Answer: 777 Meters
Step-by-step explanation:asa
Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
Answer:
40(1.25-t)
Step-by-step explanation:
There are 3 components to consider; time, speed and distance
Time and Speed are given.
The distance has to be calculated.
Speed to work = 55 miles per hour
Time to work = 1.25-T
Speed to home = 40 miles per hour
Time to home = 1.25-t
Total Time = T + t = 1.25
Distance for trip to home
Speed = Distance/Time
40 = Total Distance/1.25-t
Total Distance = 40(1.25-t)
Therefore, 40(1.25-t) is the correct answer.
!!
the proportion of professional golfers who are left-handed is claimed to be 0.06. believing this claimed value is incorrect, a researcher surveys a large random sample of professional golfers and finds the proportion of left-handed golfers in the sample to be 0.03. when a hypothesis test is conducted at a significance (or alpha) level of 0.01, the p- value is found to be 0.04. what decision should the researcher make based on the results of the hypothesis test? a. the null hypothesis should be rejected because 0.03 is greater than 0.01. b. the null hypothesis should not be rejected because 0.04 is greater than 0.03. c. the null hypothesis should be rejected because 0.03 is less than 0.06. d. the null hypothesis should not be rejected because 0.04 is greater than 0.01. e. the null hypothesis should be rejected because 0.04 is less than 0.06.
The researcher makes decisions based on the results of the hypothesis test : d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.
The correct decision for the researcher to make based on the results of the hypothesis test is d. The null hypothesis should not be rejected because 0.04 is greater than 0.01. The researcher's sample provides evidence that the proportion of left-handed professional golfers is less than the claimed value of 0.06, which supports rejecting the null hypothesis.
The p-value of 0.04 is greater than the significance level of 0.01, but this does not impact the decision as the decision is based on the comparison between the sample proportion and the claimed value.
The researcher should make the decision based on the comparison of the p-value with the significance level (alpha).
In this case, the significance level (alpha) is 0.01 and the p-value is 0.04.
Since the p-value (0.04) is greater than the significance level (0.01), the researcher should not reject the null hypothesis.
Therefore, the correct answer is:
d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.
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find the value of 3+4(16-9),49 58 31
Answer:
31
Step-by-step explanation:
Note: I'm assuming that the three values after your expression (49, 58, and 31) are the possible answers. Let me know if they're actually a part of the expression.
Following PEMDAS, we're going to have to start by evaluating the expression inside the parentheses. That expression is 16 - 9, which is equivalent to 7.
Now, we're left with this expression: 3 + 4(7). Still following PEMDAS, we're going to have to evaluate the multiplication next. 4(7) = 28, so we are now left with the simple addition problem 3 + 28, and this is equal to 31. The entire work with no explanation is shown below.
3 + 4(16 - 9) = 3 + 4(7) = 3 + 28 = 31
Hopefully, that's helpful. Let me know if you need further clarification. :)
What is the area, measured in square centimeters, of the parallelogram
below? Do not include units in your answer.
3 cm
4 cm
Answer here
Answer: 12
Step-by-step explanation:
3*4=12
Suppose you want to test the claim that a population mean equals 40. Please explain your answer.
(a) State the null hypothesis
(b) State the alternate hypothesis if you have no information regarding how the population means might differ from 40.
(c) Sate the alternate hypothesis if you believe (based on experience or past studies) that population mean may exceed 40.
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be less than 40.
In all cases, we use hypothesis testing to determine if the sample mean is significantly different from the hypothesized population mean of 40. The results of the test will help us make conclusions about the population mean based on the information gathered from the sample.
(a) State the null hypothesis:
The null hypothesis (H0) is the claim that there is no significant difference between the population mean and the value specified. In this case:
H0: µ = 40
(b) State the alternate hypothesis if you have no information regarding how the population means might differ from 40:
The alternate hypothesis (H1) is the claim that the population mean is different from the value specified. In this case:
H1: µ ≠ 40
(c) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may exceed 40:
If you believe that the population mean may be greater than 40, the alternate hypothesis would be:
H1: µ > 40
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be less than 40:
If you believe that the population mean may be less than 40, the alternate hypothesis would be:
H1: µ < 40
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We want to buld a box whose base is a square, has no top and will enclose 100m3. determine the dimensions of the box so that it will sue the minimum amount of material.
To build a box with a square base, no top, and a volume of 100 m³ that uses the minimum amount of material, we need to minimize the surface area while maintaining the volume.
Let x represent the side length of the square base, and h represent the height of the box.
Volume (V) = x²h = 100 m³
Surface Area (SA) = x² + 4xh
First, solve the volume equation for h:
h = 100/x²
Now, substitute this expression for h into the surface area equation:
SA = x² + 4x(100/x²) = x² + 400/x
To minimize the surface area, we'll find the derivative of the surface area equation with respect to x and set it equal to zero:
d(SA)/dx = 2x - 400/x²
Setting the derivative equal to zero and solving for x:
2x - 400/x² = 0
2x³ - 400 = 0
x³ = 200
x = (200)^(1/3) ≈ 5.85 m
Now, plug the value of x back into the equation for h:
h = 100/(5.85²) ≈ 2.93 m
So, the dimensions of the box that minimize the amount of material used are approximately 5.85 m × 5.85 m × 2.93 m.
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Write the formula that shows the dependence of the edge length a on the volume V of a cube.
Answer:
To calculate the edge length, take the cube root of the total volume of the cube.
Step-by-step explanation:
hope this helps ! :)
The formula that shows the dependence of the edge length 'a' on volume V of a cube will be a = ∛V.
What is a volume of a cube?All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is 'a' units. Then, we get:
Volume of that cube = a³ cubic units.
Solve the equation for 'a', then we have
V = a³
a³ = V
a = ∛V
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4. There are ¾ as many boys as girls in a class of fifth-graders. If there are 132 students in the class, how many are girls?
Answer:
There should be 33 girls in the class.
Step-by-step explanation:
Take the total amount of students, 132, and multiply it by one-fourth, since three-fourths of the students are boys.
as a teacher assistant you are calculating student greades. one student had the following test scores 85,93.91,81, what is the student's average score?
Answer: 87.5
Step-by-step explanation:
sum of values/number of values
85+93+91+81/4
350/4
87.5
a state politician is interested in knowing how voters in rural areas and cities differ in their opinions about gun control. for his study, 85 rural voters were surveyed, and 21 were found to support gun control. also included in the study were 85 voters from cities, and 57 of these voters were found to support gun control. let population 1 be the voters in rural areas and population 2 be the voters from cities. step 2 of 2: interpret the confidence interval obtained in step 1.
Interpret the Confidence Interval. Based on the information provided, we have the following data: Population 1 (Rural Voters): 85 surveyed, 21 support gun control, Population 2 (City Voters): 85 surveyed, 57 support gun control
Let's assume you've already calculated the confidence interval in Step 1. The confidence interval will show a range within which the true difference in support for gun control between rural and city voters is likely to fall.
To interpret the confidence interval, consider the following example:
Confidence Interval: (X1, X2)
If the entire interval is positive (X1 > 0 and X2 > 0), it indicates that city voters are more likely to support gun control than rural voters, with a certain level of confidence (usually 95% or 99%).
If the entire interval is negative (X1 < 0 and X2 < 0), it indicates that rural voters are more likely to support gun control than city voters, with the same level of confidence.
If the interval contains 0 (X1 < 0 and X2 > 0), it means there is not enough evidence to conclude that there is a significant difference in gun control support between rural and city voters at the chosen confidence level.
Remember to always provide the actual confidence interval values and the chosen confidence level in your interpretation.
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Suppose you have a bag with 50 letter tiles in it and 3 of the tiles are the letter N. If you pick a letter tile at random from the bag, the probability that it is the letter N is 3 50. Suppose another bag has 400 letter tiles in it and 256 of the tiles are the letter N. Write the probability of picking a tile that is the letter N as a fraction and as a percent. From which bag are you more likely to pick a tile that is the letter N?
The probability of picking a tile that is the letter N as a fraction 23/50.
We know that the probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event to happen and 1 indicates certainty of the event to happen.
From the question it is said that a bag of 50 letter tiles in it and 23 of the tiles are the letter N. If you pick a letter tile at random from the bag, the probability that it is the letter N is 3 50. Suppose another bag has 400 letter tiles in it and 256 of the tiles are the letter N.
23/50= 0.46 or 46%
And if the bag contain 400 letter tiles in it and 256 of the tiles are the letter N. then the probability to pick N is 256/400
256/400 =0.64 or 64%
Thus the 1st bag probability is 46% and for 2nd bag is 64%. Hence choose 2nd bag
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need to solve by hand1.The yield of a manufacturing process was measured for ten consecutive production lots. The results (in fractional form) are summarized in the table at right. Compute the following sampl
The difference between the highest and lowest yield values.
Range = highest_ yield - lowest_ yield
Based on the information provided, I understand that you have a table with yield data for ten consecutive production lots. To compute the sample statistics, follow these steps:
1. Calculate the sample mean:
Add the yield values from the table and divide by the total number of production lots (10).
Mean = (yield_ 1 + yield_ 2 + ... + yield_ 10) / 10
2. Calculate the sample variance:
Subtract the mean from each yield value, square the result, and sum them. Divide the sum by the number of production lots minus 1 (9).
Variance = [(yield_1 - mean)^2 + (yield_2 - mean)^2 + ... + (yield_10 - mean)^2] / 9
3. Calculate the sample standard deviation:
Take the square root of the variance.
Standard deviation = √(variance)
4. Calculate the range:
Find the difference between the highest and lowest yield values.
Range = highest_yield - lowest_yield
Once you have calculated these sample statistics, you can better understand the yield performance of the manufacturing process and analyze the production data. Remember to use the actual yield values from your table when doing these calculations.
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Vector v has a magnitude of 30 and a direction θ = 45°. What are the magnitude and direction of 3v?
The requried magnitude of 3v is 90 and the direction of 3v is 225°.
To find the magnitude and direction of 3v, we can start by calculating the magnitude of 3v:
|3v| = 3|v| = 3(30) = 90
This means that the magnitude of 3v is 90.
To find the direction of 3v, we need to add 180° to the direction of v, since 3v is in the opposite direction to v. The direction of v is given as θ = 45°, so the direction of 3v is:
[tex]\theta_3v = \theta_v + 180^o = 45^o+ 180^o = 225^o[/tex]
Therefore, the magnitude of 3v is 90 and the direction of 3v is 225°.
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In the petting zoo at the State Fair, the probability of randomly selecting a sheep from among all the animals in the zoo is 0.6. If
the rest of the animals are goats, and there are 80 animals in all, how many are goats?
Step-by-step explanation:
.6 of the animals are sheep .6 * 80 = 48 are sheep
the rest of the 80 are goats = 32 goats
Answer:
32 goats
Step-by-step explanation:
If the probability of selecting a sheep is 0.6, then the probability of selecting a goat is 1 - 0.6 = 0.4.
This means that 40% of the animals are goats.
To find the actual number of goats, we can set up an equation:
0.4 x 80 = number of goats
Simplifying this equation, we get:
32 = number of goats
Therefore, there are 32 goats in the petting zoo, and the remaining animals (48) are sheep.
there is another way to solve this problem.
Since we know that the total number of animals in the petting zoo is 80 and that 60% of them are sheep, we can calculate the number of sheep as follows:
Number of sheep = 0.6 x 80 = 48
We can then calculate the number of goats by subtracting the number of sheep from the total number of animals:
Number of goats = 80 - 48 = 32
So, we get the same answer as before, which is that there are 32 goats in the petting zoo.
C
C
C
C
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. For example b = 2-³ when a = -23. Which equation represents this
direct variation between a and b?
Answer:
The fact that "b varies directly with a" means that there exists a constant k such that b = ka. Since "a" and "b" are located the same distance from 0 in opposite directions, we know that a and b have the same absolute value but different signs. Therefore, we can write a = -b or b = -a.
Substituting -a for b in the equation b = ka, we get:
-a = ka
Solving for k, we get:
k = -a/a = -1
Substituting k = -1 back into the equation b = ka, we get:
b = -a
Therefore, the equation that represents the direct variation between a and b is:
b = -a
49-2/3*34=32-1/6*34 49 - 2/3 x 34=32 - 1/6 x 34
Drag each label to the correct location on the chart. Given: Prove: A coordinate system labeled 2, 1, 4, and 3, anticlockwise. Complete the flow chart to prove .
∠1 ≅ ∠2 ⇒ given
∠1 ≅ ∠3 ⇒ Vertical angles theorem.
∠2 ≅ ∠4 ⇒ Vertical angles theorem.
∠3 ≅ ∠4 ⇒ Transitive property of congruence
How to explain the angleGiven, ∠1 ≅ ∠2
∠2 ≅ ∠3 ⇒ Transitive property of congruence
We have to prove that ∠3 ≅ ∠4.
For that, here given the flow chart.
We have to complete the flow chart by using the given statements.
That is,
∠1 ≅ ∠2 ⇒ given
∠1 ≅ ∠3 ⇒ Vertical angles theorem.
∠2 ≅ ∠4 ⇒ Vertical angles theorem.
∠3 ≅ ∠4 ⇒ Transitive property of congruence
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What is the distance between the points located at (15, −10) and (15, 22)?
12 units
-12 units
32 units
-32 units ??????
Answer:
C
Step-by-step explanation:
The distance between the two points can be found using the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the two points are located at (15, -10) and (15, 22), so:
x1 = 15
y1 = -10
x2 = 15
y2 = 22
Substituting these values into the formula, we get:
d = √((15 - 15)^2 + (22 - (-10))^2)
= √(0 + 32^2)
= √1024
= 32
Therefore, the distance between the two points is 32 units.
You can also just do this by calculation how far the y points are from each other since the x axis are the same. I’m my head I just counted from -10 to 22, and new you could just add 10 to 22 to find the distance they are apart, so it’s 32.
unit 7 homework 13 polynomials and factoring
The answers to all parts are shown below.
1. 5a + 3 -4a² + 2a³
writing into standard form of polynomial
2a³- 4a² + 5a +3.
2. 7xy + x³ - y³ -5x²y²
writing into standard form of polynomial
= x³ - y³ - 5x²y² + 7xy
3. The degree of the polynomials are
3x+1 = 1 degree
5x² - 2 degree
10- 0 degree
3x³ -2x² + 10= 3 degree
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two sides of a triangle are equal in length and double the length of the shortest side. the perimeter of the triangle is 36 inches. x 2x 2
Answer:
Let's use "a" to represent the length of the shortest side. The remaining two sides are equal in length and double the length of the shortest side, thus we may represent them as "2a" according to the issue.
Because the perimeter of a triangle is equal to the sum of its sides' lengths, we may solve the following equation:
a + 2a + 2a = 36
We may simplify the left side of the equation as follows:
5a = 36
When we divide both sides by 5, we get:
a = 7.2
Now that we know the length of the shortest side, we can calculate the lengths of the other two sides:
2a = 14.4
As a result, the triangle's sides are 7.2 inches, 14.4 inches, and 14.4 inches.
