11. The population of the District of Columbia was approximately 572 thousand in 2000 and had been growing by about 1.15% per year.(a) Write an explicit formula for the population of DC t years after 2000 (i.e. t=0 in 2000), where Pt is measured in thousands of people.Pt = (b) If this trend continues, what will the district's population be in 2025? Round your answer to the nearest whole number. thousand people(c) When does this model predict DC's population to exceed 800 thousand? Give your answer as a calendar year (ex: 2000).During the year

Solution

Step 1

Let the number of yo-yos than toy bears = x

To calculate the equation first we need to choose two points of the table

P1 (1,1)=(x1,y1)

P2(0,9)=(x2,y2)

then we calculated the slope m

substituting the points we have

then we can calculate the equation

the equation is

Let h be the altitude of the starting position.

Since the group has gained 456 feet from the start position, then the current altitude is:

Given

x = 5

5x + 2 = 27

Procedure

d. Yes, because when x is replaced by 5 the equation is true. ​

Answer:

(8.5, - 2 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 6, - 10 ) and (x₂, y₂ ) = (23, 6 ) , then

midpoint = ( [tex]\frac{-6+23}{2}[/tex] , [tex]\frac{-10+6}{2}[/tex] ) = ( [tex]\frac{17}{2}[/tex] , [tex]\frac{-4}{2}[/tex] ) = (8.5, - 2 )

The slope intercept of a line is:

We re-write the equation given:

The graph of this line is shown below:

If the unknown number is an integer between 280 and 349;

When rounded to the nearest hundred, the unknown number is 300.

If the unknown number is an integer from 350-380;

When rounded to the nearest hundred, the unknown number is 400.

If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.

But;

When 345 is rounded to the nearest hundred, it is 300.

And the difference between the approximated value and the original value is 45.

Hence, 345 is the original number.

CORRECT ANSWER: 345

A.find s(4)

B. means that in 4 days there will be 32000 infected people

C. find t to S(t)=23

D. means there will be 23,000 infected people after 3 days

E. Graph

to draw the line we need two points which we already have but we will add another to make a table of 3 values the new value is t=1

table

graph

Answer:

27 cubic feet

Explanation:

The volume of a cube with side length L is given by

Now in our case, L = 3 ft; therefore, the volume is

which simplifies to give

which is our answer!

Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.

We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:

We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:

Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.

ANSWER

The graph of function g is the graph of function f stretched horizontally by a factor of 4.

EXPLANATION

Function g(x) is a transformation of function f(x), obtained by multiplying the variable, x, by 1/4. This is described as a horizontal stretch by a factor of 4.

Hence, the graph of function g is the graph of function f stretched horizontally by a factor of 4.

If I invest $2000 at 6% interest compounded monthly, it will take 11.58 years by the account to double in value.

What is compound interest?

The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It happens when interest is reinvested, added to the lent capital rather than paid out, or required to be paid by the borrower, resulting in interest being created the next period on the principal amount plus any accrued interest. Compound interest is a prominent concept in finance and economics.

The initial investment of $2000 at 6% compounded monthly.

Since, the interest rate of 6% is compounding monthly, then the effective annual interest rate will be

= (1+)−1i = (1+rm)m−1

Here, r = interest rate in decimals

= (1+0.0612)12−1i = (1+0.0612)12−1

= 0.061678i = 0.061678

= ×100 = 6.1678%

Now, we are using Rule 72 to calculate the doubling time

Time to double the initial amount = 72 /effective annual interest rate

Time to double the initial amount = 11.58 years

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The formula to obtain the angle of rotation is as follows:

Compare the given equation to the general equation of a conic.

Thus, the values of A, B, and C are as follows.

Substitute the values into the equation.

Find the value of the θ.

Megan sent  792 text messages in the month of October .

In the question ,

it is given that

Cost for first 600 messages = $15

additional text message charge = $0.05

Amount owed by Megan for the month of October = $24.60

Let the number of Additional messages be x.

So, according to the question

15 + 0.05x = 24.60

0.05x = 24.60-15

0.05x = 9.6

x = 9.6/0.05

x = 192

number of extra messages = 192

total messages = first 600 messages + extra messages

= 600+192

= 792

Therefore , Megan sent 792 text messages in the month of October .

The given question is incomplete , the complete question is

Megan's text messaging plan cost $15 for the first 600 messages and 5¢ for each additional text message. If she owes $24.60 for text messaging in the month of October, how many text messages did she send that month ?

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The right option is D as P(A and B) ≠ 0 only for the independent probability events for A and B.

Two events say A and B are said to be independent if the probability of the intersection of A and B is equal to the product of their respective probability, But same events are said to be mutually exclusive if the probability of the intersection of A and B is equal to zero(0).

In the given question, P(A and B) ≠ 0 can only be true if A and B are independent event and P(A) and P(B) are not equal to zero such that

P(A and B)=P(A)× P(B)≠ 0.

Hence, we can deduce from the axiom of independent events of probability that because both P(A) and P(B) are not equal to 0, P(A and B) ≠ 0.

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To prove that the sum of the remote interior angles and the exterior angle have the same value, we recall 2 things:

1.- the inner angles of a triangle add up 180 degrees

2.- angle 3 and angle 4 are supplementary which means that they add up 180 degrees.

Answer:

They are linear pair and therefore supplementary.

Triangle sum theorem.

Substitution.

Subtraction property of equality.

Work Shown:

P = 580

r = 0.135

t = 18 months = 18/12 = 1.5 years

A = P*(1+r*t)

A = 580*(1+0.135*1.5)

A = 697.45

given the expression :

We need to evaluate the expression when :

So, substitute with a , b and c at the expression

The result will be :

There is another expression :

By substitute with the values of a, b and c

so, the result will be :

Part A: Since triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.

Triangle 2 has the following sides: a, b and n

Writing it into an equation will be:

The answer is a² + b² = n²

Part B: Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?

Equation 1 (Triangle 1): a² + b² = c²

Equation 2 (Triangle 2): a² + b² = n²

Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation, it will be:

The answer is c² = n²

Part C : Now, take the square root of both sides of the equation from part B and write the resulting equation.

The answer is c = n

You have the following A, B and C points, which are transformed to the points A', B' and C', jus

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A(2, 3), B(8, 7), C(6 1)

Step 02:

Line AB

Slope formula

m = (y2 - y1) / (x2 - x1)

A (2 , 3) x1 = 2 y1 = 3

B (8 , 7) x2 = 8 y2 = 7

Step 03:

Slope of the perpendicular line, m’

m' = -1 / m

Step 04:

Line CD

m' = (y2 - y1) / (x2 - x1)

C (6 , 1) x1 = 6 y1 = 1

D ( x2, y2) x2 = x2 y2 = y2

We must test the numerical values to verify equality,

x2 = 9

y2 = 3

x2 = 4

y2 = 4

You have that the ratio of EG:FG:GH = 4:1:5.

Moreover, segment EH = 10.

In order to find EG you consider the following ratios:

EG/FG = 4/1

FG/GH = 1/5

Furthermore, EH = EG + FG + GH

The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

Radioactive decays by 1/2 of its original in 30 days.

1/2 of original → 30 days.

Divide both sides by 3

1/6 of original → 10 days

Therefore, in 10 days amount of decays will be,

1/6 of 20 ⇒ 20/6 = 3.33

The amount left = 20 - 3.33 = 16.67.

Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".

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The correlation coefficient between flow rate and amount of eroded soil is:

0.967.

The correlation coefficient is an index that measures correlation between two variables, assuming values between -1 and 1.

If it is positive, the relation is positive, meaning that the variables are direct proportional. If it is negative, the variables are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship between the variables is strong.

Given a data-set of two points, the correlation coefficient is found inserting points of the data-set into the calculator. In this problem, the points in the data-set are given as follows:

(0.31, 0.82), (0.85, 1.95), (1.26, 2.18), (2.47, 3.01), (3.75, 6.07).

Using a calculator, the coefficient is given as follows:

0.967.

Hence the last option gives the correct coefficient.

The complete problem is given by the image at the end of the answer.

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To answer this question, we need to know that two linear equation that does not have solutions must not cross to each other, that is, they do not have a common point. For this case, both lines must be parallel lines. So in the question, we need to find a parallel line to the given line. Two parallel lines have the same slope.

Then, we have that the line must pass through (12, 7), and, because it is parallel to y = -3/4x + 8, and the slope for this line is m = -3/4, then, the line equation is, applying the point-slope form of the line:

And

x1 = 12

y1 = 7

m = -3/4

Then

Then, the line equation is y = -3/4 x + 16.

We can check this if we use the elimination method as follows:

This is a FALSE result, and we do not have solutions for this system. Therefore, the line equation is y = -3/4 x + 16.

SOLUTION

We will use a Venn Diagram for this problem.

Let N represent those that use Netflix, R represent those that use Redbox and V represent those that use video store. The Venn Diagram is shown below

From the Venn Diagram above, the number in each part of a circle, represents the information

Now, how many people use Redbox?

The number of those that use Redbox is represented by the circle R, so we add all the numbers in this circle, we have

Hence the answer is 115

Given the equations:

Let's find the point where both equations intersect.

To find the point let's first find the value of x by equation both expression:

Now, equate to zero:

Now let's factor by grouping

Solve each factor for x:

We can see from the given options, we have a point where the x-coordinate is 1 and the y-coordinate is 8.

Since we have a solution of x = 1.

Let's plug in 1 in both function and check if the result with be 8.

We can see the results are the same.

Therefore, the point where the two equations meet is:

(1, 8)

ANSWER:

B. (1, 8)

The number of two-points shots made is 14

The number of free throws made is 10

The first step is to formulate a set of linear equations that represent the information in the question:

x + y = 24 equation 1

2x + y = 38  equation 2

Where:

The linear equations would be solved using the elimination method.

In order to determine the value of x, take the following steps:

Subtract  equation 1 from  equation 2

x = 14

Substitute for x in  equation 1

14 + y = 24

Combine similar terms:

y = 24 - 14

Add similar terms together

y = 10

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Answer:

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.

Step-by-step explanation: