what is the equation of a line perpendicular to y = 2x - 6 that passes through (5, 4)
(use y = m x + b)
(must solve for y to get slope)

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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There are 20 members of a basketball team. (a) The coach must select 12 players to travel to an away game. There are \(\(\binom{20}{12}\)\) ways to select the players who will travel to the away game.

To determine the number of ways to select the players who will travel, we can use the concept of combinations. We want to choose 12 players from a group of 20 players. The notation \(\(\binom{n}{r}\)\) represents the number of ways to choose r objects from a set of n objects without regard to the order of selection. In this case, we want to choose 12 players from a group of 20, so we use the combination formula:

\(\(\binom{20}{12} = \frac{20!}{12!(20-12)!}\)\)

Simplifying the expression, we get:

\(\(\binom{20}{12} = \frac{20!}{12!8!}\)\)

This gives us the total number of ways to select 12 players from a group of 20, which is the answer to the question.

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Answer: The domain is 3.5

Answer:

B. MT = CA

Step-by-step explanation:

MW should be equal to CD

AD should be equal to TW

MT should be equal to CA

Therefore B is the correct answer

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Answer:

5 units

Step-by-step explanation:

Image of the trapezoid is attached.

To find the height of the trapezoid (image attached), let's take the formula for area of a trapezoid.

The formula for area of a trapezoid is:

\( A = (\frac{a + b}{2}) h \)

Here, a and b represents the bases of the trapezoid.

a = 6

b = 10

h which represents height is unknown.

A = 40

Substitute figures:

\( 40 = (\frac{6 + 10}{2}) h \)

\( 40 = (\frac{16}{2}) h \)

\( 40 = 8 * h \)

Solve for h:

\( h = \frac{40}{8} \)

\( h = 5 \)

The height of the trapezoid is 5 units

Answer:

5 units

Step-by-step explanation:

For the company to practice price discrimination, there should not be any resale of its product, is not true if a public utility company is considered a monopolist. This is because price discrimination involves charging different prices to different groups of customers based on their willingness to pay. Resale of the product can actually facilitate price discrimination as it allows different customers to buy the product at different prices and then resell it to others. The other options are true for a monopolist, such as having upward sloping demand and supply curves, charging a price higher than its marginal revenue, and determining profit maximizing quantity at the point where marginal revenue equals marginal cost.

Let's analyze each statement:

A. The company's demand curve and supply curve are upward sloping.
This statement is NOT true for a monopolist. A monopolist faces a downward sloping demand curve, which means that they can increase the quantity sold by lowering the price. The supply curve does not apply in the traditional sense for monopolists, as they have the power to set both the price and quantity produced.

B. Its price must be higher than its marginal revenue.
This statement is true for a monopolist. Under a monopoly, the price charged by the company is higher than its marginal revenue due to the downward-sloping demand curve.

C. For the company to practice price discrimination, there should not be any resale of its product.
This statement is true. In order for a monopolist to successfully engage in price discrimination, they must prevent the resale of their product, ensuring that consumers cannot undercut the monopolist's pricing strategy.

D. Its profit maximizing quantity is determined where its marginal revenue equals its marginal cost.
This statement is true. A monopolist maximizes its profit by producing the quantity where marginal revenue equals marginal cost, and then setting the price based on the demand curve at that quantity.

So, the statement that is NOT true for a public utility company considered as a monopolist is: A. The company's demand curve and supply curve are upward sloping.

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Step 1: Concept

The axis of symmetry always passes through the vertex of the parabola. The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Step 2: Find the axis of symmetry using the formula

The axis of symmetry is a vertical line.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Therefore, the axis of symmetry is x= 1

Step 3: Find the vertex

To find the vertex, you substitute x = 1 in the equation of a parabola.

The vertex = (1,9)

Two variables that move in opposite directions are said to be inversely related.

A negative correlation is a relationship between two variables that move in opposite directions. In other words, when variable A increases, variable B decreases. A negative correlation is also known as an inverse correlation.

