The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%
Given data:
To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.
The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).
We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.
Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:
[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]
Where:
C(n, k) is the binomial coefficient (n choose k)
p is the probability of success in a single trial (0.1)
n is the number of trials (20)
To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:
P(X ≥ 2) = P(X = 2) + P(X = 3) + ... + P(X = 20)
P(X ≥ 2) = Σ(P(X = k)) from k = 2 to 20
Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]
[tex]=(1 - 0.1)^{20}[/tex]
= 0.12157
[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]
[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]
= 0.27017
P(X ≥ 2) = 1 - 0.1074 - 0.2684
P(X ≥ 2 ) = 0.60826 (approximately)
Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.
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Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
Answer:
16(2z-3) or GCF: 16
Step-by-step explanation:
32z-48 has a GFC of 16
16(2z-3)
Answer:
$16(2z-3)
Step-by-step explanation:
Prime factorization:
32: 2*2*2*2*2
48: 2*2*2*2*3
Notice any similarities:
2*2*2*2=16
$32z-$48 = $16(2z-3)
P. USE REPRESENTATIONS Sheila plans to invest $2000 or less in two different accounts. The low
risk account pays 3% annual simple interest, and the high risk account pays 12% annual simple
interest. Sheila wants to make at least $150 in interest this year.
a. Define the variables, then write and graph a system of inequalities to show how Sheila can
split her investment between the accounts.
Inconclusion the amount she invested in each account is $1,000 invested at interest rate 12% .
What is interest rate?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.Let x represent the amount invested at 3%.
. 12x +.03(2000-x)= 150
.09x+ 60 = 150
Collect like terms
.09x = 90
Divide both side by .09x
x = 90/.09
x=$1000
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DUE TOMORROW PLS HELP!!
does anyone know how to solve the area and perimeter for this parallelogram pls help!!! In details !!!
Answer:
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all four sides. x is in this case the length of the rectangle while y is the width of the rectangle. The area is a measurement of the surface of a shape. for example
You are able to find the perimeter of the rectangle by adding length and width and multiplying by two because the opposite sides of a rectangle are equal in length. Both lengths of the rectangle are the same, and both widths are the same. For example, P = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3 in).
Step-by-step explanation:
an experimenter would like to construct a 99% confidence interval with a width at most 0.5 for the average resistance of a segment of copper cable of a certain length. if the experimenter knows that the standard deviation of such resistances is 1.55. how big a sample should the experimenter take from the population? what happens if the standard deviation and the width of the confidence interval are both doubled?
64 is the standard deviation and the width of the confidence interval are both doubled .
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation. It reveals, on average, how far away from the mean each value is. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Margin of error(E)=0.5
Standard deviation(σ)=1.55
Significance level(α)=100%-99%=1% or 0.01
From Z distribution Critical value table
the Critical value(Zc)=2.58 at significance level=0.01
we know formula for the Margin of error
E = Zc * σ/√n
0.5 = 2.58 * 1.55/√n
√n = 2.58 * 1.55/0.5
√n = 3.999/0.5
√n = 7.998
n = ( 7.998)²
n = 63.968004
Aproximately
n = 64
the realtionship between the sample size and margin of error is inversly proportional.
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(1 point) if you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
The largest area that can be enclose in straight wall is 2450 m².
What is meant by the largest area?Having to maximize or decrease a geometric figure's measurements, area, or volume is a special example of a geometry word problem.Let 'x' be the length of rectangle.
Let 'y' be the width rectangle.
Perimeter = 140 meters
2x + y = 140
y = 140 - 2x
Area = xy
Put the value of y in area.
Area = x(-2x + 140)
Area = -2x² + 140x
Differentiating the area with respect to x.
dA/dx = -4x + 140
Put dA/dx = 0 to get the critical point.
-4x + 140 = 0
x = 140/4
x = 35
Largest area at x = 35.
y = 140 - 2x
y = 140 - 2×35
y = 70
Area = xy
Area = 70×35
Area = 2450 m²
Thus, the largest area that can be enclose in straight wall is 2450 m².
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overbooking: a boeing 767-300 a boeing 767-300 aircraft has 213 seats. when someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an ibm research paper by lawrence, hong, and cherrier). how many reservations could be accepted for a boeing 767-300 for there to be at least a 0.95 probability that all reservation holders who show will be accommodated?
7.82 % is probability that all reservation holders who show will be accommodated.
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.If 236 are booked.
and there is only room of 213.
if 214 or 215 or 216 ............ etc
all the way to 236
there won't be enough seats.
P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴ * ( 0.995 )²²
P( X = 214 ) = 0.08439109
= 8.44 %
P( X = 215 ) = ²³⁶C₂₁₅ * ( 0.9005 ) ²¹⁵ * ( 0.995 )²¹
= 0.0781522
= 7.82 %
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Jordan saved $225 and continues to save $45 each week. RayAnn saved $150 and continues to save $60 each week. Write and solve a system of equations using any method for the given situation.
Equation for Jordan:
Equation for RayAnn:
Solution:
??please help???
The equations using any method for the given situation illustrated that:
The equation for Jordan: 225 + 45w
The equation for RayAnn: 150 + 60w
How to calculate the equation?Let the number of weeks be represented by w. Jordan saved $225 and continues to save $45 each week. The equation for this will be:
= 225 + (45 × w)
= 225 + 45w
RayAnn saved $150 and continues to save $60 each week. The equation will be:
= 150 + (60 × w)
= 150 + 60w
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assuming that earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 1046 kilometers due north of the other?
The difference between the distance between the two cities if of 14.842 latitudes.
The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.
Therefore, the earth has 181 latitudes.
Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.
Hence the distance covered by all 181 latitudes = 2 X radius of the Earth
= 2 X 6378 km
= 12756
Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be
12756/181
= 70.475 km
Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.
Therefore the difference in latitudes between the two cities is
1046/70.475
= 14.842 latitudes
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12. Choose the correct answer.
t
5/6
7/8
1/2
3/4
l'
m
Answer: angle 1 and 4
Step-by-step explanation:
Charities can claim an extra 25% of the value of a donation back from the government. This is called gift aid. Work out how much gift aid a charity can claim on a donation of £273.50. Give your answer to the nearest penny
Answer:
Gift aid 68.38 £
Step-by-step explanation:
Proportion:
273.50 £ - 100%
X £ - 25%
Gift aid:
X = 273.50·25% / 100% = 273.50 / 4 ≈ 68.38 £
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
Two friends visited a taffy shop. Gordon bought 8 pounds of strawberry taffy and 3 pounds of banana taffy for $66. Next, Levi bought 10 pounds of strawberry taffy and 3 pounds of banana taffy for $78. How much does the candy cost?
I NEED AN ANSWER ASAP LIKE BEFORE TOMORROW
The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given,
Let's say the cost per pound of strawberry taffy is "s" and the cost per pound of banana taffy is "b".
Then, the cost of 8 pounds of strawberry taffy and 3 pounds of banana taffy will be,
8s + 3b = 66
And,
The cost of 10 pounds of strawberry taffy and 3 pounds of banana taffy will be,
10s + 3b = 78
By solving both above equations,
2s = 12
s = $6
3b = 78 - 10(6)
b = $6
Hence, "The equation formation is the form of a real word problem for some of them, thus the cost of candy for the given condition is $6".
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Solve for x 5 x + 2 = 7 x − 4
Answer: x=3
Step-by-step explanation:
5x+2=7x-4
-5x +4 -5x +4
2x=6
divide both sides by 2
x=3
Hello I’m doing my math homework I just need the answers for 23 and that’s just it . ABCDEF all right thank you please get me ASAP,
Answer:
A. -9, -6, 8, 13
B. -4/5, -1/2, -.2, .25
C. -8/3, -2 1/2, 9/2, 4.75
D. -8, -3, -1, 4
E. -1/2, -1/4, .5, 3/4
F. -3/2, -5/4, -4/5, 1.5
Step-by-step explanation:
The easiest thing to do is to put them all in the same format. Fractions are just division problems, so just divide. 4/5 is 4 divided by 5, which is .8.
Remember, the farther a negative number is from 0 on the number line, the smaller it is. So, -8 is smaller than -5. -5 is smaller than -2, etc.
EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the slope intercept form of the equation of the line through the given point with the given slope
through (-1, 0) slope = -4
Answer:
y=-4x-4
Step-by-step explanation:
we know the slope so put it in the slope intercept form
y=-4x
Now fill it in to find y intercept with the coordinates
0=-4(-1)
0=4
We need to subtract 4 to make this equation true so the y intercept is -4
The equation will become
y=-4x-4
Hopes this helps please mark brainliest
Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
Write the point-slope form of the equation of the line through the given point with the given
slope.
3) through: (5, 1), slope
=
1
5
The point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
What is equation of line ?
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Here the given point ,
=> [tex](x_1,y_1)=(5,1)[/tex]
Slope m = [tex]\frac{1}{5}[/tex]
Here using equation formula
=> [tex]y-y_1 = m ( x- x_1)[/tex]
=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
Hence the point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
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this is my last question please help asap!!
The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
The correct option is (A).
What is the average rate of change of a function?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.
Using function notation, we can define the Average Rate of Change of a function f from a to b as:
[tex]rate(m) = \frac{f(b)-f(a)}{b-a}[/tex]
The given function is [tex]g(x) = 5(2)^{x}[/tex],
Now calculating the average rate of change of function from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(2)-g(1)}{2-1}\\\\m=\frac{5(2)^{2}-5(2)^1}{2-1}\\ m=\frac{10}{1} \\m=10[/tex]
Now, calculate the average rate of change of function from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\ m = \frac{g(4)-g(3)}{4-3}\\\\m=\frac{5(2)^{4}-5(2)^3}{4-3}\\ m=\frac{40}{1} \\m=40[/tex]
The jump from m = 10 to m = 40 is "times 4".
So option (A) is correct.
Hence, The average rate of change of function [tex]g(x)=5(2)^{x}[/tex] from x = 3 to x = 4 is 4 times that from x = 1 to x = 2.
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a restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. the model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. what was the value of the correlation coefficient? responses 0.64 0.64 0.60 0.60 0.40 0.40 0.36 0.36 0.13
The value of the correlation coefficient is 0.60.
There is a 0.6 correlation coefficient between two variables, which measures the strength of the relationship.
R² is the coefficient of determination, which measures how much variation can be explained by the regression line.
This means that, the R² value of the data is 36%
R² = 36% = 0.36
Correlation coefficients measure the strength of relationships between variables in the form of square roots.
That is ; R = √R²
R = √0.36
Hence, the correlation Coefficient, R is 0.60
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The solutions of the equation x^2 - 6x + d = 0 are both integers. d is a prime number. Find d
The solutions of the equation x^2 - 6x + d = 0 are both integers and d is a prime number is 5.
How to determine the value of d?From the information, the solution of the equation x^2-6x+d=0 are integers
To find d, the numbers which can be added or subtracted to get -6 is needed which when multiplied will give a prime number
In this case - 5- 1 = -6
And when multiplied (-5×-1) will give +5 which is a prime number.
Therefore, x^2-6x+5=0
This illustrates that d is 5.
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Find the x- and y-intercepts of the graph of -7x+10y=35. State each answer as an integer or an improper fraction in simplest form.
x-intercept
The x-intercept is where y=0.
[tex]-7x+10(0)=35\\\\-7x=35\\\\x=\boxed{-5}[/tex]
y-intercept
The y-intercept is where x=0.
[tex]-7(0)+10y=35\\ \\ 10y=35\\\\y=\boxed{7/2}[/tex]
Dev’ car currently ha 18 gallon of ga in the tank. He ue about 0. 04 gallon for every mile he drive. Dev want to go on a car trip over the weekend and have at leat 2 gallon of ga left in hi tank to get to work on Monday. What i the olution of the inequality that determine how far Dev can travel over the weekend? (Example 2) Let x repreent the number of mile Dev travel
The solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Dave who is planning a car trip for weekend.
Assume that [x] represents the number of miles Dev can travel.
We can write the inequality as -
18 - 0.04x ≤ 2
0.04x ≤ 16
x ≤ 400 miles
Therefore, the solution of the inequality that determines how far Dev can travel over the weekend is -
x ≤ 400 miles.
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A. 17 B. 117 C. 163 D. 173 In the figure above, n || p. Straight line m intersects both line n and line p. What is the value of r?
evaluate the expression 8.2x- 6.1 when x=7
Answer:
51.3
Step-by-step explanation:
Since it's telling us that (x=7) then that means 8.2x is going to be multiplied
8.2(7) or 8.2 x 7.
Then you end up getting an answer of 57.4
But you are not finished yet and need to subtract 6.1
so 57.4 - 6.1 = 51.3
And your result will be (51.3)
I hope this helps you understand this problem!
At a sale, suits were sold for $130 each. If the suits originally cost $200 each, what percentage of its original price was a suit sold for?
Answer:
70%
Explan your answer :
200-130=70 and 70% of 100 = 30% so
Answer: 65
Step-by-step explanation:
0.65
×
100
=
0.65×100=
65
%
65%
A famous piece of artwork was up for bid at a museum auction. The minimum bid was $25,000.
Determine which inequality represents the bid for the artwork.
b ≥ 25,000
b ≤ 25,000
b < 25,000
b > 25,000
The inequality that represents the bid for the artwork is A. b ≥ 25,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.
Let the minimum bid be b. This will be b ≥ 25,000.
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what does the adjusted r squared tell us about the relationship between sales, price, and advertising? the model explains about 90% of the variance in sales. the model explains about 60% of the variance in sales. the model explains about 80% of the variance in sales. the model explains about 70% of the variance in sales.
The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
Define the term adjusted r squared?R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.
R-squared describes how much the variance with one variable describes the variance of the other. So, if a model's R2 is 0.50, the model's inputs can explain roughly half of a observed variation.A score of 70 to 100 shows that a specific portfolio closely reflects the underlying stock index, whereas a score of 0 to 40 indicates a relatively poor correlation the with index.Higher R-squared scores also suggest that beta measurements are more reliable. The volatility of either a security or portfolio is measured by beta.Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.
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AWNSER PLSS !How can a negative number be written in scientific notation?
determine the intercepts of the line.
-4x + 7y = 3
Answer:
x intercept = (-3/4, 0)
y intercept = (0, 3/7)
Step-by-step explanation:
just ask :))
What is the minimum number of lawns Wallace must mow in order for him to earn at least $8?
Answer:1
Step-by-step explanation:
The answer is one because the graph starts at 12$ and Wallace only needs $8.
reimond needs to order crushed rock for a courtyard what is the cost of 4.5 t at $12.50 per tonne?
The cost of 4.5 tonnes of rock is $56.25
Given,
cost of 1 tonne of rock=$12.50
then
to find cost of 4.5 tonnes of rock, multiply 12.50 with 4.5,
cost of 4.5 tonnes of rock = 4.5* 12.50 = $56.25
Thus ,the cost of 4.5 tonnes of rock is $56.25.
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