Theoretically, you should expect to get 5 questions correct by randomly guessing on a 10-question true/false quiz.
Since this is a true/false quiz with 10 questions, if you were to guess randomly on each question, you would have a 50/50 chance of getting each question correct. Therefore, the probability of guessing correctly on any one question is 0.5.
Let X be the number of questions you guess correctly. Since each question is independent of the others, we can use the binomial distribution to calculate the expected value of X.
The formula for the expected value of a binomial distribution is:
E(X) = n * p
where n is the number of trials (in this case, the number of questions) and p is the probability of success on each trial (in this case, the probability of guessing a question correctly, which we calculated to be 0.5).
So, plugging in the numbers:
E(X) = 10 * 0.5 = 5
Therefore, theoretically, you should expect to get 5 questions correct if you randomly guess on each question. However, since the minimum score to pass is 60%, you would need to get at least 6 questions correct to pass.
To answer your question, let's consider the terms "minimum score", "questions", and "true/false". You have a true/false quiz with 10 questions, and you need a minimum score of 60% correct to pass. Since you're randomly guessing, the probability of getting each question correct is 50% or 0.5.
Now, let's calculate the expected number of correct questions, X. To do this, we multiply the probability of getting a question correct (0.5) by the total number of questions (10):
X = 0.5 * 10
X = 5
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PLEASE PLEASE PLEASE HELP!!
Two gyms open their memberships to the public. Compare the gyms by calculating and interpreting the average rates of change from Week 3 to Week 5. Round answers to the nearest whole number, where appropriate.
From Week 3 to Week 5, Gym A membership increases at a rate of 32 people per week, and Gym B membership increases at a rate of 34 people per week. So, Gym B is growing faster.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
From Week 3 to Week 5, the change in the input is given as follows:
5 - 3 = 2.
From the table for Gym A and graph for Gym B, the change in the output for each gym is given as follows:
Gym A: 171 - 107 = 64 members.Gym B: 203 - 135 = 68 members.Hence the rates are given as follows:
Gym A: 64/2 = 32 members per week.Gym B: 68/2 = 34 members per week.More can be learned about the average rate of change of a function at brainly.com/question/11627203
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The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
The graphical representation that would be most appropriate for the data, given the number of different breakfast cereals sold, is,
B. Histogram, because there is a large set of data.
Since, We know that;
Histograms are used for large sets of data because they provide a visual representation of the distribution of the data. They are particularly useful for understanding the distribution of continuous variables, such as measurements or time series data.
One of the main advantages of histograms is that they allow for easy comparison of large sets of data. The use of bars to represent the data makes it easy to see the overall shape of the distribution and identify patterns or outliers. Additionally, histograms can be used to compare multiple sets of data at once, allowing for easy comparison of different groups or changes over time.
Another advantage of histograms is that they can be used to identify the underlying probability distribution of a dataset, which is useful for statistical analysis and modeling.
This is why, given the fact that the data contains information from 1, 000 different cereals, a histogram is best to show this as the data is large.
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The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 45 who smoke. Step 1 of 2 : Suppose a sample of 830 Americans over 45 is drawn. Of these people, 631 don't smoke. Using the data, estimate the proportion of Americans over 45 who smoke. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimated proportion of Americans over 45 who smoke is 0.239 or 239/1000.
Step-by-step explanation:
To estimate the proportion of Americans over 45 who smoke, we need to calculate the fraction of the sample who smoke.
The number of people who don't smoke is 631, so the number of people who smoke is:
830 - 631 = 199
Therefore, the fraction of Americans over 45 who smoke is:
199/830 = 0.239 (rounded to three decimal places)
So, the estimated proportion of Americans over 45 who smoke is 0.239 or 239/1000.
To estimate the proportion of Americans over 45 who smoke, we first need to find the number of people in the sample who do smoke. We can do this by subtracting the number of people who don't smoke from the total sample size:
Therefore, we estimate that approximately 0.240 or 24.0% of Americans over 45 smoke.
Step 1: To estimate the proportion of Americans over 45 who smoke, we first need to find out how many people in the sample do smoke. Since we have a sample of 830 Americans and 631 don't smoke, we can subtract the non-smokers from the total sample to find the number of smokers.
830 (total) - 631 (non-smokers) = 199 (smokers)
Step 2: Now, we can calculate the proportion of smokers in the sample by dividing the number of smokers (199) by the total number of people in the sample (830).