The concept of negative correlation is important for investors or analysts who are considering adding new investments to their portfolio. When market uncertainty is high, a common consideration is re-balancing portfolios by replacing some securities that have a positive correlation with those that have a negative correlation.

Here are some common examples of a negatively correlated relationship between assets:

1. Oil prices and airline stocks

2. Gold prices and stock markets (most of the time, but not always)

3. Any type of insurance payoff

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Answer:

x=-2

Step-by-step explanation:

If the slope is perpendicular to the line, then the slope of the line 2/7x+20 would be -7/2.

Whenever we need to find the slope of the line perpendicular to the given line we have to consider the negative inverse of "m" of the line in the slope-intercept form.

since the given equation is already in the slope-intercept form, viz, y=mx+b,  thus, there is no need to reconvert the given equation in any other form. Here m=2/7

and since the given line is perpendicular to the line, y=2/7x+20, thus the slope of the line will be the opposite reciprocal in the negative sign.

Hence we can say that the slope of the line perpendicular to the line, y=2/7x+20 would be -7/2.

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Answer: -2x(x-5)(x+4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

add it up and then multiply and then you divide and you got the answer so may i please have brinliest. sir

so its x27

E, "As I was saying, . . .". The salesperson should use this statement if they wished to ignore the objection.

Option E is the best choice to ignore the objection because it allows the salesperson to redirect the conversation back to their main point without directly addressing the objection. The statement implies that the objection is not important enough to interrupt the flow of the conversation.

Ignoring objections is not always the best approach in sales, but if the salesperson chooses to do so, they should use a statement like option E to redirect the conversation back to their main point.


When a salesperson wants to ignore an objection, they should choose a response that does not address the concern raised and instead redirects the conversation back to the topic they were discussing. Option e does this effectively by not acknowledging the objection and continuing with the original discussion.

To ignore an objection, a salesperson should use a statement like option e, which allows them to refocus the conversation without addressing the concern raised.

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Data

• Total phone calls: 154

• Second evening ( ,s ,): 10 more calls than the first evening ( ,f ,)

• Third evening ( ,t ,): 4 times as many calls as ,f

Procedure

We have to translate the given information into algebraic expressions.

• Maria received a total of 154 phone calls at the call center:

where f represents the first evening, s the second, and t the third.

• The second evening, she received 10 more calls than the first evening:

• The third evening, she received 4 times as many calls as the first evening:

As t and s can be used in terms of f, we will replace the second and third equations that we build in the first one:

Eliminating the parenthesis we get:

Solving for f:

Thus, the number of phone calls the first evening was 24.

Then, we have to replace this calculated value in the other equations to get s and t.

• Solving for ,s

• Solving for ,t

To prove our answers are correct, we can do the following:

Answer

• Number of phone calls the first evening: 24

• Number of phone calls the second evening: 34

• Number of phone calls the third evening: 96

There are infinitely many even integers that are divisible by 5.

By considering how any even integer can be represented as 2m, where m is an integer, it becomes evident that if 2m happens to be divisible by 5, then m will also have this quality because 5, which is a prime number, cannot divide into 2.

As a result, all even integers that aredivisible by 5 can be expressed in the format of 10n, with any n being acceptable. Examples of such numbers include:

0 (from 10 x 0 = 0)

10 (from 10 x 1 = 10)

-10 (through 10 x -1 = -10)

20 (by evaluating 10 x 2 = 20)

And similarly when exploring negative values:  

-20 (since 10 x -2 = -20), and so on.

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Answer: 23/20.

Step-by-step explanation:

given data:

probability that skene would be alive in 5years time = 3/4.

probablility that skene wife would also be alive in 5 years time = 2/5

SOLUTION:

The probability that both would be alive in 5years time.

= 3/4 + 2/5.

= 5*3 + 4*2 /20.

= 15 + 8 /20.

= 23/20.

We diagree with Marco because

and

where, in the first expression, we factorized x and got

and in the second one, we got

In summary, the first expression is equal to x and the second one is equal to zero, so they are different expressions.

9514 1404 393

Answer:

  D.  90

Step-by-step explanation:

The radius VG is the same as the radius VO. That radius is ...

  VG = VA +AG = 24 +27 = 51

Then the Pythagorean theorem tells you ...

  VO^2 = VA^2 +AO^2

  AO = √(VO^2 -VA^2)

  AO = √(51^2 -24^2) = √2025 = 45

The desired length is ...

  TO = 2·AO = 2·45

  TO = 90

Answer:

x > 1,  x < 10

Step-by-step explanation:

Part 1:

-2x < -2

Simplify (divide by -2)

-------------

Part 2:

x - 2 < 8

Simplify (add 2 to both sides)

For the exponential equation, having variable x as superscript equation has solution as,

\(x=-5,2\)

According to the equality for exponential equation property, when the bases of both side of a equation is same, then the exponents of both the terms must be equal.

The equation given in the problem is,

\(12^{x^2+5x-4}=12^{2x+6}\)

In the given equation, the base of both side is equal. For the equal base, the exponents of them can be equate as,

\({x^2+5x-4}={2x+6}\)

Arrange all the terms one side of the equation as,

\({x^2+5x-4}-{2x-6}=0\)

Solve it further as,

\({x^2+3x-10}=0\)

To solve the above quadratic equation, use the split the middle term method as,

\({x^2-2x+5x-10}=0\\x(x-2)+5(x-2)=0\\(x-2)(x+5)=0\)

Equating both the factor to the zero, we get the value of the x as -5 and 2.

For the exponential equation, having variable x as superscript equation has solution as,

\(x=-5,2\)

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Assuming question is:

3(0)= -2x+9

and we have to solve for x:

0 = -2x + 9

We take x to one side, so it becomes:

2x = 9

Now we divide by 2 on both sides:

2x/2 = 9/2

x = 9/2

The correct answer is:

Answer:

10,603 cu in

Step-by-step explanation:

For a pipe use its length instead of height: pipe volume = π * radius² * length , where radius = inner diameter/2 . The volume of a pipe is equal to the volume of a liquid inside.

Therefore,

radius = 1 inch ÷ 17 = 5 inch

length = 15 × 5 inches = 75 inches

volume = π (pi) × radius squared × length

volume = 15× (.5 x .5) × 75

volume = 15 × 5 × 2

volume = 10,603 in³

The volume of fluid in a pipe can be found given the inner diameter of the pipe and the length. To estimate pipe volume, use the following formula:

volume = π ×  

d2

4

× h

Thus, the volume of a pipe is equal to pi times the pipe diameter d squared over 4, times the length of the pipe h.

This formula is derived from the cylinder volume formula, which can also be used if you know the radius of the pipe.

volume = π × r2 × h

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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The value of ac can be found by recursively applying the given formula. The formula states that the nth term is equal to the previous term plus 1. Given that a1 = 7, we can calculate the value of ac using this recursive relationship.

To find the value of ac, we need to apply the given formula, which states that each term (except the first term) is equal to the previous term plus 1. Let's start by calculating the second term, a2.

According to the formula, a2 = a1 + 1 = 7 + 1 = 8.

Next, we can calculate the third term, a3, using the same formula. a3 = a2 + 1 = 8 + 1 = 9.

Continuing this process, we can find the values of subsequent terms. a4 = a3 + 1 = 9 + 1 = 10, a5 = a4 + 1 = 10 + 1 = 11, and so on.

By recursively applying the formula, we can determine the value of the nth term. In this case, we are interested in the value of ac. To find it, we need to continue the pattern until we reach the desired term. Since the specific value of c is not provided, we cannot determine the exact value of ac without knowing the value of c. However, we can determine the value of the nth term for any given c by following the recursive formula.

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