A one-sample z-test for a population proportion requires that n po > 10 and n(1-Po) > 10 for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size.
1. Calculate the sample size, n, needed for the test.
2. Check that npo > 10 and n(1 - Po) > 10 for both the sample and population proportions, Po.
3. Check that each sample proportion is less than or equal to 0.5.
4. Check that the sample size is more than 10 times the population size.
5. Check that the population size is more than 10 times the sample size.
6. Check that the population distribution is approximately normal.
A one-sample z-test for a population proportion is used to evaluate the difference between a sample proportion and a population proportion. Before conducting the test, it is important to check for independence, which is done by ensuring that certain conditions are met. First, npo > 10 and n(1-Po) > 10 must be true for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size. Lastly, the population distribution must be approximately normal. These conditions must be met in order for the test to be valid and reliable. If any of these conditions are not met, the test results may be inaccurate.
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A 83-inch candle burns down in 5 hours. Assuming the candles are the same
thickness and make (that is, directly proportional), how long would it take a 15-inch
candle to burn down?
Step-by-step explanation:
83 in burn in 5 hours.
so, we have a 83/5 speed ratio.
directly proportional means
y = kx
with k being constant for all values of x.
83 = k×5 = 5k
k = 83/5
15 in burn in x hours.
therefore,
15 = 83/5 × x
75 = 83x
x = 75/83 hours
this can be also calculated like this :
because of the direct proportionality, 15/x must have the same ratio as the original 83/5.
83/5 = 15/x
83x/5 = 15
83x = 75
x = 75/83 hours = 0.903614458... hours
Order the correlation coefficients from least to greatest -0.50,0.60,,98,-0.10,0.68
answer: In this case, -0.50, -0.10, 0.60, 0.68, 0.98 are all correlation coefficients and -0.50 is the least and 0.98 is the greatest among the given correlation coefficients.
but why? The correlation coefficients can be ordered from least to greatest as:
-0.50, -0.10, 0.60, 0.68, 0.98
A correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. The value of the coefficient ranges from -1 to 1, where:
A coefficient of -1 represents a perfect negative correlation, meaning that as one variable increases, the other variable decreases.
A coefficient of 0 represents no correlation, meaning that there is no linear relationship between the two variables.
A coefficient of 1 represents a perfect positive correlation, meaning that as one variable increases, the other variable also increases.
What is the distance between 60 and 120
Angela observes that a drone is flying horizontally at a constant height of 5m above the ground. If the drone is flying in the opposite direction from Angela's location at a speed of 1m/s determine the rate at which the angle of elevation (theta) decreases at the moment when (theta)=pi/6
The rate of change of the angle of elevation is approximately - 2.597 degrees per second (-0.045 radians per second). (Correct choice: C)
How to determine the rate of change of the angle of elevation
In this problem we find the case of a drone that travels horizontally, at constant height (h), in meters. The rate of change of the angle of elevation (θ'), in degrees per second, can be found from trigonometric functions and derivatives:
tan θ = y / x
Where:
x - Horizontal distance, in meters. y - Vertical distance, in meters.By derivatives:
sec² θ · θ' = - y · x⁻² · x'
θ' = - (y · x⁻² · x') / sec² θ
Where x' is the speed of the drone, in meters per second.
If we know that y = 5 m, θ = π / 6 and x' = 5 m / s, then the rate of change of the angle of elevation is:
x = y / tan θ
x = (5 m) / tan (π / 6)
x ≈ 2.887 m
θ' = - [(5 m) · (2.887 m)⁻² · (5 m / s)] / sec² (π / 6)
θ' ≈ - 2.597 degrees per second (- 0.045 radians per second)
Note - Please notice that negative sign indicates that angle is decreasing.
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fill in the blank. let where is an integer greater than___. compute the number of values of for which the sum of the squares of the digits of is at most .
Let where is an integer greater than 9. compute the number of values of for which the sum of the squares of the digits of is at most 25.
The question asks us to count the number of values of for which the sum of the squares of the digits of is at most 25. To solve this problem, we can use a loop to iterate through all possible values of starting from 9 and up. For each value of , we can then calculate the sum of the squares of the digits of by using modulo and division operations to extract each digit and square it. If the sum of the squares of the digits of is at most 25, we can add 1 to the count of values. After the loop completes, we will have the total number of values of for which the sum of the squares of the digits of is at most 25.
