find a pattern for a sequence 17, 13, 9, 5,

Using it's concept, the average rates of change are given as follows:

a. 1264.03 soda per person per year.

b. 5851.89 soda per person per year.

c. 128010.89 soda per person per year.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For this problem, the function is given as follows:

f(x) = 5.852x^4 - 0.002x³ + 0.006x² + 0.029x + 47.855.

From 1990 to 1996, we have t = 0 to t = 6, hence:

Hence the rate is:

(7632.01- 47.855)/6 = 1264.03.

1264.03 soda per person per year.

From 1990 to 2000, we have t = 0 to t = 10, hence:

Hence the rate is:

(58566.75 - 47.855)/10 = 5851.89.

5851.89 soda per person per year.

From 2005 to 2010, we have t = 15 to t = 20, hence:

Hence the rate is:

(936354.84 - 296300.39)/5 = 128010.89.

128010.89 soda per person per year.

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The distance traveled by the ball as a function of time, s(t) = 16•t² ft., and the rate of change, based on calculus, gives;

(a) During the time interval [6, 6.5], the distance traveled is 100 feet

(b) In the interval, [6, 6.5], the average velocity is 200 ft/s

(c) The calculated average velocities in ft/s, for the respective time intervals are;

[6, 6.01]. 192.16

[6, 6.001]. 192.016

[6, 6.0001]. 192.0016

[5.9999, 6]. 191.9984

[5.999, 6]. 191.984

[5.99, 6]. 191.84

The instantaneous velocity at t = 6 is v(6) = 192 ft/s

The distance traveled as a function of time is s(t) = 16•t² ft.

(a) The distance traveled during the time interval [6, 6.5] is found as follows;

s(6) = 16 × 6² = 576

s(6.5) = 16 × 6.5² = 676

The distance traveled in the interval, [6, 6.5], ∆s(t) = 676 - 576 = 100

The distance traveled during the time interval [6, 6.5] = 100 feet

(b) Average velocity = ∆s(t)/∆t

∆t = 6.5 - 6 = 0.5

Therefore;

∆s(t)/∆t = 100/0.5 = 200

The average velocity = 200 ft./s

(c) The average velocities over the given time intervals, obtained using a graphing calculator, are;

Interval. Average velocity

[6, 6.01]. 192.16

[6, 6.001]. 192.016

[6, 6.0001]. 192.0016

[5.9999, 6]. 191.9984

[5.999, 6]. 191.984

[5.99, 6]. 191.84

Given that at t = 6, as the time interval approaches zero from the right and from the left, the average velocity approaches 192 ft./s, the instantaneous velocity at t = 6, v(6) is 192 ft./s

v(6) = 192 ft./s

Using calculus, differentiation, we have;

v(t) = ds/dt = 2×16 × t = 32•t

v(6) = 32 × 6 = 192

Therefore;

v(6) = 192 ft./s

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Using probability we get (a) P(1|A) = 1/2 and (b)P(1|B) =3/4 , hence P(1|A) ≠ P(1|B).

Probability is the study of chance . The part of mathematics known as probability deals with fractional representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, 0 denotes the event's impossibility and 1 denotes certainty.

Probability is calculated by the fraction possible outcomes ÷ total outcomes

a) The first spinner has the total 4 sections. so there are 4 total outcomes.

Favorable outcome = 1

Total number of favorable outcome=2

Probability P(1|A) = favorable outcome ÷ total outcome

∴ P(1|A) =2/4 or P(1|A) =1/2

b) The first spinner has the total 4 sections. so there are 4 total outcomes.

Favorable outcome = 1

Total number of favorable outcome=3

Probability P(1|B) = favorable outcome ÷ total outcome

∴ P(1|B) =3/4 or P(1|B) =3/4

c)Therefore P(1|A)≠P(1|B)  so the events A and B are dependent.

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Answer: i think you want y=125x+225

Step-by-step explanation:

the linear equation is created by sticking these two numbers into y=mx+b

so we start at 225 feet, which means that goes where b is, and the helicopter goes up 125 per whatever, which means we put 125 where m is

The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.

It is a measure of how much the function changed per unit, on average, over that interval.

We have,

f(x) = x - 2√x

On the interval [1,9].

[1, 9] = [a, b]

The average rate of change:

= f(b) - f(a) / b - a

= f(9) - f(1) / 9 - 1

= [(9 - 2√9) - (1 - 2√1)] / 8

= [ (9 - 6) - (1 - 2) ] / 8

= (3 + 1) / 8

= 4 / 8

= 1/2

Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.

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Answer:

Step-by-step explanation:

add 99 and 36 together to get 135 degrees

Answer:

135°

Step-by-step explanation:

You add the two angles together.  

here hope this helps u

Area of triangle ΔCDE  with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.

We have a triangle ΔCDE with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ). To calculate the area of triangle when its vertices are given we have the formula as shown below,

Area of triangle ΔCDE = [tex](1/2)(x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} -y_{1} ) + x_{3} (y_{1} -y_{2} ))[/tex]

Here, [tex]x_{1}[/tex] = -4 , [tex]x_{2}[/tex] = -3 ,[tex]x_{3}[/tex] = -7 , [tex]y_{1}[/tex] = 2 , [tex]y_{2}[/tex] = 7 and [tex]y_{3}[/tex] = 6

On substituting the above values in the formula of area of triangle , we will get

Area of triangle ΔCDE = (1/2)( -4 ( 7 - 6 ) + ( -3 ) ( 6 - 2) + (-7 ) ( 2 - 7 ))

Area of triangle ΔCDE = (1/2) ( - 4 - 12 + 35 )

Area of triangle ΔCDE = 19/2

Area of triangle ΔCDE = 9.5 square units

Area of triangle ΔCDE  with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.

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Answer:

your answr would be a 13

Step-by-step explanation:

Answer:

A) 13

Step-by-step explanation:

[tex]-5 + |-18|\\where\:|-a|=|a|\:\:\mathrm{if}\:a\neq 0\\|-18| = |18|\\= -5 + 18\\Inverse\:\:the\:\:expression\\= 18 - 5\\= 13[/tex]

Answer:

Step-by-step explanation:

NO x=3

The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\\[/tex]

The quadratic equation is given below.

5k² - 20k = 15

Simplify the equation, then we have

k² - 4k = 3

k² - 4k - 3 = 0

Then the roots of the equation will be

[tex]\rm k = \dfrac{ -(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-3) }}{2 \times 1}\\\\k = \dfrac{4 \pm \sqrt {28}}{2}[/tex]

Simplify the equation, then we have

k = (4 ± 5.30) / 2

k = (4 + 5.30) / 2, (4 - 5.30) / 2

k = 4.65, -0.65

The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.

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Answer:

$19.8($2.7 subtracted off)

Step-by-step explanation:

[tex]P = 22.5(1 - 12\%)\\P = 22.5(1 - 0.12)\\P = 22.5(0.88)\\P = 19.8[/tex]

Answer:

x = 24/5

Step-by-step explanation:

Answer:

≈67.81

Step-by-step explanation:

Answer:  2x-5/3=7

Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula

The actual weight of the animal is between 450.2 and 426.2 pounds

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality can be used to show that two variables or numbers are not equal to each other.

The weight of the larger animals can be off by 12 pounds. Let x represent the actual weight of the animal. If the scale reads 438.2 lbs, hence:

|x - 438.2| = 12

x - 438.2 = 12; or -(x - 438.2) = 12

x = 450.2; or x = 426.2

The actual weight of the animal is between 450.2 and 426.2 pounds

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Answer:

6

Step-by-step explanation:

The diameter is half of the given radius, therefore, split the radius in half.

[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]

Answer:

7x+y=3 is not a linear equation.

Given

Tom got 72 marks in 8 tests.

Answer

[tex] \frac{72}{8} = 9[/tex]

he get 9 mark on average

Let the Principle be 100.

P = 100, then A = 200 and SI will be 200 - 100 = 100

YES = 100 in 10 years

Rate = 100/10 = 10%.

∴ The interest rate is 10%.

Given:

Time period = 10 years

Formula used:

SI = (P × R × T)/100

A = P + SI

Where P = main amount, R = rate, T = time, SI = primary interest

Calculations:

Monetary amount 2P

YES = 2P - P

⇒ P = (P × R × 10)/100

⇒ 1 = R/10

⇒ R = 10%

∴ The interest rate is 10%

Answer: 141.26666666667

Step-by-step explanation:

The points scored by Rodney is 20 points.

The points scored by Justin is 19 points.

x + y = 39 equation 1

x - y = 1 equation 2

Where:

x = points scored by Rodney

y = points scored by Justin

In order to determine the points scored by Justin, take the following steps:

Subtract equation 2 from equation 1 :

2y = 38

Divide both sides of the equation by 2

y = 38/2

y = 19 points

To determine the value of x, substitute for y in equation 2

x - 19 = 1

Combine similar terms: x = 19 + 1

Add similar terms together: x = 20

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The line which is perpendicular to the given line y = -x/8 + 3 is y - 8x =-2, there slopes are negative reciprocals of each other

Given data

line y = -x/8 + 3

The equation of a line is represented as y = mx + c where m represents the slope. The unique feature of perpendicular line is that the slopes are negative reciprocals of each other.

Hence we find the line that has same value of m which is the slope

using the second option: y - 8x = -2

y - 8x = 2

y = 8x - 2

y = 8x - 2

the slope here is m = 8 which is equal to the negative reciprocals of the slope in the given equation and hence the correct option

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The required expression for the given statement is 4x + 1.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

The given statement is,

the difference between nine times a number and one more than five times the number

Let x be the number.

Thus, we have

nine times a number = 9x

one more than five times the number = 1 - 5x

Thus, the numerical expression we get is

9x + (1 - 5x)

Expanding we get

9x + 1 - 5x

Solving we get

4x + 1

this is the required expression

Thus, the required expression for the given statement is 4x + 1.

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The cost equation for Debra is given by 4x + 6y = 94 and for Heather is 5x + 3y = 77.

Linear equations in two variable have one, none, or infinitely many solutions, with the highest exponent order of 1 in each of the two variables. The standard form of a two-variable linear equation is ax + by + c = 0, where x and y are variables. Solutions can also be written in pairs, for example (x, y). A two-variable linear equation system is represented graphically by two straight lines that can intersect, parallelize, or coincide.

According to the given condition, we have 2 equations:

4x + 6y = 94
5x + 3y = 77

Now, multiply by 2 on both sides of the equation 5x + 3y = 77 to obtain:

10x + 6y = 154

Now, subtracting the equation 10x + 6y = 154 and 4x + 6y = 94.

[10x + 6y = 154] - [ 4x + 6y = 94]

6x + 0y = 60

x = 10

Putting the value of x = 10 in equation 4x + 6y = 94, we get

y = 9

So, the cost of 1 hammer is 10$ and tape is 9$.

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According to the image  the x-axis, there is a reflection (- 4, 2 ).

An image that has been flipped has no points that are closer to the mirror line than the original shape. The point's coordinate must be multiplied by -1 in order to reflect it over the axis. Simply add -1 to the coordinate of the point to reflect it over the axis.

Analytic geometry, often known as coordinate geometry, is the study of geometry using coordinate points. It is possible to determine distances between points using coordinate geometry, as well as divide lines into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations.

Under the x-axis reflection.

A point (x, y) → (x, -y), so

(- 4, - 2 ) → (- 4, 2 )

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Answer: 162 million

Step-by-step explanation:

147.4 million= 147,400,00

Make a proportion:

147,400,000   -  91%

          x             - 100%

Hence,

[tex]\displaystyle\\x=\frac{147,400,000*100}{91} \\\\x=\frac{14,740,000,000}{91} \\\\x\approx162,000,000\\\\x=162 \ million[/tex]

hundred people bearajsbsj

Answer:

I don't know about this question

Answewhats the number mason

Step-by-step explanation: