What is the value of x
in the rational equation x5=618

The equation which represents the relationship between the variables is; y = 5x + 2.

As evident in the task content;

To define the variables;

Let x = amount of time in years and

y = weight of the carp.

Since the carp grows 5 pounds each year and initially weighs 2 pounds.

By the slope-intercept form equation;

y = mx + c;

Where,

m = 5 pounds

c = 2 pounds

Therefore, the required relationship which represents the situation is; y = 5x + 2.

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Answer:

Step-by-step explanation:

Firstline = 33%

Second line = 36%

Answer:

Firstline = 33%

Second line = 36%

Step-by-step explanation:

The roots in simplest form are x=-8+6i and x=-8-6i.

The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.

To complete the square, follow the steps below:

1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2

2. Square the coefficient of the x^2 term: (5x^2/2)^2

3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2

4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140

5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140

6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10

7. Simplify:
x = -8 ± √14  / 1

Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:

1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:

-5x^(2)-80x=140

2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:

-5(x^(2)+16x)=-140

3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:

-5(x^(2)+16x+64)=-140+320

4. Simplify the right side of the equation:

-5(x+8)^(2)=180

5. Divide both sides of the equation by -5:

(x+8)^(2)=-36

6. Take the square root of both sides of the equation:

x+8=±6i

7. Solve for x:

x=-8±6i

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The baker needs a total of 3 hours to decorate 4 1/2 cakes.

To decorate one cake, the baker needs 2/3 hour.

To find out how long it takes to decorate 4 1/2 cakes, we need to multiply the time for one cake by 4 1/2 i.e. 9/2

Time for 4 1/2 cakes = (2/3) x (9/2)

When the products are evaluated, we have

Time for 4 1/2 cakes = 3

So, the time taken is 3 hours

Therefore, the baker needs a total of 3 hours to decorate 4 1/2 cakes.

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Answer: a = 20°

Step-by-step explanation:

     We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. We will write an equation to solve.

               a = 180° - 90° - 70°

               a = 20°

Answer:

20 degrees

Step-by-step explanation:

Straight Angle: 180 degrees

You know that there is a right angle which is 90 degrees. You can subtract 180 by 90 to get 90. Then you are given an angle measurement of 70 degrees. Subtract 70 from 90 to get 20.

20 is the measure of the missing angle

Answer:

See below.

Step-by-step explanation:

We are asked to "expand", rather distribute the expression.

We can Distribute due to the Distributive Property.

The Distributive Property is a property that allows us to distribute the multiplier into numbers in the parentheses.

Let's distribute for this expression.

Distribute:

[tex]-5(-2d + 6)=(-5 \times -2d)+(-5 \times 6)= 10d -30[/tex]

Our distributed expression is 10d - 30.

The average number of likes per writer and the average number of comments per writer can be used to determine which website has more user engagement per a single writer

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the average number of likes per writer be L

Let the average number of comments per writer be C

Now , the number of writers for website A = 5

The number of writers for website B = 11

The average number of likes per post for A = 3500 likes

So , the average number of likes per writer A = ( 3500 / 5 ) = 700 likes

And , the average number of likes per writer B = ( 3500 / 5 ) = 700 likes

The number of comments per writer A = ( 500 / 5 ) = 100 comments

The number of comments per writer B = ( 450 / 11 ) = 40.90 comments

Hence , the average number of likes per writer and the average number of comments per writer are solved

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Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

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

If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]

and

[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.

Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.

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--The given question is incomplete, the complete question is

"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--

The diameter of the opening of the cone is approximately 8.92 units.

We can use the formula for the volume of a cone:

V = (1/3) × π × r^2 × H

where V is the volume, H is the height, and r is the radius of the base.

In this case, we are given the volume V = 196 and the height H = 12. We want to find the diameter of the opening, which is 2r.

First, we can rearrange the formula for the volume to solve for r

r = sqrt((3V) / (πH))

Plugging in the values, we get

r = sqrt((3 × 196) / (π × 12)) ≈ 4.46

So the radius of the base of the cone is approximately 4.46 units.

Finally, we can find the diameter of the opening:

d = 2r ≈ 8.92 units

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The given question is incomplete, the complete question is:

The volume of the cone is 196 cubic units. If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone?

The correlation coefficient, denoted by r, tells us how closely data in a scatterplot fall along a straight line. The closer that the absolute value of r is to one, the better that the data are described by a linear equation. If r =1 or r = -1 then the data set is perfectly aligned. Data sets with values of r close to zero show little to no straight-line relationship.

Due to the lengthy calculations, it is best to calculate r with the use of a calculator or statistical software. However, it is always a worthwhile endeavor to know what your calculator is doing when it is calculating. What follows is a process for calculating the correlation coefficient mainly by hand, with a calculator used for the routine arithmetic steps.

(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.

An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.

(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.

(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.

(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.

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Answer: 207.1875

Step-by-step explanation:

side length a = 19.5 cm

side length b = 21.25 cm

diagonal p = q = 28.841159824112 cm

perimeter P = 81.5 cm

area of rectangle A = 414.375 cm2

area of rectangle divided into a triangle = 207.1875

hope this helps

Therefore, the total tax owed by a Single filer with a taxable income of equation $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

Assuming that the taxable income of $57,000 is for the tax year 2021 and the person is filing as Single, we can use the following marginal tax rates to compute the tax owed:

Tax Rate Taxable Income Range

10% $0 - $9,950

12% $9,951 - $40,525

22% $40,526 - $86,375

24% $86,376 - $164,925

32% $164,926 - $209,425

35% $209,426 - $523,600

37% $523,601 or more

To compute the tax owed, we need to apply each tax rate to the corresponding portion of the taxable income and add up the results. Here's how we can do that:

The first $9,950 of taxable income is taxed at 10%, so the tax on this portion is $9950 x 0.1 = $995.

The next $30,575 ($40,525 - $9,950) of taxable income is taxed at 12%, so the tax on this portion is $30,575 x 0.12 = $3,669.

The remaining $17,475 ($57,000 - $40,525) of taxable income is taxed at 22%, so the tax on this portion is $17,475 x 0.22 = $3,844.50.

Therefore, the total tax owed by a Single filer with a taxable income of $57,000 for the tax year 2021 is $995 + $3,669 + $3,844.50 = $8,508.50.

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Answer:

C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.

Answer:

C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.

Step-by-step explanation:

Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will  will hold your money until you want to deposit it out of your account.

This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.

In order to graph the line whose equation is y=5/2x+2, we need to begin by plotting the point (0,2) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.

Similarly, to graph the line whose equation is y=5/2x+3, we need to begin by plotting the point (0,3) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.

In both cases, the slope of the line is 5/2, which is the coefficient of x in the equation. The slope tells us how much the line rises or falls for every unit it moves to the right. In this case, the line rises 5 units for every 2 units it moves to the right. This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.

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The expression  9-36x can be factorized as 9(1-4x)

An expression's factors are things that are multiplied by other things. A number, variable, phrase, or any other lengthier expression may be used. For instance, 2, x, and y are the factors of 2xy.

To factor the expression 9-36x completely, we need to find the greatest common factor (GCF) of the two terms and then use the distributive property to factor it out.

The GCF of 9 and 36 is 9, so we can factor out 9 from both terms:

9-36x = 9(1-4x)

Now the expression is factored completely.

So the final answer is:

9-36x = 9(1-4x)

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To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.

Here are the steps to solve the equation:

1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)

So the solution to the equation is x = -2.3513.

Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.

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Answer: 75% of $13.50 is 10.125

Step-by-step explanation:

Answer:

10.125

Step-by-step explanation:

13.50 x .75 = 10.25

Answer:

x=4, y=5

Step-by-step explanation:

[tex]x=2y-6\\ x-2y=-6\\\\y=3x-7\\y-3x=-7\\\\\\\\-3x+y=-7\\-3(2y-6)+y=-7\\-6y+18+y=-7\\-5y+18=-7\\-5y=-25\\y=5\\\\\\x=2y-6\\x=2(5)-6\\x=4[/tex]

Answer:

Let's assume that the number of text messages sent in a day is x. Then the cost of Michelle's phone plan is:

Cost of Michelle's plan = 0.22x

And the cost of Jeff's phone plan is:

Cost of Jeff's plan = 0.12x + 1

We want to find the number of text messages for which the two plans have the same cost. So we can set the two expressions for the cost equal to each other and solve for x:

0.22x = 0.12x + 1

0.1x = 1

x = 10

Therefore, for 10 text messages per day, the cost of Michelle's plan and Jeff's plan will be the same.

We can also verify this by plugging x = 10 into the two expressions for the cost:

Cost of Michelle's plan = 0.22(10) = $2.20

Cost of Jeff's plan = 0.12(10) + 1 = $2.20

So the cost of the two plans is indeed the same for 10 text messages per day.

Answer:

Step-by-step explanation:

cost m = 0.22x

cost j = 0.12x+1

0.22x=0.12x+1

0.1=1

x=10

cost m = 0.22(10) = $2.20

cost J =0.12(10)+1=$2.20

So the answer is 10

Answer:

59400

Step-by-step explanation:

59407

4 is the hundredth

0 is the number before 4 so it doesn't round up

so it's 59400

Answer:

59,400

Step-by-step explanation:

If it were 59,450 then it would be 59,500 but it is 59.407 witch would mean we are rounding down to 59,400

The distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.

The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.

Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.

Therefore, the distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.

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The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.

To solve this question we need knowledge of set theory, union and intersection.

(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.

(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.

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Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

an arrangement of elements that faithfully represent an angle. The first number on a graph indicates the distance along, while the second number indicates the distance up or down. The point (12,5), for instance, is situated 12 below and 5 above.

A sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

Explanation:

First, we need to reflect the original triangle RST across the y=x line. This will result in a new triangle that is congruent to the original one but with its vertices in different positions. The new vertices will be R(-1, -3), S(-1, -1), and T(-5, -4).

Next, we need to rotate this new triangle 90 degrees clockwise about the origin. This will result in another new triangle that is congruent to the previous one but with its vertices in different positions. The new vertices will be R'(3, -3), S'(3, -1), and T'(-1, -4), which are the vertices of △R′S′T′.

Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a reflection across the y=x line followed by a rotation of 90 degrees clockwise about the origin.

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A square is a base of a square​ pyramid.

A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called a vertex) is called a square pyramid. It is called a pentahedron, due to its five faces.

A square base and four triangles joined at the vertex make up a square pyramid. It has a square base and triangular side faces with a central vertex.

A square pyramid has three components.

Properties of a Square Pyramid:

Let's go through the attributes we looked at in the graphic above. The definition of a pyramid is the source of all these characteristics.

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Complete question:

what is a base of a square​ pyramid?

The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.

a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:

```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.

b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:

```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.

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The fourth term in the geometric sequence is -81.

What is a geometric sequence?

In mathematics, a geometric progression, also known as a geometric sequence, is a set of non-zero numbers where each term after the first is derived by multiplying the previous one by a fixed, non-zero amount called the common ratio.

We are given a sequence as 3, –9, 27, ...

We can observe that each term is being multiplied by -3.

So, the common ratio i.e. r = -3

Here x = 4 and a₁ = 3.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₄ = a₁ r⁽⁴⁻¹⁾

⇒a₄ = a₁ r³

⇒a₄ = 3 (-3)³

⇒a₄ = 3 * -27

⇒a₄ = -81

Hence, the fourth term in the geometric sequence is -81.

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Answer:

On June 1, 2013, Anchorage, Alaska experiences 18 and 1/4 hours of daylight.

In a 24-hour day, there are 24 - 18 and 1/4 = 5 and 3/4 hours without daylight.

Therefore, the number of hours without daylight on June 1, 2013 in Anchorage, Alaska was 5 and 3/4 hours.

Answer:

24-18.4=5 and3/4

Step-by-step explanation: