On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate.
Do not round your intermediate computations, and round your answer to three decimal places.
Answers
Step-by-step explanation:
so, overall, 63% will grow.
that means, every seed has a 63% chance to grow. in other words, the probabilty to grow is 0.63 (as 63% means 63 out of 100 = 0.63).
and a chance of
1 - 0.63 = 0.37
to not grow.
fewer than 8 out of 9 seeds means not 8 and not 9.
it is
1 - P(8) - P(9)
with P(x) means the probability that exactly x seeds out of the 9 grow/germinate.
the chance for a group of exactly 8 out of 9 seeds to grow is then the probabilty for 8 to grow and 1 not to grow :
0.63⁸ × 0.37 = 0.009181764...
but these are 8 seeds out of 9.
and we calculated the probability for only one possible grouping.
how many groups of 8 can we build out of 9 ?
as the sequence does not matter, and we cannot have repetitions (every seed can only count as 1), we have combinations
C(9, 8) = 9! / (8! × (9-8)!) = 9!/8! = 9
so, the total probability P(8) for exactly 8 seeds out of 9 to grow/germinate is
9 × 0.63⁸ × 0.37 = 9 × 0.009181764... = 0.082635875... ≈
≈ 0.083
now, the chance for a group of exactly 9 out of 9 seeds to grow is then the probabilty P(9) for all 9 to grow :
0.63⁹ = 0.015633814... ≈ 0.016
the probabilty that fewer than 8 out of the 9 will grow/germinate is
1 - 0.082635875... - 0.015633814... = 0.901730311... ≈
≈ 0.902
Related Questions
what is the best measure of sensors to use in the set of data below 12, 8, 15, 45, 7, 13 mean, median, mean or median, mode?
Answers
Answer:
The best measure of central tendency to use in a set of data depends on the characteristics of the data and the specific objective of the analysis. Let's examine the given data set: 12, 8, 15, 45, 7, 13.
Mean: The mean, also known as the average, is calculated by summing up all the values in the data set and dividing by the total number of values. The mean is sensitive to extreme values and can be influenced by outliers. In this case, the mean is calculated as (12 + 8 + 15 + 45 + 7 + 13) / 6 = 100 / 6 ≈ 16.67.
Median: The median is the middle value in a data set when the values are arranged in ascending or descending order. The median is not affected by extreme values and is a good measure to use when there are outliers or when the data is not symmetrically distributed. In this case, when the data set is arranged in ascending order, the median is 13, as it is the middle value.
Mode: The mode is the value that appears most frequently in a data set. It is a useful measure when we want to identify the most common value in the data set. In this case, the mode is not applicable as there are no repeated values in the data set.
Based on the characteristics of the given data set, the median is a good measure to use as it is not affected by extreme values and provides a central value that represents the middle of the data set. The mean may be influenced by the outlier value of 45, and the mode is not applicable in this case. So, the best measure of central tendency to use in this data set would be the median.
Refer to the set of data values for Diamonds below
PRICE: 6958,5885,6333,4299,9539,6921,4426,6885,5826,3670,7176,74975170,5547,13596,7521,7260,8139,12196, 14998,9736,9859,12393,25522, 11008,38794,66730,46769,28800,28868
CARATIWEIGHT):1,1,1.01,1.01,1.02,104,104,107,1.07,111,1.12,1 16,1 2,1 23,1.25,129,1.5,1.51,1.67,1.72,1.76,1.8,188,2.03,2.03,2.06,3,4.01,4.01.4.05
COLOR: 3,5, 4, 5, 2, 4, 5, 4, 5, 9,2,5,6,7,1,6,6,6,3,4,8, 5, 6, 2,8,2,1,3,6,7
(a) Use the paired data consisting of the carat weight (x) and the price (y). What is the best predicted price of a diamond with a weight of 1.6 carats?
(b) Use the paired color (x) and the price (y) data. What is the best predicted price of a diamond with a color rating of 37
Answers
linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating.
