Final answer:
There are 512 different combinations possible for an 8-number combination lock, as the same number can be reused and each of the three positions has 8 choices.
Explanation:
To calculate the number of different combinations possible for a combination lock with a dial containing 8 numbers (0 through 7), we can use the fundamental counting principle. Since the same number can be reused consecutively, there are no restrictions on the choices for each of the three numbers in the sequence. Therefore, for each position of the sequence (the first, second, and third number), there are 8 possibilities.
The total number of combinations is the product of the number of choices for each position. Thus, the number of combinations for the lock is:
8 (choices for the first number) × 8 (choices for the second number) × 8 (choices for the third number)
Doing the calculation, we get:
8 × 8 × 8 = 512
Therefore, there are 512 different combinations possible for the lock.
Below are two parallel lines with a third line intersecting them. What is X
x = 105°
Here is why:
The alternate exterior angle theorem states that alternate exterior angles are congruent.
Below I have attached a photo that will help you, the highlighted part of the image is the interior, while the parts that are not highlighted are the exterior. Inside of the two parallel lines will always be the interior.
They are alternate because they are alternating, or diagonal, across the middle line, which is the transversal.
M plus the product of 6 and n
Answer:
6n + M
Step-by-step explanation:
6 * n = 6n, 6n + M would be the answer
The expression is M +6n.
What is Algebra?
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
given statement:
M plus the product of 6 and n
So, first product of 6 and n
=6n
Now, M is added to the result
=M +6n
Hence, the expression is M + 6n
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Tom swims a 1/2 mile every 1/4 hour. How far will he swim in one hour?
Answer:
2 mlies per hour
Step-by-step explanation:
She miles 1/2 mile every 15 minutes or 1/4 hours so
1/2*4=2 miles per hour
Answer:
2 miles
Step-by-step explanation:
if he swims 1/2 a mile in a 1/4 of an hour (15 minutes) then you will divide an hour by 4 to see how many times he swam. you should get 4 1/4 hours and then you will multiply 1/2 by 4.
in a nut shell you multiply 1/2 by 4 because he swam over the time of an hour.
summarize the difference between theoretical and experimental probability
Answer:
Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out
Step-by-step explanation:
Amanda wants to sell her old car. she will open a classified ad in the Sacramento Bee. the newspaper charges $42 for the first two lines and $11 dollars each additional line. she buys a three week ad that has four lines. What is Amanda's cost?
mags wants to know what is the hottest hairstyle trend is in her town. Which is the best group to survey
A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
B.Get a list of salons in her town and circle the 5 salons that are close to her house. Survey all the hairstylists that work at each salon
C.Go to all the salons where Luna and her friends go. Survey all the hair stylists that work at each salon
D. Ask her clients that are celebrities which salons they go to. Survey all the hair stylists that work at each salon
Answer: A
Step-by-step explanation:
The best group to survey is option A. A.Get a list of salons in her town and use a deck of cards to pick 5 of them to visit. Survey all hairstylists that work in each salon.
What is the survey?Surveys represent the list of questions that should be focused on for extracting particular data from the people. It could be conducted via the phone, mail, internet, malls, etc.
Since mags want to know the hottest hairstyle trend so here he should get the list of towns and then use the deck of cards so that she should pick 5 for visiting them. Therefore, the correct option is a.
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A mechanic had 4 and one half gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answer:
Step-by-step explanation:
I believe that it's 19pints I've had a problem with this question also but I believe I have the answer HOPE THIS HELPS
Final answer:
The mechanic used 31 pints of motor oil during the day.
Explanation:
Question: The mechanic started with 4 and one-half gallons of motor oil and ended the day with 5 pints remaining. How many pints of motor oil did the mechanic use during the day?
Step-by-step explanation:
Convert 4 and one-half gallons to pints: 4.5 gallons x 8 pints/gallon = 36 pints.
Subtract the remaining 5 pints from the initial 36 pints: 36 pints - 5 pints = 31 pints.
Therefore, the mechanic used 31 pints of motor oil during the day.
A deck of cards contains 52 cards.two decks are put together and divided amount eight players.how many cards does each person get
Answer:
each person gets 13 cards
Step-by-step explanation:
if each deck contains 52 cards and two of them are put together then it would be 52x2=104 divided by 8=13
When two decks of 52 cards each are combined and divided among eight players, each player receives 13 cards.
If two decks of 52 cards are combined, there would be a total of 104 cards (52 cards per deck × 2 decks). To find out how many cards each person gets when these are divided among eight players, we divide the total number of cards by the number of players:
Calculate the total number of cards: 52 cards/deck imes 2 decks = 104 cards.
Divide this number by the number of players: 104 cards / 8 players = 13 cards/player.
So, each person would receive 13 cards.
hi what is 9times 30 divided by 9
Answer:
30
Step-by-step explanation:
9x30= 270
270/9= 30
The result of 9 times 30 divided by 9 is 30.
Evaluating a mathematical expression
To evaluate an expression in mathematics, means to find the value of the final answer after performing suitable arithmetic manipulations.
The operations required could be any combination involving addition, subtraction, multiplication, division etc.
From the information given in the question, we need to multiply 9 by 30 first,
9 * 30 = 270
Next, we divide the result by 9
270/9 = 30
The result is 30.
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The average number of shirts sold in the beach shop was 285 on Saturday in the
summer. As the temperature went lower, the average number of shirts decreased to 114
every Saturday. What was the percentage decrease of in the average number of shirts
sold in the shop?
Answer:
Decreased by 60%
Step-by-step explanation:
First take the difference to the original amount to the new amount to find the change. 285 - 114 = 171
171/285 = .6
Multiply that by 100 to get it's percent.
The amount of shirts sold decreased by 60%
Final answer:
The percentage decrease in the average number of shirts sold in the shop from 285 to 114 shirts is 60%.
Explanation:
The percentage decrease in the average number of shirts sold at the beach shop can be calculated using the following formula: Percentage decrease = ((Original Average - New Average) / Original Average) × 100. The original average is 285 shirts, and the new average is 114 shirts after the temperature decrease.
So, the calculation would be: ((285 - 114) / 285) × 100 = (171 / 285) × 100 = 0.6 × 100 = 60%.
Therefore, the percentage decrease in the average number of shirts sold in the shop is 60%.
:
A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
Answer:
students selected by teachers
Step-by-step explanation:
Final answer:
The principal should use a stratified random sample, selecting an equal number of students from each class year, to accurately represent the student body when surveying opinions on a new dress code. This method ensures each subgroup is proportionally represented and can provide an accurate estimate of the student population's opinion.
Explanation:
The principal should choose a sample that accurately represents the diverse student body at the high school when evaluating opinions on a new dress code. As such, the principal might select a stratified random sample where students are divided by classification (freshman, sophomore, junior, or senior) to ensure that each group is represented in the sample. For instance, by organizing the students' names by classification and then selecting 25 students from each group, we would obtain a total sample of 100 students (a). This resembles the stratified sampling method similar to the one used in the hypothetical polling in question Try It Σ 1.13. This approach as outlined in example 13, which involves drawing a proportionate random sample from each class, ensures that all groups are proportionately sampled, thereby allowing the sample to more accurately reflect the student population's opinion on the new dress code.
Sampling large populations as mentioned, like all algebra students in a city or public opinion in presidential elections, is a common practice and random sampling is critical to avoid bias and ensure that the survey sample represents the larger population effectively. The success of the survey depends on how well the survey targets and represents the specific population without bias, as indicated by the overall description of how surveys operate. If conducted correctly, no matter the sample size, the survey can provide accurate estimates, as seen in the case of the Gallup Poll survey effectiveness discussed.
Therefore, using a stratified random sampling technique where a proportionate number of students from each classification is selected would be the most appropriate choice for the principal to get a representative sample of the high school students' opinions on the dress code.
