Admission to a movie theater is $7 for children and $12 for adults. on a certain day, 67 people bought tickets at the theater and $704 was collected. how many children's tickets were sold and how many adult's tickets were sold?

By applying the distributive property of multiplication, the students that are correct in their approach to solving the problem are: Nico, Raj and Sandra.

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 5/2 as follows:

2/5(5 + x) = 8

Multiplying both sides by 5/2, we have:

5/2 × 2/5(5 + x) = 8 × 5/2

5 + x = 40/2

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would first of all multiply both sides by 1/2 and then 5 as follows:

2/5(5 + x) = 8

Multiplying both sides by 1/2, we have:

1/2 × 2/5(5 + x) = 8 × 1/2

1/5(5 + x) = 4

Multiplying both sides by 5, we have:

5 × 1/5(5 + x) = 4 × 5

5 + x = 20

Subtracting 5 from both sides, we have:

5 + x - 5 = 20 - 5

x = 15

In order to open the bracket and isolate the variable x, we would apply the distributive property of multiplication:

2/5(5 + x) = 8

2/5 × 5 + 2/5 × x = 8

2 + 2x/5 = 8

Subtracting 2 from both sides, we have:

2 - 2 + 2x/5 = 8 - 2

2x/5 = 6

Multiplying both sides by 5/2, we have:

5/2 × 2x/5 = 5/2 × 6

x = 30/2

x = 15.

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1. The value of x in the triangle is B. 22.5°.

2. The value of x in the triangle is B. 22.5°.

3. The value of the limit illustrated is D. 32

1. It should be noted that the total angle in a triangle is 180°. The three angles given are illustrated as:

Angle 1 = 3x

Angle 2 = x + 30°

Angle 3 = 180° - 120° = 60°

The value of x will be:.

3x + x + 30 + 60 = 180

4x + 90 = 180

4x = 180° - 90°

4x = 90°

x = 90/4.

x = 22.5°

2. Note that the question was repeated. Therefore, the answer is illustrated above The value of x is 22.5°.

3. x³ + 7x² - 4

when x = 2

x³ + 7x² - 4

= 2³ + 7(2)² - 4

= 8 + 28 - 4

= 32

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The equation for the line parallel to y=1/4x+1 that passes through the point (6,-2) is x-4y=14 as the slope for both lines are equal and using slope-point form of equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

The equation of a straight line that passes through a given point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Here,

The slope for the line will be 1/4 and the given points will be (6,-2) so the equation for the line is

y-y1=m(x-x1)

y+2=1/4(x-6)

4y+8=x-6

x-4y=14

Given that both lines have an equal slope and using the slope-point form of equation, the equation for the line parallel to y=1/4x+1 passing through the point (6,-2) is x-4y=14.

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The value of arithmetic progression of  p = 0 and q = 10

When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word.

Given that : -10,p,q,20 are in A.P

if this -10,p,q,20 are in A.P then it must follow

2b = a+ c

2p = -10 + q ... (i)

2q= p+20 ....(ii)

Solving both equation we get

Multiplying (1) with 2,

4p - 2q = -20

Now adding both the equations

4p - 2q + 2q - p = 0

3p = 0

p = 0

Then, q = 0 + 10 = 10

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Answer:

this appears to already be in standard form?

Step-by-step explanation:

standard form has x and y on one side of the =

The mean and standard deviation for the number of correct answers for such students is; μ = 6.5 and σ = 1.802776

Given there is a surprise​ true/false test with 13​ questions.

Thus, the probability of correctly guessing the answer is; p=0.5

Let "X' be the answers correctly guess by a student.

