What is the equation for the linear model in the scatter plot obtained by choosing
the two points closest to the line? Please enter an exact answer (use a simplified
fraction or whole number instead of a decimal).

A. -2x +4
B. 2x+ 4
C. Y= -7/6x + 3
D. Y= 1/2x +4

By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.

How to solve simultaneous equation?
1. Use the elimination method to get rid of one of the variables.

2. Find the value of one variable.

3. Find the value of the remaining variables using substitution.

Given that,

y = [tex]x[/tex]+3

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

First both equation are equal

[tex]x+3 = x^{2} +5x-2\\x^{2} +4x-5 =0\\x^{2} +5x-x-5=0\\x(x+5)-1(x+5)=0\\x=1, -5[/tex]

Then, substitute the value of x in y =x+3

y = x+3

at x= -5

y= -2

at x= 1

y = 1+3

y = 4

Hence, By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.

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The arc YZ represented in the diagram, its length is :

2π/3 or 4π/6

A circle's arc can be formed by any two points on its circumference.

A circle's arc length (S) = r(θ), where r is the radius and theta is the central angle in radians.

Given WY = XZ = 6,

So YZ = TZ = 3radius

and m∠XY = 140°.

so, m∠YZ = 180° - 140°.  (As a semicircle with a central angle of 180°.)

m∠YZ = 40°.

then,  m∠YZ = (40/180)°×π rad.

m∠YZ = 2π/9 rad.

then, Arc length of YZ =  = 3×(2π/9).

YZ = 6π/9.

YZ = 2π/3  or  4π/6

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Answer:

9/10 mile

Step-by-step explanation:

Distance from house to state park = 11 1/4 miles = 45/4 miles

Distance through woods
[tex]\dfrac{1}{6}\cdot \dfrac{45}{4}\\\\=\dfrac{9}{4} \text { miles}\\[/tex]

Since the distance along the stream is 2/5 of the distance in the woods,

the distance biked along the stream

= 9/4 x 2/5 = 18/20 = 9/10 mile

Using an exponential function, it is found that:

a) During the first five days, the population of organism A grew by a factor of 2^5.

b) During the next three days, the population of organism B decayed by a factor 2^(-3).

c) The expression for the total change is of 2².

An exponential function is modeled according to the following rule:

[tex]y = ab^x[/tex]

In which:

For the first five days, the population doubles each day, hence the rate of change is of:

b = 2.

The growth factor will be of:

y = 2^5 = 32

During the next three days, the population cuts in half each day, hence the rate of change is of:

b = 0.5.

Then the decay factor is of:

y = (0.5)³ = (1/2)³ = 2^(-3).

Applying properties of exponents, over the entire period, the change in the population will be of:

2^5 x 2^(-3) = 2^(5 - 3) = 2².

As when we multiply two terms with the same base and different exponents, we keep the bases and add the exponents.

The problem is given by the image at the end of the answer.

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From the situation described, it is found that:

a) The linear function that expresses her monthly cost is:

C(m) = 280 + 0.15m.

b) The slope of the graph of the cost function is of 0.15.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

In the context of the cost function in this problem:

Hence the parameters of the function are given as follows:

m = 0.15, b = 280.

The cost function for a mileage of m miles is, considering the above coefficients, is given by:

C(m) = 0.15m + 280.

With the slope of 0.15 already explained.

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20% of a 400 liter tank is 80 liters.

Answer:

Yeah good job! u got it right :)

Step-by-step explanation:

How to find perimeter?

Frist you will add up all the sides

then thats your answer :)

In this case the same logic applies

Hope this helps :3

Answer:

%23

Step-by-step explanation:

23/100

Answer:

23%

Step-by-step explanation:

Answer: y+5=3/8*(x-4)

Step-by-step explanation: Find the slope using m = y2-y1/x2-x2 which is the change of y over change of x, so the slope is m=3/8. Use the slope 3/8, and a given point (4, -5) to substitute for x1 and y1 in point slope form y -y1 = m(x-x1). So y-(-5)=3/8*(x-(4)). Now we simplify the equation so it's y+5=3/8*(x-4).

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{h}~,~\stackrel{y_2}{28}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{(-14)}}}{\underset{run} {\underset{x_2}{h}-\underset{x_1}{(-2)}}} \implies \cfrac{28 +14}{h +2}~~ = ~~\text{\LARGE 6}\implies \cfrac{42}{h+2}=6 \\\\\\ 42=6h+12\implies 30=6h\implies \cfrac{30}{6}=h\implies \boxed{5=h}[/tex]

Answer:

x^2 + y^ = 36

Step-by-step explanation:

See attached worksheet.

Given:

The car ride from Kiley's house to the airport.

Distance =24.3 miles.

Time =1/2 hour.

We know that

Substitute Distance =24.3 miles and time =1/2 hour to compute the average rate of the car ride from Kiley's house to the airport.

Hence the average rate of the car ride from Kiley's house to the airport is 48.6 miles per hour.

2)

Given that they walked 3/4 hours to the waiting area and covered the distance of 1.2 miles.

Distance =1.2 miles.

Time =3/4 hours.

we know that

Substitute distance =1.2 miles and time =3/4 hours to compute the average rate of the walk from the car to the waiting area by the gate, at the airport.

Multiplying 1.2 and 4, we get 4.8

Dividing 4.8 by 3, we get 1.6

Hence at the airport, the average rate of the walk from the car to the waiting area by the gate is 1.6 miles per hour.

Dividing the given equation by 25 we get:

Applying the natural logarithm to the above equation we get:

Finally, solving for x we get:

Answer: Option A.

The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h           (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.

Answer:

y = -3x + 5

Step-by-step explanation:

(1, 2) and (4, -7)

(x₁, y₁)       (x₂, y₂)

        y₂ - y₁          -7 - 2           -9

m = ------------- = ------------- = -------- = -3

        x₂ - x₁           4 - 1            3

y - y₁ = m(x - x₁)

y - 2 = -3(x - 1)

y - 2 = -3x + 3

  +2            +2

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

y = -3x + 5

I hope this helps!

Answer:

B. 160 hits

Step-by-step explanation:

544 × .294 = 159.936, which rounds to 160.

Where x = 3, and the value of y = 90;

For the expression y = x -2, when x = 4, y = 2, when x = -2, y = -9

Given:

y = 10x²................................1

Where x = 3, We make the required substitution

y = 10 x (3)²
y = 10 x 9

Hence,
y = 90

For the given expression:

Y = x -2.....................................2

Where x = 4, We make the required substitution

= 4 -2
hence,

y = 2

Where x = -7, We make the required substitution

y = 7

y = -7-2

Hence

y = -9

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Answer:0.8

Step-by-step explanation:

80/100= 8/10= 4/5

Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. Variables can have a wide range of values, which is why they are called variables. Thus, a variable can be thought of as a quantity that can take on different values depending on the circumstances of a given issue. As the program executes, we may store, modify, and access this data thanks to variables. All types of information can be stored in variables.

Four graphs of different nature as options.

We are required to find a graph that is not a continuous variable.

In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.

Given that,

When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.

Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.

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Based on the numbers given in the distribution, the standard deviation can be found to be 1.49

To find the standard deviation, you first have to find the mean of the distribution:

= (0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 5 ) / 9

= 15 / 9

= 1.67

You can then find the variance using financial calculators to be:

= 2.2222222

The standard deviation is:

= √variance

= √2.2222222

= 1.49

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Answer:

Step-by-step explanation:

Increasing

Domain: (-∞,∞)

Domain: -∞<x<∞

Range: (-∞,∞)

Range: -∞<y<∞

The probability that the ace of spades will be revealed before any face card (the jack, queen, or king) is 0.0769.

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.

According to given data;

Let's look at the first few probabilities; we're going to do this in reverse order, in order to find a pattern:

P(O,O,O,AS)=39/52)*(38/51)*(37/50)*(1/49)

                  =(39*38*37/3!)/(52*51*50/3!)*1/49

P(O,O,AS)=(39/3)(52/3)×1/49

        but we know that;

(n/2)=n(n-1)/2!

P,(O,O,AS) =(39/2)/(52/2)  *1/50

P(AS)=(39/0)/(52/0) *(1/52)

We now have

P(AS)+P(O,AS)+P(O,O,AS)+P(O,O,O,AS)

FROM THIS CALCULATE ;

P=0.0769

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Answer:

6z³ -z² - z + 6

Step-by-step explanation:

By using the negative sign to open the bracket and collecting like terms, we have:

6z³ + 3z² - 4z + 8 - 4z² + 3z - 2 I'm guessing it suppose to be 4z and not 4x.

= 6z³ -z² - z + 6

Option A is correct.

Answer: 673, 43

Step-by-step explanation:

As the next digit coming after the underlined digit is 2, the rounded number becomes 673,43. If instead of 2 we had 5 or above, the number should have become 673,44.

The surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.

A cylinder is defined as a solid geometric figure with straight parallel sides and a circular or oval cross section.

Surface area is the amount of space covering the outside of a three-dimensional shape.

Surface area  of the cylinder is calculated as  : - 2πr² + 2πrh

We have:

Height of the cylinder h = 8 inches

The radius r = 4 inches

π = 3.14

Surface Area  = 2(3.14)(4)² + 2(3.14)(4)(8)

surface Area = 2x 3.14 x 16 + 18.28

surface Area = 100.48 + 18.28

surface Area = 118.76 square inches

Therefore , the surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.

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The equation y = 2x² - 12x + 23 describes the function graph that includes a vertex at (3, 5) and passes through the point (5, 13).

The vertex of a parabolic equation is at the point and the vertex form is y = a(x - h)2 + k, where a, h, and k are constants (h, k).

Find the function whose graph has the vertex at (3, 5) and passes through the point in the question (5, 13).

Assuming it to be a parabolic function, we know that a parabolic equation's vertex form is y = a(x - h)2 + k, where a, h, and k are constants, and the vertex is located at the position (h, k).

As the vertex of the necessary function is at the position (3, 5), we may substitute h = 3 and k = 5 to obtain the following equation in the above equation:

y = a(x - 3)² + 5

Now that we know that the graph passes through the point (5, 13), we can change the original equation to read:

13 = a(5 - 3)² + 5,

or, 13 = 4a + 5,

or, 4a = 13 - 5 = 8,

or, a = 2.

We obtain the following from the equation y = a(x - h)2 + k by inserting a = 2, h = 3, and k = 5:

y = 2(x - 3)² + 5,

alternatively, y = 2(x² - 6x + 9) + 5,

alternatively, y = 2x² - 12x + 18 + 5,

Alternatively, y = 2x² - 12x + 23.

As a result, the function graph with the vertex at (3, 5) and the point of intersection (5, 13) yields the equation y = 2x² - 12x + 23.

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For the given equation, on rearranging, the value of x becomes = x = g / (c-b)

Rearranging parts is the act of rearranging counters, numbers, etc. to alter the way a number is shown visually; for instance, the number "4" could be shown in either of the two ways shown below.

A formula's components must be rearranged so that a different variable is the subject in order to change the formula's subject. Understanding inverse operations and how to solve equations is really helpful.

Given,

x(c- b) = g

On rearranging the equation,

x = g / (c-b)

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Answer:

geometric sequence

Step-by-step explanation:

an arithmetic sequence has a common difference d between consecutive terms.

40 - 200 = - 160

8 - 40 = - 32

no common difference thus not arithmetic

a geometric sequence has a common ratio r between consecutive terms

[tex]\frac{40}{200}[/tex] = [tex]\frac{4}{20}[/tex] = [tex]\frac{1}{5}[/tex]

[tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]

thus there is a common ratio so sequence is geometric