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Pamela has a box that contains six books of fiction, seven books of humor, five books of plays, and two books of adventure. She removes one book from the box at random. Then places the book back in the box and randomly removes another book. What is the probability that Pamela first removes a book of humor followed by a book of plays?


A. 3/5



B. 1/8



C. 7/26



D. 7/80

ANSWER

B,C,E

EXPLANATION

The given exponentiial expression is

[tex] {7}^{8} \times 7 = {7}^{8 + 1} = {7}^{9} [/tex]

The expression that simplify to

[tex] {7}^{9} [/tex]

are all equivalent to the above expression.

A

[tex] {7}^{3} \times {7}^{3} = {7}^{3 + 3} = {7}^{6} [/tex]

B

[tex] \frac{ {7}^{18} }{ {7}^{9} } = {7}^{18 - 9} = {7}^{9} [/tex]

C

[tex]( {7}^{3} )^{3} = {7}^{3 \times 3} = {7}^{9} [/tex]

D

[tex] {7}^{4} + {7}^{5} = {7}^{4} (1 + 7) = 8( {7}^{4} )[/tex]

E.

[tex] {7}^{4} \times {7}^{5} = {7}^{4 + 5} = {7}^{9} [/tex]

Therefore options B, C and E are all equivalent to the given expression.

Answer:

1/6

Step-by-step explanation:

Since anything to a negative power is 1/(a^b) where the original was a^-b, we get 6^-1 is 1/6.

6^(-1) = 1 / 6

The process of how to work out of the fractions as multiplications to each other is the simple 1:

Since anything to the negative power is 1/(a^b)

where the original were a^-b,

we get 6^-1 is 1/6.

In this we have to learn to add, or subtract, or multiply, and divide fractions or use these operations to solve the problems. Students need the clear-cut model of the fraction in order to come the grips with all the arithmetic operations. The shift of the emphasis by the multiple.

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Answer:

The lateral area is [tex]LA=125\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a right prism is equal to

[tex]LA=PH[/tex]

where

P is the perimeter of the base of the prism

H is the height of the prism

in this problem we have

[tex]P=25\ in[/tex]

[tex]H=5\ in[/tex]

substitute

[tex]LA=(25)(5)=125\ in^{2}[/tex]

Answer:

[tex]\boxed{\bold{53}}[/tex]

Explanation:

Rewrite Equation:

47 + (2 · 3)

Solve:

Follow PEMDAS Order Of Operations

2 · 3 = 6

= 47 + 6

Add

47 + 6 = 53

= 53

Mordancy.

The problem evaluates the expression 47 + 2d, by substituting d = 3. This results in 47 + 2*3, which simplifies to 47 + 6. The final answer is 53.

This is a simple algebraic problem. The expression you're asked to evaluate is

47 + 2d

and you've been told to substitute

d = 3

. So substituting, we get 47 + 2*(3). The multiplication operation takes precedence according to the order of operations, so next we calculate 2*3 to get 6. Adding this to 47 gives us 53. Therefore, the solution to 47 + 2d, for d = 3, is 53.

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ANSWER

True

EXPLANATION

The given trigonometric equation is:

[tex] { \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

We take the LHS and simplify to arrive at the RHS.

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x}{{ \cos}^{2} x} + 1[/tex]

Collect LCM on the right hand side to get;

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x + {\cos}^{2} x}{{ \cos}^{2} x} [/tex]

This implies that

[tex]{ \tan}^{2} x + 1 = \frac{1}{{ \cos}^{2} x} .[/tex]

[tex]{ \tan}^{2} x + 1 = {( \frac{1}{ \cos(x) }) }^{2} [/tex]

[tex]{ \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

This identity has been verified .Therefore the correct answer is true.

Final answer:

The equation tan²(x) + 1 = sec²(x) is true and is derived from the fundamental Pythagorean trigonometric identity.

Explanation:

The statement tan²(x) + 1 = sec²(x) is true. This is based on a well-known trigonometric identity from mathematics.

In trigonometry, the Pythagorean identity for tangent and secant states that:

tan²(x) + 1 = sec²(x)

Which comes from the primary Pythagorean identity:

sin²(x) + cos²(x) = 1

by dividing each term by cos²(x) and recognizing that:

tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x).

Step-by-step explanation:

Here is a table.

To complete the table of values for the equation y = 3 - 2x, we substitute different x values into the equation to get the corresponding y values. Thus, values for y will depend on the chosen x values.

The equation given is y = 3 - 2x. To complete the table of values for this equation, you need to substitute different values of x into the equation and solve it to get the corresponding y-values. For example, if x = 0, then y = 3 - 2(0) = 3. Following this process, you can generate a large number of points that satisfy the equation and represent these as a table of x and y values.

Below is an example of how the table might look:

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Answer:

They are equal

Step-by-step explanation:

8/10 is 80% of 10 and 80/100 is 80% of 100

Check the picture below.

so is horizontal parabola, meaning the squared variable is the "y".  It has a "p" distance of 2 units, let's notice that it opens to the right, meanign "p" is positive.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{4p(x- h)=(y- k)^2} \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ p=2 \end{cases}\implies 4(2)(x-0)=(y-0)^2\implies 8x=y^2\implies x=\cfrac{1}{8}y^2[/tex]

Answer:

C. 40x^3+70x^2+86x+42

Step-by-step explanation:

Answer:

Step-by-step explanation:

go to the left by two

Answer:

10 < [tex]\sqrt{111}[/tex] < 11

Step-by-step explanation:

The square root of 111 is approximately 10.536.

A number smaller than this is 10.

A number larger than this is 11.

Answer:

±8 = x

Step-by-step explanation:

The square root of any number is both negative and positive.

I am joyous to assist you anytime.

The slope is 3/1 or 30/10.

Explanation:

You subtract 96 and 66 which equals 30. Then you subtract 30 and 20 which then equals 10. Then you simplify it which then equals 3/1

Answer:

16.67

Step-by-step explanation:

3x² - 10 = 40

3x² = 40 + 10

x² = 50

x = 50 / 3

x = 16.67

Answer:

±5√6 / 3

Step-by-step explanation:

3x² - 10 = 40

3x² = 50

x² = 50/3

x = ±√(50/3)

x = ±5 √(2/3)

Writing in proper form:

x = ±5 (√2 / √3) × (√3 / √3)

x = ±5√6 / 3

Answer:

There are 2 correct answers. See below.

Step-by-step explanation:

The center of a regular polygon is the center of an inscribed and a circumscribed circle.

The center of a regular polygon is the center of the circumscribed circle, which touches all the vertices of the polygon equally.

The center of a regular polygon is considered the center of the circumscribed circle. This is the circle that touches all the vertices (corners) of the polygon. When dealing with a regular polygon, which has all sides and angles equal, the center of this polygon is also the center of the circle that encloses it. This special circle is known as the circumscribed circle or circumcircle. The center is equidistant to all vertices of the polygon. The centroid of a polygon, which is the geometric center where all the corner points balance evenly, is analogous to the center of the circumscribed circle in regular polygons.

Answer:

sin(mod(π/2 -x, π) -π/2) . . . . except undefined at odd multiples of π/2

Step-by-step explanation:

The derivative of the modulus of the cosine function is the same as the derivative of the cosine function between cusps: -sin(x), for -π/2 < x < π/2.

There are many ways to make that pattern repeat with period π. one of them is this:

(d/dx)|cos(x)| = sin(mod(π/2 -x, π) -π/2) . . . . . except undefined at x=π/2+kπ, k any integer

___

The graph shows the modulus of the cosine function along with its derivative as computed by the graphing calculator and its derivative as defined above.

Answer:

14 h. 30min - 15h. 30

Step-by-step explanation:

Becuase the time varies by 15 minutes each, just find the difference after  adding and subtracting and then add the nap and sleep time.

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

The first number mentioned is the least because it is the smallest, and the final number listed is the greatest because it is the biggest.

A specific little child has a typical rest of around two hours and rest for 13 hours around evening time. rest time and evening rest can each differ by around 15 minutes.

The minimum amount of the time is calculated as,

⇒ 2 - (15/60) + 13 - (15/60)

⇒ 15 - 0.5

⇒ 14.5 hours

The maximum amount of the time is calculated as,

⇒ 2 + (15/60) + 13 + (15/60)

⇒ 15 + 0.5

⇒ 15.5 hours

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

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Answer:it is an answer isn't it.

Step-by-step explanation:

Answer:

10 possible outcomes

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7}

Step-by-step explanation:

As there are 5 vowels and 2 numbers that have to be chosen, the total outcomes are

= 5x2 = 10

Each vowel can be chosen with 6 or with 7

Let S be the sample space

a vowel will be chosen first then there is possibility that either the number chosen with it is either 6 or 7 so each vowel will have two possible outcomes with the number

S = {a6, a7, e6, e7, i6, i7, o6, o7, u6, u7} ..

Answer:

[tex]y+2= -3(x-2)[/tex]

Step-by-step explanation:

The slope of the line below is [tex]-3[/tex]

We need to find point slope form of the line.

point slope form of the line formula is

[tex]y-y_1= m(x-x_1)[/tex]

Where m is the slope and (x1,y1) is the point on the line

From the given graph , point on the line is (2,-1)

slope is  [tex]-3[/tex]

Lets plug in the slope and the point in the formula

[tex]y-(-2)= -3(x-2)[/tex]

[tex]y+2= -3(x-2)[/tex]

ANSWER

[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]

EXPLANATION

The given rational expression is

[tex] \frac{x - 4}{2 {x}^{2} } \div \frac{2x + 3}{x + 4} [/tex]

We multiply by the reciprocal of the second function to get:

[tex]\frac{x - 4}{2 {x}^{2} } \times \frac{x + 4}{2x + 3} [/tex]

The product of the numerators are difference of two squares:

When we multiply out and expand we get:

[tex]\frac{ {x - }^{2} - 16}{4 {x}^{3} + 6 {x}^{2} } [/tex]

Answer:

Step-by-step explanation:

Answer:

Area of circle = 25.12 inches²

Step-by-step explanation:

Area of circle = π × r²

Area of circle = 3.14 × 8 ( We are given the diameter not the radius )

Area of circle = 25.12 inches²

Answer:

The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Lets solve the problem

- Look to the answer

# Answer D is wrong because the un-shaded octagon is not a vertical

  translation because it is not directly under the shaded octagon.

# Answer C is wrong because the un-shaded octagon is not a

  horizontal translation because it is not directly to the left of

  the shaded octagon

# Answer B is wrong because the un-shaded octagon is not a dilation

  because it is not smaller or bigger than the shaded octagon it has

  the same size

# The answer A is the right because:

∵ The shaded octagon in the first quadrant and the un-shaded

   octagon in the third quadrant

∵ The vertex of (2 , 1.5) has image (-1.5 , -2)

- The coordinates are replaced by each other the their signs are

 changed

∴ The shaded is reflected across the line y = -x

* The un-shaded octagon is a reflection because it is a flip over a

  diagonal line (y = -x)

Answer:A

Step-by-step explanation:

Answer:

[tex]\implies m\angle DAC=30\degree[/tex].

Step-by-step explanation:

DC meets  the circle at right angles because it is a tangent.

Triangle COD is a right triangle, with OD being the hypotenuse.

[tex]\cos m\angle COD=\frac{OC}{OD}[/tex].

But [tex]OC=\frac{1}{2}OD[/tex],

[tex]\implies \cos m\angle COD=\frac{\frac{1}{2}OD}{OD}[/tex].

[tex]\implies \cos m\angle COD=\frac{1}{2}[/tex].

[tex]\implies m\angle COD=\cos ^{-1}(\frac{1}{2})[/tex].

[tex]\implies m\angle COD=60\degree[/tex].

But [tex]m\angle DAC=\frac{1}{2} m\angle COD[/tex].

[tex]\implies m\angle DAC=\frac{1}{2}(60\degree)[/tex].

[tex]\implies m\angle DAC=30\degree[/tex].

Answer:

See below

Step-by-step explanation:

Actully, incase some people input it wrong, the answer is 30 degrees. DEGREES<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

so input 30 degrees

Answer:

6x - 24y

Step-by-step explanation:

First, eliminate the braces by doing the multiplications:

-30x - 12y + 36x - 12y

Then group together the same variables:

6x - 24y

arguably, you could factor out a 6 and get:

6(x-4y)

but it is a matter of taste if that is simpler...

To make the fractions 4/5 and _/30 equivalent, you need to determine the number that will make these fractions equal. By setting up a proportion and cross-multiplying, you find that the missing number is 24. Thus 4/5 is equivalent to 24/30.

The equation you are tasked to solve is 4/5 = _/30. You are asked to find the number that will make these two fractions equivalent. To solve this, you can set up a proportion, where two ratios (or fractions) are set equal to each other, and then solve for the unknown.

You have the fractions 4/5 and _/30. Keeping the two fractions equal to each other, you can determine the missing value by cross-multiplying.

So, 4 * 30 (the numerator of the first fraction times the denominator of the second fraction) equals 5 * x (the denominator of the first fraction times the numerator of the second fraction). This gives you: 120 = 5x. Solving for x, divide 120 by 5, which equals 24.

Therefore, the fraction 4/5 is equivalent to 24/30.

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ANSWER

5

EXPLANATION

The given function is

f(x)=-2x+3

We want to find the corresponding value of x=-1

We substitute x=-1 to obtain

f(-1)=-2(-1)+3

We multiply to get;

f(-1)=2+3

We now add to obtain:

f(-1)=5

The last choice is correct

Answer:

39.2 units^2.

Step-by-step explanation:

The area are in the ratio of the corresponding  linear measurements squared so

A / 80 = 7^2 / 10^2

A / 80 = 0.49

A = 80 * 0.49

=  39.2.

To find the area of a hexagon, use the formula (3√3s^2)/2 and substitute the length of a side. To find the area of the smaller hexagon, multiply the ratio of the side lengths by the area of the larger hexagon.

To find the area of a regular hexagon, you can use the formula:

A = (3√3s^2)/2

In order to find the area of the smaller hexagon, you need to know the ratio between the lengths of the sides of the smaller and larger hexagons. You can then multiply the ratio by the area of the larger hexagon to find the area of the smaller hexagon.

Find the value of the missing angle for the following oblique triangle.

C = 58.1°

The value of missing angle C for the Oblique triangle is [tex]58.1^{0}[/tex]

In given oblique triangle, angle A is [tex]67.7^0[/tex] and angle B is [tex]54.2^0[/tex].

What is Oblique triangle?

An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all three angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).

As we know that, Sum of all angles of a triangle is [tex]180^0[/tex].

A + B + C =[tex]180^0[/tex]

[tex]67.7^0 + 54.2^0 + C = 180^0[/tex]

[tex]C = 180^0 - 121.9^0[/tex]

[tex]C = 58.1^0[/tex]

Thus, the missing angle C of oblique triangle is [tex]58.1^0[/tex].

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