The students at a school assembly
were divided into 4 equal groups.
There were 73 students in each
group. Write and solve an equation
to determine the number of students
that were at the assembly.

Answer:

Using the inclusion and exclusion principle, we can calculate the percentage of members who play all three sports as follows:

60% of members play Tennis, 50% of members play Cricket, and 70% of members play Football.

Therefore, 60% + 50% + 70% = 180% of members play at least one of the sports.

However, this count includes members who play more than one sport, so we need to subtract out the members who play two sports and add back in the members who play all three sports.

20% of members play Tennis and Cricket, 40% of members play Cricket and Football, and 30% of members play Football and Tennis.

Therefore, 20% + 40% + 30% = 90% of members play at least two sports.

Subtracting this number from the total number of members who play at least one sport gives us 180% - 90% = 90% of members who play at least one sport but not all three sports.

To find the number of members who play all three sports, we need to subtract this number from the total number of members who play at least one sport:

180% - 90% = 90% of members who play at least one sport but not all three sports

180% - 90% = 90% of members who play all three sports

Therefore, according to the inclusion and exclusion principle, 90% of members play all three sports.

If someone claimed that 20% of members play all three sports, this would be incorrect based on the calculations using the inclusion and exclusion principle. The correct number of members who play all three sports is 90%, not 20%. This can be verified by using the given information about the percentage of members who play each individual sport and the percentage of members who play two sports in combination.

To clarify, the inclusion and exclusion principle states that to find the number of elements in a union of sets (in this case, the number of members who play at least one sport), we can add the number of elements in each set (the percentage of members who play each individual sport) and then subtract the number of elements that are counted multiple times (the percentage of members who play two sports in combination). We then add back in the elements that were subtracted out in the previous step (the percentage of members who play all three sports).

Using this principle, we were able to calculate that 90% of members play all three sports, rather than the 20% claimed by someone.

Step-by-step explanation:

Answer:

Only X = X - ( (X∩Y - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only X = 600 - ( (200-200) + 200 + ( 300-200) )

Only X = 600 - (0 + 200 + 100)

Only X = 600 - (300)

Only X = 300

Only Y = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (X∩Y - X∩Y∩Z) )

Only Y = 500 - ( (400-200) + 200 + ( 200-200) )

Only Y = 500 - (200 + 200 + 0)

Only Y = 500 - (400)

Only Y = 100

Only Z = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only Z = 500 - ( (400-200) + 200 + ( 300-200) )

Only Z = 500 - (200 + 200 + 100)

Only Z = 500 - (500)

Only Z = 200

Step-by-step explanation:

Answer:

6x^2+47

Step-by-step explanation:

You simple have to "plug" g(x) into f(x) for x.

f(x)=6x+11

f(g(x))=6(x^2+6)+11

f(g(x))=6x^2+36+11

f(g(x))=6x^2+47

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{2}}}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{6}(x-\stackrel{x_1}{2})\)

Answer:  y-2 = -6 (x-2)

Step-by-step explanation: Point slope form is this equation:

y-y1 = m (x-x1)

y1 is 2 because (2,2) ; The left 2 is x1 and the right 2 is y1.

(-1,20); The -1 is x2 and the 20 is y2.

If you use the equation above it helps a lot. I hope this helps you! :)

Answer:

48.50 dollars.

Step-by-step explanation:

The collector has a total of 224 coins but 74 of them are 25 cents coins. So, in order to find the number of 20-cent coins we're going to subtract the number of 25-cent coins from the total.

Number of 20-cent coins = 224 - 74 = 150.

Thus, the collector has 150 20-cent coins and 74 25-cent coins for a total of 224 coins.

Now, to know the total value of the collection we need to multiply the value of the coins by the number of coins there are of this value (we are going to do it with the 20-cent and the 25-cent coins) and then sum up our results.

Total value = 74(25) + 150 (20) = 1850 + 3000 = 4850 cents.

So the total value is 4850 cents, we know that each dollar has 100 cents so, to express this number in dollars we are going to divide it by 100 and thus we have that the total value of the collection is 48.50 dollars.

Since every year, the annual salary increases by $4,500, then in the second year the employee earns:

In the third year the employee earns:

In the fourth year, the employee earns:

In the fifth year, the employee earns:

In the sixth year, the employee earns:

In the seventh year, the employee earns:

Finally, in the eighth year, the employee earns:

Therefore, during eight years with the company the employee earned:

Answer: Third option $510,000.

Answer:

Step-by-step explanation:

easier and faster way than above:

384000 (that is, 48,000 * 8) base

384000 + 4500 (salary) * (0 + 1 + 2 + 3 + 4 +5 +6 +7) (that's every day - 1) =

384000 +4500 * (28) =

384,000 + 126000 = 510,000

Answer:

A

Step-by-step explanation:

A because a markup means the price times the number given which was 32% and 32% is the same as 0.32.

Answer:

your anser is 14080 yards

Step-by-step explanation:

u convert

Answer:

i belive its 34% becouse you are saveing 170 dollars

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The actual dimensions of the patio are 20 feet by 16 feet.

The scale factor is 1 inch to 4 feet,

This means that 1 inch on the scale drawing represents 4 feet in reality.

So the dimensions of the scale drawing are:

20 feet x (1/4) = 5 inches (length on scale drawing)

16 feet x (1/4) = 4 inches (width on scale drawing)

The area of the actual patio is:

= 20 feet x  16 feet

= 320 square feet

The area of the scale drawing is:

= 5 inches x 4 inches

= 20 square inches

The ratio of the area of the scaled drawing to the actual area of the patio is: 20 square inches : 320 square feet

To simplify this ratio, we need to convert both values to the same units.