The formula for the binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

A) The mean of the binomial distribution is given by the formula;

μ = np

μ = 13 * 0.5

μ = 6.5

The formula for standard deviation is:

σ = √(np(1 - p))

σ = √(13 * 0.5(1 - 0.5))

σ = 1.802776

B) The probability that the student getting at least 11 correct​answers is given by:

P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13)

Using online binomial probability calculator, we have;

P(X ≥ 11) = 0.01123

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Complete question is;

Several psychology students are unprepared for a surprise​true/false test with 13 ​questions, and all of their answers are guesses.

a. Find the mean and standard deviation for the number of correct answers for such students.

b. Would it be unusual for a student to pass by guessing​ (which requires getting at least 11 correct​ answers)? Why or why​not?

By using division, 2×[tex]10^{-6}[/tex] times 300 is equal to  6×[tex]10^{-4}[/tex]

Scientific notation is a form of writing a very larger number or very smaller number in a simpler form. The general form of the scientific notation is a number from 1 to 10 is multiplied by a power of 10.

Consider the unknown number as x

The first number = 2×[tex]10^{-6}[/tex]

The result of 2×[tex]10^{-6}[/tex] times x = 6×[tex]10^{-4}[/tex]

So the equation will be

2×[tex]10^{-6}[/tex] × x = 6×[tex]10^{-4}[/tex]

Move 2×[tex]10^{-6}[/tex] to the right hand side of the equation

x = 6×[tex]10^{-4}[/tex] ÷ 2×[tex]10^{-6}[/tex]

Here we have to use the division

x = 300

Hence, by using division, 2×[tex]10^{-6}[/tex] times 300 is equal to  6×[tex]10^{-4}[/tex]

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The total change to Rapunzel's score as an integer is (x - 30), where x is the initial score.

How can linear addition and subtraction be carried out?
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. It is one of the fundamental mathematical operations we employ on a daily basis.
An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction.

Let the initial score of Rapunzel be = x
Given, she first lost nine points thrice and then three points, thus her score is: x - (9*3) - 3 = (x - 30) points.
Thus, the total change to her score is (x-30) points.

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Answer:

d

Step-by-step explanation:

because you're already given the hypotenuse "c" and a side length "a"

so

8^2+ y^2=12^2

The equivalent ratio is 12: 18

The ratio is 12:_ = 16: 24

12/x = 16/ 24

x≠0, because the denominator can never be 0.

Solve the equation

12/x = 16/24

12/x = 2/3

x = 18

Therefore the equivalent ratio is 12:18.

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The order from lowest to highest is  -5, -3, -2, -1 .

What is ascending order ?

Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.

6-8=-2

7-12=-5

1-4=-3

0-1=-1

Order : -5, -3, -2, -1

Avoid becoming confused by the values following the negative sign. The value of a number decreases with increasing size after a negative sign.

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The volume of the box is 105 cubic units.

The amount of space inside a cuboid is calculated using the term "cuboid volume." Having length, breadth, and height, the cuboid is a three-dimensional shape. A shape with a certain length, breadth, and height will be obtained if we start with a rectangular sheet and keep stacking them. Length x Width x Height is the formula for calculating the cuboid's volume.

Given that : The dimensions of her boxes to be 4 x 6 x 3 units.

The volume of cuboid=7×5×3=105 cubic units.

so ,The volume of the box is 105 cubic units.

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An nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).

As given in the question,

Number of zeros of the polynomial function N = 3

Real and complex zeros = 3, 2i , -2i

Function value f(-1) = 20

f(x) = k (x-3)(x-2i)(x+2i)

⇒f(x) = k(x-3)(x²-4i²)

⇒f(x) =k(x-3)(x²+4)

⇒f(-1) = k(-1-3)((-1)² +4)

⇒ 20 =k(-4)(5)

⇒k =-1

Now , f(x) = (-1)((x-3)(x²+4)

               = (-1)(x³ -3x²+4x -12)

Therefore, nth- degree polynomial function with real coefficient for N = 3 ; 3, 2i are zeros ; f(-1) =20 is given by f(x) = (-1)( x³ -3x²+4x -12).

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Answer:

10 - 2 y

Step-by-step explanation:

The given number [tex]\frac{16}{11}[/tex] is an improper fraction.

Proper fraction = A fraction with a smaller numerator than denominator is said to be a correct fraction. A fraction whose numerator is the same as or bigger than its denominator is said to be inappropriate. Proper fractions include 3/4, 2/11, and 7/19.

Improper fraction = A fraction is called improper if the numerator is greater than the denominator. Examples are 9/2, 8/5, 10/3, etc.

When we divide 16 by 11 we get a quotient of 1 and a remainder of 5.

This fraction after solving can be represented as [tex]11\frac{1}{6}[/tex] which is a mixed fraction.

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Answer:

A.-0.15

1.52

7.17

8.38

8.75

14.15

Each person pays $79 each month.

A bill for $1,896 is paid in 12 monthly installments.

the same amount must be paid each month.

for, per month installment to be paid equals $1,896/12= $ 158

also given that, each installment will be divided equally between two people, then,

each installment for one person is equal to $ 158 /2=$79

so, $79 each person pays each month.

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Value of P(5) is 0.058 by probability.

What is a math illustration of probability?

Given that ,

p = 1 / 4 = 0.25

1 - p = 1 - 0.25 = 0.75

n = 10

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

(a) x = 5

P(X = 5) = ((10! / 5! (10 - 5)!) * 0.255 * (0.75)10 - 5

              =  ((10! / 5! (5)!) * 0.255 * (0.75)5

              =  0.058

P(5) = 0.058

(b)

P(X > 3) = 1 - P(X \leq 3)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

= 1 - 0.776

= 0.224

P(ore than 3) = 0.224

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The complete question is-

Take another guess: A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)

Answer:

the answer is x=19 writing more bc I need more characters

The probability that a sum is an even number will be 5/7.

So, the first 7 prime numbers:

Then,

By multiplying these two probabilities, we can determine the likelihood of an even sum.

Therefore, the probability that a sum is an even number will be 5/7.

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1. The money that the gym employee earns in 1 month is $1500.

2. The money that the gym employee earns in 5 months is $7500.

The gym employee earns the same amount each month and after working for three months, he earned $4,500.

In this case, the amount that he earns monthly will be:

= Total amount / Number of months

= $4500 / 3

= $1500

He earns $1500 monthly.

The money that the gym employee earns in 5 months will be:

= 5 × $1500

= $7500.

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Answer:

k=40

Step-by-step explanation:

Answer : Each week the amount goes up by $40

Answer:

C. between 14.1 and 14.2

Step-by-step explanation:

√100 × 2

√(10 × 10) × 2

10√2 = 14.14

I hope this helps!

Answer:

C. Between 14.1 and 14.2
10√2 ≈ 14.142135624

Step-by-step explanation:

Answer:

N/A

Step-by-step explanation:

which question of the three do you need the answer for?

The integer represents the new temperature is (-8) F.

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Given:

At 2 a.m. temperature = -3F

Then temperature decreased 12°F = -12 F

and then increase  7°F = +7F

Now, the temperature is

= (-3) - 12 + 7

= -3 -5

=-8 F

Hence, the temperature is (-8) F

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The 3 angles in a triangle always add up to be 180.

Call the smallest angle as x
-> The 3 angles are x, 4/3x and 5/3x
-> 4x = 180
-> 45

So, the sizes of the 3 angles are 45, 60 and 75.

In linear equations, 18.816 is the cost of 2 2/5 pounds of salmon.

What are instances of linear equations?

grocery store sells salmon = $7.84 per pound

the cost of 2 2/5 pounds of salmon = [tex]2\frac{2}{5}[/tex]  × 7.84

the cost of 2 2/5 pounds of salmon =  12/5  * 7.84

the cost of 2 2/5 pounds of salmon =   12 * 1.568

the cost of 2 2/5 pounds of salmon =   18.816

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