199 (smokers) / 830 (total) = 0.2398 (rounded to four decimal places)
As a fraction, this would be approximately 240/1000, which can be simplified to 12/50.
So, the estimated proportion of Americans over 45 who smoke based on the given data is 0.240 or 12/50.
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At a recent baseball game of 7,525 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer MUSTARD on a hot dog?
1,355
3,010
3,161
6,171
Using the relative frequency we can estimate that 1355 people will preffer mustard.
How many of the people in attendance would prefer mustard on a hot dog?To find this estimation, we need to find the relative frequency of people that preffers mustard.
To get this, take the quotient between the people that preffers mustard (27) and the total number of people surveyed (150)
It gives:
F = 27/150
Now multiply the total number of people in the game by that number:
N = 7,525*27/150 = 1354.5
Rounding we get 1355
So the correct option is the first one.
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Answer:
B
Step-by-step explanation: its 3,010. EZ
Can someone help me asap? It’s due today!! I will give brainliest if it’s correct. Select all that apply
Answer:
Step-by-step explanation: 85% of college students prefer to shop on line, while they have access to internet 90% of the day.]
So by process of elimination, response 1 and 2 is speaking of better deals and students time which wasn't discussed in the scenario.
Therefore, response 3 coincides with the convenience of the preferred reasoning for shopping online and response 4 falls into the internet access college students have 90% of the day.
So choices 3 and 4
Find the area of the indicated region under the standard normal curve.The area between z=−1.3z=−1.3 and z=1.4z=1.4 under the standard normal curve.
The area between z=-1.3 and z=1.4 under the standard normal curve is approximately 0.8224.
To find the area of the indicated region under the standard normal curve, we need to use a standard normal distribution table or a calculator.
Using a standard normal distribution table, we can find the area to the left of z=-1.3, which is 0.0968. We can also find the area to the left of z=1.4, which is 0.9192.
To find the area between z=-1.3 and z=1.4, we subtract the area to the left of z=-1.3 from the area to the left of z=1.4:
0.9192 - 0.0968 = 0.8224
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suppose that x and y are jointly discrete random variables with p(x, y) 5 d 2 n(n 1 1) 0 for x 5 1, 2, . . . , n and y 5 1, 2, . . . , x otherwise compute px(x) and py (y) and determine whether x and y are independent
To compute px(x), we sum the joint probabilities over all possible values of y:
px(x) = Σp(x,y) for all y
Substituting the given values for p(x,y):
px(x) = Σd/[(n(n+1))/2] for y=1 to x
px(x) = xd/[(n(n+1))/2]
To compute py(y), we sum the joint probabilities over all possible values of x:
py(y) = Σp(x,y) for all x
Substituting the given values for p(x,y):
py(y) = Σd/[(n(n+1))/2] for x=y to n
py(y) = (n-y+1)d/[(n(n+1))/2]
To determine whether x and y are independent, we compare the product of the marginal probabilities to the joint probability:
If px(x)*py(y) = p(x,y), then x and y are independent.
Substituting the computed values for px(x) and py(y):
px(x)*py(y) = [xd/[(n(n+1))/2]]*[(n-y+1)d/[(n(n+1))/2]]
px(x)*py(y) = (xd/n)*(n-y+1)/n
px(x)*py(y) = xd(n-y+1)/n^2
Comparing to the given value for p(x,y):
p(x,y) = d/[(n(n+1))/2]
We see that px(x)*py(y) is not equal to p(x,y) in general. Therefore, x and y are not independent.
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My data set is left skewed, therefore my mean will be _____ than my median
If your data set is left-skewed, then your mean will be less than your median.
In a left-skewed distribution, the tail of the distribution is longer on the left-hand side, which means that there are some extreme low values that pull the mean towards the left. On the other hand, the median is not affected as much by extreme values, since it only depends on the middle value(s) of the data set. Therefore, in a left-skewed distribution, the median is usually greater than the mean.
According to a study on the effects of smoking by pregnant women on rates of asthma in their children, for expectant mothers who smoke 20 cigarettes per aby day, 22.4% of their children developed asthma by the age of two in the US. A aby biology professor at a university would like to test if the percentage is lower in another country. She randomly selects 342 women who only deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds that 71 of the children developed asthma by the age of two. In this hypothesis test, the test statistic, z = and the p-value = (Round your answers to four decimal places.)
