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The slope intercept form of equation of required line is

[tex]y = \frac{2}{3}x - 2[/tex]

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Slope of the required line = [tex]\frac{2}{3}[/tex]

The line passes through (0, -2)

Equation of the required line =

[tex]y - (-2) = \frac{2}{3}(x - 0)\\y + 2 = \frac{2}{3}x\\y = \frac{2}{3}x-2[/tex]

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Answer:

30.6

Step-by-step explanation:

18/4 = 4.5

4.5 × 6.8 = 30.6

The equation of the circle for all the given values is obtained as  x² + y² + 8x + 2y + 8 = 0.

The equation for a circle can be written by knowing the coordinates of its centre and the length of its radius.

Since the radius is the distance from the centre to a point on the circle, the equation can be written by distance formula as s (x - h)² + (y - k)² = r² where (h, k) is the coordinate of the centre.

The coordinates of the centre of the circle is given as (-4, -1).

And, the radius is 3.

The general equation of the circle for centre at (h, k) and radius r is given as (x - h)² + (y - k)² = r².

Substitute the corresponding values to obtain,

(x - h)² + (y - k)² = r²

=> (x - (-4))² + (y - (-1))² = 3²

=> (x + 4)² + (y + 1)² = 9

=> x² + 8x + 16 + y² + 2y + 1 = 9

=> x² + y² + 8x + 2y + 8 = 0

Hence, the required equation for the circle is given as  x² + y² + 8x + 2y + 8 = 0.

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The height of the tree would be 25.9 meters.

Option (B) is correct.

What is the tangent ratio in trigonometry?

The ratio of the opposite side of a right triangle to the adjacent is called the tangent and is given the symbol tan.

                    tan = Opposite side/Adjacent side

A tree casts a shadow 21 m long. The angle of elevation of the sun is 51.

In the given figure, Apply the tangent ratio

                      tan51° = AB/BC

                        1.23 = h/21

                         h = 1.23 * 21

                         h = 25.9 m.

Hence, the height of the tree would be 25.9 meters.

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The sample size  appropriate for estimating the true time to within 5 min confidence level of 95% is 139

We have to get the range of the values in this distribution

The range is given as: 440 - 320

= 120

through the range rule, we would have to solve for the standard deviation

= 120 / 4

= 30

At the 95 percent level of confidence, the critical value of Z is solved as 1.96

To get the value of n which is the sample size, we would have to use the Margin of error formula

[tex]ME = z*\frac{sd}{\sqrt{n} }[/tex]

ME = 5

[tex]5 = 1.96 * \frac{30}{\sqrt{n} }[/tex]

n = 138.2976

n is approximately 139

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Answer:

a) TPR

b) NM

c) x=6

Step-by-step explanation:

a) since the angle K is the middle letter on in the first triangle, the second triangle's middle letter will be P since they correspond

b) TR is congruent to NM because if you flipped TR upside down, it would match directly with NM

c) 4x-3=21

4x=24

x=6

this is because TR and NM are congruent, so 4x-3 is equal to 21

Answer:

135.00

Step-by-step explanation:

since,he pays 70% then he keeps 30%.

and 30% of 450.00 is 135.00

Answer: 0

Step-by-step explanation:

1/2(2x+5)=3/4(x+1)+5/2

distribute 1/2 to 2x and 5

distribute 3/4 to x and 1

1/4x+5/2=5/2

subtract 5/2 to 5/2

1/4=0

multiply 1/4 by the reciprocal

4/1*1/4=0*4/1

Answer= 0

The probability that 2 of the 9 voters will prefer Candidate A is 0.30033

Given that 25 % of voters prefer candidate A

Total number of voters = 9

Do we have to calculate the probability that 2 of the 9 voters will prefer Candidate A =?

In this question, we used binomial distribution to find the probability that 2 of the 9 voters will prefer candidate A.

The binomial distribution follows the probability  mass function of:

⁹C₂ * (0.25) ² *  (0.75)⁷ =>

⁹C₂  = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/ (7 * 6 * 5 * 4 * 3 * 2 * 1) (2 * 1) =>

⁹C₂  = 9 * 8/2 = 36

Now, 36 * (1/4)² * (3/4)⁷ = 0.30033

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The most effective way to describe multivariate relationships is by means of graphs and multiple variables.

The term "multivariate analysis" refers to a broad variety of statistical methods, not simply one particular approach. These methods enable you to comprehend your data more thoroughly in light of particular commercial or real-world settings.

Multivariate analysis is therefore a key idea to understand if you're wanting to be a data analyst or data scientist.

The breadth of knowledge that multivariate analysis offers is its one key benefit. The insights you find are far more applicable to the actual world because you're drawing a lot more thorough picture of what's happening when you explore numerous factors.

There are two different kinds of multivariate analytic techniques: interdependence techniques, which examine the structure of a dataset, and dependency techniques, which examine the cause-and-effect interactions between variables.

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As a result, multivariate analysis is a crucial concept to comprehend if you wish to work as a data analyst or data scientist.

The main advantage of multivariate analysis is the breadth of knowledge it provides. Since you're looking at many different elements, you're getting a much more complete picture of what's going on, which makes the insights you discover much more applicable to the real world.

There are two major categories of multivariate analytic approaches: dependency techniques, which look at the cause-and-effect relationships between variables, and interdependence techniques, which look at the dataset's structure.

Answer:

(0, 1/3)

Step-by-step explanation:

To find the centroid of a triangle with vertices A, B, and C, we can use the following formula:

centroid = (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.

In this case, we have A = (-3, 1), B = (-2, 4), and C = (5, -2), so the centroid of the triangle is:

centroid = ((-3) + (-2) + 5) / 3, (1 + 4 + (-2)) / 3 = (0, 1/3)

Therefore, the coordinates of the centroid of ABC are (0, 1/3).

Answer:

There are three terms in this expression: 2, 8u, and 7v. A term is a value or variable (or a combination of values and variables) that is separated from other terms by a plus or minus sign. In this expression, 2 and 8u are constants, while 7v is a variable.

Answer:

4.75340042E147

Step-by-step explanation:

The speed rate at which the aircraft is gaining altitude is;

dx/dt = 250 miles per hour

Since the aircraft is climbing at 30° to the horizontal. it means there will be a vertical component which will be the altitude and also a horizontal component which will be the horizontal distance covered. while the hypotenuse will be how far it has climbed.

Let us call the vertical component x and the hypotenuse component z.

Thus, from trigonometric ratios, we can say that;

sin 30 = x/z

We are looking for how fast the aircraft is gaining altitude. Thus, using Liebniz notation, we can say this rate is; dx/dt. Thus;

sin 30 = (dx/dt)/(dz/dt)

0.5 = (dx/dt)/(dz/dt)

0.5 × (dz/dt) = dx/dt

Its' speed is 500 mph. This means dz/dt = 500

Thus;

dx/dt = 0.5 × 500

dx/dt = 250 mph

Hence, the speed rate at which the aircraft is gaining altitude is;

dx/dt = 250 miles per hour

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Step-by-step explanation:

Manage into slope interrupt form

16x = 4y + 2

4y = 16x - 2

Separate by 4

Y = 4x -1/2

Because the equating is undeviating, find 3 points and plot ruling class

(0, -1/2), (1, 3.5), (-1, -4.5)

And last, set a limit through bureaucracy

Answer:

MC donalds is a scam

Step-by-step explanation: THEY KILL BABY CHICKENS  THE ANSWER IS

Make it into slope intercept form

16x = 4y + 2

4y = 16x - 2

Divide by 4

Y = 4x -1/2

Since the equation is linear, find 3 points and plot them

(0, -1/2), (1, 3.5), (-1, -4.5)

And lastly, draw a line through them

Answer:

d ≈ 11.4 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 5, 1 ) and (x₂, y₂ ) = (6, - 2 )

d = [tex]\sqrt{(6-(-5))^2+(-2-1)^2}[/tex]

  = [tex]\sqrt{(6+5)^2+(-3)^2}[/tex]

  = [tex]\sqrt{11^2+9}[/tex]

  = [tex]\sqrt{121+9}[/tex]

  = [tex]\sqrt{130}[/tex]

  ≈ 11.4 units ( to the nearest tenth )

Answer:

5/12 phone uses less storage space

Step-by-step explanation:

Find a common denominator so you can compare the fractions easily.  Use 12.

1/2 = 6/12

5/12 < 6/12, so now you can see that the phone that uses 5/12 of storage space uses less than the one that uses 1/2

Answer:

[tex]\textsf{a)} \quad a_n=(-1)^{n-1}[/tex]

[tex]\textsf{b)} \quad a_n=3n-4[/tex]

Step-by-step explanation:

Given sequence:

1, -1, 1, -1, 1, ...

The given sequence is geometric since there is a common ratio of -1 between consecutive terms.

To find the common ratio of a geometric sequence, divide a term by the previous term:

[tex]\dfrac{a_5}{a_4}=\dfrac{1}{-1}=-1[/tex]

[tex]\dfrac{a_4}{a_3}=\dfrac{-1}{1}=-1[/tex]

[tex]\dfrac{a_3}{a_2}=\dfrac{1}{-1}=-1[/tex]

[tex]\dfrac{a_2}{a_1}=\dfrac{-1}{1}=-1[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the values of a and r into the formula to create an equation for the nth term:

[tex]\implies a_n=1 \cdot (-1)^{n-1}[/tex]

[tex]\implies a_n=(-1)^{n-1}[/tex]

Given sequence:

-1, 2, 5, 8, 11, ...

The given sequence is arithmetic since there is a common difference of 3 between consecutive terms.

To find the common difference of an arithmetic sequence, subtract consecutive terms:

[tex]a_2-a_1=2-(-1)=3[/tex]

[tex]a_3-a_2=5-2=3[/tex]

[tex]a_4-a_3=8-5=3[/tex]

[tex]a_5-a_4=11-8=3[/tex]

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given:

Substitute the values of a and d into the formula to create an equation for the nth term:

[tex]\implies a_n=-1+(n-1)3[/tex]

[tex]\implies a_n=-1+3n-3[/tex]

[tex]\implies a_n=3n-4[/tex]

Answer:

Step-by-step explanation:

To graph the equation y-2=2/3(x+4), you can follow these steps:

Begin by isolating the y term on one side of the equation. To do this, you can add 2 to both sides of the equation:

y-2+2=2/3(x+4)+2

y=2/3(x+4)+2

Next, you can simplify the right side of the equation by multiplying 2/3 by (x+4):

y=2/3(x+4)+2

y=(2/3)x+(2/3)4+2

y=(2/3)x+8/3+2

y=(2/3)x+14/3

This is the standard form of the equation y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=2/3 and the y-intercept is b=14/3.

To graph the equation, you can use the slope and y-intercept to plot the first point on the graph. The y-intercept is the point where the graph crosses the y-axis, so you can plot the point (0,14/3) on the graph.

From this point, you can use the slope to find the next point on the graph. The slope is the change in y over the change in x, so you can use the slope to find the change in y and the change in x between two points on the graph. For example, you could choose a point that is 1 unit to the right of the y-intercept, or (1,0). The change in y between these two points is (14/3)-0=14/3 and the change in x is 1-0=1. Using the slope, you can find the y-coordinate of the next point on the graph:

y2=y1+m(x2-x1)

y2=14/3+2/3(1-0)

y2=14/3+2/3

y2=20/3

You can repeat this process to plot additional points on the graph. For example, you could choose a point that is 2 units to the right of the y-intercept

Rates, however, differ for specific customers depending on their credit score, loan term, and other factors.

In conclusion, the finance charge formula is as follows:

Finance fee = Balance that is owed. Annual Percentage Rate (APR) / 365 Days in Billing Cycle.

The average cost of an ATV is between $5,000 and $15,000, with a down payment that is often between 10% and 20%.The typical deposit for recreational vehicles is in the range of 10% to 20%. You might need between $500 and $5,000 for the down payment for a UTV that ranges in price from $5,000 to $25,000.

Conventional ATV loans are provided by banks and credit unions for set terms that are typically between three and six years long. The yearly percentage rates are also fixed. Your credit score, the loan period, the cost of the ATV, and the company funding the loan will all have an impact on the APR.

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I need to score 172 in the 14th game to have an average of 152 in 14 games.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

The total score of 12 games is (12×150) = 1800.

Again I scored 156 is the 13th game.

Let I score 'x' in the 14th game.

∴ (1800 + 156 + x)/12 + 1 + 1 = 152.

(1800 + 156 + x)/14 = 152.

(1956 + x)/14 = 152.

1956 + x = 2128.

x = 2128 - 1956.

x = 172.

So, I need to score 172 in order to have an average of 152 for 14 games.

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