Plot the x- and y-intercepts to graph the equation. y = 1/3x + 1

Step-by-step explanation:

to create a vertical asymptote (a tangent of the curve in infinity) at x = n we define e.g.

f(x) = 1/(x - n)

the cost x gets to n, the much closer the function gets to 1/0 and infinity.

so, the part to get us the asymptote at x = -4 is

1/(x + 4)

the part to get us the asymptote at x = 2 is

1/(x - 2)

and the part that gives us a zero solution at x = 3 is

(x - 3)

because that is what the point (3, 0) is : when x = 3. then y = 0.

now we only need to multiply all 3 parts to combine them :

f(x) = 1/(x + 4) × 1/(x - 2) × (x - 3)

The graph of the equation y = 2x - 3 at the interval of -3 to 5 is attached below.

Graph:

Graph means the diagram that shows the variation of a variable in comparison with that of one or more other variables.

Given,

Here we have the equation y = 2x - 3

Now, we need to plot the graph of the given equation at the interval of -3 to 5..

To plot the graph for the given function,

The given interval is taken as the value of x and we have to calculate the value of y from it,

Now, we have to take the given interval  -3, -2, -1, 0, 1, 2, 3, 4, 5 are the samples value for x.

So, we have to apply the values on the equation,

Then we get the value of the function as,

x = -3 => y = 2(-3) - 3 = -6 - 3 = 9

x = -2 => y = 2(-2) - 3 = -4 - 3 = -7

x = -1 => y = 2(-1) - 3 = -2 - 3 = -5

x = 0 => y = 2(0) - 3 = 0 - 3 = -3

x = 1 => y = 2(1) - 3 = 2 - 3 = -1

x = 2 => y = 2(2) - 3 = 4 - 3 = 1

x = 3 => y = 2(3) - 3 = 6 - 3 = 3

x = 4 => y = 2(4) - 3 = 8 - 3 = 5

x = 5 => y = 2(5) - 3 = 10 - 3 = 7

The completed table is attached below.

Now, we have to plot the graph through the derived table, then we get the graph like the following.

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Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1

In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.

The square root of the variance yields the standard deviation, i.e.

Standard deviation = [tex]\sqrt{variance[/tex]

Given that sample, the variance is 49.7 and we have to calculate the standard deviation.

Standard deviation (σ) = [tex]\sqrt{variance[/tex]

= [tex]\sqrt{49.7}[/tex]

= 7.0498

=7.1

Hence, the standard deviation for the population for the given variance is 7.1

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Equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.

Given points:

(1, 1.5) and (2, 3.5)

slope m = 3.5 - 1.5 / 2 - 1

= 2/1

m = 2

substitute m and (1,1.5) in y = mx + c

1.5 = 2*1 + c

1.5 - 2 = c

c = -0.5

c = -1/2

y = mx + c

y = 2x - 1/2.

Therefore equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.

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The parent function is y = x ; shift 2 units downwards.

Given,

In the question:

The function is :

g(x) = x - 2

Now, According to the question ;

Let's know

What is the Parent function and transformation?

The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit. Reflection. A reflection on the x-axis is made on a function by multiplying the parent function by a negative. Multiplying by a negative “flips” the graph of the function over the x-axis.

According to the above statement is;

g(x) = x -2

Hence, The parent function is y = x ; shift 2 units downwards.

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Answer:  [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

=====================================================

Explanation:

The notation (g∘f)(x) is the same as g(f(x))

We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.

This is what the steps look like

[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]

Therefore,

[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.

Answer:

Unclassified

Step-by-step explanation:

Which questions would you like answered?

The system of linear equations which is used to find number of 7 -inch plates ,x and 12- inch plates y is

x+y = 15 ---(1)

7x+12y = 144 ---(2)

In the given question we have following informations,

total number of plates in kitchen cabinet = 15

diameter of each plate either 7-inch or 12-inch.

let the number of plates in kitchen cabinet with Diameter 7-inch = x

and number of plates in kitchen cabinet with Diameter 12-inch = y

the diameter of all 15 plates combined = 144 inches

from the above details we can make a system of linear equations for two variables say x and y

x + y = 15 -----(1)

7x + 12y = 144 ---(2)

equation (1), (2) made the required system of equations.

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Answer:

-5 with the exponet of 11

Answer:

-1/5 or -0.2 if you are going by fraction or decimal

The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

The equation that represents the absolute value function is expressed in in vertex form as y = a|x – h| + k, here, the vertex of the graph of the absolute value function is (h, k), while the value of a determines if the graph opens up or opens down.

The point (3, 5) is the vertex of the graph, therefore:

(h, k) = (3, 5)

Plug in h = 3 and k = 5 into, y = a|x – h| + k:

y = a|x - 3| + 5

Find the value of a, by substituting the values of the coordinates of a point on the graph, (x, y) = (5, 7), into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

2 = 2a [subtraction property]

1 = a [division property of equality]

a = 1

Substitute the value of a into the equation y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the graph].

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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It takes almost 5.7 hours the same hose to fill an aquarium measuring 26 inches by 33 inches by 35 inches.

First, we must determine how quickly the hose operates.

By dividing the volume of the first aquarium by the length of time it took to fill it, we may determine that.

The following formula can be used to determine the volume of the first aquarium: V =L*B*H

where the aquarium's length is L and its width is B

Its height is H.

Thus, the first aquarium's volume is:

V =L*B*H = 3*8*11 = 264 inches^3

We have the filling rate as:

264/3 inches ^3 per minute,

Let's now determine the second aquarium's volume.

The first formula is what we employ.

The volume is as follows:

V =L*B*H = 26*33*35 = 30030 inches ^3

Now, we divide the capacity of the second aquarium by the pace of the first aquarium to obtain the amount of time.

According to mathematics, that is:

30030 * 3/264 = 341.25 minutes = 5.7 hours approximately

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If a baseball diamond is a square that measures 90ft on each side. The  expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)²   and the distance is 127ft.

Using the Pythagoreans theorem formula

c= √ a²+b²

Where:

c = length of hypotenuse

a and b =  length of the sides of the right triangle

Let plug in the formula

c =√ (90)² + (90)²

c =√ 8100 +8100

c =√16200

c = 127.3

c = 127 ft (Approximately)

Therefore the distance is 127ft.

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Answer:

70%

Step-by-step explanation:

For emission of a surface, the average absorptivity of this surface at 1040 K is 0.899705900025.

Knowing that ε1 =0.15 and ε2 = 0.9, we first solve for the average emission, e, as follows:

ε = ε1 [tex]f_λ[/tex] [ λT]  +   ε2 [1- [tex]f_{λ}[/tex](λT)]

is also solved for reference in calculating fλ

(λ*T) = (5 μm)(1040 K)

       = 5200 μm K

[tex]f_{λ}[/tex]= 0.0003921333  when referencing this to a blackbody function.

Moving on, we solve for T1040 using the equation above:

ε = ε1 [tex]f_{λ}[/tex][λT] + ε2[1 -[tex]f_{λ}[/tex]( λT)]

  =0.9 + (0.15-0.9)0.0003921333  

  =0.899705900025

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The simple regression line is used to estimate the population regression line.

We are asked about, the simple regression line

We have options:

a. is estimated by the population regression line.

b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

c. shows the actual (or true) relation between the dependent and independent variables.

d. is used to estimate the population regression line.

e. connects the data points in a sample.

From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.

The simple regression line is used to estimate the population regression line.

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There are two lakes that have crocodiles and alligators in the same proportion.The two lakes are Lake Winnipeg and Lake Champlain.

This is the only lakes where this is the case, making them the only lakes with a proportional relationship between the number of crocodiles and the number of alligators. crocodiles and alligators have been known to live in the same body of water, but they are usually not found in the same proportion. In these two lakes, however, they are found in equal numbers.

Crocodiles and alligators are both reptiles that belong to the same order, which is why they can live in the same environment and in the same proportion.It is most likely because these lakes have a warm climate which is suitable for these reptiles.

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Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

A mathematical assertion in which you use mathematical symbols to demonstrate that two sums are equal.

As per specified data-

Let 'x' be the number of weeks required to complete the amount.

The equation becomes.

378 = 15.75x

For the number of week required.

x = 378/15.75

x = 24

Thus, Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

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Sean drew a letter (b)F.

What is Geometry construction?

