Tickets to a Broadway show cost $50 for adults and $10 for children. The total receipts for 1440 tickets at one performance were $54,000. How many adult and how many child tickets were sold?

With the formula d=vt+1/2at², we can prove that the acceleration of an object can be calculated with a=2d-2v t/t²

To solve this problem we must establish the equation, isolate the variable (a) following the rules of clearance and solve the operations:

d=vt+1/2at²

1/2at² = d - vt

at² = (d - vt)*2

at² = 2d - 2vt

a= (2d - 2vt) / t² verified

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607

#SPJ4

Answer:

1/4

Step-by-step explanation:

the answer is in the question, but If that isn't what you meant to type, 2 3/4 - 1/4 is 2.5

The percentage of decay for the exponential function: y = 18(0.75) x is 25%.

This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 0.75 which is less than 1, representing decay.

The formula for exponential decay is y=a(1-r)x.

r is the decay rate, expressed as a decimal.

In this case, r = 1 - 0.75 = 0.25 which represents 25%.

Therefore, the percentage of decay for the exponential function: y = 18(0.75) x is 25%.

Learn more about percentages on:

https://brainly.com/question/24877689

#SPJ1

Hey there!

3x + 8x

= 3 + 8

= 11x

= 11

Therefore, your answer should be:

11x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The rational number between the square root of 7 and the square root of 8 is 27/10

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The features of the rational number are given as

Value = between the square root of 7 and the square root of 8

Rewrite the value properly

So, we have

Value = between √7 and √8

Evaluate the values of √7 and √8

So, we have

√7 = 2.65

√8 = 2.83

This means that the rational number is between 2.65 and 2.83

A number between 2.65 and 2.83 is 2.7

Express as fraction

value = 27/10

Hence, the rational number between the square root of 7 and the square root of 8 is 27/10

Read more abiut rational numbers at

https://brainly.com/question/22221295

#SPJ1

Answer: 50

Step-by-step explanation:

8x4 =32

6x3=18

32+18=50

The value of x = 45°

It is given that 3 cos² 2x / ( 1 - sin 2x) = 1

3cos² 2x / ( 1 - sin 2x) = 1

As we know sin²x + cos²x = 1

3 ( 1 - sin²2x) / ( 1 - sin 2x) = 1

3 - 3 sin²2x = 1 - sin 2x

3 sin²2x - sin2x - 2= 0

As we know sin2x = 2 sin x. cos x

3( 2 sin x. cos x)² + 2 sin x. cos x  - 2 = 0

Let's take sin x . cos  x = t

3 ( 2t)² - 2t - 2 = 0

12t² - 2t - 2 = 0

12t² - 6t + 4t - 2 = 0

6t( 2t - 1) + 2(2t - 1) = 0

(6t + 2)(2t - 1) = 0

t = -1/3 , 1/2

Now put the value of t we get

sin x . cos x = -1/3 , 1/2

2 sin x . cos x = -2/3 , 1

sin 2x = -2/3 , 1

It is given that x should be between 0° to 90°.

Therefore

sin 2x = 1

sin 2x = sin 90°

2x = 90°

x = 45°

Therefore the value of x is 45°

To know more about the trigonometry value refer to the link given below:

https://brainly.com/question/25618616

#SPJ9

 In the foreign exchange market, if a Pound is equal to 1.59 USD, one Euro is equal to 1.46 USD. So roughly speaking, one Pound is equal to 1.09 Euro.

given,

a ) £1 = €1.16

    = £60 x 1.16 = 69.60

b) 0.87 pound = 1 euro

    €98.60 ,

    therefore , 98.60/0.87 = 113.33

Convert Euro to British Pound

EUR GBP

1,000 EUR 876.24 GBP

5,000 EUR 4,381.2 GBP

10,000 EUR 8,762.4 GBP

50,000 EUR 43,812 GBP

to know more about currency;

visit; brainly.com/question/14372075

#SPJ9

The equation of the line will be y = 2x - 2.

A linear equation with a degree of one is referred to as a line equation. Two variables, x, and y are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The general form of the equation of the line is given as:-

y = mx + c

Given that the equation of the line is passing through the point ( -2,0) and the slope of the line is 2.

The equation of the line will be calculated as:-

y = mx + c

-2 = 0 + c

c = -2

y = mx + c

y = 2x - 2

Therefore, the equation of the line will be y = 2x - 2.

To know more about an equation of the line follow

brainly.com/question/18831322

#SPJ1

The perimeter of rectangular classroom with its length five times its width is 108 ft.

The perimeter of rectangle is the sum of length of all its sides. Mathematically, it can be written as -

Perimeter = 2 (Length + Breadth)

Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -

Width [W] = 9 ft

Length [L] = 5W = 5 x 9 = 45 ft

The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -

[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft

Therefore, the perimeter of rectangle with its length five times its width is 108 ft.

To solve more questions on Rectangles, visit the link below-

https://brainly.com/question/13130586

#SPJ1

1. A line can be described as a one-dimensional figure without thickness or width.

2. Lines are labeled with two points (A ↔ B). Lines can be marked using lowercase letters (for example, line k).

A line is a one-dimensional figure with a length only. A line does not have width or thickness.

A line can have line segments with two endpoints. A line cannot be measured, but its segments are measurable.

There are different types of lines, including:

Thus, lines are one-dimensional with lengths and no widths or thicknesses.

Learn more about lines at https://brainly.com/question/280216

#SPJ1

Answer: Factor the expression

Factor

2(x+5)

Evaluate

2x+10

Solution

2(x+5)

Step-by-step explanation: hope this helps

If a long run athlete can run 1/2 km in 3 minutes then he can run 10 km in an hour.

Given, a long distance athlete can run 1/2 kilometer in 3 minutes.

How much distance can he cover in an hour = ?

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

Time = 60 minutes.

we know that 3 minutes = 1/2 km

therefore, distance covered in an hour = 1/2 ÷ 3/60

= 1/2 × 60/3

= 1/2 × 20

= 10

distance covered in an hour = 10 km.

hence we get the distance covered by the athlete in an hour as 10 km.

Learn more about Speed, distance and time here:

brainly.com/question/26046491

#SPJ9

The height of the candle which is a linear function with respect to time after 12 hours was 25.2 centimeters.

A linear function has a graph of a straight line.

Given that height of a candle is a linear function of the amount of time in hours it has been burning.

The slope(m) is = - 0.4 which is = -(4/10) = - (2/5).

The height of the candle after 19 hours is 22.4 centimeters, which can be written as two points (x,y) = (19,22.4).

Now to obtain the height of the candle first we have to form an equation of a line in slope intercept form to find y-intercept(b), which is,

y = mx + b.

22.4 = -(2/5).19 + b.

22.4 = -7.6 + b.

b = 22.4 + 7.6.

b = 30.

∴ y = -(2/5)x + 30.

Now to obtain the height of the candle after 12 hours we have to substitute 12 in x.

So, y = -(2/5)(12) + 30.

y = 25.2 centimeters.

learn more about linear function here :

https://brainly.com/question/21107621

#SPJ1

If he plans to spend 200 per month, then the number of months he can make withdrawals from his savings account until his balance is zero dollars is equal to 5.

First, we calculate the money earned by Nick in 6 months

Money earned per month = $400

Money earned in 6 months = 400 × 6 = 2400

If he spends $250 out of the money earned per month, then the money spent in these 6 months can be calculated as follows;

Money spent per month = 250

Money spent in 6 months = 250 × 6 = 1500

Now we calculate the money put in the saving account in 6 months by subtraction;

Money added to the saving account = 2400 - 1500 = $900

As he already had $100 in the saving account,

Total amount of money in the saving account = 900 + 100 = 1000

If he plans to spend 200 per month, then the number of months he can make withdrawals can be calculated by division

Number of months = total money in the account ÷ money spent per month

Number of months = 1000 ÷ 200 = 5

Therefore, Nick can make withdrawals for 5 months from his savings account.

To learn more about division, click here:

https://brainly.com/question/28119824

#SPJ4

The expected raise a union wage negotiator feels that   the union members will get is $1.22.

The probability of each pay raise is given below

P ($1.50 raise) = 0.40

P ($1.00 raise) = 0.30

P ($0.50 raise) = 0.20

P (no raise) = 0.10

The probability of each pay raise is then multiplied by the pay itself

Expected raise for each hour = $1.50(0.40) + $1.00(0.30) + $0.50(0.20) + $0.00(0.10)

E(x) = 0.6 + 0.52 + 0.1 + 0 (The probability of no pay at all gives 0 since the pay amount has no value)

E(x) = $1.22

Therefore, all together the union wage negotiator is able to predict a $1.22 pay raise for the workers for each time expected.

To learn more about probability. Click, https://brainly.com/question/17089724

#SPJ4

The price of the cheaper vehicle is $39,000

From the question, we are to determine the price of the cheaper vehicle

Let the cost of one of the cars b $x

and the cost of the other car be $y

From the given information,

The total price for two cars at a dealership is $108,000

That is

x + y = 108000   ----------- (1)

and

one car’s price is $9000​ less than twice the other

x = 2y - 9000       ----------- (2)

Put equation (2) into equation (1)

x + y = 108000

2y - 9000 + y = 108000

2y + y - 9000 = 108000

2y + y = 108000 + 9000

3y = 117000

y = 117000/3

y = 39000

∴ The price of one of the vehicles is $39,000

Substitute this value into equation (2)

x = 2y - 9000

x = 2(39000) - 9000

x = 78000 - 9000

x = 69000

The price of the other vehicle is $69,000

Hence, the price of the cheaper vehicle is $39,000

Learn more on Calculating cost here: https://brainly.com/question/27897521

#SPJ1

Answer:

Oy-14=12(x+1)

Step-by-step explanation:

please rate as brainliest

Answer: 1 = e

Step-by-step explanation:

If you buy 7 markers , each marker would cost 9.42 ( cents ) .

