A city with a population of 700,000 has been growing at a rate of 2% per year. If this rate continues, what would the population of this city be in 22 years?

The system of equations representing the charges for plans A and B include the following:

y = 0.2x - 50

y = 0.3x - 105

A graph of the system of equations for plans A and B are shown in the image attached below.

In order to write the system of equations representing the charges, we would have to calculate the slope of the line based on the data points described above for each plans.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (66 - 50)/(580 - 500)

Slope, m = 16/80

Slope, m = 0.2

At point (500, 50), a linear equation for plan A can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the point-slope form formula, we have;

y - 50 = 0.2(x - 500)

y - 50 = 0.2x - 100

y = 0.2x - 100 + 50

y = 0.2x - 50.

For plan B, the slope is as follows;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (69 - 45)/(580 - 500)

Slope, m = 24/80

Slope, m = 0.3

At point (500, 45), a linear equation for plan B can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - 45 = 0.3(x - 500)

y - 45 = 0.3x - 150

y = 0.3x - 150 + 45

y = 0.3x - 105.

Read more on slope here: brainly.com/question/1884491

#SPJ1

Complete Question:

Three cell phone plans, A, B, and C, each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500. These tables show the monthly charges for plans A and B when different numbers of messages are sent. Plan A Cell Phone Charges

Phone plans A and B each have a different flat monthly rate for the first 500 text messages and a different constant rate for every additional message over 500.

Plan A charges $50 monthly for 500 text messages and $66 monthly for 580 text messages.

Plan B charges $45 monthly for 500 text messages and $69 monthly for 580 text messages.

Letting x represent the number of messages over 500, and y the total monthly charges, write equations representing the charges for plans A and B. Then graph the equations for plans A and B on the same coordinate grid.

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

Learn more about derivative here:

https://brainly.com/question/32527348

#SPJ11

Answer:

Step-by-step explanation: the answer is 69-123

Answer:

a) He calculated the area, not the circumference. The equation for the area of a circle is πr², while the equation for the circumference is 2πr.

b) He would need at least 3 quarts of paint. 200.96/75≈2.68 He would need that approximately 2.68 quarts of paint, but I suppose the question is asking you the least amount of whole number quarts of paint. The answer for that would then be 3.

Answer:

1.) 0.25

2.) 0.50

3.) 0.125

4.) 2.25

Step-by-step explanation:

When turning percentages into decimals, you move the decimal point two places to the left.

EX:

25%

25.0 (move the decimal point two places to the left)

2.5

.25

0.25 (add any zeros if necessary)

Hope this helps!!

It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.

The center of mass of the curve is given by:

\(\[ [X, Y, Z] = \left[\frac{2\sqrt{6}}{5} + \frac{4}{7}(2^{\frac{3}{2}} - 1), \frac{2\sqrt{6}}{5} + \frac{4}{7}(2^{\frac{3}{2}} - 1), \frac{16\sqrt{3}}{15} + \frac{2}{5}(2^{\frac{3}{2}} - 1)\right] / \left[\frac{2\sqrt{6}}{3} + \frac{2}{3}(2^{\frac{3}{2}} - 1)\right].\]\)

Given that,

\(\[r(t) = ti + tj + \frac{2}{3}t^{\frac{3}{2}}k,\quad 0 \leq t \leq 2,\]and the density is \(a = \frac{1}{\sqrt{2}} + t\).\)

The center of mass formula is given as follows:

\(\[ [X,Y,Z] = \frac{1}{M} \left[\int x \, dm, \int y \, dm, \int z \, dm\right],\]\)

where\(\(M\)\)is the mass of the curve and \(dm\) is the mass of each small element of the curve.

So, the first step is to find the mass of the curve. The mass of the curve is given by:

\(\[ M = \int dm = \int a \, ds,\]\)

where \(\(ds\)\) is the element of arc length.

Since the curve is a wire, its width is very small. Therefore, we can use the arc length formula to find the length of the wire.

