NO LINKS!! URGENT HELP PLEASE!!!
Movies generally lose 23% of its audience for each week it is in the theatre. A movie STARTED with an audience of 196 people per viewing.
a. Equation: ________________
b. Make a chart and fill in the table for the first ten weeks.
c. Graph the function. Label each axis with a title and scale
Answers
Answers:
a) The equation is y = 196(0.77)^x
b) The chart is shown below
c) The graph is shown below
================================================
Explanation:
Part (a)
One template of an exponential equation is y = ab^x
a = starting valueb = connected to the growth rate or decay rateIn this case
a = 196b = 1-0.23 = 0.77If 23% of the audience leaves, then 77% remains. This is another way to see where b = 0.77 comes from. Exponential decay will have 0 < b < 1.
Therefore, the equation is y = 196(0.77)^x
Other equations are possible.
-------------------
Part (b)
I'll be using LibreOffice spreadsheet to make the table. Any spreadsheet software will do.
Type x into cell A1
Type 0 and 1 into cells A2 and A3 in that order.
Select cells A2 and A3. Pull down the small marker at the bottom right corner. Pull this marker down to cell A12 to get values 2 through 10 (which will be in cells A4 to A12).
Now move to cell B1. Type in y = 196(0.77)^x in this cell.
In cell B2, type in "=ROUND(196*(0.77)^A2)" without quotes. As you can probably guess, the ROUND function will round to the nearest whole number. The calculation 196*(0.77)^A2 computes the result of y = 196*0.77^x when plugging x = 0 which is in cell A2.
Do not forget about the equal sign up front.
After cell B2 is filled in, hit enter. Then pull down the smaller marker at the bottom right corner to cell B12. A bunch of whole numbers should fill in cells B3 to B12
This is what you should get for your table
[tex]\begin{array}{|c|c|} \cline{1-2}\text{x} & \text{y} = 196(0.77)^{\text{x}}\\\cline{1-2}0 & 196\\\cline{1-2}1 & 151\\\cline{1-2}2 & 116\\\cline{1-2}3 & 89\\\cline{1-2}4 & 69\\\cline{1-2}5 & 53\\\cline{1-2}6 & 41\\\cline{1-2}7 & 31\\\cline{1-2}8 & 24\\\cline{1-2}9 & 19\\\cline{1-2}10 & 14\\\cline{1-2}\end{array}[/tex]
x = week number
y = viewer count (approximate)
Example calculation:
Plug in x = 5 to get y = 196*0.77^5 = 53.05297 approximately which rounds to y = 53. Therefore, we estimate there would be about 53 people in the audience for week 5.
-------------------
Part (c)
You could use a spreadsheet to make the graph, but I find GeoGebra is more friendly for graphing. But we'll be using the data we just made in the spreadsheet.
Select cells A2 through B12. This is the 11 row by 2 column block of x,y data pairs. Do not select the headers at the top.
Copy that data and paste it into GeoGebra's spreadsheet mode.
Then select that same block of data in GeoGebra. Right-click to go to "create" then to "list of points". It will do as it describes. Eleven points will show up in the graph window. Resize and adjust the window if needed.
I'm using the following window parameters
xMin = -5xMax = 20yMin = -20yMax = 220The graph is shown in the screenshot below.
Answer:
[tex]\textsf{a.} \quad \textsf{Equation:} \;\;\;y=196(0.77)^x[/tex]
b. See below.
c. See attachment.
Step-by-step explanation:
We can model the given situation using an exponential decay equation since the weekly change in audience is a constant percentage change.
Exponential decay formula[tex]\boxed{y=a(1-r)^x}[/tex]
where:
a is the initial value.r is the percentage decrease (in decimal form).x is the time period.Given the movie started with an audience of 196 people viewing, a = 196.
Given the movie loses 23% of its audience each week, r = 0.23.
As the movie loses a constant percentage of its audience each week, let x be the number of weeks.
Substitute the values of a and r into the formula and simplify:
[tex]y=196(1-0.23)^x[/tex]
[tex]y=196(0.77)^x[/tex]
Therefore, the equation that models the given scenario is:
[tex]\boxed{y=196(1-0.23)^x}[/tex]
Create a table for the first ten weeks by substituting the values of x from zero through 10 into the equation. Round each number to the nearest whole number.
[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}$Weeks$\;x&$Audience$\;y\\\cline{1-2}\vphantom{\dfrac12}0&196\\\cline{1-2}\vphantom{\dfrac12}1&151\\\cline{1-2}\vphantom{\dfrac12}2&116\\\cline{1-2}\vphantom{\dfrac12}3&89\\\cline{1-2}\vphantom{\dfrac12}4&69\\\cline{1-2}\vphantom{\dfrac12}5&53\\\cline{1-2}\vphantom{\dfrac12}6&41\\\cline{1-2}\vphantom{\dfrac12}7&31\\\cline{1-2}\vphantom{\dfrac12}8&24\\\cline{1-2}\vphantom{\dfrac12}9&19\\\cline{1-2}\vphantom{\dfrac12}10&14\\\cline{1-2}\end{array}[/tex]
The graph of the function is an exponential decay curve, which starts at (0, 196) and approaches zero as x approaches infinity.
The x-axis represents the number of weeks and the y-axis represents the audience size.
Use a scale of x : y = 1 : 10.
Plot the points from the table and draw a smooth curve through them that approaches zero as x approaches infinity.
Related Questions
The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. Which plot represents a stemplot of the data? * Height of eruption (in.) 66 32 50 900 50 40 70 70 59 61 60 88 80 50 63 54 62 73 70 49
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The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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The values closest to these middle elements are 60 and 61 inches.
How do we use stemplot to find the middle data?To construct a stemplot for the given data, we need to separate each observation into a stem and a leaf. The stem is the digit(s) on the left-hand side of the decimal point, while the leaf is the digit on the right-hand side. The stemplot for the given data is:
3 | 2
4 | 0 9 9
5 | 0 0 0 4 4 9
6 | 1 2 3
7 | 0 0 3 0
8 | 0 8
9 | 0
To find the two values that are closest to the middle, we need to sort the data in order from lowest to highest:
We have 19 observations, so the middle two observations are the 10th and 11th values, which are 60 inches and 61 inches, respectively. Therefore, the two values closest to the middle are 60 inches and 61 inches.
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a. Find angle x
b. What kind of angle is angle x ?
Answers
Answer: if the first angle is 61° then the angle x is 119°
but if the first angle is 67 then the angle x is 113°
Step-by-step explanation:
Line is 180° that means our formula will look like that 67 or 61 + x = 180 in that case we have to calculate x ⇒ 180 - 61 or 67 = x
For each triangle, calculate the ratio of the opposite side to the adiacent side to two decimal places. How do they compare?
Answers
Answer:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
Choice C: The ratio is the same for both triangles
Step-by-step explanation:
[tex]Triangle\: 1: } \dfrac{opposite}{adjacent} = \dfrac{16}{39.6} = \boxed{0.40404\cdots}[/tex]
[tex]Triangle\: 2: } \dfrac{opposite}{adjacent} = \dfrac{48}{118.8} = \boxed{0.40404\cdots}[/tex]
So both ratios are the same. This is also because the ratios represent the tan of the angle that the adjacent side makes with the hypotenuse and this angle of 22° is same in both triangles
Simplify using the vertical method
Answers
This method can be used to quickly obtain the product of two polynomials.A-6k²+25k²-16k-15.
What is expression?Expression in math is a combination of numbers, symbols and operators that represent a mathematical quantity or operation. It can be a single number, a single variable, or a combination of numbers, variables and symbols combined together to form a mathematical statement. An expression can also include functions, such as polynomials, exponential functions, or logarithmic functions.
The vertical method involves writing the terms of the two factors side by side and multiplying them together to get the product.
(3k+5) (2k²-5k-3)
6k³ + 0k² + 0k + -15
0k³ + 10k² + -15k + 0
0k³ + 5k² + -15k + 0
0k³ + 0k² + 15k + 0
Adding the terms in each column yields the product:
A-6k³+25k²-16k-15
Therefore, the correct answer is A-6k³+25k²-16k-15.
In conclusion, using the vertical method can simplify algebraic multiplication problems by breaking them down into columns and adding the terms in each column. This method can be used to quickly obtain the product of two polynomials.
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Find the value of x. Round to the nearest degree.
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The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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The missing sides of the triangle have been identified here.
How do we solve right triangle?Trigonometric ratios relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent. If you know the measure of one of the acute angles in the triangle and the length of one of the sides, you can use trigonometric ratios to solve for the length of another side.
1) Sin x = 5/14
x = Sin-1 (5/14)
x = 21°
2) Tan x = 8/5
x = Tan-1 (8/5)
x = 58°
3) Cos x = 9/13
x = Cos-1 (9/13)
x = 46°
4) Cos x = 3/5.8
x = Cos-(3/5.8)
x = 59°
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Using the parallel lines below determine the measure of the smaller angle.
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x+114
x+72
▸
Answers
The measure of the smaller angle of the co-interior angles is 69°
What the measure of the smaller angle?Co-interior angles are simply angles that occur in between two parallel lines when they are intersected by a transversal.
The two angles add up to 180º as they occur on the same side of the transversal always.
From the image, the two co-interior angles are:
x + 114
x + 72
Since the two angles add up to 180º.
x + 114 + x + 72 = 180
Solve for x
2x + 186 = 180
2x = 180 - 186
2x = -6
x = -6/2
x = -3
Hence, the measure of the two angles are:
x + 114 = -3 + 114 = 111°
x + 72 = -3 + 72 = 69°
Therefore, the smallest angle is 69 degree.
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In the diagram shown, Δ ABC is equilateral. AD is an altitude.
10). ∠ ABD = ______.
11). ∠ ADB = ______.
12). ∠ BAD = _____.
13). ∠ CAD = _____.
Suppose AB = 6. Find:
14). BD
15). AD
16). Area of Δ ABC
Answers
The missing sides of the triangle are
10). ∠ ABD = 60 degrees
11). ∠ ADB = 90 degrees
12). ∠ BAD = 30 degrees
13). ∠ CAD = 30 degrees
How to find the missing sides in the triangle14. BD is half of the length = BC / 2 = 6/2 = 3
15. AD is the height this is solved using Pythagoras theorem as below
AD^2 = AB^2 - BD^2
AD^2 = 6^2 - 3^2
AD^2 = 36 - 9
AD = sqrt (27)
16. Area of Δ ABC
= 1/2 * base * height
= 1/2 * 6 * sqrt (27)
= 9 sqrt (3)
= 15.59 square units
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Question
Which of the following key characteristics is NOT true of a linear function?
Responses
Domain is all real numbers.
Maximum number of vertices is one.
Rate of change is constant.
There is exactly 1 y -intercept.
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1. a gallon of water weighs 8 1/3 lbs.
a. what is the weight of 25
gallons of water?
b. If the weight of an empty 25 gallon tank is 1/10 of the water it can hold, what is the weight of the tank?
c. what is the weight of a 25 gallon tank filled with water?
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B. ((8+1/3)25)/10
C. A+B
Pedrobuysawheelbarrowpricedat$86.Shippingandhandlingareanadditional30%oftheprice.HowmuchshippingandhandlingwillPedropay?
Answers
The price of the wheelbarrow is $86, and Pedro will need to pay an additional 30% of the price for shipping and handling.
To calculate the shipping and handling cost, we can first find 30% of the price of the wheelbarrow:
30% of $86 = 0.3 x $86 = $25.80
Therefore, Pedro will need to pay $25.80 for shipping and handling.
K
The reading speed of second grade students in a large city is approximately normal, with a mean of 88 words per
minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f).
(a) What is the probability a randomly selected student in the city will read more than 94 words per minute?
The probability is 0.2743.
(Round to four decimal places as needed.).
Interpret this probability. Select the correct choice below and fill in the answer box within your choice.
OA. If 100 different students were chosen from this population, we would expect
per minute.
OB. If 100 different students were chosen from this population, we would expect
minute.
OC. If 100 different students were chosen from this population, we would expect
per minute.
to read more than 94 words
to read exactly 94 words per
to read less than 94 words
Answers
If 100 different students were chosen from this population, we would expect approximately 27 of them to read more than 94 words per minute. Therefore, the correct choice is (A).
How to explain the probabilityThe probability that a randomly selected student in the city will read more than 94 words per minute is 0.2743.
z-score = (x - μ) / σ = (94 - 88) / 10 = 0.6
Therefore, the probability of a z-score being greater than 0.6 is:
P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 = 0.2743
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Brainly pls help me with this
Answers
Answer:
38.part A) 3p = 25.47
partB) $8.49
Step-by-step explanation:
38) to get the price of a game ,$25.47 will be divided by
25.47÷3=$8.49
the price of 1 game =&8.49
to get the price of 1 game , the equation will be
3p=25.47
p=25.47÷3
p=$8.49
Plot -2 1/6 and 11/6 on the number line below.
Answers
The number line where we plotting -2 1/6 and 11/6 is attached
Plotting -2 1/6 and 11/6 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-2 1/6 and 11/6
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-13/6 and 11/6
This means that we can plot -13/6 at -13 and 11/6 at point 11 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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In a 300-m-tall building, the stairwells are no more than 20 stories high. A story is approximately 3 m high. What is the maximum pressure differential in a stairwell? What is the atmospheric pressure difference between the top of the building and street level? What is the difference in static water pressure between consecutive floors?
Answers
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
We have,
Assuming a standard atmospheric pressure of 101.3 kPa.
Maximum pressure differential in a stairwell:
Since each stairwell is no more than 20 stories high and each story is approximately 3 m high, the maximum height difference between two floors in a stairwell is:
= 20 x 3
= 60 m
Using the formula for hydrostatic pressure, the maximum pressure differential in a stairwell is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(60 m)
= 58,860 Pa
The atmospheric pressure difference between the top of the building and street level:
The atmospheric pressure decreases with increasing altitude.
Using the formula for hydrostatic pressure, the pressure difference between the top of the building and the street level is:
ΔP = ρgh
= (1000 kg/m³)(9.81 m/s²)(300 m)
= 2,943,000 Pa
The difference in static water pressure between consecutive floors:
Assuming a standard density of water of 1000 kg/m³, the difference in static water pressure between consecutive floors is:
ΔP = ρgh = (1000 kg/m³)(9.81 m/s²)(3 m) = 29,430 Pa
Therefore,
The maximum pressure differential in a stairwell is 58,860 Pa.
The atmospheric pressure difference between the top of the building and the street level is 2,943,000 Pa.
The difference in static water pressure between consecutive floors is 29,430 Pa.
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The product of two numbers is 1296. If one number is16 times the other, find the number.
Answers
your aanswer is 9 ⚡
The value of numbers are,
⇒ 9 and 16
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The product of two numbers is 1296.
And, one number is 16 times the other,
Let first number = x
Hence, Second number is, 16x
So, We get;
⇒ 16x × x = 1296
⇒ 16x² = 1296
⇒ x² = 81
⇒ x = 9
Hence, first number = 9
And, Second number is,
= 16x
= 16 x 9
= 144
Thus, The value of numbers are,
⇒ 9 and 16
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ANSWER THIS FIRST GET BRAINLESS W EXPLANATION!
3. Combine terms: 12a + 26b -4b – 16a.
(a) 4a + 22b,
(b) -28a + 30b,
(c) -4a + 22b,
(d) 28a + 30b.
Answers
To solve this equation by combining terms, the answer will be: (c) -4a + 22b.
How to solve the equationTo solve the equation, we need to combine like terms together. This means that the figures with the suffix, a will come together, while those with the suffix, b will also align themselves. Going by this rule, we will have:
12a -16a + 26b -4b.
= -4a + 22b
When a higher number is to be subtracted from a smaller number, the result will be a negative number as is the case with the terms that have the 'a' initials.
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Two different functions are represented.
Function A:
X
0
1
2
3
4
f(x)
5
10
20
40
80
Function B:
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only
positive numbers.
O The domain and range of both functions contain only
positive numbers and zero.
Answers
Okay, let's analyze the two functions based on the options:
Function A:
X f(x)
0 5
1 10
2 20
3 40
4 80
Options:
Neither function A nor function B has an x-intercept. - False, function A has an x-intercept at x=0.
Neither function A nor function B has a y-intercept. - False, function A has a y-intercept at f(x)=5.
The domain and range of both functions contain only positive numbers. - False, function A has values that include 0.
The domain and range of both functions contain only positive numbers and zero. - True, the domain and range of both functions contain only non-negative numbers including 0.
Therefore, the correct choice is:
O The domain and range of both functions contain only positive numbers and zero.
Let me know if you have any other questions!
Are the functions f(x) and g(x) inverses of each other? Use composition of functions to determine your answer.
f(x) = 7x-1
x+1
g(x)
O Yes
O No
Answers
help with calculus. determine wheter each labeled point is an absolute maximum or minumum OR a relative maximum or minimum or neither
Answers
The relative maximum and minimum point as well as the absolute maximum and minimum points based on labeled points on the graph are;
Points 1, 3, and 5 are relative maximum points
Points 2 and 4 are relative minimum points
Point 5 is an absolute maximum point
Point 2 is an absolute minimum point
What is a relative maximum point?A relative maximum is a point in which the maximum with regards to the immediate surrounding points.
Therefore, the relative maximum points are;
The points 1, 3, and 5
The relative minimum points are points that are the minimum points, when compared with the surrounding points
The relative minimum are the points 2 and 4
The absolute maximum is the point which is at the highest point on the graph
The absolute maximum on the graph is therefore, the [oint 5
The absolute minimum on the graph is the point which is the minimum point compared to all other points
Therefore, the absolute minimum point is the point 2
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Fill in the blanks.
The depth of the snow in my yard is normally distributed, with a mean of 2.5 inches and a standard
deviation of 0.25 inches.
What value is one standard deviation below the mean?
Hint: Read the section on the empirical rule.
inches
What value is one standard deviation above the mean?
I
What is the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7
inches? 68
percent
Submit Question
inches
Answers
Where the above conditions existing, the probability that a randomly selected site will have a snow depth between 2.25 and 2.7 inches is 68.3 %.
What is the explanation for this ?t the value The value one standard deviation below the mean is 2.25 inches.
The value one standard deviation above the mean is 2.75 in.
To find the probability , calculate the z-scores for these values
z1 = (2.25 - 2.5 ) /0.25 = -1
z2= ( 2.7 -2.5 ) / 0.25 = 0.8
Using a standard normal distribution table ....
we can see that the probability of a z- score between -1 and 0.8 is approximately 0.683, or 68.3%.
Hence, the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7 inches is 68.3%.
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A rectangle has a height of 4x and a width of 3x +1. Express the area of the entire rectangle. Expression should be expanded. Area =
Answers
Answer:
12[tex]x^{2}[/tex]+4x
Step-by-step explanation:
area = width * height
substitution: area = (3x+1)*4x
distributive property: area = (4x*3x)+(4x*1)
simplify: area = 12[tex]x^{2}[/tex]+4x
Hi can i convert the binary number 1000000 to a hexadecimal number?
Answers
Answer: yes, the hex of the number 1,000,000 would be 40.
1. If the gross domestic product of a country is significantly higher in one year than in another, what
might account for the difference
a. population growth
b. greater available resources and technological advances
Oc. inflation
C.
d. all of these
2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have
what percentage of the nation's income
a. 20 percent
b. 3.8 percent
c. 90 percent
d. 46.8 percent
3. The economic condition most likely to be caused by a war affecting oil production in the
Mid East would be
a. demand-pull inflation
b. cost-push inflation
c. deflation
d. cost of living inflation
Answers
1. If the gross domestic product of a country is significantly higher in one year than in another, the factor that might account for the difference is d. all of these.
2. The Lorenz Curve for the United States indicates that the richest 20 percent of households have d. 46.8 percent of the nation's income.
3. The economic condition most likely to be caused by a war affecting oil production in the Mid East would be a. demand-pull inflation.
What is the gross domestic product?The gross domestic product or GDP refers to the total monetary value of goods produced and services provided in a country during one specific period.
What is the Lorenz Curve?The Lorenz Curve, developed by Max Lorenz measures income inequality or wealth inequality using a graphical representation.
What is demand-pull inflation?When there is a shortage in supply, pressure is mounted on the available quantity of an item, causing its price to increase.
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TrianglePQR is shown.
A. What are the missing side lengths in TrianglePQR
B. Explain how you arrived at your answer.
Answers
The length of the two unknown sides of the triangle are: 12√2
How to find the missing lengths of the triangle?There are different methods of finding the missing sides of triangles such as:
Pythagoras Theorem
Law of sines or sine rule
Law of cosines or cosine rule
Now, we are given an Isosceles triangle with a base length and two equal base angles.
Thus, the two unknown sides will have equal side lengths.
∠D = 90°
Thus, using sine rule:
12/sin 90 = QR/sin 45
QR = 12 * 1/√2
Rationalizing the denominator gives:
QR = 12√2
Since the two unknown sides of the triangle are equal, then we say that:
PQ = 12√2
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The interest earned on rs15000 in 3 years at simple interest is rs5400 find the rate of interest per anunm
Answers
Answer:
12%
Step-by-step explanation:
Let the rate of interest be R%
r = R% as decimal =R/100
Simple interest earned for 3 years at rate r on ₹15,000 = ₹5,400
The formula for interest earned is given by
I = Prt
where P is the principal amount (15,000)
r = annual interest rate as a decimal (to be determined)
t = number of years
Plugging in known values we get
5400 = 15000 x r x 3
= 45000 x r
r = 5400/45000
r = 0.12
Rate of interest as a percentage = r x 100 = 0.12 x 100 = 12%
Miller Toy Company manufactures a plastic swimming pool at its Westwood Plant. The plant has been experiencing problems as shown by its June contribution format income statement below:
Flexible
Budge
Actual
Sales (7,000 pools)
$265,000 $265,000
Variable expenses:
Variable cost of goods sold*
79,240
97,525
Variable selling expenses
19,000
19,000
Total variable expenses
98,240
116,525
Contribution margin
166,760
148,475
Fixed expenses:
Manufacturing overhead
Selling and administrative
Total fixed expenses
Net operating income (loss)
67,000
67,000
85,000
85,000
152,000
152,000
$ 14,760 $ (3,525)
Janet Dunn, who has just been appointed general manager of the Westwood Plant, has been given instructions to "get things under control. Upon reviewing the plant's income statement, Ms. Dunn has concluded that the major problem lies in the variable cost of goods sold. She has been provided with the following standard cost per swimming pool:
Direct materials
Direct labor
Variable manufacturing overhead
Total standard cost per unit
Standard
Quantity or
Hours
3.5 pounds
0.4 hours
0.3 hours
Standard Price or Rate
§ 2.10 per pound
$ 7.60 per hour
$ 3.10 per hour
Standard
Cost
$ 7.35
3.04
0.93
$ 11.32
During June, the plant produced 7,000 pools and incurred the following costs:
a. Purchased 29,500 pounds of materials at a cost of $2.55 per pound.
b. Used 24,300 pounds of materials in production. (Finished goods and work in process inventories are insignificant and can be ignored.)
c. Worked 3,400 direct labor-hours at a cost of $7.30 per hour.
d. Incurred variable manufacturing overhead cost totaling $8,400 for the month. A total of 2,400 machine-hours was recorded.
It is the company's policy to close all variances to cost of goods sold on a monthly basis
Required:
1. Compute the following variances for June:
a. Materials price and quantity variances
b. Labor rate and efficiency variances.
c. Variable overhead rate and efficiency variances.
2. Summarize the variances that you computed in (1) above by showing the net overall favorable or unfavorable variance for the month.
Answers
a. Materials price variance = (Standard price - Actual price) x Actual quantity
= ($2.10 - $2.55) x 24,300 pounds
= -$10,935 (Unfavorable)
b. Materials quantity variance = (Standard quantity - Actual quantity) x Standard price
= (3.5 pounds - 24,300 pounds) x $2.10 per pound
= -$48,465 (Unfavorable)
Labor rate and efficiency variances:
a. Labor rate variance = (Standard rate - Actual rate) x Actual hours
= ($7.60 - $7.30) x 3,400 hours
= $1,020 (Favorable)
b. Labor efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 3,400 hours) x $7.60 per hour
= -$23,600 (Unfavorable)
Variable overhead rate and efficiency variances:
a. Variable overhead rate variance = (Standard rate - Actual rate) x Actual hours
= ($3.10 - $8,400/2,400 hours) x 2,400 hours
= -$2,800 (Unfavorable)
b. Variable overhead efficiency variance = (Standard hours - Actual hours) x Standard rate
= (0.3 hours - 2,400 hours) x $3.10 per hour
= -$7,194 (Unfavorable)
Net overall favorable or unfavorable variance for the month:
To calculate the net overall variance, we sum up all the variances:
Overall Variance = Materials price variance + Materials quantity variance + Labor rate variance + Labor efficiency variance + Variable overhead rate variance + Variable overhead efficiency variance
= -$10,935 + (-$48,465) + $1,020 + (-$23,600) + (-$2,800) + (-$7,194)
= -$94,014 (Unfavorable)
Approximately 8% of all people have blue eyes. A random sample of 20 people is selected, find μ. Round to one decimal place. Answer
Answers
Answer:
The mean of a binomial distribution is μ = np, where n is the sample size and p is the probability of success (having blue eyes).
μ = 20 x 0.08
μ = 1.6
Rounded to one decimal place, μ is 1.6.
HELP FAST PLEASE
Question
Does each equation represent exponential decay or exponential growth?
Drag and drop the choices into the boxes to correctly complete the table.
Note: If an equation is neither exponential growth nor exponential decay, do not drag it to the table.
All choices that have numbers like a/b are fractions.
Choices:
A= (0.97)^t
y= 3.7 (0.2)^t
y= 9/11 (4)^t
P= 7/9 (5/4)^t
V= 0.8 (9)^t
P= 0.9 (8.3)^t
g(x)= 2.1(x)
Answers
The exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
If the base is larger than 1, it will be an exponential growth.
For example, [tex]3^2=9[/tex]
If the base is smaller than 1, it will be an exponential decay.
For example, [tex]0.5^2=0.25[/tex]
If the function does not have an exponent, that means there will be no exponential growth or decay.
Therefore the exponential growth functions are,
[tex]y=\frac{9}{11}(4)^t[/tex]
[tex]V=0.8(9)^t[/tex]
[tex]P=0.9(8.3)^t[/tex]
[tex]P=\frac{7}{9}(\frac{5}{4})^t[/tex]
The exponential decay functions are,
[tex]A= (0.97)^t[/tex]
[tex]y= 3.7 (0.2)^t[/tex]
The function which is neither exponential growth nor exponential decay is,
g(x)=2.1(x).
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Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days for a payment to be received and recorded, and that the month is 30 days long. (Round your answers to the nearest cent.)
$500 balance, 16%, $50 payment
(a) previous balance method $
(b) adjusted balance method $
(c) average daily balance method
Answers
Interest charge for the month = 51.69 rounded to the nearest penny.
Here, we have,
The particular month in question is 30 days long.
Your balance at the start of the month is 3,000.
Annual interest rate = 21%.
Payment = 150.00.
When the payment is made in the month, it reflects on the tax amount you pay on both the average day balance.
YOU SEND THE PAYMENT IN ON THE FIRST DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 11TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 10 (10 days)
Average daily balance is 2850 from day 11 until day 30 (20 days)
Average daily balance for the month = 10 * 3000 + 20 * 2850
= 87000 / 30
= 2900
Interest charge for the month = 0.21 * 2900 * 30 / 365
Interest charge for the month = 50.05 rounded to the nearest penny
YOU SEND THE PAYMENT IN ON THE TWENTIETH DAY OF THE MONTH.
YOUR ACCOUNT IS CREDITED ON THE 30TH DAY OF THE MONTH.
Average daily balance is 3000 from day 1 until day 29 (29 days)
Average daily balance is 2850 from day 30 until day 30 (1 day)
Average daily balance for the month = 3000 * 29 + 1 * 2850
= 89850 / 30
= 2995
Interest charge for the month = 0.21 * 2995 * 30 / 365
Interest charge for the month = 51.69 rounded to the nearest penny
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Complete Question:
Calculate the monthly finance charge for the following credit card transaction. Assume that it takes 10 days for a payment to be received and recorded and that the month is 30 days long. Round your answer to the nearest cent.
3,000 balance, 21% rate, 150 payment, average daily method
A rectangle has perimeter 70 inches, and its area is 286 sq-inches. Find the dimensions of this
rectangle. (For purposes of this problem only, the width is shorter than the length.)
length =
width=
inches
inches
Enter your answers as numbers. If necessary, round to the nearest hundredths.
Answers
Thus, the dimensions of the rectangle are - length 22 inches and width 13 inches.
Explain about the rectangle:An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). The opposite sides of a rectangular are equal and parallel. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
Let the length of rectangle be 'l'
Let the width be 'w'.
Then,
Perimeter = 2(l + w)
70 = 2(l + w)
35 = l + w
l = 35 - w ...eq 1
Now,
Area = length * width
286 = l*w ...eq 2
Put eq 1 in eq 2
286 = (35 - w)*w
286 = 35w - w²
w² - 35w + 286 = 0
Solving the quadratic equation:
w² - 22w - 13w + 22*13 = 0
w(w - 22) - 13(w - 22)= 0
(w - 22)(w - 13) = 0
w = 22 and w = 13
As, length is greater than width-
width w = 13 inch
Length l = 35 - 13 = 22 inches.
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