Which equation could represent Relationship A?

Hours worked is represented by x and Amount paid is represented by y.

Select each correct answer.


y = 18.3x

y = 18x

y = 18.1x

y = 18.6x

The length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

Let's start by using the formula for the area of a rectangle, which is:

Area = length x width

We are given that the width of the platform is (x+4) meters, so we can write:

Area = length x (x+4)

We are also given that the area of the platform is 3x^2+10x−8, so we can set these two expressions equal to each other and solve for the length:

3x^2+10x−8 = length x (x+4)

Expanding the right side, we get:

3x^2+10x−8 = length x^2 + 4length

Subtracting 4length from both sides, we get:

3x^2+10x−8−4length = length x^2

Rearranging, we get a quadratic equation:

length x^2 + 4length − 3x^2 − 10x + 8 = 0

To solve for length, we can use the quadratic formula:

length = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -3x^2 - 10x + 8. Plugging in these values, we get:

length = (-4 ± sqrt(4^2 - 4(1)(-3x^2 - 10x + 8))) / 2(1)

Simplifying under the square root:

length = (-4 ± sqrt(16 + 12x^2 + 40x - 32)) / 2

length = (-4 ± sqrt(12x^2 + 40x)) / 2

length = (-4 ± 2sqrt(3x^2 + 10x)) / 2

length = -2 ± sqrt(3x^2 + 10x)

Since the length must be positive, we take the positive square root:

length = -2 + sqrt(3x^2 + 10x)

Therefore, the length of the platform is given by the expression -2 + sqrt(3x^2 + 10x) meters.

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Answer:

Step-by-step explanation:

For reference the quadratic equations looks like this

(-b±\(\sqrt{b^2-(4*a*c)}\\\))/2a

Amy's mistake (and solution)

We can see that when amy mulitplied c she wrote 20 instead of -20 (in step 1). She can fix this by writing (4*1*-20) instead

Richard's mistake (and solution)

When richard messed up on step 5 when he wrote (6-2i)/2. You only would write the i if the negative was in the radical (but in this case it's outside). You would fix this by just getting rid of the i entirely (and keeping the 2)

I'm not really too sure how you would do three but I'll give it a shot anyways

our equation will look like this: x²+2x

which means our quadratic equation would look like this

\(\frac{-2+/-\sqrt{2^2-4*1*0}}{2}\\=\\\\\frac{-2+/-(2)}{2}\\\\\\= -1+/-(1)\\\\-1+1=0\\-1-1=-2\)

When I write +/- I mean plus or minus giving us -2 and 0 as our solutions

Therefore, $22.95 would be the best estimate for the cost of a vehicle to drive through the safari in 2011.

The estimated cost of a vehicle to drive through the safari in 2011, we need to substitute the value of x (number of years since it opened in 2005) as 6 into the regression equation y = 3.648 * 1.182x.

Plugging in x = 6, the equation becomes: y = 3.648 * 1.182 * 6

Calculating the expression: y = 25.849536

Rounding to two decimal places, the estimated cost is approximately $25.85.

Among the given options, the closest value to $25.85 is $22.95 (Option B). Therefore, $22.95 would be the best estimate for the cost of a vehicle to drive through the safari in 2011.

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Answer;

x = 7

Step-by-step explanation:

3(x - 1) - 4(5 - x) = 2(6 + x)

3x - 3 -20 + 4x = 12 + 2x

7x - 23 = 12 + 2x

7x - 2x = 23 + 12

5x = 35

x = 35/5

x = 7

Answer: (1,2)

Step-by-step explanation: In order to get 3/4 the distance, you have to use midpoint formula. Use midpoint formula to get the midpoint between M and N. In this case it would be the square root of ((x1+x2/2),(y1+y2/2)) (you can google this if it is not clear because of formatting). Once you get the midpoint of M and N, should be (-1,4) and we will call this point Z for reference, you find the midpoint of the original midpoint (point Z aka (-1,4) in our case) and point N. In doing this, your math should come out to the new point that is 3/4 to the distance. This point should be (1,2) if I am not mistaking.

Answer:

Step-by-step explanation:

Total hours:

Answer:

x = -7

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−5(x−1)=40

(−5)(x)+(−5)(−1)=40(Distribute)

−5x+5=40

Step 2: Subtract 5 from both sides.

−5x+5−5=40−5

−5x=35

Step 3: Divide both sides by -5.

−5x/−5 = 35/−5

Answer:

x = -7      

I hope I helped!!

The correct answer is option A which is the distance between A and D will be  AD = \(\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b\).

