andscaper creates a rectangular garden
side a rectangular lawn. The dimensions
the garden and lawn are shown in the
agram. Which expression represents
e area of the lawn, in square feet, in
Ctored form?

To calculate \(\frac{{f(x+h) - f(x)}}{h}\) for the function \(f(x) = ax^3\), we need to substitute the expressions into the formula and simplify.

\(f(x+h) = a(x+h)^3\\\\f(x) = ax^3\)

Now we can calculate the difference:

\(f(x+h) - f(x) = a(x+h)^3 - ax^3\)

Expanding \((x+h)^3\):

\(f(x+h) - f(x) = a(x^3 + 3x^2h + 3xh^2 + h^3) - ax^3\)

Simplifying:

\(f(x+h) - f(x) = ax^3 + 3ax^2h + 3axh^2 + ah^3 - ax^3\)

The terms \(ax^3\) cancel out:

\(f(x+h) - f(x) = 3ax^2h + 3axh^2 + ah^3\)

Now we can divide by h:

\(\frac{{f(x+h) - f(x)}}{h} = \frac{{3ax^2h + 3axh^2 + ah^3}}{h}\)

Canceling out the common factor of h:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3axh + ah^2\)

Now, we evaluate this expression again by setting h = 0:

\(\frac{{f(x+h) - f(x)}}{h} = 3ax^2 + 3ax(0) + a(0)^2\)

\(= 3ax^2\)

Therefore, when we evaluate the expression by setting h = 0, we get \(3ax^2\).

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Answer:

B

D

A

C

Step-by-step explanation:

Whatever is listed 2nd in the parentheses, do that function first. Then take that result & do the function listed first.

Answer:

1066

Step-by-step explanation:

5 mins = 410 words

410/5 = 82 so she is typing 82 words a minute

Then do 82 times 13

Answer:

I-

Step-by-step explanation:

Answer:

5.88889

Step-by-step explanation:

5 8/9

=53/9

=5.88889

Answer:5.88889

Step-by-step explanation:

you would multiply 5 by the denominator and you would get 45 then add 45 by the numinator and you would get 53 and you would get an improper fraction which is 53/9 and then you divide 53 by 9 and get 5.88889.

Answer:

{(-20, -3), (-12, -1), (-8, 0), (-4, 1), (4, 3)}

Step-by-step explanation:

Switch x and y in each ordered pair.

The inverse relation of {(-3, -20), (-1, -12), (0, -8), (1, -4), (3, 4)} is

{(-20, -3), (-12, -1), (-8, 0), (-4, 1), (4, 3)}

Answer:

it depends on the choices

Step-by-step explanation:

The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].

Part I: Effective cost per hour per employee

To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.

Base hourly wage: $12.30 per hour

Number of working hours per day: 8 (1 shift)

Number of holidays: 5

Number of vacation days: 7

First, let's calculate the total fringe benefits per hour:

Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551

Next, let's calculate the paid time off per hour:

Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours

Now, let's calculate the effective cost per hour per employee:

Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)

Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)

Part II: Reduction in labor cost

To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.

Number of working hours needed every year: 306,050

Productivity increase from 70% to 85%: 85% - 70% = 15%

First, let's calculate the initial number of workers needed:

Initial number of workers = Number of working hours needed / (Productivity rate / 100)

Initial number of workers = 306,050 / (70 / 100)

Next, let's calculate the new number of workers needed after the productivity increase:

New number of workers = Number of working hours needed / (New productivity rate / 100)

New number of workers = 306,050 / (85 / 100)

Finally, let's calculate the total dollar change in labor expense:

Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year

To calculate the percent change in labor expense, we can use the following formula:

Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100

Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.

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Answer:

Step-by-step explanation: A. One unique triangle because the three angles add up to 180 degrees

42+42+96=180

Answer:

y=2x+7

Step-by-step explanation:

I used desmos(.com)

The recursive formula for the number of regions created by n lines, where every pair of lines cross and no three lines cross at the same point, is Rn = Rn-1 + (n - 1).

Let n be a natural number representing the number of lines drawn in the plane such that every pair of lines cross and no three lines cross at the same point. Suppose we wish to determine the number of regions in the plane, including some unbounded regions rn. For instance, in the picture below, there are 5 regions in the plane, including two unbounded regions.In order to find a recursive formula for the number of regions created by n lines, we can start with the base case where n = 1. If there is only one line, there will be two regions: one bounded and one unbounded. Next, we can find a recursive formula for n lines by adding one more line and counting the number of regions it creates. When we add a new line, it will intersect every existing line once and create new intersection points. By connecting these points, we can see that the new line will divide each existing region it passes through into two parts. Additionally, it will create a new region bounded by the new line and the previous lines. Therefore, the number of regions created by adding one more line is equal to the number of regions created by the previous (n - 1) lines, plus the number of intersection points created by the new line. The number of intersection points created by the new line is equal to the number of existing lines it intersects, or (n - 1). Thus, we obtain the recursive formula:Rn = Rn-1 + (n - 1)where Rn represents the number of regions created by n lines and Rn-1 represents the number of regions created by the previous n - 1 lines.To justify why this recursion is correct, we can use mathematical induction. The base case is when n = 1, which we have already established as true. Now, assume that the recursion is true for some n = k. Then, we have:Rk = Rk-1 + (k - 1)Next, consider the case where n = k + 1. By adding one more line, we obtain the formula:Rk+1 = Rk + kWe can substitute our expression for Rk into this equation to obtain:Rk+1 = Rk-1 + (k - 1) + k = Rk + (k - 1) + k = Rk + kNow, we can see that this is the same as our formula for Rk+1, which is:Rk+1 = Rk + kTherefore, the formula is true for n = k + 1. By the principle of mathematical induction, it follows that the formula is true for all natural numbers n ≥ 1.

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The angle X of the given triangle is equal to 83.0°.

This law is represented by the equation: C²=A²+B²-2ABcosθ, where: A,B and C are the sides of a triangle and θ=angle.

For solving this question, you should apply the Law of Cosines, where:

A=8ft

B=16ft

C=17 ft

θ=X

\(C^2=A^2+B^2-2*A*B*cos\theta \\ \\ 17^2=8^2+16^2-2*8*16*cosX\\ \\ 289=64+256-256*cosX\\ \\ 256cosX=256+64-289\\ \\ 256cosX=31\\ \\ cosX=\frac{31}{256}\)

Therefore, \(arccos(\frac{31}{256} )=83.0^{\circ \:}\).

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Given the following expression:

You can follow the steps shown below in order to find an equivalent expression. But first, it is important to remember that an equivalent expression can be found by simpliying an expression.

1. According to the Product of Powers property:

Then, you can rewrite the expression as following:

2. Descompose 44 into its prime factors:

3. Substitute the above into the expression:

4. Remember the following property for Radicals:

5. Then, you can simplify the expression:

The answer is: Option A.

Answer:

\(2.077\) × \(10^{-4}\)

Step-by-step explanation:

To convert to scientific notation, you need the number to be less than 10, but greater than 1 and is multiplied by a base of 10 to the power of the number of times you moved the decimal. So you need to shift the decimal place 4 times to the right to get to 2.077 (which is less than 10, but greater than 1). The next part is that you’ll need a base number, which is 10 because your moving the decimal by 10s. Since the decimal is being moved to the right, the exponent will be negative. You moved it 4 times so it’s \(10^{-4}\). The finished answer is:

\(2.077\) × \(10^{-4}\)

Hope this helps and answers your question! :)

Answer:

top answer is -23

bottom answer is -2

Cash received for interest during  2014 was $3,500 .The following equation can be used to determine the amount of money received as interest in 2014:

Amount received as interest equals Interest Income for 2014 plus the decline in Interest Receivable

The difference between the balance of interest receivable at December 31, 2013, and at December 31, 2014, can be used to calculate the decline in interest receivable:

Reduced interest due = Interest due at December 31, 2013, minus Interest due at December 31, 2014, which equals $1,100 minus $1,400, or -$300.

The fact that the balance of interest receivable increased from 2013 to 2014 indicates that the company produced more interest money during the year than it received. In light of this, the money earned on interest in 2014 is:

Interest income from 2014 plus a decrease in interest receivable equals $3,200 minus (-$300) to $3,500 in interest payments received.

Hence, $3,500 is the correct response (C).

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Answer:

x =√969

Step-by-step explanation:

AC²=AB²+BC². (Formula)

(35)²=(16)²+BC²

1225-256=BC²

969=BC²

BC=√969

Answer:

6

Step-by-step explanation:

To breakeven means that you made exactly as much money as you spent, so if you spent $50 to make lemonade, you would need to make $50 in profits from selling to break even

first subtract the cost of making each horse from the price of selling each horse (you do this to find out how much profits he makes from one horse):

125 - 75 = 50

now divide 300 by 50 to find out how many horses need to be made to break even:

300 ÷ 50 = 6

Step-by-step explanation:

AB=BC

8x+6=6x+18

2x=12

x=6

so

AB= 48+6=54cm

BC=36+18=54cm

AD=CD

8y+20=12y-8

-4y=-28

y=7

so

AD= 84-8=76cm

CD=56+20=76cm

AE=2x+4y

AE=2×6+4×7

AE=40cm

AC=2×40=80cm

9514 1404 393

Answer:

  A)  42°

Step-by-step explanation:

The whole is the sum of the parts. Lines AH and BC cross at right angles, so angle CDE is a right angle. Then angles CDJ and JDE will have a total of 90°.

  ∠CDJ +∠EDJ = 90°

  3x° +(2x +10)° = 90°

  5x = 80 . . . . . . . . . divide by °, collect terms, subtract 10

  x = 16 . . . . . . . . divide by 5

  (2x+10)° = (2(16) +10)° = 42°

Angle EDJ is 42°.

The value of b in the given angle is 25°.

Six Different Angles

So, the balance of b is:

And ∠90° is divided into two portions which are:

Now, calculate for b as follows:

Therefore, the value of b in the given angle is 25°.

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Scientific Notation is made up of two number parts. The first part should be a number between 1 and 100. This statement is true, and the justification is given below.

Scientific notation is a method of expressing a number as a product of a decimal number between 1 and 10 and a power of 10. The decimal part is the first number part, and the power of 10 is the second. Here's an example of how to write a number in scientific notation:435,000 = 4.35 × 10⁵The number 4.35 is between 1 and 10, and the power of 10 (5) represents the number of places the decimal point should be moved to get the original number.Similarly, if the first number part of a scientific notation is not between 1 and 10, we have to adjust the power of 10 accordingly. For instance:0.0025 = 2.5 × 10⁻³Therefore, Scientific notation is made up of two number parts, and the first part should be a number between 1 and 100.

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Uma pay in order to replace her stuff as $1000.

According to the scenario, Uma's possessions worth $5,600 were stolen or destroyed due to the burglary. Since this amount is less than the coverage limit, Uma will be eligible for reimbursement from her insurance policy. However, she will still need to pay the deductible.

To calculate how much Uma will pay to replace her stolen items, we need to subtract the deductible from the total loss. In this case, Uma's total loss is $5,600, and her deductible is $1,000. Therefore, the amount she needs to pay out of pocket is $1,000.

To summarize, Uma's insurance policy will cover the remaining amount after she pays the deductible. In this scenario,

Uma will receive reimbursement for

=> ($5,600 - $1,000) = $4,600

from her insurance company.

She can use this amount to replace her stolen or destroyed possessions.

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If the statement "No sting operations are cases of entrapment" is true, then the truth values of the following statements are as follows:

a. All sting operations are cases of entrapment: F

b. Some sting operations are cases of entrapment: T

c. Some sting operations are not cases of entrapment: T

This is determined by using the traditional square of opposition.

The traditional square of opposition is a diagram that represents the logical relationships between different types of categorical propositions. Each corner of the square represents a different type of proposition, and the lines connecting the corners indicate the logical relationships between the propositions.

In this case, the statement "No sting operations are cases of entrapment" is a universal negative proposition. According to the traditional square of opposition, the truth value of the other statements can be determined as follows:

a. All sting operations are cases of entrapment. This statement is a universal affirmative proposition, and it is contradictory to the given statement. Therefore, its truth value is false (F).

b. Some sting operations are cases of entrapment. This statement is a particular affirmative proposition, and it is contrary to the given statement. Therefore, its truth value is false (F).

c. Some sting operations are not cases of entrapment. This statement is a particular negative proposition, and it is subcontrary to the given statement. Therefore, its truth value is true (T).

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Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

Answer:

X^158

Step-by-step explanation:

X^60xX^-18x(    )=X^200

X^42x(   )=X^200

x^158

The option that correctly describes the graph below is A. Piecewise function.

A piecewise function is a function that reacts in different ways based on the input received at every point in time. This function has different intervals and funtions that apply to the respective domains.

Sometimes, these graphsa re recognized by the three main parts that they have. So, the function that is represented by the graph is the piecewise function.

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In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

What in mathematics is a linear equation?

5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5

Since there are 15 values,

           their mean is 111.5/15=7.43 which is very close to the mean.

A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes

D)The shape of the histogram can be approximated with a normal curve.

E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

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