The table below shows the participation in the town soccer league during its first five seasons.
Town Recreational Soccer League Participation
Number of participants
88
95
100
108
115
Year
1
2
23
3
4
fo
5
Which is the equation of the trend line that can be generated by using the data from years 1 and 5?
Oy-6.75x-688.25
Oy-6.75x-1.75
O y-6.75x+81.25
Oy-6.75x+148.75

The equation that models the curve of best fit for this data will be y = 1.4646·(1.818)ˣ.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

Consider the scatter plot.

Then the equation that models the curve of best fit for this data will be

At (1.2, 3), then we have

[tex]\rm 3 =ab^{1.2}[/tex] ..........1

At (4, 16), then we have

16 = ab⁴  ..........2

By solving the equations 1 and 2, we have

a = 1.4646 and b = 1.818

Then the equation will be

y = 1.4646·(1.818)ˣ

Then the graph is drawn.

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The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:

s = 10 + 2 · (n - 1)     (1)

Where n is the element index.

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

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Answer:

[tex] {(x + 5)}^{2} + {(y - 5)}^{2} = 9 [/tex]

Answer:

A relation is a subset of cartesian product of two non empty sets whereas A function is a type of relation in which every element of first set has one and only image in the second set.

In a relation an element of the first set can have many images in the second set whereas in a function the first element can have only one image in the second set.

The given relation is not a function as the element 1 is related to 3 different elements in the second set.

Domain={1}

Range={7,14,21}

L1 and L2 are parallel

so the interior alternate angles are equal

4y - 40 = 3y ( interior alternate angles)

4y - 40 = x + 15 ( vertically opposite angles).

solving the first equation, we get

4y - 3y = 40

y = 40°

putting values of y= 40° in eq. 2, we get

4y - 40= x + 15

4(40) - 40 = x + 15

160 -40 = x + 15

120 - 15 = x

105° = x

7.5 pounds of the $0.82 per lb candy must be used in the mixture.

First, let's define the variables:

We want to make 9 lb of mixture, then:

x + y = 9.

And the price of these 9 pounds must be $0.91, then we can write:

x*$0.82 + y*$1.36 = 9*$0.91 = $8.19

Then we have a system of equations:

x + y = 9.

x*$0.82 + y*$1.36 = $8.19

We can isolate y on the first equation so we get:

y = 9 - x

Now we can replace that on the other equation:

x*$0.82 + (9 - x)*$1.36 = $8.19

And now we can solve this for x.

x*($0.82 - $1.36) = $8.19 - 9*$1.36

-x*$0.54 = -$4.05

x = (4.05/0.54) = 7.5

So 7.5 pounds of the $0.82 per lb candy must be used in the mixture.

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Answer:

Step-by-step explanation:

2 ( x + 3 ) / 4 ( x + 1 )

2 (x + 3) ÷4 (x + 1)

2 (x + 3) ÷ 2×2(x+1)

cancel out the 2 in the numerator with the 2 in the denominator

(x + 3) ÷ 2(x + 1)

x+3 / 2(x+1)

The area of triangle is 24 sq. units

Area of rectangle is product of its length to its breadth.

i.e., Area of rectangle = length* breadth

let A(6, -3), B(3, -6), C( -1, -2) and D( 2, 1)

Using distance formula

AB = √(3-6)²+ (-6 +3)²

AB= √9 + 9

AB= √18

AB= 3√2

now,

BC=  √(-1-3)²+ (-2 +6)²

BC = √16 +16

BC = √32

BC =4 √2

Now, Area of rectangle

= AB* BC

=  3√2 *4 √2

= 12*2

= 24 square units

Hence, area of rectangle is 24 sq. units

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Answer:

(-32, 0)

Step-by-step explanation:

Answer:

(-32,0)

Step-by-step explanation:

Answer:

252-232=20-1=19

Step-by-step explanation:

the question said in between so you don't count the first and the last numbers

The number of hours that Bret can hike with 9 liters of water is 9.6 hours.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

Water needed = 0.75 liters per hour

For x number of hours = 0.75x liters

Reserved water = 1.8 liters.

Total water needs for x hours = (0.75x + 1.8)

The number of hours that can be hiked with 9 liters will be as,

(0.75x + 1.8) = 9

x = 9.6 hours.

Hence "The number of hours that Bret can hike with 9 liters of water is 9.6 hours".

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The value of B1 shows a fall in demand as price rises by a unit. The point prediction is given as y = 306,560.8

The regression equation shows that y= 306,619-27.71.x

b1 = -27.71

The interpretation for b1 is that if the price of this good is increased by 1, then the demand for the good would fall by about 27.71.

The regression line equation is given as

y= 306,619-27.71.x

when x which is price is = 2.10

Then the value of y would be:

y = 306,619 - 27.71*2.10

y = 306,560.8

c. a 95% C1 for B1 is given as:

1.96 * 27.71.

= 54.31

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[tex] \huge \tt \underline {\green{Answer}}[/tex]

If on March 8, 2017 , one U.S. dollar worth 66.79 Indian rupees

ie. $1 = Rs 66.79

$ 1 = 66.79 × 1

$ ? = 110.66

$ = New / old

$ = 110.66 / 66.79

$ = 1.65683485552

or

$1.66 = 110.66

Examine the right triangle ABC. Which rise and run would create a similar right triangle on the same line?a rise of 6 and a run of 8a rise of 8 and a run of 6a rise of 6 and a run of 5a rise of 5 and a run of 6

Step-by-step explanation:

Answer:

740 miles

Step-by-step explanation:

$415-$230=$185

$185÷0.25 per miles =740 miles

A slope also known as the gradient of a line is a number. The correct option is A, C, and D.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

For the given question,

This can be observed in the graph, as the slope of the graph before 4 pm is positive, it can be concluded that the temperature is increased until 4 pm.

This can be observed in the graph, as the slope of the graph after 4 pm is negative, it can be concluded that the temperature is decreasing after 4 pm.

This can be probed by calculating the slope of the line between the two points. Therefore, the slope between 8 am to 12 pm will be 1, while the slope from 12 pm to 4 pm will be equal to 4/3.

Hence, the correct option is A, C, and D.

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Answer:

ACD

Step-by-step explanation:

Let [tex]f(x) = x^3 + 3x + \sin(x) - 5[/tex]. Using Newton's method to approximate a solution to [tex]f(x) = 0[/tex], we consider the recurrence

[tex]\begin{cases} x_1 = 1 \\ x_{n + 1} = x_n - \frac{f(x_n)}{f'(x_n)} & \text{for } n \ge 1 \end{cases}[/tex]

Differentiating [tex]f(x)[/tex] gives

[tex]f'(x) = 3x^2 + 3 + \cos(x)[/tex]

Then

[tex]x_2 = 1 - \dfrac{f(1)}{f'(1)} = 1 + \dfrac{1 - \sin(1)}{6 + \cos(1)} \approx 1.024238790[/tex]

[tex]x_3 = x_2 - \dfrac{f(x_2)}{f'(x_2)} \approx 1.024009549[/tex]

[tex]x_4 = x_3 - \dfrac{f(x_3)}{f'(x_3)} \approx \boxed{1.024009528}[/tex]

which agrees numerically with the actual root of [tex]f(x)[/tex] up to at least 9 digits after the decimal point.

The probability that a single can will contain 11.6 ounces or less of soda is 0.2843

The given parameters are:

x = 11.6

Mean = 12

Standard deviation = 0.7

Calculate the z value using:

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

This gives

[tex]z = \frac{11.6-12}{0.7}[/tex]

z = -0.57

The probability is then calculated as:

P(x ≤ 11.6) = P(z ≤ -0.57)

Using the z table of probabilities, we have:

P(x ≤ 11.6) = 0.2843

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a pack contains 11.6 ounces or less is

P(6) = 0.2843^6

P(6) = 0.00053

In (a), the probability that a can contains 11.6 ounces or less is 0.2843

The probability that all cans in a case contains 11.6 ounces or less is

P(36) = 0.2843^36

P(36) ≈ 0

See attachment for the normal distributions

The summary of the graph is that, as the sample size increases the probability decreases

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Answer:

5 is the answer

Step-by-step explanation:

because it is

Answer:

≈ 14.6%

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = 2.75 - 2.40 = 0.35 , then

percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )

The reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we can see in the graph there are two shapes are shown.

Figure M and Figure N

The sequence of transformations that will take figure M onto its congruent image, figure N is:

First, we need to draw a line that passes through (3, 0) and (0, -3)

The equation of the line is:

[tex]\rm y+3=\dfrac{\left(-3\right)}{-3}\left(x\right)[/tex]

y + 3 = x

y = x - 3

The reflection over the above line will take figure M onto its congruent image, figure N.

Thus, the reflection over the line y = x - 3 will take figure M onto its congruent image, figure N.

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The expression that is not rational is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

A rational expression is something of the form:

[tex]f(x) = \frac{q(x)}{p(x)}[/tex]

Such that q(x) can be any polynomial, and p(x) is a polynomial of at least degree 1.

This means that we need to have the variable "x" on the denominator.

Then is easy to recognize the expression that is not rational, is the one that does not have x on the denominator, which is the first one:

[tex]f(x) = \frac{6x}{4}[/tex]

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Answer: B

Step-by-step explanation:

I took the test and this was the correct answer

The sample size required is 2938.645

Probability is the likeliness of an event to happen.

It is given that

p = .37

∈ = 0.025

∝ = 1 - 0.995 = 0.005

∝[tex]\rm z_{\alpha/2} = z_{0.005/2} = 2.807[/tex]  (From z table)

Sample size n is given by

[tex]\rm n = (\dfrac{z_{\alpha/2}}{\epsilon})^2 p (1-p)\\\\n = (\dfrac{2.807}{.025})^2 *0.37*(1-0.37)\\\\n = 2938.645\\[/tex]

Therefore the sample size required is 2938.645

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Answer:

Area = 3.36 in²

Step-by-step explanation:

[tex]Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h[/tex] ,

where a and b are the two parallel sides, and h is the height.

[tex]Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}[/tex]

Answer:

D -6, 15

Step-by-step explanation:

Because 3,11 is the middle, and 12,7 is the other end, you can do

12 - 3 = 9

3 - 9 = 6

then

11 - 7 = 4

11 + 4 = 15

so

6 is you x and 15 is your y

Answer:

c

Step-by-step explanation:

answer is C . First last digits are forty you will have down 2 answers

Answer:

the answer to the question is C

Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

p = 0.1, n = 2.

The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]

0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.

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