The hypothesis test is:
H0: p = 0.224 (the percentage of children who develop asthma is the same in the other country)
Ha: p < 0.224 (the percentage of children who develop asthma is lower in the other country)
The sample proportion is:
p = 71/342 = 0.2076
The standard error is:
SE = sqrt[(0.224)(1-0.224)/342] = 0.0225
The test statistic is:
z = (0.2076 - 0.224) / 0.0225 = -0.7467
The p-value for this one-tailed test is:
p-value = P(z < -0.7467) = 0.2254
Therefore, the test statistic, z = -0.7467 and the p-value = 0.2254.
In this hypothesis test, we are comparing the proportion of children with asthma in another country to the proportion in the US (22.4%). Let's set up our null and alternative hypotheses:
H0: p = 0.224 (proportion of children with asthma in the other country is the same as in the US)
Ha: p < 0.224 (proportion of children with asthma in the other country is lower than in the US)
Now, we can calculate the test statistic (z) and p-value using the provided data:
n = 342 (sample size)
x = 71 (number of children with asthma)
p-hat = x/n = 71/342 = 0.2076 (sample proportion)
We also need the standard error (SE) for the sample proportion:
SE = sqrt((p0 * (1 - p0)) / n) = sqrt((0.224 * (1 - 0.224)) / 342) = 0.0260
Now, calculate the z-score:
z = (p-hat - p0) / SE = (0.2076 - 0.224) / 0.0260 = -0.6285 (rounded to four decimal places)
Next, find the p-value by looking up the z-score in a standard normal table or using a calculator:
p-value = P(Z < -0.6285) ≈ 0.2647 (rounded to four decimal places)
So, the test statistic z = -0.6285, and the p-value = 0.2647.
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Round to the nearest hundreth.
Answer:
The answer is 59 units
Step-by-step explanation:
area of sector =0/360×pir²
A=56/360×22/7×11²
A=149072/2520
A=59units
A segment is created from points A and B. To copy segment AB, which of the following needs to be identified for the construction? The distance between point A and a point not on the segment The midpoint of points A and B The midpoint between point B and a point not on the segment The distance between points A and B
To copy segment AB, D, The distance between points A and B needs to be identified for the construction.
What is a segment?A segment is a section of a line that is bounded by two unique ends and contains every point on the line between them. A segment is designated after its endpoints, therefore segment AB refers to the section of the line connecting points A and B.
To copy segment AB can be accomplished by utilizing a measuring instrument such as a ruler or tape measure to determine the distance between the two spots. Once the distance is determined, a new point that is the same distance away from point A as point B can be produced.
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Click on each box and type in a number. Backspace to erase.Question: The ages, in years, of 6 cars in a parking lot are 6, 14, 5, 1, 8, and x. If the average (arithmetic mean) of the 6 ages is 7 years, what is the value of x ?x = 8
To find the value of x, we need to follow these steps:
1. Calculate the total sum of the ages of the 6 cars.
2. Subtract the sum of the known ages from the total sum.
3. The result will be the value of x.
Step 1: Since the average age of the 6 cars is 7 years, we multiply the average (7) by the number of cars (6) to find the total sum of ages.
Total sum of ages = 7 * 6 = 42 years
Step 2: Subtract the sum of the known ages (6, 14, 5, 1, and 8) from the total sum.
Sum of known ages = 6 + 14 + 5 + 1 + 8 = 34 years
42 (total sum of ages) - 34 (sum of known ages) = 8
Step 3: The result is the value of x.
x = 8
So the value of x is 8.
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Kaitlin is saving money to buy a game. The game costs 12$ , and so far she has saved one-half of this cost. How much money has Kaitlin saved?
The amount of money saved by Kaitlin is $6.
We have,
Cost of Game= $12
Amount Kaitlin saved= 1/2 of total money
So, She saved
= 12 x 1/2
= 12 x 1/2
= 6 x 1
= $6
Thus, Kaitlin saved $6.
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Can someone please help me ASAP? It’s due today.
The option that is a valid claim is:
The number of milk chocolate pieces is between 115 and 120 pieces.
The correct option is the last option.
Determining the valid option about the claimFrom the question, we are to determine the valid option about the claim.
