The answer to this question is 0.
To add the additive inverse to the product of - 1 and -4, we must first find the product of -1 and -4. The product of -1 and -4 is 4. Now that we have found the product of -1 and -4, we can add the additive inverse to it. The additive inverse of 4 is -4, so we add -4 to 4. 4+ (-4) is equal to 0. Therefore, the answer to this question is 0.
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What is the value of letter D on the number line?
Answer:
What is the value of the letter D on the number line?
Three and twenty-five hundredthsStep-by-step explanation:
You're welcome
the weights of steers in a herd are distributed normally. the standard deviation is 200lbs and the mean steer weight is 1400lbs . find the probability that the weight of a randomly selected steer is less than 1700lbs . round your answer to four decimal places.
The probability that the weight of a randomly selected steer is less than 1700lbs is 0.9772.
To solve this problem, we need to use the standard normal distribution with a mean of 0 and a standard deviation of 1. We can convert the given data into a standard normal distribution by using the formula:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a randomly selected steer weighs less than 1700lbs. So we need to find the z-score for 1700lbs:
z = (1700 - 1400) / 200
z = 1.5
We can then use a standard normal distribution table or calculator to find the probability that a z-score is less than 1.5. This probability is 0.9332.
However, since we want to find the probability that a randomly selected steer weighs less than 1700lbs (not less than or equal to), we need to add half of the probability of the z-score being exactly 1.5 to this result:
0.9332 + 0.0228 = 0.956
Therefore, the probability that a randomly selected steer weighs less than 1700lbs is 0.9772 (rounded to four decimal places).
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Darius wrote two integers on the chalkboard. The integers she wrote were 256 and -17. How much larger is 256 than -17?
Answer: 239
Step-by-step explanation:
Darius wrote 2 integers 256 and -17. The question is asking you to solve how much larger is 256 than -17. This means you will subtract 256 by -17 which will give you 239 (256-17). The answer remains positive because 256 is larger
Hope this helps
Answer: They are exactly 273 places away.
Step-by-step explanation:
If a number is larger than another number then you need to subtract it to get the distance. In this case, you look at the subtraction to see how far away they are.
Hope this helps!
Have a blessed day!
if you consume seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level, what is the probability that you consume one or more insect fragments in more than one bar?
The probability of consuming at least one insect fragment in more than one bar is 0.3011.
Given that you consumed seven 28.35-gram (one-ounce) bars this week from a brand at the mean contamination level. The probability of finding one or more insect fragments in a 28.35-gram chocolate bar that is produced with the mean level of contamination is 0.4875.
The probability that you consume one or more insect fragments in a single bar is 0.4875The probability that you will not consume an insect fragment in a single bar is 0.5125
The probability that you will not consume an insect fragment in any of the seven bars is 0.5125⁷ = 0.0236The probability that you consume one or more insect fragments in more than one bar is 1 - 0.0236 = 0.9764The probability that you consume one or more insect fragments in more than one bar is 0.9764.
The probability that you consume one or more insect fragments in more than one bar is 0.3011.
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PLEASE HELP WORTH 15 points CURRENTLY TAKING TEST, NEED ASAP
A- The Sum of the series is 2 - 20 + 200 .. is 2/11. B- the 12th term of the geometric sequence is option C -112.
We can observe that each term in the series is obtained by multiplying the previous term by -10.
Let the first term be a = 2, and the common ratio be r = -10.
Using the formula for the sum of an infinite geometric series, we have:
So = a / (1 - r)
So = 2 / (1 - (-10))
So = 2 / 11
So the sum of the given series is 2/11.
b- We can use the formula for the nth term of a geometric sequence to find the 12th term.
aₙ = a1×rⁿ-¹
where a1 is the first term and r is the common ratio.
We are given two terms in the sequence:
a7 = 7
a56 = ?
We can use these to find a1 and r.
First, we can find the common ratio:
r = a7 / a6 = 7 / (a7 / r) = 7 / a56
Next, we can use the formula to find a1:
aₙ = a2×rⁿ-¹
Substituting the values we know:
r = 7 / a56
Simplifying:
a1= a56^6
Now we can use the formula to find a12:
a12 = a1 * r^(12-1)
Simplifying:
a12 = 7^11 * a56^(-5)
Therefore, the 12th term of the sequence is a negative number, and the only negative option given is (c) -112. So the answer is (c) -112.
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For a segment of a radio show, a disc jockey can play 8 records. If there are 12 records to select from, in how many ways can the program for this segment be arranged?
Therefore , the solution of the given problem of unitary method comes out to be 495 possible configurations for the program for this section.
An unitary method is what?The objective can be accomplished by utilizing what has been expression learned thus far, making use of this global availability, and incorporating all essential components from earlier changeable study that utilized a particular method. If the anticipated claim result actually occurs, it will be feasible to contact the entity once more; otherwise, both important processes will undoubtedly miss the statement.
Here,
Order doesn't matter in a combination issue like this one. The combination algorithm is as follows:
=> C(n, r) = r! * (n-r)!
where r is the amount of options, and n represents the total number of options. In this instance, r = 8 and n = 12 (the total amount of records) (the number of records to play). Inserting the values:
=> C(12, 8) = 12! / (8! * (12-8)!)
=> 495
There are 495 possible configurations for the program for this section.
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That the question so yh I don't get it
Answer:
25 euros
Step-by-step explanation:
The ratio is 5:2. Sean received 10 euros. This means that Cheryl received 25 euros. You can multiply both sides of the ratio by 5 to get this answer.
this is the answer for the questions
suppose that the cumulative probability of a company defaulting by years one, two, three and four are 3%, 6.5%, 10%, and 14.5%, respectively. what is the probability of default in the fourth year conditional on no earlier default?
The probability of default in the fourth year conditional on no earlier default is 14.5%. Option (4).
The probability of default in the fourth year conditional on no earlier default is equal to the probability of default in the fourth year, given that the company did not default in the first three years.
Using the conditional probability formula, we can calculate this probability as follows:
P(Default in Year 4 | No earlier default) = P(Default in Year 4 and No earlier default) / P(No earlier default)
We can calculate the numerator by multiplying the probability of default in the fourth year (14.5%) by the probability of no earlier default, which is the complement of the sum of the probabilities of default in the first three years:
P(Default in Year 4 and No earlier default) = 0.145 x (1 - 0.03 - 0.065 - 0.10) = 0.145 x 0.705 = 0.102
The denominator is simply the probability of no earlier default, which we just calculated:
P(No earlier default) = 1 - 0.03 - 0.065 - 0.10 = 0.705
Now we can substitute these values into the conditional probability formula:
P(Default in Year 4 | No earlier default) = 0.102 / 0.705 = 0.1449, or approximately 14.5%
Therefore, the probability of default in the fourth year conditional on no earlier default is 14.5%.
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Full Question : Suppose that the cumulative probability of a company defaulting by years one, two, three and four are
3%, 6.5%, 10%, 14.5%,respectively. what is the probability of default in the fourth year conditional on no earlier default?
Which of the following is not a correct comparison among the Z-distribution and all the t-distributions? Group of answer choices
A. They have the same mean.
B. They have the same unusual features.
C. They have the same standard deviation.
D. They have the same shape
E. They have the same shape.
Among the following, "They have the same unusual features" is not a correct comparison among the Z-distribution and all the t-distributions. Option B is the correct answer.
A z-distribution refers to the normal distribution of a standard set of values for a variable. If a variable has a normal distribution with a mean of 0 and a standard deviation of 1, it is said to follow a standard normal distribution, which is also known as a z-distribution.
A t-distribution is a type of probability distribution that is used in statistical analysis when the sample size is small or the population's standard deviation is unknown. T-distributions are used in a variety of statistical tests, including the t-test and the analysis of variance (ANOVA). T-distributions are a family of distributions that resemble the normal distribution, with the tails stretched to either side, based on the number of degrees of freedom.
In general, the t-distribution is less peaked and has heavier tails than the normal distribution. As the degrees of freedom increase, the t-distribution approaches the normal distribution. Thus, Option B "They have the same unusual features" is not a correct comparison among the Z-distribution and all the t-distributions.
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Rolling-circle replication of plasmids proceeds Choose one: in one direction from a single fixed origin. O in opposite directions from a single fixed origin. in one direction from multiple origin sites. O in opposite directions from multiple origin sites,
Rolling-circle replication of plasmids proceeds in one direction from a single fixed origin
Explanation:
How does Rolling-circle replication of plasmids proceed?Rolling-circle replication of plasmids is a replication mechanism in which the replication process moves in one direction from a single fixed origin. Rolling-circle replication is a process that is often seen in circular plasmid DNA. It is a process that begins with an initiator protein, which is responsible for the nicking of a single DNA strand.The initiation point allows the helix to begin unwinding in one direction.
As the DNA helix unwinds, replication is carried out in a continuous manner, and the helix is wound up behind it. During the replication process, a new strand is synthesized that is attached to the parent strand's 3' end.
Rolling-circle replication, on the other hand, is utilized to produce new plasmids that have a single strand, which can then be employed in other cells for the production of proteins or for research purposes.
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Can someone help me with this?
I'm not sure how to execute this.
Anything helps! Will give brainliest!
Answer:
165 centimeters squared.
Step-by-step explanation:
Since we have 2 shapes combined, we need to split them to make 2 rectangles. Now that we have split these two, we can find their individual areas. We know the formula to find area is L * W = A.
So now we do 15 * 7 = 105 to find the area of the shape on the left.
To find the area of the shape on the right, we do 10 * 6 = 60.
Now we add these to get 165 centimeters squared.
how many vectors may be added by the polygon method? are other methods of vector addition limited to the number of vectors that can be added? explain.
The polygon method of vector addition can be used to add any number of vectors. Other methods of vector addition, however, may be limited to the number of vectors that can be added.
The vector addition method known as the polygon method can be used to add any number of vectors. To use the polygon method, you simply place the vectors head to tail, as if constructing the sides of a polygon. The sum of the vectors is then the vector from the tail of the first vector to the head of the final vector. Polygon method of vector additionIn addition, other methods of vector addition, such as the component method, may have limits on the number of vectors that can be added. When using the component method, for example, vectors are broken down into their x- and y-components.
These components are then added to determine the total x- and y-components of the sum vector. The sum vector is then found by combining the x- and y-components. Because of this, the number of vectors that can be added using the component method may be limited by the ability to calculate the individual x- and y-components.
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Prove that 3:8 is equivalent to 12:32
Answer:
3:8 = 12:32
For easier understanding, we make 3:8 into 3/8 and 12:32 into 12/32
3/8 = 12/32
Cross multiply
3*32 = 8*12
96 = 96
Since the products are equal, the ratios are equivalent.
You can also simplify 12:32
12 / 4 = 3
32 / 4 = 8
Elisa has 31 pieces of paper left. She shares the paper equally between herself and her friend, Bella. How much paper does each person get? Between what two whole numbers does the answer lie?
Answer:
between 15 and 16
Step-by-step explanation:
31÷2=15.5 meaning 15.5 is between 15 and 16
question sebastian states that experimental and theoretical probabilities are never the same. is sebastian's statement true? why or why not?
Answer:
Step-by-step explanation:
yes
which of the following will never be a required condition of a nonparametric test?group of answer choicesdata are interval.data are ordinal.the samples are drawn from normally distributed populations.the populations being compared are identical in spread and shape.
The condition that will never be required for a nonparametric test is The data are interval. so, the correct option is A).
Nonparametric tests do not assume any specific distribution for the data and do not rely on population parameters such as mean and variance. Therefore, they can be used with data that are nominal, ordinal, or interval, without any assumption about the underlying distribution of the data.
Nonparametric tests rely on the rank ordering of the data rather than their exact values, making them robust to outliers and non-normality.
However, it is important to note that some nonparametric tests may have assumptions about the nature of the data, such as the independence of observations, or the symmetry or continuity of the distribution. These assumptions should be carefully considered before applying a nonparametric test. The correct answer is A).
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____The given question is incomplte, the complete question is given below:
which of the following will never be a required condition of a nonparametric test?group of answer choices
A) data are interval.
B) data are ordinal.
C) the samples are drawn from normally distributed populations.
D) the populations being compared are identical in spread and shape.
why is it that you can buy a double cheese burger for 99 cents and you can't even get a head of broccoli for 99 cents
A double cheeseburger costs less than a head of broccoli due to lower ingredient costs, a more efficient manufacturing process and some more reasons which are listed below:
Firstly, cheeseburgers are typically made with cheaper ingredients, such as pre-made patties, processed cheese, and pre-made buns. The manufacturing process is also more streamlined and efficient, which further reduces cost. Additionally, the demand for cheeseburgers is typically higher than that for broccoli, which helps to keep prices low.
On the other hand, broccoli requires more labor to harvest and process. It also requires more storage space, which drives up costs. The demand for broccoli is typically lower than for cheeseburgers, which also keeps prices higher.
Additionally, broccoli is more labor-intensive and requires more storage space, which further drives up its cost.
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Help me solve this, please
z = 110°
mEB = 90°
mCE = 74°
I’m not sure about x or y but I think these are right.
what is the probability of observing the expected value for the distribution of binomial(100, 0.20)?
The probability of observing the expected value for the distribution of a binomial (100, 0.20) is 0.20 (or 20%).
The probability of observing the expected value for a binomial distribution can be calculated using the following formula:
Probability = (n C r) p^r (1-p)^(n-r)
where n = number of trials,
r = expected value,
p = probability of success
For the given distribution, binomial (100, 0.20), we know that n = 100 and p = 0.20.
The expected value is given by:E(X) = np = 100 * 0.20 = 20
So, to find the probability of observing the expected value of 20, we need to plug in the values of n, r, and p into the formula:
Probability = (n C r) p^r (1-p)^(n-r)=
(100 C 20) (0.20)^20 (0.80)^80≈
0.1875 ≈ 0.20 (rounded to two decimal places)
Therefore, the probability of observing the expected value for the distribution of binomial (100, 0.20) is approximately 0.20 (or 20%).
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which is the greatest, the mean, the mode, or the median of the data set? 11; 11; 12; 12; 12; 12; 13; 15; 17; 21; 21; 21
In the following question, among the conditions given, The greatest value in the data set is 21, the mean is 13.4, the mode is 12, and the median is 12.
The greatest value is the highest number in the set, 21.
The mean is the average of the set, and is calculated by adding all the numbers together and dividing by the number of values, which in this case is 11. 11 + 11 + 12 + 12 + 12 + 12 + 13 + 15 + 17 + 21 + 21 + 21 = 163, and 163 / 11 = 13.4.
The mode is the number that appears the most often, which is 12 in this set.
The median is the middle number when all the numbers are put in order from least to greatest, which is also 12 in this set.
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What is an equation of the line that passes through the point (-5, 7) and is parallel
to the line x - 5y = 15?
Answer:
Step-by-step explanation:
What is an equation of the line that passes through the point (-5, 7) and is parallel
to the line x - 5y = 15?
We have two values, x and y, from our ordered pair.
Plugging those in we have -5 - 35y = 15
Add 5 to both sides: -35y = 20
Divide both sides by 35 : approx. 0.57
Our slope is 0.57
one thousand dollars is deposited in a savings account where the interest is compounded continuously. after 6 years, the balance will be $1370.55 . when will the balance be $1711.03 ? round to the nearest tenth of a year.
If the balance will be $1370.55 after 6 years, then The balance will be $1711.03 after approximately 14.3 years.
The formula for calculating the balance in a continuously compounded account is:
[tex]A = Pe^{rt}[/tex]
Where:
A = final balance
P = principal (initial deposit)
e = Euler's number (approximately 2.71828)
r = annual interest rate
t = time in years
We know that the initial deposit is $1000 and the balance after 6 years is $1370.55, so we can use these values to solve for the annual interest rate:
[tex]1370.55 = 1000*e^{6r}[/tex]
⇒ [tex]ln(\frac{1370.55}{1000}) = 6r[/tex]
⇒ [tex]r = \frac{ln(\frac{1370.55}{1000})}{6}[/tex]
⇒ [tex]r = 0.0345[/tex]
Now we can use the same formula to find out when the balance will be $1711.03:
[tex]1711.03 = 1000*e^{(0.0345*t)}[/tex]
⇒ [tex]ln(\frac{1711.03}{1000}) = 0.0345*t[/tex]
⇒ [tex]t = \frac{ln(\frac{1711.03}{1000})}{0.0345}[/tex]
⇒ t = 14.3 years.
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in how many ways can 4 children be arranged on a 4-animal merry go round if andy is seated on the giraffe
There are 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.
If Andy is seated on the giraffe in a 4-animal merry-go-round, the arrangement of four children on the merry-go-round can be determined as follows:
Since Andy is already seated on the giraffe, only three children are left to be seated on three other animals. The first child can be seated on any of the three remaining animals. The second child can be seated on either of the two remaining animals since one has already been occupied.
Finally, the third child can be seated on the only remaining animal. Therefore, there are three options for the first child, two options for the second child, and one option for the third child, resulting in 3*2*1 = 6 possible arrangements of four children on a 4-animal merry-go-round if Andy is seated on the giraffe.Answer:6.
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Help me!!! please show working out
The polynomial x² + x - 4 = 0 is equivalent to the rational equation [2 · (x + 2) - (x + 1)] / [(x + 1) · (x + 2)] = 1 / 2.
How to find the equivalent polynomial related to rational equation
In this problem we find the definition of a rational equation that must transformed into an equivalent polynomial. This can be done by using algebra properties:
2 / (x + 1) - 1 / (x + 2) = 1 / 2
First, use subtraction between fractions of different denominators:
[2 · (x + 2) - (x + 1)] / [(x + 1) · (x + 2)] = 1 / 2
(2 · x + 4 - x - 1) / (x² + 3 · x + 2) = 1 / 2
(x + 3) / (x² + 3 · x + 2) = 1 / 2
Second, eliminate the denominator on both sides:
2 · (x + 3) = x² + 3 · x + 2
2 · x + 6 = x² + 3 · x + 2
x² + x - 4 = 0
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A function is shown on the coordinate plane below. For what intervals is the function increasing?
pls hurry
The function is increasing over the intervals D. -6 < x < -1 and 2 < x < 3 and 4 < x < 6.
When does a function increase?A function is increasing when the slope of its graph is positive, meaning that its graph is rising from left to right.
In the given coordinate plane, the graph of the function consists of three sections, each of which has an increasing slope.
The first section is from -6 to -1, the second section is from 2 to 3, and the third section is from 4 to 6.
This means that the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6.
To confirm this, we can calculate the slope of the graph in each interval. The slope of the graph between two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1).
For the first interval, the slope is (3-(-5))/(-1-(-6)) = 8/-5 = -1.6. This is a negative value, which means the graph is decreasing over this interval. For the second interval, the slope is (4-3)/(3-2) = 1/1 = 1. This is a positive value, so the graph is increasing over this interval.
For the third interval, the slope is (6-4)/(4-2) = 2/2 = 1. This is also a positive value, so the graph is increasing over this interval as well.
Therefore, the function is increasing over the intervals -6 < x < -1 and 2 < x < 3 and 4 < x < 6, which is option D.
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val had some pencils. alex gave her three-tenths of a box of pencils. now val has nine-tenths of a box of pencils. what fraction of a box of pencils did val have to begin with?
Alex gave Val three-tenths of a box of pencils, so she began out with three-fifths of a box.
what is unitary method ?To answer mathematical issues involving proportional relationships between various quantities, one can utilize the unitary method. In other words, given that two values are related in a constant ratio, it is helpful to determine the value of one if the value of another is known. With the unitary technique, a proportion is established based on how the two quantities relate to one another. The unknown amount can then be determined using the percentage.
given
Let's refer to Val's initial supply of pencils as the unknown portion of the box as x.
The three-tenths of a box of pencils Alex provided Val matched the problem statement. Following Alex's donation, Val had the following number of pencils:
x + 3/10
Val currently possesses nine-tenths of a box of pencils, which is also disclosed. We can therefore construct the following equation:
x + 3/10 = 9/10
By taking 3/10 off of both sides, we get at:
x = 9/10 - 3/10 = 6/10
Val thus started with 6/10 of a box of pencils. When we simplify this fraction, we obtain:
x = 3/5
Alex gave Val three-tenths of a box of pencils, so she began out with three-fifths of a box.
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Answer:
she gave her 3/5
Step-by-step explanation:
a pwr core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores
The probability of finding 10 defective cores in a sample of 10 power cores is approximately 0.0000161, or about 0.0016%.
Assuming that each fuel rod is independent of each other and that the probability of finding a defective fuel rod is constant at 0.1%, we can model the number of defective fuel rods in a power core with a binomial distribution. Let X be the number of defective fuel rods in one power core, then X follows a binomial distribution with parameters n = 50000 and p = 0.1/100 = 0.001.
To find the probability of finding 10 defective cores, we can use the binomial distribution again, but with a different set of parameters. Let Y be the number of defective cores in a sample of 10 power cores, then Y follows a binomial distribution with parameters n = 10 and p = P(X ≥ 1), where P(X ≥ 1) is the probability of finding at least one defective fuel rod in one power core. We can find P(X ≥ 1) using the complement rule:
P(X ≥ 1) = 1 - P(X = 0)
= 1 - (1 - 0.001)^50000
≈ 0.3935
So, the probability of finding 10 defective cores in a sample of 10 power cores is:
P(Y = 10) = (10 choose 10) * (0.3935)^10 * (1 - 0.3935)^(10 - 10)
≈ 0.0000161
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Complete Question:
a power core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores.
if the explained sum of squares is 35 and the total sum of squares is 49, what is the residual sum of squares?
If the explained sum of squares is 35 and the total sum of squares is 49, then the residual sum of squares is 14.
The total sum of squares is a measure of the total variability in a dataset. It is the sum of the squared differences between the mean of the dataset and each individual data point. The explained sum of squares is the sum of the squared differences between the predicted value of a regression line and the mean of the dataset.
The residual sum of squares is the sum of the squared differences between the predicted value of the regression line and the actual data points. It is the amount of variability in a dataset that is not explained by the regression line.To calculate the residual sum of squares for the given example, we start with the total sum of squares.
The total sum of squares is the sum of the squared differences between the mean of the dataset and each individual data point. The mean of the dataset is calculated by summing all the values and then dividing by the number of data points.
The total sum of squares is then the sum of the squared differences between the mean of the dataset and each individual data point. For the given example, the total sum of squares is 49.
The explained sum of squares is the sum of the squared differences between the predicted value of the regression line and the mean of the dataset. The predicted value of the regression line can be found using the regression equation. The explained sum of squares for the given example is 35.
The RSS is then the difference between the TSS and the explained sum of squares. For the given example, the RSS is 49 - 35 = 14.
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Simplify the following expression.
8+16/4 • 5-3
A: 31
B: 25
C: 77
D: 27
Answer:
B.25
Step-by-step explanation:
use PEMDAS (Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).)
I need help with my homework due this morning
This is not a valid probability value, which means there must be an error in the information given.
(a) To find the values of P(A), P(B), and P(C), we can use the following formula for the probability of the union of two events:
P(A U B) = P(A) + P(B) - P(A n B)
Using this formula, we can find the value of P(A n B):
P(A U C) = P(A) + P(C) - P(A n C) = 0.70
P(Anc) = P(A') = 0.20
Since A and A' are complements, we can use the complement rule to find P(A):
P(A) = 1 - P(A') = 1 - 0.20 = 0.80
Now we can use the formula to find P(C):
P(A U C) = P(A) + P(C) - P(A n C)
0.70 = 0.80 + P(C) - P(A n C)
Since we do not know P(A n C), we cannot solve for P(C) yet. However, we can use the fact that A, B, and C are mutually exclusive, meaning they have no intersection:
P(A n B) = P(A n C) = P(B n C) = 0
Using this fact and the formula, we can solve for P(C):
P(A U C) = P(A) + P(C) - P(A n C)
0.70 = 0.80 + P(C) - 0
P(C) = 0.70 - 0.80 = -0.10
This is not a valid probability value, which means there must be an error in the information given. It is not possible for the probability of the union of A and C to be greater than the probability of A alone. Therefore, the given information is inconsistent.
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Question:
I need help with my homework due this morning
(a) Given the following information about three events A, B, and C. P(AUC) 0.70 P(Anc) 0.20 Find the values of P(A), P(B), and P(C).