What is the value of x in the solution to the system of linear equations? y=3x+2
y=x-4

Answer:

  £216

Step-by-step explanation:

The total prize will be the sum of the divisions of the prize. The difference of those divisions is given.

__

Let P represent the value of the prize. The 1:11 ratio of the parts tells us there are 1 +11 = 12 total parts, and their ratio is P/12 : 11P/12. The sum of these divisions is the whole prize:

  P/12 +11P/12 = 12P/12 = P

The difference of the two divisions of the prize is ...

  11P/12 -P/12 = £180

  10P = £2160 . . . . . . . . multiply by 12 and simplify

  P = £216 . . . . . . . . divide by 10

The total prize is £216.

_____

Additional comment

The divisions of the prize are

  £216/12 = £18  and  11×£18 = £198

The sum of those divisions is the total prize: £18 +198 = £216.

The total price (prize)the difference between the shares is £180 is £216.

Let's represent the total price as "P." According to the information given, the price is divided into a ratio of 1:11.

The total number of parts in the ratio is 1 + 11 = 12 (1 part for the first share and 11 parts for the second share).

Let the first share be "x" and the second share be "11x" (since the ratio is 1:11).

Now, the difference between the shares is £180:

11x - x = £180

Simplifying:

10x = £180

Now, divide both sides by 10 to find the value of "x":

x = £180 / 10

x = £18

Now, we can find the total price "P" by adding the shares together:

P = x + 11x

P = £18 + £198

P = £216

So, the total price (prize) is £216.

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Answer:

36 Minutes

Step-by-step explanation:

You have to find the lowest common multiple which you can do by listing the times tables for each number.

9,18,27,36,45,54

12,24,36,48,60,72

and finding the lowest multiple that matches.

Both the train will meet after 36 minutes.

Thus, both the train will meet after 36 minutes.

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Answer:

LN = 64 units

Step-by-step explanation:

Given M lies on LN, so LN = LM + MN --------------(1)

LN = 12x + 16

LM = 10x + 8

MN = 5x - 4

Substituting the values in equation 1, we get:

12x + 16 = (10x + 8) + (5x - 4)

12x + 16 = 15x + 4

15x - 12x = 16 -4

3x=12

Therefore x=4

LN= 12(4) + 16 = 64 units

The inequality described can be written as:

y < 3x + 2.

First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:

y < line.

The linear equation is of the form:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:

[tex]a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3[/tex]

And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:

y < 3x + 2.

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Answer:

I think m is 70 and n is 40 because I did a bunch of adding and subtracting

Answer:

the median will be 200.

the mode will be 402 n 398.

the mean will be 400.

[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]

[tex] \sf \red{1. \: (3x - x) (x + 2) = 0}[/tex]

[tex] \sf \red{2. \: (q + 2)^{2} - 40}[/tex]

[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]

2.soln:

(q + 2)² - 40

=> (q)² + 2.q.2 + (2)² - 40

=> q² + 4q + 4 - 40

=>q² + 4q - 36

Here, a = 1, b = 4 and c = - 36

By, using Quadratic formula

See the attachment

Answer:

oh ok. So, first, you get the equation in the form y=ax2+bx+c. Next, you calculate -b / 2a. This is the x-coordinate of the vertex. Then finally, you plug in the value of -b / 2a into the equation into the x variable and solve for the y variable. This is the coordinate of the vertex.

Step-by-step explanation:

Hope this helps!

The volume of a tennis ball is about 8.65 cubic inches

The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

From the question, we are to determine the volume of a tennis ball

From the given information,

The circumference of a tennis ball is 8 inches

That is,

C = 2πr (C is circumference)

8 = 2πr

∴ r = 8/2π

r = 4/π inches

This the radius of a tennis ball

Now, for the volume of a tennis ball

Using the formula for calculating the volume of a sphere

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

Then, the volume of a tennis is

[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]

[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]

[tex]V = \frac{256}{3\pi^{2}}[/tex]

V = 8.64607 cubic inches

V ≅ 8.65 cubic inches

Hence, the volume of a tennis ball is about 8.65 cubic inches

b. To find the amount of space within the cylinder not taken up by the tennis balls

First, we will calculate the volume of the cylinder

Using the formula for calculating the volume of a cylinder

V = πr²h

Where V is the volume

r is the radius

and h is the height

From the given information,

r = 1.43 inches

h = 8 inches

Putting the parameters into the formula, we get

V = π × 1.43² × 8

V = 16.3592π

V = 51.39 cubic inches

This is the volume of the cylinder

Now, for the amount of space within the cylinder not taken up by the tennis balls

Since there are three tennis balls,

The amount of space not taken up will be

51.39 cubic inches - 3(8.65 cubic inches)

51.39 cubic inches - 25.95 cubic inches

= 25.44 cubic inches

Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches

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Answer:

4

Step-by-step explanation:

Every number is divided by 3

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the missing number in the sequence

[tex]\star~\mathrm{324,108,36,12,(~~)}[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Since every number here is divided by 3, we divide 12 by the common ratio, 3:

[tex]\mathrm{12\div3}[/tex]

[tex]\star~\star~\mathrm{4}\star~\star[/tex]

Hope it helps you out! :)

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

The data points that fall within the mean absolute deviation are 2.9 and 3.1.

The mean absolute deviation is the mean average distance between every data point and the mean of the data set.

From the information given:

The mean absolute deviation is:

= (|5.3 - 2|)/1

= 3.3

Thus, the data points that fall within the mean absolute deviation are 2.9 and 3.1.

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As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.

Answer:

white chocolates = 3

milk chocolates = 8

ratio= 3:8

[tex] \frac{3}{8} [/tex]

0.375

Answer:

10

Step-by-step explanation:

Fish can't drown.

Correlation analysis is meant to determine the strength of a linear

relationship between variables.

The complete question is as below:-

Which of the following statements is true of the correlation analysis? The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables. The larger the correlation coefficient, the weaker the association between two variables. The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero. The Pearson correlation coefficient measures the degree of linear association that ranges from 1.0 to 10.0. The Pearson correlation coefficient measures the degree of linear association between three variables.

Correlation analysis is a test to determine the presence and or amount of relationship that exists between variables.

During a hypothesis test aimed at determining the existence of a correlation between variables, the null and alternative hypotheses are as follows;

The null hypothesis, H₀: There are no relationships between the variables

H₀: r = 0

The alternative hypothesis, Hₐ: The variables have an association

Hₐ: r ≠ 0

Therefore, the true statement of the correlation analysis is; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.

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Answer:

124

.........................

Answer:

x = 144

Step-by-step explanation:

Angle sum of heptagon = 900

5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144

Answer:

Each person get 4 slice of pizza and 2 is remaining

Answer:

Angle AED: 40
Angle BEC: 105

Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40

2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.

62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.

The distance to the earth’s horizon from point P is 281.6 miles

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

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Answer:

Answer above is wrong. See answer below.

Step-by-step explanation:

The series is a convergence series and the sum of the series is -8/3

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

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A. Four ways to solve a quadratic equation

---Factoring

---Completing the square

---Quadratic equation

---Graphing

B. Solve the equation by completing the square

x^2 - 4x - 11 = 0

x^2 - 4x = 11

x^2 - 4x + 4 = 11 + 4

(x - 2)^2 = 15

x - 2 = +/- 15

x - 2 = 15 || x = 17

x - 2 = -15 || x = -13

C. Solve the equation using the quadratic formula

Quadratic formula = [tex]\frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]

Equation = 2x^2 + 16x + 24 = 0

a = 2

b = 16

c = 24

[tex]\frac{-16 +/- \sqrt{16^2 - 4(2)(24)} }{2(2)}[/tex]

[tex]\frac{-16 +/- \sqrt{256 - 192} }{4}[/tex]

[tex]\frac{-16 +/- \sqrt{64} }{4}[/tex]

[tex]\frac{-16 +/- 8 }{4}[/tex]

[-16 + 8] / 4 = -2

[-16 - 8] / 4 = -6

x = -6, -2

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\frac{8+x}{12+x} =\frac{80}{100} =\frac{4}{5} \\40+5x=48+4x\\5x-4x=48-40\\x=8[/tex]

so she wins next 8 consecutive games to reach winning percentage of 80%.

let she loses next y games to reach winning percentage of 50 %.

[tex]\frac{16}{12+8+y} =\frac{50}{100} =\frac{1}{2} \\\frac{16}{20+y} =\frac{1}{2} \\32=20+y\\y=32-20=12y=12[/tex]

Hence she loses next 12 games to reach winning percentage of 50 %.

The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9

Find the mean of the data set

= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10

= 335 / 10

= 33.5

Mean deviation of each set;

38 - 33.5 = 4.5

48 - 33.5 =14.5

25 - 33.5 = -8.5

35 - 33.5 = 1.5

33 - 33 .5 = -0.5

37 - 33.5 = 3.5

32 - 33.5 = -1.5

34 - 33.5 = 0.5

23 - 33.5 = -10.5

30 - 33.5 = -3.5

Absolute deviation of each value

|4.5| = 4.5

|14.5| = 14.5

|8.5| = 8.5

|1.5| = 1.5

|-0.5| = 0.5

|3.5| = 3.5

|-1.5| = 1.5

|0.5| = 0.5

|-10.5| = 10.5

|-3.5| = 3.5

Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5

= 49

Mean absolute deviation = Total absolute deviation / mean

= 49/10

= 4.9

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Answer:

-1/2

Step-by-step explanation:

It mentions that the x-intercept is equal to twice the y-intercept.

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

Let :

⇒ x-intercept = (2a, 0)

⇒ y-intercept = (0, a)

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

Slope formula :

m = y₂ - y₁ / x₂ - x₁

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

Solving :

⇒ m = a - 0 / 0 - 2a

⇒ m = a / -2a

⇒ m = -1/2

Answer:

3 sides

Step-by-step explanation:

If the interior angle measures 60 degrees, this means the exterior angle measures 120 degrees.

The exterior angle of a regular polygon is given by 360/n, where n is the number of sides, so setting this equal to 120, we get that n=3 sides

The statements that are true about the given points on the line are; Options B, C and D

A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.

Let us check each of the given options;

A) There are exactly two planes that contain points A, B, and F;

If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.

Since we can't make two planes with them, then the statement is false.

B) There is exactly one plane that contains points E, F, and B;

Due to the same reasoning in part A, the statement is true assuming the points are not collinear.

C) The line that can be drawn through points C and G would lie in plane X;

The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.

D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.

E) The only points that can lie on plane Y are points E and F.

This statement is false because infinite points can lie on a plane.

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No, to be parallel the two given angles would need to be the same(corresponding angles)

The two lines are not parallel.

Answer: Exponential

After plotting the points as shown in the image, it is obvious they follow an exponential trend.