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When Boris bought his house, he got his mortgage through a bank. The mortgage was a personal, amortized loan for 91500, at an interest rate of 3.3% , with monthly payments for a term of 40 years.
Answer: As the loan is amortized, Boris will make a series of equal payments each month for the duration of the loan, with each payment comprising of both interest and principal. The amount of interest in each payment will decrease over time, while the amount of principal in each payment will increase.
To calculate the monthly payments, we can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where:
M = monthly payment
P = the principal or the loan amount = 91500
i = interest rate as a decimal = 3.3%/12 = 0.00275
n = total number of payments = 40 years x 12 months/year = 480
By substituting the values in the formula:
M = 91500 [ 0.00275 (1 + 0.00275)^480 ] / [ (1 + 0.00275)^480 - 1]
M = $439.65
So the monthly payment that Boris will make is $439.65. This amount will stay the same throughout the loan term, but the proportion of interest to principal in each payment will change as the loan is amortized.
Step-by-step explanation:
A number is multiplied by 6, and that product is added to 4. The sum is equal to the product of 2 and 23. Find the number.
Answer:
The number is 7
Step-by-step explanation:
1. Create the equation needed to solve this
Lets think of a number as x. We have a number multiplied by 6 and have 4 added to it.
We get:
6x + 4
Now this sum is equal to the product of 2 and 23. We connect this to get
6x + 4 = 2(23)
We can simplify this to
6x + 4 = 46
2. Solve for x
6x + 4 = 46
Subtract 4 from both sides
6x = 42
Divide both sides by 6
x = 7
Therefore the number is 7
Show that the following number is rational by writing it as a ratio of two integers. 52.4726172617261... Enter a fraction.
The following number is rational by writing it as a ratio of two integers. 52.4726172617261... = 52497370/999900.
In mathematics, any number that can be written as p/q where q ≠0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal.
The following number is rational by writing it as a ratio of two integers. 52.4726172617261...
let 52.4726172617261...=x
100x=5247.26172617.....
100x=5247+0.2617+0.00002617+....
S0, 0.2617+0.00002617+... is a geometric series,
[tex]S=\frac{a}{(r-1)}\\\\a=0.2617,r=0.0001\\\\s=\frac{0.2617}{0.9999}\\\\S=\frac{2617}{9999}\\\\now,\\100x=5247+\frac{2617}{9999}\\100x=\frac{52,467,370}{9999}\\\\x=\frac{52467370}{999900}[/tex]
So, 52.472617...can be written by x.
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for how many positive integers $p$ does there exist a triangle with sides of length $3p-1,$ $3p,$ and $p^2 1?$
Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.
Using triangular inequality of triangle :
sum of two sides > third side
a. 3p - 1 + p² + 1 > 3p
⇒p² > 0
True result.
b. 3p + p² + 1 > 3p - 1
⇒ p² > -2
True result.
c. 3p - 1 + 3p > p² + 1
⇒ p² -6p + 2 < 0
Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)
= ( 6 ± √28 ) 2
= 5.6 or 0.35
Integer value of p are in between 0.35 to 5.6 are :
1, 2, 3, 4, 5
Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.
For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?
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Please help with geometry questions 2, 4, 9 and 10!! Thank you
The answers to all the parts is mentioned above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the geometrical figures as shown.
{ 9 } -
We can write the proportional relationship {since both triangles are similar} as -
5/8 = x/10
{x} = 50/8
{x] = 6.25
{ 10 } -
We can write the proportional relationship {since both triangles are similar} as -
x/20 = 10/16
{x} = 200/16
{x} = 12.5
TY = 20 - 12.5
TY = 7.5
Therefore, the answers to all the parts is mentioned above.
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The circumference of a personal sized pizza at center court is 12.56 inches. Their large pizza is three times the diameter as the personalized sized pizza. What is the area of the large pizza?
The area of the large pizza is approximately equal to 112.984 square inches.
How to determine the area of a large pizza
Herein we need to determine the area occupied by a large pizza (A), in square inches, and based on given input by circumference of a small pizza (s), in inches. Then, we need the following formulas:
Circumference
s = π · D
Area
A = 0.25π · D²
Where D is the diameter, inches.
First, determine the diameter of the small pizza:
D = s / π
D = 12.56 / π
D ≈ 3.998 in
Second, calculate the diameter of the large pizza:
D' = 3 · (3.998 in)
D' = 11.994 in
Third, obtain the area of the large pizza:
A = 0.25π · (11.994 in)²
A ≈ 112.984 in²
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Lmkkkkkkkkkkkkkkkkkk
Let x be the number of $1 bills and y be the number of $10 bills.
We know that:
x + y = 59 (the total number of bills)
x + 10y = 239 (the total monetary value of the bills)
We can use the first equation to solve for one of the variables in terms of the other. For example:
x = 59 - y
We can substitute this expression for x into the second equation:
(59 - y) + 10y = 239
59 + 9y = 239
9y = 180
y = 20 (the number of $10 bills)
We can use this value of y to find the number of $1 bills by substituting it back into the first equation:
x + y = 59
x + 20 = 59
x = 39 (the number of $1 bills)
Therefore, the motel clerk has 39 $1 bills and 20 $10 bills.
Each year, a physicist measures the remaining radioactivity in a sample. she finds that it reduces by 18% each year. if there was 1.52 g of radioactive material left after 4 years}
a. Find the initial quality of radioactive material
b. Hoy many more years will it take for the amount of radioactive material to reduce to 0.2 g?
a. The initial quantity of radioactive material is 0.68 g.
b. It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
a. In order to find the initial quality of radioactive material, we will use the formula:
Initial Quality = Final Quantity * (1 - Reduction Rate)^Years
We know that -
the final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.
Initial Quantity = 1.52 g * [tex](1 - 0.18)^4[/tex]
Initial Quantity = 1.52 g * 0.452
Initial Quantity = 0.68 g
Hence, the initial quantity of the radioactive material is 0.68 g.
b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:
Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)
We know that -
the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).
Years = log(0.2 / 0.0.68) / log(1 - 0.18)
Years = 7.15
Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
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the lengths of the legs of a right triangle are 7 in. and 2 in. what is the length of the hypotenuse? enter your answer rounded to the nearest tenth in the box.
the visualization below shows voting patterns in the united states, canada, and mexico in the united nations general assembly on a variety of issues. specifically, for a given year between 1946 and 2015, it displays the percentage of roll calls in which the country voted yes for each issue. this visualization was constructed based on a dataset where each observation is a country/year pair.1
(a) List of variables is Years, Country, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.
(b) Each variable is numeric if the variable assumes number values and it will be categorical if it assumes labels.
(a) The list of variables is:
The variables that can be used in this visualization can be Years, Country, Percentage that said yes, Arms control and disarmament, colonialism, economic development, human rights, nuclear weapons, and materials, and Palestinian conflict.
(b) Category of different variables:
Years: Numerical and discrete
years are number values but the voting has not been done in the same interval so it is a numerical and discrete variable.
Country: Categorical and not ordinal
country name assumes as labels hence it is a categorical variable.
The percentage that said yes: Numerical and continuous
The percentage indicates number values so it is a numerical value.
And following is also assumed as a label so these are also categorical values:
Arms control and disarmament: categorical and not ordinal
colonialism: categorical and not ordinal
economic development: categorical and ordinal
human rights: categorical and ordinal
Nuclear weapons and materials: categorical and not ordinal.
Palestinian conflict: Categorical and not ordinal
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The complete question is:
the visualization below shows voting patterns in the united states, Canada, and Mexico in the united nations general assembly on a variety of issues. specifically, for a given year between 1946 and 2015, it displays the percentage of roll calls in which the country voted yes for each issue. this visualization was constructed based on a dataset where each observation is a country/year pair.
1) List the variables used to create this visualization.
2) Indicate wheater each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, identify as the variable is ordinal.
If f ( x ) = 2 x 2 and g ( x ) = x - 4 2 x , determine the values of the following operations:
( f g ) ( 3 )
( f - g ) ( 4 )
f g ( 2 )
( f + g ) ( 1 )
The largest value of all four operations is
The largest value of all four operations is 54
How do you determine the largest number?In order to determine the largest value of all the four operations, one needs to plug in the values into the different operations given and then generate their values. By so doing, the following deductions are made:
(f * g)(3) = 2 * (3^2) * (3 - 4 * (2 * 3)) = 54
(f - g)(4) = 2 * (4^2) - (4 - 4 * (2 * 4)) = 40
f(g(2)) = 2 * (2^2) = 8
(f + g)(1) = 2 * (1^2) + (1 - 4 * (2 * 1)) = -3
So, the largest value of all four operations is 54. Therefore, the correct answer is as given above
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rogress: The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer A motor oil retailer needs to fill 50 one quart bottles, and he has two tanks: one that contains 12 gallons of oil and one that contains 2 gallons of oil. Which will he need to fill the bottles? The 2 gallon tank is enough. He will need both tanks. The 2 gallon tank is not enough, but the 12 gallon tank is enough. Question ID: 53297 Even both tanks will not be enough.
The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.
Find the solution ?The motor oil dealer will have to use both tanks since he needs 15 gallons of oil but will still be short by one gallons.
A motor oil store has two tanks: one holds 12 gallons of oil, and the other holds 2 gallons of oil. In order to determine which tank will require to fill the bottles, the following computation must be done:
Quarts to gallons is 4 to 1.
1/4 x 60 = X
60/4 = X
15 = X
Since the motor oil vendor requires 15 gallons of oil, he must use both tanks but will still be short by 1 gallons
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Problem Gregory forms two different numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have 3 digits, and each digit is used only once. If he adds these two numbers, what is the greatest sum Gregory can get? Show your work.
The greatest sum that Gregory can get is given as follows:
1173.
How to obtain the greatest sum?When two three digit numbers are added, the numbers in the equivalent positions are added with each other, that is, the third digit is added with the third digit, the second with the second and the third with the third.
Hence the greatest sum would be obtained as follows:
The first digits would be of 5 and 6.The second digits would be of 3 and 4.The third digits would be of 1 and 2.Hence the sum would be given as follows:
642 + 531 = 1173.
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The graph above shows the cost of parking at the airport. Jay left on a business trip and had to leave his car at the airport for 5 days. Based on the graph, what is the total cost that he paid for the parking?
A.
$33.50
B.
$31.00
C.
$26.00
D.
$20.00
The total cost that he paid for the parking for 5 days is $26.00.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
The graph above shows the cost of parking at the airport,
since the graph is a straight line so it is the condition for a linear equation,
from the graph, the y-axis shows the price in dollars and the x-axis shows the number of days,
line of the graph passes from coordinates (0, 6) and (6, 30)
equation of line is y = mx + c
where c is initial cost when x is 0, y is 6
c = 6
and m = (y₂- y₁)/(x₂ - x₁)
m = (30 - 6)/(6 - 0)
m = 4
equation of line is,
y = 4x + 6
cost for 5 days,
x = 5
y = 4(5) + 6
y = 26
cost is $26.00
Hence cost for 5 days is $26.00, option C is correct.
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Algebra Tiles SOMEONE HELP ME QUICK I NEED HELP I WILL GIVE BRAINLIEST
Answer:
all
Step-by-step explanation:
all of them
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
The factorization of three polynomials (x2 - 8x + 15) = (ax + b)(cx + d) is (x-5) (x-3)
Explain about the equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
The general equation of a straight line is given by the expression y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.
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ach ant has 6 legs. How many legs do 3 ants have?
Ants 1 2 3
Legs 6 ?
Answer:
Step-by-step explanation:
the answer is 18 I think?
Answer:
18
Step-by-step explanation:
6 (legs) x 3 (ants) = 18 legs
It can also be represented as 6+6+6 (18)
hope this helps :)
please help me asap!!!
The inequality equation for the given graph is option B: y ≤ 1/3x - 4.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality equations are -
y ≥ 1/3x - 4
y ≤ 1/3x - 4
y ≤ 1/3x + 4
y ≥ 1/3x + 4
In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.
Now, write the inequality in equation form -
y = 1/3x - 4
y = 1/3x + 4
Substituting the values of x and y with origin (0,0) -
0 = 1/3(0) - 4
0 = -4
0 = 1/3(0) + 4
0 = 4
Putting the inequality symbol back -
y ≥ -4
This statement is false as seen in the graph.
y ≤ -4
This statement is true as seen in the graph.
y ≤ 4
This statement is false as seen in the graph.
y ≥ 4
This statement is false as seen in the graph.
Therefore, the equation for the graph is y ≤ 1/3x - 4.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
Two equations that have the same solution as the given equation are;
2.3. p - 10.1 = 6.49. p - 4
230.p - 1010 = 650.p - 400 - p
The correct options are B and C.
How to explain the equation?The given equation is; 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p
Simplifying the above equation by collecting like terms gives;
2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4
2.3·p - 10.1 = 6.49·p - 4
Both sides of an equation will remain equal, when both sides are multiplied by the same amount.
Multiplying both sides of the original equation by 100 gives the same solution as follows;
100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)
230·p - 1010 = 650·p - 400 - p
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Look at the problem in example. Rolando also adds money to his subway fare card.
How much does Rolando pay for 20 rides? Show your work.
Answer:
Rolando pays $63 for 20 rides
Step-by-step explanation:
this was the question right???
Is this correct???????
a set of data has a mean that is much larger than the median. which of the following statements is most consistent with this information?
This suggests that the data set has a skewed distribution with a long tail of larger values.
This suggests that the data set has a skewed distribution, meaning that the data is not evenly distributed. The mean being much larger than the median indicates that there are a few larger values in the data set that are pulling the mean up and creating a long tail of larger values. This makes the distribution look lopsided, with a majority of the values being clustered around the median, and a few larger values that are skewing the mean higher.
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20% of a is 11. What is a 
Therefore , the solution of the given problem of percentage comes out to be a value is 55.
A percentage can be specified.In mathematics, a percentage is a number any figure that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. The "%" symbol, however, is frequently used to denote it. The % amount has no dimensions and is flat. Because the numerator of percentages is 100, they are effectively fractions. To show that a number is a percentage, the percent sign (%) should be put in front of it. On a test, for instance, you would receive a 75% if you gave the answer 75 out of the total questions.
Here,
Given :
=> 20 /100 * a =11
=> a = 11 *100 /20
=> a = 1100 /20
=> a = 55
Thus , a is 55 .
Therefore , the solution of the given problem of percentage comes out to be a value is 55.
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1. Subtract
4 1/2
- 1 7/8
2. 20% of what amount is $6.50
The value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.
What are percentages?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given the following expression:
4 (1/2) - 1 (7/8)
Convert the mixed fractions into simple fractions:
9/2 -15/8
Take the LCM of the denominator:
36/ 8 - 15/8
21/8
2. 20% of x = 6.50
20/100 (x) = 6.50
20x = 650
x = 650/20
x = 32.5
Hence, the value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.
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Suppose that the annual amount of rainfall (in million tons) accumulated in a lake follows a gamma distribution with alpha = 3 and gamma = 5.
a) Find the expected annual rainfall accumulated in this lake.
b) Find the standard deviation of the annual amount of rainfall in this lake.
c) Find P(X < 4), use R.
d) Find P(2 < X < 5), use R
a) The expected annual rainfall is 15 million tons.
b) The standard deviation is the square root is 15 million tons.
c) Pgamma(4, shape = 3, scale = 5)
d) Pgamma(5, shape = 3, scale = 5) - Pgamma(2, shape = 3, scale = 5)
Gamma Distribution Probabilitiesa) The expected annual rainfall accumulated in this lake is given by the mean of the gamma distribution, which is alpha * gamma. In this case, the expected annual rainfall is 3 * 5 = 15 million tons.
b) The standard deviation of the annual amount of rainfall in this lake is given by the square root of the variance, which is the square root of alpha * gamma². In this case, the standard deviation is the square root of 3 * 5² = 15 million tons.
c) To find P(X < 4), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.
pgamma(4, shape = 3, scale = 5)
This will return the probability that X is less than 4, which is the cumulative probability.
d) To find P(2 < X < 5), we can use the cumulative distribution function (CDF) of the gamma distribution. In R, we can use the pgamma() function to find the CDF of the gamma distribution at a given value.
pgamma(5, shape = 3, scale = 5) - pgamma(2, shape = 3, scale = 5)
This will return the probability that X is between 2 and 5, which is the cumulative probability.
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