Drawing precise shapes, angles, or lines is referred to in geometry as "construction." These structures only require a compass, a straightedge (a ruler), and a pencil.

according to the question, WX is a straight line having a midpoint at Y.

YZ is drawn perpendicular to WX. And parallel to YZ  a line segment is drawn After this Geometrical construction, a letter is drawn which is F.

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For the specified requirements, 97 sample size are required.

Given that,

Confidence Interval = 95

Margin of error (m) =0.099

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the  population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 95% confidence interval ,

Z* = 1.960 , m=0.099

Using equation we get

n = (1.96/0.099)²(0.5)( 1 - 0.5 )

By solving,

n = 97.02≅ 97

The necessary sample size is 97

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The statement that is true is All rational numbers can be written as the quotient of Integers

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

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The statement that is true is All rational numbers can be written as the quotient of Integers

What are rational numbers ?

Any number that can be written as a fraction and has an integer as both the numerator and the denominator is referred to as rational number.

In a rational number, the denominator cannot be zero.

Integer refers to whole numbers. They are generally of two types the positive integers and the negative integers

Quotients refers to the end product of division example 2 ÷ 1 = 2/1

2/1 is the quotient, both 2 and 1 are integers

All decimals are rational - A counter example to this is √2

It has decimal and not a rational number because it cannot be represented as a fraction

Answer:

Step-by-step explanation:

I think this is the answer you were looking for but im not 100% sure

The only correct option that is minimized by the least squares regression line is. Option B the sum of the squared residuals.

lets check all the option -

Option A - This claim is untrue because the residuals' summation would provide a value of 0.

Option B - Because error must be kept to a minimum, the residuals must sum to zero and the line must be as close to the points as possible. Prior to summing them, we must first square the residuals, which will always result in a positive value. This option is accurate since the Least Square Regression Line minimizes the total of residuals.

Option C - This choice is incorrect because the least squares regression line cannot be created by adding the absolute values of the residuals.

Option D - This alternative is incorrect since the influence of outliers has nothing to do with the subject at hand.

Option E - Due to slope's lack of relevance to the subject at hand, this choice is also incorrect.

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Answer:

d = 3h - 6

Step-by-step explanation:

h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )

3h = d + 6 ( subtract 6 from both sides )

3h - 6 = d

The blanks in this two-column proof should be completed (filled) as follows:

Statements                                             Reasons_______________

m∠RST = 5x° and m∠UVW = 7x°                Given

∠RST and ∠UVW are supplementary

m∠RST = 5x° + m∠UVW = 180           definition of supplementary angles

5x + 7x = 180                                       substitution property of equality

12x = 180                                              addition property of equality

x = 15                                                    division property of equality

In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this context, we can logically deduce that the sum of angles RST and UVW are supplementary angles:

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In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that For every unit increase in x1, the predicted mean of Y rises by 2 units holding [tex]x_{2}[/tex] constant.

Given data,

Slope b1 = +2

Mutiple regression which means,

Use multiple linear regression to determine the relationship between two or more independent variables and one dependent variable.

The value of the dependent variable at a specific level of the independent variables (For instance, the crop's anticipated yield at specific levels of temperature, rainfall, and fertilizer application).

[tex]y = b_{0} +b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+....[/tex]

[tex]b_{1}[/tex]=2 means

The estimated mean of Y increases by 2 units for each increase of 1 unit of [tex]x_{1}[/tex], holding [tex]x_{2}[/tex] constant.

Hence, the expected mean of Y increases by two units for every unit increase in x1.

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Answer: 76

Step-by-step explanation:

Based on the given conditions, formulate: 6+10*7

Calculate the product or quotient: 6+70

Calculate the sum or difference: 76

0.5  is the p-value for this Z -test .

What is the Z test's p-value?

For a lower tail test, the test statistic z is determined to be zero that means

P(z<0)

Then p-value is

p-value = P(z<0) = 0.5 (From z score table )

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Answer:

8/2 or 4/1

Step-by-step explanation:

To find the slope, you simply count how high up one point is from another (0,0 to 2,8) and then how far over. Since 2,8 is 8 points up from 0,0 the numerator of our slope would be 8; and since 8,2 is two over from 0,0 the denominator is 2. Simplify this to 4/1.