Answer:
The monthly cost is $690.17.
Step-by-step explanation:
Each semester costs $4100.
In each semester, there are $41 spent on textbooks.
In a year:
2*4100 + 2*41 = $8282
Monthly cost
A year has 12 months. So
8282/12 = 690.17.
The monthly cost is $690.17.
27.) What shape do you create if you cut a square in
half horizontally or vertically?
Answer:
A rectangle!!
Step-by-step explanation:
When you cut a square horizontally or vertically, you get two smaller triangles that are half the area of the square. When you split the rectangle again, you get a square 1/4 the size of the regular square.
Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f
Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
Answer:
In the image, you can observe a diagram representing this problem.
We know by given that [tex]g \parallel h[/tex] and [tex]\angle 2 \cong \angle 3[/tex].
From the parallelism between line g and line h, we deduct several congruence between angles.
[tex]\angle 2 \cong \angle 1[/tex], by corresponding angles (same side of the transversal, one interior, the other exterior to parallels).
Now, to demonstrate [tex]e \parallel f[/tex], we must demonstrate a congruence between angle 2 and an angle on the intersection between line g and line f.
In the parallelogram formed, we know
[tex]\angle 2 + \angle 3+ 180-\angle 1 + x =360[/tex]
Where [tex]x[/tex] is the angle at the intersection line g and line f.
But, we know [tex]\angle 2 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 1[/tex], so
[tex]\angle 2 + \angle 2 +180 - \angle 2 +x=360\\\angle 2 + x=180[/tex]
Notice that we don't have a congruence, however there's theorem which states that the same-side interior angles of parallels are supplementary.
In this case, we use the corolary of that theorem, which states if two same-side interior angles are supplementary, then the lines are parallels.
[tex]\therefore e \parallel f[/tex]
However, according to the choices of the problem, the missin proof is "converse alternate interior angles theorem", because the problem was demonstrate using transitive property, to show that angles 1 and 3 are congruent, there by converse alternate interior angles theorem, lines e and f are parallels.
This is the same case we used, but using converse alternate interior angles theorem.
Answer:
the answer is c-
Step-by-step explanation:
converse alternate interior angles theorem
hope this is helpful
give brainliest to the other dude
You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ = 79.5 σ=79.5 dollars. You would like to be 90% confident that your estimate is within 4 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
Answer:
We need to sample at least 1069 parents.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many parents do you have to sample?
We need to sample at least n parents.
n is found when [tex]M = 4, \sigma = 79.5[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.645*\frac{79.5}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.645*79.5[/tex]
[tex]\sqrt{n} = \frac{1.645*79.5}{4}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*79.5}{4})^{2}[/tex]
[tex]n = 1068.92[/tex]
Rounding up
We need to sample at least 1069 parents.
Answer:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=79.5[/tex] represent the population standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got [tex]z_{\alpha/2}=1.64[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer
write p-20=-30 as an addition problem
The equation p-20=-30 can be rewritten as an addition problem by adding 20 to both sides of the equation. The resulting addition equation is p = -30 + 20.
Explanation:The equation p-20=-30 can be written as an addition problem by moving -20 to the other side of the equation. This is done by adding 20 to both sides of the equation, which results in the equation p = -30 + 20. In other words, you can add -30 and 20 together to find the value of p. This is how you write the equation p-20=-30 as an addition problem. So the equation becomes p= -30+20
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company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have failed to attain their fuel economy goal
Answer:
[tex]t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435[/tex]
[tex]p_v =P(t_{(49)}<-1.435)=0.0788[/tex]
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.
Step-by-step explanation:
Data given and notation
[tex]\bar X=25.02[/tex] represent the sample mean
[tex]s=4.83[/tex] represent the sample standard deviation
[tex]n=50[/tex] sample size
[tex]\mu_o =26[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 26[/tex]
Alternative hypothesis:[tex]\mu < 26[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=50-1=49[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(49)}<-1.435)=0.0788[/tex]
Conclusion
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.
Using the t-distribution, it is found that since the test statistic is more than the critical value for the left-tailed test, this is not strong evidence that they have failed to attain their fuel economy goal.
At the null hypothesis, it is tested if the fleet average is of at least 26 miles per gallon, that is:
[tex]H_0: \mu \geq 26[/tex]
At the alternative hypothesis, it is tested if it is less, that is:
[tex]H_1: \mu < 26[/tex]
We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{X} = 25.02, \mu = 26, s = 4.83, n = 50[/tex].
