pi}{6})^{18}=1^{18}(cos(18*\frac{ \pi}{6})+isin(18*\frac{ \pi}{6}))=cos3\pi +isin3\pi =cos\pi +isin\pi ;[/tex]

2) if cos(π)=-1 and sin(π)=0, then cosπ+i*sin(π)=-1.

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

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.

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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]%

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:

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.

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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.

Answer:

trust me its c i did the test on edge for me

Step-by-step explanation:

i did the test on edge

Answer:

$63.83

Step-by-step explanation:

please mark brainliest

Answer:

24

Step-by-step explanation:

7x4

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.

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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

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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.

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Answer:

2,4,9,16

Step-by-step explanation:

2

4

9

16

are range because they are exactly opposite of domain

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

Answer:

-26730

Explanation:

To find the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 -x)^{11}[/tex]

Use Binomial Expansion:

[tex](x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^{n-1} y + \ ^n C_2 x^{n-2}y^2 + ...+ \ ^n C_n y^n[/tex]

In this expansion,

[tex](3-x)^{11}[/tex]

The coefficient of [tex]x^7[/tex]

[tex]= 11C_{7} (3)^{11-7} (-x)^7[/tex]

[tex]= (330) (81) (-x^7)[/tex]

[tex]= -26730x^7[/tex]