ayuda porfa nose como se hace :'((((((((((((
esta es la fórmula: y=a(x-h)²+k​

Thus, the value of the angle x for the given angles of value 100 and 112 is found as 36.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees. As previously said, neighbouring angles are those that are close to one another.

An angle pair that forms a line is known as a "line-ar pair."

For the given triangle:

Using the triangle's angle sum property:

x + (180 - 100) + (180 - 112) = 180

(the other two angles except x are linear pair with the angles of value 100 and 112)

So,

x + 80 + 180 - 112 = 180

x = 112 - 80

x = 32

Thus, the value of the angle x for the given  angles of value 100 and 112 is found as 36.

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The equation that represents the asymptote of the function, y = tan x is: C. x = π/4.

Option A, x = -π, and Option D, x = (3π)/2, do not represent asymptotes of the graph of the function y = tan x.

Option B, x = 0, represents a vertical asymptote of the graph of y = tan x because tan x is undefined at x = π/2 + kπ, where k is an integer. Therefore, tan x is undefined at x = π/2, 3π/2, 5π/2, etc. and there is a vertical asymptote at x = 0.

Option C, x = π/4, represents a linear asymptote of the graph of y = tan x. As x approaches π/4 from either side, the tangent function approaches a straight line with slope 1 and x-intercept 0. Therefore, the equation of the asymptote is y = x - π/4.

Thus, the answer is C. x = π/4.

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i) T3(x) = 1 + x + x^2 + x^3/3

ii) R3(x) = x^4/4 + x^5/5

iii) The maximum value of f(4)(x) on the interval |x| ≤ 0.1 is 144.

iv) Yes, Taylor's inequality holds true for R3(0.1) since the maximum value of f(4)(x) on the interval |x| ≤ 0.1 is less than or equal to 144, which is smaller than the upper bound of 625/24.

i) To find T3(x), we start by calculating the derivatives of f(x) up to order 3:

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f'(x) = 1 + 2x + 3x^2 + 4x^3 + 5x^4

f''(x) = 2 + 6x + 12x^2 + 20x^3

f'''(x) = 6 + 24x + 60x^2

Then, we evaluate these derivatives at x = 0:

f(0) = 1

f'(0) = 1

f''(0) = 2

f'''(0) = 6

Using these values, we can write the Taylor polynomial of f at x = 0 with degree 3 as:

T3(x) = f(0) + f'(0)x + f''(0)x^2/2 + f'''(0)x^3/6

= 1 + x + x^2 + x^3/3

ii) To find R3(x), we use the remainder formula for Taylor polynomials:

R3(x) = f(x) - T3(x)

Substituting f(x) and T3(x) into this formula and simplifying, we get:

R3(x) = x^4/4 + x^5/5

iii) To find the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we first calculate the fourth derivative of f(x):

f(x) = 1 + x + x^2 + x^3 + x^4 + x^5

f''''(x) = 24 + 120x

Then, we evaluate this derivative at x = ±0.1 and take the absolute value to find the maximum value:

|f(4)(±0.1)| = |24 + 12| = 36

Since 36 is the maximum value of f(4)(x) on the interval |x| ≤ 0.1, we know that the upper bound for the remainder formula is 625/24.

iv) Taylor's inequality states that the absolute value of the remainder Rn(x) for a Taylor polynomial of degree n at a point x is bounded by a constant multiple of the (n+1)th derivative of f evaluated at some point c between 0 and x. Specifically, we have:

|Rn(x)| ≤ M|x-c|^(n+1)/(n+1)!

where M is an upper bound for the (n+1)th derivative of f on the interval containing x.

In this case, we have n = 3, x = 0.1, and c = 0. The (n+1)th derivative of f is f(4)(x) = 24 + 120x.

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Answer:

22.25

Step-by-step explanation:

8x+ (11*2)=200

first, multiply 11 and 2 =22

that leaves 8x+22=200

so now let's subtract the 22 from both sides

8x=178 now divide the 8

x= 22.25 so that is the most the jackets could have cost

In the given ratio problem, Eli gets 21 sweets.

Let's assume that Dylan gets 7x sweets, Eli gets 3x sweets, and Fabian gets 5y sweets.

