In a small town 68% of the people owned television 72% on radio and 12% owned neither television nor radio (1)represent the information on a Veen diagram.
(2)what percentage of the population owned television.​

Answers

Answer 1

Answer:

See attachment for Venn diagram

Percentage of only TV owners is 16%

Step-by-step explanation:

Given

[tex]TV\ Owners = 68\%[/tex]

[tex]Radio\ Owners = 72\%[/tex]

[tex]None = 12\%[/tex]

Required

Represent with a Venn Diagram

What percentage owned television

From the Venn Diagram and In sets theory; we have that

Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None

Represent Radio and TV Owners with y

[tex]Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None[/tex]

Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:

[tex]Total = 68\% - y + 72\%- y + y + 12\%[/tex]

Collect Like Terms

[tex]Total = 68\% + 72\%+ 12\%- y + y - y[/tex]

[tex]Total = 152\% - y[/tex]

In Sets, Total represents 100%; So, we have

[tex]100\% = 152\% - y[/tex]

Make y the subject of formula  

[tex]y = 152\% - 100\%[/tex]

[tex]y = 52\%[/tex]

The percentage of only TV owners is calculated by subtracting y from TV owners

[tex]\%P = 68\% - 52\%[/tex]

[tex]\%P = 16\%[/tex]

In A Small Town 68% Of The People Owned Television 72% On Radio And 12% Owned Neither Television Nor
Answer 2

Answer:

The answer is 90%

Step-by-step explanation:


Related Questions

work out angle pqr please if you know it i willl give brainliest to fastest person

Answers

Answer:

∠PQR =  67.36° (Approx)

Step-by-step explanation:

Given:

PRQ is a right triangle

∠R = 90°

PQ = 13 cm

QR = 5 cm

PR = 12 cm

Find:

∠PQR = ?

Computation:

Using trigonometry application.

SinФ = 12 / 13

SinФ = 0.92

Sin 67.36° = 0.92

So,

∠PQR =  67.36° (Approx)

coordinates of England

Answers

Answer:

52.3555 north

1.1745 west

Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of
hours ten boys watched television over the same period of time.
Which statement correctly compares the measures of center in the two sets of data?
Both the mean and median are greater for Plot A than for Plot B.
* Both the mean and median are greater for Plot B than for Plot A.
Plot A has a greater median than Plot B, but Plot B has a greater mean.
Plot B has a greater median than Plot A, but Plot A has a greater mean.
(It’s not B on edg2020 btw)

Answers

Both the mean and median are greater for plot A than for plot B. This is found by finding the mean and median for each plot and comparing them. Let me know if you need any further explanation!

Answer: Hello I have your Answer

It's A

Step-by-step explanation:

Your welcome

-4-(-1) answer the question

Answers

Answer:

-3

Step-by-step explanation:

Since you are subtracting a negative, it turns positive so it will be.

-4+1

-3

Answer:

-3

Step-by-step explanation:

-4-(-1) = -4 + 1 = -3

Find the area of the shaded region under the standard normal curve. If​ convenient, use technology to find the area. z -2.13 0 A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.13 and 0. The area under the curve between negative 2.13 and 0 is shaded. The area of the shaded region is nothing.​(Round to four decimal places as​ needed.)

Answers

Answer:

The area of the shaded region under the standard normal curve is 0.4834.

Step-by-step explanation:

A random variable X is said to have a normal distribution with mean, µ and variance σ².

Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).

The distribution of these z-variates is known as the standard normal distribution.

Compute the area under the curve between -2.13 and 0 as follows:

[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]

                           [tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]

Thus, the area of the shaded region under the standard normal curve is 0.4834.

Using the normal distribution, it is found that the area of the shaded region is of 0.4833.

In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean. Each z-score has an associated p-value,  which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.The area between two z-scores is the subtraction of their p-values.

In this problem, we want the area between Z = -2.13 and Z = 0.

Z = 0 has a p-value of 0.5.Z = -2.13 has a p-value of 0.0166.

0.5 - 0.0166 = 0.4833

The area of the shaded region is of 0.4833.

A similar problem is given at https://brainly.com/question/22940416

Solve 5(2x + 4) = 15. Round to the nearest thousandth.

Answers

[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]

Answer:

[tex]\huge\boxed{x=-0.5}[/tex]

Step-by-step explanation:

[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]

A patient with diabetes self-injected 5 units of regular insulin and 15 units of NPH insulin at 0800. When should the nurse assess this patient for signs of hypoglycemia?

Answers

Answer:

Hypoglycemia would sign at 1,000

Step-by-step explanation:

We know that a short-acting insulin (Regular insulin) work at last for 2 to 3 hours

Also intermediate acting insulin (NPH) insulin crests in 4 to 10 hours.

So, nurse assess this patient for signs of hypoglycemia 1000 to 1600

Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24

Answers

Answer:

x = -264/35

y = -36/5

Step-by-step explanation:

-6y + 11y = -36

-4y + 7x = -24

Solve for y in the first equation.

-6y + 11y = -36

Combine like terms.

5y = -36

Divide both sides by 5.

y = -36/5

Plug y as -36/5 in the second equation and solve for x.

-4(-36/5) + 7x = -24

Expand brackets.

144/5 + 7x = -24

Subtract 144/5 from both sides.

7x = -264/5

Divide both sides by 7.

x = -264/35

Answer: -264/35

Step-by-step explanation:

i did my work on a calculator

A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics expert in the field, to analyze its process. Specifically, the business has run 20 random samples of size 5 over the past month and has determined the mean of each sample.
a. Determine the estimate of the mean when the process is in control.
b. Assuming the process standard deviation is .50 and the mean of the process is the estimate calculated in part a, determine the Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process.
c. Explain the results to the vice-president of the mattress manufacturer focusing on whether, based on the results, the process is in or out of control.
Sample no. Mean of Sample
1 95.72
2 95.44
3 95.40
4 95.50
5 95.56
6 95.72
7 95.60
8 95.24
9 95.46
10 95.44
11 95.80
12 95.20
13 94.82
14 95.78
15 95.18
16 95.32
17 95.08
18 95.22
19 95.04
20 95.

Answers

Answer:

Answer to question a = 95.4

Answer to question b = UCL = 96.07

LCL = 94.73

Answer to question c = Process is still in control

Step-by-step explanation:

a. The computation of estimate mean is as shown below:-

= 95.4

b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-

= 95.4 + 0.67082

= 96.07

= 95.4 - 0.67082

= 94.73

c. The explanation is shown below:-

From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,

The Process is still in control

f(x)=3x+5 and g(x)=4x2-2 h(x)=x2-3x+1 Find f(x)+g(x)-h(x).

Answers

Answer:

f(x)+g(x)-h(x) = 3x² + 6x + 2

Step-by-step explanation:

f(x) = 3x + 5

g(x) = 4x² - 2

h(x) = x² - 3x + 1

f(x)+g(x)-h(x) means subtract h(x) from the sum of f(x) and h(x)

f(x)+g(x)-h(x) = 3x + 5 +( 4x² - 2) - (x² - 3x + 1)

Remove the brackets

That's

f(x)+g(x)-h(x) = 3x + 5 + 4x² - 2 - x² + 3x - 1

Group like terms

We have

f(x)+g(x)-h(x) = 4x² - x² + 3x + 3x + 5 - 2 - 1

Simplify

We have the final answer as

f(x)+g(x)-h(x) = 3x² + 6x + 2

Hope this helps you

Hope this helps you

Select the correct answer.

Answers

Answer:

B

Step-by-step explanation:

With limits, the first thing one should always try is direct substitution. Therefore, let's try that.

[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) \\= (\frac{(1)^2+1}{(1)+1}+(1)^2+3) \\=\frac{2}{2}+1+3\\ =1+4=5[/tex]

Therefore:

[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) =5[/tex]

If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution. 1- What percentage of a cucumber give the crop amount between 778 and 834 kg? 2- What the probability of cucumber give the crop exceed 900 kg ?

Answers

Answer:

a

   The  percentage is

            [tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]

b

   The probability is  [tex]P(Z > 2.5 ) = 0.0062097[/tex]

Step-by-step explanation:

From the question we are told that

        The  population mean is  [tex]\mu = 800[/tex]

        The  variance is  [tex]var(x) = 1600 \ kg[/tex]

        The  range consider is  [tex]x_1 = 778 \ kg \ x_2 = 834 \ kg[/tex]

         The  value consider in second question is  [tex]x = 900 \ kg[/tex]

Generally the standard deviation is mathematically represented as

        [tex]\sigma = \sqrt{var (x)}[/tex]

substituting value

        [tex]\sigma = \sqrt{1600}[/tex]

       [tex]\sigma = 40[/tex]

The percentage of a cucumber give the crop amount between 778 and 834 kg  is mathematically represented as

