Lawrence Wagner purchased a log splitter with an installment loan that has an APR of 10 percent. The log splitter sells for $997. The store financing requires a 10 percent down payment and 36 monthly payments. What is the finance charge?

The commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

Given that the commission rate is 6%

If the sales done is 33000 dollars then the commission received by the agent would be:

33000 * 0.06 = 1980

Now if the sale doubles we would have 33000 x 2

= 66000 dollars

then the commission received would be

66000 x 0.06

= $3960

Hence we would say that the commission for the sale of $33000 worth of items at 6 percent is $1980 and if the sale doubles than the commission would be $3960

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The exercise above is one of the Discontinuous Initial Value Problems (DIVP) with a Discontinuous Function.

An Initial value problem

This topic is related to multivariable calculus. It is a standard differential equation with an initial condition that describes the unknown function's value at a selected point in the domain. IVP is often used in physics for modeling.

The solution for the IVP (Initial Value Problem) whose input function g(x) is discontinuous

y" + 4y = g(x),

y(0) =1, and

y' (0) = 2

Where

g(x) = [ sin x ,  0 ≤ x ≤ π /2 ]

         [  ,  x > / 2 ]

For the lower interval and use the result to solve the upper interval.

The homogeneous solution to (1) where (1) is

y′′ + 4y = g(x), y(0) = 1, y′(0) = 2

m² + 4 = 0 → m₁,₂ = ± 2i

From this derive:

y h = c₁ Cos 2x + c₂ sin 2x

To resolve the particular solution,

y p = a cos x + b sin x

Resolving the constants a and b, let's substitute back into equation 1 above to arrive at:

-a cos x - b sin x + 4a cos x + 4b sin x = sin x

From the above,

a = 0 and b= 1/3

Rewriting the equation,

y = y h + y p = c₁ cos 2x + c₂ sin 2x + 1/3sinx

Initiation constraints

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.

Using the Initiation constraints, we solve for c₁ and c₂:

c₁ = 1, c₂ = 5/6, this leaves us with the following:

y(x) =cos2x + 5/6sin 2x + 1/3sinx,

0 ≤ x ≤ π / 2                      (2)

From the above, we must proceed to calculate the upper half of the range so that we have, y" + 4y = 0.

Using the initial constraints in combination with (2), we get y  = -(2/3) and

y' (/2) = -(5/3)

Recall that solution 2 was:

y = c₁ cos 2x + c₂ sin 2x

With the new constraints, we can resolve this get:

c₁ = 2/3, c₂ = 5/6, so

y(x) = 2/3cos 2x + 5/6sin 2x, x > /3           (3)

Combining equations 2 and 3, we have:

y(x) = [ cos 2x + 5/6 sin 2x + 1/3 sin x , 0 ≤ x ≤ π / 2 ]

      = [ 2/3 cos 2x + 5/6 sin 2x,   x > π /2 ]

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Step-by-step explanation:

4(n^3 - 6)

hope this helps

The number of words Gillan can read in 1 minute is,  165

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Gillan read 3,135 words in 19 minutes

The number of words read each minute = w

Now, it has given,

Total words = 3135

Time taken = 19 minutes

For words per minute,

we need to take ratio of total words and total time taken,

Ratio =  Total words/Time taken

         =   3135/19

         =   165

Hence, the number of words in 1 minute is 165

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Using the constant of proportionality the value of x when y is 72 is 9.

What is a COP?

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.

If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.

To find k, we can use the given information that y = 48 when x = 6 -

y = kx

48 = k(6)

k = 8

Now that we know k, we can use it to find x when y = 72 -

y = kx

72 = 8x

x = 9

Therefore, when x = 72, the value of x = 9.

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The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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Answer:

x = 6

∠D = 127

Step-by-step explanation:

In a parallelogram, opposite angles are equal and adjacent angles add to 180

⇒ ∠A = ∠C and ∠C + ∠D = 180

∠A = ∠C

⇒ 13x - 25 = 9x - 1

⇒ 13x - 9x = 25 - 1

⇒ 4x = 24

⇒ x = 24/4

⇒ x = 6

∠C =  9x - 1

= 9(6) - 1

= 54 - 1

= 53

∠C + ∠D = 180

⇒ ∠D = 180 - ∠C

= 180 - 53

= 127

Examining the word problem we can say that, Molly used 160 beads to make the necklace.

Let's assume the number of beads used to make the bracelet is x.

We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,

x + 5x = 192

6x = 192

solve for x

x = 192 / 6

x = 32

Molly used 32 beads to make the bracelet.

number of beads used to make the necklace

Number of beads used for the necklace = 5 * 32

Number of beads used for the necklace = 160

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Answer:

Eve gets 1.47 and Amelie gets 0.81

Step-by-step explanation:

the ratio is 9 to 5 so we can say 9x + 5x=2.28

14x=2.28

x=0.16

so eve gets 9x = 9(2.28/14) = 1.47

and amelie gets 5x = 5(2.28/14) = 0.81

Answer:

Arthimatic is the answer

Answer:

The area of the remaining board is (x² - 289) sq. ft.

Step-by-step explanation:

Let the sides of the bigger square board be, x feet.

It is provided that a smaller square of side length 17 feet is cut out of the bigger square board.

The area of a square is:

\(Area=(side)^{2}\)

Compute the area of the bigger square board as follows:

\(A_{b}=(side_{b})^{2}=x^{2}\)

Compute the area of the smaller square board as follows:

\(A_{s}=(side_{s})^{2}=(17)^{2}=289\)

Compute the area of the remaining board in square feet as follows:

\(\text{Remaining Area}=A_{b}-A_{s}\)

                          \(=[x^{2}-289]\ \text{square ft.}\)

Thus, the area of the remaining board is (x² - 289) sq. ft.

Answer:

Step-by-step explanation:

c=2A

An equation is formed when two equal expressions. The correct option is B.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that the cost to paint an area of 1,500 square feet is $3,000. Therefore, the equation that gives the relationship between c, cost and A, the area is,

cost = constant × area

c = k × A

$3000 = k × 1500 ft²

k = $2 per square feet

Now, the equation that gives the relationship between c and A can be written by substituting the value of k in the equation,

c = k × A

c = 2 × A

c=2A

Hence, the correct option is B.

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x=66

132/2

I hope you understand Mr. Potaaato

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

10.5

Step-by-step explanation:

250% = 2.5

What number is 250% of 4.2?
We Take

2.5 x 4.2 = 10.5

So, 10.5 is 250% of 4.2

Answer:

6 gallons 72-octane

6 gallons 84-octane

Step-by-step explanation:

(84 + 72)/2 = 78

The average octane in 72-octane and 84-octane is 78-octane.

Therefore, you need equal amounts of each.

Answer:

6 gallons 72-octane

6 gallons 84-octane

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer:

a(n)=1+(n-1)(-3)

Step-by-step explanation:

Notice there's a common difference of d=-3.

If we use the formula a(n)=a1+(n-1)d to find the nth term given the first term and the common difference, we will see that the function that describes the arithmetic sequence as a(n)=1+(n-1)(-3)

Answer:

Conclusion

     We can conclude that the believe of the  mangers of the regional banks is true

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  200

    The  mean for  Regular user is  \(\= x_1 = 143\)

    The mean for Non regular  is  \(\r x_2 = 133\)

   The standard deviation for  Regular is  \(\sigma_1 = 30\)

    The standard deviation for Non regular  is \(\sigma _2 = 34\)

   The level of significance is  \(\alpha = 0.0 5\)

The null hypothesis is

       \(H_0 : \r x_1 = \r x_2\)

The alternative hypothesis is  

      \(Ha: \r x_1 > \r x_2\)

The test statistics is mathematically represented as

        \(Z = \frac{\r x _1 - \r x_2}{\sqrt{\frac{\sima_1^}{n} } + \frac{\sigma_2^2}{n} }\)

substituting values

        \(Z = \frac{143 - 133}{\sqrt{\frac{30^2}{200} } + \frac{34^2}{200} }\)

      \(Z = 3.12\)

Now the critical value of the level of significance obtained from the z-table is

      \(t_{\alpha } = 1.645\)

 So given the fact as seen from the above calculation that  \(Z > t_{\alpha }\)

Then the Null hypothesis would be rejected as there is no sufficient evidence to back up the null hypothesis  [Which stated that the profit from both users are the same ]

Moving 5 one digit to the left, one number in which the value of digit 5 is 10 times as great as in 253,829 is in 538,290.

It means that the value of the digit is multiplied by 10.

Hence, moving the digit 5 one position to the left, and appending a zero at the end, generating the number 538,290, the value of digit 5 is 10 times as great as in 253,829.

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Answer:

They're all manufactured

Step-by-step explanation:

i think so

They are all consumable products

You need to buy more gas every now and then.

Yogurt runs out.

Cereal runs out.

Glue don't last forever.

Soap gets used up.

Yarn gets used up.

3172.97 joules is the value of x when the Richter scale rating is 3.2

The equation that relates earthquake magnitude (M) and energy (E) is:

M = 2/3 × log(E) - 1.8

We have to find the value of X when the richer scale rating is 3.1

If an earthquake with a rating of 3.2 is not usually felt, then we can assume that x corresponds to the energy released by an earthquake that is just barely felt.

According to the United States Geological Survey, an earthquake with a magnitude of 2.5 corresponds to an energy release of about 1.3 × 10⁸ joules.

Using this as a reference point, we can set up the following equation:

3.2 = 2/3 × log(x) - 1.8

Solving for x, we get:

2.3 = 2/3 × log(x)

log(x) = 3.45

x = 3172.97

Therefore, the value of x when the Richter scale rating is 3.2 is approximately 3172.97 joules.

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Answer:

35,000 - 8000=27,000 altitude

Answer:

the answer is 16

Step-by-step explanation:

because 3+1+2+2+2+2+2=16

Answer:

y > 2

Step-by-step explanation:

1) \(3(y+5)>21\)

Divide both sides by 3.

2) \(y+5>7\)

Move the constant to the right side and change it's sign.

3) \(y>7-5\)

Subtract the numbers.

4) \(y>2\)

Answer:

11

Step-by-step explanation:

i don't know

Answer:

coke red

Step-by-step explanation:

correct me if im wrong

Answer:

in 2 there are 10 fifths 10 fifths + 1 fifth = 11 fifths.

Answer:

A- 11

Step-by-step explanation:

Number = 2 1/5 = 11 / 5

Fifths = 1/5

Answer = 11/5 ÷ 1/5 = 11/5 x 5/1 =11

I hope im right!!

Answer:

D. 157.5°

Step-by-step explanation:

We can find the sum of the interior angles with this formula:

s = (n - 2)(180)

Plug in the number of sides and calculate:

s = (16 - 2)(180)

s = (14)(180)

s = 2,520

Now, divide by 16 to get the measure of one interior angle:

2520/16 = 157.5