From the given information, we know that:

[tex]5y = 7x + 21[/tex] (since Fabian gets 21 more sweets than Dylan)

We can simplify this expression by dividing both sides by 5:

[tex]y = (7/5)x + 21/5[/tex]

We can also express the ratio of the amount of sweets that Dylan gets to the amount that Fabian gets as [tex]4:5[/tex], which means that:

[tex]4x = (5/1)y[/tex]

Substituting y from the first equation, we get:

[tex]4x = (5/1)*[(7/5)x + 21/5][/tex]

Simplifying this equation, we get:

[tex]4x = 7x + 21[/tex]

[tex]3x = 21[/tex]

[tex]x = 7[/tex]

Therefore, Dylan gets [tex]7x = 49[/tex] sweets, Eli gets [tex]3x = 21[/tex] sweets, and Fabian gets [tex]5y = 70[/tex] sweets.

Hence, Eli gets [tex]21[/tex] sweets.

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The given question is in Spanish, English translation of given question is below.

The perimeter of a rectangle is 54 inches. its length is twice as wide. find the length and width of the rectangle find the area of ​​the rectangle.

The width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.

Let us assume the width of the rectangle w and the length l.

Given, the perimeter of the rectangle is 54 inches:

We know that

Perimeter = 2(length + width) = 54

2(l + w) = 54

Given, length is twice as width i.e. l=2w

2(2w + w) = 54

2(3w) = 52

6w = 54

w = 54/6

w = 9

l = 2(9)

l = 18

We know that

Area = length x width

Area = 18 x 9

= 162

Therefore, the width of the rectangle is 9 inches, the length of the rectangle is 18 inches, and the area of the rectangle is 162 square inches.

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Answer:

3y^3-9y^2+6y

Step-by-step explanation:

= 3y^3-9y^2+6y

The difference between the volume and surface area of both balls is: 108101.69 cubic centimeters.

The formula for the volume of a sphere is V = (4/3)π[tex]r^3[/tex], where r is the radius of the sphere, and the formula for the surface area of a sphere is A = 4π[tex]r^2[/tex].

Let's start by finding the radius of each ball. The diameter of the first ball is 85 cm, so its radius is 85/2 = 42.5 cm. The diameter of the second ball is 65 cm, so its radius is 65/2 = 32.5 cm.

The volume of the first ball is:

V1 = (4/3)π[tex](42.5)^3[/tex] = 256905.53 cubic centimeters

The volume of the second ball is:

V2 = (4/3)π[tex](32.5)^3[/tex] = 139379.44 cubic centimeters

The difference in volume is:

V1 - V2 = 256905.53 - 139379.44 = 117526.09 cubic centimeters

To find the difference in surface area, we plug in the radius values:

A1 = 4π[tex](42.5)^2[/tex] = 22698.16 square centimeters

A2 = 4π[tex](32.5)^2[/tex] = 13273.76 square centimeters

The difference in surface area is:

A1 - A2 = 22698.16 - 13273.76 = 9424.40 square centimeters

Therefore, the difference between the volume and surface area of both balls is: 117526.09 cubic centimeters - 9424.40 square centimeters, rounded to the nearest hundredth, is 108101.69 cubic centimeters.

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Answer:

first you do the angles time the amount of times you watched the hub and you get the answer and alia use a protractor

In this context, the slope of the line of best fit, represented by the equation y = 1.25x + 7, represents the relationship between the age of an infant (in months) and its weight (in pounds) and the independent variable, x, represents the age of the infant in months, and the dependent variable, y, represents the weight of the infant in pounds.

The slope of the line, 1.25, indicates the rate at which the infant's weight changes with respect to its age. Specifically, it shows that for each additional month of age, the infant's weight is expected to increase by 1.25 pounds. This means that, on average, an infant gains 1.25 pounds per month.

In conclusion, the slope (1.25) in this context represents the average weight gain per month for an infant, based on the data collected by the doctor. It helps to understand the general association between an infant's age and its weight, and can be useful in predicting an infant's weight at a given age. However, it's important to remember that this is an average value and individual infants may have different weight gain patterns.

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The volume of air that the beach ball will hold is 36000π cubic cm

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

The radius of the beach ball is 30 cm.

This means that

r = 30

The volume of air that the beach ball will hold is calculated as

V = 4/3πr³

Substitute the known values in the above equation, so, we have the following representation

V = 4/3π * 30³

Evaluate

V = 36000π

Hence, the volume of air that the beach ball will hold is 36000π cubic cm

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The expression that is equivalent to the one Regina wrote is y + 27/4

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

y + 9 x 3/4

This means that

Expression = y + 9 x 3/4

Expanding the above expression, we have

Expanded expression = y + 27/4

Using the above as a guide, we have the following:

The expression that is equivalent to the one Regina wrote is y + 27/4

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To find the area of a parallelogram, multiply the base length by the height. Therefore, the area of the parallelogram is 8 cm * 24 cm = 192 cm².

To find the area of a parallelogram, you can use the formula A = base × height. In this case, the given measurements are 8 cm for the base, 9 cm for the height, and 24 cm for one of the sides of the parallelogram.

First, identify the base and height of the parallelogram. In this case, the base is 8 cm and the height is 9 cm.

Next, substitute the values into the formula for the area of a parallelogram: A = base × height.

A = 8 cm × 9 cm

Multiply the base and height:

A = 72 cm²

Therefore, the area of the parallelogram is 72 square centimeters. It's important to note that the area is not drawn to scale, so the measurements given are solely used for calculation purposes.

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Check the picture below.

The total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.

To find the total cost of repayment, we need to calculate the total amount that Marvin will pay over the course of 5 years. Since he is making monthly payments, we need to first find the total number of payments he will make:

Total number of payments = 5 years x 12 months/year = 60 payments

The total amount Marvin will pay is then:

Total amount = 60 payments x $128.95/payment = $7,737.00

To find the total interest Marvin will pay, we need to subtract the original amount of the loan from the total amount he will pay:

Total interest = Total amount - Loan amount

Total interest = $7,737.00 - $6,800.00

Total interest = $937.00

Therefore, the total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.

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If you cut a 6-inch long sausage roll that is 1/2 inch thick, you can make 12 pieces.

To understand how to arrive at this answer, we need to use some basic math.

First, we need to determine the volume of the sausage roll. We can do this by multiplying the length, width, and height of the roll. In this case, the length is 6 inches, the width is 1/2 inch, and the height is also 1/2 inch. So:

Volume = Length x Width x Height

Volume = 6 x 1/2 x 1/2

Volume = 1.5 cubic inches

Next, we need to determine the volume of each individual piece. To do this, we divide the total volume of the sausage roll by the number of pieces we want to make. In this case, we want to make two equal pieces, so we divide the total volume by 2:

Volume per piece = Total volume / Number of pieces

Volume per piece = 1.5 / 2

Volume per piece = 0.75 cubic inches

Finally, we can determine the dimensions of each individual piece by using the volume per piece and the thickness of the sausage roll. We can calculate the length of each piece by dividing the volume per piece by the thickness:

Length per piece = Volume per piece / Thickness

Length per piece = 0.75 / 0.5

Length per piece = 1.5 inches

So each piece will be 1.5 inches long. To determine how many pieces we can make, we divide the total length of the sausage roll by the length of each piece:

Number of pieces = Total length / Length per piece

Number of pieces = 6 / 1.5

Number of pieces = 4

However, since we are cutting the sausage roll in half, we can make 2 sets of 4 pieces, for a total of 8 pieces.

Alternatively, if we want to make only one cut, we can make two 3-inch long pieces from each half, for a total of 12 pieces.

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The class boundaries are 0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5.

To find the class boundaries, we need to add and subtract 0.5 from the upper and lower limits of each class interval, respectively.

Using this formula, we get the following class boundaries:

Class Boundaries:

0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5

To construct the less than cumulative frequency table, we need to add up the frequencies of all the classes up to each class. For example:

Less than Cumulative Frequency Table:

Ages No. of Children Cumulative Frequency

1-3 10 10

4-6 12 22

7-9 15 37

10-12 13 50

13-15 9 59

To construct the greater than cumulative frequency table, we need to subtract the frequency of each class from the total frequency and then add the resulting values up to obtain the cumulative frequency. For example:

Greater than Cumulative Frequency Table:

Ages No. of Children Cumulative Frequency

13-15 9 59

10-12 13 50

7-9 15 37

4-6 12 22

1-3 10 10

Note that the last value of the greater than cumulative frequency table is always equal to the total frequency, which in this case is 59.

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Answer:

h = 3/2

Step-by-step explanation:

Volume of cone formula: V = 1/3 π r²h

We are given volume and the radius so we can plug in those values

1/18π = 1/3 π (1/3)²h

1/18π = 1/3 π 1/9 h

Multiply the fractions on the right side:

1/18π = 1/27πh

Multiply both sides by reciprocal of 1/27 (which is 27)

3/2π = πh

Divide both sides by π

h = 3/2

Hope this helps!

The integral  ∫(8x/2 + 2/x^3)dx evaluates to 4x^2 - 2/x^2 + C, where C is the constant of integration.

The given integral ∫(8x/2 + 2/x^3)dx is definite integral without any integration limits. To evaluate this integral, we can split it into two parts

∫8x/2 dx + ∫2/x^3 dx

We made use of the power rule of integration to simplify the first term, and the inverse power rule to simplify the second term.

Simplifying each integral, we get

4x^2 - 2/x^2 + C

where C is the constant of integration.

Therefore, the final answer to the integral is

∫(8x/2 + 2/x^3)dx = 4x^2 - 2/x^2 + C

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--The given question is incomplete, the complete question is given

" Evaluate. Assume that x>0. ∫(8x/2 + 2/x^3)dx"--

The density of the copper used in the pyramid is 8.4 g/cm³.

To find the density of the copper used in the pyramid, we first need to determine the volume of the cuboid and pyramid, and then find the mass of the copper.

1. Find the volume of the cuboid (V_cuboid):

V_cuboid = length × width × height

Since the base is a square, the length and width are both 3 cm.

V_cuboid = 3 cm × 3 cm × 8 cm = 72 cm³

2. Find the volume of the pyramid (V_pyramid):

First, find the height of the pyramid: total height (15 cm) - height of the cuboid (8 cm) = 7 cm.

V_pyramid = (1/3) × area of base × perpendicular height

The area of the base is 3 cm × 3 cm = 9 cm².

V_pyramid = (1/3) × 9 cm² × 7 cm = 21 cm³

3. Find the mass of the iron cuboid (m_iron):

Density of iron = 7.8 g/cm³

m_iron = density × V_cuboid = 7.8 g/cm³ × 72 cm³ = 561.6 g

4. Find the mass of the copper pyramid (m_copper):

Total mass of sculpture = 738 g

m_copper = total mass - m_iron = 738 g - 561.6 g = 176.4 g

5. Calculate the density of the copper (density_copper):

density_copper = m_copper / V_pyramid

density_copper = 176.4 g / 21 cm³ ≈ 8.4 g/cm³

The density of the copper is approximately 8.4 g/cm³.

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The possible values of the arc AE are 175 and 185 degrees

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

The circle R

Where the measures of  the arcs are

AB = 60

BC = 25

CD = 70

DE = 20

Add the measures of the above arcs

So, we have

AE = 60 + 25 + 70 + 20

Evaluate

AE = 175

Another possible value is

AE = 360 - minor AE

AE = 360 - 175

Evaluate

AE = 185

Hence, the possible values of the arc AE are 175 and 185 degrees

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The height of the rectangular prism is 4.4 inches

The formula for calculating the area of a rectangular prism is expressed with the equation;

A = wh

Such that the parameters of the formula are given as;

From the information given, we have that;

Area of the prism = 80 square inches

width of the rectangular prism = 18 square

Now, substitute the value, we have

80 = 18h

Divide both sides by the coefficient of the variable h, we have;

h = 80/18

divide the values

h = 4. 4 inches

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The answer is  (3.25, 2.75)

To find point B, we can use the fact that AB and BC form a 1:3 ratio. Let's start by finding the coordinates of point B.

First, we need to find the distance between A and C. We can use the distance formula for this:

[tex]d = \sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where  [tex](x1, y1) = (4, 2)[/tex]  and [tex](x2, y2) = (1, 5)[/tex]

[tex]d = \sqrt{((1 - 4)^2 + (5 - 2)^2)} = \sqrt{(9 + 9)} = \sqrt{(18)}[/tex]

Next, we need to find the distance between A and B, which we'll call x, and the distance between B and C, which we'll call 3x (since AB and BC are in a 1:3 ratio).

Using the distance formula for AB:

[tex]x = \sqrt{\\((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where [tex](x1, y1) = (4, 2)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]

[tex]x = \sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]

Using the distance formula for BC:

[tex]3x = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where [tex](x1, y1) = (1, 5)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]

[tex]3x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

Now we can set up an equation using the fact that AB and BC are in a 1:3 ratio:

[tex]x / 3x = 1 / 4[/tex]

Simplifying this equation, we get:

[tex]4x = 3(AB)[/tex]

[tex]4x = 3\sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]

And

[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

Now we have two equations and two unknowns (Bx and By). We can solve for Bx in the first equation and substitute into the second equation:

[tex]Bx = (3\sqrt{((Bx - 4)^2 + (By - 2)^2))} / 4[/tex]

[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]

[tex]81((Bx - 4)^2 + (By - 2)^2) / 16 = (Bx - 1)^2 + (By - 5)^2[/tex]

Expanding the squares and simplifying, we get:

[tex]81Bx^2 - 648Bx + 1245 = 16Bx^2 - 32Bx + 266[/tex]

[tex]65Bx^2 - 616Bx + 979 = 0[/tex]

Using the quadratic formula, we get:

[tex]Bx = (616 ± \sqrt{(616^2 - 4(65)(979)))} / (2(65))[/tex]

[tex]Bx = (616 ± \sqrt{(223456))} / 130[/tex]

[tex]Bx = 3.25[/tex] or [tex]Bx = 10.2[/tex]

We can eliminate the solution Bx ≈ 10.2 because it is outside the segment AC. Therefore, the solution is:

B = (3.25, 2.75)

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The lateral surface area of a cylinder is given by the formula:

Lateral surface area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the height of the cylinder is 8 ft and the radius of the cylinder is 4 ft (half of the diameter). So, we can plug in these values to get:

Lateral surface area = 2π(4 ft)(8 ft)

Lateral surface area = 64π square feet

Rounding to the nearest tenth, we get:

Lateral surface area ≈ 201.1 square feet (rounded to one decimal place)

Therefore, the lateral surface area of the cylinder is approximately 201.1 square feet.

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Average speed going to work is 50 mph.

Let's assume that the average speed going to work is "x" miles per hour.

Since you can travel to work in the same time it takes for you to make it 28 miles on the trip back home, we can set up an equation using the formula:

time = distance / speed

The time it takes to travel 35 miles to work is:

time to work = 35 / x

The time it takes to travel 28 miles on the return trip is:

time to return = 28 / (x - 10)

We know that both times are equal, so we can set them equal to each other and solve for "x":

[tex]35 / x = 28 / (x - 10)[/tex]

Multiplying both sides by x(x - 10), we get:

[tex]35(x - 10) = 28x[/tex]

Expanding the left side and simplifying, we get:

[tex]35x - 350 = 28x[/tex]

[tex]7x = 35[/tex]

[tex]x = 50[/tex]

Therefore, your average speed going to work is 50 miles per hour.

To solve this problem, we used the formula for speed, distance, and time. We t up an equation using the fact that the time it takes to travel to work is equal to the time it takes to travel 28 miles on the return trip. We then solved for the average speed going to work by setting the two times equal to each other and solving for "x". Finally, we found that the average speed going to work is 50 miles per hour.

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To cover a rectangular lawn of 160 feet by 160 feet with dichondra lawn food, you would need 210 pounds of fertilizer.

To find the area of the rectangular lawn

Area = Length x Width

Area = 160 ft x 160 ft

Area = 25,600 sq ft

Since one bag of lawn food can cover 4000 square feet, we need to divide the total area of the lawn by the coverage of one bag

Number of bags = Total area ÷ Coverage of one bag

Number of bags = 25,600 sq ft ÷ 4000 sq ft

Number of bags = 6.4

Since we cannot buy a fraction of a bag, we need to round up to the nearest whole number of bags, which is 7.

Therefore, we need 7 bags of lawn food to cover the rectangular lawn. To find the total weight of fertilizer needed, we multiply the number of bags by the weight of one bag

Total weight of fertilizer = Number of bags x Weight of one bag

Total weight of fertilizer = 7 bags x 30 pounds/bag

Total weight of fertilizer = 210 pounds

Thus, we need 210 pounds of fertilizer to cover the rectangular lawn.

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The LCM of 8 and 9 is 72. The GCF of 35 and 63 is 7.35 + 63 can also be written as 7 X 14.

Part A

Here we have been given 2 numbers 8 and 9. We need to find the LCM. LCM is the Lowest Common Multiple. It is the smallest number which can be divided by all the mentioned number. To take the LCM of 8 and 9 we first will factorize them

8 = 2 X 2 X 2

9 = 3 X 3

Here we see that 8 and 9 do not have any common factor. Hence we need to simply multiply them together to get

8 X 9 = 72

Part B.

We need to find GCF of 35 and 63. GCF or the Greatest common factor is the highest number that can divide all the given numbers. Here too we will first factorize 35 and 63.

35 = 5 X 7

63 = 3 X 3 X 7

Here we see that between the numbers, 7 is the only common factor

Hence, 7 is the GCF.

63 can also be written as 63 = 7 X 9

Hence we can write 35 + 3

= (7 X 5) + (7 X 9)

Taking 7 common we get

7(5 + 9)

= 7 X 14

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There are four most frequent values in the dataset that occur twice: 58, 60, 62, and 63.

Using SOCCS, I can determine the essential values and provide a description of the given dataset consisting of times for CGHS swimmers in the 50m freestyle event:

The mean (average) time is 63.0 seconds, calculated by adding all times together and dividing by the total number of observations.

To find the middle value (median), the dataset was sorted in ascending order; thus, the median is 62 seconds.

There are four most frequent values in the dataset that occur twice: 58, 60, 62, and 63.

Calculating the difference between the highest and lowest values provides the range of 23 seconds.

The variance equals approximately 60.92, computed using the formula Σ(x-mean)^2 / (n-1). The resulting standard deviation is around 7.8, presenting some variation.

SOCCS description:

This dataset displays a slightly skewed distribution to the right due to two larger numbers (71 and 81).

One significant outlier exists (81 seconds), affecting the overall outcome significantly higher than other observed times.

From the values obtained via calculation, we get an indication of a balanced dataset: the average and median values show to be quite similar, establishing central tendencies for this specific data set.

Considering its dispersion across the representation, it follows that there is variability presented within the observed durations, utilizing both the range and the comparatively high standard deviation as our objective indicators for such measurement.

In conclusion, with these results, informed insights into the swimmers’ abilities and performances are evident, pinpointing potential areas for future improvements in their training regimes.

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The possible maximum value of the expression is (d) None

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

a = bq + r

The above expression is an Euclid's Division statement

The Euclid's Division Algorithm states that "For any two positive integers a, b there exists unique integers q and r such that:"

a = bq + r

where 0 ≤ r < b.

From the question, we have

q = 4

Max r = 4

Using 0 ≤ r < b, we have

Minimum b = 5

So, we have

a = bq + r

This gives

Min a = 5 * 4 + 4

Min a = 24

The above represents the minimum value of a

The maximum value cannot be calculated because as b increases, the value of the expression also increases

Hence, the possible maximum value is (d) None

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The approximate total amount Valerie will pay for her new car is $38,287.

How much will Valerie pay in total for her new car?

To calculate how much Valerie will pay in total for her new car, we need to consider several factors.

First, let's determine the trade-in value of her 2006 Hyundai Sonata. Since the car is in good condition, Valerie will receive 87.5% of the listed trade-in price for that year, which is $6,784. Therefore, the trade-in value is approximately $5,938.80 ($6,784 * 0.875).

Now, let's calculate the total cost of the new car. The list price is $32,495, and Valerie plans to make a down payment of $1,877. Thus, the remaining amount to be financed is $32,495 - $1,877 - $5,938.80 = $24,679.20.

Next, let's consider the interest on the financing. The interest rate is 8.64% per year, compounded monthly. Over five years, this amounts to 60 monthly payments. Using an amortization formula, we can determine that the monthly payment is approximately $516.27.

Additionally, Valerie will have to pay sales tax, vehicle registration fee, and documentation fee. The sales tax is 8.23% of the total cost, which is ($24,679.20 + $2,243) * 0.0823 = $2,329.48. The vehicle registration fee is $2,243, and the documentation fee is $314. The total additional fees amount to $2,329.48 + $2,243 + $314 = $4,886.48.

Finally, to calculate the total amount Valerie will pay, we add the down payment, monthly payments, trade-in value reduction, and additional fees: $1,877 + (60 * $516.27) + $5,938.80 + $4,886.48 = $38,285.88.

Rounding to the nearest cent, Valerie will pay approximately $38,286 for her new car. Thus, the correct answer is option c: $38,287.

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