5x – 2 = 3125
Solve for x

The answer of the given question based on the the sentence into an equation is , 2x - 3 = 4.

In mathematics, equation is statement that asserts equality of the two mathematical expressions. It typically contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, division, exponentiation, and logarithm. An equation usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The values of the variables that satisfy the equation are called its solutions.

The sentence be translated into equation are as  follows:

2x - 3 = 4

where x is the unknown number.

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Answer:

Step-by-step explanation:

A

the central angle of the arc is π/3 radians.

What is circumference of a circle?

Circumference or perimeter of a circle refers to the measuring of its limits. Contrarily, a circle's radius influences the amount of space it takes up. If a circle is opened up and represented by a straight line, its circumference is equal to its length. It is usually measured in units like centimetres or metres. While utilising the formula, the radius of the circle is taken into account when calculating the circle's circumference. Therefore, we need to know the radius or diameter value to determine the circle's perimeter.

Central angle (in radians) = arc length / radius

In this case, we are not given the radius of the circle directly, but we know that the circumference of the circle is 6. We can use the formula for circumference to find the radius:

Circumference = 2 * pi * radius

6 = 2 * pi * radius

radius = 3 / pi

Now we can use the formula for the central angle:

Central angle (in radians) = arc length / radius

Central angle = 1 / (3/pi) = pi/3

Therefore, the central angle of the arc is π/3 radians.

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The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  [tex]\frac{2cm}{7 feet} = \frac{x cm }{yfeet}[/tex]

where y is the length of the line in real life. Solving for y, we get:

⇒  [tex]y = \frac{7 feet} {2cm} *x[/tex]  

⇒  [tex]y = 3.5 x feet[/tex]

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

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Answer:

The answer to this question is D

Step-by-step explanation:

i solved it

Answer:

y = 12x - 73

Step-by-step explanation:

We are given the line y=4(3x+2).

We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.

Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).

We can do the distributive property to distribute the 4 to both terms on the right side.

y=4(3x+2) => y=12x + 8

Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.

It is also the slope of line G.

We can replace m in y=mx+c with 12 for line G. We'll get:

y=12x + c

Now, we need to find c.

We can use the point (7,11) to help us find c.

Substitute 7 for x and 11 for y.

11 = 12(7) + c

Multiply.

11 = 84 + c

Subtract 84 from both sides

-73 = c

Substitute -73 as c.

y = 12x - 73

Answer:

10

Step-by-step explanation:

I do not know how to make a possibility tree, but I can explain it in words. the possibilities could be at lost, 10  

The speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

To find the speed of the boat in still water and the speed of the current, let's follow these steps:

Step 1: Let x represent the speed of the boat in still water, and y represent the speed of the current. The speed downstream is (x + y) and the speed upstream is (x - y).

Step 2: Use the formula distance = time × speed to write two equations based on the given information.

Downstream: 9(x + y) = 189

Upstream: 63(x - y) = 189

Step 3: Simplify both equations:

Downstream: x + y = 21 (divide both sides by 9)

Upstream: x - y = 3 (divide both sides by 63)

Step 4: Solve the system of equations by adding the two simplified equations:

2x = 24

x = 12

Step 5: Plug the value of x back into either equation to solve for y:

12 + y = 21

y = 9

So, the speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

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Esta es la pendiente de la recta tangente a la curva f(x) en el punto x = a.

La tangente de una derivada no es una operación matemática bien definida. Supongo que lo que se quiere encontrar es la pendiente de la recta tangente a la curva representada por la función f(x) cuya derivada es f'(x) = 6x^2 - 6x - 12 en algún punto x = a.

La pendiente de la recta tangente a la curva f(x) en el punto x = a está dada por la derivada de f(x) evaluada en ese punto, es decir:

m = f'(a)

Entonces, para encontrar la pendiente de la recta tangente a la curva de la función f(x) en el punto x = a, tenemos que evaluar f'(x) en x = a:

m = f'(a) = 6a^2 - 6a - 12

donde f(a) es el valor de la función en el punto x = a.

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Answer:

A

Step-by-step explanation:

the answer would be a because it is shown more than the others

Answer:A quart contains 4 cups or 2 pints while a gallon contains 16 cups or 8 pints. Hence, a liquid gallon is equal to 4 liquid quarts.

Step-by-step    please give me brainiest and have a nice day :)

The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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Answer:

Step-by-step explanation:

The equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.The price for t-shirts = $12 eachThe price for the sweatshirt = $15 eachLet's suppose x number of t-shirts and y number of sweatshirts bought.Then,12x + 15y = 120The equation represents the total number of t-shirts and sweatshirts bought if spend $120Thus, the equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120

The number line that shows the position of each country is added as an attachment

From the question, we have the following parameters to create the number line

See attachment for the label of each tick as a multiple of the power of 10⁷

Next, we represent each country on the number line

See attachment for the completed number line

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Answer: 64

Step-by-step explanation:

First you do, 237+192+179 which is 608.