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{25.02 - 26}{\frac{4.83}{\sqrt{50}}}[/tex]
[tex]t = -1.43[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.05 and 50 - 1 = 49 df is of [tex]t^{\ast} = -1.677[/tex]
Since the test statistic is more than the critical value for the left-tailed test, this is not strong evidence that they have failed to attain their fuel economy goal.
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Which economic indicator measures the change in prices of specific goods and services over time?
A.
Price Change Rate
B.
Consumer Price Schedule
C.
Consumer Price Index
Answer:
C. Consumer Price Index
Step-by-step explanation:
The Consumer Price Index is based on the cost of a specific shopping list of goods. It is published monthly by the US Bureau of Labor Statistics.
Find the equation of the line that Contains the point (4,-2) and is perpendicular to the line y = -2x+5
Which two figures have the same number of lateral faces?
Answer:
Cube and cuboid
Both have 6 faces
Answer:
Cube and cuboid
Both have 6 faces
g Delta Airlines is trying to determine if pilots are deliberately slowing down during a labor dispute. They know that their all their flights have a mean late time of 12.8 minutes with a standard deviation of 6.8 minutes. They took a random sample of 31 flights during the dispute and found they were 15.1 minutes late on average. Using a significance level of 0.05, is there any evidence to back the pilots claim that they are not slowing down?
Answer:
[tex]t=\frac{15.1-12.8}{\frac{6.8}{\sqrt{31}}}=1.883[/tex]
[tex]p_v =P(t_{30}>1.883)=0.0347[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12.8 at 5% of signficance and the claim makes sense.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X=15.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=6.8 represent the sample standard deviation
n=31 represent the sample size
Solution to the problem
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the pilots claim that they are not slowing down, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 12.8[/tex]
Alternative hypothesis:[tex]\mu > 12.8[/tex]
Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{15.1-12.8}{\frac{6.8}{\sqrt{31}}}=1.883[/tex]
P-value
The degrees of freedom are given by:
[tex] df = n-1=31-1=30[/tex]
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{30}>1.883)=0.0347[/tex]
Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12.8 at 5% of signficance and the claim makes sense.
Write an algebraic equation for the situation:
Daniel is six inches shorter than Ernie, how y’all is Daniel
Answer:
ernie=X so Daniel = X-6
Step-by-step explanation:
The variable, the number of hours Daniel worked, is modeled by an orange x tile. Working 3 times as many hours is modeled with 3 orange x tiles. The multiplication expression that represents the situation is 3x.y-
The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have thelr weddings in the Caribbean. A Caribbean vacation resort recently advertised In Bride Magazine that the cost of a Caribbean wedding was less than $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised? 29.7 29.4 31.7 29.0 29.1 30.5 29.1 29.8 Excel Data a. State the null hypothesis and the alternate hypothesis. (Enter your answers in thousands of dollars.) b. State the decision rule for 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) H0 if t c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) of the test statistic d. What is the conclusion regarding the null hypothesis? o not reject cost is not less n $30 Reference links for lation Mean ulation Sta
Answer:
Step-by-step explanation:
The mean of the set of data given is
Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.788 = $29788
Standard deviation = √(summation(x - mean)/n
n = 8
Summation(x - mean) = (29700 - 29788)^2 + (29400 - 29788)^2 + (31700 - 29788)^2 + (29000 - 29788)^2 + (29100 - 29788)^2 + (30500 - 29788)^2 + (29100 - 29788)^2 + (29800 - 29788)^2 = 5888752
Standard deviation = √(5888752/8) = 857.96
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ < 30000
For the alternative hypothesis,
µ > 30000
It is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 29788
µ = population mean = 30000
s = samples standard deviation = 857.96
t = (29788 - 30000)/(857.96/√8) = - 0.7
We would determine the p value using the t test calculator. It becomes
p = 0.253
Since alpha, 0.05 < than the p value, 0.253, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data did not show evidence that the mean wedding cost is not less than $30,000 as advertised
7/15+(-5/6)
What is the answer and how do I get it?
Answer:
-0.36666666666...
Step-by-step explanation:
not sure how to explain, that's a repeating number.
Round 67.62 to
the nearest whole
number.
Assume that random guesses are made for ninenine multiple choice questions on an SAT test, so that there are nequals=99 trials, each with probability of success (correct) given by pequals=0.50.5. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 44.
Answer:
The probability that the number of correct answers is 4 is 0.2461.
