. Labor Variances Ellen Chenoweth, the manager of the city of St. Paul road maintenance shop, uses standards to judge performance. Because a clerk mistakenly discarded some labor records, however, Ellen has only partial data for April. She knows that the total direct-labor flexible-budget variance was $1,643 favorable. Moreover, a recent pay raise produced an unfavorable labor price variance for April of $1,157. The actual hours of input were 1,780 and the standard labor price was $20 per hour. 1. Find the actual labor rate per hour 2. Determine the standard hours allowed for the output achieved.

Answer: 1.75

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Since the garden bed looks like the shape of a trapezoid the equation to find the area of a trapezoid is A = 1/2h (base 1 + base 2)

The area is already given so you can just plug it in. Also you can plug in the bases.

21 = 1/2h (3 + 4)

21 = 1/2h (7)  rewrite

21 = 1/2(7)h

21 = 3.5h  Divide both sides by 3.5

6 = h

Answer: $702.39

Step-by-step explanation: To find the total cost of the laptop with sales tax included, we need to add the sales tax to the listed price.

First, we need to calculate the amount of sales tax.

Sales tax = 9.75% of 639.99

Sales tax = 0.0975 x 639.99

Sales tax = 62.40

Now we can find the total cost of the laptop with sales tax included:

Total cost = listed price + sales tax

Total cost = 639.99 + 62.40

Total cost = 702.39

Therefore, the total cost of the laptop with sales tax included is $702.39.

Answer:

$98 a month

Step-by-step explanation:

1,176 divided by 12

The lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

Let's call the length of the median from vertex J to the opposite side LM, and the length of the median from vertex L to the opposite side JN. We can use the fact that the centroid divides each median into two parts, with the ratio of the longer part to the shorter part being 2:1.

First, we can find LM:

LM = 2 x QM = 2 x 10 = 20

Next, we can find JQ:

JQ = 2/3 x JN = 2/3 x 39 = 26

Finally, we can find KQ:

To find KQ, we need to use the fact that the three medians of a triangle divide each other into six smaller triangles with equal areas. Let's call the length of the third median KX. We know that the area of triangle JLK is:

1/2 x LM x JN = 1/2 x 20 x 39 = 390

Similarly, the areas of triangles JNQ, LMQ, JKP, LKP, and JLP are all equal to 390. Let's call this common area A. Then we have:

1/2 x KX x LM = A

1/2 x KX x JN = A

Dividing these two equations, we get:

LM / JN = KX / LM

Substituting the values we know, we get:

20 / 39 = KX / 20

Solving for KX, we get:

KX = 20 x (20 / 39) = 400 / 39

Now we can find KQ:

KQ = 2/3 x KX = 2/3 x (400 / 39) = 800 / 117

Therefore, the lengths we found are:

LM = 20

JQ = 26

KQ = 800 / 117

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The variables I₁ and I₂ using the matrix algebra and using the Cramer's rule are I₁ = 1 and I₂ = 1

From the question, we have the following parameters that can be used in our computation:

15I₁ + 5I₂ = 20

25I₁ + 5I₂ - 30 = 0

Rewrite as

15I₁ + 5I₂ = 20

25I₁ + 5I₂ = 30

Rewrite as

I₁     I₂

15    5    20

25   5    30

From the question, the matrix form is

AI = b

Ths matrix A from the above is

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

Ths matrix B from the above is

[tex]B = \left[\begin{array}{c}20&30\end{array}\right][/tex]

And, we have the matrix I to be

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

Start by calculating the inverse of A from

[tex]A = \left[\begin{array}{cc}15&5&25&5\end{array}\right][/tex]

So, we have:

|A| = 15 * 5 - 5 * 25

|A| = -50

The inverse is

[tex]A^{-1} = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right][/tex]

Recall that

AI = b

So, we have

[tex]I = -\frac{1}{50}\left[\begin{array}{cc}5&-5&-25&15\end{array}\right] * \left[\begin{array}{c}20&30\end{array}\right][/tex]

Evaluate the products

[tex]I = -\frac{1}{50}\left[\begin{array}{c}5 * 20 + -5 * 30&-25 * 20 + 15 *30\end{array}\right][/tex]

[tex]I = -\frac{1}{50}\left[\begin{array}{c}-50&-50\end{array}\right][/tex]

