Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤5.

The solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.

The complex numbers that are not real are represented by the fictitious unit "i." However, in order to convert complex numbers into their whole real form, we must first determine what the value of the fictitious number i is √-1.

Essentially, it was once thought that there was no difference between real and imaginary numbers in fact. Real numbers and fictitious numbers, however, were distinguished when the complex number entered the scene.

The quadratic formula is given as:

x = -b ± √ b² - 4ac ÷ 2a

In the given equation:

8x^2-4x+2=0

b = -4, a = 8, and c = 2

Substituting the value in the quadratic equation formula we have:

x = -(-4) ± √(-4)² - 4(8)(2) ÷ 2(8)

x = 4 ± √16 - 64 ÷ 16

x = 4 ± √-48 ÷ 16

The negative sign can be replaced by imaginary number (i)^2 hence:

x = 4 ± √48(i)² ÷ 16

x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16

Thus, the solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.

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Part 1:

The transformation performed from function f to function g are:

Function f is translated to the left 5 units

Function f is translated up to 1 unit.

Part 2:

The transformation performed from function f to function g are:

Function f is translated to the right 3 units

Function f is translated down to 4 units.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

We will use this concept:

f(x) = f(x - a) when translated a units to the right.

f(x) = f(x + a) when translated a units to the left.

Part 1:

f(x) = (x - 3)³ is tranform to g(x) = (x + 2)³ + 1

Now,

Translating f(x) with 5 units to the left.

f(x) = (x - 3 + 5)³

g(x) = (x + 2)³

Translating f(x) with 1 unit up.

g(x) = (x + 2)³ + 1

Part 2:

f(x) = ∛(x + 1) is tranform to f(x) = ∛(x - 2) - 4

Now,

Translating f(x) with 3 units to the right.

f(x) = ∛(x + 1 - 3)

f(x) = ∛(x - 2)

Translating f(x) with 4 units down.

f(x) = ∛(x - 2) - 4

Thus,

Part 1:

f(x) is translated with 5 units to the left and 1 unit up.

Part 2:

f(x) is translated with 3 units to the right and 4 units down.

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Answer:

50 & 200

Step-by-step explanation:

The sum of all interior angles of a quadrilateral is 360 degrees, angle D is the same as B =50

angle C = 360-50-50-60 = 200

The house's value Increase in dollars by $37,760.

The current value of the house is $509, 760.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

A house on the market was valued at $472,000.

After several years, the value increased by 8%.

Then, the value of house increased

= 472000 x 8/100

= $37,760

So, the current value of house

= 472000 + 37760

= $509, 760

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Answer:

x=3

Step-by-step explanation:

[tex]9x+11=4x+26\\5x=15\\x=3[/tex]

Answer:

Step-by-step explanation:

The X Form = 3

The solution of the inequality is, x ∈ (- ∞, 5) ∪ (10, ∞)

Where, x represent the number of totts.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

My friend Raw has either no more than 5 toots and more than 10 toots.

Now, Let number of toots = x

Hence, We get;

⇒ x < 5

And, x > 10

Thus, The solution of the inequality is,

⇒ x ∈ (- ∞, 5) ∪ (10, ∞)

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the height of the triangle formed by the diagonal and base of the TV screen.

The height of the TV is approximately 15.6 inches.

(26 inches / √2) = 18.8 inches

(18.8 inches * √2) = 26 inches

Height = (26 inches / 18.8 inches) * 18.8 inches

Height = 15.6 inches

Step 1: Calculate the hypotenuse of the triangle formed by the diagonal and base of the TV screen.

Hypotenuse = diagonal / √2

Hypotenuse = 26 inches / √2

Hypotenuse = 18.8 inches

Step 2: Calculate the diagonal of the triangle formed by the hypotenuse and base of the TV screen.

Diagonal = hypotenuse * √2

Diagonal = 18.8 inches * √2

Diagonal = 26 inches

Step 3: Calculate the height of the triangle formed by the diagonal and base of the TV screen.

Height = diagonal / base

Height = 26 inches / 18.8 inches

Height = 15.6 inches

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Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.

Random assignment of treatments is the best way to ensure that the results of the experiment are valid and not biased. Random assignment of treatments would ensure that the results are not affected by factors such as soil type, climate, and other environmental conditions. This is because random assignment of treatments would ensure that the farms that receive the insecticide treatment are not systematically different from those that do not receive the treatment. This is important in order to gain accurate results from the experiment.

Random assignment of treatments is accomplished using the following formula:

Treatment Assignment = (Number of Farms) x (Random Number between 0 and 1)

By randomly assigning treatments to the farms, we can be sure that the results are not skewed by external factors. This will allow us to better determine the effectiveness of different insecticides in controlling pests and their impact on the productivity of tomato plants.

Randomly assigning treatments to the farms is the best way to ensure that the results of the experiment are valid, unbiased, and accurate.

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The error interval for x when rounded to one decimal place as 8.7 is (8.65, 8.74).

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,

The rounded value of 8.7 is the midpoint of the error interval and any number between 8.65 and 8.74 would round to 8.7 when rounded to one decimal place.

Thus, the error interval for x when rounded to one decimal place is (8.65, 8.74).

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Answer:

100x14 = 1,400

14(10) = 140

361 * 1000 = 361,000

100(361) = 36,100

This riddle does not have any mathematical formula or calculation associated with it.

This is an impossible situation, as it is not possible for a doctor to be the patient's parent. It is also not possible for a person to be taller than a building that is 43 stories tall.

The phrase "How is a raven like a writing desk?" is a riddle posed by Lewis Carroll in his novel Alice's Adventures in Wonderland. The answer to the riddle is "they both have the potential to produce a few notes, though they are very different". This phrase does not have any mathematical formula or calculation associated with it.

This riddle does not have any mathematical formula or calculation associated with it.

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The largest possible number of intersections in a plane with 9 lines is 36, which is achieved when each line intersects with every other line.

The largest possible number of intersections in the plane where at least two of the nine lines intersect is 36. To see why this is the case, consider a construction where each of the nine lines intersects with every other line. In this construction, each line intersects with eight other lines, so the total number of intersections is 9 * 8 / 2 = 36. This construction is possible to achieve in a plane, so 36 is the largest possible number of intersections.

This result can be explained using the formula for counting the number of intersections in a set of n lines. If each line intersects with every other line in the set, the total number of intersections will be equal to n choose 2, or n(n-1)/2, where n is the number of lines. In this case, n=9, so the maximum number of intersections is 9 choose 2 = 9(9-1)/2 = 36.

It is important to note that not all sets of nine lines in a plane will have 36 intersections. The actual number of intersections will depend on the specific configuration of the lines. However, 36 is the largest possible number of intersections for a set of nine lines in a plane.

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Answer:

Step-by-step explanation:

Hey! the answer is:

They are both correct, since the equations are the same.

The probability that the next person will pay with a debit card is:

P =  0.63

We want to find he probability that the next customer will pay with a debit card.

That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.

We know that:

15 paid in cash.

50 paid with debit card.

15 paid with credit card.

For a total of 15 + 50 + 15 = 80

Then the probability is:

P = 50/80 = 0.63

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The expression which represents the amount Rita spent at the mall is 18.82d + 42. If d = 6, then the total amount spent is $154.92.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Amount spent at one store is given by the expression 18.82d + 22.

Here d is the number of items she bought at that store.

Amount spent at another store = $20

Total amount spent at the mall = 18.82d + 22 + 20 = 18.82d + 42.

If she bought 6 items, d = 6.

Total amount spent = (18.82 × 6) + 42 = $154.92

Hence the required expression to find the total amount is 18.82d + 42. And the total amount spent if the items bought is 6 is $154.92.

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840 of the 1,000 applicants were accepted to join the air force.

The given data:

Thus, selected cadets:

84% of 1,000

As, 84% is the percentile at one of the Standard deviation.

Thus, 840 of the 1,000 applicants were accepted to join the air force.

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The area of the state in square miles is 72 x 5 = 360 square miles.

The formula to calculate the area of a rectangle is A = l x w, where 'A' is the area, and 'l' and 'w' are the length and width respectively.

Therefore, the area of the state that is represented on a map by a rectangle 10 inches by 7.2 inches, is calculated by substituting the length and width into the equation, as follows: A = 10 x 7.2 = 72 inches.

Since 1 inch represents 5 miles, the area of the state in square miles is calculated by multiplying the area (in inches) by the conversion factor (5 miles per inch). Therefore, the area of the state in square miles is 72 x 5 = 360 square miles.

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The difference in the area of the square 'a' and 'b' as per given side-length is equal to 8 ( x + 1 ) square meters.

Side length of square 'a' = (2x + 1) meters

Side length of square 'b' = ( 2x + 1 + 2 ) meters

                                         = ( 2x + 3 ) meters

Area of a square 'a' = ( side length )²

                                = ( 2x + 1 )²

Area of a square 'b' = ( side length )²

                                = ( 2x +3 )²

Difference in the area of the squares = ( 2x +3 )² - ( 2x +1 )²

                                                             = ( 2x + 3 -2x -1 )( 2x + 3 + 2x + 1 )

                                                             = ( 2 ) ( 4x + 4 )

                                                             = 8 ( x + 1 )

Therefore, the difference in the area of the given squares is equal to    8 ( x + 1 ) square meters.

The side length of square 'a' is (2x + 1) meters. The side length of square 'b' is 2 meters longer than that of square a. find the difference in the area of the squares.

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The phrase can be expressed as,

v  < 9.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

We have a phrase:

The value, v, of the hat is less than $9.

The phrase can be expressed as,

v  < 9.

Therefore, the expression is v < 9.

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Answer:subtract to elimanate y

Step-by-step explanation:

The number of solutions for the system of equations is given as follows:

Zero.

The system of equations for this problem is defined as follows:

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

From the image presented at the end of the answer, the two graphs never intersect, and hence the number of solutions to the system of equations is of zero.

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In the final multiple score (fms), pass not advanced (pna) exam points are awarded for five maximum number of exam cycles.

It is a calculation system, primarily practiced by the U.S Navy in order to make sure whether sailors in the pay grade of E-3, E-4, E-5 and E-6 are eligible in order to receive the position of the next pay grade. It consists of six categories such as exam score, performance mark average (PMA), etc.

If sailors score well, they will be awarded with PNA points. In each exam cycle, a sailor can receive a maximum of 3 PNA points, i.e., for a good score, 1.5 PNA points and for a good performance mark average, another 1.5 PNA points will be awarded.

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Complete question: in the final multiple score (fms), pass not advanced (pna) exam points are awarded for what maximum number of exam cycles? a) four, b) five, c) two, d) six

The value of the equation 6 + 3p = 4p + 7 is 1

Reorder the terms:

6 + 3p = 7 + 4p

Solving for the value of p by collecting like terms

6 + 3p = 7 + 4p

Move all terms containing p to the left, all other terms to the right.

Add '-4p' to each side of the equation.

-6 + 3p + -4p = -7 + 4p + -4p

Combine like terms: 3p + -4p = -1p

-6 + -1p = -7 + 4p + -4p

Combine like terms: 4p + -4p = 0

-6 + -1p = -7 + 0

-6 + -1p = -7

Add '6' to each side of the equation.

-6 + 6 + -1p = -7 + 6

Combine like terms: -6 + 6 = 0

0 + -1p = -7 + 6

-1p = -7 + 6

Combine like terms: -7 + 6 = -1

-1p = -1

Divide each side by '-1'.

p = 1

Simplifying

p = 1

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how many students owned either a car or an ipod (but not both): =100−90=10

What is union of sets?

Union of two given sets is the littlest set which contains every one of the components of both the sets.

What is intersection of sets?

Intersection of two given sets is the biggest set which contains every one of the components that are normal to both the sets

What is the recipe for union of two sets?

The union of two sets is given by

n(A∪B) = n(A) + n(B) - n(A∩B)

Where,

An and B are the two sets.

∪ is the union

∩ is the intersection.

n(AUB)=n(A)+n(B)−n(A∩B)

     =80+60−50

=90

number of students owning a car or an ipod=90

number of students neither car nor stereo =100−90=10

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Answer:

$787.5

Step-by-step explanation:

first, you have to find how much ginny makes in a week w/o her raise\

17.5*40=700

then, you have to raise it by 12.5%, so her new salary is 112.5% of 17.5

112.5% = 1.125

700*1.125=787.5

The surveyor is interested in learning additional information about a segment of the general population. Numerous research projects call for particular interest groups to make decisions in light of their findings. This group of individuals is referred to as a sample.

What Exactly Is a Sample?

An easier-to-manage portion of a bigger group is referred to as a sample. It is a subset of individuals that shares traits with a wider population.

                                 In statistical testing, samples are utilized when population sizes are too vast for all potential participants or observations to be included in the test.

What does a research sample mean?

Sampling is the process of choosing a portion of the target population for a research project.

                                 In the vast majority of research projects, it is impossible to recruit the involvement of the entire population of interest, hence data gathering depends on a smaller group.

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Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.

here, we have,

we know that,

Every rectangle with four congruent sides is a square -> True

Every rhombus is a quadrilateral -> True

Every square is a parallelogram -> True

Every quadrilateral is a square -> False.

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The total number of flowers in the flower shop is 65.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio to tulips to roses is 5 to 8 at the flower shop.

There are 40 roses at the flower shop.

Let the total number of flowers are x.

Now, 5+8=13

8/13 ×x=40

8x=520

x=520/8

x=65

Therefore, the total number of flowers is 65.

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The total area of the shape is 165.5 in².

The total area of the shape is calculated from the area of the trapezium and the area of the base which is rectangle.

Area of the base ( rectangle ) = L x B

where;

Area of base = 16 in  x 8 in = 128 in²

Area of the trapezium = ¹/₂ ( 2a + a ) a

=  ¹/₂ ( 3a²)

=  ¹/₂ ( 3 x 5²)

= 37.3 in²

Total area =  128 in² + 37.3 in² = 165.5 in²

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Answer: 2/15

Step-by-step explanation: First multiply the numerators together and then denominators together.

Numerators= 2 and 1

(numerators) 2 x 1 = 2

Denominators= 3 and 5

(denominators) 3 x 5 = 15

Hence, you get 2/15