When Q is divided by W, the quotient is R and the remainder is E. Which of the following expressions is equal to E?

A) RW + Q
B) RW − Q
C) Q − RW
D) QW − R
E) Q/RW

The equivalent operation is: b = (a < 5) ? 12 : (d = 30);

The original if/else statement is:

if (a < 5)

   b = 12;

else

   d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.

The equivalent operation using the conditional (ternary) operator is:

b = (a < 5) ? 12 : d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.

If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.

The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.

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Answer:

Below

Step-by-step explanation:

First let's determine the slope if thus function

Let m be the slope of this function

m = [0-(-4)]/ 2-0 = 4/2 =2

So our equation is:

y = 3x +b

b is the y-intercept wich is given by the image of 0

Here it's -4

So the equation is:

y = 2x-4 wich is also y = x-2 after simplifying

●●●●●●●●●●●●●●●●●●●●●●●●

A line that is parallel to this one will have the same slope.

Examples:

● y= 2x+3

● y = 2x-7

■■■■■■■■■■■■■■■■■■■■■■■■■■

A line that is perpendicular to this one and has a slope m' satisfy this condition:

m*m'= -1

m'= -1/m

m' = -1/2

So this line should have a slope that is equal to -1/2

Answers from the choices:

y = -1/2 x +1/2

y+1= -1/2 (x-3)

The expression that represents this scenario would be l(t) = 0.28t. This expression states that the amount of liquid that has leaked at any given time is equal to 0.28 times the number of seconds that have passed.

Linear equations are mathematical equations of the type y = mx + b, with   and x and y being variables. These equations represent a straight line on a graph and are referred to be "linear" since the maximum power of the variable is 1. For example, the equation y = 2x + 3 is a linear equation since the maximum power of the variable x is 1. Linear equations are useful for representing a broad range of real-world events, such as the link between the distance an object travels and the time it takes to traverse that distance. They are a common tool in many disciplines, including physics, engineering, and economics. They are also quite simple to answer.

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Answer:  \(\textsf{4.86 per hour}\)

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Given: \(\textsf{Initial wage = 4.50, Increase = 8\%}\)

Find:  \(\textsf{New hourly wage}\)

Solution: The first step would be to create an expression to incapsulate the scenario and then we would solve for the new hourly wage and we would get our answer.

Create an expression

Simplify the expression

We were able to determine that the new hourly wage after an increase of 8% would be 4.86 per hour.

Answer:

2

Step-by-step explanation:

If you read for instance January to August, the chart looks like-

January- 2

February- 4

March- 6

April- 8

May-10

June- 12

July-14

August- 16

So reading 2 every month for 8 months is 8x2=16

Answer:

Inequality

Step-by-step explanation:

google definition

The expression "3x + 2 > 10" represents an inequality, specifically a linear inequality. It states that "three times the value of x, plus two, is greater than ten."

In algebra, linear inequalities involve variables raised to the first power and are typically represented on a coordinate plane as a shaded region above or below a straight line. The inequality "3x + 2 > 10" represents the region above the line "3x + 2 = 10" (the line where the two sides are equal) because the inequality is strictly greater than.

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Using the tangent ratio, the height of the branch can be determined. The tangent of the angle (26 degrees) is equal to the height of the branch divided by the distance from Winthorp to the tree (8 feet). By rearranging the equation and solving for the height, we find that the height of the branch is approximately 3.6 feet.

Tan(26°) = height/8. Rearranging the equation, we get height = 8 * tan(26°) ≈ 3.6 feet.

Certainly! In this scenario, we can use trigonometry, specifically the tangent ratio, to determine the height of the branch. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, the angle of observation is 26 degrees, and the adjacent side is the distance from Winthorp to the tree, which is 8 feet.

By setting up the equation tan(26°) = height/8, we can rearrange it to solve for the height. Multiplying both sides of the equation by 8 gives us height = 8 * tan(26°). Plugging in the value of the tangent of 26 degrees (which can be found using a calculator or reference table), we can calculate the height to be approximately 3.6 feet. therefore, the bird was standing on a branch at a height of approximately 3.6 feet from the ground.

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Answer:

14x-5=70 and 22x5=110

Step-by-step explanation:

i hope this helped have a good day

C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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The best line of fit can be found by using the method of least squares.

A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible).

The method of least squares is a statistical method that is used to find the line of best fit for a given set of data points. The method finds the line that minimizes the sum of the squares of the differences between the predicted values (y') and the actual values (y) for all data points.

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Answer:

Well then good luck with that woophi- I'm kidding, this is what I got! XD

Step-by-step explanation:

6 and 3/4

Hope this helped! :D

B

Step-by-step explanation:

The probability that a randomly chosen specimen has an acceptable hardness. Therefore, the probability that a randomly chosen specimen has an acceptable hardness (between 65 and 75) is approximately 0.817 (rounded to four decimal places).

To find the probability that a randomly chosen specimen has an acceptable hardness, we need to calculate the area under the normal distribution curve between the hardness values of 65 and 75. Since the hardness of the alloy follows a normal distribution with a mean of 69 and a standard deviation of 3, we can use the standard normal distribution (Z-distribution) to calculate the probability.

First, we convert the hardness values to their corresponding z-scores using the formula:

z = (x - μ) / σ

Where:

x is the hardness value,

μ is the mean (69 in this case), and

σ is the standard deviation (3 in this case).

For x = 65:

z1 = (65 - 69) / 3 = -4 / 3 = -1.3333

For x = 75:

z2 = (75 - 69) / 3 = 6 / 3 = 2

Next, we find the probability corresponding to these z-scores using a standard normal distribution table or a calculator.

P(65 ≤ X ≤ 75) = P(-1.3333 ≤ Z ≤ 2)

Looking up the values in the standard normal distribution table, we find:

P(-1.3333 ≤ Z ≤ 2) = 0.9088 - 0.0918 = 0.817

Therefore, the probability that a randomly chosen specimen has an acceptable hardness (between 65 and 75) is approximately 0.817 (rounded to four decimal places).

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Answer:

area of lawn = 15.708 square meters

Step-by-step explanation:

pi 3 squared (area of lawn and flower bed) - pi 2 squared (area of flower bed)= area of lawn

Answer:

x<3

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

7x+5<26

Step 2: Subtract 5 from both sides.

7x+5−5<26−5

7x<21

Step 3: Divide both sides by 7.

7x/7<21/7

x<3

Answer:

3

Step-by-step explanation:

Subtract 5 from both sides.

7x<21

7 goes into 21, 3 times.

Therefore, x<3

the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.

Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.

30%  / 100% =30 / 100 = x / 1.5 quarts.

We can reduce the equation further,

0.3  = x / 1.5.

0.3 * 1.5 = x

x = 0.45

We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.

As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.

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The function f(x) is \(\frac{2}{3}x^3 - 76x^2 + 150x + 2.67\).

To find f(x), we need to integrate the given slope (x-1)(2x-150) with respect to x, because the slope of a tangent line to a function is the derivative of that function. A line's slope is a gauge of its steepness. Between any two points on the line, it is calculated as the ratio of the change in the vertical coordinate (rise) to the change in the horizontal coordinate (run).

So, we have:

f'(x) = (x-1)(2x-150)

Integrating both sides with respect to x:

\(f(x) = ∫(x-1)(2x-150) dx\)

\(f(x) = \int (2x^2 - 152x + 150) dx\)

\(f(x) = \frac{2}{3}x^3 - 76x^2 + 150x + C\)

where C is an arbitrary constant of integration.

To determine the value of C, we can use the given condition f(2) = 2:

\(f(2) = \frac{2}{3}(2)^3 - 76(2)^2 + 150(2) + C = 2\)

Simplifying:

C = 2 - (8/3) + 304 - 300 = 2.67

Therefore, the function f(x) is:

f(x) = \(\frac{2}{3}x^3 - 76x^2 + 150x + 2.67\).

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The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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Answer:

2y=3x=-4

Step-by-step explanation:

grouping like terms

y+ly =4x-x=-4

2y=3x=-4

The derivative function of the given function f(x) = 5 x³ - In x is given by, f'(x) = 15 x² - 1/x.

Hence the correct option is (B).

We know that from the derivative formulae,

d/dx [xⁿ] = n xⁿ ⁻ ¹ and d/dx [ln x] = 1/x

Given the function is,

f(x) = 5 x³ - In x

Differentiating the above function with respect to 'x' we get,

d/dx [f(x)] = d/dx [5x³ - In x]

Using addition rule of derivative we get,

f'(x) = d/dx [5x³] - d/dx [In x]

f'(x) = 5 * (3x²) - 1/x

f'(x) = 15 x² - 1/x

Hence the correct option is (B).

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The question is incomplete. The complete question will be -

The P-value of the test statistic is 0.0316.

The P-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

In this case, the test statistic is z = -2.15. The P-value can be found by looking up z = -2.15 in a z-table. The z-table shows the probability of obtaining a z-score less than or equal to the z-score that is looked up.

In this case, the P-value is:

P-value = (2 * 0.0158) = 0.0316    [Check the attached image]

Therefore, the P-value is 0.0316.

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Answer:

3

Step-by-step explanation:

9/15 = x/5

15 = 3 x 5

9 = 3 x 3

Common factor is 3:

9/15 divided by 3 = 3/5

where x = 3

therefore the answer is : 3

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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The ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year is 1/6 οr 1:6. Thus, οptiοn D is cοrrect.

The relative size οf twο quantities expressed as the quοtient οf οne divided by the οther; the ratiο οf a tο b is written as a:b οr a/b.

If Sam wοrks fοr his father fοr 2/5 οf the year, then he wοrks fοr his mοther fοr the remaining time, which is 1 - 2/5 = 3/5 οf the year.

Tο find the ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year, we can write:

Sam wοrked fοr his father = 2/3 οf year

Remaining time = 1/3

Sam wοrked fοr his mοther = 1/3(remainder year)=(1/3)*(1/3)

     =1/9

Ratiο οf time spent fοr mοther and father is

= (1/9):(2/3)

=(1/3):2

= 1:6

Sο, οptiοn d) 1/6 is cοrrect answer

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Complete question:

Sam works for his father for 2/3; of the year and works for his mother = of the remainder year. What is the

ratio of the time Sam spends working for his mother to the time he spends working for his father per year?

The equation of the plane that is normal to the function at the point P(4, 2) is 64x + 192y - 832 = 0.

The gradient vector of a function gives the direction of the steepest ascent at a particular point. To find the gradient vector, we need to compute the partial derivatives of the function with respect to x and y.  Taking the partial derivative of f(x, y) = \(x^2y^3\)with respect to x, we get ∂f/∂x = \(2xy^3\).

Taking the partial derivative of f(x, y) = \(x^2y^3\) with respect to y, we get ∂f/∂y = 3x^2y^2.  Now, we can evaluate the gradient vector at the point P(4, 2) by substituting x = 4 and y = 2 into the partial derivatives. The gradient vector at P(4, 2) is ∇f(4, 2) = (2 * 4 * \(2^3\), 3 * 4^2 * \(2^2\)) = (64, 192).

Since the gradient vector is normal to the plane, we can use it to form the equation of the plane. The equation of the plane becomes 64(x - 4) + 192(y - 2) = 0, which simplifies to 64x + 192y - 832 = 0.

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Answer:

y = 140

Step-by-step explanation:

All angles inside the triangle will equal 180

Set your formula up as

180 = x + 120 + 20

180 - 120 - 20 = x

40 = x

y+x will also equal 180, therefore

180 = y + x

180 = y + 40

180 - 40 = y

140 = y

Answer:c

Step-by-step explanation:

The equation of the perpendicular line is \(y = -\frac 12x + 1\)

The points are given as:

\(F = (4,9)\)

\(G = (1,3)\)

Start by calculating the slope (m) of line FG as follows:

\(m = \frac{y_2 - y_1}{x_2 -x_1}\)

Substitute values for x's and y's.

So, we have:

\(m = \frac{9 -3}{4 - 1}\)

\(m = \frac{6}{3}\)

\(m =2\)

The equation of the line is said to be perpendicular to line FG.

So, the slope of the line is:

\(m_2 = -\frac 1m\)

This is then calculated as:

\(m_2 = -\frac 12\)

The line is said to pass through point (2,0).

So, the equation of the line is:

\(y = m_2(x - x_1) +y_1\)

This gives

\(y = -\frac 12(x - 2) +0\)

Expand

\(y = -\frac 12x + 1 +0\)

\(y = -\frac 12x + 1\)

Hence, the equation of the line is \(y = -\frac 12x + 1\)

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Answer:

(15-3)+4 = x (amount of stickers)

Step-by-step explanation:

She has fifteen but gives three to a friend, giving you the first amount and then you add the four she later gets from someone else into the total to get your final number.

No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

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Answer:

1 remainder 13

Step-by-step explanation:

:)