As many as 49 million Bison used to roam the Great Plains of the United States. When the
American settlers started hunting them for fur, meat and political purposes their survival rate
dropped to 0.81. How many million would have remained after 9 years of hunting?

Answer: 40.75

Step-by-step explanation:

So you use 73.02 minutes of talk time each month.

Cell phone is a portable electronic device that allows you to make calls, send messages, and perform various tasks such as browsing the internet.

Let x be the number of minutes of talk time you use each month.

The cost for the talk time each month is 19.80 + 0.09(x - 500), and the cost for e-mail is 0.2 * 19.80 = 3.96.

So, the total cost each month is 19.80 + 0.09(x - 500) + 3.96 = 23.76 + 0.09x - 46.04.

The total cost for 7 months is 7 * (23.76 + 0.09x - 46.04) = 166.32 + 0.63x.

We want to find the value of x that makes the total cost equal to $212.31, so we write:

166.32 + 0.63x = 212.31

Solving for x, we have:

0.63x = 45.99

x = 73.02

So you use 73.02 minutes of talk time each month

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The following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .

We have the following joint probability distribution:

X/Y  0   1

0    1/3   1/3

1      0    1/3

The entropy of X is given by

H(X) = −p log p − (1 − p) log(1 − p) = H(p)

The entropy does not depend on the values that the random variable takes (0 and 1 in this case), but only depends on the probability distribution p(x).

The joint entropy is given by

H(X, Y ) = ∑p(x, y) log p(x, y).

The joint entropy measures how much uncertainty there is in the two random variables X and Y

taken together.

The conditional entropy of X given Y is

H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y))

The conditional entropy is a measure of how much uncertainty remains about the random variable

X when we know the value of Y.

For two variables, the chain rule becomes:

H(X, Y ) = H(X|Y ) + H(Y ) = = H(Y |X) + H(X).

Thus, the following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .

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Answer:

After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.

The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:

A = A0 * (1/2)^(t/T)

where:

A0 is the initial amount (80 mg)

t is the time elapsed (17,190 years)

T is the half-life (5,730 years)

A = 80 * (1/2)^(17,190/5,730)

A = 80 * (1/2)^3

A = 80 * (1/8)

A = 10 mg * 1/2

A = 5 mg

It is found that 22 miles in 20 minutes is LESS

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We have to compare the two rates:

=> 22 miles in 20 minutes

=> 38 miles in 30 minutes

Let's simplify each rate by finding the speed, which is distance divided by time.

That is:

Speed = distance/time

For the first one:

s = 22/20 = 1.1 milesl/min

For the second one:

s = 38/30 = 1.27 milesl/min

Since 1.1 is less than 1.27, so, 22 miles in 20 minutes is less than 38 miles in 30 minutes.

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The complete question is;

Is 22 miles in 20 minutes greater than, equal to or less than 38 miles in 30 minutes?

The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.

What is the triangle inequality theorem?

The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.

We are given the lengths to be 6, 8 and 15.

Using the triangle inequality theorem,

⇒ 6 + 15 > 8

⇒ 21 > 8

Also,

⇒ 8 + 15 > 6

⇒ 23 > 8

Also,

⇒ 6 + 8 > 15

But,

⇒ 14 < 15

Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.

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The x-intercept of the composition is x = -1/2.

Remember that a linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If a liear function passes through two points (x₁, y₁) and (x₂, y₂), then the  slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For g(x) we can use (-1, 2) and (1, 6), the slope is:

a = (6 - 2)/(1 + 1) = 2

Then the function is something like:

g(x)=  2x + b

To find the value of b, we use again the point (1, 6)

g(1) = 6 = 2*1 + b

      6 - 2 = b

         4 = b

So:

g(x) = 2x + 4

Now the same for h(x), we can use the points (-1, -1) and (1, 7), we will get:

a = (7 + 1)/(1 + 1) = 4

h(x) = 4x + b

Using the point (1, 7)

h(1) = 7 = 4*1 + b

        7 - 4 = b

        3 = b

h(x) = 4x + 3

The composition is:

g( h(x)) = 2*h(x) + 4

           = 2*(4x + 3) + 4

            = 8x + 10

The x-intercept is the value of x such that:

0 = 8x + 4

-4 = 8x

-4/8 = x

-1/2 = x

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Unresolved problems are referred to be inconsistent systems.

Find the solution to the system of equations by attempting to remove one of the variables to see whether there is a single solution, no solution, or never-ending options (If these two equations' lines all fall on the same line, then

By adding -2 to the first equation

-4x - 6y = -22

the second equation after that, adding it.

5x + 6y = 14

getting x = -8

Returning to either equation, plug in the following: the first one,

2(-8) + 3y = 11

-16 +3y = 11

3y = 27

y = 9

These two lines come together at one point since there is only one possible answer. They remain dependable.

The graphs of the equations yield two distinct lines, proving the independence of this system. Should the equations result in

In a same vein, they are interdependent.

They would have produced a constant equation, such as 0 = 0, if they had been the same line and had been solved for one variable.

Thus, (D) is still true because they are reliable and separate.

The Complete Question is :

Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.

2x + 3y = 11

5x + 6y = 14

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The equation of the line that passes through the point (-1, 1) and has a slope of -1 is y = -x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, 1), a linear equation of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1(x - (-1))

y - 1 = -1(x + 1)

y = -x -1 + 1

y = -x.

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The equation of the line is y = -x

The general formula for the equation of a line is expressed with the equation;

y = mx + c

Given that the parameters are;

From the information given, we have that;

slope, m =-1

The points are (-1, 1)

Now, let's substitute the values

1 = -1(-1) +  c

expand the bracket

1 = 1 + c

collect like terms

c = 0

The equation of the line is y = -x

Hence, the equation is y = -x

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The mean difference in game scores over the six games is 12

The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.

Given the points by which a basketball team either won or lost 6 games.

- Won by 7 points = +7

- Lost by 10 points = -10

- Won by 8 points = +8

- Won by 11 points = +11

- Lost by 2 points = -2

- Won by 10 points = +10

Thus;

Mean difference of the 6 games is;

= (+7 - 10 + 8 + 11 - 2 + 10)/6

= 24/6

= 12

Hence, the mean difference in game scores over the six games is 12

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A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.

Here's how you can use a table to write an equation:

1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.

2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.

3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.

4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.

5. Substitute the coefficients from step 3 into the equation from step 4.

6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.

By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.

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A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.

Here's how you can use a table to write an equation:

1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.

2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.

3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.

4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.

5. Substitute the coefficients from step 3 into the equation from step 4.

6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.

By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.

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The number of games cole can play $12.5 to enter and $1.5 to play each game  by subtracting and dividing with $35 is 15 games.

The total money cole have is $35

To enter an amusement parks it costs around $12.5

so, remaining money by subtracting = 35-12.5 = $22.5

so, by dividing the remaining money with $1.5 paid per each game gives how many games does cole can play.The number of games cole can play $12.5 to enter and $1.5 to play each game  by subtracting and dividing with $35 is 15 games. By dividing the remaining money with $1.5 paid per each game gives how many games does cole can play. Total number of games does cole can play is 22.5/1.5 = 14 games.

Therefore , the number of games cole can play are 14 games exactly.

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The meaning of the slope and of the intercept of the linear function are given as follows:

The slope is negative -3/2, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases 3/2 of an inch every hour.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The two points for the function in this problem are given as follows:

(0,9) and (2,6).

When x = 0, y = 9, hence the intercept b is given as follows:

b = 9.

Meaning that the initial value of the problem is of 9.

The slope is given as the change in y divided by the change in x, hence:

m = (6 - 9)/(2 - 0)

m = -3/2.

Meaning that the rate of change is a decrease of 3/2 units for each unit of the input.

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Answer: The price per pound of apples is $3.75.

Step-by-step explanation:

The given matrix is non linear matrix combination of a and b matrix.

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.

Given that,

a = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right][/tex]

b = [tex]\left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex]

The given matrix is a linear combination of a and b

a - b = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right] - \left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

a - b = [tex]\left[\begin{array}{ccc}-3-5&2-1\\1-1&4-0\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

Therefore,

The given matrix is non linear matrix combination of a and b matrix.

a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]

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The length of Q'R' is 5 * 5 = 25.

The steps to find the measure of Q'R' are:

So, the measure of Q'R' is 25.

This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.

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The cost of renting a bicycle for 9 hours is $72.  The result is obtained by multiplying the rate and time duration.

The cost of rent related to time of rent. It could be cost per hour or cost per day.

The table is in the attachment to complete question.

We have the cost of renting a bicycle at Ike's Bikes.

Find the cost for 9 hours!

We take a sample of the data to find the rate.

The rate is

= $16/2 hours

= $8 per hour

Another sample will have the same result.

To rent for 9 hours, the cost will be

= $8 × 9

= $72

Hence, to rent a bicycle for 9 hours, it will cost $72.

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The product of the expression (-4) x (-4) x (-4) x y x y is -64y²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression, (-4) x (-4) x (-4) x y x y

We need to find its product,

(-4) x (-4) x (-4) x y x y

= -4³ × y²

= -64 × y²

= -64y²

Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²

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Answer:

B

Step-by-step explanation:

B..................

Answer:

1320

MDAS Method

Answer:

Your answer is 1320

Step-by-step explanation:

hope this is what you were looking for

Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;

Total gumballs in the gumball machine= 200 gumballs

Result from the random sample= 25 gumballs

From the random sample selected:

10 gumballs are red

8 gumballs are blue

5 gumballs are green

2 gumballs are white

There are 10 red gumballs in the machine.

There are 3 more green gumballs than white gumballs in the machine.

= Green gumballs - red gumballs

= 5 - 2

= 3 gumballs

There are 13 gumballs that are either blue or green in the machine.

= Blue gumballs + green gumballs

= 8 + 5

= 13 gumballs

Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.

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For each transaction in the table, the current account component, cash flow position, and type of entry on the balance-of-payments account are as follows:

1. Consumers in Japan purchasing baseball jerseys from their favorite US baseball teams: Current account component: Imports; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.

2. An American-based subsidiary remitting earnings to the parent company in Canada: Current account component: Investment income; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.

3. France providing funds to the United States as a gift to be used for the construction of a large monument: Current account component: Gifts; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.

4. A US-based company purchasing stock in a French company: This component of the financial account is known as Foreign Direct Investment (FDI). It is defined as an investment made to acquire lasting interest in enterprises operating outside of the economy of the investor.

With regards to the balance of payments, FDI is considered a capital account item, so there will be no entry on the balance of payments account. This is because FDI does not involve any money entering or leaving the economy.

In conclusion, when a transaction is made, it is important to be aware of the current account component, cash flow position, and type of entry on the balance-of-payments account that is associated with it.

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Complete question is shown in figure.

The inverse of the cube root function used to act for the situation in model is f⁻¹(x) = √x³ - 4

Inverse of the cube root function f(x)

f(x) = ∛ (x + 4) ²

To find the inverse function, let f(x) = y

So, y = ∛ (x + 4) ²

Taking the cube of both sides, we have

y³ = [∛ (x + 4) ²] ³

y³ = (x + 4) ²

Taking square root of both sides, we have

√y³ = √ (x + 4) ²

√y³ = (x + 4)

Subtracting 4 from both sides, we have

√y³ - 4 = x + 4 - 4

√y³ - 4 = x

change y with x, we have

√x³ - 4 = y

Replacing y with f⁻¹(x), we have

f⁻¹(x) = √x³ - 4

So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4

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7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.

To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:

V(t) = ∫ r(t) dt from 9:00am to t

= ∫ 7t √ dt from 0 to t

= 7/3 t^(3/2) + C

where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.

Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.

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The integral is equal to zero, since the divergence of a constant vector is always zero.

The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.

To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.

The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.

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The subset of consisting of vectors of the form is indeed a subspace.

A subspace is a special type of set within a vector space that has the same properties as the larger vector space.

In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.

The first condition is that the subset must contain the zero vector.

The second condition is that the subset must be closed under addition.

The third condition is that the subset must be closed under scalar multiplication.

Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.

The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.

Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .

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Each malleable piece of wire he can produce has a length of 2 metres.

Prime factorization

26 = 2 × 13

20 = 2² × 5

HCF = 2

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Answer:

Step-by-step explanation:

The given exponential function will grow at 6.1%

Given,

y =

To find,

identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

Solution,

We have,

y =

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x)= a(1-r)^x such that r is the growth percent.

==> 1+r = 1.061

==> r = 0.061 = 6.1%

Answer:

24.12 feet.

Step-by-step explanation:

The formula to find the diameter of a circle from its circumference is:

diameter = circumference / π

Plugging in the given values:

diameter = 75.36 feet / π

diameter = 75.36 / 3.14

diameter ≈ 24.12 feet

So, the diameter of the circular garden is approximately 24.12 feet.