The company’s earnings per share reported in its financial statements for the year ended December 31, 2020 is $1.45. The correct option is c.
To calculate earnings per share, we need to take the company's net income and divide it by the weighted average number of shares outstanding during the year.
First, let's adjust for the stock dividend on July 31. Since the dividend was 100%, we can double the number of shares outstanding to 416,000:
Jan. 1: 200,000 shares
Feb. 1: 8,000 new shares
July 31: 200,000 shares doubled to 400,000 shares
Dec. 31: 416,000 shares
Next, we need to calculate the weighted average number of shares outstanding during the year. We can do this by taking the number of shares outstanding for each period and multiplying it by the number of months those shares were outstanding:
Jan. 1 to Jan. 31: 200,000 shares x 1 month = 200,000
Feb. 1 to July 31: (200,000 + 8,000) shares x 6 months = 1,248,000
Aug. 1 to Dec. 31: 416,000 shares x 5 months = 2,080,000
Total weighted average shares outstanding: 3,528,000
Finally, we can divide the net income of $560,000 by the weighted average shares outstanding of 3,528,000 to get earnings per share of $0.1585. Multiplying this by 9 (since there are 9 months of the year remaining after February 1) gives us earnings per share of $1.4265. Rounded to the nearest penny, the answer is $1.45.
Thus, The correct option is c.
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Casey recently purchased a sedan and a pickup truck at about the same time for a new business. The value of the sedan S, in dollars, as a function of the number of years t after the purchase can be represented by the equation S(t)=24,400(0. 82)^t. The equation P(t)=35,900(0. 71)^t/2 represents the value of the pickup truck P, in dollars, t years after the purchase. Analyze the functions S(t) and P(t) to interpret the parameters of each function, including the coefficient and the base. Then use the interpretations to make a comparison on how the value of the sedan and the value of the pickup truck change over time
Answer: Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.
Step-by-step explanation:
The functions S(t) and P(t) represent the value of the sedan and pickup truck, respectively, as a function of time t in years since the purchase. Let's analyze each function:
For S(t)=24,400(0.82)^t, the coefficient 24,400 represents the initial value or starting point of the function. This means that the value of the sedan at the time of purchase was $24,400.
The base 0.82 represents the rate of depreciation or decrease in value of the sedan over time. Specifically, the sedan's value decreases by 18% per year (100% - 82%).
For P(t)=35,900(0.71)^t/2, the coefficient 35,900 represents the initial value or starting point of the function.
This means that the value of the pickup truck at the time of purchase was $35,900. The base 0.71 represents the rate of depreciation or decrease in value of the pickup truck over time.
Specifically, the pickup truck's value decreases by approximately 29% every two years, since the exponent is divided by 2.
Comparing the two functions, we can see that the initial value of the pickup truck was higher than the initial value of the sedan.
However, the rate of depreciation of the pickup truck is greater than that of the sedan. This means that the pickup truck will lose its value at a faster rate than the sedan.
For example, after 5 years, we can evaluate each function to see the values of the sedan and pickup truck at that time:
S(5) = 24,400(0.82)^5 ≈ $10,373.67
P(5) = 35,900(0.71)^(5/2) ≈ $15,864.48
We can see that after 5 years, the pickup truck is still worth more than the sedan, but its value has decreased by a greater percentage. Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.
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Brody is going to invest $350 and leave it in an account for 18 years. Assuming the interest is compounded daily, what interest rate, to the
neatest tenth of a percent, would be required in order for Brody to end up with $790?
Brody would need an interest rate of 4.5% compounded daily.
How to calculate interest rate of investment?
We can use the compound interest formula to solve the problem:
[tex]A = P(1 + r/n)^(^n^t^)[/tex]
where:
A = final amount of money ($790)
P = initial investment ($350)
r = interest rate (unknown)
n = number of times interest is compounded per year (365, since interest is compounded daily)
t = time in years (18)
So, we can plug in the given values and solve for r:
[tex]790 = $350(1 + r/365)^(^3^6^5^1^8^)[/tex]
[tex]2.25714 = (1 + r/365)^(^3^6^5^1^8^)[/tex]
[tex]ln(2.25714) = ln[(1 + r/365)^(^3^6^5^1^8^)][/tex]
[tex]ln(2.25714) = 18ln(1 + r/365)[/tex]
[tex]ln(2.25714)/18 = ln(1 + r/365)[/tex]
[tex]e^(^l^n^(^2^.^2^5^7^1^4^)^/^1^8^)^ =^ 1^ +^ r^/^3^6^5[/tex]
[tex]1.0345 = 1 + r/365[/tex]
[tex]r/365 = 0.0345[/tex]
[tex]r = 12.5925[/tex]
Therefore, Brody would need an interest rate of approximately 12.6% (rounded to the nearest tenth of a percent) in order to end up with $790 after 18 years with daily compounding.
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What is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet? Give the exact answer and approximate to two decimal places.
Thank you!
19.29 cubic feet is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet
Without knowing the specific shape of the composite figure, it is impossible to give an exact answer. However, we can provide a general formula for the volume of a cylinder with height h and diameter d, and assume that the composite figure consists of a cylinder and some other shape.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder. The diameter of the cylinder is given as 2.5 feet, which means the radius is 1.25 feet.
If the height of the cylinder is also 2.5 feet, then the volume of the cylinder is:
V_cylinder = π(1.25)^2(2.5) = 6.15π cubic feet (exact)
To approximate to two decimal places, we can use the approximation π ≈ 3.14:
V_cylinder ≈ 6.15(3.14) = 19.29 cubic feet (approximate to two decimal places)
However, since we do not know the specific shape of the composite figure, we cannot give an exact answer for its volume.
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use the given information to solve the triangle
C=135° C = 45₁ B = 10°
4)
5) A = 26°₁ a = 10₁ 6=4
6) A = 60°, a = 9₁ c = 10
7) A=150° C = 20° a = 200
8) A = 24.3°, C = 54.6°₁ C = 2.68
9) A = 83° 20′, C = 54.6°₁ c 18,1
The law of sines is solved and the triangle is given by the following relation
Given data ,
From the law of sines , we get
a / sin A = b / sin B = c / sin C
a)
C = 135° C = 45₁ B = 10°
So , the measure of triangle is
A/ ( 180 - 35 - 10 ) = A / 35
And , a/ ( sin 135/35 ) = sin 35 / a
On simplifying , we get
a = 36.50
Hence , the law of sines is solved
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what percent of stainless steel in the tank is used to make the two ends
Answer:
The percentage of stainless steel used to make the two ends of the tank cannot be determined without additional information. Please provide more details about the tank and its construction.
Step-by-step explanation:
To calculate the percentage of stainless steel used to make the two ends of the tank, we need to know the total amount of stainless steel used to make the entire tank, as well as the amount used to make the ends. Without this information, it is impossible to determine the percentage of stainless steel used for the ends.
For example, if the tank is made entirely of stainless steel, then the percentage of stainless steel used to make the ends would be 100%. However, if the tank is made of multiple materials, then the percentage of stainless steel used for the ends would depend on the amount of stainless steel used for the entire tank and the amount used for the ends.
Therefore, to calculate the percentage of stainless steel used for the ends of the tank, we need additional information about the tank's construction and materials.
A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 13. 5 feet, and a height of 15 feet. The container is completely filled with contents that weigh, on average, 0. 47 pound per cubic foot. What is the weight of the contents in the container, to the nearest pound?
Answer=1142 lbs
The weight of the component is of length of 12 feet, a width of 13. 5 feet, and a height of 15 feet, and weighs on average 0. 47 pounds per cubic foot is 1142 lbs.
To find the weight of the contents in the container, we need to first find the volume of the container.
The formula for the volume of a right rectangular prism is length x width x height.
So, the volume of the container is:
12 ft x 13.5 ft x 15 ft = 2430 cubic feet
Next, we need to multiply the volume by the weight per cubic foot:
2430 cubic feet x 0.47 lbs/cubic foot = 1141.1 lbs
Rounding to the nearest pound, the weight of the contents in the container is approximately 1142 lbs.
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A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks , the sheet is only 1. 25 meters thick. Let y represent the ice sheet's thickness (in meters) after weeks. Which of the following information about the graph of the relationship is given?
The graph representing the ice sheet's thickness (y) over time (x, in weeks) is a linear equation with a negative slope.
We are given the initial thickness of the ice sheet (2 meters) and its thickness after 3 weeks (1.25 meters). The rate of decrease in thickness is constant.
To find the slope, we can use the formula: (change in y) / (change in x). Here, the change in y is (1.25 - 2) = -0.75 meters, and the change in x is 3 weeks.
Therefore, the slope is -0.75 / 3 = -0.25 meters/week. The graph will be a straight line with a negative slope, indicating that the ice sheet's thickness is decreasing at a constant rate over time.
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(a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1, 2, 3) x + 3y + 22 = 14 14 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Ox - 1 = y - 2 = z - 3 OX-1-y-2-2-3 14 14 Y Y 2 3 X-1 _ y - 2 2-3 2 3 y 14 14 14 o 1 2
An equation of the tangent plane to the surface at the given point is x + 2y + 3z = 14. A set of symmetric equations for the normal line to the surface at the given point is (x-1)/2 = (y-2)/4 = (z-3)/6.
The gradient of the surface is given by
∇f(x, y, z) = <2x, 2y, 2z>
At point (1, 2, 3), the gradient is
∇f(1, 2, 3) = <2, 4, 6>
The equation of the tangent plane can be found using the formula
f(x, y, z) = f(a, b, c) + ∇f(a, b, c) · <x-a, y-b, z-c>
Plugging in the values we have
x + 2y + 3z = 14
The direction vector of the normal line is the same as the gradient of the surface at the given point
<2, 4, 6>
To find symmetric equations for the line, we can use the parametric equations
x = 1 + 2t
y = 2 + 4t
z = 3 + 6t
Eliminating the parameter t, we get the symmetric equations
(x-1)/2 = (y-2)/4 = (z-3)/6
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You earn $130.00 for each subscription of magazines you sell plus a salary of $90.00 per week. How many subscriptions of magazines do you need to sell in order to make at least $1000.00 each week?
Jen is filling bags with M&Ms. She has 5 1/2 cups of M&Ms. She needs 1 1/4 cups of M&Ms to fill each bag. How many bags can Jen fill completely?
Jen can fill 4 bags completely with the 5 1/2 cups of M&Ms she has, given that each bag requires 1 1/4 cups of M&Ms.
First, we need to find the total number of cups of M&Ms Jen has
5 1/2 cups = 11/2 cups
Then, we divide the total number of cups by the number of cups needed to fill each bag
(11/2 cups) ÷ (1 1/4 cups/bag)
To divide by a fraction, we can multiply by its reciprocal
(11/2 cups) x (4/5 cups/bag)
= 44/10 cups
Simplifying, we get
= 4 2/10 cups
= 4 1/5 cups
So, Jen can fill 4 bags completely.
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You spin a spinner that has 12 equal-sized sections numbered 1 to 12. Find the probability of p(even or less than 8)
The probability of getting an even number or a number less than 8 is:
P = 0.83
How to find the probability for the given event?The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.
The numbers that are even or less than 8 are:
{1, 2, 3, 4, 5, 6, 7, 8, 10, 12}
So 10 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:
P = 10/12 = 0.83
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How much must be deposited today into the following account in order to have a $110,000 college fund in 17 years? Assume no additional deposits are made.
An account with quarterly compounding and an APR of 4.9%
Therefore, an initial deposit of $37,728.66 is required to have a college fund of $110,000 in 17 years with quarterly compounding and an APR of 4.9%.
What is a deposit used for?An amount held in an account is referred to as a deposit. It might be put up in a bank as collateral for goods that are being rented out or bought. A deposit is used in many different sorts of economic transactions.
Compound interest can be calculated using the following formula to determine the required down payment:
A = P(1 + r/n)(nt)
where:
A = the future value of the account (in this case, $110,000)
P = the principal or initial deposit
r = the annual interest rate (4.9%)
n = the number of times the interest is compounded per year (4 for quarterly compounding)
t = the number of years (17)
When we enter the specified numbers into the formula, we obtain:
$110,000 = P(1 + 0.049/4)(4*17)
$110,000 = P(1.01225)⁶⁸
$110,000 = P * 2.9126
Dividing both sides by 2.9126, we get:
P = $37,728.66
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I Need help with a Math Problem
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Challenge: Six different names were put into a hat. A name is chosen 100 times and the name Fred is chosen 11 times. What is the experimental probability of the name Fred beingâ chosen? What is the theoretical probability of the name Fred beingâ chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
The experimental probability of choosing the name Fred is nothing.