Evaluate

[tex]I = \left[\begin{array}{c}1&1\end{array}\right][/tex]

Recall that

[tex]I = \left[\begin{array}{c}I_1&I_2\end{array}\right][/tex]

So, we have

I₁ = 1 and I₂ = 1

Recall that the determinant of matrix A calculated in (a) is

|A| = -50

Replace the first column in A with b

So, we have

[tex]AI_1 = \left[\begin{array}{cc}20&5&30&5\end{array}\right][/tex]

Calculate the determinant

DI₁ = 20 * 5 - 30 * 5

DI₁ = -50

Replace the second column in A with b

So, we have

[tex]AI_2 = \left[\begin{array}{cc}15&20&25&30\end{array}\right][/tex]

Calculate the determinant

DI₂ = 15 * 30 - 20 * 25

DI₂ = -50

So, we have

I₁ = DI₁ / |A| = -50/-50 = 1

I₂ = DI₂ / |A| = -50/-50 = 1

So, we have

I₁ = 1 and I₂ = 1

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Answer:

Step-by-step explanation:

you must work in a certain order, usually starting with parentheses, then exponents, then multiplication or division, and finally addition or subtraction.

The function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3).

In mathematics, a function is a relation between two sets that associates each element of the first set, called the domain, with a unique element of the second set, called the range. In other words, a function maps each input value to a unique output value.

The notation used to represent a function is f(x), where f is the name of the function and x is the input value. The output value is then given by the expression f(x).

Functions can be represented in various ways, such as tables, graphs, equations, and verbal descriptions. They are used to model real-world phenomena, analyze data, and solve problems in various fields, including science, engineering, economics, and finance.

To find the intercepts of the rational function, we set the numerator equal to zero and solve for x:

2/(2x² - x - 3) = 0

2 = 0 (there is no solution for x that makes the numerator zero)

Therefore, the rational function has no x-intercepts.

To find the y-intercept, we set x = 0:

f(0) = 2/(2(0)² - 0 - 3) = -2/3

Therefore, the y-intercept is (0, -2/3).

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

2x² - x - 3 = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 24))/4

x = (1 ± 5)/4

x = -3/2, 1

Therefore, the rational function has vertical asymptotes at x = -3/2 and x = 1.

To describe the behavior at the vertical asymptotes, we can use limits. Let's consider the vertical asymptote at x = -3/2:

lim x → -3/2+ f(x) = 2/(2(-3/2)² - (-3/2) - 3) = -∞

lim x → -3/2- f(x) = 2/(2(-3/2)² - (-3/2) - 3) = +∞

This means that as x approaches -3/2 from the right, the function approaches negative infinity, and as x approaches -3/2 from the left, the function approaches positive infinity. Therefore, the function has a vertical asymptote at x = -3/2 with a vertical (or infinite) discontinuity.

Let's now consider the vertical asymptote at x = 1:

lim x → 1+ f(x) = 2/(2(1)² - (1) - 3) = +∞

lim x → 1- f(x) = 2/(2(1)² - (1) - 3) = -∞

This means that as x approaches 1 from the right, the function approaches positive infinity, and as x approaches 1 from the left, the function approaches negative infinity. Therefore, the function has a vertical asymptote at x = 1 with a vertical (or infinite) discontinuity.

To analyze and draw the graph of the rational function, we can use the intercepts, asymptotes, and behavior at the vertical asymptotes that we found earlier. We can also find the horizontal asymptote by looking at the degree of the numerator and denominator:

Degree of numerator = 0

Degree of denominator = 2

Therefore, the horizontal asymptote is y =0

As we can see from the graph, the function has vertical asymptotes at x = -3/2 and x = 1, a horizontal asymptote at y = 0, and a y-intercept at (0, -2/3). The behavior at the vertical asymptotes is a vertical (or infinite) discontinuity.

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The complete question is:

Dev's velocity is [tex]\sqrt{5}[/tex]. Thus option B.

Kinetic energy is a amount of energy possessed when an object is in motion. Such that;

KE = 1/2 m v^2

Where m = mass, v = velocity

It is measured in Joules.

From the given question, we have;

KE = 1/2 m v^2

2KE = m v^2

v^2 = 2KE/ m

      = (2*150)/ 60

      = 300/ 60

      = 5

V = (5)^1/2

The velocity of Dev is B. [tex]\sqrt{5}[/tex].

