If x = 52 degrees, find the measures of angles 1, 2, and 3.

We take the positive root:

n = (-3 + 27) / 2 = 12. Therefore, there were 12 people in the original group of winners.

Let's assume that there were n people in the original group of winners, and each person's share was x dollars. Then we know that:

n * x = $90,000,000

After three more winners are declared, the total number of winners becomes n + 3. Each person's share is then reduced by $1,000,000, so the new share per person is (x - $1,000,000). We can then write:

(n + 3) * (x - $1,000,000) = $90,000,000

Expanding the equation, we get:

nx - $1,000,000n + 3x - $3,000,000 = $90,000,000

Simplifying, we get:

nx + 3x = $1,000,000n + $93,000,000

Factoring out x and n, we get:

x(n + 3) = $1,000,000(n + 3) + $90,000,000

Dividing both sides by (n + 3), we get:

x = $1,000,000 + ($90,000,000 / (n + 3))

We can substitute this expression for x in the first equation:

n * ($1,000,000 + ($90,000,000 / (n + 3))) = $90,000,000

Expanding and simplifying, we get:

[tex]$n^2$[/tex]+ 3n - 270 = 0

Using the quadratic formula, we get:

n = [tex](-3\± \sqrt{(729)) / 2[/tex]

n = (-3 ± 27) / 2

Since n has to be positive, we take the positive root:

n = (-3 + 27) / 2 = 12

Therefore, there were 12 people in the original group of winners.

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Using arithmetic operation it is obtained that the cost of the car 4 years ago was $5750.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Let C be the cost of the car 4 years ago.

According to the problem, the current cost of the car is 60% of the cost 4 years ago, so we can write -

3450 = 0.6C

Use the arithmetic operation of division -

To solve for C, we can divide both sides of the equation by 0.6 -

C = 3450/0.6

C = 5750

Therefore, the cost of the car 4 years ago was $5750.

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Answer:

To solve this problem, we need to find the present value of the cash flow stream using a discount rate of 12%. We can use the present value formula:

PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4

where PV is the present value, CF1, CF2, CF3, and CF4 are the cash flows at time 1, 2, 3, and 4 respectively, and r is the discount rate.

Substituting the values given in the problem, we get:

PV = 690/(1+0.12)^1 + 365/(1+0.12)^2 + 220/(1+0.12)^3 + 330/(1+0.12)^4

PV = 690/1.12 + 365/1.2544 + 220/1.4049 + 330/1.5735

PV = 616.07 + 290.76 + 156.51 + 209.38

PV = 1272.72

Therefore, the present value of the cash flow stream is $1,272.72.

Step-by-step explanation:

Answer:

The answer is 24 in

Step-by-step explanation:

This solution is for "SIMILAR TRIANGLES";

Let us letter the shape starting from left to right A-B-C-D-E

Angle A is similar to Angle E, so is Angle B similar to Angle D, that is, "Alternate interior angles" while Angle ACB is similar to Angle DCE, that is, "Vertical Angles";

Line AB = 5 in is parallel to line DE = 15 in

So, K = DE / AB = 15 / 5 = 3

Line CD = K * CB = 3 * 8 = 24 in

Answer:

The number is 4

Step-by-step explanation:

5x=20

5x/5=20/5

x=4

Step-by-step explanation:

so let the unknown be x

x+5-3=17

x+2=17

so then you carry +2 over to the left hand side which collecting of like terms

so we have

x=17-2

x=15

so therefore the unknown value x is 15

to check

we substitute 15 for x in the equation

let's go

so we have

15+5-3=17

now using this solve it .

I believe u can do it

or I just do it

so we hv the unknown to be x

x*5-3=17

5x-3=17

5x=17+3

5x=20

x=20/5

x=4

The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.

The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

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Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First, the shape is wrong

2(8×3)+2(8×4)+2(3×4)=

2(24)+2(32)+2(12)=

48+64+24=136

Answer:

To divide 3000 rupees between Teena and Beena so that they get 40% and 60% respectively, we need to follow these steps:

Step 1: Find the total percentage that Teena and Beena will receive together:

40% + 60% = 100%

This means that Teena and Beena will receive 100% of the total amount, which is 3000 rupees.

