Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an angle.

Answer:

The number of tickets that cost $ 10 is 923

The number of tickets that cost $ 20 is 1205

The number of tickets that cost $ 30 is 1111

Step-by-step explanation:

Given as :

The total number of three different tickets cost $ 10 , $ 20 and VIP seats $ 30

The total number of all tickets sold = 3239

The sale price for the tickets = $ 63720

Let The type of ticket for $ 10 = x

And The type of ticket for $ 20 = y

And The type of VIP ticket = v

According to question

The number of $ 20 tickets = The number of $ 10 tickets + 282

I.e y = x + 282

And x + y + v = 3239

Or, v = 3239 - ( x + y )

I.e v = 3239 - ( x + x +282 )

Or, v = 2957 - 2 x

Now ,

x × $ 10 + y × $ 20 = v × $ 30

Or, x × $ 10 + ( x + 282 ) × $ 20 = ( 2957 - 2 x ) × $ 30

or, 10 x + 20 x + 5640 = 88710 - 60 x

Or, 30 x + 60 x = 88710 - 5640

or, 90 x = 83070

∴  x = [tex]\frac{83070}{90}[/tex]

I.e x = 923

So, The  number of tickets that cost $ 10 = x = 923

Similarly

 y = x + 282

or, y = 923 + 282

I.e y = 1205

So, The  number of tickets that cost $ 10 = y = 1205

And

 v = 2957 - 2 x

∴ v = 2957 - 2 × 923

I.e v = 1111

So, The  number of tickets that cost $ 30 = v = 1111

Hence

The number of tickets that cost $ 10 is 923

The number of tickets that cost $ 20 is 1205

The number of tickets that cost $ 30 is 1111

Answer

Answer:

1021 of the $10 tickets, 1303 of the $20 tickets and 915 of the $30 tickets.

Step-by-step explanation:

We have 3 types of tickets:

ones that cost $10, others that cost $20 and others that cost $30.

If A is the number of $10 tickets sold, B is the number of $20 tickets sold and C is the number of $30 tickets sold we have that:

A + B + C = 3239

B = A + 282

A*10 + B*20 + C*30 = 63720

We need to solve this system of equations.

From the second equation we have B isolated, we can replace it in the other equations:

A + (A + 282) + C = 3239

A*10 + (A + 282)*20 + C*30 = 63720

Now we can isolate one of the variables in the first equation and replace it in the second, lets isolate C.

C = 3239 - 2*A - 282 = 2957 - 2*A

the third equation is now:

A*10 + (A + 286)*20 + (2957 - 2*A)*30 = 63720

Now we solve it for A:

A*10 + A*20 - A*60 + 282*20 + 2957*30 = 63720

-A*30 + 94350 = 63720

A*30 = - 63720 + 94350 = 30630

A = 30639/30 = 1021

So they sold 1021 tickets of $10.

Now we can replace it in the equation:

C =   2957 - 2*A = 2957 - 2*1021  = 915

They sold 915 $30 tickets  

They sold 1303 tickets of $20.

B = A + 282 = 1021 + 282 = 1303.

Answer:

96 ft

Step-by-step explanation:

Perimeter= a (base)+b (side)+c (side)

281 = 89 +b + c

281 -89 = b + c

192 = b+ c ( however in an iscoceles triangle, 2 sides aree equal therefore b and c will be equal)

So: 192/2 = 96

Answer:

Each of the equal sides of the roof is 96 ft long

Explanation:

Let the length of each of equal sides of given isosceles triangle be x, we know that perimeter of a triangle is equal to sum of sides of the triangle, we are given the base side to be equal to 89 feet and perimeter of the triangle equal to 281 feet.

so we can say that x + x + 89 =281 feet.

=> 2 x + 89 = 281 feet

=> 2 x = 192

=> x = 96

So, each of the equal sides is equal to 96 feet.

Tj hit 85% of the balls pitched to him.

Step-by-step explanation:

Baseballs pitched to Tj = 20

Baseballs hit by Tj = 17

Percentage = [tex]\frac{baseballs\ hit\ by\ Tj}{baseballs\ pitched\ to\ Tj}*100\\[/tex]

Percentage= [tex]\frac{17}{20}*100[/tex]

Percentage=[tex]\frac{1700}{20} = 85\%\\[/tex]

Tj hit 85% of the balls pitched to him.

Keywords: percentage, division

Learn more about division at:

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Answer:

The seventh-grade class earned more money in September by $36

Step-by-step explanation:

a)

The price of flowers in September was $1.50. In October, the price went up 20%

The increase in the price was 20*1.50/100=$0.30. So the new price is $1.80

$1.80

b) In September, the seventh-grade class sold 900 flowers for

900*1.50 = $1,350. They earned 40% of it, that is

40*1,350/100 = $540

In October they sold 700 flowers for

700*1.80 = $1260. They earned 40% of it

40*1260/100 = $504

The difference was $540-$504=$36

The seventh-grade class earned more money in September by $36

Answer:

6a + 13

Step-by-step explanation:

Given

2a + 4(a + 5) - 7 ← distribute parenthesis

= 2a + 4a + 20 - 7 ← collect like terms

= 6a + 13

Answer: 6a + 13

Step-by-step explanation: here you go: 2a + 4*(a+5) - 7

first we simplify the brackets (distributive property, you multiply 4 "a" times plus 5 times): 2a + 4a + 20 - 7

then you add those that multiply the variable separately from those that don't: 6a + 13

The lengths of the sides are 24cm, 27cm and 30cm.

Step-by-step explanation:

The ratio of lengths is 8:9:10

Perimeter = 81 cm

Let x be the length of side.

Therefore,

The length of sides is 8x, 9x and 10x.

Perimeter is the sum of 3 sides, therefore,

[tex]8x+9x+10x=81\\27x=81[/tex]

Dividing both sides by 27;

[tex]\frac{27x}{27}=\frac{81}{27}\\x=3[/tex]

Therefore, the lengths of sides are [tex]8(3), 9(3)\ and\ 10(3)[/tex]

The lengths of the sides are 24cm, 27cm and 30cm.

Keywords: triangles, perimeter

Learn more about triangles at:

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The lengths of the sides of the triangle are 24 cm, 27 cm, and 30 cm.

To find the lengths of the sides of the triangle, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter. Let's assume the common ratio between the sides is 'x'. So, the lengths of the sides can be written as 8x, 9x, and 10x. According to the problem, the perimeter of the triangle is 81 cm.

Therefore, 8x + 9x + 10x = 81.

Combining like terms, we get 27x = 81.

Dividing both sides by 27, we find that x = 3.

Substituting this value back into the lengths of the sides, we find that the lengths are 8x = 8(3) = 24 cm, 9x = 9(3) = 27 cm, and 10x = 10(3) = 30 cm.

Answer:

width =5.5ft

length =18

Step-by-step explanation:

w=x

L=2x+7

area=w*L

99 = x(2x+7)

[tex]99=2x^{2} +7x[/tex]

[tex]2x^{2} +7x-99=0[/tex]

[tex]2x^{2} +18x-11x-99=0[/tex]

2x(x+9)-11(x+9)=0

(2x-11)(x+9)=0

2x-11=0

2x=11

x=11/2

x=5.5

L=2x+7=2*5.5+7=11+7=18

Answer:

Step-by-step explanation:

2/310=5/c

simplify 2/310 into 1/155

1/155=5/c

cross product

155*5=1*c

775=c

c=775

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

m/3=32/4

simplify 32/4 into 8,

m/3=8,

m=8*3=24

m=24

Answer: 20.4444444 etc.

Step-by-step explanation:

Answer:

20.44

Step-by-step explanation:

184÷9= 20.44

Answer:

Step-by-step explanation:

[tex]x,\ y-numbers\\\\\text{The system of equations:}\\\\\underline{+\left\{\begin{array}{ccc}x+y=126\\x-y=42\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=168\qquad\text{divide both sides by 2}\\.\qquad x=84\\\\\\\text{Put the value of}\ x\ \text{to the first equation:}\\\\84+y=126\qquad\text{subtract 84 from both sides}\\y=42[/tex]

Final answer:

The two numbers that have a sum of 126 and a difference of 42 are 84 and 42.

Explanation:

To find the two numbers whose sum is 126 and whose difference is 42, we can set up a system of equations:

x + y = 126 (Sum of the numbers)

x - y = 42 (Difference of the numbers)

By adding these two equations, we can eliminate y and solve for x:

x + y + x - y = 126 + 42

2x = 168

x = 84

Now that we have the value of x, we can find y by substituting x back into either of the equations. For example:

84 + y = 126

y = 126 - 84

y = 42

Therefore, the two numbers are 84 and 42.

There are 21 nickels in the jar

Step-by-step explanation:

Ellie Mae has a jar that contains quarters and nickels

We need to find the number of the nickles in the jar

Assume that the number of nickles is x

∵ There x nickles in the jar

∵ There are 15 more nickels than quarters

∴ The number of quarters = x - 15

∵ 1 nickle = 5 cents

∵ 1 quarter = 25 cents

∵ 1 dollar = 100 cents

∵ The total value is $2.55

- Change the total value to cents

∴ The total value = 2.55 × 100 = 255 cents

∵ 5 x + 25(x - 15) = 255

- Simplify it

∵ 5x + 25x - 375 = 255

- Add like terms

∴ 30x - 375 = 255

- Add 375 to both sides

∴ 30x = 630

- Divide both sides 30

∴ x = 21

There are 21 nickels in the jar

Learn more:

You can learn more about the word problems in brainly.com/question/13174281

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Answer:

Step-by-step explanation:

347+13=360.              360 divided by 3 = 120 students signed up for basket ball

Using algebra, the number of students who listed basketball as their favorite sport is calculated to be 120, based on the information given that 347 students prefer soccer and that number is 13 less than three times the number of basketball fans.

Calculating the Number of Basketball Fans

To find the number of students who listed basketball as their favorite sport, we can use algebra. Let's call the number of basketball students x. We know that 347 students listed soccer as their favorite sport, which is 13 less than three times the number of students who listed basketball. This information gives us the equation:

3x - 13 = 347

Adding 13 to both sides to isolate the term 3x on one side, we get:

3x = 360

Dividing both sides by 3 to solve for x, we get:

x = 120

Therefore, there are 120 students who listed basketball as their favorite sport.

Answer: 5/10 (5 tenths)

Step-by-step explanation:

Since the value of 5 in 124.519 is 5 tenths, it can therefore be expressed as 5/10 in fraction form.

Answer:

1/2

Step-by-step explanation:

Since 5 is in the tenths place it can be written as

5/10

1/2(in simplified form)

Answer:

The population will be 240,116

Step-by-step explanation:

Exponential growth can be represented by the expression:

[tex]P(t) = P_i\,(1+r)^t[/tex]

where:

[tex]P(t)[/tex] is the population at time (t)

[tex]P_i[/tex] is the initial value of the population

"r" is the annual rate of growth (written in decimal form)

and "t" is the time in years.

Therefore in this situation, P(16) is what we want to find [the population after 16 years]

the initial population [tex]P_i[/tex] is 110,000

the rate of growth is 0.05 [decimal form of 5%]

and t is 16 years.

Replacing all these in the given functional form gives:

[tex]P(t) = P_i\,(1+r)^t\\P(16)=110000\,(1+0.05)^16\\P(16)=240116[/tex]

An exponential function to model a population of 110,000 that grows at 5% per year for 16 years is P(t) = 110,000 ∙ (1.05)^t. After 16 years, using this exponential function, the population would be approximately 242,884.

To model the population growth using an exponential function, we can use the formula P(t) = P0 ∙ (1 + r)t, where P(t) is the population after t years, P0 is the initial population, r is the growth rate, and t is the time in years. In this case, the initial population P0 is 110,000, the growth rate r is 5% (or 0.05), and the time t is 16 years.

The exponential growth function would be:

P(16) = 110,000 ∙ (1 + 0.05)16

To find the projected population after 16 years, we'll calculate:

P(16) = 110,000 ∙ (1.05)16
P(16) = 110,000 ∙ 2.20804
P(16) = 242,884.4

After rounding, the population would be approximately 242,884 after 16 years.

Answer:

The correct answer is 3.

Step-by-step explanation:

1. Let's resolve the expression below:

(27^5/3) ^1/5

( ∛ 27 ⁵ ) ^ 1/5 ⇒ ∛ 27 ⁵ = 27^5/3

( ∛ 3³ ⁵ ) ^ 1/5 ⇒  ∛ 3³ ⁵ = ∛ 27 ⁵

( 3 ⁵) ^ 1/5

⁵√ 3 ⁵ ⇒  ( 3 ⁵) ^ 1/5 = ⁵√ 3 ⁵

3

After making all the calculations and applying all the exponent rules, the final result is 3.

Answer:

B. 3

Step-by-step explanation:

Answer:

39.5 = tax represents the cost of shoes after the discount

Step-by-step explanation:

c=(1- 0.25)+0.08 [c+(1-0.25s] +8% tax

c= cost

s=shoes

1- 0.25=0.75+0.08= $0.83

c=$0.83

[0.83+(1-0.25s]

1-0.25=0.75

0.83+0.75 =$1.58

                    x 25

                      ___

                      39.5 = tax represents the cost of shoes after the discount

                     Correct me if i'm wrong :-D

Answer:

see explanation

Step-by-step explanation:

Since the 2 lines are parallel, then

d = 55° ( corresponding angles are congruent )

e = 55° (vertical to d and congruent )

e and f are same side interior angles and are supplementary, thus

e + f = 180°, that is

55° + f = 180° ( subtract 55° from both sides )

f = 125°

c = 125° ( alternate to f and congruent )

Hence

c = 125°, d = 55°, e = 55°, f = 125°

Answer:

5

Step-by-step explanation:

You move 3 places to the right to get to zero. And two places to the right to get to 2. 3 plus 2 is 5.

Answer:

Step-by-step explanation:

The formula of a distance between two points A and B:

d = |B - A|

We have A = -3 and B = 2.

Substitute:

d = |2 - (-3)| = |2 + 3| = |5| = 5

The combined cost for 1 pound of turkey and 1 pound of ham is $10.5

Step-by-step explanation:

Let,

Turkey = x

Ham = y

According to given statement;

4x+2y=30    Eqn 1

x = y-1.50     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]4(y-1.50)+2y=30\\4y-6+2y=30\\6y=30+6\\6y=36[/tex]

Dividing both sides by 6

[tex]\frac{6y}{6}=\frac{36}{6}\\y=6[/tex]

Putting y=6 in Eqn 2

[tex]x=6-1.50\\x=4.5[/tex]

1 turkey costs $4.5 and 1 ham costs $6.

Combined cost of 1 pound of turkey and ham each = 4.5+6=$10.5

The combined cost for 1 pound of turkey and 1 pound of ham is $10.5

Keywords: linear equations, subtraction

Learn more about linear equations at:

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Answer:

0.7 pounds of fruit

Step-by-step explanation:

Step 1. Add all fruit Ashley has been given to Aliyah, Brendan and Arley

Find the sum of;

     1.3 pounds for Aliyah

     2.4 pounds for Berndan

    1.2 pounds for Arley      

    4.9 pounds of fruits

Step 2. Subtract the total pounds given from the total pounds of fruit Ashley had.

5.6 pounds - 4.9 pounds = 0.7 pounds left

Answer; Ashley has 0.7 pounds of fruits left

Answer: 3 hours

Step-by-step explanation: 30 miles/10 hours=3 miles per hour. 9 miles/3 miles per hour= 3 hours.

Answer:

d =11t

Step-by-step explanation:

Answer: The wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Step-by-step explanation:

To calculate the wavelength of light, we use the equation:

[tex]\lambda=\frac{c}{\nu}[/tex]

where,

[tex]\lambda[/tex] = wavelength of the light  

c = speed of light = [tex]3\times 10^8m/s[/tex]

[tex]\nu[/tex] = frequency of light = [tex]3\times 10^{18}s^{-1}[/tex]

Putting the values in above equation, we get:

[tex]\lambda=\frac{3\times 10^8m/s}{3\times 10^{19}s^{-1}}=1\times 10^{-10}m[/tex]

Hence, the wavelength for X-rays with the given frequency is [tex]1\times 10^{-10}m[/tex]

Answer:

1 x 10 ^-10 m

Step-by-step explanation:

Carter's song played on 7 commercials and 5 movies.

Step-by-step explanation:

Earning per commercial = $50

Earning per movie = $130

Total earned = $1000

Total commercial and movies = 12

Let,

x be the number of commercials

y be the number of movies

According to given statement;

x+y=12     Eqn 1

50x+130y=1000    Eqn 2

From Eqn 1

x=12-y    Eqn 3

Putting value of x from Eqn 3 in Eqn 2

[tex]50(12-y)+130y=1000\\600-50y+130y=1000\\80y=1000-600\\80y=400[/tex]

Dividing both sides by 80

[tex]\frac{80y}{80}=\frac{400}{80}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=12\\x=12-5\\x=7[/tex]

Carter's song played on 7 commercials and 5 movies.

Keywords: linear equation, substitution method

Learn more about substitution method at:

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Carter had his songs played in 7 commercials and 5 movies to earn $1000 in royalties. This was determined by solving a system of linear equations.

Carter is dealing with a system of linear equations situation where he collects different amounts of royalties based on whether his music is played in commercials or movies. We can represent the number of commercials as c and the number of movies as m. Since he earns $50 per commercial, we can write the first equation as 50c, and since he earns $130 per movie, we can write the second equation as 130m. Carter earned a total of $1000 from 12 commercials and movies, which gives us two equations:

50c + 130m = 1000

c + m = 12

By solving this system of equations, we can determine the number of commercials and movies. Multiplying the second equation by 50 gives us 50c + 50m = 600, which we can subtract from the first equation to eliminate c and solve for m. Doing so, we get:

50c + 130m = 1000

-(50c + 50m = 600)

After subtracting, we are left with 80m = 400, from which we can solve for m to find that m = 5. Using the second original equation, we can now find out that c = 7.

So, Carter had his songs played in 7 commercials and 5 movies to earn a total of $1000 in royalties.

Answer:

B

Step-by-step explanation:

The sequence is ABCDEDCBABCDEDCBABCDEDCBA....

⇒The main sequence is the repitition of the sub-sequence ABCDEDCB

2010 when divided by 8 gives a quotient of 251 and a remainder of 2

251×8 = 2008

This means that after the sub-sequence ABCDEDCB is repeated for 251 times, it's last letter B is the [tex]2008^{th}[/tex] letter of the main sequence

Even after that, the sub-sequence ABCDEDCB keeps repeating and the [tex]2010^{th}[/tex] letter in the main sequence is the [tex]2^{nd}[/tex] letter of the sub-sequence ABCDEDCB, that is "B"

Final answer:

To find the 2010th letter in the repeating sequence ABCDEDCBA, divide 2010 by 9 and use the remainder to identify the letter's position in the pattern. The 2010th letter is C.

Explanation:

The sequence ABCDEDCBA consists of 9 letters. To find the 2010th letter in this pattern, we need to divide 2010 by the number of letters in the sequence. Dividing 2010 by 9 gives us 223 with a remainder of 7. This tells us that the 2010th letter is the same as the 7th letter of the sequence, because after every full repetition of 9 letters, the pattern starts over.

Let's map out the sequence: A(1), B(2), C(3), D(4), E(5), D(6), C(7), B(8), A(9). Using this mapping, the 7th letter corresponds to the letter C.

The 2010th letter in the sequence ABCDEDCBA is C.

Answer:

216 sq. cm.

Step-by-step explanation:

If we fold the paper of the given dimensions then we will get a rectangular prism with dimension 10 cm by 6 cm by 3 cm.

Now, a rectangular prism has the total surface area given by  

A = 2(LW + WH + HL)

where, L = length = 10 cm.

W = width = 6 cm. and  

H = height = 3 cm.

Therefore, total surface area = A = 2(10 × 6 + 6 × 3 + 3 × 10) = 216 sq. cm. (Answer)

Answer:

216 sq. cm.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

   5x+3y=13

+(-5x-12y=23)

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

-9y=36

y=-4

To find x plug in y into any equation.

5x+3(-4)=13

5x=25

x=5

Answer:

16(d-4)

Step-by-step explanation:

16d-64=16(d-4)