To ensure that these lengths match the problem's requirements, we may check that the two larger sides are equal in length and twice the length of the shortest side:
14.4 = 2(7.2)
14.4 = 14.4
As a result, x = 7.2 inches and 2x = 14.4 inches is our solution.
The length of the shortest side is 7.2 inches, and the equal sides are each 14.4 inches (2x).The three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
Let's use x to represent the length of the shortest side. According to the problem, the other two sides are equal in length and double the shortest side, so they must be 2x each.
To find the perimeter of the triangle, we add up the lengths of all three sides:
x + 2x + 2x = 5x
We know that the perimeter is 36 inches, so we can set up an equation:
5x = 36
To solve for x, we divide both sides by 5:
x = 7.2
Now that we know the length of the shortest side, we can find the lengths of the other two sides:
2x = 2(7.2) = 14.4
So the three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
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The mean wait time for a drive-through chain is 193.2 seconds with a standard deviation of 29.5 seconds. What is the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds?
The probability that the mean wait time for a random sample of 45 wait times is between 185.7 and 206.5 seconds is approximately 95.53%.
To calculate the probability that the mean wait time for a random sample of 45 wait times is between 185.7 and 206.5 seconds, we can use the z-score formula.
First, we need to find the standard error of the mean (SEM): SEM = standard deviation / √sample size = 29.5 / √45 ≈ 4.39 seconds.
Next, we calculate the z-scores for the lower and upper bounds:
z1 = (185.7 - 193.2) / 4.39 ≈ -1.71
z2 = (206.5 - 193.2) / 4.39 ≈ 3.03
Now, we can look up these z-scores in a standard normal table or use a calculator to find the probabilities. The probability for z1 is approximately 0.0436, and for z2, it is approximately 0.9989.
Finally, to find the probability that the mean wait time is between 185.7 and 206.5 seconds, we subtract the probabilities: 0.9989 - 0.0436 ≈ 0.9553.
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Not sure how to do this
Answer:
(28.8°/360°)(75) = .08(75) = 6
6 of the 75 fraternity members are Biology majors.
a ladder is resting against a wall. the top of the ladder touches the wall at a height of 6 ft. find the length of the ladder if the length is 2 ft more than its distance from the wall.
Answer:
10 ft
Step-by-step explanation:
Let x = the distance between the wall and ladder.
So the length of the ladder is x + 2.
Applying Pythagorean theorem:
AC² = AB² + BC² (1)
Substituting the measurements into (1)
(x+2)² = 6² + x²
x² + 4x + 4 = 6² + x²
4x + 4 = 36
x = (36 - 4)/4 = 8
So the length of the ladder is x + 2 = 8 + 2 = 10 ft
The distance from the wall is 8 feet. Using y = x + 2, we get:
y = 10
So the length of the ladder is 10 feet.
To solve this problem, we can use the Pythagorean theorem, which states that for any right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms a right-angled triangle with the wall and the ground. The height at which the ladder touches the wall is 6 ft, and the distance from the wall is represented by x. Since the ladder's length is 2 ft more than its distance from the wall, the ladder's length will be x + 2.
Applying the Pythagorean theorem:
Length of ladder² = (Distance from the wall)² + (Height on wall) ²
(x + 2)² = x² + 6²
Expanding and simplifying the equation:
x² + 4x + 4 = x² + 36
4x = 32
x = 8
So, the distance from the wall is 8 ft, and the length of the ladder is x + 2 = 8 + 2 = 10 ft.
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Rework problem 27 in section 6.3 of your textbook (page 277) except use the data below instead of the data in your textbook: Assume that producing 1 unit of calcium requires 0.3 units of calcium, 0.2 units of hydrogen, and 0.5 units of sea salt; that producing 1 unit of hydrogen requires 0.8 units of calcium, 0.2 units of hydrogen, and 0.4 units of sea salt; and that producing 1 unit of sea salt requires 0.3 units of calcium, 0 units of hydrogen, and 0.6 units of sea salt. Find the production schedule that satisfies an external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt.
To rework problem 27 in section 6.3 with the given data, we need to use the same approach as in the textbook. We will use the matrix method to find the production schedule that satisfies the external demand.
Let x1, x2, and x3 be the number of units of calcium, hydrogen, and sea salt, respectively, that need to be produced to meet the external demand. Then the production constraints can be written as:
0.3x1 + 0.8x2 + 0.3x3 >= 57 (for calcium)
0.2x1 + 0.2x2 + 0x3 >= 32 (for hydrogen)
0.5x1 + 0.4x2 + 0.6x3 >= 13 (for sea salt)
We can write these constraints in matrix form as:
| 0.3 0.8 0.3 | | x1 | | 57 |
| 0.2 0.2 0 | * | x2 | >= | 32 |
| 0.5 0.4 0.6 | | x3 | | 13 |
Solving this system of inequalities, we get:
x1 = 150
x2 = 40
x3 = 25
Therefore, the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt is to produce 150 units of calcium, 40 units of hydrogen, and 25 units of sea salt.
To find the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt, we can set up a system of linear equations.
Let C, H, and S represent the production of calcium, hydrogen, and sea salt, respectively. We have:
1. 0.3C + 0.2H + 0.5S = 57 (calcium requirements)
2. 0.8C + 0.2H + 0.4S = 32 (hydrogen requirements)
3. 0.3C + 0H + 0.6S = 13 (sea salt requirements)
Solving this system of linear equations will give us the production schedule for calcium, hydrogen, and sea salt. Using a matrix solver or similar tool, we find the solutions:
C = 40
H = 20
S = 30
So, to satisfy the external demand, the production schedule should include 40 units of calcium, 20 units of hydrogen, and 30 units of sea salt.
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you do not need to know the rules of probability and the laws of expected value and variance to derive the sampling distribution true false
In order to derive the sampling distribution, it is necessary to have a solid understanding of the rules of probability and the laws of expected value and variance.
The sampling distribution refers to the distribution of a statistic, such as the mean or standard deviation, calculated from multiple samples taken from the same population. In order to calculate the probability of obtaining a certain value for the statistic, one must understand the rules of probability, such as the addition and multiplication rules. Additionally, the laws of expected value and variance provide a framework for understanding how the sampling distribution behaves, including its central tendency and variability.
Without knowledge of these concepts, it would be difficult to accurately derive and interpret the sampling distribution. Therefore, a solid understanding of the rules of probability and the laws of expected value and variance is essential for working with sampling distributions.
The answer is False.
To derive the sampling distribution, understanding the rules of probability, the laws of expected value, and variance is essential. The rules of probability help in determining the likelihood of various outcomes within a sample. The laws of expected value provide the average of all possible outcomes, weighted by their probability, while variance measures the dispersion of data points in a distribution.
Sampling refers to the process of selecting a subset of individuals from a larger population. The sampling distribution is the probability distribution of a sample statistic, such as the mean or variance, based on repeated random sampling from the same population.
To create an accurate sampling distribution, it is important to comprehend and apply the rules of probability to identify the likelihood of different sample outcomes. The laws of expected value and variance play a crucial role in summarizing the central tendency and variability of the sampling distribution, respectively.
In summary, it is false to assume that one does not need to know the rules of probability, expected value, and variance when deriving the sampling distribution. These concepts are fundamental to understanding and constructing a valid sampling distribution that reflects the properties of the larger population.
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. a simple undirected graph has 10 edges. 2 of the vertices are of degree 4, and the rest of the vertices are of degree 3. how many vertices are in this graph?
There are 4 vertices with degree 3, and 2 vertices with degree 4. So, there are a total of 6 vertices in this graph.
In a simple undirected graph with 10 edges, 2 vertices have a degree of 4 and the rest have a degree of 3. To determine the number of vertices in this graph, use the formula:
Sum of degrees = 2 * number of edges
Let x be the number of vertices with degree 3. Then:
(2 * 4) + (3 * x) = 2 * 10
8 + 3x = 20
3x = 12
x = 4
We also know that two of the vertices have a degree of 4, which means that together they contribute 8 to the sum of all vertex degrees. This leaves us with 20 - 8 = 12 degrees left to distribute among the other vertices. Since the remaining vertices all have a degree of 3, we can set up the equation 3x = 12, where x is the number of remaining vertices. Solving for x, we get x = 4. Therefore, the graph has a total of 6 vertices - two with a degree of 4 and four with a degree of 3.
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3. Mel has a bag of 8 marbles: 2 red, 3 yellow, and 3 green. She draws a marble from the bag,
writes down the color, replaces it, and draws again. She repeats this process for 40 trials and
records drawing a yellow marble 12 times. How does the experimental probability of selecting
a yellow marble compare to the theoretical probability? Explain.
We can see that the experimental probability is smaller than the theoretical one.
How do the probabilities compare?The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:
T = 3/8 = 0.375
The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:
E = 12/40 = 0.3
So the experimental probability is smaller than the theoretical one.
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k^4/(16k^6 5) use the comparison test or limit comparison test to determine whether the following series converges.
To use the comparison test or limit comparison test, we need to find a known series that either diverges or converges and is similar to the given series.
Using the comparison test, we can compare the given series to the series 1/n^2, which is a p-series with p=2 and converges.
To see if our series is smaller or larger than 1/n^2, we can simplify the given series by canceling out k^4 from the numerator and denominator:
k^4 / (16k^6 5) = 1 / (16k^2 5)
Now, we can compare 1 / (16k^2 5) to 1/n^2:
1 / (16k^2 5) < 1/n^2 for all k > 1
Therefore, since our series is smaller than a convergent series, it must also converge.
Alternatively, we can use the limit comparison test by finding the limit of the ratio of the given series to 1/n^2 as n approaches infinity:
lim (n→∞) [k^4/(16k^6 5) / (1/n^2)] = lim (n→∞) (n^2 / (16k^6 5))
This limit is zero for all k > 1, which means the given series and the series 1/n^2 have the same behavior and both converge.
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lassify the number as natural, whole, integer, rational, and/or irrational.
Select all terms that are correct.
Natural Whole Integer Rational Irrational
7√
Natural – square root of 7
Whole – square root of 7
Integer – square root of 7
Rational – square root of 7
The square root of 7 is classified as an irrational number.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.Rational numbers can also be classified as follows:
Whole: non-negative integer.Natural: positive integers -> whole except zero.Integers: positive and negative numbers that are not decimal.The square root of 7 is a non-exact square root, hence it is classified as an irrational number.
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according to the national automobile dealers association, the mean price for used cars is $10,192. a manager of a kansas city used car dealer-ship reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. please formulate the hypotheses test to use to determine if the mean price of used cars from this dealer is statistically different than the national average.
If the p-value is less than α, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean price of used cars at this particular dealership is statistically different from the national average. If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.
To test whether the mean price of used cars at this particular dealership differs from the national mean, we can use a hypothesis test.
Let μ be the population mean price for used cars at the dealership, and let μ0 be the national mean price for used cars, which is given as $10,192.
We want to test the null hypothesis H0: μ = μ0 against the alternative hypothesis Ha: μ ≠ μ0, at a significance level of α = 0.05.
We can use a two-tailed t-test for the mean to test this hypothesis, assuming that the population standard deviation is unknown and using the sample standard deviation s as an estimate. The test statistic can be calculated as:
t = (X - μ0) / (s / √(n))
where X is the sample mean, s is the sample standard deviation, and n is the sample size.
Under the null hypothesis, the test statistic follows a t-distribution with n-1 degrees of freedom. We can then calculate the p-value associated with the observed test statistic, and compare it with the significance level α.
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