Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets than student tickets
to the fall play. If the class collected $840 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets

Answer:

hey, how you're day going

Step-by-step explanation:

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Explanation:

For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.

One pair of such angles is A and C

A+C = 180

x+y = 180 is one equation to form

The other pair of supplementary angles is B and D

B+D = 180

y-45+2x+15 = 180

2x+y-30 = 180

2x+y = 180+30

2x+y = 210 is the other equation to form

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So the system of equations we have is

[tex]\begin{cases}x+y = 180\\2x+y = 210\end{cases}[/tex]

Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.

We end up with -x = -30 which solves to x = 30

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Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y

Let's say we picked on the first equation

x+y = 180

30+y = 180

y = 180-30

y = 150

Or we could pick on the second equation

2x+y = 210

2(30) + y = 210

60+y = 210

y = 210-60

y = 150

Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.

Answer:

the union of l and m is minus 1,1,2,4,5,7,8.....and the intersection of l and m is 1.......

Answer:

Individual is represented by a single point

Step-by-step explanation:

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

?

Step-by-step explanation:

Answer:

Dependent event

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Step-by-step explanation:

Given

[tex]Total = 49[/tex]

[tex]Red = 5[/tex]

Solving (a): Are the events dependent?

Yes, they are.

When the first red candy is selected and eaten, the total number of candies reduced to 48 and the number of red candies also reduced to 4.

So, the probability of selecting a 2nd candy is dependent on the first candy selected.

Solving (b): P(Red = 2)

This is calculated as:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

The first selection has the following probability:

[tex]P(Red) = \frac{Red}{Total}[/tex]

[tex]P(Red) = \frac{5}{49}[/tex]

The second selection has the following probability:

[tex]P(Red|Red) = \frac{Red - 1}{Total - 1}[/tex]

[tex]P(Red|Red) = \frac{5 - 1}{49 - 1}[/tex]

[tex]P(Red|Red) = \frac{4}{48}[/tex]

So, we have:

[tex]P(Red = 2) = P(Red) * P(Red | Red)[/tex]

[tex]P(Red = 2) = \frac{5}{49} * \frac{4}{48}[/tex]

Reduce fraction

[tex]P(Red = 2) = \frac{5}{49} * \frac{1}{12}[/tex]

Multiply

[tex]P(Red = 2) = \frac{5}{588}[/tex]

Answer: A: 22, 33, 45.5, 56, 59

Step-by-step explanation:

The minimum is the lowest number in the data, in this case, it was 22.

Q1 is the median of the lower quartile range, anything below the median of the overall data.

Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).

Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.

Maximum is the highest number in the data set, in this case, it was 69.

Hope this helps!

Answer:

Step-by-step explanation:

Answer:

7yz

Step-by-step explanation:

You can take 7yz common from all the terms in the given expression

Answered by GAUTHMATH

Answer:

17.5ml- of 10 percent solution, 17.5ml- of 20 percent solution

Step-by-step explanation:

35:100*15=5.25- ml of alkali in the base solution

Suppose we need x ml of 10 percents solution and 35-x - of 20 percents.

Then The quantity of alkali in the first one (10 percents) is x/100*10=0.1x

when in the second one we have (35-x)/100*20= 7-0.2x of alkali

0.1x+7-0.2x=5.25

7-0.1x= 5.25

0.1x=1.75

x=17.5- 0f 10 percents

35-17.5=17.5 - of 20 percents

Answer:

400 :D

Step-by-step explanation:

Answer:

i thank the ans id 450

Step-by-step explanation:

Answer:

7/3 is the answer

Step-by-step explanation:

Answer:

(a) No solution

(b)

[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]

(c)  [tex](-6,1)[/tex]

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Solution to p(x) and f(x)

Curve p(x) and line f(x) do not intersect.

So, there is no solution to the pair of p(x) and f(x)

Solving (b): Two solutions to f(x)

This means that we select any two point on straight line f(x)

From the line of f(x), we have:

[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]

Solving (c): Solution to p(x) = g(x)

Here, we write out the point of intersection of p(x) and g(x)

From the graph, the point of intersection is: [tex](-6,1)[/tex]

Answer:

the answer to the question is a:-3

Graph is attached below ;

Answer:

Unit rate = 12 computers per day

Step-by-step explanation:

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

That is ; the gradient ;

Slope = change in y / change in x

Slope = (y2 - y1) / (x2 - x1)

y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3

Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12

Slope = 12

Unit rate = 12 computers per day

Answer:

3 times 10 ^ 9

Step-by-step explanation:

3 × 10 ^ 9 = 3000000000

Answer:

Step-by-step explanation:

Given,

[tex] {25x}^{2} - \frac{1}{49} [/tex]

[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]

Since,

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

Then,

[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]

Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).

