Clearly and neatly show all work for each problem. Round all final answers to thenearest dollar. Do not round intermediate work.Fitzwilliam is buying a new car. The sticker price for the base model is $10,000,but the options he wants will cost him an extra 15%. He then talks the dealer intogiving him 10% off. Fitzwilliam has also decided to put down a 25% downpayment on the car.Find Fitzwilliam's down payment on the car.Find the balance that Fitzwilliam needs to finance.

We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,

Applying this property to the presented case, we obtain that

Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.

Thus, the answer to the exercise is a= 2 and b = 13.

[tex]\framebox{Slope intercept: -$\dfrac{5}{3}$x+3}[/tex]

The slope intercept form of  [tex]5x+3y=9[/tex] would be written as:

[tex]-\frac{5}{3} x+3[/tex]

The first number before the decimal point is the ones place.

48.26

ones = 8

The second number after the decimal point is the hundredths place:

48.26

hundredth: 6

Set A is composed of all the even numbers equal or greater than 4 and equal or less than 8 so set A is:

The cardinalities of A and B are equal to their number of elements so we have n(A)=3 and n(B)=7.

With both sets explicitly written we can complete the true or false table. The only thing to take into account is that the symbol ∈ means "belongs to" and that ∉ means "does not belong to".

The first statement of the table is:

This is false because 12 does not belong to set A since it is not included in it.

The second statement is:

As you can see 22 is in deed one of the elements of set B which means that this statement is true.

The third one is:

This statement is false because as we saw before 6 is an element of set A.

The last statement is:

As you can see -24 is one of the elements of set B so this statement is true.

False

True

False

True

Step 1: Problem

Step 2 : Concept

QR = 136

PQS = 42 + 136 + 42 = 220

PS = 64 + 72 = 136

For the given vector  v=7i - 5j and w=-i+j,

        projwv =  6i - 6j

                   v1 = 6i -6j

                     v2 = i +j

Vector:

              A quantity that has both magnitude and direction are called vector. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.

a) projwv is the projection of v onto w. Use the following equation:

projwv = [(v•w)/((magnitude(w))2)] w

v•w = (7*-1) + (-5*1) = -12

(magnitude w)^2 = ([tex]\sqrt{1^{2} + 1^{2}}[/tex])^2 = 2

projwv = ((-12)/2)(-i + j)

            =  6i - 6j

b) The two components of the decomposed v will add to create the original vector v. v1 that is parallel to w will be the same as the projection of v onto w.

v = v1 + v2

v2 = v - v1 = (7i - 5j) - (6i -6j) = i +j

You can check that v2 is orthogonal by taking the dot product (v2•w). This equals 0.

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The given system is

First, we multiply the first equation by -3/10.

Then, we sum the equations

Since the sides of the rectangle are in ratio 5: 7

Insert x in the 2 terms of the ratio and find its perimeter using them

Equate 24x by the given perimeter 72 to find the value of x

Divide both sides by 24

Then the sides of the rectangle are

Since the rule of the area of the rectangle is A = L x W, then

The area of the rectangle is 315 square units

178.98 yd³

The shape consists of a cone and a cylinder. So we would find the volume of each and sum them together.

Volume of a cone = 1/3 πr²h

r = radius = 3 yd

h = height = 4 yd

let π = 3.14

Volume of the cone = 1/3 × 3.14 × 3 × 3 × 4

Volume of the cone = 37.68 yd³

Volume of a cylinder = πr²h

r = radius = 3 yd

h = height = 5 yd

Volume of a cylinder = 3.14 × 3 × 3 × 5

Volume of a cylinder = 141.3 yd³

Volume of the shape = Volume of the cone + Volume of a cylinder

Volume of the shape = 37.68 + 141.3

Volume of the shape = 178.98 yd³

Explanation:

This function is C(n) which means it's a function of n. It is said that n is the number of observed vehicles in a specified time interval. It cannot be negative and it has to be an integer. Therefore the domain is all integers greater or equal than zero.

Answer:

4) {0, 1, 2, 3...}

Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.

Given,

The selling cost of shelving units that are 10 years old = $800

Original cost of shelving units = $6400

Estimated residual value for 10 years = $400

Assets = Liabilities +Stockholders equity

Accumulated depreciation for 10 years=[(Original cost of the equipment-Residual value) / Useful life] ×10 years

=[($6400-$400)/10 years]×10 years

=$600×10 years

=$6000

Book value equipment=Original cost of the equipment-Accumulated depreciation for 10 years

=$6400-$6000

=$400

Calculate gain on sale of equipment.

Gain on equipment sale equals selling price minus book value of equipment

=$800-$400

=$400

Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.

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So,

We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation:

A) It's a function because each point of x has a point on y.

B. It's a discrete functions because you can't see a continuous line.

C. Domain (-3,6)

D. Range (0,3)

* C and D if each square is equivalent to 1 unit.

Given:

The vertical height is 30ft.

The angle of elevation is 30 degrees.

To find:

The distance travelled by the person from bottom to top of the escalator.

Explanation:

Let x be the slant distance.

Since it is a right triangle.

Using the trigonometric ratio formula,

Therefore, the distance travelled by the person from the bottom to the top of the escalator is 60ft.

Final answer:

The distance travelled by the person from bottom to top of the escalator is 60ft.

We have the following equation:

where x denotes the number of years after 1998.

By substituting the given information, we have that

and we need to find x. Then, by dividing both sides by 1.8208, we get

then by taking natural logarithm to both sides, we obtain

which gives

then, the number of years after 1998 is:

which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.

The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

The given parameters are

Degree = 5

Zero = 1, i, 1 + i

There are complex numbers in the above zeros

This means that, the other zeros are

Zeros = 1 - i and -i

The equation of the polynomial is then calculated as

P(x) = Leading coefficient * (x - zero)^multiplicity

So, we have

P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)

This gives

P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)

Solving further, we have

P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)

P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)

Evaluate the products)

P(x) = (x³  - x² + x - 1) * (x² - 2x + 2)

This gives

P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2

Express in standard form

P(x) = x⁵ - 2x⁴ - x⁴ + 2x³  + 2x³ + x³ - 2x²  - 2x²  - x² + 2x + 2x - 2

Evaluate the like terms

P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2

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Given

First : They assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones

Let's represent regular wreaths with r

and

Let's represent deluxe wreaths with d

Second: They assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones

We now have

we can now solve simultaneously, by subtracting the equation 1 and 2

We can subsitute d=5 in equation 1 or 2

The final answer

5 pinecones on the deluxe wreath and 3 pinecones on the regular wreath

After multiplying the value of P is 32 ft and the value of A is 64 sq. ft.

In the given question we have to find the value of P and A.

The given expression for P is

P = (4 X 8)

The given expression for A is

A = (8 X 8)

In the given P representing the perimeter of square because the formula of perimeter is

P = 4* side

A representing the area of square because the area of square is

A = side*side

So the value of P

P = (4 X 8)

P = 32 ft

The value of A

A = (8 X 8)

A = 64 sq. ft

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3+15+75+.....+46875

a1 = first term = 3

If we multiply the first term by 5, we obtain the second term.

3 x 5 = 15

15x 5 = 75

75x 5= 375

375x5= 1875

1875x5=9375

9375x5= 46875 (7th term) n=7

So,

r= 5

Apply the formula:

an= a1 * r^(n-1)

an= 3 * 5 (n-1)

Sum

Sn = a1 (1 -r^n) / 1- r

S(7) = [3 (1 - 5^7)] / 1-5

S(7) = [3 (1-78,125)] /-4

S(7) = 58,893

10% = 10/100 = 0.10

therefore:

answer: 2.5

To find Mario's current grade is to find the average of all his grades for the first quarter.

The average of his grade for the first quarter is the mean which is 70 percent.

Also, 70 percent is equivalent to a C minus

Well, I would like to know more about this problem.

If you are solving an equation it is wrong because you are adding 10 units only in one side of the equation, that is a mistake.

If this is not a process to solve the equation it is correct, it does not matter if you are only adding 10 in one side.

Given the equation system:

To solve the system and determine the value of x, first step is to write one of the equations in terms of y:

Then replace this expression in the second equation

Now that you have an expression with only one unknown, x, you can calculate its value.

Solve the parenthesis using the distributive property of multiplication

Let x be the unknown value.

Therefore we have

So we can inform from the first term that the denominator is double the numerator, since this term is equal to second term with the unknown x, same applies there also.

So,

This can be further confirmed by applying cross multiplication,

Total income= $34910

Amount spent on food = $7104

Answer:

√52 feet

Step-by-step explanation:

5 - -1 = 6

-2 - 2 = -4

6 = change in y

-4 = change in x

a² + b² = c² (pythagoras theorem)

6² = 36

-4² = 16

36 + 16 = 52

c² = 52

c = √52

Answer: square root of 52 feet

step 1

Find out the slope of the given line

we have

y+1=-(1/2)x

The slope is m=-1/2

Remember that

If two lines are perpendicular

then

their slopes are negative reciprocal

so

The slope of the perpendicular line is

m=2

step 2

Find out the equation of the line in slope-intercept form

y=mx+b

we have

m=2

point (-8,7)

substitute and solve for b

7=2(-8)+b

7=-16+b

b=23

therefore

the equation of the line is

We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.

Given the coordinates of L and M

To get the length between the two coordinates, we will follow the steps below

Step 1: List out the coordinates of L and M

step 2: calculate the distance

Since they both have the same x coordinates, we can simply subtract the y-coordinate of L from M

Therefore, the distance LM is 7 units

1) -4x=36

2) x+6=13

3) -9x=36