The classical approach to probability requires that the outcomes are​ _______.

The range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

f(x) = x² + 3x - 4

The domain of the f(x) is all real numbers

The range of the g(x) is [-6.25, ∞)

g(x) is shown in the table:

x      –6     –3     –1       4

g(x)    13      4     –2    –17

The linear function g(x) is:

[tex]\rm g(x) = \ -13=\dfrac{\left(4-13\right)}{-3+6}\left(x+6\right)[/tex]

g(x) = -3x - 5

(f + g)(x) = f(x) + g(x)

= x² + 3x - 4 - 3x - 5

(f + g)(x) = x² - 9

The domain of the function is all real numbers.

The range of the function (-9, ∞)

Thus, the range of function (f + g)(x) is (-9, ∞) option (D) is correct the linear function g(x) is g(x) = -3x - 5

Learn more about the function here:

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Answer:

Total yearly interest for the two accounts is: $570

Step-by-step explanation:

0.075*1000+0.0825*6000=570

75.0+495.0=570

Answer (it has two solutions):

I hope this helps!

Answer:

27 feet

Step-by-step explanation:

We can set up a proportion comparing the height of each object to the length of the shadow.

h/s

h/15=18/10

Cross multiply.

10*h=18*15

10h=270

Use the multiplicative Inverse

10/10=270/10

h=27

Answer:

x = 41° , y = z = 74°

Step-by-step explanation:

x and 41 are alternate angles and are congruent , then

x = 41°

the 2 sides of the triangle with vertex = 32° are congruent so the triangle is isosceles with base angles being congruent , then

y = [tex]\frac{180-32}{2}[/tex] = [tex]\frac{148}{2}[/tex] = 74°

y and z are vertically opposite angles and are congruent so

z = 74°

Answer:

[tex]\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Step-by-step explanation:

Perform the partial fraction decomposition

[tex]\int{\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)} } \, dx\\ \\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\ \\7x^3+5x^2+49x+5=(x^2+7)(Ax+B)+(x^2+1)(Cx+D)\\\\7x^3+5x^2+49x+5=Ax^3+Bx^2+7Ax+7B+Cx^3+Dx^2+Cx+D\\\\7x^3+5x^2+49x+5=Ax^3+Cx^3+Bx^2+Dx^2+7Ax+Cx+7B+D\\\\7x^3+5x^2+49x+5=x^3(A+C)+x^2(B+D)+x(7A+C)+7B+D[/tex]

Set up a system of equations and solve for each constant

[tex]\begin{cases} A + C = 7\\B + D = 5\\7 A + C = 49\\7 B + D = 5 \end{cases}[/tex]

[tex]A+C=7\\A=7-C[/tex]

[tex]7A+C=49\\7(7-C)+C=49\\49-7C+C=49\\49-6C=49\\-6C=0\\C=0[/tex]

[tex]A=7-C\\A=7-0\\A=7[/tex]

[tex]B+D=5\\B=5-D[/tex]

[tex]7B+D=5\\7(5-D)+D=5\\35-7D+D=5\\35-6D=5\\-6D=-30\\D=5[/tex]

[tex]B=5-D\\B=5-5\\B=0[/tex]

Plug solved constants in and evaluate

[tex]\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{Ax+B}{x^2+1}+\frac{Cx+D}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x+0}{x^2+1}+\frac{0x+5}{x^2+7}\\\\\frac{7x^3+5x^2+49x+5}{(x^2+1)(x^2+7)}=\frac{7x}{x^2+1}+\frac{5}{x^2+7}[/tex]

Break up integral

[tex]\int {\bigr(\frac{7x}{x^2+1}+\frac{5}{x^2+7}\bigr) } \, dx[/tex]

[tex]\int {\frac{7x}{x^2+1} } \, dx +\int {\frac{5}{x^2+7}} \, dx\\\\\int {\frac{7x}{x^2+1} } \, dx +5\int {\frac{1}{x^2+7}} \, dx[/tex]

Solve first integral

Let [tex]u=x^2+1[/tex] and [tex]du=2xdx[/tex] for the first integral. Thus, [tex]\frac{7}{2}du=7xdx[/tex]:

[tex]\frac{7}{2}\int {\frac{du}{u}}\\\\\frac{7}{2}ln(|u|)+C\\ \\\frac{7}{2}ln(|x^2+1|)+C[/tex]

Solve second integral

Since [tex]5\int {\frac{1}{x^2+7} } \, dx[/tex] is in the form of [tex]\int{\frac{1}{x^2+a^2} } \, dx[/tex], its formula is [tex]\frac{1}{a}arctan(\frac{x}{a})+C[/tex]:

[tex]5\int {\frac{1}{x^2+7} } \, dx\\\\5\bigr(\frac{1}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\bigr)\\\\\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Combine integrals