=============
The theoretical probability of choosing the name Fred is nothing
The experimental and theoretical probability of the name Fred being chosen is 0.11 and 0.167 respectively.
The question is asking for the experimental and theoretical probabilities of choosing the name Fred when six different names are put into a hat and a name is chosen 100 times.
To find the experimental probability of choosing the name Fred, divide the number of times Fred is chosen by the total number of trials (100 times). In this case, Fred is chosen 11 times.
Experimental probability of choosing Fred = (number of times Fred is chosen) / (total number of trials)
= 11 / 100
= 0.11 or 11%
For the theoretical probability, since there are six different names in the hat and each name has an equal chance of being chosen, the probability of choosing Fred is:
Theoretical probability of choosing Fred = 1 / 6
≈ 0.167 or 16.67%
If the number of names in the hat were different, the theoretical probability would change because the denominator (total number of names) would be different. For example, if there were 5 names instead of 6, the theoretical probability of choosing Fred would be 1/5 or 20%.
The experimental probability would also likely change since the outcomes of the trials would be different with a different number of names.
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The demand function for a company's product is P=26e^{-.04q} where Q is measured in thousands of units and P is measured in dollars.
(a) What price should the company charge for each unit in order to sell 2500 units? (Round your answer to two decimal places.) (b) If the company prices the products at $8.50 each, how many units will sell? (Round your answer to the nearest integer.) units
A. the company should charge approximately $18.08 per unit to sell 2500 units.
B. Q is measured in thousands, this means the company will sell about 6350 units (rounded to the nearest integer) when the price is set at $8.50 per unit.
(a) To find the price for each unit to sell 2500 units, we need to plug Q = 2.5 (since Q is in thousands) into the demand function P = 26e^(-0.04Q):
P = 26e^(-0.04 * 2.5)
After calculating the value, we get:
P ≈ 18.08
So, the company should charge approximately $18.08 per unit to sell 2500 units.
(b) To find how many units will sell if the price is $8.50, we need to solve the equation P = 26e^(-0.04Q) for Q:
8.50 = 26e^(-0.04Q)
First, we need to isolate the exponential term:
(8.50 / 26) = e^(-0.04Q)
Now, take the natural logarithm (ln) of both sides:
ln(8.50 / 26) = -0.04Q
Next, divide both sides by -0.04:
Q = ln(8.50 / 26) / -0.04
After calculating the value, we get:
Q ≈ 6.35
Since Q is measured in thousands, this means the company will sell about 6350 units (rounded to the nearest integer) when the price is set at $8.50 per unit.
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Sam built a circular fenced-in section for some of his animals. The section has a circumference of 55 meters. What is the approximate area, in square meters, of the section? Use 22/7 for π.
The approximate area of the circular fenced-in section is 950.5 square meters.
The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. We are given that the circumference of the fenced-in section is 55 meters, so we can set up the equation:
2πr = 55
We can solve for r by dividing both sides by 2π:
r = 55/(2π)
We are asked to find the area of the section, which is given by the formula A = πr². Substituting our expression for r, we get:
A = π(55/(2π))²
Simplifying, we get:
A = (55²/4)π
Using the approximation 22/7 for π, we get:
A ≈ (55²/4)(22/7)
A ≈ 950.5
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A random number generator picks a number from 12 to 41 in a uniform manner. Round answers to 4 decimal places when possible.
a. The mean of this distribution is
b. The standard deviation is
c. The probability that the number will be exactly 36 is P(x = 36) =
d. The probability that the number will be between 21 and 23 is P(21 < x < 23) =
e. The probability that the number will be larger than 26 is P(x > 26) =
f. P(x > 16 | x < 18) =
g. Find the 49th percentile.
h. Find the minimum for the lower quartile
The mean of this distribution is 26.5. The standard deviation is 8.0623. The probability that the number will be exactly 36 is P (x = 36) = 0.0286. The probability that the number will be between 21 and 23 is P (21 < x < 23) = 0.0400. The probability that the number will be larger than 26 is P (x > 26) = 0.2857. P (x > 16 | x < 18) = undefined. The 49th percentile is 29.3700. The minimum for the lower quartile is 19.75.
a. The mean of a uniform distribution is the average of the maximum and minimum values, so in this case, the mean is:
mean = (12 + 41) / 2 = 26.5
Therefore, the mean of this distribution is 26.5.
b. The standard deviation of a uniform distribution is given by the formula:
sd = (b - a) / sqrt(12)
where a and b are the minimum and maximum values of the distribution, respectively. So in this case, the standard deviation is:
sd = (41 - 12) / sqrt(12) = 8.0623
Therefore, the standard deviation of this distribution is 8.0623.
c. Since the distribution is uniform, the probability of getting any specific value between 12 and 41 is the same. Therefore, the probability of getting exactly 36 is:
P(x = 36) = 1 / (41 - 12 + 1) = 0.0286
Rounded to four decimal places, the probability is 0.0286.
d. The probability of getting a number between 21 and 23 is:
P(21 < x < 23) = (23 - 21) / (41 - 12 + 1) = 0.0400
Rounded to four decimal places, the probability is 0.0400.
e. The probability of getting a number larger than 26 is:
P(x > 26) = (41 - 26) / (41 - 12 + 1) = 0.2857
Rounded to four decimal places, the probability is 0.2857.
f. The probability that x is greater than 16, given that it is less than 18, can be calculated using Bayes' theorem:
P(x > 16 | x < 18) = P(x > 16 and x < 18) / P(x < 18)
Since the distribution is uniform, the probability of getting a number between 16 and 18 is:
P(16 < x < 18) = (18 - 16) / (41 - 12 + 1) = 0.0400
The probability of getting a number greater than 16 and less than 18 is zero, so:
P(x > 16 and x < 18) = 0
Therefore:
P(x > 16 | x < 18) = 0 / 0.0400 = undefined
There is no valid answer for this question.
g. To find the 49th percentile, we need to find the number that 49% of the distribution falls below. Since the distribution is uniform, we can calculate this directly as:
49th percentile = 12 + 0.49 * (41 - 12) = 29.37
Rounded to four decimal places, the 49th percentile is 29.3700.
h. The lower quartile (Q1) is the 25th percentile, so we can calculate it as:
Q1 = 12 + 0.25 * (41 - 12) = 19.75
Therefore, the minimum for the lower quartile is 19.75.
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6) Mary sold $192 worth of greeting cards. If she received 25% commission on her sale
now much commission did she earn?
why is 101 not in the sequence of 3n-2
101 is not in the sequence of 3n-2 because it cannot be obtained by multiplying a positive integer n by 3 and subtracting 2 from the product.
The sequence 3n-2 is a set of numbers obtained by taking a positive integer n, multiplying it by 3 and then subtracting 2 from the product. For example, if n = 1, then 3n-2 = 1. If n = 2, then 3n-2 = 4. If n = 3, then 3n-2 = 7, and so on.
Now, you may wonder why the number 101 is not in the sequence of 3n-2. To understand this, we need to determine whether there exists a positive integer n such that 3n-2 is equal to 101.
Let's start by assuming that such an n exists. Then we can write:
3n-2 = 101
Adding 2 to both sides, we get:
3n = 103
Dividing both sides by 3, we get:
n = 103/3
This means that n is not a whole number, which contradicts our assumption that n is a positive integer. Therefore, there cannot exist any positive integer n such that 3n-2 equals 101.
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Convert the given radian measure to a degree measure.
Negative 1. 7 pi
a.
153 degrees
b.
Negative 306 degrees
c.
Negative 153 degrees
d.
306 degrees
Please select the best answer from the choices provided
The given radian measure -1.7 pi is equivalent to -306 degrees.
How to convert radians to degrees?The correct answer is option (b), Negative 306 degrees. This conversion takes into account the negative sign of the radian measure, resulting in a negative degree measure to convert a radian measure to a degree measure, we use the conversion factor that 180 degrees is equal to π radians.
Given the radian measure -1.7π, we can calculate the corresponding degree measure by multiplying -1.7π by the conversion factor:
Degree measure = (-1.7π) * (180 degrees / π)
The π in the numerator and denominator cancels out, resulting in:
Degree measure = -1.7 * 180 degrees
Calculating the value, we have:
Degree measure = -306 degrees
Therefore, the correct answer is option b) Negative 306 degrees.
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58 of a birthday cake was left over from a party. the next day, it is shared among 7 people. how big a piece of the original cake did each person get?
If 58% of the birthday cake was left over from the party, then 42% of the cake was consumed during the party. That's why, each person would get approximately 8.29% of the original cake as a leftover piece the next day.
Let's assume that the original cake was divided equally among the guests during the party.
So, if 42% of the cake was shared among the guests during the party, and there were 7 people in total, each person would have received 6% of the cake during the party.
Now, the leftover 58% of the cake is shared among the 7 people the next day. To find out how big a piece of the original cake each person gets, we need to divide 58% by 7:
58% / 7 = 8.29%
Therefore, each person would get approximately 8.29% of the original cake as a leftover piece the next day.
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Use the coordinates to find the length of each side
Then find the perimeter. (Examples 1 and 2)
D(1, 2), E(1, 7), F(4, 7), G(4, 2)
A production line operation is designed to fill cans with tomato sauce with a mean weight of 20 ounces. A sample of 25 cans is selected to test whether overfilling or under filling is occurring in the production line and they should stop and adjust it. Sample statistics (mean and standard deviation) are calculated. Assume the population of interest is normally distributed.
Let the p-value be 0. 067 for this sample. At 0. 05 level of significance, it can be concluded that the mean filling weight of the population is :_________
a. Significantly different than 20 ounces
b. Not significantly different than 20 ounces
c. Significantly less than 20 ounces
d. Not significantly less than 20 ounces
At a significance level of 0.05, the critical value is typically chosen as 1.96 for a two-tailed test. Comparing this critical value with the obtained p-value of 0.067, which is greater than 0.05, indicates that the result is not statistically significant.
At 0.05 level of significance, when we fail to reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis. In this case, the null hypothesis states that the mean filling weight of the population is equal to 20 ounces. Since the data does not provide strong evidence to suggest otherwise, we conclude that the mean filling weight is not significantly different from 20 ounces.
Hence, the answer is (b) "Not significantly different than 20 ounces."
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Luka and Janie are playing a coin toss game. If the coin lands heads up, Luka earns a point; otherwise, Janie earns a point. The first player to reach 25 points wins the
game. If 24 of the first 47 tosses have been heads, what is the probability that Janie wins the game?
The probability that Janie wins the game is I.
(Simplify your answer. )
Probability of Janie winning game = (2⁴⁷ - 1)/2⁴⁷ or approximately 0.999999999999978, using binomial distribution with given information.
How can we find the probability?We can solve this probability by using the binomial distribution. Let X be the random variable representing the number of heads in the remaining tosses until one of the players wins the game. Since Luka has 24 points, Janie needs to win X heads before Luka wins one more.
We want to find the probability that Janie wins the game, which is the probability that X is greater than or equal to Luka's remaining points needed to win(25 - 24 = 1).
Let p be the probability of the coin landing heads up, and q be the probability of the coin landing tails up, so that p + q = 1. Since the coin is fair, p = q = 1/2.
Using the binomial distribution, the probability that Janie wins the game is:
P(X >= 1) = 1 - P(X = 0)
where
P(X = k) = [tex](47 - 24 choose k) (1/2)^k (1/2)^(47 - 24 - k)[/tex]
= (23 + k choose k) (1/2)⁴⁷
where k = 0, 1, 2, ..., 23.
Therefore,
P(X = 0) = (23 choose 0) (1/2)⁴⁷ = 1/2⁴⁷
P(X >= 1) = 1 - P(X = 0) = 1 - 1/2⁴⁷
Simplifying,
P(X >= 1) = (2⁴⁷ - 1)/2⁴⁷
Therefore, the probability that Janie wins the game is (2⁴⁷ - 1)/2⁴⁷ or approximately 0.999999999999978.
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Find the area of a circle with a radius of 2 2start color purple, 2, end color purple. Either enter an exact answer in terms of π πpi or use 3. 14 3. 143, point, 14 for π πpi and enter your answer as a decimal
The area of the circle is 12. 56 square units
How to determine the areaThe formula for calculating the area of a circle is expressed as;
A = πr²
This is so such that the parameters of the equation are;
A is the area of the circleπ takes the constant value of 3.14 or 22/7r is the radius of the circleFrom the information given, we have that;
Area = unknown
Radius = 2 units
Now, substitute the values into the formula, we have;
Area = 3.14 ×2²
Find the square
Area = 3.14 × 4
Multiply the values, we have;
Area = 12. 56 square units
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pls some help with this question!
Can someone help me asap? It’s due today!!
Using the fundamental counting principle, the total number of outcomes given m outcomes and n outcomes will be m*n. A helpful way to think about this is by using a tree.
Say we have 2 shirts and 3 pairs of pants. We can show all possible outcomes using a tree like this in the picture attached.
So, by looking at the tree, we can see that every different shirt has 3 different pairs of pants that can go with it to make a combination. Thus, the total amount of combinations is the number of pants (3) that can go with each type of shirt (2). So, 3*2 is 6 total combinations.
In this example, m was 2 and n was 3. Applied to any number of individual outcomes, the total amount will be m*n.
Chaz is writing an informal proof to show that circle q is similar to circle p after a similarity transformation followed by a rigid transformation which two translations in sequence should chaz use map circle q onto circle p
Chaz builds a connection between points on circle Q and points on circle P by carrying out these two translations while maintaining the size and shape of the circles.
Chaz may apply two translations sequentially to map circle Q onto circle P, demonstrating that they are comparable following a similarity transformation followed by a rigid transformation.
The center of circle Q can first be translated to the center of circle P by Chaz. The two circles' centers will match thanks to this translation.
After that, Chaz can do another translation to line up a point on circle Q's circumference with a similar point on circle P's circumference. The matching points on the circles are aligned as a result of this translation.
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Suppose a ball is thrown and follows the f(x)=-0.25(x-3)2+6.25. find the ball's initial and maximum height?
(show work)
Maximum Height of the ball: 6.25 units
To find the initial and maximum height of the ball following the function f(x) = -0.25(x-3)^2 + 6.25, we need to evaluate the function at the initial position and find the vertex of the parabola.
Initial height:
When the ball is initially thrown, it's at position x=0. Plug this value into the function:
f(0) = -0.25(0-3)^2 + 6.25
f(0) = -0.25(-3)^2 + 6.25
f(0) = -0.25(9) + 6.25
f(0) = -2.25 + 6.25
f(0) = 4
The initial height of the ball is 4 units.
Maximum height:
The maximum height corresponds to the vertex of the parabola. Since the function is in the form f(x) = a(x-h)^2 + k, the vertex is at the point (h, k). In our case, h = 3 and k = 6.25.
The maximum height of the ball is 6.25 units.
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A rectangular patio is 10 feet by 13 feet. what is the length of the diagonal of the patio? (use pythagorean theorem: a² + b ²= c²)
The length of the diagonal is c = √269 feet.
To get the length of the diagonal of a rectangular patio, we can use the Pythagorean theorem, which states that for a right triangle with legs of length a and b, and hypotenuse of length c, a² + b² = c². In this case, the legs of the right triangle are the length and width of the rectangular patio, which are 10 feet and 13 feet, respectively. Let's use a and b to represent these lengths.
a = 10 feet
b = 13 feet
We want to find the length of the diagonal, which is the hypotenuse of the right triangle. Let's use c to represent this length.
a² + b² = c²
10² + 13² = c²
100 + 169 = c²
269 = c²
Now we need to find the square root of 269 to get the length of the diagonal.
c = √269
c ≈ 16.4 feet
So the length of the diagonal of the rectangular patio is approximately 16.4 feet. We can also find the ratio of the length, width, and diagonal of the rectangular patio.
length:width = 10:13
width:length = 13:10
length:diagonal = 10:√269
width:diagonal = 13:√269
diagonal:length = √269:10
diagonal:width = √269:13
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