A highly rated community college has over 60,000 students and seven different campuses. One of its highest density classes offered is Introduction to Statistics. The statistics course is required for nearly every major offered at the college and therefore is considered a strategic course for the college. The college's leadership is very interested in the relationship between the class size of its statistics courses and students' final grades for the course. Specifically, the college is concerned with the low pass rate of some of its class sections and is determined to remedy the situation. The college's institutional research department recently collected data for analysis in order to support leadership's upcoming discussion regarding the low pass rate of some of its statistics class sections. Final grades from a random sample of 300 class sections over the last five years were collected. The research division also conducted analysis, using archived data, to determine the class size of these 300 class sections. The Class Number, Campus, Class Size, Average Final Grade, Number of "F"s, Average G.P.A. and Successful/Unsuccessful data were collected for these 300 class sections. StatCrunch Data Set Assume that the distribution of Average G.P.A. for all of the college's Introduction to Statistics class sections over the past five years has the same shape, mean, and standard deviation as the Average G.P.A. data. If it is reasonable based on your visual analysis of a histogram of the Average G.P.A. data, use the sample mean (2.66) and sample standard deviation (0.23) from the Average G.P.A. data together with the Normal distribution to answer all of the following questions. Calculate the probability of randomly selecting a class section from the population with an average G.P.A. less than 2.50. nothing% (Round to two decimal places as needed.) Calculate the probability of randomly selecting a class section from the population with an average G.P.A. greater than 3.00. nothing% (Round to two decimal places as needed.) Calculate the probability of randomly selecting a class section from the population with an average G.P.A. between 2.35 and 2.80. nothing% (Round to two decimal places as needed.) Calculate the average G.P.A. that represents the 90th percentile of all Introduction to Statistics class sections over the past five years. nothing (Round to two decimal places as needed.)
Answers
The probability of randomly selecting a class section from the population with an average G.P.A. less than 2.50 is approximately 24.91%. The probability of randomly selecting a class section from the population with an average G.P.A. greater than 3.00 is approximately 6.84%.
To calculate the probabilities and the average GPA for the given questions, we can use the sample mean (2.66) and sample standard deviation (0.23) from the Average G.P.A. data, assuming they represent the population.
1. The probability of randomly selecting a class section from the population with an average G.P.A. less than 2.50 can be calculated using the z-score formula and the standard normal distribution.
The z-score is (2.50 - 2.66) / 0.23 = -0.6957. Using a standard normal distribution table or software, we find the probability to be approximately 24.91%.
2. The probability of randomly selecting a class section from the population with an average G.P.A. greater than 3.00 can be calculated using the z-score formula and the standard normal distribution.
The z-score is (3.00 - 2.66) / 0.23 = 1.4783. Using a standard normal distribution table or software, we find the probability to be approximately 6.84%.
3. The probability of randomly selecting a class section from the population with an average G.P.A. between 2.35 and 2.80 can be calculated by finding the area under the standard normal curve between the corresponding z-scores.
The z-scores for 2.35 and 2.80 are (-0.9130) and (0.6522) respectively. Using a standard normal distribution table or software, we find the probability to be approximately 46.20%.
4. To compute the average G.P.A. that represents the 90th percentile of all Introduction to Statistics class sections over the past five years, we need to find the corresponding z-score. Using a standard normal distribution table or software, we find the z-score to be approximately 1.2816.
We can then calculate the average G.P.A. using the formula: average G.P.A. = (z-score * standard deviation) + mean.
Substituting the values, we get (1.2816 * 0.23) + 2.66 = 2.9668. Therefore, the average G.P.A. that represents the 90th percentile is approximately 2.97.
Note: It is important to keep in mind that these calculations are based on the assumption that the sample accurately represents the population.
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Related Questions
Lars has $90 to buy tickets to the zoo for some of his family. He will buy an equal number of child and adult tickets.
Ticket Cost ($)
Child 7.00
Adult 12.00
The inequality 7n+12n≤90 can be used to find the number of each type of ticket he can buy. What is the greatest number of each type of ticket that Lars can buy?
He can buy -BLANK- child tickets and -BLANK- adult tickets.
Answers
The greatest number combination,
He can buy 6 child tickets and 4 adult tickets.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
Lars has $90 to buy tickets to the zoo for some of his family.
He will buy an equal number of child and adult tickets.
Ticket Cost ($)
Child 7.00
Adult 12.00
The inequality,
7n+12m ≤ 90 can be used to find the number of each type of ticket he can buy.
When either number of tickets is zero,
So, the greatest number of child tickets is 7 x 12 ≤ 90.
Hence, n = 12.
The greatest number of adult tickets,
7 x 12 ≤ 90.
Hence, m = 7.
Combine tickets,
When n = 6 and m = 4,
Then the total = 10.
Whne n = 10 and m = 1, total = 11.
Therefore, he can buy 6 child tickets and 4 adult tickets.
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How long would it take, in seconds, for a small raindrop (1000μm) to fall 1,500 feet? Use Table 7.1
a. 114.5 sec O
b. 114.5 min O
c. 19,650 secO
d. 0.009 sec
Answers
The correct answer is b. 114.5 min.A small raindrop (1000μm) takes 114.5 min to fall 1,500 feet .
To calculate how long it would take for a small raindrop (1000μm) to fall 1,500 feet, we can use Table 7.1, which provides the fall time for different sizes of objects.
First, let's convert 1,500 feet to micrometers (μm). Since 1 foot is equal to 30.48 centimeters (cm) and 1 cm is equal to 10,000 micrometers (μm), we have:
1,500 feet * 30.48 cm/foot * 10,000 μm/cm = 457,200,000 μm.
Now, looking at Table 7.1, we find that a small raindrop (1000μm) falls in approximately 0.009 seconds.
Therefore, for a raindrop to fall 457,200,000 μm, we can use proportionality:
1000 μm : 0.009 sec = 457,200,000 μm : x sec.
Cross-multiplying, we get:
1000 * x = 0.009 * 457,200,000,
x = (0.009 * 457,200,000) / 1000,
x ≈ 4114.8 seconds.
So, it would take approximately 4114.8 seconds for a small raindrop (1000μm) to fall 1,500 feet.
To convert this to minutes, we divide the seconds by 60:
4114.8 seconds / 60 = 68.58 minutes.
Rounded to one decimal place, it would take approximately 68.6 minutes.
Therefore, the correct answer is b. 114.5 min.
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ms. lee is shopping for a new electric warer heater. brand A cost $575 and uses 442 kiliwatt- hours per month. brand B cost $651 and uses 397 kiliwatt-hours per month. if electricity costs $0.17 per kilowatt-hour, how much would ms. lee save on electricity per month by buying brand B
Answers
Answer:
7.65
Step-by-step explanation:
Brand A:
442(times)0.17=75.14 each month
Brand B:
397(times)0.17=67.49 each month
75.14-67.49=7.65
Ms.Lee would save 7.65 each month with brand B
a table or spreadsheet used to systematically evaluate options according to specific criteria is a ________.
Answers
A table or spreadsheet used to systematically evaluate options according to specific criteria is a decision matrix.
A decision matrix is a table or spreadsheet used to systematically evaluate options based on specific criteria. It is a tool commonly used in decision-making processes to objectively assess and compare different choices.
The decision matrix organizes the criteria in rows and the options in columns. Each cell in the matrix represents the evaluation or score of an option based on a particular criterion. The criteria can be weighted to reflect their relative importance in the decision-making process.
By filling out the decision matrix with scores or ratings for each option and criterion, a comprehensive evaluation can be performed. The matrix allows decision-makers to visualize and compare the performance of different options against the criteria, helping them make more informed and structured decisions.
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There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a blue marble is 5/9.
There are 63 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answers
EXPLANATION:
first we work out what all the marbles equal which is 9/9=63
Then we work out what 1/9 of the marbles are! Which is 1/9= 7 marbles!!
Then we work out what 5/9 of them are! Which is 5/9= 35 marbles
Then now we work out 4/9 which is our RED marbles! We do 4 times 7 which equals 28 red marbles!!
if you want to check to add the two numbers and they equal 63!
ANSWER= 28 red marbles
4. Bob spent $30 playing paintball which
included a $16 entry fee and $3.50 per hour of
play. How many hours did Bob play?
Answers
Answer: 4 hours
Step-by-step explanation:
First, set up an equation. We know that Bob spent $30 on playing paintball so we use that as our 'answer.' We need to find how many hours Bob played so we need to use x, a variable to find it. We also add 16 because we need to account for the entry fee.
3.50x + 16 = 30
Secondly, solve for x. Move 16 across the equal sign(=). Every time you move across the =, you're going to want to change the sign (if it's addition or subtraction). Since it was +16 and we're moving it, it's now -16.
3.50x = 30 - 16
Calculate 30 - 16 = 14.
Now we have
3.50 x = 14.
To calculate x, we're going to need to divide 3.50 from x. Since we multiplied by x we need to do the opposite across the =.
x = 14 / 3.50
x = 4
Bob spent 4 hours playing paintball.
You can plug it in to check answers as well
3.50 (4) +16 = 30
Find the area of the circle to the nearest hundredths ( Use 3.14 for pi) (4cm)
Answers
Answer: 50.24 cm²
Step-by-step explanation:
ASSUMING THE RADIUS OF THE CIRCLE IS THE 4 CM
The formula for the area of a circle is pi(3.14) * r(4)^2
\(3.14*4^2\)
\(3.14*16\)
\(50.24\)
Hope it helps <3 :D
a class has nine boys and eleven girls. any two boys will fight if they are next to each other. how many ways can the teacher line up the students so that no two boys stand next to each other? byju's
Answers
The teacher can line up the students in 3991680 ways so that no two boys stand next to each other.
Given, A class has nine boys and eleven girls.
Any two boys will fight if they are next to each other.
Ways can the teacher line up the students so that no two boys stand next to each other:
The total number of students = 9 + 11 = 20.
To count the total number of arrangements such that no two boys stand next to each other, we will count the total number of arrangements of all students and then subtract the arrangements where two boys are together.
Let's take two cases :
1. Case 1: When a girl stands on both ends, there are 11 ways to do this.
After placing the girls, the number of possible ways to arrange boys in such a way that no two boys are standing next to each other can be calculated using the permutation formula.
(n - r + 1)P(r) = (9 - 1 + 1) P(9) = 9P9 = 9!
Thus, the total number of arrangements in this case = 11 × 9!
2.Case 2: When a boy stands on one end and a girl on the other, there are 2 ways to do this.
After placing the girl and boy, the number of possible ways to arrange boys in such a way that no two boys are standing next to each other can be calculated using the permutation formula.
(n - r + 1)P(r) = (9 - 1)P(8) = 8P8 = 8!
Thus, the total number of arrangements in this case = 2 × 8!
Thus, the total number of arrangements in which no two boys stand next to each other is = (11 × 9!) + (2 × 8!)
= 11 × 362880 + 2 × 40320= 3991680.
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I need help PLEASE !!!! Write a cosine function that has an amplitude of 2, a midline of 4 and a period of 4.
Answers
Answer:
\(\mathbf{y = 2cos ( \dfrac{\pi}{2}(x - 0) + 4}\)
Step-by-step explanation:
The standardized cosine function is ;
\(\mathbf{y = Acos (Bx + C) +D}\)
Amplitude |A| = 2
Period \(\dfrac{2 \pi}{B }= 4\)
2π = 4B
\(B = \dfrac{2 \pi}{4}\)
\(B = \dfrac{\pi}{2}\)
Midline y = 4; D = 4
Phase shift; since no phase shift is given; then C = 0
The cosine function: \(\mathbf{y = 2cos ( \dfrac{\pi}{2}(x - 0) + 4}\)
among games with a spread around 5, from 3.5 to 6.5, including both 3.5 and 6.5, what was the mean of the outcomes?
Answers
The mean outcome for these 10 games with a spread between 3.5 and 6.5 is 4.95.
To find the mean of the outcomes of games with a spread between 3.5 and 6.5, we need to know the outcomes of all the games within that range.
Assuming that we have a set of data containing the outcomes of all games with a spread between 3.5 and 6.5, we can calculate the mean by summing up all the outcomes and dividing by the total number of games.
For example, let's say we have the following outcomes for 10 games with spreads between 3.5 and 6.5:
Game 1: 4.5
Game 2: 5.5
Game 3: 6.5
Game 4: 4.0
Game 5: 3.5
Game 6: 5.0
Game 7: 6.0
Game 8: 3.5
Game 9: 4.5
Game 10: 5.5
To find the mean outcome, we add up all the outcomes and divide by 10:
(4.5 + 5.5 + 6.5 + 4.0 + 3.5 + 5.0 + 6.0 + 3.5 + 4.5 + 5.5) / 10 = 4.95
Therefore, the mean outcome for these 10 games with a spread between 3.5 and 6.5 is 4.95.
It's important to note that this calculation assumes that all the games within the given spread are equally represented in the dataset, and that there are no significant outliers or anomalies that may skew the mean outcome.
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After 4 months of a new nutrition program, Rashid has lost 16% of his original weight. he lost 36 lb. What was Rashid's original weight?
Answers
36*100/16
36 times 100 then divide by 16
Answer:
225 lb
Step-by-step explanation:
Let x be Rashid's original weight.
If 16% of Rashid's original weight is 36 lb then:
\(\implies 0.16x=36\)
To find Rashid's original weight solve for x:
\(\implies \dfrac{0.16x}{0.16}=\dfrac{36}{0.16}\)
\(\implies x=225\)
Therefore, Rashid's original weight is 225 lb.
A line passes through the points (-1,-7) and (7, 1). Write its equation in slope intercept
Answers
Answer:
y = x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 1, - 7 ) and (x₂, y₂ ) = (7, 1 )
m = \(\frac{1-(-7)}{7-(-1)}\) = \(\frac{1+7}{7+1}\) = \(\frac{8}{8}\) = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (7, 1 ) , then
1 = 7 + c ⇒ c = 1 - 7 = - 6
y = x - 6 ← equation of line
There are 14 girls and 12 boys in a class. What is the ratio of girls to students?
Answers
Answer:
7:13
Step-by-step explanation:
There are 14 girls and 12 boys, so there are 26 students in total. Since we are looking for the ratio of girls to students, the ratio will be 14:26. To simplify it, we will divide 14 and 26 by their greatest common factor: 2. We will get the ratio of 7:13.
I hope this helped! :)
I-Ready
Describe Angle Relationships in Triangles - Quiz - Level H
The figure shoys a triangle with unknown angles.
Which equation shows the relationship between the angles in the triangle?
mL1 + mL2 + mL3 = 360°
mL1 + mL2 + mL3 = 180°
mL1 + mL2 = 360° + mL3
mL1 + mL2 = 180° + mL3
Answers
The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.
What is the relationship between the angles of the triangle?The equation that shows the relationship between the angles in the triangle is determined as follows;
The sum of angles in a triangle is equal to 180 degrees.
So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;
angle 1 + angle 2 + angle 3 = 180
We can re-write the equation as follows;
m∠1 + m∠2 + m∠3 = 180
Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.
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A system described by equation y= -2x+0 . Which of the follwing is correct?
A.
The system does not satisfie the principle of homogeneity and superposition
B.
The system satisfies the principle of homogeneity
C.
The system satisfies the principle of superposition
D.
The system is linear
Answers
The following is correct: The system is linear. The correct option is D
A system is considered linear if it satisfies the principles of homogeneity and superposition. Let's examine the given equation y = -2x + 0.
Principle of Homogeneity: A system satisfies homogeneity if scaling the input results in a proportional scaling of the output. In other words, if y(t) is the output for input x(t), then for any constant 'a,' the output for 'a * x(t)' should be 'a * y(t)'. Let's check this property for the given equation:
For a constant 'a':
y(at) = -2(at) + 0
y(at) = -2ax + 0
Now, we see that the output for 'a * x(t)' is 'a * y(t)'. Hence, the system satisfies the principle of homogeneity.