Let \(\(r(t) = f(t)i + g(t)j + h(t)k\)\) be the equation of the curve over the interval \(\([a,b]\).\) The length of the curve is given by:

\(\[ L = \int_a^b ds = \int_a^b \sqrt{\left(\frac{dr}{dt}\right)^2 + \left(\frac{d^2r}{dt^2}\right)^2} \, dt.\]\)

Here, \(\(\frac{dr}{dt}\), and \(\frac{d^2r}{dt^2}\) can be calculated as:\[\begin{aligned} \frac{dr}{dt} &= i + j + \sqrt{2t}k, \\ \frac{d^2r}{dt^2} &= \frac{1}{2\sqrt{t}}k. \end{aligned}\]\)

Using the above formulas, we can calculate the length of the curve as:

\(\[ L = \int_0^2 \sqrt{1 + 2t} \, dt = \frac{4\sqrt{3}}{3}.\]\)

Thus, the mass of the curve is given by:

\(\[ M = \int_0^2 (1/\sqrt{2} + t)\sqrt{1 + 2t} \, dt = \frac{2\sqrt{6}}{3} + \frac{2}{3}(2^{\frac{3}{2}} - 1).\]\)

Next, we need to find the integrals of \(x\), \(y\), and \(z\) with respect to mass to find the coordinates of the center of mass.

\(\[ X = \int x \, dm = \int_0^2 t(1/\sqrt{2} + t)\sqrt{1 + 2t} \, dt = \frac{2\sqrt{6}}{5} + \frac{4}{7}(2^{\frac{3}{2}} - 1), \]\[ Y = \int y \, dm = \int_0^2 t(1/\sqrt{2} + t)\sqrt{1 + 2t} \, dt = \frac{2\sqrt{6}}{5} + \frac{4}{7}(2^{\frac{3}{2}} - 1), \]\[ Z = \int z \, dm = \int_0^2 \frac{2}{3}t^{\frac{3}{2}}(1/\sqrt{2} + t)\sqrt{1 + 2\)

\(t} \, dt = \frac{16\sqrt{3}}{15} + \frac{2}{5}(2^{\frac{3}{2}} - 1).\]\)

Learn more about center of mass here :-

https://brainly.com/question/27549055

#SPJ11

Unfortunately, I am unable to directly interpret or visualize figures or images. However, I can provide you with a general explanation. In a discretized reservoir using block-centered grids, the standard ordering refers to the arrangement of grid cells or blocks in a particular pattern.

This pattern is often used to establish the connectivity and adjacency relationships between the cells in the reservoir model. Typically, the standard ordering arranges the grid cells in a sequential manner, starting from the top-left corner and moving row by row. Each grid cell represents a discrete volume or unit in the reservoir. The non-zero elements, indicated by the "x" positions in the coefficient matrix, would correspond to the active or connected cells within the reservoir model. These active cells are the ones that contribute to fluid flow and other reservoir properties. To visualize the discretized reservoir using the standard ordering, you would need to refer to the coefficient matrix and determine the dimensions of the reservoir model, such as the number of rows and columns. Then, starting from the top-left corner, you can represent each active cell or block using a graphical representation, such as a square or rectangle, in a sequential manner based on the standard ordering. This way, you can construct a visual representation of the discretized reservoir model.

Learn more about coefficient here: brainly.com/question/13431100.

#SPJ11

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

More can be learned about absolute value functions at brainly.com/question/3381225

#SPJ1

Answer:

$3,297,580.00

Step-by-step explanation:

We know

1 school bus = $824,395.00

How much money does Mateo need to buy 4 school buses?

We take

824,395.00 x 4 = $3,297,580.00

So, Mateo need $3,297,580.00 to buy 4 school buses.

The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

To learn more about trapezoid click :

https://brainly.com/question/12221769

#SPJ1

The closest option to the reorder point is 71.40 pounds.

To determine the reorder point, we need to find the demand during the lead time and the safety stock.

First, let's calculate the demand during the lead time. The mean daily rate is 15 pounds, and it takes 4 days for the order to arrive. So, the mean demand during the lead time is 15 pounds/day * 4 days = 60 pounds.

Next, let's calculate the safety stock. The pizza shop wants to limit the probability of a stockout to 7 percent. We can find this value using the z-score table.

Looking up the z-score corresponding to a 7 percent probability, we find that it is approximately 1.89.

The standard deviation is given as 6 pounds.

So, the safety stock is calculated as 1.89 * 6 pounds = 11.34 pounds.

Finally, the reorder point is the sum of the mean demand during the lead time and the safety stock.

Reorder point = 60 pounds + 11.34 pounds = 71.34 pounds.

Therefore, the closest option to the reorder point is 71.40 pounds.

To learn more click the below link

https://brainly.com/question/14214111

#SPJ11

The value of w from the given equation is w=(x-3y+1)/3.

Given  an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.

The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.

x=3y+3w-1

Now take w at one end and all other variables in other end.

3w=x-3y+1

Now divide both sides by 3.

3w/3=(x-3y+1)/3

Now cancel 3 from numerator and denominator in left side.

w=(x-3y+1)/3

Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.

Learn more about equation at https://brainly.com/question/2972832

#SPJ1

The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

Learn more about arithmetic sequences

brainly.com/question/28882428

. #SPJ11

Answer:

option 4

Step-by-step explanation:

-3.4x + 4.7 - (3 + 2.9x) = -3.4x + 4.7 - 3  - 2.9x  (combine like terms)

                                   = -3.4x - 2.9x + 4.7 - 3

                                  = - 6.3x + 1.7

If two number have same sign, add and put the common sign for the answer.

If two numbers have different sign, subtract and the answer will have the sign of the bigger number

Answer:X=1

Step-by-step explanation:

The answer is:

x > 2

Work/explanation:

The inequality is:

\(\sf{2x+4 > 8}\)

To solve, start by subtracting 4 from each side:

\(\sf{2x > 4}\)

Divide each side by 2

\(\sf{x > 2}\)

Using the arrangements formula, it is found that 907,200 arrangements can be formed using the letters in the word FORGETTING.

The number of possible arrangements of n elements is given by the factorial of n, that is:

\(A_n = n!\)

When there are repeating elements, with the number of times given by \(n_1, n_2, \cdots, n_n\), the number of arrangements is given by:

\(A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}\)

In this problem, the word FORGETTING has 10 letters, of which G and T repeat twice, hence the number of arrangements is given by:

\(A_{10}^{2,2} = \frac{10!}{2!2!} = 907,200\)

More can be learned about the arrangements formula at https://brainly.com/question/25925367

#SPJ1

Answer:

utvut

Step-by-step explanation:

hvuyvytuccu

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

For more suchy questions on distance visit:

https://brainly.com/question/28551043

#SPJ8

The resulting polynomial when 5x -6 is subtracted from 3x² -6x +2 is; 3x² -11x +8.

It follows from the task content that the polynomial 5x -6 is to be subtracted from 3x² -6x +2.

Hence, the subtraction goes thus; 3x² -6x +2 -(5x-6).

Hence, 3x² -6x +2 -5x+6

= 3x² -11x +8.

Read more on polynomial subtraction;

https://brainly.com/question/9351663

#SPJ1

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

To learn more about probability

https://brainly.com/question/9653825

#SPJ4

Answer:

\(\sqrt[3]{3}\)

Step-by-step explanation:

use the Pythagoras Theorem

Since you have the hypotenuse (6"), just go backwards. 62 = 36 = a2 + b2.

Old coordinate (0,-1)

New coordinate (1,0)

The translation is

Verification

Image of (0,-1) is (0,1)

Image of (1,0) is (-1,0)

Answer:

(x + 1, y + 1)

Step-by-step explanation:

Translation of x-coordinate :

Translation of y-coordinate :

Hence, the points which describes the change :

Solving by factoring in steps shown below

Answer:

\(\textsf{1. \quad $x=1, \quad x=-\dfrac{2}{5}$}\)

\(\textsf{2. \quad $x=1, \quad x=3$}\)

Step-by-step explanation:

Solving quadratic equations by factoring

Given equation:

\(5x^2=3x+2\)

Subtract (3x + 2) from both sides:

\(\implies 5x^2-(3x+2)=3x+2-(3x+2)\)

\(\implies 5x^2-3x-2=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=5 \cdot -2=-10\)

\(\implies b=-3\)

Therefore, the two numbers are -5 and 2.

Rewrite \(b\) as the sum of the two numbers:

\(\implies 5x^2-5x+2x-2=0\)

Factor the first two terms and the last two terms separately:

\(\implies 5x(x-1)+2(x-1)=0\)

Factor out the common term (x - 1):

\(\implies (5x+2)(x-1)=0\)

Apply the zero-product property:

\(\implies 5x+2=0 \implies x=-\dfrac{2}{5}\)

\(\implies x-1=0 \implies x=1\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=-\dfrac{2}{5}}\)

Given equation:

\(\implies x^2-4x+3=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=1 \cdot 3=3\)

\(\implies b=-4\)

Therefore, the two numbers are -3 and -1.

Rewrite \(b\) as the sum of the two numbers:

\(\implies x^2-3x-x+3=0\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-3)-1(x-3)=0\)

Factor out the common term (x - 3):

\(\implies (x-1)(x-3)=0\)

Apply the zero-product property:

\(\implies x-1=0 \implies x=1\)

\(\implies x-3=0 \implies x=3\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=3}\)

Answer:

45

Step-by-step explanation:

x+5 =50

x=45

x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.

Given that total number of seats is 10,000 and there are two levels pricing.

Thus by observing the equation, x + y = 10,000,

10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.

Since there are two level pricing,

50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.

Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.

Learn more about algebraic equations here:

brainly.com/question/14737296

#SPJ4

The two rejection areas in using a two-tailed test and the 0.01 level of significance are:

Option e. Above 2.58 and below -2.58.

A two-tailed test is used when we want to test if the mean of a population is different from a specific value. In this case, we have two rejection areas, one in each tail of the distribution. The 0.01 level of significance means that we have a 1% chance of rejecting the null hypothesis when it is actually true.

To find the rejection areas, we need to look at the critical values for the 0.01 level of significance in a two-tailed test. These values are found in a Z-table or can be calculated using a calculator. The critical values for a two-tailed test and the 0.01 level of significance are 2.58 and -2.58. This means that any value above 2.58 or below -2.58 will be in the rejection areas and will lead us to reject the null hypothesis.

Therefore, the correct answer is e. Above 2.58 and below -2.58.

More information about two-tailed test here: https://brainly.com/question/28334447

#SPJ11

So, depending on the original coordinates, moving down 9 units and left 2 units will end up in either the third or fourth quadrant of the coordinate plane.

A coordinate is a set of values that specifies the position of a point or an object in a geometric space. In a two-dimensional space, such as the Cartesian plane, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal position (or abscissa) of the point and y represents the vertical position (or ordinate) of the point.

Here,

Starting from an arbitrary point (x, y), if we move down 9 units and left 2 units, we will end up at the point with coordinates (x - 2, y - 9). The new x-coordinate is obtained by subtracting 2 from the original x-coordinate, since we moved 2 units to the left. The new y-coordinate is obtained by subtracting 9 from the original y-coordinate, since we moved 9 units down.

The quadrant we end up in depends on the original coordinates (x, y) and the direction of the movement. If we start in the first quadrant (x > 0, y > 0) and move down and left, we will end up in the third quadrant (x < 0, y < 0).

If we start in the second quadrant (x < 0, y > 0) and move down and left, we will also end up in the third quadrant (x < 0, y < 0).

If we start in the third quadrant (x < 0, y < 0) and move down and left, we will end up in the fourth quadrant (x > 0, y < 0).

If we start in the fourth quadrant (x > 0, y < 0) and move down and left, we will still end up in the fourth quadrant (x > 0, y < 0).

To know more about coordinate,

https://brainly.com/question/29189189

#SPJ1

Answer:

Is this what you are looking for....

Answer:

x=±√3 or ±1.732

Step-by-step explanation:

5x²-9=6

5x²=6+9

5x²=15

x=±√15/5

x=±√3