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

The formula utilised to find the distance between two points is;-

X = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

We have the coordinates of the point A = (0, 0) and D is  (0, b).By applying the formula to find the distance between A and D.

AD = \(\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b\).

Therefore the correct answer is option A which is the distance between A and D will be  AD = \(\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b\).

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The two linearly independent solutions of the given differential equation are:

Y₁ = 1 - 3x²

Y₂ = x - 3bx²

What is Power series method?

The power series method is a technique used to find solutions to differential equations by representing the unknown function as a power series. It involves assuming that the solution can be expressed as an infinite sum of terms with increasing powers of the independent variable.

To find two linearly independent solutions of the given differential equation y" + 6xy = 0, we can use the power series method and assume that the solutions have the form:

Y₁ = 1 + a²x³ + açx² + ...

Y₂ = x + b₁x² + bṛx³ + ...

Let's find the coefficients by substituting these series into the differential equation and equating coefficients of like powers of x.

For Y₁:

Y₁" = 6a²x + 2aç + ...

6xy₁ = 6ax + 6a²x⁴ + 6açx³ + ...

Substituting these into the differential equation:

(6a²x + 2aç + ...) + 6x(1 + a²x³ + açx² + ...) = 0

Equating coefficients of like powers of x:

Coefficient of x³: 6a² + 6a² = 0

Coefficient of x²: 2aç + 6a = 0

Solving these equations simultaneously, we get:

6a² = 0 => a = 0

2aç + 6a = 0 => 2aç = -6a => ç = -3

Therefore, the coefficients for Y₁ are: a = 0 and ç = -3.

For Y₂:

Y₂" = 6bx + 2bṛ + ...

6xy₂ = 6bx² + 6bṛx³ + ...

Substituting these into the differential equation:

(6bx + 2bṛ + ...) + 6x(x + b₁x² + bṛx³ + ...) = 0

Equating coefficients of like powers of x:

Coefficient of x³: 6bṛ = 0 => bṛ = 0

Coefficient of x²: 6b + 2b₁ = 0

Solving this equation, we get:

6b + 2b₁ = 0 => b₁ = -3b

Therefore, the coefficients for Y₂ are: bṛ = 0 and b₁ = -3b.

In summary, the two linearly independent solutions of the given differential equation are:

Y₁ = 1 - 3x²

Y₂ = x - 3bx²

Please note that the given problem did not provide specific values for α, b₄, and b₇, so these coefficients cannot be determined.

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Answer:

-3

Step-by-step explanation:

Answer: 2.3

Step-by-step explanation: 2 and 1/3 is equivalent to 2.3

Answer:

2.3

Step-by-step explanation:

Hope this helps! (:

Total 64900 stamps more is needed to be collected so the group can break the record.

The current record is 150,000.

Friends collected 10,000, 75,000, and 100 stamps

Let the total stamps need to be collected to break the world record be x,

The total stamps collected should be greater than 150000 to break the world record

10000 + 75000 + 100 + x > 150000

85100 + x > 150000

x > 64900

The total stamps need to be collected is greater than 64900 to break the world record.

Therefore, 64900 stamps need to be collected so the group can break the record.

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Answer:

21

Step-by-step explanation:

21

Answer:

i think ur answer would be 21

Step-by-step explanation:

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The area of the figure formed by the dilation is 36 square units.

Area is particularly essential in modern mathematics. In addition to its importance in geometry and calculus, area is linked to the determination of determinants in linear algebra and is an essential feature of surfaces in differential geometry.

A dilation occurs when an figure is reduced to a smaller size using a fixed center.

From the given diagram we can find the sides of the square that is the transformed image as 9 - 3 = 6 units

Area of the A'B'C'D' square = 36 square units.

Side of the original square = 18 units.

Area of the ABCD square = 18² = 324 square units

Scale factor of dilation = 324/36 = 9 times.

Hence from the figure we can calculate the area of the transformed figure to be 36 square units which is dilated by a factor of 9 times.

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The margin error is 6.

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.

A higher error indicates a high chance that the result of the sample reported may not be the true reflection of the whole population. A higher margin indicates that the survey results may stray from the actual views of the total population. On the other hand, a smaller margin indicates that the results are close to the true reflection of the total population, which builds more confidence in the survey.

The margin of error is equal to half the width of the entire confidence interval.

The margin error is:

\(\frac{66-54}{2}= \frac{12}{2} = 6%\)

Thus, the margin error is 6.

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The time for the trough to have 80 gallons of water is 5 minutes.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of minutes be represented as m.

The trough already contains 25 gallons of water, and the rancher is adding 11 gallons per minute. This will be:

25 + 11m =80

Collect like terms

11m = 80 - 25

11m = 55

Divide

m = 55 / 11

m = 5

Therefore, there will be 5 minutes.

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In the rhombus WXYZ, the length of one side, WX, is given as 4 cm. The other sides of the rhombus have the same length due to its properties, so all sides of the rhombus have a length of 4 cm.

A rhombus is a quadrilateral with all sides of equal length. In this case, the given length of one side, WX, is 4 cm. Since a rhombus has all sides congruent, we can conclude that all the sides of the rhombus WXYZ also have a length of 4 cm.

Hence, the lengths of all sides of the rhombus WXYZ are as follows:

WX = 4 cm

XY = 4 cm

YZ = 4 cm

ZW = 4 cm

All four sides of the rhombus WXYZ are equal in length and measure 4 cm.

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The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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The amount left is an illustration of equivalent expressions.

All three expressions can be used to represent the amount left

The given parameters are:

\(\mathbf{Paycheck =X}\)

\(\mathbf{Savings =20\%}\)

The amount left is:

\(\mathbf{Amount = Paycheck \times (1 - Savings)}\)

So, we have:

\(\mathbf{Amount = X\times (1 - 20\%)}\)

Substitute 250 for A

\(\mathbf{Amount = 250 \times (1 - 20\%)}\)

Express percentage as decimal

\(\mathbf{Amount = 250 \times (1 - 0.20)}\)

\(\mathbf{Amount = 250 \times 0.80}\) ---- this represents option (A)

Expand \(\mathbf{Amount = 250 \times (1 - 20\%)}\)

\(\mathbf{Amount = 250 - 250 \times 20\%}\)

\(\mathbf{Amount = 250 - 250 \times 0.20}\) ---- this represents option (B)

Express 250 as X in \(\mathbf{Amount = 250 - 250 \times 0.20}\)

\(\mathbf{Amount = X - X \times 0.20}\) ---- this represents option (C)

Hence, all three expressions can be used to represent the amount left

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Answer: \(25 \frac{31}{63}\)

Step-by-step explanation:

The picture in this scenario is simply a rectangle.  The area of a rectangle is length * width.  Thus, simply multiply the two provided values.

3 1/7 = 22 / 7

8 1/9 = 73 / 9

\(\frac{22}{7} *\frac{73}{9} = \frac{1606}{63}\)

1606/63 = 25 31/63

Hope it helps and let me know if you want me to elaborate :)

I'm pretty sure its 2r, because you are multiplying the number of red marbles by 2 to get how many blue marbles there are.

Answer: 40x70x70

Step-by-step explanation:

the lines x = 0, y = x and the parabola y=2-x²in the first quadrant. The center of mass of the thin plate is located at x = 2/3 and y = 4/3.

To find the center of mass of the thin plate, we need to calculate the x-coordinate (x) and y-coordinate (y) separately.

The x-coordinate of the center of mass (x) is given by the formula:

x= (1/A) * ∫(x * ρ(x, y) dA)

where A is the area of the region and ρ(x, y) is the density function.

The y-coordinate of the center of mass (y) is given by the formula:

y= (1/A) * ∫(y * ρ(x, y) dA)

In this case, the region is bounded by x = 0, y = x, and the parabola y = 2 - x² in the first quadrant.

First, we need to find the area A:

A = ∫(y_max - y_min) ∫(x_max - x_min) dx dy

= ∫(2 - x²) ∫(x - 0) dx dy

= ∫(2x - x³/3) dy from y = 0 to y = x

= ∫(2x - x³/3) (x) dx from x = 0 to x = 2

= 2

Next, we calculate x:

x = (1/2) * ∫(x * ρ(x, y) dA)

= (1/2) * ∫(x * 3) dA

= (3/2) * ∫(x) dA

= (3/2) * ∫(x) (2 - x²) dx from x = 0 to x = 2

= 2/3

Finally, we calculate y:

y= (1/2) * ∫(y * ρ(x, y) dA)

= (1/2) * ∫(y * 3) dA

= (3/2) * ∫(y) dA

= (3/2) * ∫(y) (2 - x²) dx from x = 0 to x = 2

= 4/3

Therefore, the center of mass of the thin plate is located at x = 2/3 and y = 4/3.

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Answer: each movie costs 7$

Step-by-step explanation: 41-6=35 and you divide that by 5 which is 7

Answer:

each movie cost $7

Step-by-step explanation:

41 - 6 = 35

35 / 5 = 7

Careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

By including another variable in a regression analysis, several outcomes are possible. Let's consider the statements you provided one by one:

1. Decrease the regression R^2 if that variable is important:

  - If the added variable is important and has a meaningful relationship with the dependent variable, it can increase the explanatory power of the regression model, thereby increasing the R^2.

However, if the added variable is not relevant or has a weak relationship with the dependent variable, it can decrease the R^2.

2. Decrease the variance of the estimator of the coefficients of interest:

  - Including additional variables in a regression model can sometimes help to reduce the variance of the coefficient estimators for the variables of interest.

This is because including more relevant variables can help to explain some of the variance in the dependent variable, leaving less unexplained variance for the coefficients of interest.

3. Eliminate the possibility of omitted variable bias from excluding that variable:

  - Omitted variable bias can occur when an important variable is not included in the regression model.

Including all relevant variables in the model can help reduce the risk of omitted variable bias, as it allows for a more comprehensive analysis of the relationship between the dependent variable and the independent variables.

4. Look at the t-statistic of the coefficient of that variable and include the variable only if the coefficient is statistically significant at the 1% level:

  - The t-statistic measures the statistical significance of a coefficient. Inclusion of a variable in a regression model is often based on its statistical significance.

If the coefficient of the variable is statistically significant at the desired significance level (e.g., 1%), it suggests that the variable has a meaningful impact on the dependent variable and can be included in the model.

It is important to note that the effect of including an additional variable in a regression model depends on various factors such as the relationship between the variables, sample size, multicollinearity, and the specific research context.

Therefore, careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

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It will take 1.5 years to get a simple interest of birr 60 on birr 800 at a rate of 5% per annum.

Here's how to calculate it step by step:

1. The formula for simple interest is: I = P*R*T, where I is the interest, P is the principal, R is the interest rate, and T is the time in years.

2. We are given the values of I, P, and R, and we need to find T. So we can rearrange the formula to solve for T:

T = I / (P*R)

3. Now we can plug in the given values and solve for T:

T = 60 / (800*0.05)

4. Simplifying the equation gives us:

T = 60 / 40

5. And finally, solving for T gives us:

T = 1.5

So it will take 1.5 years to get a simple interest of birr 60 on birr 800 at a rate of 5% per annum.

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Answer:

Ms. Gregg could buy 4 apples and 6 bananas

Step-by-step explanation:

You can split the money and try to get even on each fruit by, getting 4 apples which would be 8 dollars on 4 apples then the extra money would be left over for the bananas which would be six dollars and since the bananas are only 1 dollar you can buy 6 with the leftover money.

The percent increase in the cost of the uniform from last year to this year is 25%.

To find the percent increase in the cost of the uniform from last year to this year, we need to calculate the difference between the two prices, divide it by the original price, and then multiply by 100 to express the result as a percentage.

The difference between this year's price and last year's price is:

$65 - $52 = $13

The original price (last year's price) is $52.

So the percent increase in the cost of the uniform is:

percent increase = (difference / original price) x 100

percent increase = ($13 / $52) x 100

percent increase = 0.25 x 100

percent increase = 25%

Therefore, the percent increase in the cost of the uniform from last year to this year is 25%.

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Answer:

This gives us a square with an area of 225 square units.

Step-by-step explanation:

To find the dimensions of the rectangle with the largest area for a given perimeter of 60, we need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

In this case, we know that P = 60, so we can write:

60 = 2l + 2w

Simplifying this equation, we get:

30 = l + w

To find the largest area of the rectangle, we need to maximize the product of the length and the width, which is the formula for the area of a rectangle, A = lw.

We can solve for one variable in terms of the other using the equation above. For example, we can write:

w = 30 - l

Substituting this expression for w into the formula for the area, we get:

A = l(30 - l)

Expanding and simplifying this expression, we get:

A = 30l - l^2

This is a quadratic equation in l, which has a maximum value when l is halfway between the roots. We can find the roots using the quadratic formula:

l = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = -1, b = 30, and c = 0, so we get:

l = (-30 ± sqrt(30^2 - 4(-1)(0))) / 2(-1)

Simplifying, we get:

l = (-30 ± sqrt(900)) / -2

l = (-30 ± 30) / -2

So the roots are l = 0 and l = 30. We want the smaller value first, so we take l = 0 and find w = 30. This would give us a rectangle with zero area, so it is not a valid solution.

The other root is l = 30, which gives us w = 0. Again, this is not a valid solution because we need both dimensions to be positive.

Therefore, the dimensions of the rectangle with the largest area for a perimeter of 60 are:

l = 15 and w = 15

This gives us a square with an area of 225 square units.

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