There are 720 different choices if order matters and there are 120 different choices if order does not matter.
Calculating the number of different choicesa) If order matters,
The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).
So the total number of choices is:
10 x 9 x 8 = 720
Therefore, there are 720 different choices if order matters.
b) If order does not matter,
We need to divide the number of choices by the number of ways the three numbers can be arranged.
Since there are 3 numbers, they can be arranged in 3! = 6 ways.
So the number of choices when order does not matter is:
(10 x 9 x 8) / 6 = 120
Therefore, there are 120 different choices if order does not matter.
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Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1,5) y P₂=(-2,-6)
Cómo resolver este ejercicio de ecuaciones lineales de dos puntos
The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)
In mathematics, how do you find coordinates?To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.
It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.
We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)
Using the values provided:
P1 = (-1.5, Y1) (-1.5, Y1)
P2 = (-2, -6) (-2, -6)
These values can be used as substitutes in the formula:
m = (-6 - Y1) / (-2 - (-1.5))
Making the denominator simpler:
m = (-6 - Y1) / (-2 + 1.5)
m = (-6 - Y1) / (-0.5)
m = 12 + 2Y1
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Question:
Formula: m=;
X₂-X1
P₁ = (X₁, Y₁) P₂ = (X2, Y₂)
1) P₁=(-1.5) and P₂=(-2,-6)
How to solve this exercise of linear equations of two points.
Part A: Graph the system of equations {−2x+y=6x−y=1
Part B: Determine the solution from Part A.
Answer:
Step-by-step explanation:
An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.
Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)
From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).
PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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a particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. twenty fish are placed in a tank containing this concentration of chemical in water. a find the probability that exactly 14 survive. b find the probability that at least 10 survive.
A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore
a. The probability that exactly 14 fish survive is 0.263b. The probability that at least 10 fish survive is 0.983How do we calculate the probability?a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263
b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.
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Exercise 16.8. Prove Theorem 16.8 following the outline below: Let p be a prime number that is irreducible in Zi]. We wish to show that Z,[i] is a field. Let [c] + [d]i be a nonzero element of Zp[i], with [c] and [d] in Zp. (Thus we may take c and d to be integers representing their congruence classes.) We need to prove that [cl+ Idi is a unit. 1. Notice that [c +(di is a unit if one of [e and [d is [0 and the other is not. 2. Having taken care of the case in which one of [c and [d is the zero congruence class in Zp, suppose now that [cj and [d are both nonzero elements of Zp[i]. Observe that in Zj, the prime p cannot divide c + di (why?), so that p and c+ di are relatively prime. 3. Deduce that in this case, by Theorem 16.7, there exist Gaussian integers r and s such that (c + d)r = 1 + ps. 4. Supposer e fi for integers e and f. Deduce that in Zp[l. 5. Conclude that Zpli] is a field.
The theorem is Every nonzero element in the ring has an inverse, hence we deduce that Z[i]/(p) is a field. For any prime number p that is irreducible in Z[i], as asserted, Z[i]/(p) is a field.
Proof of Theorem is Let p be a prime number that is irreducible in Z[i]. We want to show that Z[i]/(p) is a field, where (p) denotes the ideal generated by p.
Suppose that [c] + [d]i is a nonzero element of [tex]Z[i]/(p)[/tex], where [c] and [d] are congruence classes in Zp.
If one of [c] and [d] is [0], then [c] + [d]i is a unit, since the other element is nonzero. So, suppose that [c] and [d] are both nonzero in Zp.
We observe that p cannot divide c + di in Z[i] since p is irreducible in Z[i] and it cannot divide both c and d. Therefore, p and c + di are relatively prime in Z[i].
By Theorem 16.7, there exist Gaussian integers r and s such that [tex](c + di)r = 1 + ps.[/tex]
Now, suppose that [e] + [f]i is another nonzero element of Z[i]/(p), where [e] and [f] are congruence classes in Zp. We want to show that [e] + [f]i is also a unit.
Since p and c + di are relatively prime, there exist integers u and v such that [tex]pu + (c + di)v = 1[/tex] , by Bezout's identity.
Multiplying both sides by e + fi, we get:
[tex]pue + (c + di)ve + (ce - df) + (cf + de)i = e + fi[/tex]
Therefore, [tex](e + fi)(ue + vi(c + di)) = (e + fi)(1 - (cf + de)i)[/tex]
Multiplying both sides by the conjugate of (e + fi), we get:
[tex](e + fi)(e - fi)(ue + vi(c + di)) = (e^2 + f^2)[/tex]
Since p is irreducible in Z[i], it is also prime. Thus, Z[i]/(p) is an integral domain, which means that the product of two nonzero elements is nonzero. Therefore, [tex]e^2 + f^2[/tex] is nonzero in Zp, and
so [tex](e + fi) (ue + vi(c + di))[/tex] is a unit in Z[i]/(p).
We conclude that Z[i]/(p) is a field since every nonzero element has an inverse in the ring.
Therefore, Z[i]/(p) is a field for any prime number p that is irreducible in Z[i], as claimed
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a. in the sample: i. what is the average value of birthweight for all mothers? ii. for mothers who smoke? iii. for mothers who do not smoke? b. i. use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. what is the standard error for the estimated difference in (i)? iii. construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers.
a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.
ii. For mothers who smoke is 6.82 pounds.
iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:
Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
w = 28 miles
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides.
The sum of the lengths of the sides is w + 28 + 28.
The perimeter is 84.
w + 28 + 28 must equal 84.
w + 28 + 28 = 84
Now we solve for w.
Add 28 and 28.
w + 56 = 84
Subtract 56 from both sides.
w = 28
Answer: w = 28 miles
A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using ἁ =0.05 instead of ἁ =0.05
c. using ἁ =0.05 instead of ἁ =0.01
d. giving the drug to 25 randomly selected students instead of 50.
e. using a two-sided test instead of a one-sided test.
The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.
The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.
To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.
However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.
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Angela made 23 cards for her friends. She wants to make 19 more cards. How many cards will she make in all?
By using addition calculation, we determine that Angela will end up making 42 cards in total.
Angela made 23 cards for her friends, but she wants to make even more to share with others. To determine how many cards she will make in total, we need to add the number of cards she has already made with the number of cards she plans to make.
So, we add 23 (the number of cards she has made) and 19 (the number of cards she plans to make) so in total, she will make:
23 + 19 = 42
Therefore, Angela will make 42 cards in all.
By using simple arithmetic calculation of basic addition, we find that Angela will make 42 cards in all.
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11x + 9y=-20 x= -5y-6
Use substitution method pls
The solution to the system of equations is (x, y) = (1, -1) where the given equations are 11x+9y=-20 and x=-5y-6.
What is substitution method?The substitution method is a technique used in algebra to solve systems of equations by replacing one variable with an expression containing another variable. The goal is to eliminate one of the variables so that we can solve for the other one.
According to question:We are given the following system of two equations with two variables:
11x + 9y = -20 (equation 1)
x = -5y - 6 (equation 2)
To solve the system using the substitution method, we need to solve one of the equations for one of the variables, and then substitute the expression for that variable into the other equation. Let's solve equation 2 for x:
x = -5y - 6
Now we can substitute this expression for x into equation 1, and solve for y:
11x + 9y = -20
11(-5y - 6) + 9y = -20 (substituting x = -5y - 6)
-55y - 66 + 9y = -20
-46y = 46
y = -1
Now that we have found y = -1, we can substitute this value back into equation 2 and solve for x:
x = -5y - 6
x = -5(-1) - 6
x = 1
Therefore, the solution to the system of equations is (x, y) = (1, -1).
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1. Describe the relationship you see between elevation and temperature in these data sets.
In response to the stated question, we may state that The scatter plot indicates a clustering pattern in the data, and as elevation increases, temperature drops.
What exactly is a scatter plot?"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."
"A scatter plot is also known as a scatter chart, scattergram, or XY graph. The scatter diagram plots numerical data pairings, one variable on each axis, to demonstrate their connection."
Because the graph is a scatter plot, the data displays a clustering pattern.
We may deduce from the figure that as height increases, temperature falls.
As a result, C and E are the proper choices.
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The correct question is -
The scatter plot shows the relationship between elevation and temperature on a certain mountain peak in North America. Which statements are correct?
A. The data shows one potential outlier
B. The data shows a linear association
C. The data shows a clustering pattern
D. The data shows a negative association
E. As elevation increases, temperature decreases
trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 11 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 99 and 128 miles in a day. round your answer to four decimal places.
The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
What is the standard deviation?Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.
The formula for the probability that a truck drives between 99 and 128 miles in a day is:
[tex]Z = (X - \mu) /\sigma[/tex]
where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:
[tex]Z = (99 - 120) / 11 = -1.91[/tex]
The value of Z for 128 miles driven per day is:
[tex]Z = (128 - 120) / 11 = 0.73[/tex]
Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:
[tex]P(-1.91 < Z < 0.73) = 0.7734[/tex]
Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.
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Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
You answer would be mate it would be x=66
2 Rema has two jobs. In one year, she worked 276 hours at her first job. In the same year, she worked 3 times the number of hours at her second job. How many hours did Rema work that year at her second job?
Answer:
Step-by-step explanation:
Kind of like rema from the song calm down calm down!!
you an find it on youtub
Will give brainly award
Using the other endpoint of the diameter, and the center of the circle write an equation of the circle
Answer:
Step-by-step explanation:
C(1,2), radius=6
Equation using [tex](x-h)^2+(y-k)^2=r^2[/tex]:
[tex](x-1)^2+(y-2)^2=36[/tex]
What is the number of normal subgroups of order 7 in a group of order 14?
In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,
we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.
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An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 24.1 minutes.
find
A. The 95% confidence interval is (,)
B.The 99.5% confidence interval is(,)
C. A surgeon claims that the mean surgery time is between 133.71 and 140.09 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.
D. Approximately how many surgeries must be sampled so that a 95% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
F.Approximately how many surgeries must be sampled so that a 99% confidence interval will specify the mean to within ±3 minutes? Round up the answer to the nearest integer.
The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by, (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).
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Fill in the blank A ____ is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution
answer options are
histogram
frequency polygon
scatterplot
normal quantile plot
Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.
What is a Normal Quantile Plot?
A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.
It plots sample data versus a theoretical normal distribution.
In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.
A normal quantile plot can be used to evaluate the following:
Whether or not a data set is normally distributedA data set's skewnessA data set's outliersA data set's center and spread whether or not a transformation is required to make a data set normally distributed.The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The second figure.
Step-by-step explanation:
The first figure's perimeter is:
70 in + 42 in + 56 in = 168 inches.
And the second figure's perimeter is:
42 in + 33 in + 33 in + 64 in = 172 inches.
Therefore, Figure 1 < Figure 2.
What is the solution to the trigonometric inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2pi radians?
From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).
To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:
Rewrite the inequality in terms of tangent:
Divide both sides by cos(x) to get:
tan(x) > 1
Find the solutions of the equation tan(x) = 1:
tan(x) = 1 when x = π/4 or x = 5π/4.
Check the sign of tangent in the intervals between the solutions:
We need to check the sign of tan(x) for x values in the following intervals:
(0, π/4), (π/4, 5π/4), and (5π/4, 2π).
In the interval (0, π/4), tan(x) is positive and less than 1.
In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.
In the interval (5π/4, 2π), tan(x) is negative and less than -1.
Determine the solution set:
Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:
π/4 < x < 5π/4
In interval notation, we can write:
(π/4, 5π/4)
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What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.
what is Combination?In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.
The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:
[tex]nCk = n! / (k! *(n-k)!)[/tex]
where n! denotes the factorial of n, i.e., the product of all positive integers up to n.
by the question.
Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:
[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]
Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]
Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).
Since a_i >= 4 for i=1, we have:
[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]
Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:
[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]
This gives us:
[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]
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(1 point) Suppose f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x,y) comes before (z, w) if x
Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.
Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.
In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point
To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]
Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)
Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)
To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.
(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.
Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).
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Need help to solve this please!!
Answer:
0.999
Step-by-step explanation:
If the driver wore a seat belt, that is the only column we have to look at.
The chance the driver survived is number survived / number total.
Plugging in, we get 412,042/412,493, or about 0.999.
Hope this helps!
hi i want help with maths and the question i need help is
there are 32 students in a class and 20 of them owns at least one pet. what if the fraction of the class own pets? give answer in simplest form.
Get back to me quickly
Answer: 3/5
hope this helped you. Please brainliest! :D
Step-by-step explanation: If I am wrong tell me :D
make a simple linear regression model using education level as independent variable. if the education level is 14 years, the estimated annual income is
The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.
If the education level is 14 years,
To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.
This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.
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The bottom of a cylindrical container has an area of 10 cm2. The container is filled to a height whose mean is 4 cm, and whose standard deviation is 0.2 cm. LetVdenote the volume of fluid in the container. Find μV.
The value of μV is 40 cm³.
Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².
We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³
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Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
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Cindy rides her bike with a constant speed of 8 miles per hour how long will she take to a travel a distance of 2 miles
Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.
What is the formula for Time?The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.
What is the formula for Speed?The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.
In the given question,
We can use the formula:
time = distance / speed
where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.
Substituting the given values, we get:
time = 2 miles / 8 miles per hour
Simplifying, we get:time = 0.25 hours.
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If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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