What is the definition of the range of a function?

Step-by-step explanation:

Multiply the number outside the brackets to the numbers inside:

So,

9 * 9x = 81x

9 * 2y = 18y

9 x -6 = -54

So the simplified or equivalent expression is:

81x + 18y - 54

Answer:

B. x² - 13x + 42

Step-by-step explanation:

The rate of change of the number of mosquitoes on a tropical island for 0 ≤ t ≤ 30 is modeled by r(t). The behavior and interpretation of the rate of change will depend on the specific context and characteristics of the function r(t).

Let's explain this in detail below:

For 0 ≤ t ≤ 30, the rate of change of the number of mosquitoes on a tropical island at time t days is modeled by r(t). This implies that r(t) is the derivative of the mosquito population, P(t), with respect to time, t. In other words, r(t) = dP/dt, where dP/dt is the change in the population P with respect to the change in time t over an infinitesimal time period. Hence, the mosquito population changes as a function of time due to the mosquito's life cycle, the environment, and other factors that influence their survival.

The mosquito population model helps us to understand how their population changes over time and the factors that influence them. Mosquitoes reproduce and die, and these processes are captured in the mosquito population model. The model also considers the environment, which includes rainfall, humidity, temperature, and other factors that affect mosquito breeding, feeding, and survival.

Additionally, mosquito control measures such as insecticides, repellents, and other interventions also affect mosquito populations. Understanding the rate of change of mosquito populations is crucial for predicting mosquito-borne disease outbreaks and designing effective control strategies.

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Answer:

I estimate he hit 400 bats.

Step-by-step explanation:

I am going to set up a ratio to solve.

Joseph hits about 2 out of every 5 bats, and we want to find out the number of hits we had if he was up to bat 1,000 times.

\(\frac{2}{5} = \frac{x}{1000}\)

Cross multiply to solve.

2(1000) = 5(x)

2000 = 5x

Divide by 5 on both sides.

X = 400

I estimate he hit 400 bats.

Answer:

Step-by-step explanation:

yes it will be always irrational

EG :

1) 2 , root(3) , 2 + root(3)

2) 4 , root(8) = 2root(2) , 4 + 2root(3)

etc

Answer:

-21

Step-by-step explanation:

mn/p - n

= 4×9/(-3) - 9

= -36/3 - 9

= -12 - 9

= -21

Answer: 12.3 cm

Step-by-step explanation:

          We are given the perimeter and all but one of the missing side lengths. The perimeter is equal to all of the side lengths added together. Using this information, we can create an equation to solve for the missing length, ?.

? = 65.9 cm - (9.2 cm + 4.7 cm + 4.7 cm + 2.2 cm + 9.2 cm + 2.2 cm + 12 cm + 4.7 cm + 4.7 cm)

? = 65.9 cm - 53.6 cm

? = 12.3 cm

Answer:

Line S as the other people stated, the lines will never intersect no matter how far it goes.

Answer:23

Step-by-step explanation:

Mrs. McDonald have 8 rabbits in total.

The correct exponential expression and its value 2³ = 8.

Given in the Question:

Number of rabbits = 2

We will solve the question, using given information:

1st time counting : 2 × 2 = 4

2nd time counting : 4 × 2 = 8

The exponential expression will be 2 × 2 × 2 = 8or 2³ = 8

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The fraction will increase by 140% .

Given,

Numerator is increased by 20% .

Denominator is decreased by 50% .

Then,

Lets call one number x and the other one y

first you have the fraction x/y

When you increase the numerator by 20% you get 1.2

when you increase the denominator by 50% you get 0.5

Then you get the fraction 1.2x/0.5y

Since fractions are basically division you divide 1.2 by 0.5 which is 2.4

2.4 as a percent is 240%

you subtract that from 100 and you get 140% .

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To determine the reactions at support A using the method of integration, we draw a free-body diagram, apply the equations of equilibrium, and solve for the vertical reaction V(A). The horizontal reaction at A is zero.

To determine the reactions at support a using the method of integration, we need to draw a free-body diagram of the beam and apply the equations of equilibrium. Let's assume that the beam is simply supported at points A and B, and that there is a point load P acting at a distance x from point A.

The free-body diagram of the beam is shown below:

```

        |<---L--->|

        A         B

        |         |

   <----|---------|---->

        |         |

        P         |

        |         |

        V(A)      V(B)

```

where L is the length of the beam, V(A) and V(B) are the vertical reactions at points A and B, respectively.

To apply the equations of equilibrium, we need to sum the forces and moments acting on the beam. Since the beam is in static equilibrium, the sum of the forces and moments must be zero.

Summing the forces in the vertical direction, we get:

V(A) + V(B) - P = 0

Summing the moments about point A, we get:

-V(B) * L + P * x = 0

Solving these equations simultaneously, we get:

V(A) = P * (L - x) / L

V(B) = P * x / L

Therefore, the reactions at support A are a vertical reaction of V(A) = P * (L - x) / L and no horizontal reaction, since the beam is free to rotate at point A.

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Answer:

16 units²

Step-by-step explanation:

Formula for the area of a parallelogram is given as, A = b*h

Where,

Base (b) = 4

Height (h) = √(5² - 3²) = 4 (Pythagorean theorem)

Plug in the values

Area of parallelogram, A = 4*4

= 16 units²

Answer:

Distributive property

Step-by-step explanation:

After traveling northwest for 80 kilometers, Alfred the Great turns southwest and moves until he is due west of London. By using the Pythagorean theorem we find that He is now approximately 49.97 kilometers away from London.

After Alfred the Great leaves London and travels in the northwest direction for 80 kilometers, he turns and continues his journey in the direction S65°W until he reaches a point due west of London. To determine the distance between his current location and London, we can break down his movements into components.

First, let's consider the northwest movement. Traveling in this direction forms a right triangle with the north and west directions. Since northwest is halfway between north and west, we can divide the 80 kilometers equally between the north and west components. This means that Alfred has traveled 40 kilometers north and 40 kilometers west from London.

Next, he turns and moves in the direction S65°W until he is due west of London. This means he is moving southwest, but not directly west. To find the southwest component of his movement, we can use trigonometry.

The angle between the southwest direction (S65°W) and the west direction is 65°. Using this angle, we can calculate the southwest component of his movement. Let's call this distance "x". Since Alfred has already traveled 40 kilometers west, the remaining distance due west is 40 - x kilometers.

Now, we can use trigonometry to find the value of "x". In a right triangle with an angle of 65°, the side adjacent to the angle is the southwest component, and the hypotenuse is the total distance traveled. We can use the cosine function to solve for "x".

cos(65°) = (40 - x) / 80

Rearranging the equation, we get:

(40 - x) = 80 * cos(65°)

x = 40 - 80 * cos(65°)

Calculating this value, we find that x is approximately 12.515 kilometers.

Therefore, the remaining distance due west is 40 - x, which is approximately 27.485 kilometers.

To find the total distance between Alfred's current location and London, we can use the Pythagorean theorem. The north and west components form a right triangle, so we have:

Distance^2 = (40 km)^2 + (27.485 km)^2

Solving this equation, we find that the distance is approximately 49.97 kilometers.

Therefore, Alfred the Great is approximately 49.97 kilometers away from London.

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The error term is a random variable with an expected value of zero.2. The error term is normally distributed

The assumptions underlying the simple linear regression model `y = Bo + B1x + e` are: 1.

The variance of the error term e is constant across all values of x.Thus, the assumptions that are underlying the simple linear regression model `y = Bo + B1x + e` are the second and the third options, which are "The error term is normally distributed." and "The variance of the error term e is constant across all values of x." respectively.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

No they don't (unless I messed up)

Step-by-step explanation:

([{3x=9} 2]=81) - ([{x=3}+1]=4) =77

([{2x=10} 2]=100) + {[(2x=25)-4]=21} = 79

The given linear system can be represented as a matrix equation:

A * X = B

where `A` is the coefficient matrix, `X` is the variable matrix, and `B` is the constant matrix.

The augmented matrix for the system is:

[-6 1 4 -2 | 1]

Using Gaussian elimination or row reduction, we can transform the augmented matrix to its row-echelon form:

[1 -1/6 -2/3 1/3 | -1/6]

[0 1 2/3 -1/3 | 1/6]

[0 0 0 0 | 0 ]

This row-echelon form implies that the system has a dependent variable since the third row consists of all zeros. In other words, there are infinitely many solutions to the system. The dependent variable, denoted as `x3`, can be expressed in terms of free parameters `s1` and `s2`.

Therefore, the set of solutions to the given linear system is:

x1 = -1/6 + (2/3)s1 - (1/3)s2

x2 = 1/6 - (2/3)s1 + (1/3)s2

x3 = s1

x4 = s2

where `s1` and `s2` are arbitrary real numbers that serve as parameters. These equations represent the general form of the solution, accounting for the infinite possible solutions.

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Answer:

$620

Step-by-step explanation:

Answer: conjecture

Step-by-step explanation:

A conjecture is a statement or an opinion based on logical reasoning or trivial facts that are always true. It does not require any proof.

Thus, A conjecture is a statement that you conclude to be true based on logical reasoning.

Note:

Answer:

2 1/6 yards

Step-by-step explanation:

Nina made 14 curtains of the same length out of 30 1/3 yards of fabric. What is the length of the curtain?

14 curtains = 30 1/3 yards

1 curtain = x yard

Cross Multiply

14 curtains × x yard = 30 1/3 yards × 1 curtain

x yards = 30 1/3 yards × 1 curtain /14 curtains

x yards = 30 1/3 yards /14

x yards = 30 1/3 ÷ 14

x yards = 91/3 × 1/14

x yards = 91/42

x yards = 2 7/42

x yards = 2 1/6 yards

Therefore, the length of the curtain is 2 1/6 yards

The inverse function is  v⁻¹ = ( v/T)^1/3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that the formula of the volume of the sphere is,

⇒ v = 4/3 πr³

T = 4/3π

Now,

To determine the inverse function we can solve the formula for the term r as;

⇒ v = 4/3 πr³

Multiply by 3/4 we get;

⇒ 3v/4 = πr³

Divide by π both side, we get;

⇒ 3v/4π = r³

Substitute r = v⁻¹ in above equation, we get;

⇒  v⁻¹ = ( v/T)^1/3

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Answer:

A: $6

B: $2.01

C: $0

D: $4.50 or $7.50

E: 0 ≤ x ≥ 10

F: The more expensive you make the toy then that will mean that less people will want to buy it for its high price.

Step-by-step explanation:

{Data Expunged}

Answer:(4,-3); 2x-7y=14

Step-by-step explanation:

Answer:

that graph will feature an area delimited by a line of slope m passing through the origin (0,0). Since m>0 the slope is positive, meaning the line goes up. Since the equation is y > mx, the inequality sign being >, that means the area represented will be ABOVE the line drawn.

Answer:

down 6,right 4, rotate 180 degrees assuming we are starting from the blue heart.

Step-by-step explanation:

If the sample size in part c is larger, then the sample standard deviation will be a better estimate of the population

standard deviation.  If the sample size is smaller, then the sample standard deviation will be less reliable and may not

be a good estimate of the population standard deviation.

To describe the standard deviation in part c relative to the population standard deviation from which the samples were

generated, you can use the concept of the sample standard deviation.

The sample standard deviation is a measure of the variation in a set of data that is calculated by taking the square root

of the variance of the data set. The variance is the average of the squared differences from the mean. It is important to

note that the sample standard deviation is an estimate of the population standard deviation, which is the true measure

of the variability in the population. The larger the sample size, the closer the sample standard deviation will be to the

population standard deviation. Therefore, if the sample size in part c is larger, then the sample standard deviation will

be a better estimate of the population standard deviation.

Conversely, if the sample size is smaller, then the sample standard deviation will be less reliable and may not be a

good estimate of the population standard deviation.

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