Step-by-step explanation:
Let X = number of correct answers.
The probability that an answer is correct is,P (X) = p = 0.50.
The total number of questions is, n = 9.
The event of an answer being correct is independent of the other answers.
The success of each trial is defined as a correct answer with equal probability of success for each trial, i.e. 0.50.
The random variable X follows a Binomial distribution with parameter n = 9 and p = 0.50.
The probability mass function of X is:
[tex]P(X=x)={9\choose x}\times0.50^{x}\times (1-0.50)^{9-x};\ x=0,1,2,3...[/tex]
Compute the value of P (X = 4) as follows:
[tex]P(X=4)={9\choose 4}\times(0.50)^{4}\times (1-0.50)^{9-4}[/tex]
[tex]=126\times 0.0625\times 0.03125\\=0.24609375\\\approx 0.2461[/tex]
Thus, the probability that the number of correct answers is 4 is 0.2461.
(I need help ASAP)
- Which name doesn’t apply to the figure?
A. square
B. rhombus
C. parallelogram
D. quadrilateral
Answer:
A- square
Step-by-step explanation:
A square should have 4 right angles.
Which of the hypotheses below would be suited for testing with a one-variable chi-square test? It was hypothesized that more people would choose the number 7 as their 'lucky' number than any other number. People who choose the number 7 as their 'lucky' number are significantly more superstitious than people who choose the number 13 as their 'lucky' number. Choice of 'lucky' number is directly related to measures superstition. All of these.
Answer:
It was hypothesized that more people would choose the number 7 as their 'lucky' number than any other number.
Step-by-step explanation:
Given that one variable chi-square is used to test whether a single categorical variable follows a hypothesized population distribution. The Chi Square statistic compares the tallies or counts of categorical responses between two (or more) independent groups
The null hypothesis (H0) for the test is that all proportions are equal.
The alternate hypothesis (H1) is given condition in the question.
A. It was hypothesized that more people would choose the number 7 as their 'lucky' number than any other number.
This is suited for testing with a one-variable chi-square test because we are testing if the proportion of people who choose number 7 is greater than the proportion of any other numbers. So, we are therefore comparing more than 2 proportions.
B. People who choose the number 7 as their 'lucky' number are significantly more superstitious than people who choose the number 13 as their 'lucky' number.
This is not suited for testing with a one-variable chi-square test. A z test is more preferable in this instance because we are testing just two proportions.
C. Choice of 'lucky' number is directly related to measures superstition.
This is not suited for testing with a one-variable chi-square test because chi square test is not used for showing relationship between variables.
D. All of these. Since option A is correct, this option can not be correct.
A Starbucks coffee costs $4.50. What is the total price if the sales tax rate is 7%?
Answer:
$4.815
Step-by-step explanation:
4.50 x 7/100=0.315
then add 4.50+0.315=4.815
Prove that the diagonals of a parallelogram bisect each other.
Name the coordinates for point C.
A: (2a, 2b + 2c)
B: (2a, 2b)
C: (2a, 2c)
D: (2a + 2b, 2c)
Answer:2a + 2b, 2c
Step-by-step explanation:
3 friends are sharing 1/2 of a blueberry ....how much pie would each friend get
Answer:
each friend would get 1/6 when you divide 1/2 by 3
Step-by-step explanation:
Each friend receives 1/6 of the pie.
The student asked how much pie each of three friends would get if they share 1/2 of a blueberry pie. To find the answer, you simply divide the half of the pie by three, since there are three friends sharing it. That is, 1/2 ÷ 3.
You can think of this division as splitting the 1/2 of the pie into three equal parts. Each friend would get 1/6 of the pie, because 1/2 ÷ 3 = 1/6. This intuitively makes sense because if a pie is cut into six equal slices, three slices (which is half the pie) can be shared by three friends, giving each one slice.
what is two plus two
Answer:
4
Step-by-step explanation:
Question- what is two plus two
Answer- 2+2=4
The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohm's Law, V = IR, to find how the current I is changing at the moment when R = 337Ω, I = 0.01A, dV/dt = -0.07V/s, and dR/dt = 0.06Ω/s. (Round your answer to six decimal places.)
Answer:
The current is decreasing at a rate 0.000209 ampere per second.
Step-by-step explanation:
We are given the following in the question:
[tex]R = 337\Omega\\I = 0.01 A\\\\\dfrac{dV}{dt} = -0.07\text{ V/s}\\\\\dfrac{dR}{dt} = 0.06\text{ ohm/s}[/tex]
According to the Ohm's Law:
V = IR
Differentiating we get,
[tex]\dfrac{dV}{dt} = I\dfrac{dR}{dt} + R\dfrac{dI}{dt}[/tex]
Putting values, we get,
[tex]-0.07 = (0.01)(0.06)+ (337)\dfrac{dI}{dt}\\\\(337)\dfrac{dI}{dt} = -0.07-(0.01)(0.06) =-0.0706\\\\\dfrac{dI}{dt} = \dfrac{-0.0706}{337} = -0.000209\text{ A/s}[/tex]
Thus, the current is decreasing at a rate 0.000209 ampere per second.
A teacher interested in determining the effect of a new computer program on learning to read conducted a study. One hundred students were randomly assigned to one of two groups. The first group used the computer program while the second group did not. Both groups were tested to determine how much their reading levels improved. The results for the two groups were compared. What kind of study is this?
1.This is an experiment because a treatment was applied to a group.
2.This is an experiment because students were able to choose which group to join.
3.This is a survey because students were randomly assigned to groups.
4.This is a survey because a treatment was applied to both groups
Answer:
c
Step-by-step explanation:
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.049.0 and 54.054.0 minutes. Find the probability that a given class period runs between 51.2551.25 and 51.7551.75 minutes. Find the probability of selecting a class that runs between 51.2551.25 and 51.7551.75 minutes.
Answer:
10% probability that a given class period runs between 51.25 and 51.75 minutes.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability of finding a value X between c and d, d greater than c, is given by the following formula:
[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]
Uniformly distributed between 49 and 54 minutes
This means that [tex]b = 54, a = 49[/tex]
Find the probability that a given class period runs between 51.25 and 51.75 minutes.
[tex]P(51.25 \leq X \leq 51.75) = \frac{51.75 - 51.25}{54 - 49} = 0.1[/tex]
10% probability that a given class period runs between 51.25 and 51.75 minutes.
How do I find the complement?
Let U={1,2,3,6,10,13,14,16,17} . Determine the complement of the set {3,10,16}
Let A be some subset of a universal set U. The "complement of A" is the set of elements in U that do not belong to A.
For example, if U is the set of all integers {..., -2, -1, 0, 1, 2, ...} and A is the set of all positive integers {1, 2, 3, ...}, then the complement of A is the set {..., -2, -1, 0}.
Notice that the union of A and its complement make up the universal set U.
In this case,
U = {1, 2, 3, 6, 10, 13, 14, 16, 17}
The set {3, 10, 16} is a subset of U, since all three of its elements belong to U.
Then the complement of this set is all the elements of U that aren't in this set:
{1, 2, 6, 13, 14, 17}
The complement of a set A with respect to a set B includes elements in B that are not in A. The complement of the set {3,10,16} within {1,2,3,6,10,13,14,16,17} is {1,2,6,13,14,17}. The process involves removing elements in A from B.
Explanation:In mathematics, specifically in set theory, the complement of a set A, with respect to a set B, refers to the elements in set B that are not in set A. Let's use this definition to find the complement of {3,10,16} in the universal set U={1,2,3,6,10,13,14,16,17}.
First, list all the elements in U. Next, remove those elements which appear in the set {3,10,16}. The remaining elements constitute the complement of {3,10,16} given U. With this procedure, we find that the complement of {3,10,16} with respect to U is {1,2,6,13,14,17}. This method can be applied to any sets within a given universal set to find their complements.
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The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces and a standard deviation of 4.5 ounces. 10 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( 15 , 4.5 ) What is the distribution of ¯ x ? ¯ x ~ N( 15 , ) What is the probability that one randomly selected person drinks between 14.5 and 16.5 ounces of coffee per day? For the 10 people, find the probability that the average coffee consumption is between 14.5 and 16.5 ounces of coffee per day. For part d), is the assumption that the distribution is normal necessary? YesNo Find the IQR for the average of 10 coffee drinkers. Q1 = ounces Q3 = ounces IQR: ounces
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: the amount of coffee a person drinks per day. (ounces)
This variable has a normal distribution with μ= 15 ounces and σ=4.5 ounces.
10 randomly selected persons where surveyed.
a) X~N(μ;σ²) ⇒ X~N(15;20.25)
b) The sample means has the same distribution as the original variable except that the population variance is affected by the sample size:
X[bar]~N(μ;σ²/n) ⇒ X[bar]~N(15;20.25/10) ⇒ X[bar]~N(15;2.025)
c)
You need to find the probability that one random person drinks between 14.5 and 16.5 ounces of coffee per day, symbolically:
P(14.5 ≤ X ≤ 16.5)
For this part, since you need to calculate the probability that one person drinks between 14.5 and 16.5 ounces of coffee daily out of the whole population of people that drink coffee, you have to work using the distribution of the variable:
X~N(15;20.25)
To reach the correspondent probability you have to first standardize both bonds of the interval using Z=(X-μ)/δ~N(0;1):
P(14.5 ≤ X ≤ 16.5)
P(X ≤ 16.5) - P(X ≤ 14.5)
P(Z≤ (16.5-15)/4.5) - P(Z≤ (14.5-15)/4.5)
P(Z≤ 0.33) - P(Z≤ -0.11)= 0.62930 - 0.45620= 0.1731
d)
In this item, you need to calculate the probability that one out of the ten people surveyed drinks on average between 14.5 and 16.5 ounces of coffee.
P(14.5 ≤ X[bar] ≤ 16.5)
To calculate the correspondent probability you have to work using the distribution od the sample mean: X[bar]~N(15;2.025) and the standard normal: Z=(X[bar]-μ)/(δ/√n)~N(0;1)
P(X[bar] ≤ 16.5) - P(X[bar] ≤ 14.5)
P(Z≤ (16.5-15)/1.42) - P(Z≤ (14.5-15)/1.42)
P(Z≤ 1.06) - P(Z≤ -0.35)= 0.85543 - 0.36317= 0.49226
e)
Yes. Without the assumption that the variable had a normal distribution, you wouldn't be able to use the standard normal distribution to calculate the asked probabilities.
There is a possibility to apply the Central Limit Theorem to approximate the sampling distribution to normal if the sample was large enough (n ≥30) which is not the case.
f)
You need to find the IQR for the average consumption of coffee for a sample of 10 persons.
For this, you have to work using the distribution of the sample mean X[bar]~N(15;2.025)
The 1st quartile is the value that divides the bottom 25% of the distribution from the top 75%, symbolically:
P(X[bar]≤x[bar]₀)= 0.25
First, you have to determine the value of Z that accumulates 0.25 of probability:
P(Z≤z₀)= 0.25
z₀= -0.674
Now using the formula Z=(X[bar]-μ)/(δ/√n), you have to "reverse" the standardization, i.e. clear the value of X[bar]:
z₀=(x[bar]₀-μ)/(δ/√n)
-0.674=(x[bar]₀-15)/1.42
-0.674*1.42= (x[bar]₀-15)
x[bar]₀= (-0.674*1.42)+15
1st Quartile x[bar]₀= 14.0429 ounces
The third quartile is the value that divides the bottom 75% of the distribution from the top 25% of it:
P(X[bar]≤x[bar]₀)= 0.75
As before, the first step is to determine the corresponding value of Z:
P(Z≤z₀)= 0.75
z₀= 0.674
z₀=(x[bar]₀-μ)/(δ/√n)
0.674= (x[bar]₀-15)/1.42
0.674*1.42= x[bar]₀-15
x[bar]₀= (0.674*1.42)+15
3rd Quartile x[bar]₀= 15.9571
The IQR is the difference between Q3 and Q1:
IQR= 15.9571 - 14.0429= 1.9142
I hope this helps!
An amusement park has a diameter of 975 feet and has a circular walking path around the entire park. the maintenance worker has to walk around the park 3 times a day how far does he walk a day
Answer: 2925 feet a day
Step-by-step explanation:
you gotta multiply 975 x 3 and you gonna 2925.
How many 1 sixths are in 2 and why !!!! PLeASE HURRY
Round 7.6378 to the nearest 0.1
Answer:
7.64
Step-by-step explanation:
What -3 as a decimal
Answer:
-0.03
Step-by-step explanation:
Answer:
-.03 hope this helps
The problem I need to solve is rt=w and I need to solve for r I need help
Answer:
r = w/t
Step-by-step explanation:
To solve this problem, we need to isolate the variable r, or get it alone by itself on the left side of the equation. To do this, we must get rid of the t. Since the r and t are multiplied together, we must divide by t to get the r alone. This is modeled below:
rt = w
rt/t = w/t
r = w/t
Hope this helps!