Then the total differential is

[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]

[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]

[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]

Answer:

C. The representative failed to have Tim initial by the fuel level on the Check-Out sheet.

Step-by-step explanation:

After reading the paragraph, we can eliminate B, by seeing that the representative did give him a copy of the Check-Out sheet, as quoted. "Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.".

We can also eliminate A and D, as the contract stated nothing about dents or the oil level in the car.

The answer is C, as the representative failed to have Tim initial on the Check-Out sheet. That is a requirement for the contract to be valid, as stated. "The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter.". However, Tim never initialed by the fuel level, as stated here. "...the agency representative turned on the car, took note of the fuel level, and indicated it on the Check-Out sheet. Since Tim didn’t have any questions, the clerk handed him the keys and a copy of the Check-Out sheet and wished him well.". No where here does it state that Tim initialed on the Check-Out sheet, meaning that he didn't. Him not doing so invalidates the contract.  

Answer:

x=–2

Step-by-step explanation:

x-8=-10

x=-10-8

x=–2

Answer:

-8= -10

, = -10+8

, = -2

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]

Answer:

Hello,

polynomial is x²-x+1

Step-by-step explanation:

if a=b*c+r then a=c*b+r

Using a long division, see the picture.

Answer:

Step-by-step explanation:

there are function that "invert" each other..

subtraction inverts addition...

3+2 = 5 ... 5-2 = 3

division inverts multiplication

5*2 = 10 ... 10/2 = 5

Using that concept, "factoring" is basically the inverse of multiplication

3x^2 + 9x can be factored to 3x(x+3)

if you multiply that out it reverts back to the original equation

so  x^2 + 5x + 6 factors to (x+3)(x+2)

if you multiply that out (foil it)

you get x^2 + 5x + 6

Mark as braianlist

15 multiple by 5 equal 75 -390 equal 315 -15equal 200

Answer:

2.45

Step-by-step explanation:

Given that :

α = 0.05

Larger sample variance= numerator, sample size = 9

Smaller sample variance = denominator, sample size = 21

Hence,

DFnumerator = n - 1 = 9 - 1 = 8

DFdenominator = n - 1 = 21 - 1 = 20

Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;

F critical = 2.447

F critical = 2.45

Answer:

y = 54/25 when x = 4.

Step-by-step explanation:

y is given by the equation:

[tex]\displaystyle y = p\times q^{x-1}[/tex]

Where p and q are numbers.

We are also given that when x = 1, y = 10 and when x = 6, y = 0.7776.

And we want to determine the value of y when x = 4.

Since y = 10 when x = 1:

[tex]\displaystyle (10) = p\times q^{(1)-1}[/tex]

Simplify:

[tex]10 = p \times q^0[/tex]

Any number (except for zero) to the zeroth power is one. Hence:

[tex]p=10[/tex]

Thus, our equation is now:

[tex]y = 10\times q^{x-1}[/tex]

When x = 6, y = 0.7776. Thus:

[tex](0.7776) = 10\times q^{(6)-1}[/tex]

Simplify and divide both sides by ten:

[tex]\displaystyle 0.07776 = q^5[/tex]

Take the fifth root of both sides:

[tex]\displaystyle q = \sqrt[5]{0.07776}[/tex]

Use a calculator. Hence:

[tex]\displaystyle q = \frac{3}{5} = 0.6[/tex]

Our completed equation is:

[tex]\displaystyle y = 10\times \left(\frac{3}{5}\right)^{x-1}[/tex]

Then when x = 4, y equals:

[tex]\displaystyle \begin{aligned} y &= 10\times \left(\frac{3}{5}\right)^{(4)-1} \\ \\ &= 10\times \left(\frac{3}{5}\right)^3 \\ \\ &= 10\times \left(\frac{27}{125}\right) \\ \\ &= \frac{54}{25}\end{aligned}[/tex]

Answer:

67

Step-by-step explanation:

DM=JM-JD=84-17=67

Answer:

Step-by-step explanation: