Tickets for a children's musical cost 3.50 for adults and 2.00 for children. If 250 tickets were sold for a total of 650.00 how many tickets of each kind were sold

Answer:

k=-1

Step-by-step explanation:

1-2k-2k=5

1-4k=5

4k=1-5

4k=-4

k=-4/4

k=-1

Answer:

24,393 subscribers

Step-by-step explanation:

This is exponential decay problem. The formula for exponential decay is:

[tex]F=P(1-r)^t[/tex]

Where

F is the future value (what we are looking for, in 7 years)

P is the present amount (that is 51,000)

r is the rate of decrease per year (r = 10% = 10/100 = 0.1)

t is the time, in years (t = 7)

Now substituting, we get:

[tex]F=P(1-r)^t\\F=51,000(1-0.1)^7\\F=51,000(0.9)^7\\F=24,393.14[/tex]

Rounding to nearest whole number,

Number of subscribers after 7 years = 24,393 subscribers

Using the exponential decay formula, a magazine with an initial 51,000 subscribers will have approximately 24,393 subscribers left in 7 years if subscriptions decline by 10% annually.

The question is asking to predict the number of magazine subscribers after a period of 7 years, assuming a 10% annual decline. To calculate this, we can use the formula for exponential decay, which is A = P(1 - r)^t, where A is the amount after time t, P is the initial principal amount (51,000 subscribers), r is the rate of decline (10% or 0.10), and t is the time in years (7 years). Calculating this, we get:

Now, calculate the value of A:

A = 51,000(1 - 0.10)^7

A = 51,000(0.90)^7

A = 51,000(0.4782969)

A ≈ 24,393 subscribers (after rounding to the nearest whole number).

Therefore, if the magazine subscriptions continue to decline at a rate of 10% per year, the magazine is predicted to have approximately 24,393 subscribers in 7 years.

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

(x-7)(x+2)=0

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

Answer:

x = - 2, x = 7

Step-by-step explanation:

Given

x² - 5x = 14 ( subtract 14 from both sides )

x² - 5x - 14 = 0 ← in standard form

Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)

The factors are - 7 and + 2, since

- 7 × 2 = - 14 and - 7 + 2 = - 5, thus

(x - 7)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 7 = 0 ⇒ x = 7

Answer:

20%

Step-by-step explanation:

A pair of jeans cost $45  before the sale.

The sale is taking $9 off of the original price.

Then

$45 - 100%

$9 - x%

Write a proportion:

[tex]\dfrac{45}{9}=\dfrac{100}{x}[/tex]

Cross multiply:

[tex]45\cdot x=9\cdot 100\\ \\45x=900\\ \\x=\dfrac{900}{45}\\ \\x=20\%[/tex]

Answer:

The sale price is $46.75

Step-by-step explanation:

Answer:45x-5 is the answer

Step-by-step explanation:

(4,1) and 5,5 add them both

Answer:

B.) The graph is a line that goes through the points (1,4) and (2,8).

Step-by-step explanation:

1.) (4) + 4 = 4((1) +1)

2.) 8 = 4 + 4

3.) 8 = 8 --> Correct

4.) (8) + 4 = 4((2) + 1)

5.) 12 = 8 + 4

6.) 12 = 12 --> Correct

The graph that shows the solution set for the inequality -5/2x -3<2 is a number line with an open circle at -2 and an arrow pointing to the left.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To graph the solution set for the inequality -5/2x -3<2, you first need to solve the inequality for x.

-5x -6 < 4

-5x < 4 + 6

-5x < 10

x < -2

The graph of the solution set for the inequality x < -2 is a number line with an open circle at -2 and an arrow pointing to the left. The open circle indicates that -2 is not included in the solution set, and the arrow pointing to the left indicates that all values to the right of -2 are included in the solution set.

Hence, the correct answer would be an option (C).

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Answer:

x=2, y=1. (2, 1).

Step-by-step explanation:

x=2y

2x+5y=9

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

2(2y)+5y=9

4y+5y=9

9y=9

y=9/9

y=1

x=2(1)=2

Answer:

x=21.33....

Step-by-step explanation:

2/3=x/32

cross product

3*x=2*32

3x=64

x=64/3

x=21.3

Answer:

11+6i

Step-by-step explanation:

(3+4i)+(8+2i)=11+6i

Answer:

[tex]\frac{y}{2}=\frac{x}{1}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding vertical sides are y and 2

The corresponding horizontal lines are x and 1

so

The proportion is equal to

[tex]\frac{y}{2}=\frac{x}{1}[/tex]

Answer:

Step-by-step explanation:

[tex]-1(2x+3)-2(x-1)\qquad\text{use the distributive property}\\\\=(-1)(2x)+(-1)(3)+(-2)(x)+(-2)(-1)\\\\=-2x-3-2x+2\qquad\text{combine like terms}\\\\=(-2x-2x)+(-3+2)\\\\=-4x-1[/tex]

Answer:

-4x-1

Step-by-step explanation:

-1(2x+3)-2(x-1)

-2x-3-2x+2

-2x-2x-3+2

-4x-3+2

-4x-1

Answer:

Option D. [tex]y=2x+2[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case A) we have

[tex]y=-2x[/tex]

Is a equation of the form [tex]y=kx[/tex]

The value of k=-2

This equation represent a proportional relationship

case B) we have

[tex]y=2x[/tex]

Is a equation of the form [tex]y=kx[/tex]

The value of k=2

This equation represent a proportional relationship

case C) we have

[tex]y=-2x+0[/tex]

The line passes through the origin, because the y-intercept is b=0

This equation represent a proportional relationship

case D) we have

[tex]y=2x+2[/tex]

The line not passes through the origin, because the y-intercept is not equal to zero (b=2)

This equation not represent a proportional relationship

Answer:

$5 per hour

Step-by-step explanation:

12*4=48 hours

240/48=5

Answer:

The second step of this method is

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]

The value of the given expression is

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]

Step-by-step explanation:

Given expression is [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]

To find the value of the given expression  [tex]5+(-1)+(-5)+(-2)+11+(-7)+2[/tex]:

Arranging positive and negative addends  by using the associative and commutative properties of the given expression as below:

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=5+11+2+(-1)+(-5)+(-2)+(-7)[/tex]

[tex]=(5+11+2)-(1+5+2+7)[/tex]

[tex]=18-15[/tex]

[tex]=3[/tex]

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]

The second step of this method is

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=(5+11+2)-(1+5+2+7)[/tex]

The value of the given expression is

[tex]5+(-1)+(-5)+(-2)+11+(-7)+2=3[/tex]

y = 4.5x

Explanation:

9 ÷ 2 = 4.5

18 ÷ 4 = 4.5

27 ÷ 6 = 4.5

Answer:

Step-by-step explanation:

-3(c-1) = 33

c - 1 = 33/ -3

c -1 = -11

c = -11 +1

c = -10

Answer:

-10

Step-by-step explanation:

-3 (c-1 ) = 33

Divide both sides by -3

c-1 = -11

Add 1 to both sides

c = -10

Answer:

length of rectangle=6cm

width of rectangle=11cm

Step-by-step explanation:

let, width of rectangle=x

length of rectangle=x-5

area of rectangle=[tex]length\times(width)[/tex]

given area of rectangle=66

so 66=[tex]x\times(x-5)[/tex]

66=x^2-5x

x^2-11x+6x-66=0

x(x-11)+6(x-11)=0

(x+6)(x-11)=0

x=-6,11

here x=11 is acceptable

length of rectangle=x-5=11-5=6cm

length of rectangle=6cm

width of rectangle=11cm            answer

Answer:

[tex]\$ 199[/tex]

Step-by-step explanation:

Given: Maria spent $2388 for natural gas, last year.

Maria chooses to use balance billing process to pay this year´s gas bill.

Balance billing is a billing practice, where provider bill you the difference between total cost and allowed amount. It can be paid partially or monthly. It generally in practice for medical billing as healthcare bill are generated for difference between total cost and amount which is paid through insurance.

Now, lets find out monthly bill paid by Maria.

We know there are 12 months in a year.

∴ Monthly payment= [tex]\frac{\$ 2388}{12} = \$ 199[/tex]

∴Maria will pay $199 monthly as her gas bill this year.

Maria's monthly payment for natural gas this year using balance billing will be $199.

Step 1

Balance billing is a method where a utility company estimates the annual energy usage and divides it into equal monthly payments. To find Maria's monthly payment for natural gas this year, we divide the total amount she spent last year by 12 months.

Total amount spent last year = $2,388

Step 2

Monthly payment this year = Total amount spent last year / 12 months

[tex]\[ \text{Monthly payment} = \frac{2388}{12} = 199 \][/tex]

Maria's monthly payment for natural gas this year, using balance billing, will be $199, calculated by dividing the total amount she spent last year by 12 months.

The distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower is : [tex]\[\(28 \text{ inches}}\][/tex].

To find the distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower, we need to understand the mathematical model for the suspension bridge cable. This cable typically forms a parabolic shape.

Let's establish our coordinate system:

- Place the origin [tex]\((0, 0)\)[/tex] at the lowest point of the cable.

- The towers are at [tex]\(x = -40\)[/tex] inches and [tex]\(x = 40\)[/tex] inches since they are 80 inches apart.

- The height of the towers is 16 inches.

The equation of the parabola can be written in the vertex form [tex]\(y = ax^2\)[/tex] since the vertex is at the origin [tex]\((0, 0)\)[/tex].

At the position of the towers (x = ±40 inches), the cable is 16 inches high:

[tex]\[y(40) = 16\][/tex]

[tex]\[a(40)^2 = 16\][/tex]

[tex]\[1600a = 16\][/tex]

[tex]\[a = \frac{16}{1600} = \frac{1}{100}\][/tex]

So, the equation of the parabola is:

[tex]\[y = \frac{1}{100}x^2\][/tex]

We need to find the point where the cable is 1.44 inches above the roadway:

[tex]\[\frac{1}{100}x^2 = 1.44\][/tex]

[tex]\[x^2 = 1.44 \times 100 = 144\][/tex]

[tex]\[x = \pm\sqrt{144} = \pm 12\][/tex]

Therefore, the points where the cable is 1.44 inches above the roadway are [tex]\(x = 12\)[/tex] inches and [tex]\(x = -12\)[/tex] inches.

The distance from [tex]\(x = 12\)[/tex] inches to the nearest tower at [tex]\(x = 40\)[/tex] inches is:

[tex]\[40 - 12 = 28 \text{ inches}\][/tex]

Similarly, the distance from [tex]\(x = -12\)[/tex] inches to the nearest tower at [tex]\(x = -40\)[/tex] inches is:

[tex]\[-12 - (-40) = 28 \text{ inches}\][/tex]

Thus, the distance between the point where the cable is 1.44 inches above the roadway and the base of the nearest tower is:

[tex]\[\boxed{28 \text{ inches}}\][/tex]

Answer:

The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].

Step-by-step explanation:

Given :

Radius of Ferris wheel r = 70 feet.

The distance between the wheel and the ground = 4 feet.

Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.

So the x coordinate of center of wheel must  be 0 , and y coordinate = 70 + 4 = 74

Thus, Coordinates of center = (0,74)

The equation of circle is given by :-

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Now center (h,k) = (0,74) and r = 70 , we get

[tex]x^2+(y-74)^2=(70)^2[/tex]

Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].

Answer:

Y = 8 + 6X is correct answer.

Step-by-step explanation:

Let y be the total lenght of tree and x is number of years that has past after tree plantation.

So the total lenght of tree after x years can be presented with the help of equation given below.

 Y = 8 + 6X

* This equation show that there is direct relationshop between number of years and total height of tree.

For example after 3 years the height of three will be

Y = 8 + 6(3) = 26 inches

Answer:

Problem 4:

Radius = 11 cm.

Circumference = 69.08 cm.

Problem 5:

Radius = 14 mm.

Circumference = 87.92 mm.

Problem 6:

Radius = 9 inches.

Circumference = 56.52 inches.

Problem 7:

Diameter = 32 ft.

Circumference = 100.48 ft.

Problem 8:

Diameter = 26 yards.

Circumference = 81.64 yards.

Problem 9:

Diameter = 12 cm.

Circumference = 37.68 cm.

Step-by-step explanation:

Problem 4:

Given:

Diameter GH = 22 cm

We need to find the radius EF and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius EF = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 22 = 11 \ cm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 22 = 69.08\ cm[/tex]

Hence Radius = 11 cm

Circumference = 69.08 cm.

Problem 5:

Given:

Diameter OP = 28 mm

We need to find the radius MN and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius MN = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 28 = 14 \ mm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 28 = 87.92\ mm[/tex]

Hence Radius = 14 mm

Circumference = 87.92 mm.

Problem 6:

Given:

Diameter EF = 18 inches

We need to find the radius CD and Circumference of the circle.

Now radius is given by half of the diameter

Also Circumference is given by π times diameter.

Radius CD = [tex]\frac{1}{2}\times Diameter = \frac{1}{2}\times 18 = 9 \ in[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 18 = 56.52\ in[/tex]

Hence Radius = 9 inches.

Circumference = 56.52 inches.

Problem 7:

Given:

Radius GH = 16 ft

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter KJ = [tex]2 \times radius = 2 \times 16 = 32 \ ft[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 32 = 100.48\ ft[/tex]

Hence Diameter = 32 ft.

Circumference = 100.48 ft.

Problem 8:

Given:

Radius LM = 13 yards

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter NO = [tex]2 \times radius = 2 \times 13 = 26 \ yards[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 26 = 81.64\ yards[/tex]

Hence Diameter = 26 yards.

Circumference = 81.64 yards.

Problem 9:

Given:

Radius NO = 6 cm

We need to find the Diameter CD and Circumference of the circle.

Now Diameter is given by twice the radius.

Also Circumference is given by π times diameter.

Diameter PQ = [tex]2 \times radius = 2 \times 6 = 12 \ cm[/tex]

Circumference = [tex]\pi \times Diameter = 3.14 \times 12 = 37.68\ cm[/tex]

Hence Diameter = 12 cm.

Circumference = 37.68 cm.

Answer:

The interest earned was $50.95

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=1\ year\\ P=\$1,000\\ r=5\%=5/100=0.05\\n=4[/tex]  

substitute in the formula above

[tex]A=1,000(1+\frac{0.05}{4})^{4*1}[/tex]  

[tex]A=1,000(1.0125)^{4}[/tex]  

[tex]A=\$1,050.95[/tex]  

Find the interest earned I

we know that

[tex]I=A-P[/tex]

substitute the values

[tex]I=\$1,050.95-\$1,000=\$50.95[/tex]

Answer:

B

Step-by-step explanation:

if you gain yards its plus 4 yards or how ever many yard to gain or lose.

Answer:

+4

Step-by-step explanation:

Because you GAIN 4

Answer:

True

Step-by-step explanation:

Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles

Answer: True

Step-by-step explanation:

Answer:

The Proof is below.

Step-by-step explanation:

Given:

[]MNOP is a Parallelogram

U is any point on side OP

To Show:

ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)

Proof:

Theorem:

If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.

If they have same altitude, they will lie between the same parallels.

Hence the area of the triangle will be equal to half that of the parallelogram.

Area of Parallelogram will be twice of Area of Triangle

∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )

Also,

[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]

Substituting equation 1 we get

[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]

[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]

[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved

Answer: The three consecutive numbers are 23, 24 and 25, and 25 Is obviously the largest.

Step-by-step explanation:

Answer: 23 , 24 , 25

Step-by-step explanation:

Consecutive numbers are numbers that follow each other in order.

Let the first number be x , the second number be x + 1 and the third number number be x + 2.

From the first statement :

Their sum implies :

x + x +1 + x + 2 = 72

3x + 3 = 72

Subtract 3 from both sides of the equation:

3x + 3 - 3 = 72 - 3

3x = 69

Divide through by 3

3x/3 = 69/3

Therefore :

x = 23

Therefore :

The numbers are

23 , 24 and 25

Answer:

7 without going over

Step-by-step explanation:

The number 7 can go into 50 a total of 7 times with 1 remainder.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9.

The number 7 can go into 50 a total of 7 times because 50 / 7 = 7 with 1 remainder.

To understand this, consider that when you divide 50 by 7, you are trying to find out how many groups of 7 can be created from 50. Since 50 is a multiple of 7 (50 is divisible by 7 with 1 remainder), there will be an integer number of groups. In this case, that integer is 7, so 7 groups of 7 can be created from 50.

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