The answer of two iterations of newton's method to approximate a zero of the function using the given initial guess is 1.5262!
Iterative formula, what is it?Iteration refers to doing a procedure repeatedly. Starting with an initial value, enter it into the iteration formula to get a new value. Next, use the new value for the next substitution, and so on, to solve an equation using iteration.
By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1,
and by using the previous guess, xn, like so-
xn+1 = xn - f(xn)/f'(xn)
and herethe case is f(x) = cos(x), and so f'(x) = -sin(x).
Also, furthermore, cos(x)/(-sin(x)) = -cot(x).
here, we have to simplify the formula to get a better guess for a zero to:
xn+1 = xn + cot(xn)
x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...
And x3 = 2.06170... + cot(2.06170...) = 1.52615...
Ans = 1.5262!
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The ratio of the number of girls to the number of boys was 3 to 5. If 2,520 were present, how many were girls and how many were boys?.
There were 1575 boys and 945 girls.
What does the ratio mean?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3.
A ratio is a number with no units.
According to the information provided to us, there were 3 girls for every 5 boys.
3 to 5 girls to boys are the ratio.
The sum is 8.
We need to find the number of girls and boys
Out of 2,520, 3 to 5 girls were present.
We have 3/8(2520) = 7560/8 girls, which comes to 945.
For boys, 5/8(2520) = 12600/8 boys, which equals 1575.
Therefore, there were 945 girls and 1575 boys respectively.
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suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a pc. find the probability that this person is a graduate student. show your work
The probability that this person is a graduate student is 0.3833.
From the recent census
40% of its students mainly used Ma- cintosh computers.
At the time of the census, 67% of the school's students were undergraduates.
In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers.
We have to find the probability that this person is graduate student.
Let A represent the event that student uses Mac.
So P(A)=40%=0.4, P(A')=60%=0.6
Then let B be the event that randomly chosen student is undergraduate·
So, P(B) = 67%=0.67, P(B')= 33%=0.33
Further, 23% of respondents were graduate. Students who said they used PCs as their Primary Computers
So P(B'∩A')=23%=0.23
If we select a student at random from among those who were part of the Census and learn that student mainly uses PC, then probability that this person is a graduate student is:
P(B'|A') = P(B'∩A')/P(A')
P(B'|A') = 0.23/0.6
P(B'|A') = 0.3833
Hence, the probability that this person is a graduate student is 0.3833.
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The right question is:
Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Ma- cintosh computers (Macs). The rest mainly used PCs. At the time of the census, 67% of the school's students were undergraduates. The rest were gradu- ate students. In the census, 23% of the respondents were graduate students who said that they used PCs as their primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a PC. Find the probability that this person is graduate student. Show your work.
what are the odds of randomly generating an even number with the first two odd numbers and unique numbers
The odds of randomly generating an even number with the first two odd numbers and unique numbers = [tex]\frac{10}{16}= \frac{5}{8}[/tex].
Sum will be even if either both numbers are odd or both numbers are even .
So, Total no. of way to select numbers for making sum even
= 5C2 + 4C2 = 10 + 6 = 16
And, Total numbers of ways to select two odd numbers such that sum is even = 5C2 = 10
Probability that both numbers are odd = [tex]\frac{10}{16}= \frac{5}{8}[/tex]
Hence the answer is the odds of randomly generating an even number with the first two odd numbers and unique numbers = [tex]\frac{10}{16}= \frac{5}{8}[/tex].
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Find the dimensions of a rectangle whose width is 8 meters less than its length, and whose area is 153 square meters.
Answer:
Dimensions: 15 cm × 7 cm
Step-by-step explanation:
Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If an answer does not exist, enter DNE.) Х f(x) x2 + 9 local maximum value (3,6) 6) x _3, local minimum value x
The required local maximum and minimum values of f using both the First and Second Derivative Tests.
What does local maximum and minimum value mean?The local maxima is a point inside a stretch at which the capability has a most extreme worth. The outright maxima is likewise called the worldwide maxima and is the point across the whole area of the given capability, which gives the most extreme worth of the capability.
The local minima is the info an incentive for which the capability gives the base result values. The capability condition or the diagram of the capability isn't once in a while adequate to see as the nearby least. The subordinate of the capability is exceptionally useful in tracking down the nearby least of the capability.
According to given data in the question:f(x)=x/x^2+9
differentiate with respect to x
df(x)/dx = d(x/x^2+9)/dx = -2/x^2+2x^2/9
second derivative = 3/x^3+2x^3/3
Put this derivative equal to zero, then we will put given points, if it becomes negative then the point is on maxima, if it is positive then is on minima.
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a sample of 2,500 people was asked how many cups of coffee they drink in the morning. you are given the following sample information. cups of coffee frequency 0 600 1 800 2 900 3 200 2,500 the expected number of cups of coffee is . a. 1.28 b. 2.28 c. 1.5 d. 2
After using the mean, the expected number of cups of coffee is 1.28. So the option a is correct.
In the given question, a sample of 2,500 people was asked how many cups of coffee they drink in the morning.
We have to find the expected number of cups of coffee.
x Frequencyf(x) x^2 x∙f(x) x^2∙f(x)
0 600 0 0 0
1 800 1 800 800
2 900 4 1800 3600
3 200 9 600 1800
Total 2500 3200 6200
Mean = Sum of f.x/Sum of f
Mean = 3200/2500
Mean = 1.28
Mean = 1.28
The expected number of cups of coffee is 1.28.
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Solve for K.
F = kq
K = ____.
Answer:
K=F/q
Step-by-step explanation:
construct the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall. assume the population is approximately normal. step 3 of 4: find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
To find the critical value that should be used in constructing the 80% confidence interval for the average amount spent by 8 to 11 year olds on a trip to the mall.
What is critical value?the proper z-score for an 80% confidence interval must first be established. Both a z-table and a z-score calculator may be used for this.Using a z-table, i may search up the value of z such that 80% of the area under the standard normal curve is to the left of z to get the z-score. This number is around 0.84.We can then use this z-score to calculate the 80% confidence interval by taking the sample mean and adding or removing the product of the z-score and the standard error of the mean. The standard error of the mean is computed by dividing the standard deviation by the square root of the sample size.
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in a study of the u.s. census, informants would be , whereas respondents would be .
In a study of the u.s. census, informants would be statisticians respondents would be any U.S.citizens
Detailed meaning of survey research: Survey research is a research method involving the use of standardized questionnaires or interviews to collect data about people and their preferences, thoughts, and behaviors in a systematic manner. Although census surveys were conducted as early as Ancient Egypt, survey as a formal research method was pioneered in the 1930-40s by sociologist Paul Lazarsfeld to examine the effects of the radio on political opinion formation in the United States. This method has since become a very popular method for quantitative research in the social sciences.
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What is the greatest common multiple of 10 and 40?.
The greatest common multiple of 10 and 40 is 10.
What is meant by greatest common multiple?The greatest common divisor (GCD) of two or more integers, where at least one of them is not zero, is the largest positive integer that is a divisor of both numbers. For example, the GCD of 8 and 12 equals 4.
In the divisibility preorder relation, the GCD of a and b is their greatest positive common divisor. This signifies that a and b's common divisors are the same as their GCD divisors. The Euclidean algorithm or Euclid's lemma are widely used to establish this. This is the definition of "greatest" in the context of GCD generalizations.
Foe calculating the GCD of 10 and 40, we have to find the factors of 10 and 40.
Factors of 10:
1, 2, 5, 10
Factors of 40:
1, 2, 4, 5, 10, 20, 40
From all these factors we have to choose the greatest factor that is exactly divisible by both 10 and 40 are 1, 2, 10, and 5.
So, the greatest common multiple of 10 and 40 is 10.
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Find the coordinates of the turning point on the curve with equation y=9 18x-3x^2
The coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).
Any equation of the form [tex]axx^{2} + bx + c = 0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
It is given that:
The quadratic equation is:
y = 9 + 18x - 3x²
To find the turning point:
Graph the above quadratic equation;
From the graph:
The maximum point from where the graph starts to decrease is (3,36)
Thus, the coordinates of the turning point on the curve with the equation y = 9 + 18x - 3x² is (3,36).
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What is the equation of the line that passes through the points (-2,-5) and (-4,-4)
The equation of the line that passes through the points (-2,-5) and (-4,-4): y = -1/2x - 6.
What is the Equation of a Line?Given the following points that a line passes through below:
(-2, -5) and (-4, -4).
First, find the slope (m):
Slope (m) = change in y / change in x = (-4 -(-5)) / (-4 -(-2))
Slope (m) = 1/-2
Slope (m) = -1/2.
Find the y-intercept (b) by substituting m = -1/2 and (x, y) = (-4, -4) into y = mx + b:
-4 = -1/2(-4) + b
-4 = 2 + b
-4 - 2 = b
-6 = b
b = -6
To write the equation of the line, substitute m = -1/2 and b = -6 into y = mx + b:
y = -1/2x - 6
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Help this question is truly annoying me in part c. Its bare jarring me off right now. Help Please. I won't be able to sleep with this in my mind I beg ahlie.
Answer:
4.2
Step-by-step explanation:
you look at where x=-1.5 and it’s about 4.2 where it is
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The table ummarize reult from 984 pedetrian death that were caued by automobile accident. Pedetrian intoxicated
Ye. No
Driver Intoxicated - Ye 51. 75
No 239. 619
If one of the pedetrian death i randomly elected, find the probability that the pedetrian wa intoxicated or the driver wa not intoxicated
If one of the pedestrian death is randomly elected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated 0.6290.
Divide the applicable variety with the aid of using the whole variety. In this case, the applicable variety they may be requesting is "neither pedestrian nor driver."Neither/Total = 619/984 = 0.6290.Rounded to 4 figures that is 0.6290.This, of course, assumes that the published desk is formatted successfully and is correctly legible.Read more about pedestrian :
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For each sequence find the first 4 terms and the 10th term n 5 , , , , ...,
The first 4 terms are 6,7,8,9 and the 10th term is 15 for given sequence.
Given:
n + 5
substitute n = 1,2,3,4....
= n+5
= 1+5
= 6
= 2+5
= 7
= 3+5
= 8
= 4+5
= 9
First four terms are 6,7,8,9
[tex]T_10 =[/tex] a + (n-1)d
= 6 + (10-1)1
= 6+9*1
= 15
10th term = 15
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Full question:
For each sequence find the first 4 terms and the 10th term:
n + 5.
X corporation has 2100 shares outstanding. John owns 900 shares, Mary owns 400 shares Z corporation owns 400 shares and Y partnership owns 400 shares. John and Mary are equal partners of Y partnership. John owns 30 percent of Z corporation. A Applying stock attribution rules, how many shares are owned by John B Assume John owns 60 percent of Z corporation, how many shares are owned by John?
Answer:
Step-by-step explanation:
it 10
find the missing side. round to the nearest 10th.
i need the answer to all 3, will mark brainliest
Answer:
6) x=20.64
7) x=12.423
8) x=26.5
Step-by-step explanation:
Two quantities, x and y, are directly proportional. If x is halved, what happens to y? clear check it is doubled. It is squared. It is multiplied by 12. It depends on the starting value of x.
When x and y are directly proportional and when x is halved then y is also halved or (C) it is multiplied by 1/2.
What do we mean by directly proportional?DIRECTLY PROPORTIONAL: connected, i.e., one grows or shrinks in proportion to the other. His income is directly correlated with the number of units he sells.
If we spend Rs. 50 on two pens, as an example.
For four pens, it will cost us 100 Rs.
When the ratio x:y1 is constant, two values, x and y, are said to be inversely proportional to one another.
So, if a relationship between two variables, x and y, can be represented in the form y/x = k OR y = kx, it represents a proportionate variation.
Then,
If x rises, y will follow.
If x declines, y will follow.
So, we obtain:
When x is cut in half, y does as well.
Therefore, when x and y are directly proportional and when x is halved then y is also halved or (C) it is multiplied by 1/2.
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Correct question:
Two quantities, x and y, are directly proportional. If x is halved, what happens to y?
a. clear check it is doubled.
b. It is squared.
c. It is multiplied by 1/2.
d. It depends on the starting value of x.
f(x)={x+4 x<5
8 5
2x-1 7
for “f(x)” exculpate the following
a. f(0)
b. f(6)
SHOW ALL WORK PLEASE
Answer:
a. 4 b.8
Step-by-step explanation:
a.
0 ∈ x<5
f(x)=x+4
f(0)=0+4=4
b.
6 ∈ 5≤x<7
f(x)=8
f(6)=8
Which polynomial function's graph is shown here?
OA)/(x) = (x + 1)(x+3)(x+4)
OB)/(x) = (x + 1)(x-3) (x+4)
OC)/(x) = (x-1) (x+3)(x-4)
OD)/(x) = (x-1) (x-3) (x-4)
In an application to etimate the mean number of mile that downtown employee commute to work round trip each day, the following information i given: n = 20 = 4. 33 = 3. 50 The point etimate for the true population mean i
Using T-test, the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.
T-Test:
When population data are limited, small samples should be used to estimate confidence intervals for the population mean. If your sample size is less than 30 and we don't know the population standard deviation, then you have the normal distribution instead, and use the t distribution instead of the normal distribution.
We have given that,
Estimate the mean number of mile that downtown employee commute to work round trip each day,
sample mean (X-bar) = 4.33
sample size (n) = 20
standard deviations of sample (s) = 3.50
we have to calculate the value of true population .
The degree of freedom is going to be equal to (20 - 1 )= 19 for the sample size, 20. The confidence interval is 95 percent. The level of significance of the alpha is 100% - 95% = 5% that's confidence interval is 5 percent, which is basically in decimal.05.
Upper limit of Population mean = x-bar + t∗s√n
t value at 0.05 and degree of freedom 19 is 2.09
Upper Limit : 4.33 + 2.09×3.50√20
=5.965~ 6
the upper limit for a 95 percent confidence interval estimate for the true population mean is: 5.965.
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Complete Question:
In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n=20, Xbar-4.33, s-3.5.
Based on this information, the upper limit for a 95 percent confidence interval estimate estimate for the true population mean is:
a)1,638
b) 3,5
c) 4,33
d) 4.33 +- 1.638
Identify the variation as direct, inverse, joint or combined. Y = 7x inverse combined joint direct.
The given variation y = 7x is a direct variation where any increase in the variable x also increases the value of the variable y.
The given variation is represented as -
y = 7x
We have to identify if the given variation is direct or inverse or joint or combined.
Let us first the different mathematical relationships mentioned here.
Direct variation is a mathematical relationship established between two different variables that can be represented in the form of an equation where one variable is a multiple of the other by a constant.Inverse variation is a mathematical relationship established between two different variables where any increase in one variable leads to the decrease in the other variable.Joint variation is a mathematical relationship where one variable is dependent on two or more variables.Combined variation is a mathematical relationship which is basically a combination of direct, inverse, as well as joint variation.Now that we know the definitions of different types of variations, let us look into the given variation, which is -
y = 7x
We can see that the variable y is 7 times the multiple of another variable x. Thus, this is a case of direct variation such that any increase in the variable x also increases the value of the variable y.
Therefore, the given variation y = 7x is a direct variation type.
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How do you know if two polynomials are relatively prime?.
two polynomials are relatively prime if the greatest common divisor of the two polynomial is 1
How do you prove two polynomials are relatively prime?
Two polynomials from Z[x] are called evaluationally relatively prime if the greatest common divisor of the two polynomials in Z[x] is 1 and gcd(f(t),g(t)) = 1 for all t ∈ Z.
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What are the coefficients for the binomial expansion of (a + b)3? 1, 4, 6, 4, 1 1, 1 1, 2, 1 1, 3, 3, 1.
For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1
What is meant by coefficient?The constant coefficient is the coefficient that is not connected to any variables in an expression. For example, the constant coefficients in the formulas above are 3 and c, respectively. The leading coefficient is the coefficient associated to the variable with the highest degree in a polynomial. For example, in the formulas above, the leading coefficients are 2 and a, respectively.
We have,
The binomial expansion (a + b)³,
We know that,
The formula for binomial expansion,
(u + v)ⁿ = ⁿC₀uⁿv⁰ + ⁿC₁uⁿ⁻¹v¹ + ⁿC₂uⁿ⁻²v² + ⁿC₃uⁿ⁻³v³
Now,
u = a,
v = b,
And, n =3
Now,
By putting values,
(a + b)³ = ³C₀a³b⁰ + ³C₁a³⁻¹b¹ + ³C₂a³⁻²b² + ³C₃a³⁻³b³
(a + b)³ = ³C₀a³b⁰ + ³C₁a²b¹ + ³C₂a¹b² + ³C₃a⁰b³
Now,
By using combination formula,
On solving we get,
(a + b)³ = a³+3a²b+3ab²+b³
So,
Now,
The coefficients of :
a³ = 1,
3a²b = 3,
3ab² = 3,
b³ = 1,
So,
For the given binomial expression the coefficients of (a+b)³ are 1, 3, 3, 1
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Answer: the answer is d
Step-by-step explanation:
I took the tes
Members of a softball team raised $1186. 50 to go to a tournament. They rented a bus for $842. 50 and budgeted $21. 50 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.
By solving the equation we know that 15 players can be brought to the tournament.
What do we mean by equations?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions.
For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
So, we know that:
Softball players raised $1186.50 to attend a tournament.
They allocated $21.50 for meals per player and paid $842.50 for the bus rental.
We must apply the following calculation to determine the total number of players they are permitted to bring:
Formula: Total amount of money= fixed cost + unitary variable cost × number of players
1186.50 = 842.50 + 21.50 × number of players
1186.50 - 842.50 = 21.50 × number of players
344/21.50 = number of players
15 = Number of players
Therefore, by solving the equation we know that 15 players can be brought to the tournament.
