A popular video game retailer develops apps. The total profit, in dollars per day, after x days can be modeled by the function R(x) = 3x3 – 21x2 + 21x + 45. The total cost, in dollars per day, after x days, can be modeled by the function C(x) = x2 – 2x – 3. What is (R - C)(10) and what does it mean in the context of the problem?

a
$532, the total revenue made after 10 days
b
$532, the profit made after 10 days
c
$1078, the profit made after 10 days
d
$2255, the total revenue made after 10 days

Hello,

I hope you and your family are doing well!

The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. Since the sum of 5 consecutive odd numbers is 145, we can set up the equation:

(a + (a + 4)) / 2 * 5 = 145

where a is the first term in the sequence.

Solving this equation gives us:

a = -23

The third number in the sequence is the third odd number after a, which is a + 4. Substituting -23 for a gives us:

(-23) + 4 = -19

Therefore, the third number in the sequence is -19.

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Each partner needs to pay $41 to bring the balance to $0.

What is the linear equation in one variable?

The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

Let x be the amount each partner pays.

We can set up the equation as follows:

(-123) + 3x = 0

To solve for x, we can add 123 to both sides of the equation:

(-123) + 123 + 3x = 0 + 123

This simplifies to:

3x = 123

To solve for x, we can divide both sides of the equation by 3:

(3x)/3 = 123/3

This simplifies to:

x = 41

Therefore, each partner needs to pay $41 to bring the balance to $0.

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Probability p(Royal flush)= 4/2598960 = 1/649740

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.

The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.

Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960

So, P(royal flush)= 4/2598960 = 1/649740

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The required probability will be 127/128 that getting at least one tail when tossing seven.

We know that the total number of sides on a coin [Tail, Heads] =2

The probability of getting a tail = 1/2

The  probability of getting no tail = 1 -1/2 = 1/2

According to the "at least once" rule, when a coin is tossed n times, the chance of obtaining at least one tail is given by:-

P(at least one tail) = 1 - [P(no tail)]ⁿ

In this case, n=7

Then, the probability of getting at least one tail is given by:-

P(at least one tail) = 1 - (1/2)⁷

P(at least one tail) = 1 - (1/128)

P(at least one tail) = 127/128

Thus, the required probability will be 127/128 that getting at least one tail when tossing seven.

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Answer:

12 yards

3+4+5=12

3+4=7

7+5=12

Answer:

12, needed to be multiplied ( which I don't think so) 60

Step-by-step explanation:

I really don't have a "step by step explanation" but 4+5=9+3=12

or: 4x5=20x3=60

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

For a triangle to be Right Angled , It should obey the Pythagoras Theorem

[tex]c^{2} = a^{2}+b^{2}[/tex]

c = hypotenuse

a = perpendicular side

b = base

Hence

if c = 5 , a = 3 and b = 4

Then

[tex]c^{2} = a^{2}+b^{2}[/tex]

[tex]5^{2}= 3^{2}+4^{2}[/tex]

25 = 3 + 16

25 = 25

So

It obeys the Pythagoras Theorem

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

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Answer:

Buying two T-shirts for 5 dollars is a better deal.

Step-by-step explanation:

If you bought one T-shirt for 3 dollars, that would be more than half of the money than two T-shirts. Therefore, it's a better deal to get 2 T-shirts for 5 dollars.

Answer:

[tex]e = \frac{bd}{v - bc} [/tex]

Step-by-step explanation:

[tex] \frac{v}{b } - c = \frac{d}{e } [/tex]

[tex] = > multiply \: bothsides \: by \: e[/tex]

[tex] = > \frac{v}{b} \times e - c \times e = \frac{d}{e} \times e[/tex]

[tex] \frac{ve}{b} - ce = d[/tex]

[tex] = > multiply \: both \: sides \: by \: b[/tex]

[tex] \frac{ve}{b} \times b - ce \times b = bd[/tex]

[tex] = > ve - bce = bd[/tex]

[tex] = > e(v - bc) = bd[/tex]

[tex] = > divide \: both \: sides \: by \: (v - bc)[/tex]

[tex] = > e = \frac{bd}{v - bc } [/tex]

The graph showing the transformation of the function y = 2ˣ, with points (0, -1), and (1, -4), as well as an horizontal asymptote of y = 2, indicates that the equation of the graph in the form y = A·2ˣ + k is; y = -3·2ˣ + 2

The asymptote is a line that can be drawn on the graph such that the curve of the graph approaches the line without touching it as the values of the variables increase.