Then you do, 800-608 which is 192.

Lastly, you do 192 divided by 3 which gives you 64 as your final answer. So you have to do 192/3 for the 3 7th grade classes to get an equal amount of the prize money.

                                            [tex]192/3=64 \dollars[/tex]

                                             Hope this helps!

Answer:

Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.

Step-by-step explanation:

To find the value of the truck after 12 years, we need to apply the seven-eighths decrease to the original value each year. Let's set up an equation:

Value after 12 years = $58,000 x (7/8)^12

Simplifying, we get:

Value after 12 years = $58,000 x 0.028

Value after 12 years = $1,624

Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.

Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

[tex]A(t)=P(1+r/n)^n^t[/tex], where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

[tex]5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t[/tex]

Answer:

0.25

Step-by-step explanation:

The cost per ounce of candy can be calculated by dividing the total cost of the box by the number of ounces in the box. Since 1 pound equals 16 ounces, the cost per ounce is $4.00 / 16 ounces = $0.25 per ounce.

So the cost per ounce of candy is $0.25.

Answer: 16/1 16x4 = 64/4

At the end, Antonio has 4 cups of milk leftover.

We know that Antonio has 1 gallon of mil, and he needs to use 3 quarts of milk for the recipe.

Then we need to perform a change of units, we know that:

1 gallon = 4 quarts.

Then after he uses 3 quarts, he will have 1 quart remaining, and now we want to know how many cups is that, we know that:

1 quart = 4 cups.

So Antonio has 4 cups leftover.

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The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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We can use factorization method to solve quadratic equation.

And, The value of solution of the quadratic equation is,

⇒ x = 2, 6

We have to given that;

Quadratic equation is,

⇒ x² - 8x = - 12

Now, We can simplify as;

⇒ x² - 8x = - 12

⇒ x² - 8x + 12 = 0

Factorized it as;

⇒ x² - (6 + 2)x + 12 = 0

⇒ x² - 6x - 2x + 12 = 0

⇒ x (x - 6) - 2 (x - 6) = 0

⇒ (x - 2) (x - 6) = 0

⇒ x = 2, 6

Thus, We can use factorization method to solve quadratic equation.

And, The solution is,

⇒ x = 2, 6

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Answer:

The area of a square is given by the formula A = s^2, where s is the side length. If Doug has 8 square pieces of wood, each with a side length of s centimeters, the total area of all the pieces can be expressed as:

8s^2 = 200

To solve for s, we can simplify the equation by dividing both sides by 8:

s^2 = 25

Now we can create a quadratic equation by subtracting 25 from both sides:

s^2 - 25 = 0

This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 0, and the constant term is -25. Doug can use this equation to find the side length of each piece of wood by solving for s using methods such as factoring, completing the square, or using the quadratic formula.

Answer: the missing angle has a measure of 90 degrees, which is option (d).

Step-by-step explanation:

20 + 70 + x = 180

We are able include the two known angles and after that subtract the result from 180 to induce the degree of the lost point:

20 + 70 = 90

180 - 90 = 90

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.

Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.

To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.

If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.

By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.

Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.

The time taken to reach her destination while travelling at her initial speed is 2 hours.

To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.

Therefore, the percentage increase in speed

= (30/120) x 100

= 25%.

Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.

Therefore, the correct answer is 200%.

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The payback period for Product A is 2.21 years and the payback period for Product B is 1.85 years, NPV of A = $21,215 and NPV of B = -$50,256. Product A: IRR = 28.28%, Product B: IRR = 29.58%, A: PI = 1.00, B: PI = 0.91, A: SRR = 0.49 or 49%, B: SRR = 0.44 or 44%.

Payback period is a financial metric used to evaluate the time required to recover the initial investment made in a project or investment opportunity.

To calculate the payback period, we need to find out how long it takes for the initial investment to be recovered by the annual cash inflows. We calculate the cumulative cash inflows for each year and determine in which year the cumulative cash inflows exceed the initial investment.

Product A:

Year 1: $380,000 - $170,000 - $68,000 - $86,000 = $56,000

Year 2: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $56,000 = $112,000

Year 3: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $112,000 = $168,000

Year 4: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $168,000 = $224,000

Year 5: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $224,000 = $280,000

The payback period for Product A is 2.21 years (rounded to two decimal places).

Product B:

Year 1: $460,000 - $206,000 - $108,000 - $66,000 = $80,000

Year 2: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $80,000 = $160,000

Year 3: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $160,000 = $240,000

Year 4: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $240,000 = $320,000

Year 5: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $320,000 = $400,000

The payback period for Product B is 1.85 years (rounded to two decimal places).

To calculate the net present value (NPV), we need to discount the cash inflows and outflows using the company’s discount rate of 20% and then subtract the initial investment.

Product A:

[tex]NPV = -$340,000 + ($56,000/(1+0.20)^1) + ($112,000/(1+0.20)^2) + ($168,000/(1+0.20)^3) + ($224,000/(1+0.20)^4) + ($280,000/(1+0.20)^5)[/tex]

NPV = -$340,000 + $38,611 + $64,357 + $79,396 + $81,193 + $77,658

NPV = $21,215

Product B:

[tex]NPV = -$540,000 + ($80,000/(1+0.20)^1) + ($160,000/(1+0.20)^2) + ($240,000/(1+0.20)^3) + ($320,000/(1+0.20)^4) + ($400,000/(1+0.20)^5)[/tex]

NPV = -$540,000 + $66,667 + $111,111 + $114,882 + $99,425 + $97,659

NPV = -$50,256

To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV of the cash inflows and outflows equal to zero. We can use a financial calculator or spreadsheet software to solve for the IRR.

Product A: IRR = 28.28%

Product B: IRR = 29.58%

To calculate the profitability index (PI), we divide the present value of the future cash inflows by the initial investment.

Product A:

PV of future cash inflows = $38,611 + $64,357 + $79,396 + $81,193 + $77,658 = $341,215

PI = $341,215/$340,000

PI = 1.00

Product B:

PV of future cash inflows = $66,667 + $111,111 + $114,882 + $99,425 + $97,659 = $489,744

PI = $489,744/$540,000

PI = 0.91

To calculate the simple rate of return (SRR), we divide the average annual cash inflow by the initial investment.

Product A:

Average annual cash inflow = ($56,000 + $112,000 + $168,000 + $224,000 + $280,000)/5 = $168,000

SRR = $168,000/$340,000

SRR = 0.49 or 49%

Product B:

Average annual cash inflow = ($80,000 + $160,000 + $240,000 + $320,000 + $400,000)/5 = $240,000

SRR = $240,000/$540,000

SRR = 0.44 or 44%

6a.

Based on the payback period, Product B is preferred because it has a shorter payback period of 1.85 years compared to Product A’s payback period of 2.21 years.

Based on the net present value, Product A is preferred because it has a positive NPV of $21,215 compared to Product B’s negative NPV of -$50,256.

Based on the internal rate of return, Product B is preferred because it has a higher IRR of 29.58% compared to Product A’s IRR of 28.28%.

Based on the profitability index, Product A is preferred because it has a PI of 1.00, indicating that for every dollar invested, we receive one dollar in return. Product B has a PI of 0.91, indicating that for every dollar invested, we receive only $0.91 in return.

Based on the simple rate of return, Product A is preferred because it has a higher SRR of 49% compared to Product B’s SRR of 44%.

6b. Based on the simple rate of return, Lou’s division should accept Product A because it has a higher SRR of 49% compared to Product B’s SRR of 44%. However, other measures such as the net present value and internal rate of return suggest that Product A may not be the best choice.

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Answer: 1. the probability of both balls being red is 3/8 or 0.375. 2.unlikely to occur

Step-by-step explanation:

Answer:

62.50

Step-by-step explanation:

The event is more likely to occur because there are 4 more red balls than white balls. The probability of 2 white balls selected are 37.50, which means that the probability of 2 red balls selected are 62.50.

The shape that is a concave hexagon with two pairs of congruent sides is an irregular hexagon.

A hexagon is defined as the type of polygon that is made up of six sides and six angles that sums up to 720° and also have 6 vertices.

A hexagon can be of various irregular shapes such as concave, convex and complex irregular shapes.

The properties of irregular hexagon include the following:

The concave irregular hexagon has two pairs of congruent sides that are equal in measurement.

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The cross product of (a - b) and (a + b) is: [-8, -8, -2].

Given the vectors a = (3, 4, -7) and b = (4, 5, 8), you want to compute the cross product of (a - b) and (a + b).

First, let's compute the vectors (a - b) and (a + b):

a - b = (3 - 4, 4 - 5, -7 - 8) = (-1, -1, -15)

a + b = (3 + 4, 4 + 5, -7 + 8) = (7, 9, 1)

Now, let's compute the cross product of the two vectors:

(-1, -1, -15) × (7, 9, 1) = [(-1)(9) - (-1)(1), (-15)(1) - (-1)(7), (-1)(7) - (-1)(9)] = [-8, -8, -2]

So, the cross product of (a - b) and (a + b) is: [-8, -8, -2].

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Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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