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for how many pairs of consecutive integers in is no carrying required when the two integers are added?
The number of pairs of consecutive integers in is no carrying required when the two integers are added are 156.
How we make the pairs of consecutive integers?At the point when the last 3 digits of the continuous numbers are _999 and _000. Just conceivable case-1999, 2000
At the point when the last 2 digits of the continuous numbers are _ _ 9 9 and _ _ 0 0. Potential cases-5 (Comparing to (0,1) (1,2) (2,3) (3,4) (4,5) in the 100th spot)
At the point when the last digit of the successive numbers is of the structure _ _ _ 9 and _ _ _ 0. Potential Cases-5*5 = 25
At the point when none is of that structure. Potential cases-5*5*5 = 125
Reply = 125+25+5+1 = 156
Thus,there are 156 ways to make the pairs of the consecutive integers.
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if you are looking to expand your company's presence online internationally, which of the following should you consider with regards to your online content?
You should consider option B - Translated but also locally adapted for the audience, with regard to your online content.
Any content that exists as digital data is considered online content. Otherwise called advanced media, computerized content is put away in computerized or simple capacity in unambiguous configurations.
A company's website should become more international in terms of content and supported languages if it wants to expand globally.
The content of a website must not only be translated into the language of the audience or user in that country but also adapted to fit the cultural and linguistic characteristics of that language, both of which are essential for expanding a website's or company's presence online internationally.
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(complete question)
If you are looking to expand your company's presence online internationally, which of the following should you consider with regards to your online content?
A . Translated by an automated tool only
B Translated but also locally adapted for the audience
C Translated into the native language
D Left the same, and not translated
help!!!!!!!!!!!!!explain and answer!!!!!!!
Answer:
a) 125 ml milk
b) 7.5g
Step-by-step explanation:
since 8 pancakes you need 250 ml of milk then you divide 250 by 2 since 8/2 is 4
250/2
125 ml milk
b)
We do the same as the other problem we find how much you need for 4 pancakes
5/2
2.5
Now you multiply by 3 since 4x3=12
2.5x3
7.5 g
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a chef is deciding on the schedule for the week of lunch specials for her restaurant. she makes 22 different dishes that she can put on the schedule. for each of the seven days of the week, she must select one dish for the lunch special. how many ways are there for her to select the schedule for the week if she does not select the same dish more than once? note that it matters which dish is served on which day for the schedule of daily specials.
The total ways are there for her to select the schedule for the week = [tex]\frac{22!}{15!}} \\\\[/tex]
Given, She makes 22 different dishes for each of the seven days of the week.
Total ways are there for her to select the schedule for the week = [tex]$ ^{22}P_7[/tex]
As We know,
[tex]$ ^nP_k=\frac{n!}{(n-k)!}} \\[/tex]
[tex]$ ^{22}P_7=\frac{22!}{(22-7)!}} \\\\[/tex]
[tex]\ $ ^{22}P_7=\frac{22!}{15!}} \\\\[/tex]
Hence, The total ways are there for her to select the schedule for the week = [tex]\frac{22!}{15!}} \\\\[/tex]
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The probability that Maria succeeds at any given free-throw is 75%. She was curious how many free-throws she can expect to succeed in a sample of 10 free-throws.
She simulated 25 samples of 10 free-throws where each free-throw had a 0.75 probability of being a success.
Maria counted how many free-throws were successes in each simulated sample. Here are her results:
5: 0 successes
6: 5 successes
7: 8 successes
8: 6 successes
9: 6 successes
10: 1 success
We need to use her results to estimate the probability that she succeeds at fewer than 7 free-throws in a sample of 10 free-throws. First, find out how many successes were less than 7 (out of 25), which is 5. now, we divide 5 by 25 (5/25, formula being number/total attempts) and simplify into a decimal, which comes out to 0.2
The probability that she succeeds at fewer than 7 free-throws is 0.19
How to determine the probability?The table of values is given as
5: 0 successes
6: 5 successes
7: 8 successes
8: 6 successes
9: 6 successes
10: 1 success
From the above readings, the throws less than 7 are
5: 0 successes
6: 5 successes
So, the number of success is
Success = 0 + 5
Success = 5
The probability is then calculated as
P = Success/Total
So, we have
P = 5/(0 + 5 + 8 + 6 + 6 + 1)
Evaluate
P = 5/26
So, we have
P = 0.19
Hence, the probability is 0.19
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