By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.
What is Equation?
An equation is a mathematical statement that states the equality of two expressions. It is made up of two parts—the left side and the right side—that are separated by an equal sign (=). The left side of an equation is made up of terms, which are numbers and/or variables, and the right side is made up of a single number or variable. Equations are used to solve for unknown values in mathematics, science, and engineering.
The best predicted price of a diamond with a weight of 1.6 carats can be found by using a linear regression equation. This equation uses the paired carat weight (x) and the price (y) data to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the carat weight increases. The equation can then be used to calculate the predicted price of a diamond with a weight of 1.6 carats.
The best predicted price of a diamond with a color rating of 3 can be found by using the paired color (x) and the price (y) data. Using the data, a linear regression equation can be used to produce a line that best fits the data. The slope of the line will help determine the rate at which the price changes as the color rating increases. The equation can then be used to calculate the predicted price of a diamond with a color rating of 3.
In conclusion, linear regression equations can be used to accurately predict the price of a diamond given its carat weight or color rating. By fitting a line to the paired data, the slope of the line can be used to determine the rate of change in price for a given increase in carat weight or color rating. This can then be used to accurately predict the price of a diamond with a given carat weight or color rating.
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Supplementary angles
Answers
Answer:
∠AGB or ∠EGD.
Step-by-step explanation:
∠AGB & ∠EGD make a straight line with ∠BGD which means they're supplementary.
Answer: ∠BGA
Step-by-step explanation:
Starting Angle: ∠BGD
Supplement: ∠BGA
HELP DUE ASAP!!!!!
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year. A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils. A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils. Which class lost the most pencils overall based on the data displayed? Mr. Simpson's class; it has a larger median value 14.5 pencils Mr. Johnson's class; it has a larger median of 11 pencils Mr. Simpson's class; it has a narrow spread in the data Mr. Johnson's class; it has a wide spread in the data
Answers
The spread of the data can also be considered, but it does not necessarily indicate which class lost the most pencils overall. Mr. Simpson's class has a narrower spread than Mr. Johnson's class, but this only means that the data in Mr. Simpson's class is more consistent, not that they lost fewer pencils overall.
Therefore, the answer is: Mr. Simpson's class; it has a larger median value 14.5 pencils.
how long will it take $5000 to grow to $6000 at an annual rate of 9% compounded monthly
Answers
A = P(1 + r/n)^(nt)
where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know that P = $5000, A = $6000, r = 0.09 (9%), and n = 12 (since interest is compounded monthly). We can solve for t algebraically:
A = P(1 + r/n)^(nt)
$6000 = $5000(1 + 0.09/12)^(12t)
$6000/$5000 = (1 + 0.09/12)^(12t)
1.2 = (1.0075)^(12t)
log(1.2) = log(1.0075)^(12t)
log(1.2) = 12t * log(1.0075)
t = log(1.2) / (12 * log(1.0075))
t ≈ 4.58
Therefore, it will take about 4.58 years (or about 55 months) for $5000 to grow to $6000 at an annual rate of 9% compounded monthly.
A = P(1 + r/n)^(nt)
where:
A = the amount of money in the account after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we want to find the time it takes for an investment of $5000 to grow to $6000 at an annual rate of 9% compounded monthly. So we have:
P = $5000
A = $6000
r = 0.09 (9% annual interest rate)
n = 12 (compounded monthly)
We want to solve for t, the number of years. So we can rearrange the formula to solve for t:
t = (log(A/P)) / (n * log(1 + r/n))
Substituting the values we have:
t = (log(6000/5000)) / (12 * log(1 + 0.09/12))
Simplifying:
t = 3.10 years (rounded to two decimal places)
Therefore, it will take approximately 3.10 years (or about 37 months) for an investment of $5000 to grow to $6000 at an annual rate of 9% compounded monthly.
Congruent angles. Help me solve!
Answers
Answer: ∠FGE
Step-by-step explanation:
Congruent: Have the same angle measure
Starting Angle: ∠BGC
Angle Of Congruence: ∠FGE
Indirect measurement, pls help, I am stuck on this question.
Answers
The building is 246 feet tall.
What are similar triangles?Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.
To determine the height of the building, we have;
height of pole = 7 ft
total length of the building's shadow = 167 ft
the length of the shadow of the pole = 4.75 ft
Let the height of the building be represented by h. On comparison, we have;
4.75/ 167 = 7/h
4.75h = 167 x 7
= 1169
h = 1169/ 4.75
= 246.11
The building is 246 ft. tall.
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Linda agreed to lend money to Alex at a rate of 9 percent per year,
contingent he would pay her 300.00 in interest over a four year period. What was the minimum mount Alex could borrow
Answers
Answer:
$731.71
Step-by-step explanation:
300 over 4 years = 75$ per yr
9% per year so 4 years interest = (1+9%)^4 = 1.41
so effective int rate for 4 years is 41%.
41% * x = 300
x = $731.71
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
Plot the points on the graphing calculator, and then determine the linear regression equation: y = -.7222x + 7.2111
The closest equation is A.
Solve for x: x - 2 = 10
A: 2
B:8
C:10
D:12
Answers
Answer:
12 is the answer
Step by step explanation
to get answer move all terms not containing x to the right side of the equation
(-23u^4 z^2 +32u^7 z^7 -12u^2 z) ÷ -4u^4 z^2
Answers
(-23u^4 z^2 +32u^7 z^7 -12u^2 z) / (-4u^4 z^2) = (-4u^4 z^2)(32u^3 z^5 - 8u^2 + 3) / (-4u^4 z^2)
The -4u^4z^2 terms cancel out, leaving:
(32u^3 z^5 - 8u^2 + 3) / u^4z^2
Therefore, the simplified expression is (32u^3 z^5 - 8u^2 + 3) / u^4z^2.
you need 18 lb of peeled and cored apples to make applesauce.apples have a yield percentage of 78%, how many pounds of whole apples are needed
Answers
You would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
Explanation:
To find out how many pounds of whole apples are needed to make 18 lbs of peeled and cored apples with a yield percentage of 78%, we can use the following formula:
Pounds of whole apples needed = (Pounds of peeled and cored apples needed) / Yield percentage
Plugging in the values we have:
Pounds of whole apples needed = 18 lb / 0.78Pounds of whole apples needed = 23.077 lb (rounded to three decimal places)
Therefore, you would need approximately 23.077 pounds of whole apples to make 18 pounds of peeled and cored apples with a 78% yield percentage.
The Indian cricket team won 50% of the matches played in the first two weeks of the
NatWest series in Australia. However, at the end of the series its success rate was 75%. If
the team had played 6 matches in the first two weeks and they then won all the matches
they played after the first two weeks, how many matches did they play after the first
two weeks?
Answers
Answer:
the Indian cricket team played 13 matches after the first two weeks.
Step-by-step explanation:
Let's assume that the Indian cricket team played x matches after the first two weeks.
We know that the team won 50% of the matches played in the first two weeks. So, out of the 6 matches played in the first two weeks, they won 0.5*6 = 3 matches.
We also know that at the end of the series, their success rate was 75%. This means that out of the total number of matches played in the entire series, they won 75% of them. Let's say the total number of matches played in the series is y. Then, we can write:
Number of matches won = 0.5*6 + x (matches won in the first two weeks + matches won after the first two weeks)
Total number of matches played = 6 + x (matches played in the first two weeks + matches played after the first two weeks)
According to the given information, the success rate at the end of the series was 75%. So we can write:
Number of matches won / Total number of matches played = 75/100
Substituting the values, we get:
(0.5*6 + x) / (6 + x) = 75/100
Simplifying this equation, we get:
12 + 4x = 25 + 3x
x = 13
Therefore, the Indian cricket team played 13 matches after the first two weeks.
There's a train going at 96km/h and another at 109km/h, how long will it take them to pass each other?
Answers
The time it would take for the trains to pass each other, would be 58.54 minutes.
How to find the time taken ?The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.
To find this time, we first need to find the combined speeds of the trains to be :
= 96 + 109
= 205 km / h
With the combined speed, the time till they pass each other would be:
= Distance between trains / Combined speed
= 200 / 205
= 58. 54 minutes
= 0. 98 hours
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The time it would take for the trains to pass each other, would be 58.54 minutes.
How to find the time taken ?The trains were initially 200 km apart and so we need to find the time till they pass each other, with the speeds they are currently going at.
To find this time, we first need to find the combined speeds of the trains to be :
= 96 + 109
= 205 km / h
With the combined speed, the time till they pass each other would be:
= Distance between trains / Combined speed
= 200 / 205
= 58. 54 minutes
= 0. 98 hours
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Glad for any help, it's a statistics problem and I have the image linked below.
Answers
The 95% confidence interval for the mean time for all players is given as follows:
Between 7.14 minutes and 10.74 minutes.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 10 - 1 = 9 df, is t = 2.2622.
Inserting the data-set into a calculator, the parameters are given as follows:
[tex]\overline{x} = 8.94, s = 2.52, n = 10[/tex]
Then the lower bound of the interval is given as follows:
8.94 - 2.2622 x 2.52/sqrt(10) = 7.14 minutes.
The upper bound of the interval is given as follows:
8.94 + 2.2622 x 2.52/sqrt(10) = 10.74 minutes.
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I need help with this
Answers
An equation is y = -12/3 when x = 3, y = -4.
What is equation?
An equation is a mathematical statement that indicates that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables that satisfy the given conditions.
If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:
x × y = k
where k is a constant of proportionality. To find the value of k, we can use the given information.
When x = 3, y = -4:
3 × (-4) = k
k = -12
Now we can substitute k into the equation to get:
x × y = -12
This is the equation relating x and y. To find y when x = 3:
3 × y = -12
y = -12/3
Therefore, when x = 3, y = -12/3.
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An equation is y = -12/3 when x = 3, y = -4.
What is equation?
An equation is a mathematical statement that indicates that two expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find the value of unknown variables that satisfy the given conditions.
If x and y vary inversely, it means that as x increases, y decreases and vice versa. We can write this relationship as:
x × y = k
where k is a constant of proportionality. To find the value of k, we can use the given information.
When x = 3, y = -4:
3 × (-4) = k
k = -12
Now we can substitute k into the equation to get:
x × y = -12
This is the equation relating x and y. To find y when x = 3:
3 × y = -12
y = -12/3
Therefore, when x = 3, y = -12/3.
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Which function is represented by the graph below?
Answers
A rectangular storage container with an open top is to have a volume of 20 cubic meters. The length of its base is twice the width. Material for the base costs 20 dollars per square meter. Material for the sides costs 3 dollars per square meter. Find the cost of materials for the cheapest such container.
Answers
The cost of the materials for the cheapest container is when width = 1.5 m
Given data ,
Let's use "w" metres to represent the rectangular storage container's width. The length would be "2w" metres since the base's length is twice as long as its width.
The container's height is indicated by the letter "h" metres.
Volume is determined by the following formula:
20 = (2w)(w)(h) 20 = 2w²h
The equation may be rearranged to represent "h" in terms of "w":
h = 20 / (2w²)
The container's "w" and "h" surface area is the next item to discuss. The surface area would be made up of the base and the four sides as the container has an open top.
We are given that the cost of material for the base is $20 per square meter and the cost of material for the sides is $3 per square meter
Cost of base material = 20 x 2w² = 40w² dollars
Cost of side material = 3 x 4wh = 12wh dollars
Total cost of material = Cost of base material + Cost of side material = 40w² + 12wh dollars
Now we can substitute the expression for "h" that we derived earlier:
Total cost of material = 40w^2 + 12w(20 / (2w²)) = 40w² + 120 / w
To find the value of "w" that minimizes the cost of material, we can take the derivative of the total cost of material with respect to "w" and set it equal to zero, then solve for "w":
d/dw (40w² + 120 / w) = 0
80w - 120 / w² = 0
On multiplying by w² on both sides , we get
80w = 120
Divide by 80 on both sides , we get
w = 3/4 m
Hence , the width of the rectangular box is w = 1.5 meter
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The accompanying data represent the percentages of teenagers in various countries that have used certain drugs. Complete parts (a) through (c)
below.
Country
Drug 1, x
Other Drugs, y
A
23
3
B с
17 41
2 21
D52
E
38
15
(=
(Round to two decimal places as needed.)
F
18
9
G
23
15
HS2
5
1
8
NO
2
CI
J
54
32
K
:
H
35
25
a. Determine the correlation coefficient between the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs.
Answers
Answer:
-1.82
Step-by-step explanation:
It won't let me write the explanation for some reason. I'll put it in the comments below
Determine the order of the matrix.
VA/L
1
5
-1 1 1 -5
-3 5 7
Answers
The order of a matrix is 2 x 5.
We have,
The order of a matrix is in the form of:
= number of rows x number of columns
Now,
The given matrix has 2 rows.
The given matrix has 5 columns.
Now,
= number of rows x number of columns
= 2 x 5
Thus,
The order of a matrix is 2 x 5.
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limh→0(5e^x−5e^(x+h))/3h
Answers
We define ln(x)=int[(1 , x)(1/t)dt], then (ln(x))’=1/x . Define e^x as the inverse of ln(x) .
Then lim [ln(1+x)/x] =lim 1/(1+x) =1 as x approaches to 0 (using the Hp rule). Let ln(1+y)=x then y=e^x-1 and lim[ln(1+y)/y]=lim[x/e^x-1]=1 as x approaches to 0. then limit[(e^h-1)/h]=1 as h approaches to 0 . We have
lim[(5e^x-5e^(x+h))/3h]=(5/3)lim[(e^x-(e^x)(e^h))/h]=(5/3)e^xlim[(1-e^h))/h]=
-(5/3)e^xlim[(e^h-1))/h]=-(5/3)e^x as h approaches to 0.
Find the length of CD. The length of BE is 28in
Answers
The length of the segment CD given the length of BE is 42 inches
Finding the length of CD given the length of BEFrom the question, we have the following parameters that can be used in our computation:
The length of CD = ?The length of BE is 28inUsing the proportional ratio from the triangle, we have
CD = 1.5 * BE
substitute the known values in the above equation, so, we have the following representation
CD = 1.5 * 28
Evaluate
CD = 42
HEnce, the lengtth is 42 inches
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A game uses a single 6-sided die. To play the game, the die is rolled one time, with the following results:
• Even number = lose $9.
• 1 or 3 = win $2
• 5 = win $10
What is the expected value of the game?
Answers
how do you find the perimeter of an object
Answers
Answer:
width*2 +length *2
Step-by-step explanation:
How do I find the squareroot?
Answers
Answer:
Step-by-step explanation:
Factoring a square root means that you are finding the closest numbers that multiply together. The easiest square roots are ones that factor directly into squares, such as √100, but more complicated ones involve several square roots, such as √225. Here are the steps to finding the square root using factoring:
1. Find the factors. Factors are the numbers you multiply to find the total under the square root symbol. For √100, the factors would be √(10 x 10). The factors of √225 would be √(25 x 9).
2. Separate the factors into their own square roots. Because both factors of √100 are 10, the square root of 100 is 10. For √225, you would separate the factors under their own square root signs, so the formula would be √25 x √9.
3. Solve for the individual squares. Next, you would find the squares of each of the individual factors. √25 = 5 and √9 = 3. The remaining formula will look like 5 x 3.
4. Finish solving the equation. Now that you know what the simplified squares are, you will find that 5 x 3 = 15. So, √225 = 15.
Hope that helps!
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.
find dy/dx of y= ln(1-x^2/1+x^2)
Answers
The derivative of y with respect to x is:
[tex]dy/dx = -4x / (1 - x^4)[/tex]
How to find derivative ?The chain rule and the quotient rule must be utilized in order to determine the derivative of y with respect to x.:
First, we can rewrite y as follows:
[tex]y = ln[(1 - x^2)/(1 + x^2)][/tex]
Let's define two functions:
[tex]u = 1 - x^2[/tex]
[tex]v = 1 + x^2[/tex]
Then, y can be rewritten in terms of u and v as:
y = ln(u/v)
Now, we can use the chain rule to find the derivative of y with respect to u and v, respectively:
[tex]dy/du = 1/u\\dy/dv = -1/v[/tex]
Using the quotient rule, we can find the derivative of y with respect to x:
[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)[/tex]
[tex]du/dx = -2x\\dv/dx = 2x[/tex]
Substituting in the values we get:
[tex]dy/dx = (dy/du) * (du/dx) + (dy/dv) * (dv/dx)\\= (1/u) * (-2x) + (-1/v) * (2x)\\= -2x/(1 - x^2) - 2x/(1 + x^2)\\= -4x / (1 - x^4)[/tex]
Therefore, the derivative of y with respect to x is:
[tex]dy/dx = -4x / (1 - x^4)[/tex]
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(AWARDING 90 POINTS!!!) Does this data set have any outliers?
{667, 667, 505, 435, 844, 435, 346, 667, 346, 779, 222}
Yes, 222 is an outlier.
Yes, 667 is an outlier.
Yes, 844 is an outlier.
No, there are no outliers.
Answers
Answer:
Yes, 222 is an outlier
Step-by-step explanation:
{222, 346, 346, 435, 435, 505, 667, 667, 667, 779, 844}
Q1 = 435
Q3 = 667
IQR = Q3 - Q1 = 232
222 is below Q1 - 1.5*IQR (104)
find the circumference of a circle circumscribed about a right triangle with legs 5 centimeters and 3 centimeters
Answers
Answer:
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
Step-by-step explanation:
To find the circumference of a circle circumscribed about a right triangle with legs 5 cm and 3 cm, we can use the Pythagorean theorem to find the length of the hypotenuse, which is also the diameter of the circle.
Using the Pythagorean theorem, we have:
c^2 = 5^2 + 3^2
c^2 = 25 + 9
c^2 = 34
c = sqrt(34)
So the diameter of the circle is sqrt(34) cm, and the radius is half of the diameter, or sqrt(34)/2 cm.
The circumference of a circle is given by the formula:
C = 2 * pi * r
where pi is approximately 3.14 and r is the radius of the circle.
Substituting the value of the radius, we get:
C = 2 * 3.14 * sqrt(34)/2
C = 3.14 * sqrt(34)
Therefore, the circumference of the circle circumscribed about the right triangle with legs 5 cm and 3 cm is approximately 18.85 cm (rounded to two decimal places).
b: if jen and ricky each randomly select an egg from their farm, who is more likely to select an egg classified as medium
Answers
Rick is more likely to select a large egg. Jens probability for a large egg is87.5 ricks is 90.7
What is Probability?
Probability is a fundamental concept that gauges the plausibility of an event taking place. It is expressed numerically within the range of 0 to 1, with values corresponding to complete impossibility and absolute certainty respectively.
When probability values take on an exact midpoint value such as 0.5, they indicate equal probabilities for both possible outcomes. Experts use probability models before making significant decisions in fields such as science, engineering, finance, and speculative markets like gambling.
The study of these apprehension methods and their application form the foundation of probability theory, which helps analyze chance events' rules and guidelines.
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