Suppose a city with a population of 200,000 has been growing at a rate of 6% per year. If this rate continues, find the population of this city in 11 years.

Answer:

x = 4, y = 12

Step-by-step explanation:

The opposite angles of a cyclic quadrilateral sum to 180° , then

25x - 2 + 7y - 2 = 180

25x + 7y - 4 = 180 ( add 4 to both sides )

25x + 7y = 184 → (1)

--------------------------

22x + 7 + 7y + 1 = 180

22x + 7y + 8 = 180 ( subtract 8 from both sides )

22x + 7y = 172 → (2)

Subtract (2) from (1) term by term to eliminate y

3x + 0 = 12

3x = 12 ( divide both sides by 3 )

x = 4

Substitute x = 4 into either of the 2 equations and solve for y

Substituting into (1)

25(4) + 7y = 184

100 + 7y = 184

7y = 84 ( divide both sides by 7 )

y = 12

The variable has a global scope and is related to mathematical expressions or equations for representing the unknown value.

In mathematics, the concept of scope is not directly applicable to variables in the same way it is in computer programming. In mathematics, variables typically have a global scope, meaning they are valid and accessible throughout the entire mathematical expression or equation in which they are defined.

Mathematical variables are used to represent unknown values or quantities, and their scope is typically determined by the mathematical expression or equation in which they are used. Variables in mathematics can be used within their defined context, such as an equation or formula, to represent specific values or relationships between quantities. They do not have the same localized scope as variables in programming, where their visibility is limited to specific parts of a program.

In summary, in mathematics, variables typically have a global scope, and their scope is determined by the mathematical expression or equation in which they are used.

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Answer:

\(8t\leq 100\)

Step-by-step explanation:

T-shirts-t

\(8t\leq 100\)

Answer:

Sx+8

Step-by-step explanation:

S standing for shirts and x meaning the number of shirts bought

The allowance time, if the standard time is 234.15 minutes and the basic time is 233.4 minutes is 0.75 minute

To calculate the allowance time, we can use the following formula:

Allowance time = Standard time - Basic time

Thus, Allowance time = 234.15 minutes - 233.4 minute = 0.75 minutes

Therefore, the allowance time is 0.75 minutes.

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The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

Step-by-step explanation:

14. y = -2/3x + 10. This is parallel to 2x -3y because they have the same slope.

15. y = -1/2x and y = -1/2x + 2. These are perpendicular because the slope is the opposite reciprocal to the slope of y = 2x + 3, which is 2.
The slopes of the lines of the 2 equations are the same. Because of that, we can state that 2 lines that are perpendicular to the same line are parallel. This can be further supported by the Perpendicular Transversal Theorem, which says the same thing.

Hope this helps!

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

Step-by-step explanation:

Given the profit function P(x) = -6x² +288x -3162, you want to find the value of x and the value of P(x) corresponding to maximum profit.

The vertex of the parabola described by ax²+bx+c lies on the line of symmetry:

  x = -b/(2a)

This will be the value of x that is a maximum when a < 0.

The value of the function at that point can be found by evaluating the quadratic expression for the value of x just found.

Maximum profit is had when ...

  x = -(288)/(2(-6)) = 24

That maximum profit is ...

  P(24) = (-6(24) +288)(24) -3162 = 144(24) -3162 = 294

For maximum profit, 24 tables should be made per day. The maximum profit is $294 per day.

The correct Fourier transform of the signal y(n) = 3x[n]n (n) is 3X(e−j(v−3n)).

Explanation:

Given information: a signal x[n] having the corresponding Fourier transform X(c j), and another signal y(n) = 3x[n]n (n) .

We know that, the Fourier transform of y(n) is given by:

Y(e^jv)=sum from - infinity to infinity y(n)e^jvn.

where y(n) = 3x[n]n (n)

Substituting y(n) in the above equation, we get:

Y(e^jv) = 3 * sum from - infinity to infinity x[n]n (n) * e^jvn.

We know that, the Fourier transform of x[n]n (n) is X(e^j(v-2pi*k)/3).

Therefore, substituting the value of y(n) in the above equation, we get:

Y(e^jv) = 3 * sum from - infinity to infinity x[n]n (n) * e^jvn

= 3X(e^j(v-3n)).

Hence, the Fourier transform of the signal y(n) = 3x[n]n (n) is 3X(e−j(v−3n)).

Conclusion: The correct Fourier transform of the signal y(n) = 3x[n]n (n) is 3X(e−j(v−3n)).

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Answer:

-4

Step-by-step explanation:

5(x+3)=2x+3

5x+15=2x+3

5x-2x=3-15

3x=-12

3x/3=-12/3

x=-4

Answer:

Equivalent

Step-by-step explanation:

2/3 times 2=4/6

4/6 divided by 2=2/3

(hope this helps :P)

Answer:

26 feet, Oliver will have to travel 26 feet deep.

Step-by-step explanation:

8 feet added to 18 feet will be your answer.

Answer:26 feet, Oliver will have to travel 26 feet deep.

Step-by-step explanation:Okay so if you draw a line graph going vertical and you number it 1-32 ( this is if you have to show work ) a is a 11 feet deeper and b is 23 feet deeper

Answer: 64

Step-by-step explanation:

(47 + 39) - 22

= 86 - 22

= 64

The area of the figure formed by the dilation is 36 square units.

Area is particularly essential in modern mathematics. In addition to its importance in geometry and calculus, area is linked to the determination of determinants in linear algebra and is an essential feature of surfaces in differential geometry.

A dilation occurs when an figure is reduced to a smaller size using a fixed center.

From the given diagram we can find the sides of the square that is the transformed image as 9 - 3 = 6 units

Area of the A'B'C'D' square = 36 square units.

Side of the original square = 18 units.

Area of the ABCD square = 18² = 324 square units

Scale factor of dilation = 324/36 = 9 times.

Hence from the figure we can calculate the area of the transformed figure to be 36 square units which is dilated by a factor of 9 times.

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Answer:

40 in.

Step-by-step explanation:

A=(a+b)/2 x h

Because he wanted the audience glued to their seats, the stage manager pasted paste on the programmes.

Even before the first rehearsal, the stage manager is involved in the performance. During

He or she is in charge of preparing all the materials during what is known as "PREP WEEK."

for the opening of the rehearsals. The first step is for actors to completely TRUST the stage management.

Being structured from the first minute of the first rehearsal is essential to gaining that trust.

The stage manager is accountable for attending each rehearsal during the rehearsal time to

aid the director, create CUE SHEETS, let the actors know what the director wants, and all the

Develop strong working connections with DEPARTMENT HEADS, who are perhaps the most crucial, everyone involved in the show.

The director frequently moves on to another production after the first performance.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Points found on y = h(x) are (7, -6) and (-2,-1).

Using these two points, we will solve for the exact equation of y = h(x).

To solve the equation, we will get the slope (m) of the two points first using the following formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1} =\dfrac{-1-(-6)}{-2-7} =\dfrac{5}{-9} =-\dfrac{5}{9}\)

Now that we have a slope, we can now proceed in solving the equation using Point-Slope Formula.

 \(y-y_1=m(x-x_1)\)

\(y-(-6)=-\dfrac{5}{9}(x-7)\)

  \(y+6=-\dfrac{5}{9}(x-7)\)

 \(9y+54=-5x+35\)

 \(9y=-5x+35-54\)

     \(9y=-5x-19\)

     \(y=-\dfrac{5}{9}x-\dfrac{19}{9}\)

Now that we have the equation of the dashed line, we will now solve for its inverse function y = h^-1 (x).

To solve for the inverse, we will reverse y and x with each other. The new equation will be:

\(x=-\dfrac{5}{9}y -\dfrac{19}{9}\)

From that equation, we will now equate or isolate y.

\(x=-\dfrac{5}{9}y -\dfrac{19}{9}\)

\(x=-\dfrac{5y-19}{9}\)

\(9x=-5y-19\)

\(5y=-9x-19\)

\(y=-\dfrac{9}{5}x -\dfrac{19}{5}\)

In this equation, our slope (m) here is -9/5 and our y-intercept is at (0, -19/5). The graph for this equation will look like this.

Drag the endpoints of the solid segment to the coordinates shown above to graph y = h^-1 (x).

Or drag the endpoints to (-6,7) and (-1,-2). It's the same graph anyway.

The sample size, n is 9 and the sample mean, m is 41.33.

The exam has possible points and the scores for the students in the third classroom are as follows: 30 48 44 32 44 44 32 48 50.

We are asked to determine the sample size(n) and sample mean(m).

Sample size refers to the number of observations included in a study. In this question, the number of observations is equal to the number of scores in the third classroom. Hence, the sample size(n) is equal to n.

Now, the formula of the sample mean(m) is given as  

                m = Sum of all observations/Total Number of observations

          m =  30 + 48 + 44 + 32 + 44 + 44 + 32 + 48 + 50/9

          m = 372/9

          m = 41.33

Hence, the sample mean(m) of the scores for the students in the third classroom is 41.33.

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Answer:

995.26

Step-by-step explanation:

I'm not sure but this is what I got

Answer:

b=20 or b=-20

Step-by-step explanation:

Keep in mind the meanings of the values of the discriminant:

If b^2-4ac=0, then the quadratic will have only 1 solution (double root)

If b^2-4ac<0, then the quadratic will have no real solutions

If b^2-4ac>0, then the quadratic will have 2 unique solutions

In this case, to get one real solution, the discriminant must be set up as b^2-4ac=0. Setting up the equation we get:

b^2-4(4)(25)=0

b^2-400=0

b^2=400

b=20 or b=-20

So the values of b would have to be either 20 or -20

The values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

Given the quadratic equation \(4x^2+bx+25= 0\), for this expression to have a real solution, the discriminant must be greater than zero

D > 0

b^2 - 4ac > 0

Given that a = 4, b = b, c = 25

b^2 - 4(4)(25) > 0

b^2 - 400 > 0

b^2 > 400

b > ±20

Hence the values of b will cause 4x^2+bx+25=0 to have one real solution is -20 and 20

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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Trump/ Pence 2020!!!

Answer:

\(m^{10}\)

Step-by-step explanation:

\(m^2m^5m^3\\=m^{2+5+3}\\\\=m^{10}\)

===============================================

Explanation:

I'm assuming you meant to write m^2 * m^5 * m^3

If so, you add the exponents to get 2+5+3 = 10 which is the exponent over the original base m. The base does not change.

The rule I used is a^b*a^c = a^(b+c). We see that the base stays the same at 'a' the whole time.

-----------

A longer way to do this is to expand out m^2 into m*m. We have two copies of m multiplied together.

Similarly, m^5 = m*m*m*m*m. We have five copies now.

Saying m^2*m^5 will have seven copies because

m^2*m^5 = (m*m) times (m*m*m*m*m) = m*m*m*m*m*m*m = m^7

Tacking on m^3 will add on three more copies of m to multiply out, giving 10 copies of m total to multiply. This alternative method is not advised since there is a possibility to lose track and make an error somewhere. The formula in the previous section is preferred. Though I recommend you try this second method out to see how/why the formula works.

The graph will cross the x-axis if the multiplicity of the real root is odd.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

For polynomials, the graph will cross the x-axis if the multiplicity of the real root is odd, and just touch the x-axis if the multiplicity of the real root is even. (The multiplicity of the root is the number of times it occurs as a root)

(a) y=(x+1)^2(x-2) The graph crosses at x=2 (multiplicity 1) but touches at x=-1 (mulitplicity 2)

(b) y=(x-4)^3(x-1)^2 The graph crosses at x=4 (multiplicity 3) but touches at x=1 (m=2)

(c) y=(x-3)^2(x+4)^4 The graph touches at x=3 and x=-4 as the multiplicities are both even.

The graphs: (a) black, (b) red, (c) green

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Answer:

Step-by-step explanation:

f(t) = 40×0.5^t

Answer:

68°

Step-by-step explanation:

Here,

As we know that the sum of two supplementary angles are 180°. So,

→ (2x – 8)° + (3x – 2)° = 180°

→ 2x° – 8° + 3x° – 2° = 180°

→ 5x° – 10° = 180°

→ 5x° = 180° + 10°

→ 5x° = 190°

→ x = 190° ÷ 5°

→ x = 38°

Supplementary angles are,

→ 2(38°) – 8

→ (76 – 8)°

→ 68°

→ 3(38°) – 2

→ (114 – 2)°

→ 112°

Therefore, the measure of the smaller angle is 68°.