A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 113, and the sample standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about μ if the sample size, n, is 26.
(b) Construct a 95% confidence interval about μ if the sample size, n, is 15.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 26.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Answers
a) The 95% confidence interval about μ with n = 26 is given as follows: (109, 117).
b) The 95% confidence interval about μ with n = 15 is given as follows: (107.5, 118.5).
c) The 90% confidence interval about μ with n = 26 is given as follows: (109.7, 116.3).
d) The intervals could not have been computed if the population was not normally distributed, as the sample size is less than 30.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample mean and standard deviation for this problem are given as follows:
[tex]\overline{x} = 113, s = 10[/tex]
The critical values are given as follows:
95% confidence, 25 df: 2.0595.95% confidence, 14 df: 2.1448.90% confidence, 25 df: 1.7081.The bounds of the interval for item a are given as follows:
[tex]113 - 2.0595\frac{10}{\sqrt{26}} = 107.5[/tex][tex]113 + 2.0595\frac{10}{\sqrt{26}} = 118.5[/tex]The bounds of the interval for item b are given as follows:
[tex]113 - 2.1448\frac{10}{\sqrt{15}} = 109[/tex][tex]113 + 2.1448\frac{10}{\sqrt{15}} = 117[/tex]The bounds of the interval for item c are given as follows:
[tex]113 - 1.7081\frac{10}{\sqrt{26}} = 109.7[/tex][tex]113 + 1.7081\frac{10}{\sqrt{26}} = 116.3[/tex]The Central Limit Theorem states that the intervals can only be calculated for non-normal populations if the sample size is greater than 30.
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Related Questions
A boat travels 50 miles downstream in 2 hours and it takes 5 hours to travel back upstream. What is the speed of the boat if it were in still water and what is the speed of the river current?
Answers
The 50 mile distance traveled downstream and back that takes 2 hours and 5 hours respectively gives;
The speed of the boat in still water = 17.5 mphThe river current flows at 7.5 mphHow can the boat speed be calculated?Let v represent the speed of the boat and let u represent the speed of the river current.
Distance the boat travels downstream = 50 miles
Time taken to travel downstream by the boat = 2 hours
Time taken to travel back upstream = 5 hours
[tex]velocity = \frac{distance}{time} [/tex]
Therefore;
Which gives;
[tex]v + u = \frac{50}{2} = 25...(1)[/tex]
v + u = 25[tex]v - u = \frac{50}{5} = 10...(2)[/tex]
v - u = 10Adding equation (1) to equation (2) gives;
(v + u) + (v - u) = 2•v = 25 + 10 = 35
2•v = 35
v = 35 ÷ 2 = 17.5
The speed of the boat, v = 17.5 mphu = 25 - v
Which gives;
u = 25 - 17.5 = 7.5
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Simplify the problem
Answers
Answer:
B. 2√3+4
Step-by-step explanation:
3√3+4−√3
=2√3+4 (Decimal: 7.464102)
pls need help
ersrsreerre
Answers
The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
How to compute the value?It should be noted that from the information given, we are given the information about three salesmen and their sales.
The total earnings for salesman A will be:
= (1300 × 3) + 65 × (11 + 14 + 16)
= 3900 + 2730
= 6630
The total earnings for salesman B will be:
= 300 × 3 + 40 × (14 + 15 + 13)
= 900 + 1680
= 2580
The total earnings for salesman C will be:
= 900 × 3
= 2700
Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
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Geometry question please help!
Answers
Answer:
4
Step-by-step explanation:
Since,
The width of the Longer gear is 7, and the smaller gear has a width of 3..
7-3 = 4
Hope it helps...
Marking me as Brainliest would help me... :(
What is the Pythagorean theorem
Answers
Answer:
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Pythagoras Theorem Equation
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Answer:
The Pythagoras theorem states that:The sum of the squares on the edges of a right triangle angle is equal to the squareon the hypotenuse.Mathematically stated as: a² +b² = c²Hope this helps.Good luck ✅.How many three-digit positive integers have three different digits?
Answers
648 is the three-digit positive integers have three different digits
According to the statement
we have given that there are three positive digit number are formed with three distinct digits.
And we have to find that the how many words are formed with distinct numbers.
So, to solve this type of problem the Combination formula is best.
Because it provides the all possibilities that from how many ways numbers are formed.
So, from a combination formula
here we take 9 two times because first time when we let a number then remaining numbers are 9. and second time remaining numbers are also 9 because we let the distinct number but for third number there will be a probability that choosing number will be same.
So, Three digit positive number become from 9*9*8 =648
So, 648 is the three-digit positive integers have three different digits.
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3
Seven students cut 5 inches of thread from a spool for a school project. What number represents the change in the
amount of the thread on the spool?
O-40 inches
3
O-35 inches
-29 inches
-26 inches
Answers
Answer:
35 inches
Step-by-step explanation:
7 x 5 = 35 lol
The number which represents a change in the amount of thread on the spool exists 35 inches.
What are mathematical operations?In mathematics, an operation exists as a process that takes zero or more input values to a well-defined output value.
Given: Length of thread a student cuts = 5 inches
Total number of students that cut thread = 7
Length of thread a student cuts = 5 inches
Length of thread 7 student cuts = 5 [tex]*[/tex] 7 = 35 inches
The negative length that 7 students cut from the spool exists the number that represents a change in the amount of thread.
The number which represents a change in the amount of thread on the spool exists 35 inches.
Therefore, the correct is option b) 35 inches.
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PLS I NEED HELP
2. Write the rule for the linear function. Remember a function rule is written using f(x).
Answers
Answer:
[tex]f(x) = \frac{1}{2}x + 5[/tex]
Step-by-step explanation:
So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.
The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]
The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.
We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run
[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]
So plugging this into the slope-intercept form you get the function
[tex]f(x) = \frac{1}{2}x + 5[/tex]
An insurance company study shows that 9% of U. S. adults have diabetes. Suppose 8 US adults are selected at random. LetX be the number of US adults among the 8 selected that have diabetes. Find the mean and standard deviation of X.
Answers
Using the binomial distribution, it is found that:
The mean of X is of 0.72.The standard deviation of X is of 0.81.What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are given as follows:
n = 8, p = 0.09.
Hence the mean and the standard deviation are, respectively:
E(X) = np = 8 x 0.09 = 0.72.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8 \times 0.09 \times 0.91} = 0.81[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Which logarithmic equation is equivalent to 82 = 64?
2 = log Subscript 6 Baseline 64
2 = log Subscript 64 Baseline 8
8 = log Subscript 2 Baseline 64
64 = log Subscript 2 Baseline 8
Answers
Answer: Choice B
[tex]2 = \log_{8}(64)[/tex]
======================================================
Explanation:
The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.
The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.
2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
The logarithmic equation equivalent to 82 = 64 is:
2 = log Subscript 64 Baseline 8
This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.
Hence, 2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
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An article in the British Medical Journal [“Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotrips,” (1986, Vol. 292, pp. 879–882)] found that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. The traditional method was 78% effective.
(a) Is there evidence that the success rate for PN is greater than the historical success rate? Find the P-value.
(b) Explain how the question in part (a) could be answered with a confidence interval.
Answers
The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
According to the statement
we have given that the percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. And
The traditional method was 78% effective.
we have to show that the success rate for PN is greater than the historical success rate then
we use the percentage formula to find the success rate of the new method. So,
(a) Total patients = 350
Success rate in number of patient = 289
Percentage of success rate = (289/350)*100
Then after calculating
Percentage of success rate = 82.57%
It is clear that the outcome success rate is 82.57% which is greater than traditional method.
(b) we have a 95% confidence that the success rate of new method is higher than the older method from a confidence interval of 2.262 and 3.67
So, The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.
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What will it cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard?
Answers
$1078.56
What is the formula of the area of the rectangle?The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As cost of carpet is given in square yard. so convert area of rectangle in square yard.
1 square feet = 9 square yard
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
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$1078.56 is the cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard.
What will it cost to carpet a rectangular floor?Given:
A rectangular floor measuring 21 feet by 18 feet.The carpets cost $25.68 per square yard.Find:
Cost to carpet a rectangular floor.Solution:
The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As the cost of the carpet is given in square yard. so convert an area of the rectangle into a square yard.
1 square foot = 9 square yards
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
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Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?Answer the questions to show how to write and simplify expressions that represent the problem
4. Which expression, the original expression or the expanded expression, involves finding the total cost first, then calculating the tax on that total?
Answers
Answer:
$4.50
Step-by-step explanation:
Okay so, first add both.
50+40 is 90, then multiply 90 by the tax percent which is
90x5%=4.5
If expression then,
x=money that they have to pay.
5%(50+40)=x (the original)
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FRAME AN EQUATION AND SOLVE IT. NEED HELP ASAP I only have 5 minutes!
Answers
Answer:
The answer to your question is 125
Step-by-step explanation:
x = 25 X 5= 125.
The required number is 125.
I hope this helps and have a good day!
carl is 7 years older than angela. the sum of five times carl's age and four times angela's age is 197. how old is each now
Answers
The ages of Carl and Angela given from the expression is 25 years and 18 years respectively
EquationAngela's age = xCarl's age = x + 7sum of five times carl's age and four times angela's age is 1975(x + 7) + 4x = 197
5x + 35 + 4x = 197
9x = 197 - 35
9x = 162
x = 162/9
x = 18
So,
Angela's age = x
= 18 years
Carl's age = x + 7
= 18 + 7
= 25 years
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point(s) possible
Set up a ratio for the following information and reduce to lowest terms: $3 per day for 12 employees for 39 days.
Answers
Answer:
3:12:39
Step-by-step explanation:
The ratio of amount for 1 day, number of employee and total number of days is 1 : 4 : 13.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given information are,
Amount for 1 day = $3,
Number of employee = 12,
Total number of days = 39.
The ratio of amount for 1 day, number of employee and total number of days
= 3 : 12 : 39
Simplify the ratio by dividing it to 3,
= 1 : 4 : 13
The required ratio is 1:4:13.
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Let m = X^2 + 3.
What is (x^2+3)^2+7x^2+21=-10 in terms of m?
OR
Let m=x^2+3m=x
2
+3m, equals, x, squared, plus, 3.
Which equation is equivalent to (x^2+3)^2+7x^2+21=-10(x
2
+3)
2
+7x
2
+21=−10left parenthesis, x, squared, plus, 3, right parenthesis, squared, plus, 7, x, squared, plus, 21, equals, minus, 10 in terms of mmm ?
Answers
The Equation in terms of m, m^2+7m+10=0
What is substituting in the equation ?
substituting means changing or replacing the values in the given equation.
Calculation:
Given equation is (x^2+3)^2+7x^2+21=-10
and m= X^2 + 3.
make the given equation in the form X^2 + 3,
now,
(x^2+3)^2+7x^2+21=-10
(x^2+3)^2+7(x^2+3)=-10
where,
X^2 + 3= m
after putting the value or replacing the values
we get, m^2+7m=-10
m^2+7m+10=0
the above equation is in the form of "m".
The Equation in terms of m, m^2+7m+10=0
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Answer:
m^2+7m+10=0
Step-by-step explanation:
Give brainly lol
Refer to the figure below.
BED and CEA are
angles.
A
C
E
D
B
Answers
Answer:
both two
Step-by-step explanation:
because it is in alphabetical order
A preimage can never be congruent to Which of the following is the notation for a translation that moves a figure 2 units right and 2 units up?
(x, y) → (2x, 2x)
(x, y) → (x − 2, y − 2)
(x, y) →
(x, y) → (x + 2, y + 2)its image.
Answers
The notation for the translation is (x, y) → (x + 2, y + 2)
How to determine the translation?The translations are given as:
2 units right2 units upThe above implies that we add 2 to the x coordinate and 2 to the y coordinate.
So, we have:
(x, y) → (x + 2, y + 2)
Hence, the notation for the translation is (x, y) → (x + 2, y + 2)
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Translate to a proportion and solve.
148.5 is 59 1/5% of what?
Answers
The actual value is 250.
Applying simple percentage formula here,
let x be the whole value
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250.
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The actual value is 250.
Applying percentage formula here,
let x be the value:
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250
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A recent survey points to the transformation underway in the automotive retail landscape. A study found that automobile executives believe the number of physical automotive retail outlets, as we know them today, will be reduced by 30% to 50%. Eighty-two percent of automobile executives strongly agree that the only viable option for physical retail outlets will be the transformation into service factories, used car hubs, or focusing on an ID-management approach, where the customer is recognized at every single touchpoint. What additional information would you want to know about the survey before you accepted the results of the study?
Answers
The additional information would you want to know about the survey before you accepted the results of the study will be:
What sampling design was used?What was the population from which the design was selected?What was the response rate?How to illustrate the information?In research of human subjects, a survey is a list of questions aimed for extracting specific data from a particular group of people.
Surveys may be conducted by phone, mail, through the internet or in malls. From the information, a recent survey points to the transformation underway in the automotive retail landscape.
It is important to know the sampling design that was used, the population from which the design was selected and the response rate.
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Which term has a degree of 8?
A.8xy
OB. -22³5
OC. 9ry
OD. 3x²y4
Answers
The term that has a degree of 8 is -2x³y⁵
How to find the degree of a polynomial?The polynomial above is a monomial. A monomial is a polynomial with a single term.
Therefore, the degree of a monomial is the sum of the exponents of all its variables.
In other words, a monomial is a number, a variable or a product of a number and a variable where all exponents are whole numbers.
Hence, the term with degree of 8 is -2x³y⁵
Degree = 0 + 3 + 5 = 8
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Given: 3x+12=8x−18 algebraic proofs
Step Reason
3x+12=8x−18
12=5x−18
30=5x
6=x
x=6
Answers
The value of x comes out to be 6 from the algebraic equation.
Solving the Given Algebraic Equation for x:
Given algebraic equation is,
3x + 12 = 8x - 18
⇒ 12 = 8x - 3x -18
8x - 3x - 18 = 12
5x - 18 = 12
5x = 12 + 18
5x = 30
x = 30 / 5
x = 6
What is an algebraic equation?
A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.
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What is the simple interest rate on a $2100 investment paying $1,559.46 interest in 15.8 years?
Answers
The simple interest rate is 4.7%
How to determine the simple interest rate?The given parameters are:
Principal = $2100
Interest = $1,559.46
Time = 15.8 years
The simple interest is calculated as:
I = PRT
Make R the subject
R = I/(PT)
So, we have:
R = 1559.46/(2100 * 15.8)
Evaluate
R = 0.047
Express as percentage
R = 4.7%
Hence, the simple interest rate is 4.7%
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does this represent two quantities that are proportional
Answers
Answer:
from looking at this we can see
1*4=4
2*4=8
3*4=12
6*4=24
a
Hope This Helps!!!
HELLO! I need aid with my assignment please, all the equations and to be solved. Please!
Answers
By using excel sheet we can get the answers for the difference t test.
The two kinds of formula are used in the excel . One from the data analysis the t test assuming equal variances as nothing was mentioned.
But if the t test for the means is used there might be slight variation in the values.
The other formula was of descriptive statistics.
The data was
No of feedback (sec) Feedback (sec) Difference
45 54 9
33 50 17
59 58 -1
32 38 6
30 42 12
27 35 8
29 38 9
59 66 7
64 65 1
38 55 17
For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
The difference t test gives
Count=N 9 9
Mean 41.2 49.67
Mean Difference 8.4
Standard Deviation 14.967 11.97
Variance 223.944 143.25
Standard Error 2.0824
t = -1.322
df = 16
t Critical two-tail 2.119905285
Confidence Level(95.0%) 4.802039614
Lower CI (95.0%) = 3.6
Upper CI(95.0%)= 13.2
t stat for 0.01= 4.561578674
t Critical two-tail 3.249835541
Confidence Level(99.0%) 6.055710988
Lower CI (99.0%) = 2.345
Upper CI(99.0%)= 14.457
For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
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A ladder is 8 feet 2 inches tall. How tall is it in inches?
Answers
Answer:
The ladder is 98 inches tall in inches.
Step-by-step explanation:
1 foot = 12 inches.⇒ 8 (feet) × 12 (inches) = 96 inches
⇒ Add the extra 2 inches
⇒ 98 inches tall.
In the figure below, the radius of the larger circle is 6,8 and the radius of the smaller circle is 4.5. Which of the following best approximates the area of the shaded region? Note: The figure is not drawn to scale. O 14.45 O 16.62 O 25.99 O 81.65 O 145.27
Answers
A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.
A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.
The area of a circle can be determined by the given expression:
Area = π[tex]r^{2}[/tex]
where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]
So, the area of the shaded region can be determined as:
Area of the shaded region = area of the larger circle - area of the smaller circle
Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]
= π (46.24 - 20.25)
= [tex]\frac{22}{7}[/tex] x 25.99
= [tex]\frac{571.78}{7}[/tex]
Area of the shaded region = 81.683
Thus the appropriate answer to the question is option D. 81.65.
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Find an angle between 0 and 360 that is coterminal with -60.
Answers
The angle which is coterminal with -60 between 0 and 360 is; 300°.
Which angle is coterminal with -60?Since, it follows that the representation of the angle -60 corresponds to 60° span in the clockwise direction.
Therefore, by going the conventional anticlockwise direction, the angle which is coterminal with -60 is; 300°.
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In the binomial probability distribution function, nCx represents the number of ways of obtaining x successes in n trials. True or False?
Answers
In the binomial distribution for probability function, [tex]_{n}C_{x}[/tex] represents the number of ways of obtaining x successes in n trials: True
What is binomial distribution?The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
The underlying assumptions of the binomial distribution are that each trial has exactly one possible outcome, that each trial has the same success chance, and that each trial is either independent of or mutually exclusive with every other trial.
As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.
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