From the given information,
A sample of chocolate from the local candy shop contained 17 milk chocolate pieces out of a sample of 50. An entire batch of chocolate contains 350 pieces
To determine the option about the population that is valid claim, we will determine the number of milk chocolate in an entire batch.
We know that
17 are milk chocolate out of a sample of 50.
Let the number of milk chocolate in an entire batch be x.
If there 17 milk chocolate out of 50 samples
Then,
There will be x chocolate out 350 samples
50 × x = 350 × 17
x = (350 × 17)/ 50
x = 119
Thus,
The 119 milk chocolates in an entire batch
The valid claim is:
The number of milk chocolate pieces is between 115 and 120 pieces.
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Forensic Science Forensic scientists use the following law to determine the time of death of accident or murder victims. If T denotes the temperature of a body t hr after death, then T = T0 + (T1 − T0)(0.97)t where T0 is the air temperature and T1 is the body temperature at the time of death. John Doe was found murdered at midnight in his house; the room temperature was 74°F and his body temperature was 93°F when he was found. When was he killed? Assume that the normal body temperature is 98.6°F. (Round your answer to two decimal places.) hours ago
John Doe was killed approximately 4.06 hours ago.
To determine the time of death for John Doe, we will use the given formula: [tex]T = T0 + (T1 - T0)(0.97)^t[/tex],[/tex]where T is the body temperature at time t, T0 is the air temperature (74°F), and T1 is the body temperature at the time of death (93°F).
We are trying to find the time (t) when John Doe's body temperature was 98.6°F (normal body temperature). So, we'll set T equal to 98.6°F and solve for t:
[tex]98.6 = 74 + (93 - 74)(0.97)^t[/tex]
To solve for t, follow these steps:
1. Subtract 74 from both sides:
[tex]24.6 = 19(0.97)^t[/tex]
2. Divide by 19:
[tex]1.2947 ≈ (0.97)^t[/tex]
3. Take the natural logarithm of both sides:
ln(1.2947) ≈ [tex]ln((0.97)^t)[/tex]
4. Apply the logarithm power rule:
ln(1.2947) ≈ t * ln(0.97)
5. Divide by ln(0.97):
t ≈ ln(1.2947) / ln(0.97)
6. Calculate t:
t ≈ 4.06
So, John Doe was killed approximately 4.06 hours ago.
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Use cylindrical coordinates to evaluate the integral I=∭ Wx 2+y 2dV when W is the region in 3-space lying inside the cylinder x 2+y 2=25 and between the planes z=−5 and z=1. Use cylindrical coordinates to evaluate the integral I=∭ WydV when W is the solid lying above the xy-plane between the cylinders x 2+y 2=2,x 2+y 2=4, and below the plane z=x+6. 1. I=112π 2. I=224π 3. I=0 4. I=112 5. I=224
The answer is (3) 0.
For the first integral, we have:
I = ∭W x^2 + y^2 dV
Using cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
where 0 <= r <= 5, 0 <= theta <= 2pi, and -5 <= z <= 1.
Also, dV = r dz dr d(theta)
Substituting these into the integral, we have:
I = ∭W r^2 dV
= ∫(0 to 2pi) ∫(0 to 5) ∫(-5 to 1) r^2 (r dz dr d(theta)) dz dr d(theta)
= ∫(0 to 2pi) ∫(0 to 5) [(r^4/4)(1 - (-5))] dr d(theta)
= ∫(0 to 2pi) ∫(0 to 5) (13r^4/4) dr d(theta)
= ∫(0 to 2pi) [(13/20)r^5] from 0 to 5 d(theta)
= ∫(0 to 2pi) (13/20)(5^5) d(theta)
= (13/20)(3125)(2pi)
= 112pi
Therefore, the answer is (1) 112π.
For the second integral, we have:
I = ∭W y dV
Using cylindrical coordinates, we have:
x = r cos(theta)
y = r sin(theta)
z = z
where 2 <= r <= 4, 0 <= theta <= 2pi, and 0 <= z <= x+6.
Also, dV = r dz dr d(theta)
Substituting these into the integral, we have:
I = ∭W y dV
= ∫(0 to 2pi) ∫(2 to 4) ∫(0 to r cos(theta)+6) r sin(theta) (r dz dr d(theta)) dz dr d(theta)
= ∫(0 to 2pi) ∫(2 to 4) [(r^3 sin(theta)/3)(r cos(theta)+6)] dr d(theta)
= ∫(0 to 2pi) ∫(2 to 4) [(r^4/3) cos(theta) + 2r^3/3] sin(theta) dr d(theta)
= ∫(0 to 2pi) [(4^4/3 - 2^4/3)(cos(theta)/4) + 2(4^3/3 - 2^3/3)/3] sin(theta) d(theta)
= ∫(0 to 2pi) [(16/3)(cos(theta)/4) + (32/3)] sin(theta) d(theta)
= 0
Therefore, the answer is (3) 0.
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$15 for 6 pounds and $90 for 36 pounds
QuestionSuppose the height of plants in a certain region is normally distributed with a mean of u=15 inches and a standard deviation of o = 3 inches. Approximately what percentage of plants in this region are between 10 and 14 inches tall? Bonus (5pts): plot a graph for this problem.
Using a table or calculator, we find that the area between z = -1.67 and z = -0.33 is approximately 0.3121 or 31.21%. Therefore, approximately 31.21% of plants in this region are between 10 and 14 inches tall.
we will use the concepts of standard, percentage, and deviation. We know that the mean height (µ) of plants is 15 inches and the standard deviation (σ) is 3 inches. We want to find the percentage of plants with heights between 10 and 14 inches.
Step 1: Calculate the z-scores for 10 and 14 inches.
z = (X - µ) / σ
For X = 10 inches:
z1 = (10 - 15) / 3 = -5/3 ≈ -1.67
For X = 14 inches:
z2 = (14 - 15) / 3 = -1/3 ≈ -0.33
Step 2: Find the percentage of plants corresponding to these z-scores using a z-table or calculator.
P(-1.67 < Z < -0.33) = P(Z < -0.33) - P(Z < -1.67)
Using a z-table or calculator, we find:
P(Z < -0.33) ≈ 0.3707
P(Z < -1.67) ≈ 0.0475
Step 3: Calculate the percentage of plants between 10 and 14 inches.
Percentage = (0.3707 - 0.0475) * 100% ≈ 32.32%
Next, we look up the area between these two z-scores in a standard normal distribution table. This area represents the percentage of plants in the region between 10 and 14 inches tall.
As for the bonus, I'm unable to plot a graph here, but you can use graphing software to plot a normal distribution curve with a mean of 15 and a standard deviation of 3. Shade the area between 10 and 14 inches to represent the percentage of plants in this range.
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A sum of 2709 is to be given in the form 63 prizes. If the prize of either 100 or 25, find the number of prizes given each type
For a sum of $20709, prize is of either $100 or $25, there will be 15 prizes of $100 and 48 prizes of $25.
Let's assume that x prizes are given for $100 and y prizes are given for $25. Then, we can set up a system of two equations based on the given information,
x + y = 63 (the total number of prizes is 63)
100x + 25y = 2709 (the total value of the prizes is $2709)
We can solve this system of equations by substitution or elimination. Here, we will use the elimination method, multiplying the first equation by 25, we get,
25x + 25y = 1575
75x = 1134
Dividing both sides by 75, we get,
x = 15.12
Since we cannot have a fractional number of prizes, we can round this down to 15 (because it is closer to 15 than to 16).
Substituting x = 15 in the first equation, we get,
15 + y = 63
Solving for y, we get,
y = 48
Therefore, 15 prizes are given for $100 and 48 prizes are given for $25.
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pls help 32 points dont have much time
Answer: I would say B srry if I'm wrong
Step-by-step explanation:
To find the volume of the prism, we need to multiply the area of the base by the height. The base of the prism is made up of 6 cubes arranged in a rectangle, so its area is:
Base area = length x width Length = 2 cubes = 1 foot Width = 3 cubes = 1.5 feet Base area = 1 x 1.5 = 1.5 square feet
The height of the prism is also equal to one cube, which is 1/2 feet.
Therefore, the volume of the prism can be calculated as follows:
Volume = Base area x Height Volume = (1.5 square feet) x (0.5 feet) Volume = 0.75 cubic feet
a factory has a machine which bends wire at a rate of 10 unit(s) of curvature per second. how long does it take to bend a straight wire into a circle of radius 6?
It would take (6π/5) seconds to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second.
