the average price of a movie ticket was $4.35 in 1996. the average price of a movie ticket was $9.16 in 2020. what was the average rate of change? if this rate continues, predict the cost of a movie ticket in 2025.

Answer:

See below ~

Step-by-step explanation:

Graph 1 : y = -3x + 3

Graph 2 : y = 6x + 6

Graph 3 : y = 6x + 9

Graph 4 : y = -7x + 1

Recall slope intercept form of a line

where b is y intercept

Whatever m be b is constant for line .

So we can find the equations through y intercepts

#1

The most probable according to our options is 3

So equation is

#2

Y intercept just over 5 .It must be 6

#3

y intercept around 10

.Most probable according to options is 9

#4

Just above the origin the y intercept is present.

Using the binomial distribution, it is found that there is a 0.0108 = 1.08% probability of the coin landing tails up at least nine times.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that is lands tails up at least nine times is given by:

[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{10,9}.(0.5)^{9}.(0.5)^{1} = 0.0098[/tex]

[tex]P(X = 10) = C_{10,10}.(0.5)^{10}.(0.5)^{0} = 0.001[/tex]

Hence:

[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0098 + 0.001 = 0.0108[/tex]

0.0108 = 1.08% probability of the coin landing tails up at least nine times.

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Answer:

Let DC be the tower and BC be the building. Then,

∠CAB=45

o

,∠DAB=60

o

,BC=20 m

Let height of the tower, DC=h m.

In right △ABC,

tan45 o = AB/BC

1=20/AB

AB=20m

In right∆ABD,

tan 60°=BD/AB

√3=h+20/20

h=20(√3-1)m

√a × √b = √ab

only if at atleast one among a,b is positive

here both a,b is non negative so not possible

Step-by-step explanation:

Remember when expanding radicals,

[tex] \sqrt{ab} = \sqrt{a} \times \sqrt{b} [/tex]

When expanding radicals into two radicals, we don't let our radicand have two negative answers.

[tex]i = \sqrt{ - 1} [/tex]

[tex] {i}^{2} = - 1[/tex]

We don't do this

[tex] (\sqrt{ - 1} ) {}^{2} = \sqrt{ - 1 \times - 1} [/tex]

[tex] - 1 = \sqrt{1} [/tex]

[tex] - 1 = 1[/tex]

Answer:

240

Step-by-step explanation:

see photo for solution

Step-by-step explanation:

x - 2y = -3,____1 , 8x - 6y = 16____ 2

x - 2y = -3

x = 2y -3 ____ equation 3

eqn 3 in 2

2=> 8x - 6y = 16

8(2y-3) - 6y = 16

16y - 24 - 6y = 16

10y = 16 + 24

10y = 40

y = 40 / 10

y = 4

y=4 in eqn 3

3=> x = 2y - 3

x = 2(4) - 3

x = 8 - 3

x = 5

x = 5 , y = 4

-2y-2y = 20 , x - 7y = 14___ 1

-2y-2y = 20

-4y = 20

y = 20/ -4

y = -5

y = -5 in eqn 1

1=> x - 7y = 14

x - 7(-5) = 14

x - (-35) = 14

x + 35 = 14

x = 14 - 35

x = -21

x = -21 , y = -5

Using the binomial distribution, we have that:

a) The distribution is given by:

b) 0.3125 = 31.25%.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, we have that:

The distribution is given by the probability of each outcome, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{4,0}.(0.5)^{0}.(0.5)^{4} = 0.0625[/tex]

[tex]P(X = 1) = C_{4,1}.(0.5)^{1}.(0.5)^{3} = 0.25[/tex]

[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]

[tex]P(X = 3) = C_{4,3}.(0.5)^{3}.(0.5)^{1} = 0.25[/tex]

[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625[/tex]

The probability of at least 3 daughters is given by:

[tex]P(X \geq 3) = P(X = 3) + P(X = 4) = 0.25 + 0.0625 = 0.3125[/tex].

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Answer:

133°

Hope this helps!!!

The regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, butbut the actual value is 225.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dot's relationship.

Here the scatter plot is not given, but we can draw the scatter plot using the data which is given with two variables such as (x, y) and the line which is best fit of the given data.

From the data given, we can write the line of best fit in slope and y-intercept form:

y = mx + b

Plug m = 10 and b = 125

y = 10x + 125

The number of fat grams in an item having that number of fat calories.

As we have the regression line:

y = 10x + 125

Put x = 1 in the regression line:

y = 10(1) + 125

y = 135 calories

For x = 12

y = 10(12)+125 = 245

But the actual value from the graph is 225.

Thus, the regression line is y = 10x + 125, and the value of calories is 135, and when x = 12 the value of y = 245 from the regression line, but but the actual value is 225.

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Answer:

y = 2x + 7

Step-by-step explanation:

Answer:

{27.5, 29, 34}.

Step-by-step explanation:

In order they are

24 27 28 28 29 31 32 36 38

The Median = middle value = 29.

Lower quartile =  mean of 27 and 28 =  27.5.

Upper quartile =  mean of 32 and 36 = 34.

Answer:

{27.5, 29, 34}

Step-by-step explanation:

Arrange in increasing order :

Lower Quartile :

Median :

Upper Quartile :

Answer:

76°

Step-by-step explanation:

Taking the cosine ratio of the angle of depression :

area of rectangle= length × width

= 19×33

= 627 sq units

well, the cheap answer is, simply multiply the top and bottom of one fraction by the other fractions denominator, Check the picture below.

The calculated value of the height of figure 1 is (d) 4 units

from the question, we have the following parameters that can be used in our computation:

The figures

The figure 1 is similar to figure 2

So, we have

4x/(x + 1) = 2x/x

When evaluated, we have

4x = 2x + 2

So, we have

2x = 2

Evaluate

x = 1

This means that

Height = 4 * 1

Evaluate

Height = 4

Hence, the height of figure 1 is 4 units

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Answer:

74 I believe

180 - 32 = 148

148/2 = 74

Hope this helps!

Answer:

[tex]x + x + 32 = 180(sum \: of \: inside \: the \: triangle \: is180) \\ 2x = 180 - 32 \\ x = \frac{148}{2} \\ x = 74[/tex]

Answer:

78m

Step-by-step explanation:

6942 ÷ 89 = 78, here you go!

Answer:

bridget types at the fastest rate as he can type 60 words per minute

The value of a, b and c from the given expression above are 15, 1 and 4 respectively

Indices are written in form of exponential expression. Given the expression

[tex]\sqrt[4]{15}[/tex]

We are to write the expression in the form

[tex]a^{b/c}[/tex]

This is simplified as shown

[tex]\sqrt[4]{15}= 15^{1/4}[/tex]

Compare both expression

a = 15

b = 1

c = 4

Hence the value of a, b and c from the given expression above are 15, 1 and 4 respectively

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Answer:

x=+-√10+3

Step-by-step explanation:

x^2=6x+1

x^2-6x=1

To create a trinomial square on the left side of the equation, find a value that is

equal to the square of half of b

a is the number next to x^2

b is the number next to x

c is the last number

b is -6

half of b is -3

square of half of b is 9

put 9 on both sides of the = sign

x^2-6x+9=1+9

x^2-6x+9=10

(x-3)^2=10

take the square root of both sides of the = sign

√(x-3)^2=√10

x-3=√10

x=+-√10+3

Answer:

9/19  or  47.4% (nearest tenth)

Step-by-step explanation:

A roulette wheel is numbered 1 to 36 with 0 and 00.

Therefore, there is a total of 38 evenly-spaced pockets.

The number of odd numbers from 1 to 36 is 18

(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35)

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

[tex]\implies \textsf{Probability of odd number}= \sf \dfrac{18}{38}=\dfrac{9}{19}=47.4\%[/tex]

Roulette wheel contains 1 to 36 numbers excluding 0 and 00

Total odd nos

{1,3,5,7,9,11,13,15,17,19,21,23,25,29,31,33,35}

Probability

Answer:

x = 27.4

Step-by-step explanation:

[tex]\sf \angle Q+ \angle R+ \angle S=180^{o} [/tex]

[tex]\sf 34.6 + 118 + x = 180[/tex]

Add 34.6 and 118 = 152.6

[tex]\sf 152.6+x=180[/tex]

Subtract 152.6 from both sides.

[tex]\sf x=180 - 152.6[/tex]

Subtract 152.6 from 180 = 27.4.

Therefore, the missing angle "x" is 27.4.

Answer:

option 3, [tex]972\pi in^{3}[/tex]

Step-by-step explanation:

The formula to find the volume of a sphere is [tex]\frac{4}{3} \pi r^{3}[/tex]

where r os the radius

given: diameter = 18in

radius = diameter / 2

radius = 18 / 2

r = 9in

Plug in radius:

[tex]\frac{4}{3} \pi (9)^{3}\\\\\frac{4\pi (9)^{3}}{3} \\\\Factor (9)^{3}: (3)^{6}\\\\\frac{(3)^{6} * 4\pi }{3} \\\\[/tex]

cancel common factor: 3

[tex]3^{5} * 4\pi \\3^{5} = 243\\243 * 4\pi\\972\pi[/tex]

Let me know if you have any questions !

Answer:

8.318

Step-by-step explanation:

writing a number in three decimal places means writing the number in a way that there will be three digits in the number after the decimal point.

to three decimal places= 8.318

Answer:

1) 9y^10

2) 560u^16 v^15

Step-by-step explanation:

Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³

the volume of a hemisphere is half the volume of a sphere, so

V = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3}[/tex] πr³ = [tex]\frac{2}{3}[/tex] πr³ , then

V = [tex]\frac{2}{3}[/tex] π × 3.2³

  = [tex]\frac{2}{3}[/tex] π × 32.768

  ≈ 68.63 cm³ ( to 2 dec. places )

Answer:

X Intercepts: (2, 0), (-6, 0),

Y Intercepts: (0, – 12)

minimum: (-2,-16)

Step-by-step explanation:

A) what are the x intercepts

X- axis interception points of x²+ 4x– 12:

(2,0), (-6,0)

B)what is the y intercepts

Y-axis interception point of x² + 4X – 12:

(0, – 12)

X Intercepts: (2, 0), (-6, 0), Y Intercepts: (0, – 12)

C)what is the maximum and minimum value

Parabola equation in polynomial form

The parabola params are:

a=1, b=4,c= -12

xv= -b/2a

xv= -4/2.1

simplify

xv=-2

Plug in xv = -2 to find the yv value

yv= -16

Therefore the parabola vertex is (-2, – 16)

If a<0. then the vertex is a maximum value

If a>0. then the vertex is a minimum value

a=1

minimum=(-2,-16)

Using trigonometric ratio, the length of the ladder that reached the window is 20.03 feet

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let l represent the length of the ladder, using trigonometric ratio:

sin(64) = 18/l

l = 20.03 feet

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An example of a statistcal question that Sam could write about is the weight of the members of a sample of 100 dogs.

Statistical question can be regarded as the question that needed alot of data processing before one can answer it.

When choosing a Statistical question, one should know that it will involve collection of data for processing such as classification of the pet base on their weights.

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