Given : The total cost ( in cents ) of x + 2 markers is x³ + 5 x ² + 2 x - 8 .

To find : cost of 1 marker

Cost of 1 marker = ( x³ + 5 x ² + 2 x - 8 ) / ( x + 2 )

                            = [tex]x^{2}[/tex] + 3 x - 4

Substituting value of 7 in cost function

   =  [tex]x^{2}[/tex] + 3 x - 4 at x = 7

= 49 + 21 - 4

Cost of 7 markers = 66

Cost of 1 marker = 66 / 7

                            = 9.42

Therefore , if you buy 7 markers , each marker would cost 9.42 ( cents ) .

To learn more on cost function follow link :

https://brainly.com/question/2292799

#SPJ4

Answer:

10

Step-by-step explanation:

10 multiplied by 10 is 100. Therefore,the square root of 100 is 10

Answer:

-8

Step-by-step explanation:

(2)(-8)/2 convert it to a fraction and use fraction bar.

-16/2 = -8  Multiplication first then division

Note order of operations Division or multiplication which ever is first. also because the top of the fraction has parentherses do that first.

q3: -9, 1

q4: No

The reason there are multiple answers for this question is because of the absolute value sign. to solve this you can isolate the absolute value onto one side and solve for the positive and negative possibilities.

step 1: isolate the absolute value

|3(x+4)|+8=23 ----> |3(x+4)|=15

step 2: remove the absolute value sign the remember that now it has two answer possibilities where 15 can be both negative and positive and still be right. Then just solve just like you would a normal equation.

3(x+4)= +-15 ----> x+4= +-5

x = -9, 1

0.03337327...   is expression to four decimal places. e⁻³.

The significance of an exponential function

e⁻³ in your calculator, which gives you 0.03337327...

Since you need 4 decimal places, you need to look at the 5th decimal place. If it's 5 or more, you add 1 to the 4th decimal place. If it's less than 5, you leave the 4th decimal as it is.

In this case, the 5th decimal place is 7 and the 4th is 3. Since 7>5, the 4th decimal place changes from 3 to 4.

Learn more about exponential function

brainly.com/question/14355665

#SPJ4

The single logarithm of log 3 + 4 log x is = log (3x^4).

What is a logarithmic function?

A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1

Write the given logarithmic expression in a single logarithm. log 3 + 4 log x

Given logarithmic expression is log 3 + 4 log x

Applying given properties of logarithmic function;

log a + log b = log (ab)

2 log a = log a²

Now, log 3 + 4 log x = log 3 + log x^4

= log (3x^4)

Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).

To learn more about the logarithmic functions, visit here:

https://brainly.com/question/13473114

#SPJ4

The corresponding growth factor of +70% is 1.7

The formula for the annual rate of change is

                    1 ± r             (1)

where r = rate of change

and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.

According to the question we have been given the growth that is +70%. Since there is plus sign therefore it is a growth factor.

Thus, r = + 0.7

Putting this value in equation (1) we get

= 1 + 0.7

= 1.7

Hence the corresponding growth factor of +70% is 1.7

Learn more about growth factor here : https://brainly.com/question/27161222

#SPJ4

Express 81 and 16 as a product of their prime factors. Apply the power rule for indices stating (a^m)^n = a^mn. Simplify the expression:

81=3x3x3x3 = 3^4

16 = 2x2x2x2 = 2^4

Thus, (3^4 x y^16 / 2^4 x X^12) ^ 1/2

3^4/2y^16/2 / 2^4/2 X^12/2

3^2 y^8 / 2^2 X^6 = 9y^8 / 4X^6

9y^8/4X^6 = (3/2)^2X^6y^8

Find more on indices at: brainly.com/question/28595104

#SPJ4

Solving for the variable 'a' gives the equation a = u - k

A subject of formula can be defined as a variable written in terms of other variables in an equation or given expression.

It is also recognized as the variable that is being worked out in an equation or expression.

Given the equation:

u=a+k

To make the variable 'a' the subject of formula, we have to take all other variables to the other side of the equality sign, making the variable 'a' stand alone.

We then have;

u - k = a

This is also written as;

a = u - k

Thus, solving for the variable 'a' gives the equation a = u - k

Learn more about subject of formula here:

https://brainly.com/question/21140562

#SPJ1

According to the solving this implies that the  1:3  ratio of 60 is 20.

A ratio expresses the number of times one number contains another. For example, if a dish of the fruit contains eight oranges and six lemons, the orange-to-lemon proportion is eight to six. Similarly, the lemonade and orange proportion is 6:8, while the orange to fruit weight ratio is 8:14.

Ratios are used to compare the two quantities by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Let us find 1/3 of 60.

We can write 1/3 of 60

= 1/3 × 60.

= 20.

According to the solving this implies that the  1:3  ratio of 60 is 20.

To know more about ratio visit:

https://brainly.com/question/1504221

#SPJ9