Converting the area of the scale drawing to square feet:

= 20 square inches x  (1/144) square feet/square inch

= 0.1389 square feet

So the ratio of the area of the scaled drawing to the actual area of the patio is:

0.1389 square feet : 320 square feet

Or, in simplified form:

1 : 2306.56

Thus,

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

Learn more about scale factors here:

https://brainly.com/question/29464385

#SPJ1

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

We can call the smallest number '2n'

The next number can be '2n + 2' and the last number can be '2n + 4'

So, 2n + 2n + 2 + 2n + 4 = 114

Simplify this to get:

6n + 6 = 114

- 6 from both sides

6n = 108

/ 6 on both sides

n = 18

2(18) = 36

It would be 36

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

Read more about measure of centres

brainly.com/question/15214370

#SPJ1

Answer:

The Clown grabbed 126 balloons

Step-by-step explanation:

Answer:

61

  ^

  ^

  ^                                                                 65                                 73

  ^                                      79                        ^                                  ^

  ^                                      ^                           ^                                  ^

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

  Test 1                            Test 2                   Test 3                       Test 4

Answer: the test doesn't explain the order it was taken or dates. So it can be misleading

Step-by-step explanation:

The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

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

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ9

The first three non zero terms in the Taylor polynomial approximation to the given DE is y(t) = t + t²/2 -(3/2)t³ .

In the question ,

it is given that ,

the differential equation is

y'' + 9y + 5y³ = Cos(10t)   ...equation(1)

y(0) = 0, y'(0) = 1

for y = 0 , the differential equation is

y''(0) + 9y(0) + 5{y(0)}³ = Cos90)

y''(0) + 9 + 5 = 1 ;

y''(0) = 1.

differentiating equation(1) with respect to "t" , we have

y''' + 9y' + 15y²y' = -10Sin(10t)

y'''(0) + 9y'(0) + 15{y(0)}².y'(0) = -10Sin(0)

y'''(0) + 9 + 0 = 0

y'''(0) = -9

The Taylor series is given by

y(t) = y(0) + y'(0)t + 1/2.y''(0)t² + 1/3!.y'''(0)t³ + ....

Now substituting the values of y(0) , y'(0) , y''(0) , y'''(0) , we have

y(t) = 0 + 1.t + 1/2.t² + 1/6.(-9)t³ + ....

= t + t²/2 - 3/2.t³ + ...

Therefore , the first three terms are t , t²/2 , -3/2.t³   .

Learn more about Taylor Series here

https://brainly.com/question/13163878

#SPJ4

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

Learn more about angle of depression here:

https://brainly.com/question/13514202

#SPJ1

Answer:

The value of dz/dx is 27x^2 + 2y

Step-by-step explanation:

We have to given the function z = 9x^3 - 4y^2 + 2xy and we have to find the partial derivative of the given function. In the given function, we have to find partial derivation with respect to x. Therefore, the other values will be considered as constant and during the partial derivation, the constant value will become zero.

\(z=9x^3-4y^2+2xy \\\frac{dz}{dx} = 9\times 3x^{3-1} -0 +2y \\\frac{dz}{dx} =27x^2 + 2y \\\)

Therefore, the value of dz/dx is 27x^2 + 2y

Answer:

I hope this will be helpful for you.

Answer:

its samanthas ocupation

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

I just took the test and i got this question right with that answer.

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

Learn more about Probability at:

https://brainly.com/question/24756209

#SPJ1

Answer:

AE=19

EAD=34

Step-by-step explanation:

Look at the image for step by step help.

-Hope this helped

Answer:

Mean = 1.73 mm

Standard deviation = 0.0698 mm

Step-by-step explanation:

Given:

Sample size, n = 40

Mean, u = 6.803

Standard deviation = 0.275

a) Given that one inch is 2.538 centimeters, to find the mean in millimeters we have:

\( 6.803 * \frac{1}{100} \)

Converting to cm, we have:

\( 6.803 * \frac{1}{100} * 2.538 = 0.173 cm\)

Converting to mm, we know 1cm = 10 mm,

0.173 * 10 = 1.73 mm

b) Given that one inch is 2.538 centimeters, to find the standard deviation in millimeters we have:

\( 0.275 * \frac{1}{100} \)

Converting to cm, we have:

\( 0.275 * \frac{1}{100} * 2.538 = 0.00698 cm\)

Converting to mm, we know 1cm = 10 mm,

0.00698 * 10 = 0.0698mm

In this exercise we have to use the knowledge of statistics to calculate the car production, so we have to:

Given the following information, we have:

A) Find the convertion to the mean in milimeters, will be:

\(6.803*(1/100)*2.538=0.173 cm\\=1.73 mm\)

B) Find the convertion to the stardard deviation in milimeters, will be:

\(0.275*(1/100)*2.538=0.00698\\=0.0698 mm\)

See more about statistics at brainly.com/question/10951564

Answer:

147

Step-by-step explanation:

V = h * S = h * Pi R^2 = h * Pi * d^2/4 = 7.5 * 3.14 * 25 / 4 = 147.188

i would go with either a or b

Answer:

5 miles

Step-by-step explanation:

15-10=5

hope it helps

Answer:

5 miles

Step-by-step explanation:

15 - 10 = 5

Answer:

rational

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

The most reasonable temperature for a snowy day is given as follows:

C. -6°C

Considering that it snows, the temperature is either negative or very low positive, as snow only happens on temperatures close to freezing (like 2º C) or negative.

17ºC and 26ºC are far from cold enough to generate snow, hence the most reasonable temperature for a snowy day is given as follows:

C. -6°C

More can be learned about snow at https://brainly.com/question/18520972

#SPJ1