[tex]\biggr[\frac{7}{2}ln(|x^2+1|)+C\biggr]+\biggr[\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C\biggr]\\ \\\frac{7}{2}ln(|x^2+1|)+\frac{5}{\sqrt{7}}arctan(\frac{x}{\sqrt{7}})+C[/tex]

Answer:   [tex]\frac{x^{20}}{y^{15}}[/tex]

This is the same as writing (x^20)/(y^15)

===================================================

Work Shown:

[tex]\left(x^{-4}y^3\right)^{-5}\\\\\left(x^{-4}\right)^{-5}*\left(y^3\right)^{-5}\\\\x^{-4*(-5)}y^{3*(-5)}\\\\x^{20}y^{-15}\\\\\frac{x^{20}}{y^{15}}[/tex]

In the second step, I used the rule that (a*b)^c = (a^c)*(b^c)

In step 3, I used the rule (a^b)^c = a^(b*c)

In the last step, I used the rule a^(-b) = 1/(a^b)

Answer:

Cindy has $45 and Emily has $60

Step-by-step explanation:

let x be the amount of money , then

[tex]\frac{1}{2}[/tex] x + [tex]\frac{2}{3}[/tex] x = 105

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

3x + 4x = 630 , that is

7x = 630 ( divide both sides by 7 )

x = 90

Cindy has [tex]\frac{1}{2}[/tex] × 90 = $45

Emily has [tex]\frac{2}{3}[/tex] × 90 = $60

Answer:

123 milligrams

Step-by-step explanation:

76 : 3.1 = x : 5

76 * 5 = 3.1x

x = 76*5/3.1 = 123 milligrams

Answer:

20

Step-by-step explanation:

9/g+2h+5

g=3

h=6

=9/3+2(6)+5

=3+12+5

=20

hope dis helps.

pls brainliest!!!!!

Answer:

  4x +3y = -3

Step-by-step explanation:

The standard form equation can be written from ...

  (y2 -y1)x -(x2 -x1)y = (y2 -y1)x1 -(x2 -x1)y1

  (-13 -3)x -(9 -(-3))y = (-16)(-3) -(12)(3)

  -16x -12y = 12

The standard form has a positive leading coefficient, and all terms mutually prime. We can get that by dividing the equation by -4:

  4x +3y = -3

_____

Additional comment

The form we used above for the equation of the line essentially comes from the fact that the slope of a line is the same everywhere:

  (y2 -y1)/(x2 -x1) = (y -y1)/(x -x1)

Multiplying by the product of denominators and separating variable terms from constant terms gives the form used above.

Answer:

hypotenuse= 26

Step-by-step explanation:

c= a^2 + b^2

10^2 + 24^2= 26

Answer:

  $750

Step-by-step explanation:

Tim's share price changes by $2.24 -2.49 = -0.25, so the change in the value of his investment is ...

  (3000 shares)(-0.25/share) = -$750

Tim takes a loss of $750 when he sells.

Answer:

Step-by-step explanation:

$\$1170$

Bob's initial investment is given by

Initial Investment =3,000×$1.25=$3,750.

When Bob sells the shares, he sells them for

Sold for price=3,000×$0.86=$2,580.

Therefore Bob's total LOSS is given by

Loss =$3,750−$2,580=$1,170.

Answer:

The area of the small square is 1 cm^2

Step-by-step explanation:

The large square consist in four identical rectangles and one small square.

Then the area of the small square will be equal to the difference between the area of the large square and the areas of the rectangles.

Because we have 4 equal rectangles, if R is the area of one rectangle, and S is the area of the large square, the area of the small square will be:

area = S - 4*R

We know that the area of the large square is 49 cm^2

Then:

S = 49cm^2

Remember that the area of a square of side length K is:

A = K^2

Then the side length of the large square is:

K^2 = 49 cm^2

K = √(49 cm^2) = 7cm

And we know that the diagonal of one rectangle is 5cm.

Remember that for a rectangle of length L and width W, the diagonal is:

D = √(L^2 + W^2)

Then:

D = √(L^2 + W^2) = 5cm

And for how we construct this figure, we must have that the length of the rectangle plus the width of the rectangle is equal to the side length of the large square, then:

L + W = 7cm

L = (7cm - W)

Replacing this in the diagonal equation, we get:

√((7cm - W)^2 + W^2) = 5cm

(7cm - W)^2 + W^2 = (5cm)^2 = 25cm^2

49cm^2 - 14cm*W + W^2 + W^2 = 25cm^2

2*W^2 - 14cm*W + 49cm^2 = 25cm^2

2*W^2 - 14cm*W + 49cm^2 - 25cm^2 = 0

2*W^2 - 14cm*W + 24cm^2 = 0

We can solve this for W using the Bhaskara's formula, the solutions are:

W = [tex]\frac{-(-14)(+/-)\sqrt{14^{2}-4(2)(24) } }{2(2)}[/tex]

Then we have two solutions, and we only need one (because the length will have the other value)

We can take:

W = (14 cm + 2cm)/4  = 4cm

Then using the equation:

L + W = 7cm

L + 4cm = 7cm

L = 7cm - 4cm = 3cm

L = 3cm

Now remember that the area of one rectangle of length L and width W is:

R = L*W

Then the area of one of these rectangles is:

R = 4cm*3cm = 12cm^2

Now we can compute the area of the small square:

area = S - 4*R = 49cm^2 - 4*12cm^2 = 1cm^2

The area of the small square is 1 cm^2

This took me ages to complete so please brainliest

Answer:

At age 20, you will be 90 in

20 is not a perfect square.

36 = 6 times 6.

49 = 7 times 7.

68 is not a perfect square.

121 = 11 times 11.

400 = 20 times 20.

Hope this helps

Answer:

x = - [tex]\frac{7}{2}[/tex], x = - 3

Step-by-step explanation:

Given

2x² + 13x = - 21 ( add 21 to both sides )

2x² + 13x + 21 = 0 ← in standard form

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 21 = 42 and sum = + 13

The factors are + 6 and + 7

Use these factors to split the x- term

2x² + 6x + 7x + 21 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) + 7(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x + 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = - [tex]\frac{7}{2}[/tex]

Using Venn probabilities, it is found that there is a 0.65 = 65% probability that a fan item selected at random will have at least one defect.

In a Venn probability, two non-independent events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In this problem, the given probabilities are [tex]P(A) = 0.4, P(B) = 0.5, P(A \cap B) = 0.25[/tex], hence, the "or probability", also called the "at least one" probability, is given by:

[tex]P(A \cup B) = 0.4 + 0.5 - 0.25 = 0.65[/tex]

0.65 = 65% probability that a fan item selected at random will have at least one defect.

More can be learned about Venn probabilities at https://brainly.com/question/25698611

Answer:

3:5 & 18:30

Step-by-step explanation:

To find an equivalent ratio, just multiply or divide both terms by the same number. For the two I did, I divided by 3 for one, and multiplied by 2 for the other, but there are infinite possibilities. Hope this helped!

Answer:

3=x+5

Step-by-step explanation:

Answer:

x + 5 = 3

Step-by-step explanation:

"Three is 5 more than a number."

The word is indicates that 3 is the final number, or rather, what the equation equals.

Then, 5 more than a number, shows the rest of your equation. A number is just your variable, so any letter. We'll use X. Then, it says that the answer (3) is 5 more than x. So, your equation is:

x + 5 = 3

At the end of the fourth month, we would have a total number of 4800 readers. The factor by which the number changes monthly is 2 and we would have 2n number of readers the following month

Data;

The difference in number of people who read from month to month will be

[tex]0 = 300\\1 = 2 * 300 = 600\\2 = 2 * 600 = 1200\\3 = 2 * 1200 = 2400\\4 = 2 * 2400 = 4800[/tex]

At the end of the fourth month, we would have a total number of 4800 readers.

The factor by which the number changes monthly is 2. From the pervious calculation, we can see a constant increase by a factor of 2 month to month.

Since we already established that the factor by which the readers increase is by two, we can simply say that at the next month, we would have 2n number of readers.

[tex]next month = 2 * n = 2n[/tex]

Learn more on linear equations here;

https://brainly.com/question/14323743

Answer:

a. 4, b.20

Step-by-step explanation:

There are 4 quarter mile laps in 1 mile, so you multiply the miles covered by 4 to find out the quarter mile laps.

a. 1x4=4

b. 5x4=20

Answer:

a. 4, b. 20

Step-by-step explanation:

A quarter mile is 1/4 a mile is 4/4 so if Jim runs 4 quarter miles he will run a mile so 4 is your answer. Since we know that a quarter mile is 1/4 and a mile is 4/4 we multiply 4*5 and get 20.

Answer:

Step-by-step explanation:

Mark BRAINLIEST

Thank you ☺️☺️

95 times 2 is 190.

90 times 2 is 180, and 5 times 2 is 10.

180 + 10 = 190.

Answer:

Step-by-step explanation:

3ab + 7a² + 2b² - (7a² - 4ab + 2b²) = 3ab + 7a² + 2b²  - 7a² + 4ab - 2b²

Now combine like term. Like terms have same variable with same power.

= 3ab + 4ab  + 7a² - 7a²  + 2b² - 2b²

= 7ab

Answer:

umm i think A C D E ?

Step-by-step explanation:

because theyre all the same. some is just distribution. you should wait for another opinion though because im too lazy to check for B