Approximately 2.62% of college students sleep for more than 8.3 hours.
To determine the proportion of college students who sleep for more than 8.3 hours, we need to use the provided information: the average sleep time is 7 hours per night with a standard deviation of 40 minutes (which is equivalent to 2/3 of an hour or 0.67 hours). Since the sleep time is normally distributed, we can use the Z-score formula to find the proportion.
First, calculate the Z-score: Z = (X - μ) / σ, where X is the desired sleep time (8.3 hours), μ is the average sleep time (7 hours), and σ is the standard deviation (0.67 hours).
Z = (8.3 - 7) / 0.67 ≈ 1.94
Now, we can use a Z-table to find the proportion of students who sleep for more than 8.3 hours. The table value for a Z-score of 1.94 is approximately 0.9738. However, this value represents the proportion of students who sleep 8.3 hours or less. To find the proportion of students who sleep more than 8.3 hours, subtract the table value from 1:
Proportion = 1 - 0.9738 ≈ 0.0262
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are you smarter than a second-grader? a random sample of 54 second-graders in a certain school district are given a standardized mathematics skills test. the sample mean score is x
It is difficult to say much more about the sample mean score.
If we know the sample mean score, which is denoted by x in your question, we can use it to make some inferences about the overall population of second-graders in that school district. However, we would need more information about the distribution of scores, such as the standard deviation or the range, to draw any conclusions about the entire population.
For example, if we assume that the distribution of scores is approximately normal, we could use the sample mean and standard deviation to calculate a confidence interval for the population mean score. This interval would give us a range of scores within which we can be reasonably confident the true population mean falls.
Without more information about the sample or the population, it is difficult to say much more about the sample mean score.
Complete question: Are you smarter than a second-grader? A random sample of 45 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x-54. Assume the standard deviation of test scores is o = 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have different math skills from the nationwide average. Use the a=0.05 level of significance and the P-value method with the TI-84 calculator al Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses.
Previous question
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A researcher investigated the number of reports of police officer misconduct as a function of officer-reported on-the-job stress and got the following results Minimal Stress Moderate Stress Severe Str
A researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct.
As a researcher, the investigation into the number of reports of police officer misconduct in relation to on-the-job stress levels is an important area of study. However, it is essential to ensure that ethical considerations are followed throughout the research process to avoid any potential misconduct.
In terms of the findings,, the results showed a relationship between on-the-job stress and the number of reported incidents of misconduct. Specifically, officers who reported higher levels of stress experienced more incidents of misconduct compared to those who reported minimal stress. It is crucial to further examine the factors contributing to this relationship and develop strategies to mitigate the negative impact of on-the-job stress on police officers.
Based on your question, a researcher conducted a study investigating the relationship between police officer-reported on-the-job stress and the number of reports of officer misconduct. The stress levels were categorized as minimal, moderate, and severe. However, the specific results were not provided in your question.
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Heart 1 is translated 3 units down to heart 2. Which shows this transformation? On a coordinate plane, heart 1 is shifted 4 units down and 4 units to the right. On a coordinate plane, heart 1 is reflected across the x-axis to heart 2. On a coordinate plane, heart 1 is shifted 4 units to the right and is rotated to form heart 2. On a coordinate plane, heart 1 is shifted down 3 units to form heart 2.
PLEASEEEE HEEEEELLPPPP IM TIMMMEEEDDDDD!!!!!!!! 15 POINTS!!!
A diagram and graph that shows this transformation include the following: D. On a coordinate plane, heart 1 is shifted down 3 units to form heart 2.
What is a transformation?In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.
By critically observing the geometric figures, we can reasonably infer and logically deduce that a vertical translation of heart 1 down by 3 units in order to produce heart 2 is a graph that correctly shows this transformation.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which of these is a correct expansion of (3x – 2)(2x2 + 5)?
A. 3x • 2x2 + 3x • 5 + (–2) • 2x2 + (–2) • 5
B. 3x • 2x2 + 3x • 5 + 2 • 2x2 + 2 • 5
C. 3x • 2x2 + (–2) • 2x2 + 2x2 • 5 + (–2) • 5
The correct expansion of (3x – 2)(2[tex]x^2[/tex] + 5) is 3x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5. Thus, option A is the right answer to the given question.
To expand an expression of multiplication of two variables to two variables is done as follows:
1. We take the first term of the first expression which in this case is 3x
2. We multiply it by the first term of the second expression. In this case, we get 3x • 2[tex]x^2[/tex].
3. Subsequently we multiply the first term with further terms and add them. In the given case, the expression we get is 3x • 2[tex]x^2[/tex] + 3x • 5
4. Then we take the second term of the first expression and repeat the above steps and add it to the existing equation.
We get x • 2[tex]x^2[/tex] + 3x • 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5 as the answer.
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A researcher asked 120 people if they preferred swimming in a pool or swimming at the beach. The data collected show that two out of 10 people preferred swimming at the beach. What was the total number of people who preferred swimming at the beach?
A. 12
B. 60
C. 2
D. 24
PLEASE ANSWER WITH EXPLANATION / WORK
The total number of people who preferred swimming at the beach is: 24
How to find the probability of selection?In survey sampling, the term probability of selection is one that refers to the chance (i.e. the probability from 0 to 1) that a member (element) of a population can be chosen for a given survey.
We are told that two out of 10 people preferred swimming at the beach. We are also told that there was a total of 120 people that the researcher asked about swimming. Thus:
Fraction of people that prefer swimming = 2/10 = 0.2
Thus, number of people that prefer swimming in a sample of 120 people is: 0.2 * 120 = 24 people
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Determina cuáles de las siguientes expresiones son proposiciones. 1. Sube al 1
1.cuarto piso.
2.el triangulo ABC es equilatero
3. ¿que es un àngulo obtuso?
4. la suma de una medida de dos angulos complenmetanrios es igual a 90
5. un triangulo es isoceles si tiene solamente dos angualos congruentes
Identify which transformation or sequence of transformations identified below will map triangle ABC onto triangle DEF.
A Single transformation maps triangle ABC onto triangle DEF.
Given that Reflection the single transformation maps ABC onto A'B'C' is reflection .
The rigid transformations can map triangle Δ ABC onto triangle Δ DEF is reflection then translation .
The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .
However pair of triangles can be proven congruent by the HL theorem is rotation then translation .
Thus, rigid transformation S can map Triangle ABC onto Triangle DEF is reflection then rotation .
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If a is uniformly distributed over [−12,15], what is the probability that the roots of the equation
x^2 + ax + a + 35 = 0
are both real? ___
To determine the probability that the roots of the given quadratic equation are both real, we need to find the values of a for which the discriminant of the equation is non-negative.
The discriminant of the quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac. In this case, the discriminant of the given equation is:
a^2 - 4(a+35)
For the roots to be real, this discriminant must be non-negative. That is:
a^2 - 4(a+35) ≥ 0
Simplifying this inequality, we get:
a^2 - 4a - 140 ≥ 0
Factorizing the left-hand side, we get:
(a-14)(a+10) ≥ 0
This inequality is satisfied for a ≤ -10 or a ≥ 14, or when a is in the interval [-12, -10) or (14, 15].
Since a is uniformly distributed over the interval [-12, 15], the probability that lies in the interval [-12, -10) or (14, 15] is:
Probability = Length of the interval [-12, -10) + Length of interval (14, 15] / Total length of the interval [-12, 15]
Probability = (2 + 1) / (15 - (-12))
Probability = 3/27
Probability = 1/9
Therefore, the probability that the roots of the given quadratic equation are both real is 1/9.
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Arianna deposits $500 in an account that pays 3% interest, compounded semiannually. How much is in the account at the end of 2 years.
There will be $530.68 in the account at the end of 2 years, if Arianna deposits $500 in an account that pays 3% interest, compounded semiannually.
How much is in the account at the end of 2 years?The formula accrued amount in a compounded interest is expressed as;
A = P( 1 + r/n )^( n × t )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $500
Compounded semi annually n = 2
Time t = 2 years
Interest rate r = 3%
Accrued amount A = ?
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03
Plug the values into the above formula:
A = P( 1 + r/n )^( n × t )
A = $500( 1 + 0.03/2 )^( 2 × 2 )
A = $500( 1 + 0.015 )^( 4 )
A = $530.68
Therefore, the accrued amount is $530.68.
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A candy machine has candies of four are avea apple blackberry cherry (C) and doublemint (Dj The cand we wel eed and when you drop a quarter in the machine you get two random candies at the same time. The servation is the of the two candies Winto the sample space for this to experiment What is the sample **7 Choose the collect answe dew OA AA AB AC AD AB BC BC BD CA CB CC.CO DA DO DG DO OB WA AB AC AD SE BC BO CO CO DO OC. An AC ADC.DOCX On ABC
Using the given information, we can list out all the possible pairs of candies:
AA, AB, AC, AD, BC, BD, CC, CO, DA, DC, DO, OB, OC
Therefore, the sample space for this experiment is {AA, AB, AC, AD, BC, BD, CC, CO, DA, DC, DO, OB, OC}.
I understand that you would like to know the sample space for getting two random candies at the same time from a candy machine with four types of candies: Apple (A), Blackberry (B), Cherry (C), and Double mint (D).
The sample space for this experiment is the set of all possible outcomes, which in this case is the set of all possible pairs of candies that can be obtained from the machine.
To determine the sample space, we need to list all possible combinations of two candies. Here they are:
1. AA
2. AB
3. AC
4. AD
5. BA
6. BB
7. BC
8. BD
9. CA
10. CB
11. CC
12. CD
13. DA
14. DB
15. DC
16. DD
The sample space for this experiment consists of 16 possible outcomes.
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it is possible for a small treatment effect to still be statistically significant. group of answer choices true false
True. It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.
We have,
Statistical significance is determined by the p-value, which measures the probability of obtaining the observed results if the null hypothesis (no difference between groups) is true.
A small treatment effect may still produce a low p-value if the sample size is large enough to detect even small differences.
However, the clinical significance of the treatment effect should also be considered in addition to statistical significance.
Thus,
It is possible for a small treatment effect to still be statistically significant if the sample size is large enough.
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Estimate the product of 153 and 246 
The estimated product of 153 and 246 is 37500.
Estimating the product of 2 numbersIn order to estimate the product of 153 and 246, both numbers need to be rounded off to the nearest 10 as follows:
153 ≈ 150246 ≈ 250Next, the rounded numbers can be multiplied as follows:
150 x 250 = 37500
In other words, an estimate of the product of 153 and 246 is 37500.
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What’s the answer I need help pls? Can somebody give me the answer pls plssss?
Answer:
The determinant of this matrix is
2(5) - (-7)(-2) = 10 - 14 = -4.
This matrix has an inverse, but there are some square matrices whose determinant is zero and therefore do not have an inverse. Abid's friend is correct. So a + b + c + d = 2 + (-7) + (-2) + 5 = -2.
PLS HELP!!
Heather rolled a number cube two times, and both times it landed on five. Heather rolls on more time. Which is the theoretical probability that it will land on a five?
Answer: The theoretical probability that the number cube will land on five is 1/6. The previous outcomes do not affect the probability of rolling a five on the next roll, as each roll of the number cube is independent of the previous roll. Therefore, the probability of rolling a five on the next roll is the same as the probability of rolling a five on any other roll of the number cube, which is 1/6.
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
All the wording makes it confusing, but it is a simple probability of rolling a 5 out of the 6 faces on the die. It only asks about that time, so the probability doesnt increase or decrease at all depending on what was rolled before
Simplify the polynomial expression. (64m^8n^12)^1/2
The simplified value of the polynomial-expression "√(64m⁸n¹²)" is 8m⁴n⁶..
A "Polynomial-Expression" is an expression which consists of variables, coefficients, and exponents having operations of addition, subtraction, multiplication, and non-negative integer exponents.
To simplify the given polynomial expression √(64m⁸n¹²), we can use the property of square-roots which states that √(a×b) = √a × √b;
So, We have
⇒ √(64m⁸n¹²) = √(64) × √(m⁸) × √(n¹²),
Now, we simplify each of square roots separately:
⇒ √(64) = 8, because 8×8 = 64;
⇒ √(m⁸) = m⁴, because m⁴×m⁴ = (m⁴)² = m⁸;
⇒ √(n¹²) = n⁶, because n⁶×n⁶ = (n⁶)² = n¹²,
Substituting the values,
We get,
⇒ √(64m⁸n¹²) = 8m⁴n⁶
Therefore, the simplified polynomial expression is 8m⁴n⁶.
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The given question is incomplete, the complete question is
Simplify the polynomial expression. √(64m⁸n¹²).
Suppose the average life for new tires is thought to be bell-shaped and symmetrical with a mean of 45,000 miles and a standard deviation of 4,000 miles Based on this information, what interval of miles would approximately 95% of tires be expected to last within?A 41000 10 49.000B. 42,000 to 47.000C 45,000 to 49.000D 37 000 to 53000
The interval of miles in which approximately 95% of tires are expected to last within is from 37,000 to 53,000 miles.
To answer your question, we'll use the given information about the bell-shaped and symmetrical distribution with a mean and standard deviation.
Mean (μ) = 45,000 miles
Standard Deviation (σ) = 4,000 miles
For a bell-shaped and symmetrical distribution, approximately 95% of the data falls within 2 standard deviations of the mean. We can use this to find the interval:
According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean. In this case, two standard deviations below the mean is 45,000 - (2*4,000) = 37,000 and two standard deviations above the mean is 45,000 + (2*4,000) = 53,000.
Lower Bound: μ - 2σ = 45,000 - 2(4,000) = 45,000 - 8,000 = 37,000 miles
Upper Bound: μ + 2σ = 45,000 + 2(4,000) = 45,000 + 8,000 = 53,000 miles
So, approximately 95% of tires would be expected to last within the interval of 37,000 to 53,000 miles. The correct answer is D. 37,000 to 53,000.
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Along with the wood, Jack is also using some nails to build the shelves. One box of nails has a mass of kilograms (kg).
Jack used between and of the nails in the box.
How many kilograms of nails did Jack use to build the shelves? Show your work or explain your answer.
Answer:
The answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails
Step-by-step explanation:
2 3/4 kg as an improper fraction is 11/4 kg
1/2 of 11/4 = 1/2 x 11/4
= 11/8
= 1 3/8 kg
3/4 of 11/4 = 33/16
= 2 1/16 kg
1 3/8 kg and 2 1/16 kg of nails
Thus the answer to your problem is, Between 1 3/8 kg and 2 1/16 kg of nails
Lisa is turning 12 this month! For her birthday party, Lisa got a bright pink cube-shaped piñata with a big "12" printed on each side. The piñata's edges are each 1.5 feet long. What is the volume of the piñata? Write your answer as a whole number or decimal. Do not round. cubic feet
The volume of the piñata is 3.375 cubic feet.
Now, To find the volume of the piñata, we need to calculate the volume of a cube.
Hence, We can do this by multiplying the length of one edge by itself three times.
In this case, each edge of the piñata is 1.5 feet long,
so we can write;
Volume of piñata = (1.5 feet) x (1.5 feet) x (1.5 feet)
Simplifying this expression, we get:
Volume of piñata = 3.375 cubic feet
Therefore, the volume of the piñata is 3.375 cubic feet.
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use the graph to evaluate the compostable (f•g)(0)=
Answer: The answer is 3
Step-by-step explanation: I had the same question.
Write an equation to match each graph
Answer: y = |x|
Explanation :
It doesn't seem to be moved in translated in any way. The normal equation for this graph is y = |x|
Can someone help me asap? It’s due today!! I will give brainliest if it’s all correct. Select all that apply
The data are matched as shown below
Data 1 - d
Data 2 - c
Data 3 - a
Data 4 - b
How to match the data with the correct interquartile rangeIQR is an abbreviation for interquartile range
The interquartile range is calculated using the formula
= top quartile - bottom quartile
Data 1
top quartile = 11
bottom quartile = 5
IQR = 11 - 5 = 6
Data 2
top quartile = 11
bottom quartile =7
IQR = 11 - 7 = 4
Data 3
top quartile = (8 + 9)/2 = 8.5
bottom quartile = (15 + 12)/2 = 13.5
IQR = 13.5 - 8.8 = 5
Data 4
top quartile = 9
bottom quartile = 12
IQR = 12 - 9 = 3
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if the ^abc is 32, and the ^dba is 143 find ^aoc and ^ocd
Examining the figure, the missing angles are
angle AOC = 148 degrees
angle OCD = 21 degrees
How to find the anglesLine AB and CB are tangents to the circle and hence will make angle 90 degrees at the point of tangent.
OA bisects angle AOC and angles ABC
In triangle AOB
90 + 32/2 + angle AOB = 180 degrees
angle AOB = 180 - 90 - 32 / 2
angle AOB = 74 degrees
angle AOC = 74 x 2 = 148 degrees
Using inscribed angle theorem
angle D = 1/2 x angle AOC
angle D = 74 degrees
In quadrilateral ABCD
143 + 32 + 74 + angle C = 360
angle C = 360 - 143 - 32 - 74
angle C = 111 degrees
angle OCD = 111 - 90
angle OCD = 21 degrees
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Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 suggested in the article "Dynamic Ride Sharing: Theory and Practice"T). (Round your answer to three decimal places) (a) What is the probability that the number of drivers will be at most 19? (b) What is the probability that the number of drivers will exceed 29
a) The probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.
b) The probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.
(a) To find the probability that the number of drivers will be at most 19, we need to use the Poisson distribution formula:
P(X ≤ 19) = e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + ... + e^(-20) * (20^19/19!)
Using a calculator or statistical software, we get P(X ≤ 19) ≈ 0.088.
(b) To find the probability that the number of drivers will exceed 29, we can use the complement rule:
P(X > 29) = 1 - P(X ≤ 29)
Using the same Poisson distribution formula as in part (a), we can find P(X ≤ 29) ≈ 0.963. So,
P(X > 29) = 1 - 0.963 = 0.037 (rounded to three decimal places).
Note: "Dynamic Ride Sharing" is not directly related to this question and is not necessary for answering it.
Hi! I'd be happy to help you with your question.
(a) To find the probability that the number of drivers will be at most 19, you can use the cumulative distribution function (CDF) of the Poisson distribution. The parameter for this distribution is μ = 20. The formula for the Poisson CDF is:
P(X ≤ k) = Σ (e^(-μ) * (μ^x) / x!) for x = 0 to k
In this case, k = 19. Plugging in the values and calculating the sum, we get:
P(X ≤ 19) ≈ 0.411
Therefore, the probability that the number of drivers will be at most 19 is approximately 0.411 or 41.1%.
(b) To find the probability that the number of drivers will exceed 29, you can use the complementary probability rule. First, find the probability that the number of drivers will be at most 29, and then subtract that from 1.
P(X > 29) = 1 - P(X ≤ 29)
Using the Poisson CDF formula with k = 29 and μ = 20:
P(X ≤ 29) ≈ 0.996
Now, subtract this value from 1:
P(X > 29) = 1 - 0.996 ≈ 0.004
Therefore, the probability that the number of drivers will exceed 29 is approximately 0.004 or 0.4%.
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which one of these best illustrates a probability distribution at it relates to next year's economy? multiple choice question. 25 percent chance the economy will grow at 5 percent or more 40 percent chance of recession; 60 percent chance of a normal economy 5 percent chance of a depression and 25 percent chance of a recession 15 percent chance of a boom and 5 percent chance of a depression
The best illustration of a probability distribution as it relates to next year's economy is "40 percent chance of recession, 60 percent chance of a normal economy". Option B is correct.
This choice accurately represents a probability distribution by assigning probabilities to different outcomes (recession and a normal economy) based on their likelihoods. The 40 percent chance of a recession and 60 percent chance of a normal economy provide a clear indication of the potential outcomes and their corresponding probabilities.
This distribution allows for a more realistic assessment of the future state of the economy, acknowledging the possibility of both positive and negative scenarios. By presenting these probabilities, decision-makers can better understand the potential risks and make informed choices based on the likelihood of different economic outcomes.
This probability distribution offers a balanced perspective, highlighting the uncertainty and potential variations that may occur in the next year's economy.
Option B holds true.
This question should be provided as:
Which one of these best illustrates a probability distribution at it relates to next year's economy? Multiple choice question:
A. 25 percent chance the economy will grow at 5 percent or more. B. 40 percent chance of recession; 60 percent chance of a normal economy.C. 5 percent chance of a depression and 25 percent chance of a recession.D. 15 percent chance of a boom and 5 percent chance of a depression.Learn more about probability distribution: https://brainly.com/question/23286309
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At a concession stand,
The number of popcorns that were sold at the concession stand, given the amount made, was 88 popcorns.
How to find the number of popcorns sold ?To find the number of popcorns that were sold, two equations are needed to show the relationship between the popcorn and nachos sold.
The equations assume x is popcorns and y is nachos:
x + y = 172
1.10 x + 2.35 y = 294.20
Using substitution:
y = 172 - x
Solve the second equation:
1. 10 x + 2. 35 ( 172 - x ) = 294. 20
1.10 x + 404. 20 - 2.35 x = 294. 20
- 1.25 x = - 110
x = 88
In conclusion, 88 popcorns were sold.
