Which of the sets of ordered pairs represents a function? (4 points)

A = {(−4, 5), (1, −1), (2, −2), (2, 3)}
B = {(2, 2), (3, −2), (9, 3), (9, −3)}

you can do both or neither as well THX

Answer:

A. Y = 2/9

B. X =  11/24

C. X = 2.64

Two events are independent if the occurrence of one event does not affect the probability of the other event.

Two events are independent if the occurrence of one event does not affect the probability of the other event. This means that the outcomes of the two events are not related and the probability of one event happening does not change based on whether the other event occurred or not.

For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the probability of getting a certain number on the die roll. The two events are independent.

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Answer: his average speed on the second day is 35 miles per hour

Step-by-step explanation:

Bill spends two days driving from point a to point b

Let x = his speed on the first day.

Let y = his speed on the second day

Speed = distance / time

Time = distance / speed

Total time spent on the trip is 18 hours

Let time that he spent on the first day be t hours

Time that he spent on the second day will be 18 - t

Bill drove 2 hours longer on the second day than on the first day. This means

t = 18 - t + 2

t+t = 18+2

2t = 20

t = 10

He spent 10 hours on the first day.

He spent 18-10 = 8hours on the second day.

Bill drove at an average speed of 5 miles per hour faster than he drove on the second day. This means that

x = y + 5 - - - - - - - -- 1

Distance travelled on the first day = speed on the first day × time spent. This becomes

10 × x = 10x miles

Distance travelled on the second day = speed on the second day × time spent. This becomes

8 × y = 8y miles

He drove a total of 680 miles over the course of the 18 hours. This means that

10x + 8y = 680 - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

10(y + 5) + 8y = 680

10y + 50 + 8y = 680

10y + 8y = 680 - 50

18y = 630

y = 630/18 = 35 miles per hour

x = y + 5 = 35 + 5

x = 40 miles per hour

The cube of a positive number divided by its square simplifies to the number itself, based on the exponent subtraction rule in algebra.

The question involves a mathematical concept where the cube of a positive number is divided by the square of the same number. Mathematically, if we denote the positive number as 'x', then the expression would be x3/x2. According to the laws of exponents, when we divide two powers with the same base, we subtract the exponents. Thus, x3/x2 = x3-2 = x. This implies that the cube of 'x' divided by the square of 'x' simplifies to just 'x'. This is a fundamental mathematical operation under the topic of exponentiation and simplification of algebraic expressions.

The estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable. Each ramp will have a length of 2 1/12 feet, and no wood will be left over.

To determine if the estimate of cutting 6 ramps from a 12 1/2 feet long board is reasonable, we can calculate the length of each ramp by dividing the total length of the board by the number of ramps.

12 1/2 feet is equivalent to 12 + 1/2 feet. To divide by a fraction, we can multiply by the reciprocal. So, when we divide 12 1/2 by 6, we get (12 + 1/2) / 6 = 12/6 + 1/2 / 6 = 2 feet + 1/12 feet = 2 1/12 feet.

Therefore, each ramp will have a length of 2 1/12 feet. Since 6 ramps multiplied by 2 1/12 feet is 12 1/2 feet, the estimate is reasonable. No wood will be left over.

The question is about continuous compound interest in finance. Given initial investment, final amount, and interest rate, we utilize the formula for continuous compound interest to calculate how many years it will take for the investment to reach a certain value.

The subject in this question is interest compounding in mathematics, specifically in the field of finance. Compounding continuously involves the application of the formula for continuous compound interest, which is A = P*e^(rt), where:

In Mazie's case, we have P=$4500, A=$7400, and r=4.3% or 0.043 in decimal form. We're solving for t, the time. Therefore, by substitution, we have 7400=4500*e^(0.043t). Solving for 't' will provide us the number of years it takes for the account to grow to $7400.

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Answer:

[tex]25 = f(g(-2))[/tex]

Step-by-step explanation:

[tex]g(-2) = -2 - 3 = -5 \\ \\ f(-5) = {[-5]}^{2} = 25 \\ \\ 25 = f(g(-2))[/tex]

I am joyous to assist you anytime.

Answer:

perpendicular lines.

Step-by-step explanation:

by using the Pythagorean theorem

 use the height and half the base dimension for the 2 edges of a triangle and the slope ( slant height) would be the hypotenuse

 so:  SQRT(height ^2 + half of base^2) = hypotenuse ( Slant height)

To obtain the image of triangle ∆PQR after a 180° rotation about the origin, we applied the rotation formula to each vertex, resulting in the new coordinates P'(-1, 1), Q'(-3, 2), and R'(-3, 4). Connecting these points forms the rotated triangle ∆P'Q'R'.

To draw the image of triangle ∆PQR after a 180° rotation about the origin, we'll need to find the new coordinates of the vertices P', Q', and R'. The general formula for rotating a point (x, y) by 180° about the origin is to negate both the x and y coordinates, resulting in the point (-x, -y). Let's apply this formula to each vertex:

Vertex P(1, -1) is rotated to P'(-1, 1).

Vertex Q(3, -2) is rotated to Q'(-3, 2).

Vertex R(3, -4) is rotated to R'(-3, 4).

Now, we have the new coordinates for the vertices of the rotated triangle ∆P'Q'R'. Let's plot these points on a coordinate plane:

P'(-1, 1)

|

|

| Q'(-3, 2)

| /

|/

R'(-3, 4)

The triangle ∆P'Q'R' is formed by connecting these three points, and it is the image of ∆PQR after a 180° rotation about the origin.

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Answer:

The measure of the arc CBA is equal to 190°

Step-by-step explanation:

95 x 2 = 190

The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

What is mean by Probability?

The term probability refers to the likelihood of an event occurring.

Given that;

You will roll a 5 on the red cube and a 1 or a 2 on the blue cube.

Now,

Sides of cube dice = 6

Hence, For red cube;

P (r) = 1/6

And, For blue red;

P (B₁ or B₂) = P(B₁) + P (B₂)

                = 1/6 + 1/6

                = 1/3

Thus, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube = 1/6 x 1/3

                          = 1/18

Therefore, The probability that you will roll a 5 on the red cube and a 1 or a 2 on the blue cube will be 1/18.

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Question:

Evaluate f(x)= 1.8 X 2^x for x=6

Answer choices:

A: 115.2

B: 2176.78

C: 21.6

Answer:

A:115.2

Step-by-step explanation:

F(x) F(6)

=1 . 8 • 2 • 1

=1 . 8 • 261

=1 . 8 • 64115.2

=115.2

Hence, your answer is A:

33

[tex]\frac{x-7}{x} = \frac{2x-10}{2x+12}[/tex] → x = [tex]\frac{21}{2}[/tex]

AC = x + x + 12 = [tex]\frac{21}{2} + \frac{21}{2}[/tex] +12 = 33

Answer:

[tex]f(x)=3|x-2|-1[/tex]

Step-by-step explanation:

Identify the function that has a vertex of (2,-1) and is stretched vertically by a factor of 3.

The option are absolute function, So the parent function is y=|x|

Vertex form of absolute function is

[tex]y=|x-h|+ k[/tex] where (h,k) is the vertex

vertex of (2,-1) h=2, k =-1

the function becomes

[tex]f(x)=|x-2|-1[/tex]

function is stretched vertically by a factor of 3

when f(x) is vertically stretched by a factor of 'a'.We multiply the factor with f(x)

[tex]f(x)=3|x-2|-1[/tex]