Principle of Superposition: A system satisfies superposition if the output for the sum of two inputs is equal to the sum of the outputs for each individual input. Mathematically, if y1(t) is the output for x1(t) and y2(t) is the output for x2(t), then for any constants 'c1' and 'c2', the output for 'c1 * x1(t) + c2 * x2(t)' should be 'c1 * y1(t) + c2 * y2(t)'.
In the given equation, y = -2x + 0, the output for 'c1 * x(t) + c2 * x(t)' is '-2(c1 + c2) * x(t) + 0', which can be simplified to 'c1 * y(t) + c2 * y(t)'. Hence, the system satisfies the principle of superposition.
Since the system satisfies both the principles of homogeneity and superposition, it is linear (option D).
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Forty percent of a number is greater than one-half the number decreased by 15. Which inequality can be used to determine the number?A 40x > x /2 - 15B 40x > 2x - 15C 0.40x > x/2 - 15D 0.4x < x/2 - 15
Answers
The inequality can be used to determine the number is 0.4x > x/2 - 15
The term inequality means the unequal relationship between the two or more expressions.
Here we have given that Forty percent of a number is greater than one-half the number decreased by 15.
And we need to find the number that is used to determine the inequality.
While we looking into the given question, let us consider x be that unknown number.
Then based on the given statement, we have divide it into two parts.
First, forty percent of the number and it can be written as 40%x or 0.4x.
Next is one-half the number is 1/2 x or x/2
When we combine the whole statement,
Then we get the inequality,
=> 0.4x > x/2 - 15
Therefore option (c) is correct.
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Gerri says that if a number is a multiple of 9 it is also a multiple of 3.Do you agree? Explain.
Answers
3x3=9
So, whenever 9 can go into something, it will take 3 times as many 3s to go into that number.
Example:
3 nines = 27
9 threes = 27
9 is 3 times as many as 9.
To sum everything up, Gerri is correct. This is because 3 is a factor (goes into 9 evenly) of 9.
(I don’t think I did too great of a job explaining, but you just need the last paragraph, the example was just there for reference)
If this did not answer your question, or your confused, please feel free to leave a comment!
2x² - x-6=0 resuelve
Answers
Answer:
x = -3/2 x=2
Step-by-step explanation:
2x² - x-6=0
Factor
(2x ) (x ) =0
6 = 2*3
2*-2 +3 = -1
(2x +3 ) (x -2 ) =0
2x+3 =0 x-2 =0
2x = -3 x=2
x = -3/2 x=2
A private company distribute 6% of its profit as a bonus among its 40 shareholder if each shareholder received rs90000as a bonus find the total profit of the company
Answers
Answer:
Total Profit = Rs6,000,000
Step-by-step explanation:
Let P stand for the private company's total profit. We are told that 6% of the profit was given a total of 40 shareholders. Since aech shareholder received Rs9000, we can determine the total profit:
P = (40 sharholders)*(Rs9000/shaeholder) = Rs360,000
RsThis represents 6% of the total profit, P:
(6%)*P = Rs360,000
(0.05)*P = Rs360,000
P = (Rs360,000)/(0.06)
P = Rs6,000,000
Gladys has just purchased a new home. The house was priced at $105,000,
and she chose a 40-year mortgage at 5.2%. What will her total cost be?
A. $24,776
B. $297,312
C. $249,739
D. $249,906
Answers
Answer: the answer is C
Step-by-step explanation: AP3X
The total cost is $249,739.
What is Mortgage Rate?A mortgage rate is the interest rate on a mortgage. Mortgage rates are set by the lender and might be fixed, remaining constant during the length of the loan, or variable, varying with a benchmark interest rate. Borrowers' mortgage rates differ depending on their credit profile.
We have,
P = $105, 000
T = 40 year
R = 5.2%
Using
Monthly payment, P = C[i(1+i\()^n\)]/[(1+i\()^n\)-1]
P = 105,000 [ 0.052/12(1+0.052/12\()^{480\)]/[(1+0.052/12\()^{480\\\)-1]
P = 105,000 [ 0.00433 (7.8426)] / [7.8426 -1]
P = 105,000 [ 0.03372318] / (6.8426)
P = $249,739
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The kivetsky family had an adjusted gross income of $119,245. 61 they included medical deductions on schedule a. They had $14,191 in medical expenses. Medical insurance covered 80% of these expenses. The IRS allows medical and dental expenses deductions for the amount that exceeds 7. 5% of a taxpayer´s adjusted gross income. How much can they claim as a medical deductions?
Answers
The Kivetsky family can claim $8,943.42 as their medical deductions.
To calculate the amount the Kivetsky family can claim as medical deductions, we need to follow these steps:
Step 1: Calculate the threshold for medical deductions:
Threshold = 7.5% of adjusted gross income
Threshold = 0.075 * $119,245.61
Threshold = $8,943.42
Step 2: Calculate the deductible medical expenses:
Deductible Expenses = Medical Expenses - (Medical Expenses * Insurance Coverage)
Deductible Expenses = $14,191 - ($14,191 * 0.8)
Deductible Expenses = $14,191 - $11,352.8
Deductible Expenses = $2,838.2
Step 3: Determine the allowable medical deductions:
Allowable Medical Deductions = Max(Deductible Expenses, Threshold)
Allowable Medical Deductions = Max($2,838.2, $8,943.42)
Allowable Medical Deductions = $8,943.42
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The standard length of a piece of cloth for a bridal gown is 3.25 meters. A customer selected 35 pcs of cloth for this purpose. A mean of 3.52 meters was obtained with a variance of 0.27 m2 . Are these pieces of cloth beyond the standard at 0.05 level of significance? Assume the lengths are approximately normally distributed
Answers
The pieces of cloth are beyond the standard at 0.05 level of significance.
We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.
The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:
H0: μ = 3.25
The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:
Ha: μ > 3.25
We can calculate the test statistic as:
t = (x - μ) / (s / √n)
where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).
Plugging in the values, we get:
t = (3.52 - 3.25) / (0.52 / √35) = 3.81
Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.
Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.
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In a hypothesis test for population proportion, you calculated the p-value is 0.01 for the test statistic, which is a correct statement of the p-value?
Group of answer choices
a)The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.
b)The p-value indicates that it is very likely to observe a test statistics equally or more extreme when the null hypothesis is true.
c)The p-value is calculated assuming the alternative is true.
Answers
The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.
In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.
The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.
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WILL GIVE BRAINLIEST INSTANTLY!!!1
Find the AREA of the shaded region.
(see photo)
Green text (what the arrow is pointing to) says: 8.7in
black text says: 63 degrees
Answers
Answer:
Step-by-step explanation:
\(\frac{a}{A}=\frac{\theta }{360^o}\\ \\ a=\frac{\pi r^2 \theta}{360^o}\\ \\ a=\frac{\pi (8.7)^2(126^o)}{360^o}\\ \\ a=\frac{9536.94\pi}{360}in^2\\ \\ a\approx 83.23 in^2\)
ore time on the Internet: A researcher polled a sample of 1012 adults in the year 2010 , asking them how many hours per week they spent on the Internet. The sample mean was 10.01 with a standard deviation of 13.90. A second sample of adults was taken in the year . For this sample, the mean was with a standard deviation of . Assume these are simple random samples from populations of adults. Can you conclude that the mean number of hours per week spent on the Internet differs between and
Answers
Sample 1: Mean=10.01, Standard deviation=13.90 Sample 2: Mean
=11.43, Standard deviation
=14.10
Sample size of 1st year = n1
= 1012Mean of 1st year sample
= X1 = 10.01Standard deviation of 1st year sample
= s1
= 13.90Sample size of 2nd year
= n2
= 1012Mean of 2nd year sample
= X2
= 11.43
Standard deviation of 2nd year sample = s2
= 14.10 Let us assume a significance level of α = 0.05, which implies that the critical region consists of 2.5% in both tails (since it is a two-tailed test).
Therefore, we do not have sufficient evidence to conclude that the mean number of hours per week spent on the Internet differs between 2010 and another year.
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An equo equila Teral Traingle has
nearest mm workout The Lower
bound of its Perimeter mcm
sides of Lenght 6.2 cm correct to
Answers
Answer:
Step-by-step explanation:
Given parameters:
Dimensions of the equilateral triangle = 6.2cm
Unknown:
Perimeter = ?
Solution:
The perimeter of the triangle is the sum of all its sides;
Perimeter = 3(L) for an equilateral triangle;
Perimeter = 3(6.2) = 18.6cm
to the nearest mm = 19.0cm
a payroll clerk addresses five paychecks and envelopes to five different people and randomly inserts the paychecks into the envelopes. find the probability of each event. (a) exactly three paychecks are inserted in the correct envelopes. (no response) seenkey 1/12 (b) at least three paychecks are inserted in the correct envelopes.
Answers
The required probability for the given different events are as follow,
Probability that exactly three paychecks are inserted in the correct envelopes = 1/12
probability of at least three paychecks is 1/4.
Probability that exactly three paychecks are inserted in the correct envelopes, use the formula for permutations,
Probability 'P'
=[ (number of ways to choose 3 correct envelopes) x (number of ways to choose 2 incorrect envelopes) x (number of ways to arrange the paychecks in the correct envelopes) ] / (total number of ways to arrange the paychecks in the envelopes)
Number of ways to choose 3 correct envelopes out of 5 is
5C3 = 10
Number of ways to choose 2 incorrect envelopes out of 5 is
5C2 = 10
Number of ways to arrange the 3 correct paychecks in their correct envelopes is 3! = 6
Number of ways to arrange the 2 incorrect paychecks in their incorrect envelopes is 2! = 2.
Total number of ways to arrange the paychecks in the envelopes is
5! = 120.
Probability that exactly three paychecks are inserted in the correct envelopes is,
Probability
= (10 x 10 x 6 x 2) / 120
= 1/12
Probability that at least three paychecks are inserted in the correct envelopes,
Exactly 3 paychecks are inserted in the correct envelopes
Exactly 4 paychecks are inserted in the correct envelopes
All 5 paychecks are inserted in the correct envelopes
Probability of exactly 3 paychecks being correct is 1/12.
Number of ways to arrange the paychecks in the envelopes is 1.
P(exactly 4 correct)
= (number of ways to choose 4 correct envelopes) x (number of ways to choose 1 incorrect envelope) x (number of ways to arrange the paychecks) / (total number of ways to arrange the paychecks)
= 5C4 x 1 x 4! / 5!
= 1/5
Probability of all 5 paychecks being inserted in the correct envelopes is 1/5! = 1/120.
Required probability
= 1/12 + 1/5 + 1/120
= 1/4
Therefore, the probability of exactly and at least 3 paychecks being inserted in the correct envelopes is equal to 1/12 and 1/4 respectively.
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Use the rational expression below to match the variables on the left with their excluded value(s) on the right.
Answers
The value of b = 4
How to solveThe function becomes undefined when the denominator goes to 0
3x² - 48 = 0
3x² = 48
x² = 16
x = +/ 4
From the given choices, it's x = 4
Rational expressions that utilize ratios of polynomial expressions are referred to as rational expressions. These can be written in the format p(x)/q(x), where both p(x) and q(x) are polynomials with the constraint that q(x) cannot equal zero.
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(0)
In a fraction, which tells you the number of parts by which the upper number is being divided? numerator diagonal quotient denominator
Answers
The denominator in a fraction tells you the number of parts by which the upper number is being divided.
A fraction is a way to represent a part of a whole. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts in the whole. For example, in the fraction 2/5, the numerator is 2, which means we are considering 2 out of the total 5 parts in the whole. The denominator, in this case, is 5, which represents the total number of equal parts in the whole. Therefore, the denominator is the number of parts by which the numerator is being divided, or the size of each of the equal parts.
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h²=p²+b² make b the subject of formula
Answers
Answer:
done same as before put value and do process like simplify
Explanation:
h^2 = p^2 + b^2
b^2 = h^2 - p^2
b = sqrt(h^2 - p^2)