       [tex]P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )[/tex]

    Generally  [tex]\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)[/tex]

So

      [tex]P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )[/tex]

      [tex]P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)[/tex]

From the z-table  the value for  [tex]P(z_1 < 0.85) = 0.80234[/tex]

                                            and [tex]P(z_1 < -0.55) = 0.29116[/tex]  

So

             [tex]P(x_1 < X < x_2 ) = 0.80234 - 0.29116[/tex]

             [tex]P(x_1 < X < x_2 ) = 0.51118[/tex]

The  percentage is

            [tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]

The probability of cucumber give the crop exceed 900 kg is mathematically represented as

             [tex]P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )[/tex]

substituting values

             [tex]P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )[/tex]

             [tex]P(X > x ) = P(Z >2.5 )[/tex]

From the z-table  the value for  [tex]P(Z > 2.5 ) = 0.0062097[/tex]

 

Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle? ​

Answers

Answer:

7.5 cm²

Step-by-step explanation:

Dimensions of the large ∆:

[tex] base (b) = 3cm, height (h) = 9cm [/tex]

[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]

Dimensions of the small ∆:

[tex] base (b) = 2cm, height (h) = 6cm [/tex]

[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]

Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²

What is the solution of 3(x + 4) = -12 ? Group of answer choices 3 0 8 -8

Answers

Answer:

Step-by-step explanation:

3(x + 4) = -12

3x+12 = -12

3x= -12-12

3x= -24

x = -24/3

x= -8

Answer:

x = -8

Step-by-step explanation:

3(x+4) = -12

3*x + 3*4 = -12

3x + 12 = -12

3x = -12 - 12

3x = -24

x = -24/3

x = -8

Check:

3(-8+4) = -12

3*-4 = -12

can you please help ?

Answers

Answer:

69

Step-by-step explanation:

The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.

We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.

[tex]\frac{5(x)}{2} -6[/tex]

[tex]\frac{5(30)}{2}-6[/tex]

[tex]\frac{150}{2}-6[/tex]

[tex]75-6[/tex]

[tex]69[/tex]

Simplify to create an equivalent expression. 4(-15-3p)-4(-p+5)

Answers

Answer:

- 8p - 80

Step-by-step explanation:

Given

4(- 15 - 3p) - 4(- p + 5) ← distribute both parenthesis

= - 60 - 12p + 4p - 20 ← collect like terms

= - 8p - 80

Answer:

-8p -80

Step-by-step explanation:

4(-15-3p)-4(-p+5)

Distribute

-60 -12p +4p -20

Combine like terms

-60-20 -8p +4p

-80-8p

-8p -80

Help Quick Please. Will give brainliest.

Answers

Answer:

72[tex]\sqrt{3}[/tex] units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = ST = a = 12 and h = RS

To calculate RS use the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , thus

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )

RS = 12[tex]\sqrt{3}[/tex]

Thus

A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²

A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?

Answers

Answer:

8.8 pounds

Step-by-step explanation:

Given the following :

Combined weight loss which occurred within a week = 28 kg

Number of days in a week = 7 days

1 kilogram (kg) = 2.2 pounds

Combined weight loss in pounds that occurs within a week:

Weight loss in kg × 2.2

28kg * 2.2 = 61.6 pounds

Assume weight loss occurred at a constant rate :

Weight lost by the group per day :

(Total weight loss / number of days in a week)

(61.6 pounds / 7)

= 8.8 pounds daily

Answer:

88

Step-by-step explanation:

Found the answer and I am doing the quiz rn lel

a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years

Answers

Answer:

1,267 wolves

Step-by-step explanation:

Initial population of wolf = 850 wolves

If the wolves increases by 7% each year, yearly increment will be 7% of 850

=  7/100 * 850

= 7*8.5

= 59.5 wolves.

This shows that the wolves increases by 59.5 each year.

After 7 years, increment will be equivalent  to 59.5 * 7 = 416.5

The wolf population after 7 years = Initial population + Increment after 7 years

= 850 + 416.5

= 1266.5

≈ 1267 wolves

Hence the population of the wolves after 7 years is approximately 1,267 wolves

Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be

a. 0.25
b. 0.3333
c. 0.42
d. 0.48

Answers

Answer:

The correct option is (b) 0.3333.

Step-by-step explanation:

The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].

The standard error is given as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]

Compute the standard deviation of the sample mean as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

    [tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]

Thus, the standard deviation of the sample mean is 0.3333.

Write "six and thirty-four thousandths" as a decimal

Answers

Answer:

6.034

Step-by-step explanation:

6 is a whole number.

.034 because it is 34 thousandths, not 34 hundredths.

Which is the solution to the inequality?
2 3/5 <b-8/15​

Answers

Answer:

3 2/15 <b

Step-by-step explanation:

2 3/5 <b-8/15​

Add 8/ 15 to each side

2 3/5 + 8/ 15 <b-8/15​ + 8/15

2 3/5 + 8 /15 <b

Get a common denominator

2 3/5 *3/3 + 8/15

2 9/15 + 8/15 < b

2 17/15 < b

2 + 15/15 + 2 /15 < b

3 2/15 <b

Answer:

B > 3 2/15

Step-by-step explanation:

Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide

Answers

Answer:

150,000

Step-by-step explanation:

1 m = 100 cm

260 m = 260 * 100 cm = 26000 cm

15 m = 15 * 100 cm = 1500 cm

area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2

area of 1 tile = 26 cm + 10 cm = 260 cm^2

number of tiles needed = 39,000,000/260 = 150,000

Answer: 150,000 tiles

Correct answer is 150000 tiles. Hope this helps ya

The following shape is based only on squares, semicircles, and quarter circles. Find the area of the shaded part.

Answers

Answer:

this? hope it helps ........

Answer:

The answer is area=32pi-64 and the perimeter is 8pi

Step-by-step explanation:

Jullian measures the distance he drives to work each day using the odometer on his car, which measures distance in miles, accurate to the nearest tenth of a mile. Using that measurement, he claims that the exact distance he drives to work is 11.7 miles. Use complete sentences to explain why jullian is incorrect

Answers

Answer:

Kindly check explanation

Step-by-step explanation: Jullian's claim that the distance she drives to work is exactly 11.7miles is incorrect because, in other to record or get the exact result of a certain calculation such as Jullian's Distance, the value of the distance obtained will not be approximated or rounded. In this scenario, Distance was to the nearest tenth of a mile, thereby altering the true outcome of the calculation.

The word exact means that what is stated is very precise and does not fall below or above in any respect. However, a number whose accuracy is to the nearest tenth of a mile, violates this assertion.

Solve this system of equations:

3x - 2y = -8
y=3/2x - 2

PLEASE WRITE THE STEPS

Answers

Hey there! I'm happy to help!

We see that y is equal to 3/2x-2. We can replace the y in the first equation with 3/2x-2 because they are equal and we can solve for x.

3x-2(3/2x-2)=-8

We use the distributive property to undo the parentheses.

3x-3x+4=-8

We combine like terms.

4=-8

We see that since there is no x anymore, there cannot be a solution. We have no x value to solve for the y value either, so there is no solution to this system of equations.

Have a wonderful day! :D

Which of the following is a correct interpretation of the expression -4 - (-7)?

Answers

Answer:

D

Step-by-step explanation:

So we have the expression:

[tex]-4-(-7)[/tex]

First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:

[tex]-4-(-7)\\=-4+7[/tex]

When adding on the number line, we move to the right.

Therefore, the correct interpretation is the value 7 digits to the right of -4.

D is the correct answer.

Answer:

D.  the number that is 7 to the right of -4 on the number line

Step-by-step explanation:

interpret -4 - (-7)

=  -4 +7

therefore

the number that is 7 to the right of -4 on the number line

so its D.

Jilk Inc.'s contribution margin ratio is 62% and its fixed monthly expenses are $45,000. Assuming that the fixed monthly expenses do not change, what is the best estimate of the company's net operating income in a month when sales are $132,000?

Answers

Answer: $ 36,840.

Step-by-step explanation:

contribution margin=62% =0.62

fixed monthly expenses = $45,000

Sales =  $132,000

We assume that the fixed monthly expenses do not change.

Then, company's net operating income = (contribution margin×Sales )-fixed monthly expenses

=$( (0.62×132000)-45000 )

= $ (81840-45000)

= $ 36,840

Hence, the best estimate of the company's net operating income in a month when sales are $132,000 is $ 36,840.

5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.​

Answers

Answer:

  an isosceles right triangle

Step-by-step explanation:

The square of the length of a side can be found from the distance formula:

  d^2 = (x2-x1)^2 +(y2-y1)^2

The square of the length of WX is ...

  WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74

The square of the length of XY is ...

  XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148

The square of the length of YW is ...

  YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74

The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.

You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.

Answers

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

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