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The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

Answer:

13

Step-by-step explanation:

First of all riley saved 200.73$ she needs 1,290.78$ so,

1290.78$-200.73$=1090.95$

she earns 83.85$ a week

then, 1090.95÷83.85= 13

13 weeks

The horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.

The force can be broken down into its horizontal and vertical components using trigonometry.

Horizontal component:

cos(42) = adjacent/hypotenuse

adjacent = cos(42) * 110 N

adjacent ≈ 80.34 N

Vertical component:

sin(42) = opposite/hypotenuse

opposite = sin(42) * 110 N

opposite ≈ 74.62 N

Therefore, the horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.

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The median the most useful measure of central tendency for these

times: is A) The median is not affected by an outlier.

The median is the middle value in a set of data when the values are arranged in order. In this case, the median of Brandon's climbing times would be 16, because it is the fourth value when the times are arranged in order:

13, 13, 14, 16, 17, 18, 35

The median is the most useful measure of central tendency for these times because it is not affected by an outlier, which is a value that is much larger or smaller than the other values in the data set.

In this case, the value 35 is an outlier, because it is much larger than the other values. If we were to use the mean as the measure of central tendency, the outlier would greatly influence the result. However, the median is not influenced by outliers, and therefore provides a better representation of the typical climbing time for Brandon.

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Answer:

B and D

Step-by-step explanation:

A and C are linear because they are going in a straight line. E is going downwards, so it is decreasing. That leaves B and D, which have exponential growth.

On sοlving the prοvided questiοn we can say that equatiοn Miles already ran -target distance = Miles still tο run 60 - 24 = 36 miles left tο run

A mathematical equatiοn is a fοrmula that links twο statements and uses the equals sign (=) tο indicate equality. In algebra, an equatiοn is a statement that demοnstrates the equality οf twο mathematical expressiοns.

We may begin by subtracting the miles Mοna has already ran frοm her οbjective distance tο get the number οf miles she must run each day tο accοmplish her gοal:

Miles already ran - target distance = Miles still tο run

60 - 24 = 36 miles left tο run

Since there are three days left in the week, Mοna must run:

36 miles ÷ 3 days = 12 miles per day

On a number line, we may begin with 24 and add 12 fοr each remaining day:

24 ------ 36 ------ 48 ------ 60

Tο represent this οn a number line, we can start at 24 and add 12 fοr each remaining day:

|---|---|---|---|---|---|---|

0 5 10 15 20 25 30 35 40

^ ^ ^

Day 5 6 7

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Matching each function with the transformation that took place gives:

g(x) = -(x - h)ⁿ: Reflection across the x-axis

j(x) = axⁿ + k: Translation of k units up

m(x) = (x + h)ⁿ - k: Translation of h units to the left

Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.

In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.

Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.

Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.

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The two lines are parallel because they have thesame slope and different y intercept

If two non-vertical lines that are in the same plane has the same slope. However the lines will have different y intercept.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Therefore putting the equations 15x−6y=−5 and 5x−2y=5 into that form.

15x-6y = -5

-6y = -15x-5

y = 5x/2 +5/6

for the second equation,

5x-2y =5

-2y = -5x-5

y = 5x/2 +5/2

therefore , the two lines are parallel because they have the same slope( 5/2) and different y intercept.

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The right circular cylindrical tank which is 5 m long and 13 m in diameter holds about 663,325 liters of liquid approximately.

The formula to find the volume of a right cylindrical tank is

V = πr²h, where 'r' is the radius and 'h' is the height.

Given that, the height is 5 m and the diameter is 13 m.

Radius = Diameter/2.

Radius = 13/2 = 6.5 m.

We know that, π = 3.14.

Now, we can substitute the values in the formula.

V = 3.14×(6.5)²×5.

V = 3.14×6.5×6.5×5

V = 663.325 cubic meters.

Now, we have to convert cubic meters into liters.

We need to multiply by 1000 as a thousand liters are in one cubic meter.

663.325×1000 = 663,325.

Therefore, the tank holds about 663,325 liters of liquid approximately.

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Answer: 601 meters

Step-by-step explanation:

First, let's find the midpoint between the "Falcon Flyer" and the "Sprinter".

