Prove: The diagonals of a square are perpendicular.

An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

Given that,

A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.

The pipe is located 9 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 9 inches from the vertex (0,0)

9 inches is the focus of the mirror

The distance between the vertex and the focus = 9

Since parabola is upwards and vertex is (0,0) we use formula,

[tex]4py = x^{2}[/tex]  

Where,

p is the distance between the vertex and focus p = 9

Now,

[tex]4*9*y = x^{2}[/tex]    

[tex]36y =x^{2}[/tex]

Now isolate y by dividing 36 on both sides, we get

y = [tex]\frac{x^{2} }{36}[/tex]

Therefore,

An equation of the parabola that models the cross section of the mirror is, y = [tex]\frac{x^{2} }{36}[/tex]

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The correct answer is e) approximately normal with a mean 122 and standard deviation 0.35.

In this case, the distribution of the sample mean of IQ scores will be approximately normal because the sample size of 200 is sufficiently large. This is known as the Central Limit Theorem, which states that the distribution of the sample mean will be approximately normal as long as the sample size is large enough, regardless of the shape of the distribution of the population.

The mean of the sample mean distribution will be 122, which is the same as the mean of the population. The standard deviation of the sample mean distribution will be smaller than the standard deviation of the population because it is calculated using the sample size rather than the population size.

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Answer:

Three and four  and five  and zero.

Step-by-step explanation:

Answer:

3 and 4

Step-by-step explanation:

The given type of effect is called predictive.

What is linear regression?

When predicting a variable's value based on the value of another variable, linear regression analysis is used. The dependent variable is the one you're trying to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.

Given:

A variable with a value of x1 x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable.

Linear regression is one of the most generally utilized predictive displaying methods.

It is spoken to by a condition = + + , where an is the catch, b is the slant of the line and e is the blunder term.

This condition can be utilized to predict the estimation of an objective variable dependent on a given predictor variable(s).

The predictor variable is the name given to an autonomous variable utilized in regression examinations.

The predictor variable gives data on a related ward variable concerning a specific result.

Hence, the given type of effect is called predictive.

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The three types of set based on the number of elements is empty set, finite set and infinite set.

In mathematics, a set is a collection of unique objects. The number of elements in a set can be finite or infinite.

An empty set is a set with no elements. It is also called a null set. For example, a set of natural numbers less than 0.

Finite set is a set containing finite number of elements, that is the number of elements in the set is countable. For example, a set of natural numbers less than 100.

Whereas infinite set is a set with infinite number of elements, that is the number of elements in the set is not countable. For example, a set of natural numbers.

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The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Let us find three consecutive integers whose sum is 399. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 399. Therefore, you can write the equation as follows:

(X) + (X + 1) + (X + 2) = 399

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 399

3X + 3 = 399

3X + 3 - 3 = 399 - 3

3X = 396

3X/3 = 396/3

X = 132

Which means that the first number is 132, the second number is 132 + 1 and the third number is 132 + 2. Therefore, three consecutive integers that add up to 399 are 132, 133, and 134.

Hence , The formula for 3 consecutive integers (X) , (X + 1) , (X + 2) if the first number is supposed to be x.

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Answer: x= 4/k

Step-by-step explanation:

Answer:

B.) [tex]\frac{4}{k}[/tex]

Step-by-step explanation:

[tex]3kx+24=9kx\\3(kx+8)=9kx\\\frac{3(kx+8)}{3}=\frac{9kx}{3}\\kx+8=3kx\\(kx+8)-kx=(3kx)-kx\\8=2kx\\\frac{8}{2k}=\frac{2kx}{2k}\\\frac{4}{k}=x[/tex]

Answer:

320 teenagers

Step-by-step explanation:

10% = 0.1

Take 3200 times 0.1 = 320

So, there are 320 teenagers attended the football game.

The  polynomial function that could be represented by the graph is; f(x) = x³ + x² - 6x

Let us find the zeros of the polynomial from the graph. The zeros of the polynomial will be the points where the graph crosses the x-axis.

Thus, we see that the graph crosses the x-axis at x = -3, 0 and 2. Thus, the factors of the polynomial are;

(x - 0), (x + 3) and (x - 2)

Therefore, the equation of the polynomial is;

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

Expanding this gives us;

f(x) = x(x² + x - 6)

f(x) = x³ + x² - 6x

We conclude that is the equation of the polynomial represented by the graph.

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Answer:

( x + 6, y + 4)

Step-by-step explanation:

Let's pick point S at ( -9, -4); it changes to point S' at ( -3, 0)

The x increase by 6, and the y increase by so the answer is

( x + 6, y + 4)

Answer: I don't know

Step-by-step explanation:

Answer:

$6,232.89 or $6,232.90

Step-by-step explanation:

A=P(1+(r/n))^nt

A= 3000(1+(.075/12))^12*10

A= 3,232.89

3,232.89+3000= 6,232.89

Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].

Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].

To produce a result equal to 0, add the original number and the additive inverse by simply reversing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.

A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is represented by 1/x or x/1. A fraction a/b has a multiplicative inverse of b/a. Divide 1 by the real number to obtain the multiplicative inverse of the number.

A function that "undoes" another function is called an inverse. In other words, if f(x) generates y, then y entered into the inverse of f creates x. An invertible function is one that has an inverse, and the inverse is indicated by the symbol [tex]f^{-1}[/tex] .

Additive inverse of [tex]x^{2}[/tex] is [tex]-x^{2}[/tex].

Multiplicative Inverse of [tex]x^{2}[/tex] is [tex]x^{-2}[/tex].

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The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

First we define a reference system.

Let's assume the horizontal axis as positive towards the right.

Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.

The equilibrium equation is given by:

-20-25+F=0

Where,

F: force with which Gunther pulls the rope.

Clearing F we have:

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

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Number of combinations = 56 combinations can be created from the letters in the word "friendly"

Points to remember

nCₐ = n!/(r!(n - r)!)

The given word is "FRIENDLY"

F R I E N D L Y is a 8 letter word.

To find the number of combinations

5 letters can be selected from 8 letter = 8C₅

8C₅ = 8!/(8 - 5)!5!

= 8!/3!5!

= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)

= 8 * 7

=  56

5 letter combinations can be created from the letters in the world “friendly = 56

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The amount of fabric used on the headband and wristband for each player is 27.64 inches.

The operations that we use in particular actions like adding and taking away things or adding multiple times, diving things, etc.

The four basic Mathematical operations are addition, subtraction, multiplication, and division.

Here in this problem, we use divisions to solve the problem,

Given that,

Nancy uses 866.18 inches of fabric on headbands for 43 players and 3 coaches. 378.83 inches of fabric used on wristbands for the players only.

Number of headbands made with 866.18 inches

= 43 (player's) + 3 (coach's)  

= 46 headbands

The amount of fabric used for 1 head band = (866.18)/46 = 18.83 in

378.83 inches of fabric used on wristbands for the players only.  

The amount of fabric used for each wristband = 378.83/43 = 8.81 in

Amount of fabric used on headband and wristband = 18.83 + 8.81

= 27.64 inches

Therefore,

The amount of fabric used on the headband and wristband for each player is 27.64 inches.

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Answer: I am bad at math, but I'd say _> is the sign...

Step-by-step explanation:

elloooo

The perimeter of the new TV will be 179.77 inches.

From the information, the TV was 32 inches (across the diagonal) and had a perimeter of 87.16 inches and the new TV is 66 inches across the diagonal.

It should be noted that the perimeter simply means the total length of the boundary of the object. This will be calculated thus:

= (66 × 87.16) / 32

= 5752.56 / 32

= 179.77 inches.

In conclusion, the perimeter is 179.77 inches.

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The cost of each pen would be 5 dollars.

What is a unit value?

When the expenditures or value of production of an item is divided by the quantity, the result is known as a unit value. Context: The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities

The shopkeeper has 56 pens. and he sold them for 280 dollars

Cost of each pen = total amount/ number of pens

                            = 280/56

                            =10/2

                            = 5

Hence, the cost of each pen would be 5 dollars.

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7.500 (rounded to 4 decimals) sum of the numbers on the balls.

Suppose we select two distinct balls

Then we have the following possibilities of selecting two balls

(2,2), (2,2) ............, i.e. 2 ways to get a sum of 4...............(2+2 = 4 and 2+2 = 4)    

(2,5), (2,5), (5,2), (5,2), i.e. 4 ways to get a sum of 7...............(5+2 = 7 and 2+5 = 7)    

(2,6), (2,6), (2,6), (2,6), i.e. 4 ways to get a sum of 8...............(2+6 = 8 and 6+2 = 8)    

(6,5), (5,6) , i.e. 2 ways to get a sum of 11...............(5+6 = 11 and 6+5 = 11)    

total number of possible outcomes =  2(for a sum of 4) + 4(for a sum of 7) + 4(for a sum of 8) + 2 (for a sum of 11)

= 2 + 4 + 4+2

= 12

So, P(getting a sum of 4) = (number of ways to get a sum of 4)/total number = 2/12

similarly,

P(getting a sum of 7) = (number of ways to get a sum of 7)/total number = 4/12

P(getting a sum of 8) = (number of ways to get a sum of 8)/total number = 4/12

P(getting a sum of 11) = (number of ways to get a sum of 11)/total number = 2/12

We know that expected value E[x] = sum of all individual sum values by their respective probability

= 4*(2/12) +7*(4/12) +8*(4/12) +11*(2/12)

= 0.6667 + 2.3333 + 2.6667 + 1.8333

= 7.500 (rounded to 4 decimals)

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Answer:

Step-by-step explanation:

The phase of the systems life cycle during which users are trained to use the new system is called the implementation phase. In this phase, the new system is installed and made operational, and users are trained on how to use it effectively. This phase typically follows the design and development phases and precedes the maintenance phase.

What is the main focus of the implementation phase in the systems life cycle?

The main focus of the implementation phase is training users to use the new system effectively. This includes installing the system and making it operational, as well as providing necessary support and training to ensure users are able to utilize the system efficiently.

The phase of the systems life cycle during which users are trained to use the new system is the implementation phase. This is the phase where the new system is actually implemented and made available for use by the users. It is important to provide training to users during this phase so that they are able to effectively use the new system and understand its functionality.

Therefore, users are trained to use the new system during the implementation phase.

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The implementation phase of the systems life cycle is the time when users are taught how to utilize the new system.

The new system is installed, made operational, and users are instructed on how to utilize it efficiently during the implementation phase. In most cases, this phase comes after the design and development phases and comes before the maintenance period.

Why is user training important during the implementation phase of the systems life cycle?

User training is important during the implementation phase of the systems life cycle because it ensures that users are able to effectively use the new system and understand how it works. This is essential for the successful adoption and utilization of the system by the organization. Without proper training, users may struggle to use the system effectively, leading to reduced productivity and potentially even causing issues with data accuracy and integrity. By providing thorough user training, organizations can ensure that their employees are able to use the new system efficiently and effectively, leading to a successful implementation.

The implementation phase of the systems life cycle is the time when users are taught how to utilise the new system. In this stage, the new system is really put into use and made accessible to users. During this stage, it's crucial to give users training so they can utilize the new system correctly and comprehend its functions.

Therefore, during the implementation phase, users are instructed on how to utilize the new system.

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The sum of the integers from 1 to 100 is 5050. You can find this sum by adding all of the integers together or by using the formula for the sum of an arithmetic series.

In this case, there are 100 terms, and the average of the first and last term is (1 + 100) / 2 = 50.5, so the sum is 100 * 50.5 = 5050.

Another way to find the sum is To find the sum of the integers from 1 to 100, we can add all of the integers together. This can be done by starting with 1 and repeatedly adding 1 to get the next integer, or by using a calculator or computer program to do the calculations for us.

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No, the biconditional statement isn't true because It's not necessary that if a polygon has four sides, then It will be a square.

What is Biconditional statement?

A statement that combines a conditional statement with its opposite is known as a biconditional statement. So, if and only if the other conditional is also true, the first conditional is true.

Let's elaborate the statement, “If a polygon is a square, then it has four sides.”

We know that a square has four equal sides and So, if a polygon is a square, it must have four equal sides which states that the given statement is true.

But, if we see its converse, "If a polygon has four sides, then it is a square". It is not necessary that the polygon will be a square.

eg. A parallelogram and  rectangle also have four sides, So it could either be a parallelogram, rectangle or a square.

Hence, The given statement is correct but the converse of it, is not correct.

So, It can't be called a biconditional statement.

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Figure P is the result transformation figure O by the rule (x + 1, y-4). In other words, figure O shifted 1 unit left and 4 units downward direction.

What is meaning transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation. Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

The two-dimensional shape without any transformations is known as a preimage or inverse image. The transformed figure is shown in the image.

The coordinate of vertices of figure O are (2,4), (3,5), and (4,2).

The coordinate of vertices of figure P are (3, 0), (4,1), and (5, -2).

The difference between x-coordinates is (3 - 2) = (4 - 3) = (5 - 4) = 1.

The difference between y-coordinates is (0 - 4) = (1 - 5) = ( -2 - 2) = -4.

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The answer to the expression -( 7 4x )= 9 is -7, since subtracting 7 from both sides of the equation leaves us with 4x = 2, and then dividing both sides of the equation by 4 gives us x = -7.

The expression -( 7 4x ) = 9 can be solved by using basic algebraic operations. First, we subtract 7 from both sides of the equation to obtain -4x = 2. This is because when subtracting a number from both sides of an equation, we are essentially adding the opposite of that number to both sides. Then, we divide both sides of the equation by 4 to obtain x = -7. This is because when dividing both sides of the equation by a number, we are essentially multiplying both sides by the inverse of that number. Therefore, the answer to the expression is -7.

-(7 4x ) = 9

-7 - 4x = 9

-4x = 2

x = -7

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2 is a  prime number because it has only two factors (1 x 2).

A natural number greater than one that is not the product of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than 1 that is not prime.

Numerical tables, which were typically printed before calculators and computers, were used to record all primes or prime factorizations up to a certain limit. The Sieve of Eratosthenes is the most well-known method for making a list of prime numbers.

Given why 2 is prime,

The natural numbers greater than 1 with exactly two factors, i.e. 1, and the number itself, are known as prime numbers.

so 2 has only two multiple

1 and 2,

Hence 2 is a prime number.

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Answer:

Number of international passengers increased then decreased whereas the number of domestic passengers constantly increased

Step-by-step explanation: