Answer:
The answer to your question is: first piece = 4 in, second piece = 8 in, third piece = 12 in
Step-by-step explanation:
Data
total length = 24 inches
first piece = x in
second piece = 2x
third piece = 3x
Equation
x + 2x + 3x = 24
6x = 24
x = 24/6
x = 4 lengths of the first piece
second piece = 2(4) = 8 inches
third piece = 3(4) = 12 inches
Use the theorem in Sec. 77, involving a single residue, to evaluate the integral of f (z) around the positively oriented circle |z| 3 when intergral c f(z) dz, f(z) = (z^3(1-3z))/(1+z) (1+2z^4)
The integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi times the sum of the residues of the poles of f (z) inside the circle.
The poles of f (z) inside the circle are z = 0 and z = −1/2.
The residue at z = 0 is f (0) = 0.
The residue at z = −1/2 is f (−1/2) = −7/16.
Therefore, the integral of f (z) around the positively oriented circle |z| = 3 is equal to 2πi (−7/16) = −7πi/8.
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in a proof what is the reason that justifies this statement: segment bp is congruent to segment bp.
The necessary explanation is that segment BP is congruent to segment BP, which is the common side of both triangles.
Two figures or items are congruent in geometry if they have about the same size, or if one has the same shape and size as its mirror counterpart.
As seen in the illustration, segment BP and segment BP are congruent since segment BP is the common side of both triangles BPS and BPY.
As a result, the necessary explanation seems to be that segment BP is congruent to segment BP and that segment BP is the identical side of both triangles.
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The dinner bill came to $72.48 and Julio tipped the waiter 15%. What is the total price of dinner?
Answer: $83.35
Step-by-step explanation:
Find 15% of 72.48 = 10.87
10.87 + 72.48 = 83.35
What is the slope of a line parallel to a line whose equation is 10x+12y=-120
The slope of a line parallel to the line having equation 10x+12y=-120 is -5/6.
What is the slope of a line parallel to another line?
Parallel lines are coplanar and they never intersect.
Slope is a measure of the angle of a line from the horizontal.
Since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.
According to the given question:
Given equation of line is 10x+12y=-120
Converting this to slope-intercept form we get
y = -5/6 x + 10
Clearly slope of this line is -5/6
Any line parallel to this line will have the same slope
Therefore the slope of a line parallel to the given line is -5/6
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what is the solution to f(x)=g(x) ? select each correct answer.
The solution to f(x) = g(x) is
x = 0
x = 1
What do you mean by a solution?
We can substitute a value, or values, for a variable (such as x), making the equation true and thus finding a solution. All values of x in the domain, such that f(x) = g, are the solutions if two functions, f, and g, both map to the same co-domain.
as in: x + 2 = 7.
5 + 2 = 7 is what we get when we substitute 5 for x.
Given that 5 + 2 = 7, x = 5 is a solution.
Solution Explained:
A set of values in the table that tell us what the values of each function f(x) and g(x) are for a given value for the variable "x" is already giving us a hint.
We can infer from the table that f(x) decreases when x>0 and moves in the opposite way when x0.
G(x) follows a distinct path; it grows as x increases and shrinks as x lowers.
As a result, there is not much room for equality between the two functions.
You can thus utilize the points shown in the table to begin your test.
f(0)= 0,25 ^ 0=1 since a number raised to 0 is always 0.
g(0)=-0.75 * 0 + 1 = 1
f(1)=0.25^1=0.25 since a number raised to 1 is always equals to itself
g(1)=-0.75*1+1=0.25
So f(x)=g(x), when x=1 and when x=0
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A hot chocolate recipe calls for 2/3 cup of milk.Slade wants to make 1/2 of the recipe.How much milk should Slade use?
Answer: Slade should use 1/3 cup of milk
Step-by-step explanation:
2/3 divided by 1/2 = 1/3
In other words, if you have 2 of something and you give someone half, you would give them 1.
Make g the subject of the formula w=7- square root g
The value of g is g = w² - 14w + 49, according to the question.
What do you mean by formula?
A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.
According to the given question,
We have :
w = 7 - √g
Firstly isolate the g,
w = 7 - √g
Do the opposite of PEMDAS, first subtract 7 from both sides,,
w (-7) = -√g + 7 (-7)
w - 7 = -√g
Now, multiply -1 (as -√g is the same as -1√g) to both sides
-1(w - 7) = √g
-1w + 7 = √g
To get rid of the square root, you must square both sides,
Note: -1w is the same as -w.
Note: you are squaring all the terms on the other side, not just one.
(-w + 7)² = (√g)²
g = (-w + 7)²
g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or g = (-w + 7)² )
Use the FOIL method (First, Outside, Inside, Last)
(-w)(-w) = w²
(-w)(7) = -7w
(7)(-w) = -7w
(7)(7) = 49
g = w² - 7w - 7w + 49
Then, simplify (combine all like terms):
g =w² - 7w - 7w + 49
g = w² - 14w + 49
Therefore, the value of g = w² - 14w + 49 .
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I NEED HELP FAST!!!! Let s represent the number of games a baseball fan attends. Enter an inequality that represents all values of s for which buying a main box season ticket is less expensive than buying single-game main box tickets.
You are writing an article for your school newspaper about the Oakland Athletics. Season tickets go on sale next week and you have been assigned to write an article to help fans determine whether they should buy season tickets or single-game tickets based on their expected attendance at the games this season.
Buying a season ticket allows you to attend all 81 home games for a single price. Without a season ticket you have to pay for every single game that you attend.
Image result for Oakland Athletics Tickets Box Office
The table shows different ticket price options.
In this task you will answer six questions about the ticket price options and recommend which is best for fans. Be sure to show all your work for each item.
1. A season has 81 home games. If you purchase a season ticket in the bleacher section , what is the cost per game, in dollars for this ticket?
.2. Complete the table based on the single game ticket for seats in the Left field reserve section.
Step-by-step explanation:
The key role for CPS is to minimize stigma and be an ambassador for recovery. Describe a situation where you had to confront stigma
The tape diagram below represents 100%. What percent is represented by the shaded area?
Answer:
Below
Step-by-step explanation:
shaded area is 3 out of 4 or 3/4 which is .75 which represents 75%
list three ways a rectangle and a square are different
Answer:
one way is that they both have four sides.
another way is that they both have straight lines.
and the other way is that they both have 4 corners.
Step-by-step explanation:
Answer:
According to the web: "A square has four equal sides. In a rectangle, the opposite sides are equal. The diagonals of a square bisect each other at 90°. The diagonals of a rectangle bisect each other at different angles."
Step-by-step explanation:
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
in how many ways can we seat 6 people at a round table if john and sam insist on sitting next to each other? (two seatings are equivalent if one is a rotation of the other.)
If John and Sam insist on sitting next to each other, there are 48 different ways we can make a round table seat six people.
What is permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here,
There is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.
But John and sam are tied together so thet are the equaivalent of one person.
so that is only 4 people.
4!*2 (because it could be john, sam or sam, john)
2*3*4*2 = 48 permutations
In 48 ways we can make seat 6 people at a round table if john and sam insist on sitting next to each other.
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What type of pair of angles are∠2 and angle∠11 ?
The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.
What is an alternate interior angle?When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.
Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.
To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.
Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.
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You go to a store that is offering a 20% discount for students! You
decide to buy a book for $15.40. You also have a coupon for $5 off after
the discounted price. What is the cost of the book after the discount and
coupon?
The cost of the book after the discount and coupon is $7.32
How to determine the cost of the book?From the question, we have the following parameters that can be used in our computation:
Amount = $15.40
Coupon = $5 offer
Discount = 20% off
This means that
Total amount = Amount * (1 - Discount) - Coupon
So, we have
Total amount = 15.40 * (1 - 20%) - 5
Evaluate
Total amount = 7.32
Hence, the total amount = 7.32
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the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151. (a) estimate the population variance σ2. (b) compute a 99 percent two-sided confidence interval for σ2.
The population variance of the capacities is 30.76
the capacities (in ampere-hours) of 10 batteries are 140, 136, 150, 144, 148, 152, 138, 141, 143, 151.
The number of observations n = 10
mean = (x₁ + x₂ + x₃.....x₁₀)/10
mean = (140 + 136 + 150 + 144 + 148 + 152 + 138+ 141 + 143 + 151)/10
mean = 1443/10 = 144.3
variance = ∑(x - mean)²/(n - 1)
variance = ((140 - 144.3)² + (136 - 144.3)² + (150 - 144.3)² + (144- 144.3)² + (148 - 144.3)² + (152 - 144.3)² + (138 - 144.3)² + (141-144.3)² + (143 - 144.3)² + (151 - 144.3)²)/(10 - 1)
variance = 276.9/9 = 30.76
Therefore, the population variance of the capacities is 30.76
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A barn is 100 feet long and 40 feet wide (see figure). A cross section of the roof is the inverted catenary given below. Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.)
The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
What is integration?
It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet
Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
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In a study of helicopter usage and patient survival, among the 56,074 patients transported by helicopter, 235 of themleft the treatment center against medical advice, and the other 55,839 did not leave against medical advice. If 40 of
the subjects transported by helicopter are randomly selected without replacement, what is the probability that none
of them left the treatment center against medical advice?
The probability is
(Round to three decimal places as needed.)
The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.
Given,
The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.
Hypergeometric distribution:
The probability of x successes is given by:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
The parameters are:
x is the number of successes.
N is the size of the population = 56074
n is the size of the sample = 40
k is the total number of desired outcomes = 235
The number of unique combinations of x objects from a set of n elements is provided by the following formula:
Cₙ,ₓ = n! / x! (n - x)!
The probability that none left against medical advice is P(X = 0), so:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀
= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) / C₅₆₀₇₄, ₄₀
= 0.845
The probability is 0.845 = 84.5%.
Therefore,
The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%
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On a map of a park three inches represents twenty feet, how many inches would represent 12 feet?
Answer:
1.8 inches
Step-by-step explanation:
find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like coordinates.
Given,
In response to our inquiry:
Add "-9y²" to each side of the equation.
4x² + 9y² + -9y² + -1z² = 36 + -9y²
9y² + -9y² = 0 when equivalent phrases are combined.
4x² + 0 + -1z² = 36 + -9y²
4x² + -1z² = 36 + -9y²
Add "z²" to both sides of the equation.
4x² + -1z² + z² = 36 + -9y² + z²
Therefore,
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like dimensions.
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For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: f (x) = negative 9 x squared + 7 x Table A a b c up or down y-intercept -9 -7 0 down (0,0) Table B a b c up or down y-intercept 2 7 0 down (0,0) Table C a b c up or down y-intercept 9 7 0 down (0,0) Table D a b c up or down y-intercept -9 7 0 down (0,0) a. Table A c. Table C b. Table B d. Table D
Examining the function -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0
How to find the y interceptsWhere a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².
The coefficient of x² is a and in this function is -9
A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards
The y intercept
-9x² + 7x = 0
x(-9x + 7) = 0
x = 0
-9x + 7 = 0
-9x = -7
x = 7/9
the y intercept is 0 ad 7/9
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2x
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A tax of 5% is applied to the bill.
Zoe decides to leave a tip of 15% on the entire bill (including the tax).
let the bill cost $x.
So, the price after tax and tip
= x+ 5% of x+ 15% of x
= x + 0.05x + 0.15x
= x + 0.20x
= 1.2x
Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x
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Suppoe the original quantity i 175 and the new quantity i 126. Write an expreion that repreent the percent change. Find the percent change and expre it a a rational number
The percent change for the expression for the given rational number is 28%.
Define the term percent change?A quantity's percentage change is equal to the ratio of such difference between the quantity's current value and its starting value multiplied as 100. When a quantity's ultimate value is determined by increasing or decreasing a percentage of its original value, there is always an change in the quantity's percentage change (or percent change).As the stated question-
Original quantity = 175
New quantity = 126
Difference = Original quantity - New quantity
Difference = 175 - 126
Difference = 49
Percentage change = Difference/Original quantity x 100 %
Percentage change =49/175 x 100%
Percentage change = 28%
Thus, percent change for the expression for the given rational number is 28%.
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Select the correct answer. What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]? x f(x) -6 2.5 -2 2.5 0 2 2 0 3 5 A. 5 B. 2.5 C. 1 D. 0.5\
The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.
What is an average rate of change?An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:
a = -2; f(a) = 2.5
b = 3; f(b) = 5
Substituting the given parameters into the formula, we have the following;
Average rate of change = (5 - 2.5)/(3 - (-2))
Average rate of change = 2.5/5
Average rate of change = 0.5.
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The coupon rate of a bond determines the percentage of interest earned on the bond each year. Samantha purchased a five-year municipal bond for $600. After the bond matured five years later, she had received a total of $720 in principal plus interest payments. What is the coupon rate of Samantha's bond?
4%
5%
10%
12%
20%
The required coupon rate of Samantha's bond is 4%.
Explain coupon rate of bond.The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c
According to question:We have,
principal amount = $600
Amount after five year = $720
Interest of five year = $(720 - 600) = $120
Then,
Interest of one year = $120/5 = $24
Now,
Coupon rate = ($24/600)×100 = 4%
Thus, required coupon rate is 4%.
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Please help! you have to find the product
Answer:
-4x^2 - 6x
Step-by-step explanation:
2x(-2x-3)
Use the distributive property to multiply 2x by -2x - 3.
-4x^2 - 6x
The variables a and b are proportional. When a=12 we
know b=3. What is the value of a when b=5?
O 17
9
20
O 14
Answer:
b = 20
Step-by-step explanation:
the variables a and b are proportional , so the equation relating them is
a = kb ← k is the constant of proportion
to find k use the condition a = 12 , b = 3
12 = 3k ( divide both sides by 3 )
4 = k
a = 4b ← equation of proportion
when b = 5 , then
a = 4 × 5 = 20
Rewrite 16a4b + 8ab3 using a common factor.
2a4b(8 + 4ab3)
4ab(4a3 + 8ab3)
8ab(2a4b + 8ab3)
8ab(2a3 + b2)
The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given expression is,
16a⁴b + 8ab³
Simplify the expression, by factor method,
8 x 2 x a x a x a x a x b + 8 x a x b x b x b
The common term is 8ab,
8ab(2a³ + b²)
The required expression is 8ab(2a³ + b²).
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**WILL MARK BRAINLIEST AND GIVE 30 POINTS**
Mrs. Thomason and Mrs. Ardoin are kayaking in the bayou in the same direction.
a) Mrs. Ardoin is boating at a constant speed of 15 miles per hour. Write an expression that shows how many miles Mrs. Ardoin has gone after x hours.
b) Mrs. Thomason starting kayaking of an hour before Mrs. Ardoin. If Mrs. Ardoin has been kayaking for x hours, how long has Mrs. Thomason been kayaking?
c) Mrs. Thomason is kayaking at a constant speed of 9 miles per hour. Write an expression that shows how many miles Mrs. Thomason has gone after Mrs. Ardoin has been riding for x hours.
d) Use your expressions to find when Mrs. Thomason and Mrs. Ardoin will meet.
a) The expression that shows how many miles Mrs. Ardoin has gone after x hours is of: s(t) = 15t.
b) Mrs. Thomason has been kayaking for x + 1/3 hours.
c) The expression that shows how many miles Mrs. Thomason has gone after Mrs. Ardoin has been riding for x hours: s(t) = 9t + 3.
d) They will meet after half an hour.
How to define the linear functions?The linear functions for the position are defined as follows:
s(t) = vt + s(0).
In which the variables are given as follows:
v is the velocity.t is the time.s(0) is the initial position.Mrs. Ardoin is boating at a constant speed of 15 miles per hour, hence his equation is of:
s(t) = 15t.
Mrs. Thomason has been kayaking for a third of an hour more than Mrs. Ardoin, at a rate of 9 miles per hour, hence his initial position is of:
s(0) = 1/3 x 9 = 3 miles.
Thus the equation is of:
s(t) = 9t + 3.
They will meet when:
15t = 9t + 3
6t = 3
t = 0.5.
Hence after half an hour.
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assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. if 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125.
The probability that the mean blood pressure will be less than 125 is 0.9938
The mean of the pressure readings = 123
The standard deviation = 9.6
Total population = 144
The value is less than 125
The equation of the z-score is
z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])
Substitute the values in the equation
z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])
= 2 / (9.6/12)
= 2 / 0.8
= 2.5
Using the statistical table
The probability of that their mean blood pressure less than 125
P(z < 2.5) = 0.9938
Therefore, the probability is 0.9938
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Solve for x.
y=69
5x+15=y+2x-5
The solution of x in the equation is 79/3
How to determine the solution of x?From the question, we have the following parameters that can be used in our computation:
y = 69
5x + 15 = y + 2x - 5
Substitute y = 69 in the equation 5x + 15 = y + 2x - 5
So, we have
5x + 15 = 69 + 2x - 5
Collect the like terms
This gives
5x - 2x =69 - 5 + 15
Evaluate the like terms
This gives
3x = 79
Divide both sides by 3
x = 79/3
Hence, the solution is 79/3
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The probability of obtaining a head when a certain coin is flipped is about 0.65 Whi ch of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times? A. 0.14 B. 0.37 0.39 0.60 0.65
The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.37
Given:
P = 0.65
1-P = 1-0.65 = 0.35
n = 25
x = 15
The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.
Favorable Results/Total Results = x/n, where Probability(Event)
using binomial distribution:
P(X = x ) = ⁿCₓ (P)ˣ (1-P)ⁿ⁻ˣ
∴ Heads obtained 15 or fewer times
P(X ≤ 15)
we use exceed formula:
P(X≤15) = BINOM DIST(15,25,0.65,FALSE)
= 0.3696920
≈ 0.37
Hence we get the required answer.
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