Kyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why AM = 6.

A. Definition of Perpendicular Bisector
B. Definition of Midpoint
C. Addition Property
D. Subtraction Property

Answer:

Step-by-step explanation:

The function f(x) = 4x/(x-16) has two vertical asymptotes at x = 16. This can be seen by taking the limit of the function as x approaches 16 from the left and right sides.

On the left side, as x approaches 16 from the left, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach -∞. This results in a limit of -∞, indicating a vertical asymptote at x = 16.

On the right side, as x approaches 16 from the right, the denominator, (x-16), will approach 0, while the numerator, 4x, will approach +∞. This results in a limit of +∞, also indicating a vertical asymptote at x = 16.

The end behavior of the function is that as x approaches +∞, the function will approach +∞, and as x approaches -∞, the function will approach -∞.

The price per square foot of a vacant lot that measures 50' x 102' and sold for $108,250 is $21.23.

To find the price per square foot of the vacant lot, we need to divide the total price by the total area of the lot.

We can find the area of the lot by multiplying the length by the width:

Area = 50' x 102' = 5100 sq.ft

Then, we can divide the total price by the total area to find the price per square foot:

Price per sq.ft = Total Price / Total Area

Price per sq.ft = 108,250 / 5100

Price per sq.ft = 21.23

Therefore, the price per square foot of the vacant lot is $21.23.

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Four complex numbers are present. fulfilling the following equations of a sequence of complex numbers is √3, - √3, √15 i, - √15 i .

A sequence is an arrangement of numbers, or "terms." Terms like 2, 5, and 8 are examples. By taking advantage of a specific pattern some sequences use, they can be made to go on forever. To continue the sequence, add 3 and use the example of 2,5,8. In a succession of words, there exist formulas that show where to look. In mathematics, a sequence is a collection of items that are arranged in some manner (or events). Because it has parts, it is similar to a set (also called elements or terms). The length of the sequence is defined as the total, possibly unlimited number of ordered objects. arranging two or more elements in a sensible sequence. Chronological.

given

Complex conjugation refers to the real line's reflection of the complex plane. Z or z can be used to represent the complex conjugate of z. Similar real and imaginary parts exist in the complex conjugate, but with the opposite sign on the imaginary portion.

This means that z=a+ib follows from z=a+ib.

Four complex numbers are present. fulfilling the following equations of a sequence of complex numbers is √3, - √3, √15 i, - √15 i .

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If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is 0.3940.

By employing the criteria that certain events have occurred, the Bayes Theorem allows us to determine the posterior probability. 

Given that,

E: Purchaser has extended Warranty.

A: He chooses a basic model.

B: He chooses a deluxe model.

P(A) = 0.42

P(B) = 0.58

P(E/A) = 0.44

P(E/B) = 0.49

The probability that a randomly selected customer has an extended warranty is given by:

P(E)= P(E/A)*P(A)+P(E/B)*P(B) = 0.44*0.42 + 0.49*0.58= 0.469

If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is given by:

P(A/E)= P(E/A)*P(A)/P(E) = 0.44*0.42/0.469 = 0.3940

Thus, If a randomly selected purchaser has an extended warranty the probability that he or she has a basic model is 0.3940.

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Answer: 176 BLUE marbles

Explanation:

First --> Total marbles ==> 264 / 0.60 = 440

Second --> Hence, the total number of BLUE marbles is 440 - 264 = 176

and there is 176 BLUE marbles

Answer:

660

Step-by-step explanation:

first, 264 yellow marbles.

the percentage of yellow is 60.

If total percentage is 100 then, blue is 100-(yellow percentage)

that is: 40 percent

the next sentence.

total marbles of blue is:

divide both sides by 0.4

x= 660.

The possible values for f and g are -2, 2, -4, 4, -1, 1.

What is inequality?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

If fg^2 = 32, then either fg = ±4, ±2, or ±1. If f < 20 and g < 20, then the possible values for f and g are:

f = 2, g = 4

f = 4, g = 2

f = 1, g = 4

f = 4, g = 1

f = 2, g = 2

f = 1, g = 1

Hence, the possible values for f and g are -2, 2, -4, 4, -1, 1.

