The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ____million.

Answer:

Part A is 100

Part B is 50

Part C is 25

all of it goes down by 15 so just keep subtracting

Step-by-step explanation:

I used common since and a sheet of paper

The area of the cylinder's base is 1÷4π.x² is the correct option

What is a cylinder?

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.

The cylinder seems to be a rectangle from the side perspective and a circle from the top view.

Since a cylinder has a curved form and no straight lines, it lacks vertices in contrast to cones, cubes, and cuboid shapes. Two of its faces are round.

According to the question volume of the cylinder is

1. πr^2h = πr^3

h=r=x/2

2.

The radius of cylinder is

= x/2

3.

The area of the cylinder's base is

= πr^2

= (π x^2)/4

4.

The height of the cylinder is =

radius= height =x/2

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do 180-32=148 and then do 148÷2=74

Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is

The end behavior of function typically says the characteristics of the function at the ends

The given function is:

f(x) = −x⁴ − 2x³ + 2x² − 5

The end behavior is determined by the leading Coefficient =  −x⁴  and it is described as

x ⇒ ∞ f(x) ⇒ ∞

x ⇒ -∞ f(x) ⇒ -∞

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BY using the inequality,

(67 + 65 + 64 + 88 + 2x)/5 ≥ 73,

we find the score she must make on final exam to pass the courses with an average of 73 or higher is x>=80.

An inequality is a mathematical statement that shows that one quantity is greater than or less than another quantity.

The average, or mean, of a set of numbers is a measure of the central tendency of the set.

This inequality states that the average of Shureka's scores on the four tests and the final exam must be greater than or equal to 73 in order for her to pass the course. Solving for x, we find that x ≥ 80.

The meaning of the answer to part (a) is that Shureka must make a score of 80 or higher on the final exam in order to pass the course with an average of 73 or higher. In other words, if Shureka makes a score of 80 or higher on the final exam, her average score on the five tests will be 73 or higher, which is the minimum required to pass the course. If she makes a score lower than 80 on the final exam, her average score will be less than 73, and she will not pass the course.

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√5 km/h fast is the distance between the ships changing at 4:00 PM .

What is the Pythagorean theorem ?

The Pythagorean theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                      This is represented by the equation a2 + b2 = c2 in common algebraic notation.

Ship A is sailing 25 km/h east and Ship B is sailing 15 km north. They are giving us the time frame, which is 4 hours ( t = 4). Recall that Distance = Rate * time. Let us find the distance for each ship after 4 hours

Ship A Ship B

d=25*4 = 100 km d=15*4= 60 km

the Pythagorean theorem.

a2+b2=c2

(30)2+(60)2=c2

c=30√(5)

From the question, "How fast" is asking us for a rate. The rate on the hypotenuse side. We have to take the derivative of the pythagorean theorem with respect to time.

2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

Solve for dc/dt

dc/dt = [a(da/dt) + b(db/dt)] / c

dc/dt = [30(-25) + 60(15)] / 30√5 ****Note: we have -25 as time increases, the distance is smaller

dc/dt = √5 km/h

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There are solutions when k = -1 and when k = -3

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

|x + 3| - 2 = k

Removing the modulus sign

x + 3 - 2 = k -----(i) = x + 1 = k

-x - 3 - 2 = k -----(ii) -x - 5 = k

Putting k = -1

(i) x = -2 and (ii) x = -4

Putting k = -3

(i) x = -4 and (ii) x = -2

Since, x has solution on both the values of k

We can say that,

There are solutions when k = -1 and when k = -3

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Answer: 4 red and 12 blue

Step-by-step explanation: Answer to 9

We know that for every red rose, he plants 3 blue flowers. The rate is 1:3. If he grows 16, there will be 4 red roses and 12 blue ones. This is because the rate is 1:3 then there are 4 flowers in all. This is 1/4 of how much he wants to grow. So multiply each type of plant by 4. 1 times 4 is 4, so there are 4 red ones. 3 times 4 is 12, so there are 12 blue ones. Hope this helps!

Option B is the graph best represents the most reasonable distribution of the differences.

Any variable whose value is uncertain or any function that values each result of an experiment is referred to be a random variable. Discrete (having definite values) or continuous random variables are also possible (any value in a continuous range).

As a result, the random variables are so-called because it is impossible to determine their value with certainty; instead, we can only guess, and this estimate is known as the probability that a random variable will have a given value.

Here we assume the random variable X denotes the difference between the outcomes of rolling the two dice.

here the number of rolls is 500. As we know by central limit theorem every distribution approaches to normal distribution irrespective of the parent distribution. Since Normal is symmetric about the mean the most reasonable distribution is the second figure.

Option B is the correct answer.

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The complete question is as follows:

Answer:

Infinitely many

Step-by-step explanation:

2x+y=1

4x+2y=2

Divide both sides of the second equation by 2.

2x + y = 1

This is the same as the first equations. Both equations are the same equation. Since you have only one equation and two variables, there is an infinite number of solutions.

Answer: Infinitely many

The area of the shaded region is given as follows:

0.879.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Considering the percentile, the area in this problem is given by one subtracted by the p-value of z = -1.17, which is of 0.121.

Hence:

1 - 0.121 = 0.879.

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The phrase can be expressed as 3x-6, 3(x-2), x+2x-2-4, 4x-x+4-10 and x+x+x-2-2-2 and so on

It consists of several mathematical symbols organized in such a way that it can express mathematical concept.

Mathematical  phrase can be written in one or more different pattern to show the same expression.

As per question given, the phrase is expressed by

3x-6, where x is used to represent a number

the phrase can be written in 3(x-2)

other variable expressions of same phrase are x+2x-2-4

or 4x-x+4-10 or x+x+x-2-2-2

hence, a phrase can be written in one or more pattern to show same expression.

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Answer:

minimum value = 10

Step-by-step explanation:

the minimum value is at the left side of the whisker in the box plot, then

minimum value = 10

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }\cdot 6^2 ~~}{2}\implies A=12\pi \implies A\approx 37.68[/tex]

Answer:

f(x)=x/2-4

-f(x)=a

a=x/2-4

x=a/2-4

a/2-4=x /×2

a-8=2x

a=8+2x -> f^-1(x)=8+2x

Because both of its x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5 according to symmetry, the vertex's x-coordinates are 5/2.

A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).

Here,

The parabola is symmetric around its vertex. This means that the roots are the same horizontal distance away from the vertex. Furthermore, we can apply the midpoint formula on the given roots to find the x coordinate of the vertex.

Find the midpoint of 2 and 3 to get

(2+3)/2 = 5/2

The x-coordinates of its vertex is 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.

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Answer:

[tex]y=2/11[/tex]

Step-by-step explanation:

[tex]\lim{t \to \pm \infty} R(t)=\lim_{ t \to \pm \infty} \frac{30t+525}{165t+7000} =\frac{30}{165}=\frac{2}{11}[/tex]

a) The probability that both are girls is of: 21/150.

b) The probability that both are from the same school is of: 0.7333 = 73.33%.

How to obtain the probabilities?

The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

One girl from school A -> 7/15 probability.

One girl from school B -> 3/10 probability.

Hence the probability that both are girls is of:

p = 7/15 x 3/10 = 21/150.

The probability that the two boys are from the same school can be given by these two cases:

School A: 8/15 x 7/14.

School B: 7/10 x 6/9.

Then the probability is of:

p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.

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Answer: (fog)(x) = f(g(x)) = f(6x) = 5(6x) = 30x

So (fog)(x) = 30x, which is a polynomial in simplest form

To paint , 7 rooms in white or yellow, 128 possible outcomes are there.

The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.

There are seven rooms in the house and each can be painted either yellow or white.

And probability of total number of different outcomes

= total number of options

So, total number of different outcomes = 2⁷

 Total number of different outcomes = 128

Therefore the total number of outcomes are 128.

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The complete question is;

A house has seven rooms. Each room can be painted white or yellow. How many possible outcomes are there?

Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.

Assuming (x, y), R

To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:

If (x, x)R for all x R x x for all x R, which is false.

b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."

In this case, x y y x for all (x, y) R, which is false.

c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.

In this case, x y and y x x = y are false.

not in opposition.

c. Transitive: If "x" and "y" are related, then

For all values of x, y, and z R, 'x' is connected to 'z'.

For any x, y, and z R, x y, y z x z.

True.

Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.

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To develop an equation to predict the surface area of a person as a function of their height and weight using numerical methods and MATLAB, you can follow these steps:

The required details for MATLAB in given paragraph

Begin by organizing the given data into two separate arrays: one for height (H) and one for weight (W). For example, you might create the following arrays:

H = [182 180 179 187 189 194 195 193 200];

W = [74 88 94 78 84 98 76 86 96];

A = [1.92 2.11 2.15 2.02 2.09 2.31 2.02 2.16 2.31];

Use the MATLAB function "polyfit" to fit a polynomial function to the data. You can specify the degree of the polynomial function based on the number of variables you want to include in the model. For example, to fit a second-degree polynomial function, you can use the following command:

p = polyfit(H,A,2);

This will fit a polynomial function of the form A = p(1) * H^2 + p(2) * H + p(3) to the data, where p(1), p(2), and p(3) are the coefficients of the polynomial.

Use the MATLAB function "polyval" to evaluate the fitted polynomial function at a specific value of H. For example, to estimate the surface area for a person with a height of 187 cm, you can use the following command:

A_estimated = polyval(p,187);

This will return the estimated surface area for a person with a height of 187 cm. You can use similar commands to estimate the surface area for different values of H

what do you mean by MATLAB?

MATLAB (short for "Matrix Laboratory") is a programming language and software environment for numerical computation, visualization, and programming. It is commonly used in scientific, engineering, and mathematical fields to analyze and visualize data, develop algorithms, and build mathematical models.

A function in MATLAB is a self-contained block of code that performs a specific task or computation. Functions are useful because they allow you to reuse code and make your programs more modular and easier to understand. In MATLAB, you can define your own functions or use built-in functions that are provided with the software.

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Answer:

the football team sells 805,000 tickets each season

Step-by-step explanation:

average number of tickets sold per match=23,000

the average number of games played each session=35

the number of tickets sold on average each session = 23,000 x 35 which equals 805,000

so the average football club sells 805,000 tickets each season

Answer:

36.96 calories

Answer: 128 square centimeters

Step-by-step explanation:

If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.

Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.

Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.

Area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

As given in the question,

Given values to find area under the standard normal curve = 0.97 to 1.26

From the table of area under the given standard normal curve

z - score of 0.97 is equal to 0.33398

z-score of 1.26 is equal to 0.39617

Area under given standard normal curve between z-scores 0.97 and 1.26

= P ( 0.97 < z < 1.26 )

= 0.39617 - 0.33398

= 0.06219

Therefore, the area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.

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The number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, M Attend to Precision Ricardo has 325 tiles to make 4 mosaics.

Here, the number of tiles need for each mosaic is 325/4

4|325|81

  324

______

    1

Therefore, the number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.

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