To calculate the time it takes to bend a straight wire into a circle of radius 6 using a machine that bends wire at a rate of 10 unit(s) of curvature per second, we need to find the length of the wire and then divide it by the rate of curvature.
The circumference of a circle with a radius of 6 is 2πr = 2π(6) = 12π. Therefore, the length of the wire that needs to be bent is 2πr = 12π.
Now we can calculate the time it takes to bend the wire by dividing the length by the rate of curvature:
Time = length of wire / rate of curvature = (12π units) / (10 units/second)
Simplifying, we get:
Time = (6π/5) seconds
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Let's say we wanted to use the Beck Depression Inventory (BDI) to assess and diagnose depression. The BDI would be an example of:a. a variableb. a measurement instrumentc. datad. internal validity
The Beck Depression Inventory (BDI) would be an example of a measurement instrument.
A measurement instrument is a tool or technique used to measure or assess a particular variable or construct, in this case, depression. The BDI is a standardized self-report questionnaire that is widely used to assess the severity of depressive symptoms. It consists of 21 questions or items that ask the respondent to rate the intensity of their depressive symptoms on a 4-point scale. The total score on the BDI can be used to classify the severity of depression and guide treatment decisions.
In contrast, a variable is a characteristic or attribute that can take on different values or levels, such as age, gender, or income. Data refers to the collection of measurements or observations obtained from a particular study or investigation. Internal validity is a concept that refers to the extent to which a study is designed and conducted in a way that minimizes the potential for bias or confounding variables.
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What would be the volume of the cylinder?
Step-by-step explanation:
Volume = area of end x height
= pi r^2 x 8
= pi 2^2 * 8 = 32 pi units^3 <====exact answer
If ⅆyⅆt=6e−0. 08(t−5)2, by how much does y change as t changes from t=1 to t=6 ?
(A) 3. 870 (B) 8. 341 (C) 18. 017 (D) 22. 583
Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).
To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.
∫₁⁶ 6e[tex].^{(-0.08(t-5)^2)}[/tex] dt
We can use the substitution u = t - 5 to simplify the integral:
∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex] du
Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:
∫₋₄¹ 6e[tex].^{(-0.08u^2)}[/tex] du ≈ 3.870
Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).
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Gloria took our a 30-year mortgage for $70,000 at 7.5%. How much will she pay over 30 years?
Answer:
Step-by-step explanation:
To calculate how much Gloria will pay over 30 years for her $70,000 mortgage at 7.5%, we need to use the formula for a standard mortgage payment, which is:
P = L[c(1 + c)^n]/[(1 + c)^n - 1]
Where:
P = the monthly payment
L = the loan amount
c = the monthly interest rate (annual interest rate divided by 12)
n = the total number of payments (30 years multiplied by 12 months per year)
First, we need to calculate the monthly interest rate:
c = 7.5% / 12 = 0.00625
Next, we need to calculate the total number of payments:
n = 30 years x 12 months per year = 360
Now we can plug in these values to the formula:
P = 70000[0.00625(1 + 0.00625)^360]/[(1 + 0.00625)^360 - 1]
P = $493.95
Therefore, Gloria will pay $493.95 per month for 30 years for her $70,000 mortgage at 7.5%. Over the course of the 30 years, she will pay a total of:
Total Payments = P x n = $493.95 x 360 = $177,822
So, Gloria will pay a total of $177,822 over 30 years for her $70,000 mortgage at 7.5%.
Estimate the mean and standard deviation of the underlying normal distribution from which the following data has been generated, using the probability plot method. -1.83 4.99 2.49 4.33 5.40 4.38 3.73 4.72 3.67 1.25 3.04 1.23 3.19 2.33 1.36 2.88 5.52 0.27 -3.58 7.42
We can estimate that the underlying normal distribution from which the data was generated has a mean of 3 and a standard deviation of 1.
To estimate the mean and standard deviation of the underlying normal distribution from the given data using the probability plot method, we need to first create a probability plot of the data.
After creating the probability plot, we can visually inspect it to see if the data points fall on a straight line. If the data points fall on a straight line, then we can assume that the data is normally distributed. We can then use the slope of the line to estimate the standard deviation and the intercept of the line to estimate the mean.