Step 2: Calculate the amount that Beena will receive:

60% of 3000 rupees = 0.6 x 3000 = 1800 rupees

Step 3: Calculate the amount that Teena will receive:

40% of 3000 rupees = 0.4 x 3000 = 1200 rupees

Therefore, Beena will receive 1800 rupees, while Teena will receive 1200 rupees

Answer:

6

Step-by-step explanation:

16 Ounces in a pound

6x8=48

48/8=6

Answer:

3 pounds

Step-by-step explanation:

total pie = 8

weight of 1 pie = 6 ounces

weight of 8 pie = 6 ounces × 8

                         =  48 ounces

ounce into pound

1 ounce =0.0625 (divide ounces by 16)

48 ounces ÷ 16

=3 pounds

the baker made 3 pounds od apple pie

Answer:

To find the x and y intercepts, we set x and y to zero respectively:

x-intercept: setting y = 0 gives us 6/(x^2 - 5x - 6) = 0, which has no real solutions.

y-intercept: setting x = 0 gives us s(0) = 6/(-6) = -1.

To find the vertical asymptotes, we set the denominator equal to zero and solve for x:

x^2 - 5x - 6 = 0

(x - 6)(x + 1) = 0

This gives us two vertical asymptotes at x = 6 and x = -1.

To find the horizontal asymptote, we need to look at the behavior of the function as x approaches infinity and negative infinity. As x becomes very large in magnitude, the terms involving x^2 become much larger than the terms involving x or the constant term, and so we can ignore those terms. This gives us:

s(x) ≈ 6/x^2 as x → ±∞

Therefore, the horizontal asymptote is y = 0.

In summary:

x-intercept: none

y-intercept: (0, -1)

vertical asymptotes: x = 6 and x = -1

horizontal asymptote: y = 0

If you have anymore questions, feel free to comment and I will answer them 8-5 I am on.

Step-by-step explanation:

Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .

A mathematical expression seems to be a combination of digits, symbols, and operators (like +, -,, and ) that denotes a relation or quantity. A single figure or variable can constitute an expression, as can a collection of several numbers, constants, and operators. It is possible to depict mathematical connections, functions, and processes using expressions. There are various categories into which expressions can be divided, including numerical, algebraic, polynomial, rational, and exponential expressions. These can be assessed by carrying out the relevant operations in the mathematical operation order, i.e., parentheses operations first, multiplication or division second, addition or subtraction third.

given

[tex]5x11ab^2(2a^5b^4)[/tex]

We may multiply 5x11 using the distributive property, and then multiply the variables using exponentiation rules to simplify the formula

[tex]5x11ab^2(2a^5b^4):[/tex]

[tex]55ab^2(2a^5b^4)[/tex] is equal to [tex]5x11ab^2(2a^5b^4)[/tex]

= [tex]110a^(1+5)b^(2+4)[/tex] (using the product rule of exponents)

= [tex]110a^6b^6[/tex]

Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .

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After Simplifying, we get:  [tex]5x^3y^2 + xy - 2xy^4[/tex]

Pοlynοmials are algebraic expressiοns made up οf cοefficients and variables. Occasiοnally, variables are referred tο as indeterminates.

Fοr pοlynοmial expressiοns, additiοn, subtractiοn, multiplicatiοn, and pοsitive integer expοnents are all pοssible; hοwever, divisiοn by variable is nοt. x²+x-12 is an illustratiοn οf a single-variable pοlynοmial. Three terms are invοlved in this example: x², x, and -12.

The Greek wοrds "pοlynοmial" and "nοminal," which tοgether mean "many terms," are the sοurce οf the English wοrd pοlynοmial. There is nο limit tο the number οf terms that a pοlynοmial can have.

When we add the twο pοlynοmials term by term, we get:

[tex](3x^3y^2 - 5xy^4 - 2xy) + (2x^3y^2 + 5xy^4 + 3xy) = 3x^3y^2 + 2x^3y^2 - 5xy^4 + 5xy^4 - 2xy + 3xy[/tex]

Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]

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Answer:

5x^3y^2+xy (C)

Step by Step:

(3x^3y^2 − 5xy^4 − 2xy) + (2x^3y^2 + 5xy^4 + 3xy) =

3x^3y^2 − 5xy^4 − 2xy + 2x^3y^2 + 5xy^4 + 3xy =

(3 + 2)x^3y^2 + (-5 + 5)xy^4 + (-2 + 3)xy =

5x^3y^2 + xy

hope this helps (btw it's C)

Answer: Velocity,  v= distance/time

Given: distance=95km & time= 2 hours

Velocity= 95/2 = 47.5km/hour

Step-by-step explanation:

Now, Distance= 165 km and we got velocity= 47.5km/hour

                          = 47.5 =165/time

Time taken =      165/47.5= 3hours and 50 minutes.

Therefore, Time taken to remaining 165 km of her trip is 3hours and 50 minutes.

The height and the radius of the figure will remain unchanged as the figure is being just rotated around the axis and not transformed.

A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:

Translation

Dilation

Reflection

Dilation is the only one of these changes that modifies the original shape's size; the other two just change the shape's placement.

Here in the question,

The figure is being rotated not dilated so the dimensions of the new figure will remain the same.

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Answer: Without additional information about the trap, it is not possible to determine the value of m or any other measurements of the shape. Could you please provide more information or context for the problem?

Answer:

The function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]

Step-by-step explanation:

We are given

The costs of a company are represented by the function

[tex]C(x)=3.7x+9,000[/tex]

Its revenues are represented by the function

[tex]R(x) = 4.6x[/tex]

we know that

[tex]\text{Profit = Revenue - Cost}[/tex]

[tex]P(x)=R(x)-C(x)[/tex]

now, we can plug

[tex]P(x)=4.6x-(3.7x+9,000)[/tex]

now, we can simplify it

[tex]P(x)=0.9x-9,000[/tex]

So,

the function that represents the company's profits is [tex]P(x)=0.9x-9,000[/tex]

The equation used to find the break-even point is 0.9x - 9000.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have,

The costs of a company are represented by the function

C(x) = 3.7x + 9,000

and, revenues function

R(x) = 4.6x

For Break even point

Profit = Revenue - cost

P = 3.7x + 9000 - 4.6x

P = 0.9x - 9000

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Answer:

Step-by-step explanation:

Answer:

Mark gets $4800
Sofia gets $2400

Step-by-step explanation:

Let M, S and T represent the amounts that Mark, Sofia and Tina get respectively

We have the following

M = 2S
S = M/2

T = S/2 = M/2 ÷ 2 = M/4

Therefore the ratio of M : S; T can be expressed in terms of M as
M : M/2 : M/4

Multiplying throughout by 4 gives
4M : 2M : M

Removing the common M the proportion is

4 : 2 : 1

If T = 1200 then from T = S/2, s = 2T = 2 x 1200 = 2400

Since M = 2S, M = 2 x 2400 = 4800

So

Mark gets $4800
Sofia gets $2400

The ratio of the amounts obtained
4800: 2400: 1200

Dividing by 1200 gives us
4800/1200: 2400/1200: 1200/1200

= 4 : 2 : 1

Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

Here,

The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:

V = h/3 * (A + √(A*B) + B)

where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.

In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:

A + B = 40 + 12 = 52 m²

√(AB) = √(4012) = √(480) = 4*√(30)

Substituting these values into the formula, we get:

V = 3/3 * (52 + 4√(30) + 12)

V = 68 + 4√(30)

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Answer: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.

If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.

Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.

Step-by-step explanation:

Answer:

-------------------------

Since angle α is between 0° and 90°, it is in the first quadrant and therefore all sin α, cos α and tan α are positive numbers.

Use the following identities:

Given tan α = 2.4. Using identities, find cosine as follows:

Find sine:

The value g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis is 2.

What is parenthesis?

Parenthesis, also known as round brackets, are a type of punctuation used in writing to enclose additional information within a sentence that is not essential to the meaning of the sentence, but can provide clarification, emphasis, or further explanation. They are usually shown as two curved lines facing each other, like this: ().

For example, consider the sentence: "The concert, which was held at the arena last night, was sold out (as expected)." The words "as expected" are enclosed in parentheses, indicating that they are not necessary to the main meaning of the sentence, but provide additional information that may be of interest to the reader.

Parentheses can also be used to enclose mathematical equations, citations, or references in writing.

In this problem, we first need to substitute the given values of x in the functions f(x) and g(x).

f(x) = x - 2

f(3) = 3 - 2 = 1

g(x) = 2x - 6

g(4) = 2(4) - 6 = 2

So, [tex] \frac{g(4)}{f(3)} = \frac{2}{1} = 2[/tex]

Therefore,the value of g(4)/f(3) is 2.

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Answer: 4500

Step-by-step explanation:

1st 0, 1, 2, 3 ,5 ,6 ,7 ,8 ,9

2nd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9

3rd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9

4th 1, 3, 5, 7, 9

9 x 10x 10 x 5= 4500

Answer:

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

Step-by-step explanation:

The equation for a quadratic graph can be expressed in the Vertex form:

[tex]y = a(x-h)^{2} + k[/tex]

Where:

[tex](h, k)[/tex] = Vertex of the parabola

        = Extreme point of the parabola

Step I:
By reading from the graph:

    [tex](h, k)[/tex]  = [tex](-3, 3)[/tex]

Substitute the values of h and k in the above equation:

[tex]y = a[x- (-3)]^{2} + (3)[/tex]

[tex]y = a(x + 3)^{2} + 3[/tex]

Step II:

Determine a:

Based on the shape of the graph (which is an upside down U), the value of a will be negative:

Count one unit to the right from the vertex and see how far do you go down to touch the graph:

From the graph:

It seems you need to move 2 units down

∴a = [tex]-2[/tex]

Step III:
Substitute this value of a in the above equation:

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

Answer:

11

Step-by-step explanation:

because 11+11=22 so there are no different with two 11s

Answer:

The surface area of an object is the total area of all its faces. For a cube with sides of length 9 inches, the surface area can be calculated as follows:

The cube has six faces, all of which are identical squares.

The area of one square face is 9 inches x 9 inches = 81 square inches.

Therefore, the total surface area of the cube is 6 x 81 square inches = 486 square inches.

So the surface area of a cube with sides of 9 inches is 486 square inches.

The correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.

The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

The given expression is: -5m - 3n for m = 1, n.= -4 and -2p + r for p = -3, and r = -2.

The correct steps are:

For, -5m - 3n substitute the value of m = 1 and n = -4:

-5(1) - 3(-4)

-5 + 12 = 7

For -2p + r:

-2(-3) + (-2)

6 - 2 = 4

Hence, the correct answer for the expression  is -5(1) - 3(-4) = 7 and -2p + r = 4.

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(1.5)x + 1.5 = 30 and 1.5x = 28.5 are the correct equations that Beverly could use to determine how many marbles are in the bag.

Let x be the number of marbles in the bag.

Each marble weighs 1.5 grams and the bag weighs 1.5 grams.

Therefore, the total weight of the marbles and the bag is 1.5x + 1.5 grams.

But we know that the total weight is 30 grams.

So, we can write the equation:

1.5x + 1.5 = 30

Simplifying this equation, we get:

1.5x = 28.5

Therefore, the number of marbles in the bag is x = 19.

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The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is given as follows:

0.0006 = 0.06%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 4.2, \sigma = 0.8, n = 42, s = \frac{0.8}{\sqrt{42}} = 0.1234[/tex]

The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is equivalent to the probability of a sample mean between 193.2/42 = 4.6 and 201.6/42 = 4.8.

The probability is the p-value of Z when X = 4.8 subtracted by the p-value of Z when X = 4.6, hence:

Z = (4.8 - 4.2)/0.1234

Z = 4.86

Z = 4.86 has a p-value of 1.

Z = (4.6 - 4.2)/0.1234

Z = 3.24

Z = 3.24 has a p-value of 0.9994.

Hence:

1 - 0.9994 = 0.0006 = 0.06%.

The missing section is given by the image presented at the end of the answer.

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