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To find the equivalent expression with the fewest symbols possible for 1/3(3j6),One third of three times the value of six, which is equal to one times the value of two.

1/3(3j6)

= 1/3(3*6)

= 1/3(18)

= 18/3

= 6

= 1j2

To find the equivalent expression with the fewest symbols possible for 1/3(3j6), we need to start by multiplying 3 and 6 together. This gives us the result of 18. Next, we divide 18 by 3, which gives us the result of 6. Finally, we express the result as 1j2, which is the equivalent of 1/3(3j6) with the fewest possible symbols. By following these steps, we can easily calculate the equivalent expression with the fewest symbols. In this case, it is 1j2. The process of calculating the equivalent expression with the fewest symbols is relatively straightforward, but it is important to remember to use the correct order of operations when performing calculations. To ensure accuracy, it is best to work step by step, multiplying 3 and 6 together first and then dividing 18 by 3 to get the final result of 1j2.

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The trigonometrical ratios of the triangle are:

sin∠X = x/z

cos∠X = y/z

tan∠X = x/y

sin∠Y = y/z

cos∠Y = x/z

tan∠Y = y/x

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

Thus, we have the following trigonometric ratios in the triangle:

sin∠X = x/z

cos∠X = y/z

tan∠X = x/y

sin∠Y = y/z

cos∠Y = x/z

tan∠Y = y/x

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Since X, Y, and Z are independent random variables, the probability of one event occurring has no bearing on the likelihood of the other events. In this instance, the probabilities of X, Y, and Z are 30%, 40%, and 20%, respectively.

We must take into account the possibility that both events could occur simultaneously when determining the likelihood that either X or Y will occur. The occurrences where both X and Y occur would be doubly counted if we just added the probabilities of X and Y. To circumvent this, we employ the following formula for the chance of two events occurring together:

P(X or Y) = P(X) + P(Y) - P (X and Y)

This formula takes into account the fact that we must deduct the probability of X and Y's intersection (i.e., the likelihood that they both occur) from the total of each variable's individual probabilities.

Given that X and Y are independent events, P(X and Y) = P(X) * P(Y) = 0.3 * 0.4 = 0.12 is known.

P(X or Y) is therefore equal to P(X) + P(Y) - P(X and Y) = 0.3 + 0.4 - 0.12 = 0.68 = 68% 

 So, according to option most approximately option is A.

Therefore, 70% would be the most accurate response.

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The 3rd-degree polynomial has at least one or three real roots.

Yes, a third degree polynomial can have all real roots. This is because a third degree polynomial has at least one real root, as it is the lowest degree polynomial that can have an imaginary root. The other two roots can be real or imaginary, depending on the coefficients of the polynomial. If the discriminant of the polynomial is greater than or equal to zero, the polynomial will have all real roots. In a cubic polynomial, only one or three real roots are present. Polynomials having odd degrees have at least one real root. A cubic equation's graph must at least once cross the x-axis, giving you at least one real root. Only a quadratic polynomial has two real roots. Quadratic polynomials are those having a degree of two. Polynomials can be represented on the graph, on that basis we can determine whether the roots are real or not.

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The value of a and b is 1.

The probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is ab, where a and b are integers.

To find the value of a and b, we need to determine the total number of ways Nate can place the disk (the denominator of the probability fraction) and the number of ways he can place the disk so that it touches an equal number of shaded and unshaded squares (the numerator of the probability fraction).

Since the center of the circle must be at the meeting point of four squares, the only possible places for the center are the points where four squares meet. Since the grid is made of 2 cm x 2 cm squares, there are 4 shaded squares and 4 unshaded squares. So, there are 4 centers that could be placed on a shaded square and 4 centers that could be placed on an unshaded square.

So the denominator of the probability fraction is 8.

Now, to calculate the numerator, we need to determine the number of ways Nate can place the disk so that it touches an equal number of shaded and unshaded squares.

As the center of the circle is at the meeting point of four squares, the center of the circle is placed at the intersection of 2 shaded and 2 unshaded squares.

So, the numerator of the probability fraction is 8.

Therefore, the probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is 8 ÷ 8 =1.

So the value of a and b is 1.

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Answer:

x = 1/2

y = 7/2

Step-by-step explanation:

Mate, you almost solved the question there by yourself.

You were at the last step.

-6x + 3 = 0

Add 6x on both sides,

-6x + 3 + 6x = 6x

3 = 6x

Divide 6 on both sides,

3/6 = 6/6 x

1/2 = x

So, y = 7x

y = 7/2

Answer:

11)  y = -x + 9

12) y = 4x - 16

13) y = x - 5

14) y = -2x + 4

15)y =  0.5x - 3

Step-by-step explanation:

In all these equations isolate y by moving the other terms to the left side and dividing by the coefficient of x to get the slope intercept form

11)

x + y = 9

y = -x + 9 by moving x to the right side

12)
4x - y = 16

-y = -4x + 16

Multiply by -1 to get y = 4x - 16

13)

2x - 2y = 10

-2y = -2x + 10

Divide by -2 to get y = x - 5

14)

4x + 2y = 8

2y = -4x + 8

Divide by 2 to get y = -2x + 4

15)
x - 2y = 6

-2y = -x + 6

Divide by -2 to get y = x/2 - 6 = 0.5x -3

Answer:

The total boxes would be 625,000

Step-by-step explanation:

5,000,000÷8=625,00

If you have 5,000,000 toys and each box holds 8 toys, you need to divide the number of toys that will fit into a box from the total number of toys

Driving to the supermarket is Joshua. He covers 7.5 miles since he goes an average of 0.56 miles per minute.

By dividing the entire specific number by sum of all the values, the average can be obtained. A mean may indeed be calculated by adding all of the values in a sample of data. In other terms, a means is also known as the arithmetic mean. The average is referred to as having a mean.

The provided function is

d(t) = 0.5t

Simply substitute it to get the figure set t = 15

7.5 miles are equal to d (15) 0.5 (15).

To get the distance, use the range equations d = st, which says "distance equals force times time." Rate and speed are equivalent because they both indicate a specific length of distance per unit time, such like km/h or kilometers per hour. R = s = d/t is true if clip r and mobility s are equal.

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Company A charges $90 for unlimited mileages, while company B charges $75 initial fee and #0.6 per mile driven. Company A will  charge less than company B if the number of miles driven is greater than 25 miles or m > 25.

To solve the problem, we need to translate the word problem into equations.

Let C(A) and C(B) represent the cost charged by company A and B respectively. Let m = the number of mileages.

Company A charges $90 and allows unlimited mileage, it means the charge is a constant and it is not a function of mileage.

Hence,

C(A) = 90

Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. Hence,

C(B) = 75 + 0.6 m

The inequality that translate: for what mileages will company A charge less than company B is:

C(A) < C(B)

90 < 75 + 0.6 m

To solve the above inequality, subtract 75 from both sides:

90 - 75 < 75 + 0.6 m - 75

15 < 0.6 m

m > 15/0.6

m > 25

Hence, if the mileages > 25 miles, company A charges less than company B.

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We may calculate the corresponding value of z = 1.476 using a conventional normal right-tailed z-table.

Find the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table (e.g. whole number and the first digit after the decimal point). It is 1.0 in this instance. We then look up the last number, which in our example is 0.09, from across table (on top).

The amount of standard deviations a scoring or value (x) is from the mean is the number of Z scores (Z value). Z-score quantifies data dispersion in other terms. Z-score, informally, indicates however many standard deviations a number (x) is below or above population mean (µ).

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Answer:

the first one

Step-by-step explanation:

using the vertical line rule, we can see that a vertical line would intersect the first graph more than once at any point to the right of the vertex. this cannot be said for the other graphs

On solving the provided question, we can say that the probability of guessing the sequence 2^99 possible combinations.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.

As soon as you realize there are more heads than tails, you realize you require at least 50 of them, and you ask 100 people to select 50 locations for them to go.

Considering that you have 250 options for the remaining coins, there are a total of (100 pick 50) + 250 combinations that are feasible.

There are 299 potential options if you simply inquire as to whether the first coin will land on heads.

Asking whether there are more heads than tails is preferable because, according to Wolfram Alpha, 299 is larger than (100 pick 50) + 250.

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Answer:

There are several ways to write a proof, depending on the level of rigor and formality required. Some common methods include:

1- Direct proof: A direct proof is a logical argument that begins with the premises and uses logical deduction to arrive at the conclusion.

2- Proof by contradiction: A proof by contradiction starts by assuming the opposite of what needs to be proven and then showing that this leads to a contradiction.

3- Proof by contrapositive: A proof by contrapositive is a proof that starts by assuming the negation of the desired conclusion and then showing that this leads to the negation of the premises.

4- Proof by induction: A proof by induction is a proof that starts by showing that a statement is true for the first few natural numbers, and then showing that if it is true for a particular natural number, it must also be true for the next natural number.

5- Proof by construction: A proof by construction is a proof that shows the existence of a mathematical object by giving an explicit construction of it.

6- Proof by exhaustion: A proof by exhaustion is a proof that considers all possible cases and shows that in each case the statement is true.

7- Proof by casework: A proof by casework is a proof that is split into several cases, each of which is considered separately.

8- Proof by diagram: A proof by diagram is a proof that uses a visual representation to show that a statement is true.

These are some of the common ways of writing proof, and there could be other ways as well. It is important to use the most appropriate method for the problem at hand, and to clearly explain and justify each step of the proof.

Answer:

$25.80

Step-by-step explanation:

Since we need to mark up the price of something, we need to find what 20% of 129 is, then add it to 129. To find our 20%, we put 129 in a fraction like this and get:

[tex]\frac{129}{5} = 25.8[/tex]

So, the markup is $25.80.

Hope this helped!

Answer: x = 3

Step-by-step explanation: Plug g(x) in to get 11 = 3x+2. Do algebra and you get x = 3

Naturally, the task did not require the values of the two variables.Each tree costs $47 and each bush is $23.

Although I don't have subtotals for the bushes and trees, I could try to add the bushes and trees to get 19 bushes and 6 trees, but this wouldn't help me at all.

So I'll choose two variables ("b" for the quantity of bushes and "t" for the quantity of trees) and construct an equational structure:

13b + 4t = 487 is the first order.

second order: 6b plus 2t equals 232.

When I divide the second row by -2, I obtain:

13b + 4t = 487

-12b – 4t = –464

Therefore, b must equal 23.

Using back-solving, I discover that t = 47.

Naturally, the task did not require the values of the two variables.

The answer, when translated back into English, is:

Each tree costs $47 and each bush is $23.

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Answer:

Step-by-step explanation:

The line passes through points (2,1) and (0,-5)

Using this, we can find the slope, which is

change in y/change in x = -6/-2 = 3

Therefore the slop of this line is 3.

Next, the y-intercept of this line is -5.

So we can find the equation of this line in slope-intercept form which is:

y=3x-5

On solving the provided question, we can say that the linear equation, will be  10.50x + 12.50y = 4 => x = 23.1 => y = 3.21

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

a large pizza costs =  $10.50 with no toppings other than cheese

Jason wants 4 toppings on his pizza for a cost of =  $12.10

the linear equation, will be

10.50x + 12.50y = 4

x = 23.1

y == 3.21

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The value of x from the triangle is x = 30

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ABC

Now , the length of the side b = x

The length of the side a = x + 2

The measure of sin A = 4/5

The measure of sin B = 3/4

So , to find the value of x , we use the law of sines

a / sin A = b / sin B

Substituting the values in the equation , we get

( x + 2 ) / ( 4/5 ) = x / ( 3/4 )

On simplifying the equation , we get

5 ( x + 2 ) / 4 = 4x / 3

Multiply by 3 on both sides of the equation , we get

15 ( x + 2 ) / 4 = 4x

Multiply by 4 on both sides of the equation , we get

15 ( x + 2 ) = 16x

15x + 30 = 16x

Subtracting 15x on both sides of the equation , we get

x = 30

Therefore , the value of x is 30

Hence , the value of x is 30

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Answer:

Francesca

Step-by-step explanation: