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Movies generally lose 23% of it's audience for each week in the theatre. A movie STARTED with an audience of 196 people per viewing.
Answers
Answers:
a) The equation is [tex]y = 196(0.77)^x[/tex]
b) See image attachment below
c) See image attachment below
d) Week 10
=======================================================
Explanation:
a)
One common template for an exponential equation is [tex]y = a*b^x[/tex] where 'a' is the starting amount and b is the growth or decay factor.
a = 196 is the starting amount of people who saw the movie per showtime
b = 1-0.23 = 0.77 is the decay factor. If the view count goes down by 23%, then we keep the remaining 77%
Therefore we go from [tex]y = a*b^x[/tex] to [tex]y = 196(0.77)^x[/tex]
x = number of weeks
y = number of people, per viewing, who saw the movie for the particular week
--------------------
b)
Plug in x = 0 to find that y = 196
Plug in x = 1 to get y = 150.92 which rounds to y = 151 since we're talking about the number of people
Repeat for x = 2 all the way up to x = 9 to account for the first ten weeks. We stop at 9 instead of 10 because we started at x = 0.
The table is shown in the attachment below next to the graph.
I'm not sure why your teacher put a dollar sign over the second column of the table when it should be the number of people. It might be a typo. If they meant to do it, then there's missing information about ticket prices.
--------------------
c)
The graph is shown below. You can plot each (x,y) point on the same grid and then draw a curve through them. A much quicker way is to use software like GeoGebra (which is what I used) or Desmos or a pocket calculator. There are tons of many options to pick from. Feel free to choose your favorite.
The blue dashed segments on the graph visually help verify the result of part (d). We have y = 20 lead to an x value somewhere between x = 8 and x = 9. When submitting the graph to your teacher, you'll leave out the blue dashed segments.
--------------------
d)
Refer to the table we made in part (b). We have x = 9 lead to y = 19 approximately which is when y is below 20 people. Recall that x = 0 refers to week 1, so x = 9 refers to week 9+1 = 10. Week ten is where the view count drops below 20 people per showing.
If you wanted to use the graph in part (c), then you'd follow the blue dashed line mentioned earlier. Start at the y axis at y = 20. Trace the blue dashed line until reaching the curve. Then drop straight down to arrive somewhere between x = 8 and x = 9. Round up to x = 9. Then make the adjustment to go from x = 9 to week ten.
If you want an algebraic method, then follow the steps below.
Plug in y = 20 and solve for x. We'll need to involve logarithms to isolate the exponent.
[tex]y = 196(0.77)^x\\\\20 = 196(0.77)^x\\\\20/196 = (0.77)^x\\\\0.1020408 \approx (0.77)^x\\\\(0.77)^x \approx 0.1020408\\\\\text{Log}\left((0.77)^x\right) \approx \text{Log}(0.1020408) \\\\x*\text{Log}\left(0.77\right) \approx \text{Log}(0.1020408) \\\\x \approx \text{Log}(0.1020408)/\text{Log}\left(0.77\right) \\\\x \approx 8.7325564 \\\\[/tex]
This rounds up to x = 9 leading to week ten as the answer.
As confirmation
[tex]y = 196(0.77)^x = 196(0.77)^8 \approx 24.22 \approx 24\\\\y = 196(0.77)^x = 196(0.77)^9 \approx 18.65 \approx 19\\\\[/tex]
Answer:
Part (a)We can model this as an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is growth factorx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
As the movie theatre lost 23% of its audience each week, the growth (decay) factor will be 100% - 23% = 77% → 0.77
Given:
a = 196b = 0.77x = times (in weeks)y = audience (in number of people)Substitute the given values into the formula to create the exponential equation:
[tex]y=196(0.77)^x[/tex]
Part (b)[tex]\begin{tabular}{| c | r |}\cline{1-2} \bf weeks & \bf audience \\\cline{1-2} 1 & 150.92\\\cline{1-2} 2 & 116.21\\\cline{1-2} 3 & 89.48\\\cline{1-2} 4 & 68.90\\\cline{1-2} 5 & 53.05\\\cline{1-2} 6 & 40.85\\\cline{1-2} 7 & 31.46\\\cline{1-2} 8 & 24.22\\\cline{1-2} 9 & 18.65\\\cline{1-2} 10 & 14.36\\\cline{1-2}\end{tabular}[/tex]
**all values rounded to 2 dp**
Part (c)see attached for graph
Part (d)Set y < 20 and solve for x:
[tex]\begin{aligned}196(0.77)^x & < 20\\\\(0.77)^x & < \dfrac{5}{40}\\\\\ln (0.77)^x & < \ln\left(\dfrac{5}{49}\right)\\\\x\ln (0.77) & < \ln\left(\dfrac{5}{49}\right)\\\\x & > \dfrac{\ln\left(\dfrac{5}{49}\right)}{\ln (0.77)}\\\\x & > 8.732555795\end{aligned}[/tex]
Therefore, the movie audience will fall below 20 people per viewing during the 9th week.
Related Questions
A rectangle has sides that are 7 and 2/5 inches wide and 11 and 2/3 inches long. What is the perimeter of the rectangle?
Answers
Answer:
38.1333333334
Step-by-step explanation:
Perimeter of rectangle:
2 × (length + width) inches
2 × (7 2/5 + 11 2/3) inches
2 × 19.0666666667 inches
38.1333333334
Circle the exponent
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Answer:
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Answer:
x = 108 , y = 72
Step-by-step explanation:
x and 108 are alternate exterior angles and are congruent , then
x = 108
x and y are same- side exterior angles and sum to 180° , that is
x + y = 180
108 + y = 180 ( subtract 108 from both sides )
y = 72
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Answer:
(d) 112 m²
Step-by-step explanation:
The area of a parallelogram is given by the formla ...
A = bh . . . . . . where b is the base length and h is the height
__
Here, the base is divided into parts, but their total length is 5m+9m = 14m. The height is given as 8m, so the area is ...
A = (14 m)(8 m) = 112 m²
The area of the parallelogram is 112 square meters.
__
Alternate solution
You can also figure this as the sum of the areas of the two triangles and that of the center rectangle.
A = 2(1/2bh) +bh
A = 2(1/2(5 m)(8 m)) +(9 m)(8 m) = 40 m² +72 m² = 112 m²
what is the sum of 9+10?
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Answer:
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Step-by-step explanation:
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Answer:
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Quadrant I examples:
(2, 5)(3, 4)(7, 1)Quadrant II examples:
(-1, 5)(-6, 2)(-4, 7)Quadrant III examples:
(-3, -4)(-7, -1)(-8, -5)Quadrant IV examples:
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Huuuurrry plllzzzzzz. Determine the equation of the line that passes through the given points (2,6) and (4,16)
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Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope of the lineb is the y-intercept (the value of y when the line passes through the y-axis)To find linear equations in slope-intercept form:
Determine the slopePlug the slope into the general formDetermine the y-intercept by isolating bPlug the b back into the equationSolving the QuestionWe're given:
The line passes through the points (2,6) and (4,16)First, determine the slope of the line.
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are points that fall on the line
⇒ Plug in the given points (2,6) and (4,16):
[tex]m=\dfrac{16-6}{4-2}\\\\m=\dfrac{10}{2}\\\\m=5[/tex]
⇒ Therefore, the slope of the line is 5. Plug this back into the general form:
[tex]y=5x+b[/tex]
Now, determine the y-intercept.
[tex]y=5x+b[/tex]
⇒ Plug in one of the given points:
[tex]6=5(2)+b\\6=10+b\\b=-4[/tex]
⇒ Therefore, the y-intercept is -4. Plug this back into our original equation:
[tex]y=5x-4[/tex]
Answer[tex]y=5x-4[/tex]
are positive 4 and negative 4 equal to each other?
Answers
Answer:
Step-by-step explanation:
no, because positive 4 is 8 more than negative 4.
Answer:
one positive n one negative equals a positive
Step-by-step explanation:
no?
A repair company charges a one-time service fee and an hourly rate for the time needed to complete each job. The
table shows the amounts the company used for these charges over four consecutive years.
Charges for Repair Jobs
Year
12 3 4
Service Fee $20 $25 $30 $35
Hourly Rate $52$55 $58 $61
Part A
Using the data in the table, what would the company's service fee and hourly rate, in dollars, be in year 8? Enter
your answers in the first and second response boxes.
Part B
What total amount, in dollars, would the company charge for a job that requires 3 hours of work in year 9? Enter
your answer in the third response box.
Part A: Service Fee
Part 1: Hourly Rate
Answers
Answer:
A: Service Fee = $55
Hourly Rate = $ 73
B: $288
Step-by-step explanation:
A: the service rate increases by $5 per year, so year 8 would be $20 more than year 4 (5*4)
The hourly rate increases by $3 per year, so year 8 would be $12 more than year 4 (3*4)
B. Service fee for year 9 would be $60 ($5 more than year 8) and the hourly rate would be $76 per hour ($3 more than year 8). This gives you Service Fee + (Hourly rate * 3) = $60 + ($73*3) = $60 + $228 = $288
B form.
Given the system of equations below, write the system in AX
- 112 - 13y = - 62
72 - 3y = 25
[3]
Il
Answers
Answer:
[tex]X=\left[\begin{array}{cc}-5&2\\0&8\\8&1\end{array}\right][/tex]
Step-by-step explanation:
Solving the given matrix equation, we find ...
X = (1/4)(C - B)
These operations, subtraction and multiplication by a scalar, are done on a term-by-term basis. A calculator or spreadsheet can do these for you.
For example, the middle right term (row 2, col 2) is ...
(38 -6)/4 = 32/4 = 8
Answer:
[tex]X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]
Step-by-step explanation:
[tex] Given \:\: B=\begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix} \: and\: C=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]
To Solve: 4X + B = C
[tex]\implies 4X + \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}[/tex]
[tex]\implies 4X =\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}- \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}[/tex]
[tex]\implies 4X =\begin {bmatrix} -12-8 & 6-(-2)\\-1 -(-1)& 38-6\\24-(-8) & -6-(-10)\end{bmatrix}[/tex]
[tex]\implies 4X =\begin {bmatrix} -12-8 & 6+2\\-1 +1 & 38-6\\24+8 & -6+10\end{bmatrix}[/tex]
[tex]\implies 4X =\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]
[tex]\implies X =\frac{1}{4}\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}[/tex]
[tex]\implies X =\begin {bmatrix} \frac{-20}{4} & \frac{8}{4}\\\\\frac{0}{4}& \frac{32}{4}\\\\ \frac{32}{4} & \frac{4}{4}\end{bmatrix}[/tex]
[tex]\implies X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}[/tex]
Identify the lateral area and surface area of a regular square pyramid with base edge length 11 cm and slant height 15 cm, rounded to the nearest tenth.
Answers
The surface area of the square pyramid is: 451 cm²
The lateral surface area of the square pyramid = 330 cm²
What is the Lateral Surface Area and Surface Area of a Square Pyramid?Surface area = a² + 2al, where a is the base edge and l is the slant height.
Lateral Surface Area = 2al.
Given the following:
a = 11 cml = 15 cmSurface area = a² + 2al = 11² + 2(11)(15)
Surface area = 451 cm²
Lateral Surface Area = 2al = 2(11)(15)
Lateral Surface Area = 330 cm²
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The lateral and surface area of a square base pyramid with side length of 11 cm and slant height of 15 cm are 330 cm² and 451 cm².
Surface area of a pyramidsurface area = A + 1 / 2 ps
where
A = area of the basep = perimeter of the base s = slant heightTherefore,
surface area = 11² + 1 / 2 × (11 × 4) × 15
surface area = 121 + 1 / 2 × 44 × 15
surface area = 121 + 330
surface area = 451 cm²
Lateral area of a square pyramidlateral area = 1 / 2 ps
lateral area = 1 / 2 × 44 × 15
lateral area = 330 cm²
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Find the exact circumference of each circle using the given inscribed or circumscribed polygon.
Answers
Answer:
58π mi.
Step-by-step explanation:
The diameter of the circle = the hypotenuse of the right triangle ( by the angle subtended by a diameter theorem).
By Pythagoras:
diameter^2 = 40^2 + 42^2
= 3364
Diameter = 58 mi.
Now the circumference
= diameter * π
= 58π mi.
Find the amount of tax and the tax rate. Round to nearest hundredth of a percent.
Cost of item: $76
Selling price: $89.83
Answers
since the selling price is 89.83 and the cost of is 76, the tax amount is 89.83 - 76 = 13.83.
if we take 76 to be the 100%, what is 13.83 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 76 & 100\\ 13.83& x \end{array} \implies \cfrac{76}{13.83}=\cfrac{100}{x} \\\\\\ 76x=1383\implies x=\cfrac{1383}{76}\implies x\approx 18.20[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
11
220
X
Answers
Answer: X is 11,
Step-by-step explanation:
Hope it helps you
Which polygon has two sets of parallel sides?
Answers
Answer:
C
Step-by-step explanation:
C is rectangle
Rectangles have 2 sets of parallel lines
explanation: i just know things
33
The base of a right rectangular prism has
an area of 172.5 square centimeters and
a height of 8 centimeters. What is the
volume, in cubic centimeters, of the
right rectangular prism?
A 180
B 280
C 1,280
D 1,380
3
Answers
Answer:
D 1,380
Step-by-step explanation:
V = area of base × height
V = 172.5 cm² × 8 cm
V = 1380 cm³
You ask four people to the prom. If X is the number of "yes" responses, what is E(X)? Assume equal probability for
"yes" and "no" response.
Answers
Answer:
e is the amount of people
Step-by-step explanation:
4 x so let’s say you have two x you have 50% of the people that said yes.
What are the solutions of this quadratic equation? 9x^2+10=5
Answers
Answer:
No solution
Step-by-step explanation:
9x² + 10 = 5
⇔ 9x² = 5 - 10
⇔ 9x² = -5
This is impossible because 9x² > 0 and -5 < 0
please help!
Matrices
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Scalar factor Multiplication in Matrix.
So from the above matrix, -3A , is just simply multiplying the -3 to every element of the matrix, so we get as,
===> -3A = | -9 -18 |
| -24 -21 |
| -6 6 |
hence the correct option is B.
need answer asap thank you
Answers
Answer:
56
Step-by-step explanation:
First of all, if the width of the frame is 2, then add 2 to both sides of 7 to get the frame length7 + 2 + 2 = 11Do the same for 33 + 2 + 2 = 7Area of frame and white rectangle combined = 11 × 7 = 77Area of white rectangle is 7 × 3 = 21Now to get the area of the blue bit, subtract 21 from 77This gives you 56if you were to flip the coin 15, how many times will the coin land on tails based on experimental probability? jordan flipped a count of 45 times.His result are below: heads: 24 tails: 21
Answers
Answer:
It will land 7.5 times on tails, which is rounded up to 8 times
Step-by-step explanation:
there are 2 possibilities, heads or tails
so you divide 15 in 2 and get 7.5
The coin will land 7 times tail based on the experimental probability.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
When the coin tossed 45 times.
Head= 24, tail = 21
So, fraction of appearing tail will be
= 21 / 45
= 0.466667
Now, if the coin tossed 15 times then the coin land on tails
= 15 x 0.466667
= 7
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PLEASE HELP PLEASE PLEASE
Answers
Answer:
Sublimation - is the transformation from a solid to gas.
Hope this helps!
Identify the terms and like terms in the question 3n+7-n-3
Answers
Answer:
like terms: (3n,-n),(7,-3)
Step-by-step explanation:
Answer:=2n+2
Step-by-step explanation:
3n+7-n-3=2n+2
Identify the range of the function shown in the graph.
Answers
Answer:
B.
Step-by-step explanation:
the range is the y values of the line.
so it would be [3, 6]
pleaseeee helpp!!!! Nowwww
Answers
Answer:
ITS B because sqrt 11 is 3.something
Step-by-step explanation:
a radioactive substance that has half-life lof 32 years. Find the constant k in the decay formula for the substance
I put up 50 PTS if you just say a random word I will report you
Answers
Answer:
[tex]\displaystyle k = \frac{1}{32}\ln\frac{1}{2} \approx -0.02166[/tex]
Step-by-step explanation:
The decay formula is given by:
[tex]\displaystyle P(t) = P_0e^{kt}[/tex]
Where k is some constant, P₀ is the initial population, and t is the number of years.
Because the substance has a half-life of 32 years, P(t) = 1/2P₀ when t = 32. Substitute:
[tex]\displaystyle \frac{1}{2}P_0 = P_0 e^{k(32)}[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} \frac{1}{2} & = e^{32k} \\ \\ \ln\left(e^{32k}\right) & = \ln\left(\frac{1}{2}\right) \\ \\ 32k & = \ln\frac{1}{2} \\ \\ k & = \frac{1}{32}\ln\frac{1}{2} \\ \\ &\approx -0.02166\end{aligned}[/tex]
In conclusion, the value of k is about -0.02166.
The value of k in the exponential decay formula is k = 0.022
How to find the value of k?To find the constant k in the decay formula for the radioactive substance, we can use the formula for exponential decay, which is given by:
N(t) = N₀*exp(-kt)
where:
N(t) is the amount of the radioactive substance at time t.N₀ is the initial amount of the substance at t = 0 (time of measurement).e is the base of the natural logarithm (approximately 2.71828).k is the decay constant we need to find.t is the time elapsed (in this case, t is measured in years since the half-life is given in years).The half-life of the substance is the time it takes for half of the substance to decay, which is 32 years in this case. So, after one half-life, N(t) = N₀ / 2.
Now, let's set up the equation for one half-life:
N(t) = N₀ * exp(-k * 32)
Since N(t) = N₀ / 2 after one half-life, we can write:
N₀ / 2 = N₀ * e^(-k * 32)
Now, divide both sides by N₀:
1/2 = exp(-k * 32)
To solve for k, take the natural logarithm (ln) of both sides:
ln(1/2) = -k * 32
k = ln(1/2) / -32
k = 0.022
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help with geometry pleaseeee will mark the brainiest!
Answers
Answer:
384.29 in²
Step-by-step explanation:
The radius of these circles is 5 in.
- As the radii are equal, and 4 of them are used to make up the side of the square. [20 ÷ 4 = 5]
To find the area of circle, you use the formula [tex]\pi r^{2}[/tex]
[tex]\pi[/tex] · (5)² = 25[tex]\pi[/tex]
The area of the square equals the length x width
20 · 20 = 400
To find the area of the shaded region, subtract these values.
400 - 25[tex]\pi[/tex] ≈ 389.29 in²
ANSWERS THESEEESS!!!!
Answers
Número 14 es B