The x-coordinate of the midpoint is (50 + 400)/2 = 225.

The y-coordinate of the midpoint is (300 + 550)/2 = 425.

So the midpoint is (225, 425).

Now we need to find the distance between the midpoint and the "Air Rider". Using the distance formula:

d = sqrt[(800 - 225)^2 + (250 - 425)^2]

d = sqrt[(575)^2 + (-175)^2]

d = sqrt[330625 + 30625]

d = sqrt(361250)

d ≈ 601.041

So the distance you will walk on this shortcut is approximately 601 meters.

Answer: #1

Step-by-step explanation:

In situation number one, the equation for the garden's area would be [tex]x^2[/tex] which is nonlinear. The other questions map to linear equations in the form [tex]y = mx + b[/tex]

Answer:

Linear relationship always produces a straight line and are without exponential.

2.the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

3.the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

Step-by-step explanation:

Hope this helps! =D

The expression that can be used to find out the amount of time it would take Sal to finish the remaining homework is C. 4 / 9 x 3 / 5 .

To find the expression that would show the time it would take for Sal to finish his homework, the formula would be:

= Proportion of questions remaining x Time taken to finish one question

Proportion of questions remaining:

= 1 - 5 / 9

= 4 / 9

Time taken to finish one question:

= 3 / 5 minutes

The expression is therefore:

4 / 9 x 3 / 5

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There are 100 cookies.

To find the number of cookies, we can set up a proportion using the given ratio of cookies to glasses of milk, which is 4:1. Let x be the number of cookies:

4/1 = x/25

Now, cross-multiply and solve for x:

1 * x = 4 * 25

x = 100

Based on the given data, the age of Mr. Wright currently is 30 years

If Micah is 3 years old, then Lilly is twice as old, which means that

Lilly is 2 * 3 = 6 years old.

Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:

5 * 6 = 30 years old.

Therefore, Mr. Wright is 30 years old.

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The probability that either event will occur is given as follows:

P(A or B) = 0.83.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The "or probability" is defined as follows:

P(A or B)=P(A) + P(B) - P(A and B).

From the Venn Diagram, the probabilities of each event are given as follows:

Hence the or probability is given as follows:

P(A or B) = 0.5 + 0.3333 + 0

P(A or B) = 0.83. (rounded to the nearest hundredth).

The Venn diagram is given by the image presented at the end of the answer.

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Answer:

If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:

f(x) = (x-1)(ax + b)

where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:

f(x) = (x-1)(ax + b) = 4x² - 4x - K

Expanding the left side of the equation, we get:

ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K

Now we can equate the coefficients of the like terms on both sides of the equation.

The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:

a = 4

The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:

b - a = -4

Substituting a=4, we get:

b - 4 = -4

Solving for b, we get:

b = 0

So the polynomial can be written as:

f(x) = (x-1)(4x + 0) = 4x² - 4x

Therefore, K = 0.

To find the roots of the equation, we need to set f(x) = 0 and solve for x:

4x² - 4x = 0

Factor out 4x:

4x(x - 1) = 0

So the roots of the equation are x = 0 and x = 1.

Recall the general equation for a line in slope-intercept form:

[tex]y=mx+b[/tex]

where:

[tex]\text{y = y-coordinate}[/tex]

[tex]\text{m}=\bold{slope}[/tex]

[tex]\text{x = x-coordinate}[/tex]

[tex]\text{b = y-intercept}[/tex]

In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:

[tex]-4x+y=0[/tex]

[tex]-4x +4x+y=0+4x[/tex]

[tex]\implies y=4x+0[/tex]

Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.

If you were to graph the line, you would see the intersection at (0,0):

graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]

Answer:

x = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take square root of both sides )

x = [tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]

The surface area of the square pyramid is 416.23 ft²

The surface area of a square pyramid is given by the formula:

A = a² + 2a√(a²/4 + h²)

Where a is the base length of the square pyramid and h is the height of the square pyramid.

From the figure, we have: a = 10 ft and h = 15 ft

A = a² + 2a√(a²/4 + h²)

A = 10² + 2*10√(10²/4 + 15²)

A = 100 + 20√(100/4 + 225)

A= 100 + 20√250

A = 416.23 ft²

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Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

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Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240