The required form of the exponential equation is; y = A·2ˣ + k

Where;

k = The horizontal asymptote

The graph included in the question indicates that an horizontal asymptote is indicated by the line y = 2

= 2

Points on the graph of the transformed function are (1, -4), (0, -1)

When x = 0, y = -1, therefore;

-1 = A·2⁰ + 2

A·2⁰ + 2 = -1 - 2 = -3

A = -3

The equation for the graph is therefore;

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The values shown by the thermometer of 87 °F and 94 °F which in degrees Celsius are 31 °C and 34 °C indicates that the relationship is not a proportional relationship. The correct option is therefore;

A proportional relationship is one in which one  variable is a constant multiple of the other, such that the ratio of each data pair is a constant.

The ratio of the two temperatures are therefore;

[tex]\dfrac{87}{31}[/tex] and  [tex]\dfrac{94}{34}[/tex]

31 is a prime number, therefore'

[tex]\dfrac{87}{31} \neq \dfrac{94}{34}[/tex]

The ratio of the ordered pair of a proportional relationship  is constant, the ratio of the specified values is not constant, therefore, the relationship is not a proportional relationship.

The correct option is therefore;

No there is not a proportional relationship because 87 over 31 does not equal 94 over 34

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10ml  of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

percentage, a relative value indicating hundredth parts of any quantity.

We need to find how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

Let x = number of ml of 20% acid

x mL of 20% acid plus (20 - x )mL of 100% acid  = 20 mL of 60% acid

0.20x+1.00(20-x)=0.6(20)

0.20x+20-x=12

20-0.8x=12

Subtract 20 on both sides

-0.8x=12-20

-0.8x=-8

Divide both sides by -0.8

x=10

Hence, 10ml  of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

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The equation will be 44.50 w + 106.37 = 239.87, and it will take 3 weeks to collect money for gaming chair.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data provided in the question,

Cost of new gaming chair = $239

Savings for gaming chair = $106.37

Each week earning = $44.50

Then the expression will be,

44.50 w + 106.37 = 239.87

44.50 w = 239.87 - 106.37

w = 133.5/44.50

w = 3

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Answer:

Factor for this problem is

2(2c+1)(c+2)

Answer:(c+2)(4c+2)      

Step-by-step explanation:

Factor by grouping

(c+2)(4c+2)      

Answer:

61 is the mode.

Step-by-step explanation:

Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).

Answer:

61 is the correct answer

Answer:

4

Step-by-step explanation:

Let's think of this as a cube with layers.

(Layer = height)

If the first layer has 20, and the cube has a total of 80, we can use this equation:

80 = 20 × number of layers

Let's figure out how many times we need to multiply 20 to get 80.

20 × 4 = 80

The cubes height is 4.

Answer:

Step-by-step explanation:

The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:​

Volume = l x w x h (base area times height)

we use the inverse formula

Height = 80 : 20 =

4

Answer:

36

Step-by-step explanation:

[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]

Step-by-step explanation:

5(2+3)-3*4²

=5*5-3*16

=25-48

=-23(A)

The 7th term of the sequence is 136.6875

From the question, we have the following sequence that can be used in our computation:

12, 18, 27....

In the above sequence, we can see that the previous term is multiplied by 1.5 to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = 1.5aₙ₋₁

a₄ = 1.5 * 27

Evaluate the products

a₄ = 40.5

Solving further, we have

a₅ = 40.5 * 1.5

Evaluate the products

a₅ = 60.75

Solving further, we have

a₆ = 60.75 * 1.5

Evaluate the products

a₆ = 91.125

Solving further, we have

a₇ = 91.125 * 1.5

Evaluate the products

a₇ = 136.6875

Hence, the 7th term is 136.6875

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The probability of select 4 women from the group is, P = 35.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: You have a group of 20 people, 7 are women and the remaining people are men.

7 are women then 13 are men.

No. of ways in which 4 women can be chosen from 7 women are 7C4.

So, the probability of select 4 women from the group is,

[tex]P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35[/tex]

Hence, the probability of select 4 women from the group is, P = 35.

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The two solutions of the quadratic equation are:

x  = 1.135

x= -1.468

A general quadratic equation:

a*x^2 + b*x + c = 0

Has solutions of the form:

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

Here the quadratic equation is:

3*x^2 + x - 5 = 0

So the values are:

a = 3

b = 1

c = -5

Replacing that in the quadratic formula for the solutions we will get:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]

Thus, the two solutions are:

x = (-1 + 7.81)/6  = 1.135

x = (-1 - 7.81)/6 = -1.468

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The domain of an inverse function, f1, is the domain of a function, f(x) (x). The range of f1 is the scope of f(x) (x).

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) (= g(f(x)) = x. The initial value is fetched via a function that is its inverse.

The opposite is called inverse. In mathematics, an inverse operation is one that reverses the effects of a preceding operation. Inverse operations refers to the set of two opposing operations.

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Answer: a= (-10)

Step-by-step explanation:

step 1- move the -7 to the other side of the equal sign to combine with -17.

step 2- to do this we need to make -7 positive so instead of (-17) -7, it would be (-17) +7.

step 3- leaving you with

a= (-10) hope this helped :)

The number of handshakes that occur in Tom's workshop is 105

Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person

To find: Number of handshakes

Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.

Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]

The formula for a combination is

[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 15 and r = 2, we get

[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]

On cancelling out 13! from numerator and denominator , we get

[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]

A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.

The formula is

[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]

Where n = number of distinct objects to choose from

C = Combination

r = spaces to fill

The number of handshakes that occur in Tom's workshop is 105

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Answer:

x = 5

Step-by-step explanation:

Since the lines with red arrows are parallel, we can use the ratios

(28 - 12)/28 = 4x/35

35(16) = 28(4x)

560 = 112x

x = 560/112

x = 5

The values of the angles are m∠ A = 112.5°, m∠ B = 67.5°, m∠ C = 67.5°, and m ∠D = 112.5°

Considering the regular octagon, the sum of angles in an octagon is 1080°. This implies each angle in the octagon will be 1080/8 = 135°

Thus, you can label the angle as shown in the image attached

c + m<A + 135° = 360°  (the sum of angle at a point is 360°)

Since c = m<A (identical sides)

m<A + m<A + 135° = 360°

2 m<A = 360-135

m<A = 225/2 = 112.5°

m<B + m<A = 180°  (Between two parallel lines, consecutive interior angles add up to 180°)

m<B + 112.5° = 180°

m<B = 180-112.5 = 67.5°

m<C = <B    (base angles of isosceles trapezoids are equal)

m<C = 67.5°

m<D = m<A    (base angles of isosceles trapezoids are equal)

m<D = 112.5°

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The minimum length of the slanted poles needed to support the fly is 20 feet.

What is a Pythagoras theorem?

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

To find the minimum length of the slanted poles, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the slanted pole) is equal to the sum of the squares of the other two sides (the heights of the tent and fly).

We are given that the height of the tent is 12 feet and the height of the fly is 16 feet. The Pythagorean theorem can be written as follows:

c² = a² + b²

where c is the length of the slanted pole, a is the height of the tent, and b is the height of the fly.

Substituting in the given values, we get:

c² = 12² + 16²

= 144 + 256

= 400

Taking the square root of both sides gives:

c = √400

= 20

Therefore, the minimum length of the slanted poles needed to support the fly is 20 feet.

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According to the given information the slope of the linear function containing these points is of 1.

The graph of a linear function is a horizontal line. The following is the form of a linear transformation. a + bx = y = f(x). One regression coefficient or one predictor variables make up a linear function.

A linear function is modeled by:

y=mx+b

In which:

In this problem, the points given are: (-10, 22) and (14, 26), hence, the slope is given by:

[tex]y_2=26 ,y_1=22 ,x_2=14 , x_1=10\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\text { m }=\frac{26-22}{14-10}\\\\\m=1[/tex]

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The equation is [tex]36x-y=145[/tex].

The domain is (∞,-∞), {x,x∈R}.

What is the domain of a function?

The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.

Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).

let us take the slope of these 2 points,

[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]

Now, using the slope, we can find the required equation:

[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]

The domain for the function is (∞,-∞), {x,x∈R}.

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(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.

Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.

Given data:

Principal = $1050 per month

Time = 30 year

        = 30 × 12

        = 360 months

Interest rate = 8%  

                    = 0.08/12

                    = 0.006667 monthly

(a) We get here first maximum amount of loan by present value of annuity as

Present value of annuity = principal ×  [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex]           .........(1)

Put here value we get

value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]

value of annuity = $143097.67

(b) Total amount  = principal × time period

                            = $1050 × 360

                            = $378000

(c) Total amount of interest paid will be

interest amount = total amount paid - loan amount

interest amount  = $378000 - $143097.67

interest amount  = $234902.33

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Using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, we know that:

Jenna has 50 pieces of laundry.

She removed her 10 favorite shirts.

50 - 10 = 40

She divided the rest into 8 piles.

40/8 = 5

Therefore, using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

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