Suppose a town has a population of 5,000 residents but that the population is decreasing by 200 people each year. Write a linear function to represent the population of the town in terms of the numbers of years. After how many years will the town have a population of 1,800? When will the town have only 400 residents?

3.88 milligrams is equal to 0.0388 centigrams, as milligrams are converted to centigrams by moving the decimal point two places to the left.

To convert from milligrams to centigrams, we need to understand their relationship in the metric system. There are 10 milligrams in 1 centigram and 100 centigrams in 1 gram.

Given the value of 3.88 milligrams, we need to convert it to centigrams. To do this, we move the decimal point two places to the left, resulting in 0.0388 centigrams. This is because there are 10 milligrams in 1 centigram, so dividing 3.88 milligrams by 10 gives us the equivalent value in centigrams.

Therefore, 3.88 milligrams is equal to 0.0388 centigrams. It's important to keep track of decimal placement when converting between different units of measurement in the metric system.

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Answer:

\( \sqrt{ \frac{9}{2} } \)

Answer:

\(x = \sqrt{70} \)

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

the total number of calories in the jar of peanut butter, x, and the total number of calories in the jar of jelly, y

The difference in the total number of calories in a jar of peanut butter and a jar of jelly is 3,545

Now we use total calories ,which was 2/23 of the jar of peanut butter and 2/33 of the jar of jelly

x minus y = 3545 and StartFraction 2 Over 23 EndFraction x + StartFraction 2 Over 33 EndFraction y = 430

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I think it is I'm very sorry if it's wrong :)

1. f(x) =\(1 - 4x^2 + 8(x^2)^2/2! - ...\) this represents a power series representation for the function f(x) = \(1 - 4x^2.\)

2.f(x) = \(-3 - x^6 + (x^6)^2/2! - ...\) this represents a power series representation for the function f(x) =\(-3 - x^6.\)

1. For the function f(x) =\(1 - 4x^2,\) we can express it as a power series by expanding the terms around x = 0. We can rewrite the function as f(x) =\(1 - 4x^2 = 1 - 4(x^2) = 1 - 4(x^2)^1.\)

By using the binomial series expansion, we have:

f(x) = \(1 - 4(x^2)^1 = 1 - 4(x^2)(1) + 4(1)(-1)(x^2)^2/2! + ...\)

Simplifying the terms, we get:

f(x) =\(1 - 4x^2 + 8(x^2)^2/2! - ...\)

The interval of convergence can be determined by considering the values of x for which the series converges. In this case, the power series representation of f(x) will converge for values of x within the interval (-1, 1). The endpoints x = -1 and x = 1 are excluded from the interval of convergence.

2. For the function f(x) = -\(3 - x^6,\)we can similarly express it as a power series by expanding the terms around x = 0. We can rewrite the function as f(x) =\(-3 - x^6 = -3 - (x^6)^1.\)

Expanding the series using the binomial series expansion, we have:

f(x) =\(-3 - (x^6)^1 = -3 - (x^6)(1) + (1)(-1)(x^6)^2/2! + ...\)

Simplifying the terms, we get:

f(x) = \(-3 - x^6 + (x^6)^2/2! - ...\)

The interval of convergence for this power series representation is the set of values of x for which the series converges. In this case, the power series representation will converge for all values of x since there are no terms dependent on x. Therefore, the interval of convergence is (-∞, ∞).

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Answer:

Step-by-step explanation:

We can use proportions to solve for the height of the monument:

Let h be the height of the monument.

Then, we have:

h/12 = 3/4

Cross-multiplying, we get:

h = (12 x 3)/4 = 9 meters

Therefore, the height of the monument is 9 meters.

Answer:

r+17=8r+7

r=10+8r

r=2

Step-by-step explanation:

Answer:

1257cm²

Step-by-step explanation:

L'aire d'un cercle = \(\pi\)r²

=  \(\pi\)\(\frac{d}{2}\)²

=  \(\pi\)\(\frac{40cm}{2}\)²

=  \(\pi\)(20cm)²

=  \(\pi\)400cm²

= 1256.63706144cm²

The result of 490 divided by 7 is 70.

To calculate 490 divided by 7, we can perform long division as follows:

        70

   __________

7  |  490

   -  49  (7 times 7)

   _______

         0  (no remainder)

In the first step, we divide 7 into the first digit of 490, which is 4. The quotient is 0, and we bring down the next digit, which is 9.

Next, we divide 7 into 49. The quotient is 7, and there is no remainder.

Therefore, the answer to 490 divided by 7 is 70.

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Answer: Number of sociology books sold = 143 books

              Number of physics books sold = 143 + 45 = 188 books

Step-by-step explanation:

Let us take the number of sociology books sold = x

Number of physics books sold = x+45

So now we can form an equation

x+x+45 = 331

2x+45 = 331

2x = 331-45

2x = 286

x = 286 ÷ 2

x = 143

Answer:

You can get the answer of 1,2,3,4,5 or 6. Each are 1/6 likely to be rolled.

Step-by-step explanation:

The die has 6 sides. If you were to roll the die 6 times you have the chance to roll the side with 1. The chances of rolling a 1 are 1/6.

Wxndy~~

Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

x=2

Step-by-step explanation:

0.023...

hope it helps...!!!

Answer: She uses more than 2 cups of water per day.

Step-by-step explanation:

It takes 2 minutes to brush your teeth and if you times that by 3 you get 6 so she spends 6 minuntes per day brushing her teeth and water runs fast. so if your leaving the water on for 6 mintues your filling up much more than 2 cups

Answer:

Step-by-step explanation:

Using the formula for calculating heat energy H = mcΔT

m = mass of the aluminum (in g/kg)

c = specific heat capacity of aluminum

ΔT = change in temperature = T - Ti (in °C)

T is the final temperature

Ti is the initial temperature

Given m = 100.0g,  c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?

Substituting the given values into the formula;

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

The final temperature of the metal is 31.81°C

Answer:

31.81c

Step-by-step explanation:

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

Answer: The correct equation that matches the statement "The product of a number, x, and 0.28 is 13.44" is:

0.28x = 13.44

This equation states that when a number x is multiplied by 0.28, the result is 13.44.

Step-by-step explanation:

The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.

As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.

In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.

It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.

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The solution to the equation is x = 17/30.

To solve the equation, start by combining like terms on both sides.

On the left side, we have the fraction 2/3 and the term -4x.

On the right side, we have the fraction 7/2 and the term -9x.

To combine the fractions, we need a common denominator.

The least common multiple of 3 and 2 is 6.

So, we can rewrite 2/3 as 4/6 and 7/2 as 21/6.

Now, the equation becomes:

4/6 - 4x = 21/6 - 9x

Next, let's get rid of the fractions by multiplying both sides of the equation by 6:

6 * (4/6 - 4x) = 6 * (21/6 - 9x)

This simplifies to:

4 - 24x = 21 - 54x

Now, we can combine the x terms on one side and the constant terms on the other side.

Adding 24x to both sides gives:

4 + 24x - 24x = 21 - 54x + 24x

This simplifies to:

4 = 21 - 30x

Next, subtract 21 from both sides:

4 - 21 = 21 - 30x - 21

This simplifies to:

-17 = -30x

Finally, divide both sides by -30 to solve for x:

-17 / -30 = -30x / -30

This simplifies to:

x = 17/30

So the solution to the equation is x = 17/30.

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Answer:

-10 is the opposite of 10

Step-by-step explanation:

-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.

The limit of the given function is  π/2.

What is a limit?

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals.

Here, we have

Given: \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

We have to find the limit of the given function.

=  \(\lim_{(x,y) \to \pi, \pi /2} y sin(x-y)\)

Now, we substitute the value of each variable.

x = π and y = π/2

= y sin(x-y)

= π/2sin(π-π/2)

= π/2sinπ/2

= π/2sin(90°)   (∴sin90° = 1)

= π/2×1

= π/2

Hence, the limit of the given function is  π/2.

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Answer:

The answer should be 6.63

Bd and bc form a right triangle with cd

Use the Pythagorean theorem

Cd = sqrt( 12^2 - 10^2)

Cd = sqrt( 144-100)

Cd = sqrt(44) = 2sqrt(11)

In linear equations,   x = 5 is value of x .

What are instances of linear equations?

-7x-3x+2=-8x-8

-7x -3x + 8x = -8 - 2

 -10x + 8x = -10

  -2x = -10

   x = 5

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Answer:

1.         x=2+3y/2

2.         x=−3/2+4y

hope this helps!!:)

Step-by-step explanation:

Based on the calculations, the numerical length of line segment FG is equal to 11 units.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2).

Based on the given line segment (see attachment), we have:

EF + FG = EG

9 + x + 9 = 10x

18 + x = 10x

10x - x = 18

9x = 18

x = 18/9

x = 2.

Now, we can solve for line segment FG:

FG = x + 9

FG = 2 + 9

Line segment FG = 11 units.

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Answer:

18

Step-by-step explanation:

If she catches 6 pop flies in 5 games, that averages to 1.2 pop flies per game.

So if you multiply 1.2 by 15 you get 18 pop flies per game.

Answer:

18

Step-by-step explanation:

She catches 6 pop flies each 5 games she plays. (5x3=15)

6x3=18

Answer: 55°

Step-by-step explanation:

∠YAZ + ∠YAX = 180° because they are linear pairs

∠YAZ + ∠YAX = 180°

∠YAZ + 125 = 180

Subtract both sides by 125

∠YAZ = 55°

Hope that helped!