Find the y intercept y = – 17 x + 12.

As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G i.e m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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As AB is the perpendicular bisector of IK so we conclude that the right option is AJ=BJ.

What is perpendicular bisector?

A precise drawing in which a line is split in half by another line that is at a 90-degree angle to the original line is known as a perpendicular bisector. To divide into two equal portions is to bisect. When two lines intersect at a straight angle, they are perpendicular.

What is the perpendicular of two points?

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

Option J can not be true as A can not be the midpoint of IK as A is not on IK.  Because J is on the IK as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. Hence, J is assumed as the midpoint of IK.

Option H) i.e IJ = JK can not be true because AJ does not necessarily equal to BJ.

Option G)  i.e  m∠IAJ  also does not true necessarily true. The reason is simple i.e AJ is arbitrary.

So, Option f)  i.e AJ = BJ is the correct Answer as AB is the perpendicular bisector of IK, dividing or cutting it i,e IK into two equal segment parts. So it can be assumed that that J is the midpoint as but it doesn't necessarily mean that IJ = JK, also it is true that perpendicular lines meet at 90 degree. Hence, statement F i.e AJ = BJ  is true.

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First:

Quotient: [tex]2x^{2} -11x+58[/tex]

Remainder: [tex]-294[/tex]

Second:

Quotient: [tex]x^{3} -5x^{2} +17x-83[/tex]

Remainder: [tex]422[/tex]

Third:

Quotient: [tex]2x-3[/tex]

Remainder: [tex]12[/tex]

The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The inequalities are,

2( x +6 ) > -6( x +1) +2

2x + 12 > -6x - 6 + 2

2x + 6x > -12 - 6 +2

8x > -16

x > -2

-3x - 1 ≥ 20

-3x ≥ 21

x ≥ -7

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Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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Luka will require 24 cups of water to make lemonades as calculated from the data given.

The quantity of sugar which he use is twice the amount of lemon which he us ,

= 2 x 3 = 6

and ,

as we know the amount of water is 4 times as much as lemon juice

Therefore, amount of water

= 4 * 6

= 24

A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.

A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.

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Answer:G(x) = 3/4 |x|, nevertheless that is the same that G(x) = |3/4x|.

Step-by-step explanation:

Note that given that 3/4 is less than 1 the original function is compressed.

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The number of boxes of sugar that Alonso can buy are 4.5 boxes.

Given is that Alonso went to the market with $55 to buy eggs and sugar. He knows he needs a package of 12 eggs that costs $2.75. After getting the eggs, he wants to buy as much sugar as he can with his remaining money.

The money remaining after buying 12 eggs : {r} = $(55 -2.75).

Cost of one box of sugar = $11.5

The number of boxes that he can buy are -

n = (55 - 2.75)/11.5

n = 4.5 boxes {approx.}

Therefore, the number of boxes of sugar that Alonso can buy are 4.5 boxes.

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The probability that less than three of the chosen consumers think that currency won't be used in 20 years is 0.293.

According to the statement, 40% of consumers think cash will be unnecessary in 20 years. Let us assume that eight consumers are chosen at random.

We need to determine the likelihood that fewer than three of the chosen consumers think currency will be obsolete in 20 years.

We will use the properties of probability distribution in the given scenario.

We know that for randomly selected variable the properties of combination are used.

P(X=1) + P(X=2) = C¹₈ × 40 × 60⁷ + C²₈ × 40² × 60⁶

P(X=1) + P(X=2) = 0.293

Therefore, there is a 0.293 percent chance that fewer than 3 of the chosen customers think that cash will be obsolete in 20 years.

The ratio of likely outcomes to all scenarios that are feasible, to all possible outcomes is called probability.

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

This claim asserts that under certain conditions, the average of many samples (observations) of a random variable without finite mean and variance is itself a random variable, whose distribution converging to either a normal distribution as the number of samples increases.

Disclaimer: The complete question is :

40% of consumers believe that cash will be obsolete in the next 20 years. Assume that only 8 consumers are randomly selected. Find the probability that less than 3 of the selected consumers believe that cash will be obsolete in the next 20 years .

(Round to three decimal places as needed.)

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Dependent variable: t (total cost of the pizza)

Independent variable: x (number of extra toppings)

Equation: t = 10.50 + 1.50x

To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:

t = 10.50 + 1.50(3)

t = 10.50 + 4.50

t = 15.00

So the total cost of the pizza with 3 extra toppings is $15.00.

What is Dependent Variables?

The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.

What is Independent Variables?

Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.

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