difference of cubes
​

Annie's social style, based on the given information, is most likely to be categorized as "expressive".

Inductive reasoning is a form of defining determinations by proceeding with patterns specific to the usual. It's generally distinguished from deductive reasoning, where it proceeds from general knowledge to specific conclusions.

Here,
Annie's social style, based on the given information, is most likely to be categorized as "expressive". Expressive individuals are generally spontaneous, impulsive, and energetic. They prioritize personal and social needs over practical considerations and tend to make decisions based on their opinions and feelings, rather than objective data or analysis. They are often outgoing, enthusiastic, and creative, but may also be impatient, easily distracted, and prone to taking risks. This description matches the traits attributed to Annie in the scenario.

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The length of median CP is 48.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

Since the triangles are congruent, corresponding sides are equal. So, we have:

AB = DE (corresponding sides)

BC = EF (corresponding sides)

Now, we can use the formula for the length of a median of a triangle, which states that the median to a side of a triangle is half the length of the side that it intersects. Thus, we have:

CP = (1/2) AB

FQ = (1/2) DE

Substituting the values we have for AB and DE, we get:

CP = (1/2) AB = (1/2) DE = FQ

So, we can equate the expressions for CP and FQ, and solve for x:

3x - 12 = 2x + 8

x = 20

Now that we know the value of x, we can substitute it back into either expression for CP or FQ to find the length of CP:

CP = 3x - 12 = 3(20) - 12 = 48

Therefore, the length of median CP is 48.

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Answer:The correct equations are y²-5y=750, 750-y(y-5)=0 ,(y+25)(y-30)=0

Step-by-step explanation: Let the length=y

                                                   breadth=y-5

area of rectangle= length*breadth

750=y(y-5)

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we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

What is ratio ?

Ratio can be defined as given value divided by total value.

Let's assume that we have x liters of milk and y liters of water. We want to find the ratio in which water must be mixed with milk to gain 25% on selling the mixture at cost price.

If we sell the mixture at cost price, we will not make any profit or loss. So, let's first calculate the cost price of the mixture.

Assuming that the cost price of milk is the same as the cost price of water, the cost price of x liters of milk and y liters of water is:

Cost price = Cost price of milk + Cost price of water

= x * cost price of milk + y * cost price of water

Since we are not making any profit or loss, the selling price of the mixture will be the same as the cost price.

Now, to gain a profit of 25%, the selling price must be 125% of the cost price. So, we have:

Selling price = 125% of cost price

= 1.25 * (x * cost price of milk + y * cost price of water)

We know that the mixture contains only milk and water, so the total volume of the mixture is x + y liters.

Now, we can set up an equation to find the ratio of water to milk:

y/x = (1 - 1.25) / (1.25 - 0)

y/x = -0.2

Simplifying this equation, we get:

y = -0.2x

This means that for every 1 liter of milk, we need to mix it with 0.2 liters of water in order to gain a 25% profit when selling the mixture at cost price.

In terms of ratio, the ratio of water to milk is:

0.2 : 1

or

1 : 5 (by simplifying the ratio by multiplying both sides by 5)

Hence, we need to mix milk and water in the ratio of 1:5 to gain a profit of 25% when selling the mixture at cost price.

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Answer:

Step-by-step explanation:

Answer:21 dimes and 28 quarters

Step-by-step explanation:

If a basketball player makes 40% of his shots from the free throw line, then the mean for  the number of shots that he makes is 0.928

Since the basketball player makes 40% of his shots from the free throw line and he takes 3 shots, the number of shots he makes, x, can take on the values 0, 1, 2, or 3.

The probability of making a shot is 0.4, so the probability of missing a shot is 0.6. Since each shot is independent, we can use the binomial probability formula to calculate the probability of making x shots:

P(X = x) = (3 choose x) × (0.4)^x × (0.6)^(3-x)

where (3 choose x) is the binomial coefficient that represents the number of ways to choose x items from a set of 3.

To find the mean for x, we need to multiply each possible value of x by its probability and then sum the results:

E(X) = 0 × P(X = 0) + 1 × P(X = 1) + 2 × P(X = 2) + 3 × P(X = 3)

Substituting the binomial probabilities into this formula, we get:

E(X) = 0 × (1) × (0.6)^3 + 1 × (3 choose 1) × (0.4)^1 × (0.6)^2 + 2 × (3 choose 2) × (0.4)^2 × (0.6)^1 + 3 × (1) × (0.4)^3 × (0.6)^0

E(X) = 0 + 0.432 + 0.432 + 0.064

E(X) = 0.928

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The triangle XYZ has a scale factor of 2.53 and hence side length XY is

7.6 units.

The scale factor defines a variable in a ratio of two different measurements.

Sometimes drawings of large models are represented in a scale factor of a smaller unit.

Given, The side WV, of the triangle UVX is 6 and the corresponding side XZ  of triangle 15.2.

So, The scale factor is 15.2/6 = 2.53.

Therefore, The side length XY = 3×2.53 = 7.6.

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a) Note that  the probability that the 10th transistor  produced is the first with a defect is: ≈ 0.0171

b) The probability that the machine produces no defective transistors in a batch of 100 is: ≈ 0.1338

c) The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:  = 50

d) The expected value and standard deviation for the number of transistors produced before the first with a defect is ≈ 18.71

e)  Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

(a) Since each transistor is independent, the probability that the 10th transistor produced is the first with a defect is the same as the probability that the first 9 transistors are not defective and the 10th one is defective. The probability that a transistor is not defective is 1 - 0.02 = 0.98. Therefore, the probability is:

P(1st defective on 10th) = (0.98)⁹ x 0.02 ≈ 0.0171

(b) The probability that the machine produces no defective transistors in a batch of 100 is:

P(no defects in 100) = (0.98)¹⁰⁰ ≈ 0.1338

(c) The number of transistors produced before the first with a defect follows a geometric distribution with parameter p = 0.02. The expected value of a geometric distribution is 1/p, so the expected number of transistors before the first defective one is:

E(X) = 1/p = 1/0.02 = 50

The variance of a geometric distribution is (1-p)/p², so the standard deviation is:

σ = √((1-p)/p²)

= √(0.98/0.0004)

≈ 22.36

(d) The expected value and standard deviation for the number of transistors produced before the first with a defect are calculated in the same way as in (c), but with a different value of p:

E(X) = 1/p = 1/0.05 = 20

σ = √((1-p)/p₂)

= √(0.95/0.0025)

≈ 18.71

(e) Increasing the probability of an event affects the mean and standard deviation of the wait time until success in opposite ways.

As the probability of an event increases, the expected wait time until success decreases. In other words, the mean becomes smaller. However, as the probability of an event increases, the variability in the wait time until success also increases.

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Answer:

(a) 0.0167

(b) 0.1326

(c) The expected value, mean, μ = 50        SD, σ = 49.4975

(d) The expected value, mean, μ = 20        SD, σ = 19.4936

(e) Increasing the probability of an event decreases the mean and standard deviation of the wait time until success.

Step-by-step explanation:

The cubic function is one where the coefficient a, b, c, and d are correlational the variable are real numbers and are polynomial numbers. The function is either one or three real roots. The graph of the function is a cubic curve.

The example of a cubic function is that of  the forms of y = ax3 + bx2 + cx + d, where the a, b, c, and d are constants. The cube root function is inverse to the cube function.  

Hence they are increasing option A is correct.

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Answer:

Sure In this context, a weak negative linear relationship between the number of hours worked and the amount of donations collected means that as the number of hours worked by Thor each week increases, the amount of donations collected by the organization each week decreases, but the relationship is not very strong.

When we say that the correlation between two variables is weak, we mean that there is a low degree of association between them. In this case, the negative correlation suggests that there is a tendency for the amount of donations collected to decrease as the number of hours worked increases, but the relationship is not very strong, meaning that there is a lot of variability in the data and it is difficult to make strong predictions or conclusions based on this relationship alone.

It is important to note that correlation does not necessarily imply causation, so a weak negative linear relationship between the number of hours worked and the amount of donations collected does not necessarily mean that one variable causes the other. Other factors may be influencing the amount of donations collected by the organization each week, and further analysis would be required to determine the nature and strength of these relationships.

Step-by-step explanation:

The value of the composition of functions are

a) f o g ( 5 ) = 1315

b) g o f ( 5 ) = 59

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the value of the the function be f ( x ) = x² + 6x

Let the value of the function g ( x ) = x + 4

Now , the composition of functions is given by

f o g ( 5 ) is given by

g ( 5 ) = 5 + 4 = 9

So , the value of f ( 9 ) = ( 9 )² + 6 ( 9 ) = 81 + 54 = 135

Therefore , the value of f o g ( 5 ) = 135

Now , the composition of functions is given by

g o f ( 5 ) is given by

f ( 5 ) = ( 5 )² + 6 ( 5 ) = 25 + 30 = 55

Now , the value of g ( 55 ) = 55 + 4 = 59

Therefore , the value of g o f ( 5 ) = 59

Hence , the composition of functions are solved

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The adjacent angles are ∠GFD and ∠JIF. The correct option is D.

The lines and angles are denied as when the two parallel lines are intersected by the transversal lines it forms different types of angles the angles are adjacent angles, supplementary angles, opposite angles, and alternate angles.

The adjacent angle is defined as the angle which is just side by side with another angle.

Here in the given image, the two adjacent angles are ∠GFD and ∠JIF. Because the angle ∠GFD is just in front of the angle ∠JIF.

Therefore, the correct option is D the adjacent angles will be ∠GFD and ∠JIF.

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In the equation 11z=66-11, what is the next step in the equation solving sequence?

Two possibilities: You can subtract 66–11 then divide both sides by 11 OR you can divide both sides by 11 and do the subtraction as 6–1. I would usually do it the first way, but some might prefer the second.

In a case whereby volume of this sphere is 904.32 cubic inches the surface area of this sphere can be expressed as 452.16 in^2

The concept here is using the surface area formula which is

A = Area = (4 π r^2 )  

V= Volume =( 4/3 π r^3)

Then A / V = 3 / r

Also, r = [(3 * V / 4 *  π)^1/3 ]

Then we can substitue the values as

π = 3.14

volume = 904.32 cubic inches

=[ (3 * 904.32 / (4 *  π))^1/3]

= 6 inch

Hence ,  A =( 3 / 6 * V )

= (1/2 * 904.32)

= 452.16 in^2

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Complete question:

The volume of this sphere is 904.32 cubic inches. What is the surface area of this sphere?

Use a 3.14 and round your answer to the nearest hundredth.

The equation has no real solution.

Mathematical expression is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ y = 4 (x + 1)³ + 8

Now, All the zeroes are find by substitute y = 0,

⇒ y = 4 (x + 1)³ + 8

⇒ 0 = 4 (x + 1)³ + 8

⇒ 4 (x + 1)³ = - 8

⇒ (x + 1)³ = - 8

⇒ x + 1 = ∛- 8

⇒ x + 1 = ∛8i²

⇒ [tex]x + 1 = 2i^{2/3}[/tex]

⇒ [tex]x = 2i^{2/3} - 1[/tex]

Hence, It has no real solution.

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Booth's additional funds needed (AFN) for the coming year is $365.

What is additional funds?

Additional Funds Needed (AFN) is a way of calculating how much new funding will be required, so that the firm can realistically look at whether or not they will be able to generate the additional funding and therefore be able to achieve the higher sales level.

Use the following formula to calculate Booth's additional funds needed (AFN) -

AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)

where -

A* = Total assets excluding spontaneous liabilities

S = Sales

ΔS = Increase in sales

L* = Total spontaneous liabilities

MS1 = Net income (1 - RR), where RR is the retention ratio (1 - payout ratio)

Start by calculating A* and L*.

Since we are told that spontaneous liabilities increase at the same rate as sales, we can use the percentages provided to calculate the required increases in each account -

Accounts receivable: ΔAR = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500

Inventories: ΔINV = 0.5(S1 - S0) = 0.5(2000 - 1000) = 500

Accounts payable: ΔAP = 0.5(S1 - S0) = 0.5(1000 - 500) = 250

Accruals: ΔACC = 0.5(S1 - S0) = 0.5(1000 - 500) = 250

A* = Total assets - spontaneous liabilities

= $1000 - ($200 + $50 + $250 + $50 + $250)

= $200

L* = Spontaneous liabilities

= $200 + $50 + $250 + $50

= $550

Next, calculate the increase in fixed assets that would be required if Booth operated at full capacity -

ΔFA = (FCR)(ΔS)

where FCR is the fixed assets capacity ratio, given by -

FCR = Actual sales / Full capacity sales

= $1000 / (2 x $1000)

= 0.5

ΔFA = (0.5)(1000)

= 500

Now calculate AFN using the formula -

AFN = (A*/S)ΔS - (L*/S)ΔS - MS1(RR)

= ($200 / $1000)(1000) - ($550 / $1000)(1000) - ($30)(0.5)

= $365

Therefore, the value is obtained as $365.

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The Booth Company's sales are forecasted to double from $1,000 in 2016 to $2,000 in 2017. Here is the December 31, 2016, balance sheet:

Cash  $  100  Accounts payable  $   50

Accounts receivable  200  Notes payable  150

Inventories  200  Accruals  50

Net fixed assets  500  Long-term debt  400

Common stock  100

Retained earnings  250

Total assets  $1000  Total liabilities and equity  $1000

Booth's fixed assets were used to only 50% of capacity during 2016, but its current assets were at their proper levels in relation to sales. Spontaneous liabilities and all assets except fixed assets must increase at the same rate as sales, and fixed assets would also have to increase at the same rate if the current excess capacity did not exist. Booth's after-tax profit margin is forecasted to be 3% and its payout ratio to be 50%. What is Booth's additional funds needed (AFN) for the coming year? Round your answer to the nearest dollar.

The three vertices will give us the dilated figure.

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.

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Answer:

The volume of the rectangular prism is 96.

Step-by-step explanation:

Use the formula L × W × H to get your answer. Plug in the givem measurements. 8 × 4 × 3 = 96.

The solution of the given problem of area comes out to be the regular decagon is approximately 324.16 cm².

Its surface area is a reliable indicator of its overall size. When figuring out the right triangle squared, the environment is taken into account. The surface area of everything determines its overall size. The total of the volumes from each of the twelve vertical sides makes up the water volume inside a cuboid. Utilize the following formula to get the box's dimensions: The region is represented by 2lh, 2lw, & 2hW. (SA). The area is represented by the flexible shape's entire surface area.

Here,

The area of ​​a regular decagon can be calculated using the formula:

Area = (perimeter x apothem) / 2

For a regular decagon with a side of 6.8 cm and an apothem of 9.52 cm, the perimeter can be calculated as 10 times the length of the side, that is:

Perimeter = 10 x 6.8 cm = 68 cm

Therefore, the area of ​​the decagon is:

Area = (68 cm x 9.52 cm) / 2 = 324.16 cm²

So, the area of ​​the regular decagon is approximately 324.16 cm².

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Answer:

Step-by-step explanation:

Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diagonal of the square is twice the radius of the circle, or 10 mm.

To find the area of the square, we can use the formula A = s^2, where s is the side length of the square. The diagonal of the square is √2 times the side length, so we have:

10 mm = √2 x s

s = 10 mm / √2

The area of the square is:

A = s^2 = (10 mm / √2)^2 = 100 mm^2 / 2 = 50 mm^2

To find the area of the circle, we can use the formula A = πr^2, where r is the radius of the circle. We are given that the radius is 5 mm, so:

A = π(5 mm)^2 = 25π mm^2

To find the shaded section, we need to subtract the area of the circle from the area of the square. The shaded section is the remaining area of the square after the circle has been inscribed. Therefore, the shaded section is:

Shaded Section = Square Area - Circle Area

Shaded Section = 50 mm^2 - 25π mm^2

Shaded Section ≈ 10.79 mm^2 (rounded to two decimal places)

Answer:

-$32

Step-by-step explanation:

Credited = Positive Change

Debited = Negative Change

48-80 = -32

-$32

The trigonometric ratios are given as follows:

a) cos(y) = -0.94.

b) sin(x) = 0.94.

The tree bisects an angle into two equal angle measures, one of which is of 70º and the other of which is of x.

Hence the measure of x is given as follows:

x = 70º.

The sine is given as follows:

sine of 70 degrees = 0.94.

The sum of the measures of the internal angles of a triangle is of 180º, hence the missing internal angle is of 20º.

An internal angle is supplementary with it's external angle, hence the value of y is given as follows:

y = 180 - 20

y = 160º.

Then the cosine is of:

cosine of 160 degrees = -0.94.

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The correct statement is:

E) There is exactly one solution at (1, -2).

What is equation ?

An equation is a mathematical statement that indicates that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation typically consists of two sides separated by an equal sign (=). The values of the variables that make the equation true are called solutions or roots of the equation. Equations are used to model a wide range of phenomena in mathematics, science, engineering, and other fields, and they play a central role in problem-solving and mathematical analysis.

According to given conditions:

To solve the system of equations:

y = 4x - 6 ...(1)

x + 3y = -5 ...(2)

We can use substitution or elimination method. Here, we will use the substitution method:

From equation (1), we have y = 4x - 6.

Substitute y = 4x - 6 in equation (2):

x + 3(4x - 6) = -5

Simplifying the above equation, we get:

13x - 18 = -5

Adding 18 on both sides, we get:

13x = 13

Dividing both sides by 13, we get:

x = 1

Substitute x = 1 in equation (1):

y = 4(1) - 6 = -2

Therefore, the solution to the system of equations is (1, -2).

So, the correct statement is:

A) There is exactly one solution at (0, -6). (Incorrect)

B) There is exactly one solution at (12). (Incorrect)

C) There is no solution. (Incorrect)

D) There are infinitely many solutions. (Incorrect)

The correct statement is:

E) There is exactly one solution at (1, -2).

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The graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

To graph the linear equations, we will use the values in the table to plot points on the coordinate plane, and then connect the points to form lines.

For Bid 7:

X y

0 5

3 50

5 80

7 110

10 155

For Bid 8:

X y

0 40

3 70

5 90

7 110

10 140

We can now plot these points on the coordinate plane and connect them to form two lines. Hence we obtain  Graph of Bid 7 and Bid 8

The x-axis represents the number of books, and the y-axis represents the cost. The title of the graph is "Comparison of Bids for Book Printing Services." We can see that Bid 7 is represented by the blue line, while Bid 8 is represented by the orange line.

To create the legend, we can add a key that explains which line represents which bid. For example, we could add a note at the bottom of the graph that says "Blue line: Bid 7, Orange line: Bid 8."

Overall, the graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.

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The measure of angle m2 is 65°, the reason is interior opposite angles.

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

We are given that;

The measure of angle 1= 65°

Now,

By interior opposite angle property

Angle 1 = Angle 2

Substituting the value of angle 1

65°= angle 2

Therefore, by interior angle property the answer will be 65°.

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Answer:

deprication a/c Dr. 30,00,000

To land a/c 30,00,000

Step-by-step explanation:

deprication is an expense so, according to modern rules of accounts Dr. debit all assets & expenses and cr. credit all income, capital, all liability

(assets ) land value is deprecating so, deprication is an expense so, we Dr. deprication a/c expense is an increase (name the expense) and the value of land (assets) is diminishing Or depricating so, cr. land a/c

Point C is located at -1 3/8

Hope that helps!

Answer: the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

Step-by-step explanation:

(-2, 5) and (-4,-5) are two points in the coordinate plane.

The first point (-2, 5) has an x-coordinate of -2 and a y-coordinate of 5. This point is 2 units to the left of the y-axis and 5 units above the x-axis.

The second point (-4, -5) has an x-coordinate of -4 and a y-coordinate of -5. This point is 4 units to the left of the y-axis and 5 units below the x-axis.

To find the distance between these two points, we can use the distance formula:

distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the coordinates of the two points, we get:

distance = sqrt[(-4 - (-2))^2 + (-5 - 5)^2] = sqrt[(-2)^2 + (-10)^2] = sqrt[104]

So the distance between the points (-2, 5) and (-4, -5) is approximately 10.198 units.

you would save $6,000 in annual fuel expenses.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  you drive 40,000 miles per year and gas averages $4 per gallon

Since,

Fuel expenses = (Miles driven / Miles per gallon) x Price per gallon

For the SUV, with an average of 16 miles per gallon, the fuel expenses would be:

Fuel expenses for SUV = (40,000 / 16) x 4 = $10,000

For the hybrid car, with an average of 40 miles per gallon, the fuel expenses would be:

Fuel expenses for hybrid car = (40,000 / 40) x 4 = $4,000

To find the difference in fuel expenses between the two vehicles, we subtract the fuel expenses for the hybrid car from the fuel expenses for the SUV:

$10,000 - $4,000 = $6,000

Therefore, by owning a hybrid car averaging 40 miles per gallon instead of an SUV averaging 16 miles per gallon, you would save $6,000 in annual fuel expenses.

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Answer:

25

Step-by-step explanation:

let farhan's age be x and his cousin's age be y

sum of ages = x + y = 38

7 years ago (so x-7 and y-7), farhan was thrice as old as his cousin, so 3 * his cousin's past age = farhan's past age= 3 *(y-7) = x-7

subtract y from both sides in the first equation to solve for x

x = 38-y

substitute this into the second equation

3 *(y-7) = 38-y-7

3y-21 = 31-y

add y to both sides to put all y values on one side

4y  -21 = 31

add 21 to both sides to solve for y

4y = 52

y = 13

sum of ages = x + y = 38 = 13 + x so x = 25 = 38-13