To determine the number of different ratings combinations possible, we can use the combination formula. Since there are five possible ratings (very poor, poor, fair, good, and excellent) and 29 students in the class. Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
The formula we can use is:
nCr = n! / r!(n-r)!
where n is the total number of items (in this case, the number of ratings), and r is the number of items we are choosing (in this case, the number of students).
Using this formula, we can find the number of different ratings combinations possible by plugging in the values:
nCr = 5! / 29!(5-29)!
nCr = 5! / 29!(-24)!
nCr = 5 x 4 x 3 x 2 x 1 / (29 x 28 x 27 x 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
nCr = 657,800
Therefore, there are 657,800 different ratings combinations possible for the 29 students in the statistics class.
In this scenario, there are 29 students and a 5-point scale for rating their instructor. To determine the number of different rating combinations possible, we will use the concept of combinations with repetitions allowed.
In this case, the formula for combinations with repetitions is given by:
C(n+r-1, r) = C(n+r-1, n-1), where n is the number of ratings (5) and r is the number of students (29).
Using the formula, we get:
C(5+29-1, 29) = C(33, 29) = 33! / (29! * 4!)
Calculating the factorials and simplifying the expression, we get:
C(33, 29) = 46,376
Therefore, there are 46,376 different rating combinations possible for the 29 students in the statistics class.
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Volumes of a Composite Solid
12.
10 cm
4 cm
4cm
The volume of composite solid is 418.67 cm³.
We have to find the volume of Cone and cylinder.
First, Volume of Cone
= (1/3)πr²h
Given that the radius (r) of the cone is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:
= (1/3) (3.14) (5)² (4)
= 104.67 cm³
Second, Volume of cylinder
= πr²h
Given that the radius (r) of the cylinder is 5 cm and the height (h) is 4 cm, we can substitute these values into the formula:
= π (5)² (4)
= 3.14 x 100
= 314 cm³
Thus, the volume of composite solid
= 314 + 104.67
= 418.67 cm³
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In a regular polygon (all sides and angles are equal-sized), the measure of each exterior angle is 12.5%
of the measure of each Interior angle.
Write and solve an equation to find m, the measure of each exterior angle.
Equation
Answer
Using the given information, the measure of each exterior angle in the polygon is 20°
Measure of angles in a polygon
From the question, we are to determine the measure of each exterior angle in the polygon
Let the number of sides in the polygon be n.
Sum of exterior angles in a polygon = 360°
Thus,
Measure of one exterior angle = 360°/n
From the given information,
The measure of each exterior angle is 12.5% of the measure of each interior angle
The measure of each interior angle = (n - 2)180° / n
Thus,
360°/n = 12.5% of (n - 2)180° / n
360° = 12.5% of (n - 2)180°
Solve for n
360° = 0.125 × (n - 2)180°
360° = (n - 2)22.5°
360° = 22.5n° - 45°
22.5n° = 360° + 45°
22.5n° = 405°
n = 405°/22.5°
n = 18
Then,
Measure of each exterior angle = 360° / 18
Measure of each exterior angle = 20°
Hence, the measure of each exterior angle is 20°
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write an integral that expresses the average monthly u.s. gas consumption during the part of the year between the beginning of april (t
The specific form of the function G(t) and the limits of integration would depend on the available data or assumptions about gas consumption during the specified months.
To express the average monthly U.S. gas consumption during the part of the year between the beginning of April and the end of September, we can set up an integral to calculate the average value of a function over a specific interval.
Let's denote the gas consumption as a function of time, G(t), where t represents the months from April to September. We'll integrate this function over the interval [April, September] to find the average gas consumption.
The integral that represents the average monthly U.S. gas consumption is:
(1 / (September - April)) ∫[April, September] G(t) dt
In this integral, G(t) represents the gas consumption in a given month, and the integration is taken over the interval from April to September. The average gas consumption is obtained by dividing the integral by the length of the interval (September - April).
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what is the length of the line
The length of the line is given as follows:
B. 12 units.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The parameters for this problem are given as follows:
Length of the line is the hypotenuse.Horizontal change is of 10 units.Vertical change is of 6 units.Hence the length of the line is given as follows:
l² = 10² + 6²
[tex]l = \sqrt{10^2 + 6^2}[/tex]
l = 12 units. (rounded up).
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what factor should -8-7i be multiplied by to find the quotient? enter any complex numbers in the form .
The factor that -8 - 7i should be multiplied by to find the quotient is 1 + 2i and the quotient is (-22 - 23i) / 5.
When dividing complex numbers of the form a + bi by another complex number of the form c + di, we use the following method:
Multiplying both the numerator and denominator by the conjugate of the denominator, c - di, we get:
(a + bi)(c - di)/(c + di)(c - di) = [(ac + bd) + (bc - ad)i]/(c² + d²)
where a, b, c, and d are real numbers and i is the imaginary unit with the property i² = -1.
In the given question, the denominator is 1 - 2i, so its complex conjugate would be 1 + 2i. Therefore, we need to multiply -8 - 7i by 1 + 2i in both numerator and denominator to get the quotient: (-8 - 7i)(1 + 2i) / (1 - 2i)(1 + 2i) = (-8 - 23i - 14) / (1 + 4) = (-22 - 23i) / 5
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a bicycle wheel has a diameter of 2.8 ft if it rotates at 40 rpm how far will it travel in 2 hours
In a math class with 27 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 17 students who completed the assignment. There were 15 students who passed the test and also completed the assignment. What is the probability that a student who passed the test did not complete the homework?
The probability that a student who passed the test did not complete the homework is 1 / 6.
How to find the probability ?This is a conditional probability problem and we are looking for the probability that a student who passed the test did not complete the homework.
Assuming event A is the event that a student passed the test and B is event that a student completed the assignment.
We have :
P ( B' | A ) = P ( A ∩ B ' ) / P (A)
P ( B' | A ) = ( 3 / 27 ) / ( 18 / 27 )
P ( B' | A ) = 3 / 18
P (B' | A ) = 1 / 6
In conclusion, the probability that a student who passed the test did not complete the assignment is 1/6.
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cody builds mailboxes. if he charges $20 for each mailbox, his total revenue will be
To determine Cody's total revenue if he charges $20 for each mailbox, we need to know the number of mailboxes he sells. Let's denote the number of mailboxes as 'n'.
Cody's total revenue can be calculated by multiplying the price per mailbox ($20) by the number of mailboxes sold (n):
Total revenue = Price per mailbox × Number of mailboxes sold
Total revenue = $20 × n
Therefore, Cody's total revenue will be $20n, where 'n' represents the number of mailboxes he sells.
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sometimes two variables are statistically correlated, but there is actualy a third variable that is driving this relationship. an example provided in class was the correlation between ice cream sales and violent crimes, where the third variable was temperature. what is the name of this type of correlation
The type of correlation that occurs when two variables are statistically correlated due to the influence of a third variable is called a spurious correlation.
A spurious correlation is a type of correlation that occurs when two variables are statistically related to each other, but the relationship is not causal. Instead, the relationship is driven by the influence of a third variable that is related to both variables. This type of correlation can be misleading and can lead to incorrect conclusions if not properly understood.
For example, consider the relationship between ice cream sales and violent crime. Studies have found a positive correlation between these two variables, meaning that as ice cream sales increase, so do violent crimes. However, it is unlikely that there is a causal relationship between these two variables. Instead, the real cause of the correlation is likely the temperature. As the temperature increases, people are more likely to buy ice cream and to be out and about, which increases the opportunity for violent crime to occur. Thus, the temperature is the third variable that is driving the spurious correlation between ice cream sales and violent crime.
It is a type of correlation where there is no causal relationship between the two variables that are correlated. Instead, the correlation is driven by the influence of a third variable that is related to both variables. In the example given, the correlation between ice cream sales and violent crimes is spurious, as the real cause of the correlation is the temperature, which influences both variables.
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A photographer had to change the size of his cover photo. He increased the length by 30% and decreased the width by 10%. By what percent was the area of the final photo changed?
Answer:
17%---------------------
Let the dimensions be x and y.
The area is:
A = xyWhen sides have changed we get:
x + 30% = x + 0.3x = 1.3xy - 10% = y - 0.1y = 0.9yThe new area is:
A = 1.3x * 0.9y = 1.17xyThe difference in areas is:
1.17xy - xy = 0.17xyIt represents 17% increase.
a bag contains four red marbles and seven blue marbles. you randomly pick a marble and then pick a second marble without returning the marbles to the bag. what is the probability that both marbles are red.
Answer:
6/55
Step-by-step explanation:
4 red + 7 blue = 11 marbles in total
P(first red) = 4/11.
we now have 10 marbles left. 3 of them are red.
P(second red) = 3/10
P(both red) = 4/11 X 3/10 = 12/110 = 6/55
in the year 2018, it was estimated that approximately 28,000 floridians were homeless. a social worker estimates that 78% of these people were age 18 and up. in the distribution of ages of homeless floridians, an 18 year old would be considered what percentile? group of answer choices 22nd percentile 78th percentile 28th percentile 18th percentile
The an 18-year-old homeless Floridian would be considered at the 22nd percentile in the distribution of ages of homeless Floridians.
the social worker estimated that 78% of the homeless population in Florida in 2018 were age 18 and up, which means that 22% of the homeless population were under 18 years old. Therefore, an 18-year-old would be at the 22nd percentile in the age distribution of homeless Floridians.
based on the given information, an 18-year-old homeless Floridian would be at the 22nd percentile in the age distribution of homeless Floridians.
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Need help with the first three
Answer:
6 books
6 packages of mints
It would cost $240.00 is carpet was purchased.
Step-by-step explanation:
If 2 books cost 16.40, then one book costs 16.40/2 = 8.20 each.
50/8.20 = 6.1 rounded. You cannot buy part of a book, so 6 books may be purchases.
If 2 packages of mints cost .69, then I package costs .69/2 = .345
2.25/ .345 = 6.5 rounded. You cannot buy .5 of a package, so you can purchases 6 packages.
192/16 = 12
There are 12 square meters of flooring
12 x 20 = 240
Helping in the name of Jesus.
ANSWER ASAP
What is the volume of the smaller cylinder?
V = 1000
Put the sides together: 4/6
Cube the sides (for volume you cube): 64/216
Then put the volume across from the side that has that volume: 64 x
----- = -----
216 3375
Cross multiply.
It should then equal this: 216x=216000
Divide by 216 and then you find x, which in other words the volume
x = 1000
A force of 60 newtons is applied to a 10 cm² surface. The force applied is then increased by 15 newtons and the surface area is increased by 15 cm². Shayna says "The pressure decreases by more than 40%" Is Shayna correct? Yes/No yes, You must show how you get your answer. Show your working h pressure = force area
amazon claims that if you are a prime member, 85% of your packages will arrive within two business days. you have decided that you want to know if this claim is true. you take a simple random sample of 25 students at your school and 19 of the students claim that their packages arrived within two business days of ordering. a. what is the population proportion? what is the sample proportion? please use correct symbols in your answer.
Population proportion (claim): p = 0.85
Sample proportion: [tex]\hat p[/tex]= 19/25
What is proportion?
In statistics, proportion typically refers to the proportion or percentage of individuals or items in a population that have a specific characteristic or belong to a certain category.
In this scenario, the population proportion refers to the proportion of all Prime members' packages that arrive within two business days. The claim made by Amazon is that this population proportion is 85%.
Let's denote the population proportion as p.
a. The population proportion:
p = 0.85
The sample proportion, on the other hand, refers to the proportion of packages that arrived within two business days among the 25 students in the random sample. We can calculate the sample proportion using the number of students who claimed their packages arrived within two business days.
Let's denote the sample proportion as [tex]\hat p[/tex] (pronounced "p-hat").
Given:
Number of students in the sample (n) = 25
Number of students who claimed their packages arrived within two business days (x) = 19
b. The sample proportion:
[tex]\hat p[/tex] = x / n
[tex]\hat p[/tex] = 19 / 25
Therefore, the sample proportion is 19/25.
To summarize:
Population proportion (claim): p = 0.85
Sample proportion: [tex]\hat p[/tex] = 19/25
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a sample of n sludge specimens is selected and the ph of each one is determined. the one-sample t test will then be used to see if there is compelling evidence for concluding that true average ph is less than 7.0. what conclusion is
For the sample of n sludge specimens is selected and the conclusion and the pH of each one is determined.
Null hypothesis:The null hypothesis will be rejected in favour of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0.
A) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
B) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
C) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
D) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
E) Reject the null hypothesis. There is sufficient evidence that the true average pH is less than 7.0.
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At first, a tank was completely filled with water. A pump was turned on for some time to drain water from the tank. The line graph shows the volume of water in the tank over 40 minutes.
a)how much water was drained out of the tankin one minute
b)how long will it take for the water to be drained out of the tank completely?
see the attachment below.
10 liters of water was drained out of the tank in one minute and it would take 80 minutes to completely drain the water
How much water was drained out of the tankin one minuteThis is the slope of the graph
From the graph, we have
(x, y) = (0, 800) and (40, 400)
So, we have
Slope = (400 - 800)/(40 - 0)
Evaluate
Slope = -10
This means that 10 liters of water was drained out of the tank in one minute
How long for the water to be drained out of the tank completely?From (a), the equation of the line would be
y = -10x + 800
When the water is completely out, we have
-10x + 800 = 0
So, we have
x = 80
This means that it would take 80 minutes
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Given: △STQ,
ST = TQ,
SD ⊥ TQ ,
m∠1=32°
Find: m∠S, m∠T, m∠Q
The angles in the triangle are as follows:
m∠S = m∠Q = 58°
m∠T = 64°
How to find the angles of a triangle?The unknown angles in the triangle can be found as follows:
In the triangle STQ, ST = TQ and SD is perpendicular to TQ.
Therefore, let's find the unknown angles as follows:
Hence, base on ST = TQ, STQ is an isosceles triangle. Therefore,
m∠S = m∠Q
Therefore,
m∠Q = 180 - 90 - 32
m∠Q = 58 degrees
m∠S = m∠Q = 58 degrees
Finally,
m∠T = 180 - 58 - 58
m∠T = 64 degrees
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HELP!!! Please solve this logarithmic equation for the value of the equation. Be sure to check for extraneous solutions. Thank you!
[tex]D:2x > 0\wedge x+2 > 0\\D:x > 0 \wedge x > -2\\D: x > 0[/tex]
[tex]\log_42x+\log_4(x+2)=2\\\log_4(2x(x+2))=2\\2x^2+4x=4^2\\2x^2+4x-16=0\\x^2+2x-8=0\\x^2+2x+1-9=0\\(x+1)^2=9\\x+1=3 \vee x+1=-3\\x=2 \vee x=-4[/tex]
[tex]-4\not\in D[/tex]
Therefore [tex]x=2[/tex].
Given that P(A|B)=0.22 and P(B)=0.46, what is P(A AND B)?
Round your answer to three decimal places.
P(A AND B) is approximately 0.101 (rounded to three decimal places).
Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
To find P(A AND B), we can use the conditional probability formula:
P(A AND B) = P(A|B) * P(B)
Given:
P(A|B) = 0.22
P(B) = 0.46
Plugging in the values:
P(A AND B) = 0.22 * 0.46
Calculating the result:
P(A AND B) = 0.1012
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three fire hydrants in a neighborhood are represented on a map. the coordinates of the fire hydrants are (0,0) , (2,5) , and (7,y) . the fire hydrants are arranged in a right triangle, where y is a natural number less than 10 . find y .
We can use the distance formula to find the distances between the fire hydrants and determine whether they form a right triangle. The value of y is 4.
The distance between (0,0) and (2,5) is:
√((2-0)² + (5-0)²) = √29
The distance between (0,0) and (7,y) is:
√((7-0)² + (y-0)²) = √(49 + y²)
The distance between (2,5) and (7,y) is:
√((7-2)² + (y-5)²) = √(25 + (y-5)²)
If these distances form a right triangle, then the Pythagorean theorem must be satisfied:
(√29)² + (√(49 + y²))² = (√(25 + (y-5)²))²
Simplifying this expression, we get:
29 + 49 + y² = 25 + (y-5)²
Expanding the square on the right-hand side, we get:
29 + 49 + y² = 25 + y² - 10y + 25
Simplifying this expression, we get:
y = 4
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The mean weight for a typical bunch of bananas in grocery stores is 3.54 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3.54 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of tests the hypotheses H 0: Mu = 3.54 pounds; pounds. What is a Type II error in this situation?
Answer: Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3.54 pounds when the true mean weight is actually less than 3.54 pounds.
The fourth choice in this scenario is the Type II error: (d) Using the sample mean, the owner determines that the average weight of all the banana bunches is more than 3.54 pounds even though the real average weight is lower.
When the null hypothesis—in this case,
The average weight of the banana bunches is 3.54 pounds—is not accepted despite being erroneous, a Type II mistake takes place.
In other words, despite the cargo of bananas not meeting the requisite weight criteria, the owner fails to reject it. In this case, the owner may experience a loss in sales or reputation as a result of the poor quality of the bananas, as well as losses from selling the underweight bananas at a loss or even throwing them away.
The probability of making a Type II error can be minimized by increasing the sample size or decreasing the significance level (alpha level) of the test. However, a Type II error can never be completely eliminated.
Therefore, the correct option is d.
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consider the following solution of 9x-7= -70
what properties of equality can justify the two steps in the solution
A.addition and division property
B. addition and multiply property
C. subrtraction and mutiply property
D. subtraction and division property
Answer:
A. Addition and division property--------------------------
The first step involves addition of 7 to both sides and the second step involves division of both sides by 9.
They indicate the addition and division property of equality respectively.
Therefore correct choice is A.
Lessons are 55 mins
long. A history lesson
ends at 3:30pm
what time did it
start?
ive been finding it rlly difficult pls can someone explain it in depth?
Answer:
The history class started at 2:35 pm
Step-by-step explanation:
To find the before time or starting time, we need to subtract 55 min from 3:30.
We cannot subtract 55 min from 30 min.
1 hour = 60 minutes. 3 : 30 can be written as 2: 90 minutes
Now subtract,
2 : 90
- : 55
2 : 35
The history class started at 2:35 pm
What is the range of the following: 68, 56, 40, 10, 51, 15
Answer:58
Step-by-step explanation:
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
To find the range of the following set of numbers: 68, 56, 40, 10, 51, 15
First, we need to find the largest and smallest numbers in the set.
The largest number is 68 and the smallest number is 10.
So, the range is:
68 - 10 = 58
Therefore, the range of the set of numbers is 58.
A map of three airstrips labeled
A, B, and C is shown below. About
how far is airstrip C from airstrip A
Answer:
192.17 mi
Step-by-step explanation:
Kelly can drive 45 miles on 5 gallons of gas. If Kelly keeps driving at this same rate, how far can she travel on 33 gallons of gas.
(A) 279
(B) 345
(C) 297
(D) 927
Answer:
(C) 297
Step-by-step explanation:
Write a proportion. 45 miles is to 5 gallons as x miles is to 33 gallons.
45 / 5 = x / 33
9 = x / 33
x = 297
An urn contains 6 red beads, 4 blue beads, and 2 green beads. If a single bead is picked at random, what is the probability that the bead is blue?
Give your answer as a fraction.
[tex]|\Omega|=6+4+2=12\\|A|=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}\approx33.3\%[/tex]
Answer:
Step-by-step explanation: 6 + 4 + 2 = 12 (denominator)
Put 4 (blue beads) in numerator
4/12 reduces to 1/3
Final answer is 1/3
Why did the congruent triangles get caught cheating?
because their sides were corresponding.
answers:
1. aas (g).
2. sas (h).
3. sss (n).
4. asa (s).
5. hl (c).
6. none - aaa (t).
7. asa (0).
8. none - ssa (d).
9. aas (i).
10. sas (w).
11. sss (p).
12. hl (r).
13. asa (e).