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The full question is:
At a concession stand, popcorn costs $1.10 and nachos cost $2.35. One
day, the receipts for a total of 172 popcorn and nachos were $294.20.
How many popcorns were sold?
A store buys a jackey for 20$ and sells it to there cosutomer 80% more than that, what is the selling price
How do I figure this out?!
A. Optgion C is correct. y = - 4/5x + 94
b. The distance that Maria would have covered from her house is given as 58 meters
How to solve for the distance abd the slopeThe formula to use here is
y2 - y1 / x2 - x1
= 70 - 94 / 30 - 0
= - 24 / 30
divide through by 6
= - 4 / 5
y = - 4/5x + 94
When x = 45
y = - 4/5x + 94
= -4 / 5 * 45 + 94
y = 180 / 5 + 94
y = -36 + 94
y = 58
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Suppose that X and Y are random variables with the same variance. Show that X - Y and X + Y are uncorrelated.
X - Y and X + Y are uncorrelated. To show that X - Y and X + Y are uncorrelated, we need to show that their covariance is zero.
The covariance between X - Y and X + Y is given by:
[tex]Cov(X - Y, X + Y) = E[(X - Y)(X + Y)] - E[X - Y]E[X + Y][/tex]
Expanding the first term:
Cov(X - Y, X + Y) = E[X^2 - Y^2] - E[X - Y]E[X + Y]
Using the fact that X and Y have the same variance, we have:
[tex]E[X^2 - Y^2] = E[(X - Y)(X + Y)] = E[X^2] - E[Y^2][/tex]
And since X and Y have the same variance[tex], E[X^2] = E[Y^2][/tex], so we can simplify:
[tex]E[X^2 - Y^2] = 0[/tex]
Next, we can expand the second term:
E[X - Y]E[X + Y] = (E[X] - E[Y])(E[X] + E[Y])
Since X and Y have the same variance, we have E[X] = E[Y], so:
E[X - Y]E[X + Y] = (E[X] - E[X])(E[X] + E[X]) = 0
Putting it all together:
Cov(X - Y, X + Y) = 0 - 0 = 0
Therefore, X - Y and X + Y are uncorrelated.
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(Chapter 12) The vector <3, -1, 2> is parallel to the plane 6x-2y +4z = 1
The vector is parallel to the plane the vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1
To determine if the vector <3, -1, 2> is parallel to the plane 6x - 2y + 4z = 1, we need to check if the vector is orthogonal (perpendicular) to the normal vector of the plane.
Find the normal vector of the plane.
The normal vector of a plane is given by the coefficients of x, y, and z in the equation of the plane. In this case, the normal vector is <6, -2, 4>.
Check if the given vector is orthogonal to the normal vector.
Two vectors are orthogonal if their dot product is equal to 0. Let's compute the dot product between the given vector <3, -1, 2> and the normal vector <6, -2, 4>:
Dot product = (3 * 6) + (-1 * -2) + (2 * 4) = 18 + 2 + 8 = 28
Since the dot product is not equal to 0 (28 ≠ 0), the given vector <3, -1, 2> is not orthogonal to the normal vector of the plane.
The vector <3, -1, 2> is not orthogonal to the normal vector of the plane 6x - 2y + 4z = 1, which means it is parallel to the plane.
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a normal distribution has a mean of 39 and a standard deviation of 4. using the empirical rule, find the approximate probability that a randomly selected x-value from the distribution is in the given interval
The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
So, if we want to find the approximate probability that a randomly selected x-value from the distribution is in a given interval, we need to determine how many standard deviations away from the mean the interval is and then use the empirical rule.
For example, let's say we want to find the approximate probability that a randomly selected x-value from the distribution is between 31 and 47.
First, we need to determine how many standard deviations away from the mean 31 and 47 are.
To do this, we can calculate the z-scores for each value using the formula:
z = (x - mean) / standard deviation
For x = 31:
z = (31 - 39) / 4 = -2
For x = 47:
z = (47 - 39) / 4 = 2
So, the interval from 31 to 47 is two standard deviations away from the mean.
Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate probability that a randomly selected x-value from the distribution is between 31 and 47 is approximately 95%.
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