Using the given data, we can create a probability plot as follows:
- First, we need to order the data from smallest to largest:
-3.58 -1.83 0.27 1.23 1.25 1.36 2.33 2.49 2.88 3.04 3.19 3.67 3.73 4.33 4.38 4.72 4.99 5.40 5.52 7.42
- Next, we need to calculate the percentiles for each data point:
0.5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 99.5%
- We can then plot the percentiles on the y-axis and the ordered data on the x-axis.
After creating the probability plot, we can see that the data points fall approximately on a straight line. This suggests that the data is normally distributed. We can then estimate the mean and standard deviation of the underlying normal distribution as follows:
- The slope of the line is approximately 1, which suggests that the standard deviation of the underlying normal distribution is approximately 1.
- The intercept of the line is approximately 3, which suggests that the mean of the underlying normal distribution is approximately 3.
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For a business meeting, Tristan is making copies of his presentation. The number of copies Tristan will have to make is dependent upon the number of people who plan to attend. c = the number of copies p = the number of people who plan to attend Which of the variables is independent and which is dependent? p is the independent variable and c is the dependent variable c is the independent variable and p is the dependent variable Submit
Answer: independent = p, dependent = c
Step-by-step explanation: the number of copies Tristan makes, or c, depends (is DEPENDENT) on the number of people who plan to attend, which is INDEPENDENT on the amount of copies
the number of copies is a reaction (DEPENDS) on the amount of people, not the other way around.
For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. True or False
For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.
The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.
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Identify the null and alternative hypothesis for the givenscenario:Students earning a Master's degrees takes on average 4.9 years to graduate. The dean of a major university claims the Master students at his university graduate earlier than 4.9 years. H: _ 4.9 v Ha:
In this scenario, we need to identify the null and alternative hypotheses. The null hypothesis represents the status quo or the current belief, while the alternative hypothesis represents the claim or what we want to test against the null hypothesis.
H0: The average time for Master's students to graduate is 4.9 years.
Ha: The average time for Master's students to graduate is less than 4.9 years (alternative hypothesis).
The null hypothesis (H₀) states that the average time it takes for students to graduate with a Master's degree is 4.9 years. The alternative hypothesis (Hₐ) represents the claim made by the dean, which is that Master's students at his university graduate earlier than 4.9 years.
So, the null and alternative hypotheses can be written as:
H₀: μ = 4.9
Hₐ: μ < 4.9
where μ represents the average time it takes for students to graduate with a Master's degree at the dean's university.
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A triangular prism has the dimensions shown.
A triangular prism is shown. The height of the prism is twelve feet. The height of the triangular base is three feet. The base of the triangular base is x.
What is the length x
if its volume is 72
cubic feet?
The length of the base of the triangular base is 4 feet.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The formula for the volume of a triangular prism is:
V = (1/2)bh x h
where b is the base of the triangular base, h is the height of the triangular base, and h is the height of the prism.
Substituting the given values, we get:
72 = (1/2)(x) x 3 x 12
Simplifying, we get:
72 = 18x
Dividing both sides by 18, we get:
x = 4
Therefore,
The length of the base of the triangular base is 4 feet.
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Answer:
The length, x, of the base of the triangular base of the prism is 4 ft.
Step-by-step explanation:
The volume of a regular prism can be found by multiplying the area of its base by its height.
[tex]\boxed{\textsf{Volume of a regular prism}=\textsf{Base area} \times\textsf{height}}[/tex]
The base of a triangular prism is a triangle.
The area of a triangle is half the product of its base and height.
Given that b = x and h = 3, the area of the triangular base of the prism is:
[tex]\begin{aligned}\textsf{Area of triangular base}&=\dfrac{1}{2} bh\\\\&=\dfrac{1}{2} \cdot x \cdot 3\\\\&=\dfrac{3}{2}x\; \sf ft^2\end{aligned}[/tex]
To find the value of x, substitute the given volume, v = 72 ft³, the given height, h = 12 ft, and the found area of the base into the formula for volume, and solve for x:
[tex]\begin{aligned}\textsf{Volume}&=\textsf{Base area} \cdot \textsf{Length}\\\\\implies 72&=\dfrac{3}{2}x \cdot 12\\\\72&=\dfrac{36}{2}x \\\\2 \cdot 72&=2 \cdot \dfrac{36}{2}x \\\\144&=36x\\\\\dfrac{144}{36}&=\dfrac{36x}{36}\\\\4&=x\end{aligned}[/tex]
Therefore, the value of x is 4 feet.