Exponential Regression
The table below shows the population, P. (in thousands) of a town after 12 years.
0
72
P 2400
3
2801.27
7
3608.71
12
14
4974.15 5426.17
19
6898.37
(a) Use your calculator to determine the exponential regression equation P that models the set of
data above. Round the value of a to two decimal places and round the value of b to three decimal
places. Use the indicated variables.
P =
(b) Based on the regression model, what is the percent increase per year?
96
(c) Use your regression model to find P when n = 13. Round your answer to two decimal places.
The population of the town after
P =
thousand people
(d) Interpret your answer by completing the following sentence.
years is
thousand people.

The given scale is

This means each two inches of the scale represents 4 feet of the actual size (or each inch is equivalent to two feet).

So, if the dimensions of the scale are 15 inches by 3.5 inches, then the actual dimensions would be 30 feet by 7 feet.

The perimeter would be

The area would be

To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:

Now to find the slope of the line

we write it in slope-intercept form y=mx+b:

from this form we conclude that this line has slope 7.

Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:

Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:

Plugging the values we know we have that:

Therefore the equation of the line is:

The graph of f(x) is a parabola with "arms up"

The vertex of the parabola is (0,-3)

Then we can know all the problem ask us:

increasing: (-3, infinity)

decreasing: (minus infinty, -3)

DNE maximum, beacuase it's arbitrarily large.

The minimum is the vertex: minimum of -3 at x = 0

The domain is all real numbers

The range is [-3, infinity)

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To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:

We focus on a and b. Always will be a squared x, but a and b vary. a lot

A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.

Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.

Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"

When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.

All the information the problem ask, you can get it by those numbers.

To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100

Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:

For the same value of x, the first function is 100 and the second 2

Given

Solution

Formula

Now

The midpoint M of the line segment joining the points C=(6,2) and D=(2,8). is

For the given situation:

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes

The factor of the above function is (2x + 3) (3x + 4)

To creat a 4 - digit code, we need to consider that for each digit we have 10 options:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.

Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:

We multiply 4 times 10.

And the result is:

He has 10,000 ways to create a 4-digit code.

System of Equations

When Neegan paddles the kayak upstream, the real rate (speed) is the difference between the rate that Neegan paddles in still water and the rate of the water against his paddling.

When he goes downstream, the real rate is the sum of the rates because the water and Neegan push in the same direction.

He takes 4.2 hours to paddle for 21 miles against the current, so the real rate is 21/4.2 = 5 mi/h

He takes only 3 hours to return, so the real speed is 21 / 3 = 7 mi/h.

Let:

x = rate at which Neegan paddles in still water

y = rate of the current.

We set the system of equations:

x - y = 5

x + y = 7

Adding both equations:

2x = 12

Divide by 2:

x = 6

Substituting in the second equation:

6 + y = 7

Subtracting 6:

y = 1

Neegan paddles at 6 mi/h in still water. The rate of the current is 1 mi/h

(Third choice)

The perimeter of a triangle is given by the sum of all it is sides.

Now, we have the next measures:

- The longest side of a triangle is 5in longer than the shortest side.

- The medium side is 4 inches longer than the shortest side

Then, the perimeter is given by:

P = (s+5)+(s+4)+s

If the perimeter is P=21 inches:

21 = (s+5)+(s+4)+s

Solve for s:

21 = s+5+s+4+s

21 = 3s + 9

21-9 = 3s

12 = 3s

s = 12/3

s= 4

Therefore,

The shortest side of the triangle is 4 inches.

The medium side is s+ 4 = 4+ 4 = 8 inches

The longest side is s+5 = 4+5 = 9 inches

The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.

This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.

In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.

Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.

Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.

The difference is however $2.79 - $2.36 = $0.43.

Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.

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The time that it will take the pipe to fill the pool if the drains left open is 10 hours.

From the information, one inlet pipe can fill an empty pool in 6 hours and a drain can empty the pool in 15 hours.

The information illustrated that the input pipe gills 1/6 if the pool and the drain empties 1/15 in the pool every hour

The required time taken will be:

= 1/6 - 1/15

= 5/30 - 2/30

= 3/30

= 1/10

Therefore, the time taken is 10 hours.

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we have that

the area of parallelogram is equal to

A=b*h

we have

b=14 mm

Find the value of h

tan(60)=h/7 -----> by opposite side divided by the adjacent side

Remember that

so

h=7√3 mm

substitute

A=14(7√3 )

Answer:

68

Step-by-step explanation:

100-68-12-11=9

12+11=23

100-23-9=68

1)To construct the line parallel to given line passing through given point, first take a point on the line.

2)Here in the problem that point is Q.

3)Join PQ.

4)After joining PQ, copy the angle made by PQ by constructing the arc MN with steel point of compass on Q. Keep same disttance and get arc M'N' by keeping steel point on P. Then measure length MN on the angle PQR and cut arc by placing steel point on M' and cutting the arc to get point N'.

5) Join PN' and extend till point S.

6) PS is parallel to QR.

Solution of an inequality

We can express the solution (s) of inequalities in several forms.

Here we will use two of them: The set-builder notation and the interval notation.

Let's solve the inequality

x - 1 ≤ 9

Adding 1 to both sides of the inequality:

x ≤ 10

The solution in words is "all the real numbers less than or equal to 10"

In set-builder notation:

{x | x <= 10}

In interval notation: (-inf, 10]

We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center

So we need to solve the following equation for x:

The first step would be substracting 8 from each side of the equation:

The next step is to square

fixed earnings = $80 ( for 8 hour shift)

Number of mobile phones he sells = m

Commision for each mobile phone sold = $20

Amount he earns in 1 shift (e) = flat + number of phones* commision

e = 80 + 20m

e= 20m + 80 (D)

Given:

To evaluate the function at x=1, we simplify the given relation first:

We let:

y=f(x)

We plug in x=1 into the above function:

Therefore,

Solution

For this case since we want to verify if a circle can be circumscribed in the quadrilateral we can use the following Theorem:

Theorem: If a quadrilateral is incribed in a circle then the opposite sides are supplementary

And we cna verify:

105+ 98= 203

82 +75= 157

Then we can conclude that the answer is:

False

The scenarios that demonstrate a proportional relationship for each person's income are :

Consider the income as y in each scenario

Scenario 1

Millie works at a car wash and earns $17.00 per car she washes.

Consider the number of car she washes as x

y = 17x

y ∝ x

This is a proportional relationship

Scenario 2

Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.

The relationship will be

y = 25 +12.50x

where x is the number of hours

This is not a proportional relationship

Scenario 3

Carla makes sandwiches at her job and earns $7.85 per hour.

The relationship will be

y = 7.85x

y ∝ x

Where x is the number of hours

This is a proportional relationship

Scenario 4

Tino is a waiter and makes $3.98 per hour plus tips.

The relationship will be

y = 3.98x + tips

Where x is the number of hours

This is not a proportional relationship

Hence, the scenarios that demonstrate a proportional relationship for each person's income are

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Answer:

• Plan B, by $4

• 140 minutes

Explanation:

Part A

From the graph, at 40 minutes, the costs of the plans are:

• Plan A: $4

• Plan B: $8

Plan B costs more by $4.

Part B

The point where the costs are the same is the time at which the two graphs intersect.

When the number of minutes = 140 minutes

• Cost of Plan A = $14

• Cost of Plan B = $14

Thus, the two plans cost the same for 140 minutes of long-distance call.

• If the time spent is less than this amount, Plan B costs more.

We need to know about scale factor to solve the problem. Matthew's mark last term was 50%.

It is given that Matthew's marks increased by a factor of 3/2 this term. This means that whatever marks Matthew had received in his previous term, it was increased by 3/2 this term. If we consider his original marks to be x, then we can get the increased marks by multiplying x by 3/2. We know that the new marks is 75%, we need to find the value of x.

3x/2=75

x=75x2/3=25x2=50

Therefore the marks Matthew received in the previous term is 50%.

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If the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x² then Zeros exists at x = 0, 0, 1, 2.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that exists combined utilizing mathematical operations like addition, subtraction, multiplication, and division exists directed to as a polynomial (No division operation by a variable).

Let the polynomial function be P(x) = [tex]x^4[/tex] − 3x³ + 2x²

P(x) = x²(x² - 3x + 2)

factoring the above polynomial function, we get

P(x) = x·x(x - 1)(x - 2)

Zeros exists at x = 0, 0, 1, 2

P(x) exists degree 4, so it will contain four roots. You only entered three which exists probably why it came up as wrong. The x² term contains a multiplicity of 2, so it counts twice.

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We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:

Then we can find the value of the angle by applying the inverse function of tangent, like this:

Let's replace the values from the figure into this equation to find x, like this:

Then, x equals 57.4°

we have the following:

Answer:

q = -1

Step-by-step explanation:

We are given the inequality [tex]11-\frac{64}{q} > 60[/tex]

We want to find out which value of q is a solution to the inequality. In other words, which value of q makes the statement true?

We can substitute the values given for q into the inequality to see this.

Let's start with q=2.

Replace q with 2.

[tex]11-\frac{64}{2} > 60[/tex]

Divide 64 by 2.

64/2= 32

11 - 32 > 60

Subtract 32 from 60

11-32 = -21

-21 > 60

The inequality reads "-21 is greater than 60", which is false (negative numbers are less than positive ones).

This means q=2 is NOT an answer.

Next, let's try q=-2

[tex]11 - \frac{64}{-2 } > 60[/tex]

64/-2 = -32

11 - - 32 > 60

- - 32 means subtracting a negative, which is the same as adding 32 to 11.

11 + 32 > 60

43 > 60

This is also NOT true (it reads "43 is greater than 60").

So q=-2 is also NOT an answer.

Now, let's try q = -1

[tex]11-\frac{64}{q} > 60[/tex]

[tex]11-\frac{64}{-1} > 60[/tex]

64/-1=-64

11 - -64 > 60

11 + 64 > 60

75 > 60

This reads "75 is greater than 60".

This is a true statement, meaning q = -1 IS an answer.

We are technically done, but just to be sure, we can check q=1 as well.

[tex]11 - \frac{64}{q} > 60[/tex]

[tex]11 - \frac{64}{1} > 60[/tex]

11 - 64 > 60

-53 > 60

This reads "-53 is greater than 60", which is false.

So this confirms that q = -1 is the only option that is an answer.

We were told that Mai made $192 for 12 hours of work. This means that the amount that she made per hour is

192/12 = $16

Given that her constant rate is $16 per hour,

let x = the number of hours would she have to work to make $128. Then, we have the following equations

1 = 16

x = 128

By crossmultiplying, we have

16x = 128

x = 128/16

x = 8

She has to work for 8 hours

The number line always goes from negative to positive :

It increases from left to right

SInce negative is always on the left side of the zero

Snumber greater than zero are always positive

i.e. x > o

ANSWER:

D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4

STEP-BY-STEP EXPLANATION:

We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4