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The parent functions are defined with all coefficients with value 1.

They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...

Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.

We will use the quadratic parent function:

We will adjust the coefficient a of the quadratic function in order to include (-1,5)

Then, our transformed function is:

The missing integer that makes the following addition statement true is -1.

The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.

Mathematically, the commutative law of addition can be represented using the following formula:

A + B = B + A.

An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.

Now, we would determine the missing number:

x + 3 = 2

x = 2 - 3

x = -1.

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Complete Question:

Find the missing integer that makes the following addition statement true.

+ 3 = 2

To be able to get the expected value of Z, we will be using the following formula:

We get,

Therefore, the expected value of Z is -12.29.

Based on the given parameters, the amount of the investment after 2 years is $3123

The given parameters about the compound interest are

Principal Amount, P = $3000

Interest Rate, R = 2%

Time, t = 2

Number of times, n = 4 i.e quarterly

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

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

Substitute the known values in the above equation

A = 3000 * (1 + 2%/4)^(2 * 4)

Express 2% as decimal

A = 3000 * (1 + 0.02/4)^(2 * 4)

Evaluate the sum

A = 3000 * (1.005)^8

Evaluate the exponent

A = 3000 * 1.041

Evaluate the product

A = 3123

Hence, the value of the investment is $3123

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1. The total amount that was paid for the car will be $23960.

2. The interest that Mai pay on the loan will be $1160.

1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.

The total amount that was paid for the car will be:

= $3800 + ($420 × 4 years)

= $3800 + ($420 × 48)

= $3800 + $20160

= $23960

2. The interest that Mai pay on the loan will be:

= $23960 - $22800

= $1160

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ANSWER:

STEP-BY-STEP EXPLANATION:

We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.

We know that "a number" would be x.

Therefore:

The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.

This simply means the numbers from -10 to 8.

Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.

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Answer: 100

Step-by-step explanation:

First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )

Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100

( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )

recall the formula for velocity, which involves distance and time:

velocity = distance / time

since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:

4.5 km/h = 10 km / t

multiply both sides by the time (t)

4.5 * t = 10

divide both sides by 4.5 in order to isolate t completely

t = 10 / 4.5

then

t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds

Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.

After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.

A function from a set X to a set Y assigns exactly one element of Y to each element of X.

The set X is known as the function's domain, and the set Y is known as the function's codomain.

The given function is f(x) = -2/3x +5.

To obtain f(-1/2), we must substitute the value of x with -(1/2).

f(x) = -2/3x +5

f(-1/2) = -2/3×(-1/2) + 5

f(-1/2) = (2/6) + 5

f(-1/2) = 0.333 + 5

∴ f(-1/2) = 5.3333

Therefore, the value of the function f(-1/2) obtained after substituting        x = -1/2 is 5.333.

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length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and  the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.

PART A

Volume of Cylinder = 2 Litres

Radius of cylinder = r = 10 cm

We need to find the length of a cylinder .

We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]

On substituting the values of Volume of Cylinder and r , we get

2 = π( [tex]10^{2}[/tex])h

h = 2 / 100π = 0.0064 cm

Here h = length of a cylinder

The length of a cylinder is  0.0064cm .

PART B

radius of a cylinder = r

volume of cylinder = 45 cm³

length of cylinder = h = 4 cm

Volume of Cylinder = π[tex]r^{2} h\\[/tex]

45 = 3.14 [tex]r^{2}[/tex] (4)

[tex]r^{2}[/tex] = 3.5828

r = 1.8928

Radius of a cylinder is 1.8928cm.

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We are given the following two numbers to compare

Let us simplify them

So, we can compare them as

The quantity on the left side is greater than the quantity on the right side.

Answer:

Step-by-step explanation:

Answer:

x > 6 with an open point

Hope this helps!

Step-by-step explanation:

-2 ( x + 6 ) > -4x

-2x - 12 > -4x

-(-4x) - 2x > -(-12)

4x - 2x > 12

2x > 12

x > 6

To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,

So that:

We say, that the cost of each text message is $0.09.

The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.

Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:

P(X > 51.75)

= P(Z > [(number - mean) / standard deviation)]

= P(Z > [(51.75 - 54.6) / 5.7)]

= P(Z > -0.5)

= 1 - P(Z = -0.5)

This will be looked at in the z table.

= 1 - 0.3805

= 0.6915

Therefore, the probability is 0.6915.

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Answer:

[tex]x = - 8[/tex]

Step-by-step explanation:

[tex]8x = 4x - 32 \\ 8x - 4x = - 32 \\ 4x = - 32 \\ x = - 8[/tex]

Answer:  −8x − 12y − 18q − 42p

Step-by-step explanation:

i did the exam xD

The representation of the expression is x/2 - 10 = -18

The mathematical statement is given as

"10 less than the quotient of a number and 2 is -18"

In expressions, quotient mean divide i.e. /

So, we have the following representation

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than a number/2 is -18"

Let the number be x

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  10 less than x/2 is -18"

Less than as used here means minus

So, we have

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 is -18

Rewrite as

"10 less than the quotient of a number and 2 is -18" ⇒  x/2 - 10 = -18

Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is  x/2 - 10 = -18

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Given

A right angle triangle is removed from the rectangle to create the shaded region.

That is,

To find: The area of the shaded region.

Explanation:

It is given that,

That implies,

The area of the shaded region is,

Hence, the area of the shaded region is 39ft^2.

Answer:

The answer to your question is: B

Explanation:
based on the statistics given, this answer best fits the Queston.

The slope of the line that passes through points (10,4) and (7, 3) is 1/3

Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:

m = Change in y-coordinates/Change in x-coordinates

m = (y₂– y₁)/(x₂ – x₁)

Since we are given two points (10,4) and (7, 3),  where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3

From  the formula we get,

m = (y₂-y₁)/(x₂-x₁)

 = ( 3-4)/(7 - 10)

 = -1/-3

 =1/3

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Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.

The most well known polar equation rules are given as follows:

For the first pair, when x = 2, we have that:

rcos(θ) = 2.

r = 2/cos(θ)

r = 2 sec(θ), as one divided by the cosine is the secant.

For the second pair, we have that:

x² + y² = 36.

x² + y² = r², hence:

r² = 36

r = 6.

For the third pair, we have that:

x² + y² = 2y

r² = 2rsin(θ).

r²/r = 2sin(θ).

r = 2sin(θ).

For the fourth pair, we have that:

[tex]x = \sqrt{3}y[/tex]

[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]

[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]

Then the angle theta is given as follows:

θ = arctan(sqrt(3)/3) = pi/6.

For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.

The image at the end of the answer shows all the matched pairs.

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After evaluating the limit we have came to find that the limit of  [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1

The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.

In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]

Evalue -∞ as x

⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]

⇒ 1

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The value of a that makes the solution of the equation is 1/2.

Given,

The equation: 3(2x - 4) = 4(ax - 2)

Solve,

3(2x - 4) = 4(ax - 2),

Open the bracket and multiply:

6x - 12 = 4ax - 8

Add 12 to both sides

6x -12 + 12 = 4ax + 12 - 8

We get,

6x = 4ax + 4

Add - 4ax to both sides:

6x - 4ax = 4ax - 4ax + 4

We get,

6x - 4ax = 4

Take x = 1

Then,

6 × 1 - 4a × 1 = 4

6 - 4a = 4

Now,

Add - 6 to both sides

6 - 6 - 4a = 4 - 6

We get,

-4a = -2

That is,

4a = 2

a = 2/4 = 1/2

That is,

The value of a that makes the solution of the equation is 1/2.

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Answer:

Step-by-step explanation:

Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.

But here i will use and and or

By the rules of probability

P(A or  B) = P(A) + P(B) - P( A and  B)  
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75

The complement of a set A is all the elements not in A
P(A') = 1 - P(A)

If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and  B)' = 1 - P(A or B) = 1- 0.75 = 0.25

P(A|B)  = P(A and  B)/P(B) = 0.35/0.65 = 0.54

P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78

Answer:

1.4 Relations and Functions

A relation is a correspondence between two sets. If x and y are two

elements in these sets and if a relation exists between x and y, then x

corresponds to y, or y depends on x.

DEFINITION OF A FUNCTION:

Let X and Y two nonempty sets. A function from X into Y is a relation that

associates with each element of X, exactly one element of Y.

However, an element of Y may have more than one elements of X

associated with it.

That is for each ordered pair (x,y), there is exactly one y value for each x,

but there may be multiple x values for each y. The variable x is called the

independent variable (also sometimes called the argument of the

function), and the variable y is called dependent variable (also

sometimes called the image of the function.) x = y2 is not a function from X into Y, because there

is not exactly one y value for each x.

Solving for y, you get y =

which means there are two possible values for y

Step-by-step explanation:

The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.

Thus, we can see that the largest five-digit multiple of 15 could be ;

12345

Since it must be all distinct and nonzero. so the correct digit is 12345.

Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.

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Answer:

what

Step-by-step explanation:

i think maybe like… actually

The value of x that makes m parallel to n is 90 degrees.

The value of x that makes m and n parallel is 15.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The value of x that makes the line ma and n parallel can be calculated as follows:

180 - x  = x (alternate exterior angle)

180  = 2x

x = 180 / 2

x = 90 degrees

2.

3x - 15 + 150 = 180(supplementary angles)

3x = 180 - 150 + 15

3x = 45

x = 45 / 3

x = 15

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