The product of two consecutive odd integers is 1 less than twice their sum. Find the integers.
Two consecutive odd integers are [tex]2k+1[/tex] and [tex]2k+3[/tex], for some integer [tex]k[/tex].
Their product is [tex](2k+1)(2k+3)=4k^2+8k+3[/tex].
Twice their sum is [tex]2(2k+1+2k+3)=2(4k+4)=8k+8[/tex]
Since the product is 1 less than twice the sum, we have
[tex]\underbrace{4k^2+8k+3}_{\text{the product}}=\underbrace{8k+8}_{\text{twice the sum}}-1[/tex]
So, we have
[tex]4k^2-4=0 \iff 4k^2=4 \iff k^2=1 \iff k=\pm 1[/tex]
If [tex]k=1[/tex], the integers are 3 and 5
If [tex]k=-1[/tex], the integers are -1 and 1.
In both cases, in fact, we have:
3*5 = 15, which is one less than 2(3+5)=2*8=16(-1)*1=-1, which is one less than 2(-1+1)=0In a histogram, are the lengths of the rectangles proportional to the width of the bars?
Answer:
No
Step-by-step explanation:
In different scenarios, the data will be different. However, sometimes, it's impossible to draw a histogram with equal widths, so in order to maintain clarity and fairness, the area of the bars should actually be proportional to the frequency, which is usually the y-axis of the graph or height of the bars.
Hope this helps!
Answer:
No
Step-by-step explanation:
Length is the frequency density which is obtained by:
Frequency/width
Height is not proportional to width.
Frequency is proportional to the area of the rectangle
If a boat depreciates in value according to the simple interest formula y=20000(.92)^2 find the rate of decay write a percentage
Answer:
Y=16928
Step-by-step explanation:
Create a row vector vA=1:3:34 that has 12 elements. Then, create a new nine-element vector vB from the elements of vA such that the first five elements are the first five elements of the vector vA, and the last four are the last four elements of the vector vA. Use the colon symbol to address a range of elements. (Do not type the elements of the vector vA explicitly.)
Step-by-step explanation:
Create a row vector vA=1:3:34 that has 12 elements.
Matlab Code:
vA = [1:3:34]
Where vA = [starting element:difference:ending element]
Ouput:
vA = 1 4 7 10 13 16 19 22 25 28 31 34
Create a new nine-element vector vB from the elements of vA such that the first five elements are the first five elements of the vector vA, and the last four are the last four elements of the vector vA
Matlab Code:
% get first five elements from vector vA
vB1 = vA(1:5)
% get last four elements from vector vA
vB2 = vA(9:12)
% combine them together to form row vector vB
vB = [vB1, vB2] (comma or space both are fine)
Ouput:
vB1 = 1 4 7 10 13
vB2 = 25 28 31 34
vB = 1 4 7 10 13 25 28 31 34
Suppose that a recent poll found that 49% of adults believe that the overall state of moral values is poor. Complete parts (a) through (c). (a) For 250 randomly selected adults, compute the mean and standard deviation of the random variable X, the number of adults who believe that the overall state of moral values is poor. The mean of X is nothing. (Round to the nearest whole number as needed.) The standard deviation of X is nothing. (Round to the nearest tenth as needed.)
Answer:
The mean of X is 122.5 and the standard deviation is 7.9.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
[tex]n = 250, p = 0.49[/tex]
So
[tex]E(X) = np = 250*0.49 = 122.5[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{250*0.49*0.51} = 7.9[/tex]
The mean of X is 122.5 and the standard deviation is 7.9.
Suppose that a hypothesis test is conducted. 12 out of 100 subjects have the necessary qualities. The null hypothesis is that the proportion of the subjects who have the necessary qualities is equal to 0.2, while the alternative hypothesis is that this proportion is less than 0.2. The p-value is 0.023. Using a 5% significance level, state the conclusion to the hypothesis test in context. A : The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. B : The p-value is less than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities. C : The p-value is less than the significance level, so we do not reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is equal to 0.2. D : The p-value is more than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2. E : The p-value is more than the significance level, so we do not reject the null hypothesis. We cannot conclude anything about the proportion of the subjects who have the necessary qualities.
Answer:
Option A
The p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
Step-by-step explanation:
Normally, in hypothesis testing, the level of statistical significance is often expressed as the so-called p-value. We use p-values to make conclusions in significance testing. More specifically, we compare the p-value to a significance level "α" to make conclusions about our hypotheses.
If the p-value is lower than the significance level we chose, then we reject the null hypotheses H0 in favor of the alternative hypothesis Ha. However, if the p-value is greater than or equal to the significance level, then we fail to reject the null hypothesis H0
though this doesn't mean we accept H0 automatically.
Now, applying this to our question;
The p-value is 0.023 while the significance level is 0.05.
Thus,p-value is less than the significance level of 0.05 chosen and so we reject the null hypothesis H0 and can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
The only option that is correct is option A.
Answer: A: The p-value is less than the significance level, so we reject the null hypothesis. We can conclude that the proportion of the subjects who have the necessary qualities is less than 0.2.
Step-by-step explanation:
Here, p value = 0.023
significance level = 0.05
As p value < 0.05
Which proportion can you use to find the value of a?
Given:
The given triangle is a similar triangle.
The length of the hypotenuse is 18 units.
The length of the leg is a.
The length of the part of the hypotenuse is 16 units.
We need to determine the proportion used to find the value of a.
Proportion to find the value of a:
We shall find the proportion to determine the value of a using the geometric mean leg rule.
Applying the leg rule, we have;
[tex]$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$[/tex]
Substituting the values of hypotenuse, leg and part, we get;
[tex]\frac{18}{a}=\frac{a}{16}[/tex]
Thus, the proportion used to find the value of a is [tex]\frac{18}{a}=\frac{a}{16}[/tex]
Hence, Option D is the correct answer.
To find the value of 'a', set up a proportion where the ratios are equivalent. Determine the missing dimensions by cross-multiplying and solving for 'a'. Make sure ratios are in consistent units when setting up the proportions.
Explanation:To find the value of a, we can use the concept of proportions, which involves setting two ratios equal to one another. The provided ratios are related to scale drawings or conversions between units, a common topic in mathematics, especially in geometry and measurement units.
For example, if we have the proportion Length=1/50=0.5/5, we can cross multiply to find that 5 * 1 = 50 * 0.5, which simplifies to 5 = 25, indicating an error as the units must be consistent. Instead, it seems we are meant to find a when we have Length=w/30=0.5/, where w represents the width and should be calculated accordingly.
Another example is using scale to determine area. If we know the scale factor, we can find missing dimensions by setting up the appropriate proportion, such as in Example 4.8.4.2, where a scale measurement is given alongside a scale factor. Writing the proportion would involve equating the scale measurement with the actual measurement times the scale factor.
What is 3+3×3-3+3 equal to
Answer:
12
Step-by-step explanation:
Use pemdas. You do multiplication first.
3×3=9
3+9-3+3
Now add
3+9=12
Subtract:
12-3=9
Add:
9+3=12
Answer:
Your answer should be 18
Step-by-step explanation:
3 + 3 = 6
6 × 3 = 18
18 - 3 = 15
15 + 3 = 18
25. One of the silos pictured below holds corn, and the other holds hay. Chopped corn and hay are blown into the tops of the silos through pipes running up from the ground. a. The silos have a radius of 3 meters and a height of 18 meters. What is the volume, to the nearest cubic meter, of one of these silos? b. If a blower can load 1 cubic meter of hay in 3 minutes, how many hours (to the nearest .1 hour) will it take to fill one of these silos?
Answer:
a. 509 m³
Step-by-step explanation:
a. Assume that the silos are cylinders with a circular base. The volume of a silo is given by:
[tex]V = \pi *r^2*h[/tex]
If the radius (r) is 3 meters, and the height (h) is 18 meters, the volume is:
[tex]V = \pi *3^2*18\\V=509\ m^3[/tex]
Total volume is 509 m³
b. If the flow rate is 1 m³ per 3 minutes, the time required to fill the whole 509 m³ is:
[tex]t=509\ m^3*\frac{3\ min}{1\ m^3}*\frac{1\ h}{60\ min}\\t=25.45\ h[/tex]
It will take 25.45 or roughly 25.5 h to fill one of these silos.
Name the property that justifies the statement. 17 = 17
Step-by-step explanation:
I think when you will multiply 17 by 1 the answer is 17 so 17 = 17
Concert ticket sales of £21,000 are split in the ratio of 2 : 5 between the venue and the band.
How much money does the venue make from the ticket sales?
Answer:
Step-by-step explanation:
£21000/7=3000
I got seven by adding 2 and 5
3000 times 2=6000
3000 times 5 = 15000
6000:15000
6000 for the venue
15000 for the band
The amount of money the venue makes from the ticket sales is £6000.
How much does the venue make?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The amount the venue makes = 2/7 x 21000 = £6000
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a nutrition major at wright state was studying the relationship between carbohydrates (x) and calories (y). for example, a serving of a particular brand of wheat pasta yielded 42 carbohydrates and 210 calories. after collecting x and y data on many kinds of foods, the student determined the slope of the regression line to be 4.0 and the y intercept to be 3.0. if a new food is tested, and the number of carbohydrates (x) is 100, what would be the predicted calories (y’)?
Answer:
The predicted calories would be 403 calories.
Step-by-step explanation:
We have a linear regression model relating y: calories with x: carbohydrates, which has a slope of 4.0 and a y-intercept of 3.0.
Then, the model equation is:
[tex]y=4.0x+3.0[/tex]
With these model we can predict the calories values for any amount of carbohydrates, within the interval within which this model is valid.
If a new food is tested, and the number of carbohydrates (x) is 100, the predicted value will be:
[tex]y(100)=4.0(100)+3.0=400+3=403[/tex]
The predicted calories would be 403 calories.
Rewrite f(x) =x+1/x-1 in the form f(x)= a/x-h +k
Answer:
f(x) = 2/(x -1) +1
Step-by-step explanation:
[tex]f(x)=\dfrac{x+1}{x-1}=\dfrac{(x-1)+2}{x-1}=\dfrac{x-1}{x-1}+\dfrac{2}{x-1}\\\\\boxed{f(x)=\dfrac{2}{x-1}+1}[/tex]
Lauren simplified the expression (m Superscript negative 7 Baseline) Superscript negative 5 as shown. (m Superscript negative 7 Baseline) Superscript negative 5 = m Superscript negative 7 + (negative 5) Baseline = m Superscript negative 12 Baseline = StartFraction 1 Over m Superscript 12 Baseline EndFraction Which statement explains Lauren’s error? She should have subtracted the exponents instead of adding them. She should have multiplied the exponents instead of adding them. She should have found –2, not negative 12, as the exponent when she added. She should have written m Superscript negative 12 as m Superscript 12.
Answer:
She should have multiplied the exponents instead of adding them.
Step-by-step explanation:
Lauren simplified the expression (m Superscript negative 7 Baseline) Superscript negative 5 as shown.
(m⁻⁷)⁻⁵(m Superscript negative 7 Baseline) Superscript negative 5 = m Superscript negative 7 + (negative 5) Baseline = m Superscript negative 12 Baseline = StartFraction 1 Over m Superscript 12 Baseline EndFraction
(m⁻⁷)⁻⁵ = m⁻⁷⁺⁽⁻⁵⁾ = m⁻¹² = 1/m¹²Correct solution:
(nᵃ)ᵇ = nᵃᵇ required property, power of the power is the product of the powers(m⁻⁷)⁻⁵ = m⁽⁻⁷⁾⁽⁻⁵⁾ = m³⁵Correct answer option describing the error made:
She should have multiplied the exponents instead of adding them.
Answer:
B
Step-by-step explanation:
When rounded to the nearest 100 I am the smallest whole number that becomes 5,000 what number am I
Step-by-step explanation:
Let the number to be identified be represented as x
Given, when rounded to the nearest 100 I am the smallest whole number that becomes 5,000
Therefore, the number is above 4000 and it is a whole number.
When rounded to the nearest 100, I am the smallest whole number that becomes 5,000
The smallest whole number must be 4950 when ronded to 100,it becomes 5000.
The number is 4950
Find the smallest perimeter and the dimensions for a rectangle with an area of 36 in squared. The smallest perimeter for a rectangle with an area of 36 in squared is nothing in. (Simplify your answer.) The dimensions of this rectangle are nothing in. (Simplify your answers. Use a comma to separate answers.)
Final answer:
The smallest perimeter for a rectangle with an area of 36 square inches is 24 inches, and the dimensions that achieve this are those of a square, specifically 6 inches by 6 inches.
Explanation:
The smallest perimeter of a rectangle with an area of 36 square inches is achieved when the rectangle is a square because the sides are equal, and a square minimizes the perimeter for a given area. The formula for the area of a square is area = side², so if we have an area of 36 square inches, the side length of the square is √36, which equals 6 inches. Using this side length, we can calculate the perimeter of the square, which is perimeter = 4 × side, giving us a perimeter of 6 inches × 4, which is 24 inches.
The smallest perimeter we can have is 24 inches, and the dimensions of the rectangle (in this case, a square) that give us this smallest perimeter are 6 inches by 6 inches.
How do you round up to the nearest hundreth
Answer:
the second digit from the decimal, round it based on the the thousandth if above 5 round it to the next number 4 and below round it to the same number
Step-by-step explanation:
say for example 10.246 this would round to 10.25
another example is 10.244 this would round to 10.24
Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°.
Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. Angle B C A is 40 degrees.
What is the measure of minor arc BD?
40°
50°
80°
100°
Answer:
D. 100
Step-by-step explanation:
correct on edu2020
Based on the calculations, the measure of minor arc BD is equal to 100°.
Given the following data:
Angle BCA = 40°.What is a line segment?A line segment can be defined as a part of a line that is bounded by two (2) distinct points and has a fixed length.
Based on the information given, we can deduce the following:
Angle BAD = 2(BCA)
Angle BAD = [tex]2\times 40[/tex]
Angle BAD = 80°.
Also, angle ABC and ADC both have a measure of 90 degrees because angle BCD is a circumscribed angle.
Note: The sum of the interior angles in a quadrilateral is equal to 360°.
[tex]ABC + ADC + BAD + BCD = 360\\\\90+90+ BAD + BCD = 360\\\\180+ BAD + BCD = 360\\\\BAD + BCD = 360-180\\\\BAD + BCD = 180[/tex]
For the minor arc BD:
[tex]BCD =180-BAD\\\\BCD =180-80[/tex]
Angle BCD = 100°.
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A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since termination of the molding process (x, in hours). Summary quantities include n = 15, SSResid = 1236.046, and SSTo = 25460.897. Calculate the coefficient of determination. (Give the answer to four decimal places.)
Using the given values of SSResid and SSTo, we can calculate the coefficient of determination as 0.9518 or 95.18 percent.
Explanation:The coefficient of determination, denoted as r², represents the percentage of variation in the dependent variable that can be explained by the variation in the independent variable using the regression line. To calculate the coefficient of determination, divide the sum of squares of the residuals (SSResid) by the total sum of squares (SSTo), and then subtract the result from 1. In this case, the coefficient of determination can be calculated as follows:
r² = 1 - (SSResid / SSTo)
Substituting the given values, we get:
r² = 1 - (1236.046 / 25460.897)
Calculating this expression gives an answer of approximately 0.9518. Therefore, the coefficient of determination is approximately 0.9518 or 95.18 percent.
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