In 2012, the population of a city was 6.53 million. The exponential growth rate was 2.79% per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018. c) When will the population of the city be 10 million? d) Find the doubling time.​

The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;

x = 5 ⇒ x - 5 = 0.

(x - 5)²

x = -3 ⇒ x + 3 = 0.

(x + 3)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 5)²(x + 3)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;

-7.5 = a(0 - 5)²(0 + 3)

-7.5 = a75

a = -7.5/75

a = -0.1.

Therefore, the required polynomial function is given by:

p(x) = -0.1(x - 5)²(x + 3)

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Answer:

Please help me by marking me the brainliest.

The area of the triangle is 9 units^2

Step-by-step explanation:

Area of triangle = 1/2(6*3)

                          =1/2(18)

                          =9

Answer:

18

Step-by-step explanation:

AC=AB

BC^2=AB^2+AC^2

162+162=324

Square root of 324 is 18.

The spreadsheet formula that will calculate the post-split number of outstanding shares in C3 will be C3*(B2/C2).

Assuming the split ratio has been inputted in cells B2 and C2, one can easily ascertain the post-split number of outstanding shares in cell C3 by simply using the following formula:

=C3 × (B2/C2).

In this case, the equation multiplies the pre-split quantity of outstanding shares by the ratio written down in cells B2/C2 for the determination of resulting post-split number of outstanding shares that are in cell C3.

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Answer:

Step-by-step explanation:

The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.

If John wants to make a 30% profit on the price he paid for the bike, he needs to sell it for:

$270 + 30% of $270 = $270 + $81 = $351

To offer a 10% discount on the marked price, he needs to calculate the price that includes the discount. Let's call this price "x".

90% of the marked price "x" is the same as the price he wants to sell the bike for ($351):

0.9x = $351

x = $390

Therefore, John should mark the bike at $390 to offer a 10% discount and still make a 30% profit on the price he paid for.

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Answer:

Step-by-step explanation:

You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.

Let w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...

  61(w+257) +110(w) = 307745

Simplifying the equation, we have ...

  171w +15677 = 307745

  171w = 292068 . . . . . . . . subtract 15677

  w = 1708 . . . . . . . . . . . divide by 171

  w+257 = 1965 . . . day passes sold

1965 day passes and 1708 weekend passes were sold.

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The value of SV, given that point J is the centroid, would be A. 9.

Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:

JV = 1 / 3 x SV

Knowing this, we can make SV the subject of the formula to become:

(JV = 1 / 3 x SV ) / 1 / 3

3 x JV = SV

SV = 3 JV

SV would then be:

SV = 3 x JV

SV = 3 x 3

SV = 9

In conclusion, SV would be 9.

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Answer:

answer is B. 9 :)

Step-by-step explanation:

Answer:

18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.

19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.

Step-by-step explanation:

An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²

Here, we have,

According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.

Substitute into the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

We know that the area of a rectangle is l × w

When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000

When w = 20, length = 120 - 40 = 80,  area =  80 x 20  = 1600

When w = 40, length = 120 - 80 = 40.  area = 40 x 40 = 1600.

So, the completed table will be

Width            Length          Area

10                    100              1000

20                    80              1600

40                    40              1600  

w                  120 - 2w        (120 - 2w) w

In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have;

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

A = 120W -2W²

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The Height of the given rectangular prism is:  (x + 1) - 4/(x³ + 3x² + 8)

In algebra, polynomial long division is defined as an algorithm used in dividing a polynomial by another particular polynomial of the same or even lower degree, which is a generalized version of the common arithmetic technique called long division. It can be done easily by hand, because it separates a supposedly complex division problem into smaller ones.

We are given:

Volume of a rectangular prism =  (x⁴ + 4x³ + 3x² + 8x + 4), and the area of its base is (x³ + 3x² + 8)

Thus, height is:

                   x + 1

x³ + 3x² + 8|x⁴ + 4x³ + 3x² + 8x + 4

                -  x⁴ + 3x³ + 0   + 8x

                           x³ + 3x² + 4

                         - x³ + 3x² + 8

                                        -4

Thus:

Height = (x + 1) - 4/(x³ + 3x² + 8)

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The area of the circular pateo is 50.24 square yards.

Remember that for a circle of radius R, the area is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:

R = 4yd/2

R = 2 yd

Replacing that in the area formula we will get:

A = 3.14*(2yd)²

A = 50.24 yd²

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It should be noted that 81.85% of the scores are between 72 and 87.

The probability that a score is greater than 77 is approximately 0.8413.

a) The z-score for 72 is calculated as:

z = (72 - 82) / 5 = -2

The z-score for 87 is calculated as:

z = (87 - 82) / 5 = 1

0.8413 - 0.0228 = 0.8185

So, approximately 81.85% of the scores are between 72 and 87.

b) The z-score for 77 is calculated as:

z = (77 - 82) / 5 = -1

1 - 0.1587 = 0.8413

Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).

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The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

Option B is the correct answer.

We have,

From the figure,

We have,

The polygon has three points.

The points are in ordered pairs.

We see that,

Each number has four units.

So,

1 unit = 0.25 units

Now,

The coordinates of the polygon are:

(3 units, -3 units) = (0.75, -0.75)

(0, 5 units) = (0, 1.25)

(-4 units, 2 units) = (-1, 0.50)

Thus,

The set of ordered pairs of the polygon is:

(0.75, -0.75), (-1, 0.5), (0, 1.25)

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The possible outcomes for each of the given events are:

A {1, 3, 5, 7}

B {3, 4, 5, 6}

The possible outcomes for the experiment are {1, 2, 3, 4, 5, 6, 7, 8}.

The two given events are:

A "The marble selected is an odd number"

The outcomes for this event are the odd numbers that are outcomes for the experiment, then the outcomes here are {1, 3, 5, 7}

The second event is:

B "The marble selected has a number from 3 to 6."

The possible outcomes here are {3, 4, 5, 6}

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Answer:

C) 23/32

Step-by-step explanation:

count how many lines there are in all

32

Then count from beginning to X

23

The distance of X is 23/32

Answer:

Step-by-step explanation:

(a)  

16

36

​

=

4

9

​

36:16=9:4

(b)  

144

324

​

=

4

9

​

324:144=9:4

(c)  

1125

125

​

=

1125

125

​

=

45

5

​

=

9

1

​

∴125:1125=1:9

Answer:5.03

1.26 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

5u^2 - 8u + 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -8, and c = 2. Substituting these values, we get:

u = (8 ± sqrt(64 - 40)) / 10

u = (8 ± 2sqrt(6)) / 10

Therefore, either:

A line on the graph which could represent this scenario is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this line, it can be modeled by this equation:

y = mx + c

y = 2x/3 + (-6)

y = 2x/3 - 6

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The two expressions "8m+4-3m" and "3+ m+2m+1+2m​" are equivalent because they simplify to the same-value.

To determine if the two expressions are equivalent, we can simplify each expression and then compare them.

Simplifying the first -expression,

We have,

⇒ 8m + 4 - 3m can be simplified by combining like terms;

⇒ 8m - 3m + 4 = 5m + 4

Next, Simplifying the second-expression,

we have,

⇒ 3 + m + 2m + 1 + 2m can also be simplified by combining like-terms:

⇒ (1 + 3) + (m + 2m + 2m) = 4 + 5m

So we have:

(i) 8m + 4 - 3m = 5m + 4

(ii) 3 + m + 2m + 1 + 2m = 4 + 5m

Since both simplified expressions are equal to "5m + 4", we can conclude that the two original expressions are equivalent.

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Answer:

d y                              x+1

-----   = (l x+1 l + 2) x -----------------------

d x                            (l x+1 l + 2) x lx+1l

Answer: A' will be at (-2,0)

Step-by-step explanation:

Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)

Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)

Answer: The total sum of all monthly payments required to pay off this loan is $410,932.

To calculate this, we need to first find the amount of the loan that is not covered by the deposit. The deposit is 20% of $300,000, or $60,000, so the remaining amount of the loan is $300,000 - $60,000 = $240,000.

Next, we need to calculate the monthly payment on the loan. We can use the formula for a fixed-payment loan to do this:

Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))

The monthly interest rate is the annual interest rate divided by 12, or 0.0394 / 12 = 0.003283.

The number of months is the number of years times 12, or 30 x 12 = 360.

Plugging these values into the formula gives:

Payment = ($247,249 x 0.003283) / (1 - (1 + 0.003283)^(-360)) = $1,151.80

Finally, we can find the total sum of all monthly payments by multiplying the monthly payment by the number of months:

Total payments = $1,151.80 x 360 = $410,932 (rounded to the nearest whole number).

Step-by-step explanation:

The category that had the highest relative frequency is given as follows:

Have chores.

To obtain the relative frequencies for each item, we must add the rows/columns that represent the items in this problem.

Hence the relative frequencies for each item are given as follows:

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Answer:

n = -5

Step-by-step explanation:

We know that when two lines are perpendicular, the slopes of the two lines are negative reciprocals as

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we're usually not given, and m1 is the slope of the line we're given

Thus, we know that m2 must equal -1/2 from the formula since m1 is 2:

[tex]m_{2}=-\frac{1}{2}[/tex]

Of course, -1/2 is already simplified so m2 is the slope of the line passing through (8, n) and (2, -2)

To find n, we must use our knowledge of the slope formula that gives us the slope, m:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point on the line and x2 and y2 are another point on the line:

If we allow (8, n) to be our x1 and y1 point and allow (2, -2) to be our x1 and y2 point and -1/2 to be our m, we can now solve for m by plugging everything into the slope formula and solving for n (aka y1 in the formula:

[tex]-1/2=\frac{-2-n}{2-8}\\ \\-1/2=\frac{-2-n}{-6}\\ \\3=-2-n\\\\5=-n\\\\-5=n[/tex]

We can even check that we get -1/2 when we plug in -5 into the slope formula:

[tex]-1/2=(-2-(-5))/(2-8)\\-1/2=(-2+5)/(-6)\\-1/2=3/-6\\-1/2=-1/2[/tex]

Answer:

Step-by-step explanation:

Complementary means angles that add up to 90°

Based on that you can write and equation by adding the 2 angles and making equal to 90

2x+6+1/2x=90          combine like terms on left

5/2x+6=90               subtract both sides by 6

5/2x=84                   multiply by the reciprocal of 5/2 => 2/5

x=168/5 or 33.6

Using trigonometric relations we can see that:

6) θ = 30°

7)   θ = 60°

We can see a right triangle where we want to find the value of θ, we know the hypotenuse and the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opp cath)/hyp

Replacing what we know:

sin(θ) = 6/12 = 1/2

Then we know that θ = 30°

For the second one we know the adjacent cathetus and the hypotenuse, here we need to use the cosine relation:

cos(θ) = 5/10

cos(θ) = 1/2

then θ = 60°

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The rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

To find the rate at which the temperature of the compound rose, we need to divide the change in temperature by the time interval during which the change occurred.

The temperature rose 3¹/₂ degrees every 2/3 of an hour. To write this as a fraction, we can first convert 3¹/₂ to an improper fraction:

3¹/₂= 7/2

Now, we can write the rate of change as a fraction:

Rate of change = (7/2) / (2/3)

To divide by a fraction, we can multiply by its reciprocal:

Rate of change = (7/2) x (3/2)

Simplifying, we get:

Rate of change = 21/4

Therefore, the rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

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