In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new book shelf is large enough to hold 10 of the books. (a) How many ways can you select and arrange 10 of the 17 books on the shelf? Notice that here we will allow the books to end up in any order. Explain. (b) How many ways can you arrange 10 of the 17 books on the shelf if you insist they must be arranged alphabetically by author? Explain. 6. How many triangles are there with vertices from the points shown below? Note, we are not allowing degenerate triangles - ones with all three vertices on the same line, but we do allow non-right triangles. Explain why your answer is correct. 14. We have seen that the formula for Pln,k) is Your task here is to explain why this is the right formula. (a) Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make? Explain your answer and why it is the same as using the formula for P(12,5). (b) Using the scenario of the 12 chips again, what does 12! count? What does 7! count? Explain. (c) Explain why it makes sense to divide 12! by 7! when computing P(12,5) (in terms of the chips). (d) Does your explanation work for numbers other than 12 and 5? Explain the formula P(n,k) = using the variables n and k.

Answer: m∠A = 72°, m∠C = 56°

Step-by-step explanation: All triangles interior angles add up to 180, This is an isosceles triangle which by rule mean that angles m∠A and m∠B and the same value of 72°. Now it becomes an equation to find m∠C, of

72 + 72 + x = 180.

144 + x = 180

x = 56

The circumcenter of a triangle formed by (4,2), (3,-3) and (2,2) is located at (3, -0.4).

The circumcenter of a triangle is the point of intersection of the three perpendicular bisectors of the sides of a triangle.

Let A = vertex at (4,2)

B = vertex at (3,-3)

C = vertex at (2,2)

Get the midpoint of each side.

midpoint = [(x₂ + x₁)/2 , (y₂ + y₁)/2]

side AB : midpoint = [(3 + 4)/2 , (-3 + 2)/2] = (3.5, -0.5)

side AC : midpoint = [(4 + 2)/2 , (2 + 2)/2] = (3, 2)

side BC : midpoint = [(3 + 2)/2 , (-3 + 2)/2] = (2.5, -0.5)

Get the slope of each side.

slope = (y₂ - y₁) / (x₂ - x₁)

side AB : slope = (-3 - 2) / (3 - 4) = 5

side AC : slope = (2 - 2) / (2 - 4) = 0/-2 = 0

side BC : slope = (2 - -3) / (2 - 3) = -5

Determine the equation of the line of each of the three perpendicular bisectors of the sides of a triangle, that passes through the midpoint and with a slope equal to the negative reciprocal of the slope of the side.

y = mx + b

perpendicular bisector of AB :

-0.5 = -1/5(3.5) + b   ;   b = 0.2   ;   y = -1/5x + 0.2

perpendicular bisector of AC :

since AC is a horizontal line, x = 3

perpendicular bisector of BC :

-0.5 = 1/5(2.5) + b   ;   b = -1   ;   y = 1/5x - 1

Since x is already equal to 3, substitute the value of x in the two other equation and solve for y.

y = -1/5x + 0.2

y = -1/5(3) + 0.2

y = -0.4

y = 1/5x - 1

y = 1/5(3) - 1

y = -0.4

Hence, the circumcenter of the triangle is located at (3, -0.4).

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Option B is the statement which is  not sufficient to prove the congruence of two triangles.

In all the other options we get to know about three parts of the triangle using which we can prove their congruency .

Option B says ,

Two sides of one triangle are congruent respectively to the two sides of another triangle.

In this statement there is no mention about the third side or a third angle.

Therefore, using option B we cannot prove the congruence of two triangles.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

" ≅ " is the congruence symbol.

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The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.

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a) A dollar is 40% of four dimes.

b) 8% of a dollar is equal to 1 nickel and 3 cents.

c) A dollar is equal to 135% of 5 quarters and 1 dime.

A value or ratio stated as a fraction of 100 is known as a percentage in mathematics. Frequently, the percent symbol (%) or the abbreviation "pct" are used to indicate the percentage. The word "percent" derives from "percent," a contraction of "per centum," which meant per hundred.

1 dime equals 10 cents, as we all know. Thus, 4 dimes equal 40 cents. 4 dimes are consequently 40% of a $1.

We are aware that a nickel costs five cents and a penny one cent. Therefore, 8% of a dollar is equal to 1 nickel and 3 cents.

We are aware that a quarter equals 25 cents and a dime equals 10 cents. 5 quarters and 1 dime are therefore 135% of a dollar.

Therefore,

A dollar is 40% of four dimes.

8% of a dollar is equal to 1 nickel and 3 cents.

A dollar is equal to 135% of 5 quarters and 1 dime.

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The complete question is:

"What percentage of a dollar is the value of each coin combination?

a. 4 dimes

b. 1 nickel and 3 pennies

c. 5 quarters and 1 dime"

The total amount that should be left including 18% tip is $176.5

What is percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the percent sign, "%". A % is a number without dimensions and without a standard measurement.

We are given that you and your friend ordered a meal worth of $149.58

Now also we want to leave a tip of 18% of the total amount.

Hence the total amount that should be left is needed to be calculated

To do that we first calculate the 18% of the total amount then add it to the original amount

18% of the total value is

[tex]149.58*\frac{18}{100}\\ =26.92[/tex]

This is the value of tip that needed to be given

Now we add this to the original price

We get

149.58+26.92

=176.50

The total amount that needs to be paid with tip is $176.5

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Answer:

h(t) - 94t + 129.

Step-by-step explanation:

The amount must be $164,313.82 deposited in her local bank. which is the correct answer would be an option (C).

For yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.

Let's assume that the amount would be P deposited in her local bank

As per the given question, the required solution would be as:

P = 18000[1 - (1 + 9/100)⁻²⁰]/0.09

P = 18000[1 - (1 + 0.09)⁻²⁰]/0.09

P = $164,313.82

Therefore, the required amount must be $164,313.82 deposited in her local bank.

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On solving the provided question, we got to know that ∠ H + ∠ K = 45°.

K therefore has a 135° measure.

A unique kind of quadrilateral created by parallel lines is a parallelogram. A parallelogram might have different angles between its neighboring sides, but it must have parallel opposite sides in order to be considered one. If a quadrilateral's opposite sides are parallel and congruent, it is a parallelogram. As a result, a parallelogram is a quadrilateral with both pairs of opposite sides being parallel and equal.

the K-value of the angle.

First of all, we should be aware that the sum of the adjacent angles in the parallelogram ABCD, which has the angles A, B, C, and D, is 180°.

[tex]angle A + angle B = 180\\ angle B + angle C = 180\\ angle C + angle D = 180\\ angle A + angle D = 180[/tex]

They're considered to be a linear pair.

As a result, the parallelogram HIJK, whose angle H = 45°, is what we have.

Therefore, ∠ H +∠K = 180° (linear pair),

∠ K = 180° - 45°

∠ K = 135°,

and

∠ H + ∠ K = 45°.

K therefore has a 135° measure.

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8

x = 6

9

x=7

10

x= 15

see explanation in image

because you know that m and n are parralell you can use the vertical angle theorem as well as the fact that lines in a straight angle add to 180

if you have any questions just comment

After 3 seconds will it take for it to fall 112 feet.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given:

The distance s that an object falls varies directly with the square of the time, t , of the fall.

⇒ D = KT^2

Where D is the distance

T is the time

K is the proportionality constant

As an object falls 16 feet in one second.

⇒  D = 16, T = 1

⇒ 16 = K(1)^2

   16 = K

Therefore, the equation becomes

D = 16T^2

To find the how long will it take for it to fall 112 feet.

Here D = 112 feet

Plug D = 112 in the above equation.

112 = 16T^2

7 = T^2

T = √7

T = 2.65

T ≈ 3

Hence after 3 seconds will it take for it to fall 112 feet.

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The diameter of the top of the trash ball is 5 inch.

A straight line that runs through the middle of a body or figure from the sideways particularly a circle or sphere is called as a diameter of a circle or sphere.

Given that the diameter of top of the trash can is 20 inch.

And the diameter of trash ball is 1/4th of the diameter of trash can.

The diameter of trash ball = 1/4 ( the diameter of trash can )

The diameter of trash ball = 1/4 (20 inch)

The diameter of trash ball = 20/4

The diameter of trash ball = 5 inch.

Therefore, the diameter of the top of the trash ball is 5 inch.

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The complete question is;

Raquel is playing a game where she throws balled-up paper called a “trash ball” into her trash can. The diameter of the top of the trash can is 20 inch . Raquel wants the “trash ball” to have a diameter that is 1/4 the diameter of the top of the trash can. What should the diameter of Raquel's “trash ball” be? .

Of the following, a sequence which is not a geometric sequence is 3, 6, 9, ... (Option A)

A geometric sequence refers to a sequence in which each term is determined by multiplying the preceding term by the same value which is called the common ratio (r). Hence, the common ratio determined by dividing a term by preceding term is constant in a geometric sequence.

In the given options,

A) r = 6/3 ≠ 9/6

B) r = 9/3 = 27/9 = 3

C) r = 8/4 = 16/8 = 2

D) r = -7/7 =7/-7 = -7/7 = -1

As the common ratio r is constant for option B, C and D, they are geometric sequences. The ratio between consecutive terms is not the same for option A, it is not a geometric sequence.

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Answer:

So, it will take between 4 and 5 bags of quickrete to fill the tube.

Step-by-step explanation:

To find the volume of the sonotube, you can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the tube and h is the height.

First, you need to find the radius of the tube. The diameter of the tube is 10 inches, so you can divide that by 2 to get the radius: r = 10 inches / 2 = 5 inches.

Then, you can plug the radius and height into the formula to find the volume of the tube: V = πr^2h = π(5 inches)^2(48 inches) = about 235.61 inches^3.

To find the number of bags of quickrete you will need to fill the tube, you need to convert the volume of the tube to cubic feet and then divide by the number of cubic feet in a bag of quickrete.

First, you can convert the volume of the tube to cubic feet by dividing by 1728 (the number of cubic inches in a cubic foot): V = 235.61 inches^3 / 1728 inches^3/ft = about 0.14 cubic feet.

Then, you can divide this volume by the number of cubic feet in a bag of quickrete to find the number of bags you need: 0.14 cubic feet / (1 cubic foot / 30-40 bags) = about 4-5 bags.

So, it will take between 4 and 5 bags of quickrete to fill the tube.

For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

In the given question, we have to state true or false for the given statement.

In our programs, we frequently want to be able to "conditionally" execute certain actions, i.e., "if this is true, then do X, but if this other thing is true, then do Y." It's similar to how we dress when we get out of bed: "If it's sunny, I wear sunglasses, but if it's raining, I take an umbrella." In our programs, we can use if statements, if/else statements, and conditional expressions to do things conditionally.

If a condition is true, an if statement instructs the computer to run a certain piece of code. Only if x is bigger than 0 do we output a message in the following code:

We would be able to see the message on the canvas since x is 5, which is bigger than 0. If we modified x to -1, the message wouldn't appear at all because x wouldn't be greater than 0.

A conditional expression is one that can only be evaluated as either true or false, and the x > 0 qualifies as one. A boolean value is one that can only be either true or false (as opposed to a number or a string). For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

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The right question is:

State in predicate calculus that an array of int, say a, is sorted. You may use the Java expression syntax (e.g., a.length, a[i], ==, and <) and logical operators (&&).

Simplifying an exponential equation can be done by using different laws of exponents.

In this case, we can use the power rule and negative exponent rule

Power rule:

[tex](a^x)^y=a^x^y[/tex]

Negative exponent rule:

[tex]a^-^y=\frac{1}{a^y}[/tex]

1. Use the negative exponent rule

[tex](10x^2)^-^3=\frac{1}{(10x^2)^3}[/tex]

2. Use the power rule and simplify

[tex]10^3=1000[/tex] and [tex](x^2)^3=x^6[/tex]

∴[tex]\frac{1}{1000x^6}[/tex]

Answer:

= 10x⁻⁶

Step-by-step explanation:

2*-3 = -6

then:

[tex]10x^{2^{-3}} = 10x^{-6}[/tex]

= 10x⁻⁶

The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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The area of the rhombus inside a square formed by two equilateral triangles is 1.856 cm².

Here we have to find the area of the rhombus.

Data given:

sides of a square = 2√3 cm

Let ABCD be a square whose sides are 2√3 cm.

As two triangles are inscribed in a square so ABE and CDG be equilateral triangles in square ABCD.

The altitude of the equilateral triangle ABE and CDE = 2√3 sin 60°

= 2√3 × √3/2

= 3cm

The diagonal EG of the rhombus EFGH = 2√3 - 2(2√3 - 3)

= 2.535 cm

The diagonal FH of the rhombus, EFGH = 2√3 - 2(√3tan 30°)

= 1.464 cm

The formula for the area of the rhombus = d1 × d2 / 2

where d1 and d2= diagonal of a rhombus

Now the area of the rhombus EFGH = EG × FH / 2

= 2.535 × 1.464 / 2

= 1.856 cm².

Therefore the area of the rhombus is 1.856 cm².

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Answer: Two dimensions.

Straight sides.

Congruent (equal-length) sides.

An interior and exterior.

Equal interior angles.

Equal exterior angles.

Step-by-step explanation:

Answer: 32% probability of going to the beach given the information provided in the weather forecast.

Step-by-step explanation:

The probability of going to the beach is equal to the probability of it not raining times the probability of going to the beach if it does not rain. Therefore, the probability of going to the beach is equal to (1 - 0.6) * 0.8 = 0.4 * 0.8 = 0.32.

Answer:2

Step-by-step explanation:took a test

The terminal point is 0.36 radii to the right of the circle's center.

The terminal point is 0.93 radii above the circle's center.

Here, the 3 O'clock line is OA and the terminal point is on the line OP.

The angle θ = 1.2 radians

Let the radius = r

The distance of the terminal point to the right of the center = OQ

= r × cos θ

= r × cos 1.2  

= r × 0.36

So, it is equal to 0.36 radii

The distance of the terminal point above the center = PQ

= r × sin θ

= r × sin 1.2

= r × 0.93

So, it is equal to 0.93 radii.

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We can compute Amy's monthly budget for each question using division operations, as follows:

1. Amy's monthly budget for textbooks and course supplies is $100.

2. Amy's monthly budget for rent, utilities, and food is $1,422.

3. Amy's monthly budget for personal and miscellaneous costs is $251.

4. Amy's total monthly budget is $1,825.

The total monthly budget is the total budget divided by the period (nine months).

Division operations can be used to determine the individual monthly budgets for each expense class by dividing the total cost by 9.

Textbooks and Course Supplies =         $900      $100

Rent, Utilities, and Food =                   $12,798   $1,422

Personal & Miscellaneous Expense = $2,259     $251

Transportation =                                      $468       $52

Total non-tuition expenses =             $16,425  $1,825 ($16,425/9)

The number of months for the year = 9 months

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Answer:

9

Step-by-step explanation:

8x - 4x = 36

4x = 36

x = 36/4 = 9

Answer:

9

Step-by-step explanation:

8n-4n=36

n=9

8(9)-4(9)=36

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

Hence, in this problem, the function g(x) is exponential, as when the input x is increased by one, the output g(x) is multiplied by two.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

Hence, in this problem, the function f(x) is linear, as when the input x is increased by one, the output f(x) is increased by a constant of six.

The problem is given by the image shown at the end of the answer.

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Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.

Function is a relation or expression involving one or more variables.

The zeros are:

x = 3/2

x = -3/2

x = (3/2)*i

x = (-3/2)*i

First, for a given function f(x), we define the zeros as the values of x such that:

f(x) = 0.

Then we must solve:

f(x) = 16*x^4 - 81 = 0

Solving this for x leads to:

16*x^4 = 81

x^4 =  81/16

x^2 = ±√(81/16) = 9/4

x = ±√±(9/4) = ±3/2 and ±(3/2)*i

So there are 4 zeros, and these are:

x = 3/2

x = -3/2

x = (3/2)*i

x = (-3/2)*i

Where the two complex zeros come from evaluating the second square root on

-9/4.

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Answer:

Option B

Step-by-step explanation:

Use the formula

[tex]x = \frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex]

now input the values. In equation [tex]x^{2} - 5x + 7 = 0[/tex], a = 1, b = -5 & c = 7

By taking positive sign we get,

[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

⇒[tex]x = \frac{-(-5)+\sqrt{(-5)^{2}-4.1.7 } }{2.1}[/tex]

⇒[tex]x = \frac{5+\sqrt{25-28 } }{2}[/tex]

⇒[tex]x = \frac{5+\sqrt{-3 } }{2}[/tex]

In the same way, by taking minus sign, we get [tex]x = \frac{5-\sqrt{-3 } }{2}[/tex]

The sum of the two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8 is 11x³-2x²+3x+11.

Algebraic expressions called polynomials include coefficients and variables. For polynomial expressions, we can perform mathematical operations like addition, subtraction, multiplication, and positive integer exponents. Polynomial addition is the process of adding like terms from two or more algebraic equations while maintaining the sign of each term.

Here, given two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

First, arrange the given polynomials. The polynomials were already arranged from the increasing to decreasing order of degree. Then,

(4x³+2x²-4x+3)+ (7x³-4x² +7x+8)

Second, group the like terms from both polynomials.

(4x³+7x³)+(2x²-4x²)+(-4x+7x)+(3+8)

Now, simplifying the combining terms, we get,

11x³-2x²+3x+11

The answer is 11x³-2x²+3x+11.

The complete question is -

Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. Find the sum of 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

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The value of a in the diagram is 24°

a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

From the diagram the three angles of the triangle are a + 36, 3a, 2a

a + 36 + 2a + 3a = 180( sum of angles in a triangle is 180°)

6a + 36 = 180

6a = 180 - 36

6a = 144

a = 144/6

a = 24°

In conclusion the value of a is 24°

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