Of the statistical processes we have covered throughout this course, which would be most helpful to determine if study hours and sleep could help estimate a student's test score?
Answers
Answer:
Pearson correlation coefficient
Explanation:
The Pearson correlation coefficient, also simply called correlation coefficient measures the linear correlation between two sets of data/variables, independent variables and dependent variable. A correlation coefficient may only be between -1 and 1 where +1 denotes a perfect positive correlation between variables(both variables increase together), 0 is no correlation, and -1 is perfect negative correlation between variables(one decreases while other increases).
Related Questions
928.89 The 8 in the ones place is ____________ times the value of the 8 in the tenths place.
Answers
Answer:
0.1 times
hope this helps
have a good day :)
Step-by-step explanation:
Avril wants to puts trim around the border of one of the walls in her room. The dimensions of the wall is 10 x 15 ft. Will she need to find the area or the perimeter of the wall to figure out how much trim she needs? How much trim does she need?
Answers
Answer:Perimeter, 50ft
Step-by-step explanation:since it is around the answer is 50 ft
find the coordinates of B if the coordinates of A are (5,-4) and the midpoint of AB are (3,-2)
Answers
Answer:
B(1, 0)Step-by-step explanation:
A(5, -4) ⇒ \(x_A=5,\quad y_A = -4\)
M(3,-2) ⇒ \(x_M=3,\quad y_M=-2\)
Point M(3, -2) being the midpoint of AB means that \(x_M-x_A=x_B-x_M\)
\(3-5=x_B-3\\\\-2=x_B-3\\\\x_B=1\)
and \(y_M-y_A=y_B-y_M\)
\(-2-(-4)=y_B-(-2)\\\\-2+4=y_B+2\\\\y_B=0\)
For a result to be considered _____, the chances of its occurring as a result of random error are often less than 5 percent.
Answers
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
What is Random error?A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).
It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.
Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.
According to the given data,
For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.
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Michael drove 14 miles. Stephanie
drove 12 miles. How many more
miles did Michael drive than Stephanie?
Answers
Answer:
2 more miles
Step-by-step explanation:
14-12=2
Can you mark me as brainliest, if not its fine :)
Waldo Books needs to decide how many copies of a new hardcover release to purchase for its shelves. The store has assumed that demand will be 50, 100, 150, or 200 copies next month, and it needs to decide whether to order 50, 100, 150, or 200 books for this period. Each book costs Waldo $20 and can be sold for $30. Waldo can sell any unsold books back to the supplier for $4.
(a) Which option should Waldo choose if it uses the maximax criterion?
(b) Which option should Waldo choose if it uses the maximin criterion?
(c) Which option should Waldo choose if it uses the equally likely criterion?
(d) Which option should Waldo choose if it uses the criterion of realism with a = 0.7?
(e) Which option should Waldo choose if it uses the minimax regret criterion?
Answers
Answer:
(a) Maximax criterion: Order 200 books.
(b) Maximin criterion: Order 200 books.
(c) Equally likely criterion: Order 200 books.
(d) Criterion of realism with a = 0.7: Calculate the expected payoff based on the chosen value of a and select the corresponding option.
(e) Minimax regret criterion: Order 200 books.
Step-by-step explanation:
The maximax criterion involves selecting the option with the highest possible payoff. We will calculate the maximum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 = $1500
Maximum payoff = $1500Payoff for ordering 100 books:
Revenue = 30 * 100 = $3000
Maximum payoff = $3000Payoff for ordering 150 books:
Revenue = 30 * 150 = $4500
Maximum payoff = $4500Payoff for ordering 200 books:
Revenue = 30 * 200 = $6000
Maximum payoff = $6000Based on the maximax criterion, Waldo should choose the option of ordering 200 books since it has the highest maximum payoff.(b) Maximin Criterion:
The maximin criterion involves selecting the option with the highest minimum payoff. We will calculate the minimum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 - (20 * 50 - 4 * 50) = $900
Minimum payoff = $900Payoff for ordering 100 books:
Revenue = 30 * 100 - (20 * 100 - 4 * 100) = $1800
Minimum payoff = $1800Payoff for ordering 150 books:
Revenue = 30 * 150 - (20 * 150 - 4 * 150) = $2700
Minimum payoff = $2700Payoff for ordering 200 books:
Revenue = 30 * 200 - (20 * 200 - 4 * 200) = $3600
Minimum payoff = $3600Based on the maximin criterion, Waldo should choose the option of ordering 200 books since it has the highest minimum payoff.(c) Equally Likely Criterion:
The equally likely criterion assumes that each demand level is equally likely to occur. We will calculate the expected payoff for each option and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = (30 * 50 + 4 * (50 - 50)) / 4 = $375
Expected payoff = $375Expected payoff for ordering 100 books:
Expected revenue = (30 * 100 + 4 * (50 - 100)) / 4 = $750
Expected payoff = $750Expected payoff for ordering 150 books:
Expected revenue = (30 * 150 + 4 * (50 - 150)) / 4 = $1125
Expected payoff = $1125Expected payoff for ordering 200 books:
Expected revenue = (30 * 200 + 4 * (50 - 200)) / 4 = $1500
Expected payoff = $1500Based on the equally likely criterion, Waldo should choose the option of ordering 200 books since it has the highest expected payoff.(d) Criterion of Realism with a = 0.7:
The criterion of realism involves assigning a weight (0 ≤ a ≤ 1) to the optimistic payoff and the remaining weight (1 - a) to the pessimistic payoff. We will calculate the expected payoff for each option using the given value of a and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = a * (30 * 50) + (1 - a) * (30 * 50 - 20 * 50 + 4 * 50) = $450a
Expected payoff = $450aExpected payoff for ordering 100 books:
Expected revenue = a * (30 * 100) + (1 - a) * (30 * 100 - 20 * 100 + 4 * 100) = $900a
Expected payoff = $900aExpected payoff for ordering 150 books:
Expected revenue = a * (30 * 150) + (1 - a) * (30 * 150 - 20 * 150 + 4 * 150) = $1350a
Expected payoff = $1350aExpected payoff for ordering 200 books:
Expected revenue = a * (30 * 200) + (1 - a) * (30 * 200 - 20 * 200 + 4 * 200) = $1800a
Expected payoff = $1800aTo find the maximum expected payoff, we can compare the values of a * 450, a * 900, a * 1350, and a * 1800 for different values of a. The optimal value of a will determine the corresponding option.(e) Minimax Regret Criterion:
The minimax regret criterion involves calculating the regret for each option and selecting the one with the minimum regret. Regret represents the difference between the maximum possible payoff and the actual payoff.Regret for ordering 50 books:
Regret = 6000 - (30 * 50 - (20 * 50 - 4 * 50)) = $5250
Minimum regret = $5250Regret for ordering 100 books:
Regret = 6000 - (30 * 100 - (20 * 100 - 4 * 100)) = $4200
Minimum regret = $4200Regret for ordering 150 books:
Regret = 6000 - (30 * 150 - (20 * 150 - 4 * 150)) = $3150
Minimum regret = $3150Regret for ordering 200 books:
Regret = 6000 - (30 * 200 - (20 * 200 - 4 * 200)) = $2100
Minimum regret = $2100Based on the minimax regret criterion, Waldo should choose the option of ordering 200 books since it has the minimum regret.
Waldo Books is facing a decision theory problem. By different criteria, the decision to order books can change. By maximax, Waldo should order 200 books, by maximin, 50 books. By equally likely, realism, and minimax regret criteria, computations considering payoffs, optimism levels, and potential regrets are needed.
Explanation:This is a "decision theory problem" in the field of business and economics. Let's calculate the profit from each option. Profit will be $10 for each book sold (revenue of $30 minus cost of $20) and a loss of $16 for each book not sold (cost of $20 minus resell value of $4).
Maximax criterion is when Waldo selects the alternative with the highest possible outcome. In this case, Waldo should order 200 books as he could make the most profit if demand is also at 200. Maximin criterion is when Waldo chooses the option with the best worst-case scenario. Here, Waldo should order 50 books as this would minimize the potential for unsold books. For the equally likely criterion, each level of demand is assumed to be equally probable, so the average profit for each order size should be calculated. The number with the highest average profit should be chosen. In the criterion of realism (also considered a 'compromise' criterion), there's a coefficient of optimism (a value between 0 and 1) that measures the decision-maker's optimism. Here, 'a' is 0.7. The larger the 'a', the more optimistic the decision-maker is. We calculate [a*(max payoff)+(1-a)*(min payoff)] for each alternative and pick the largest. The minimax regret criterion is about minimizing the maximum regret. Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision with the smallest maximum 'regret' is chosen. Learn more about Decision Theory here:
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In a social group, 62 members enjoy dancing and 28 members enjoy hiking. If each of the 75 members in the group enjoys dancing or hiking, how many members enjoy both dancing and hiking?
Answers
Answer: 162
Step-by-step explanation:
so you will have to do 62+28+75=162
15 member enjoy both dancing and hiking.
What is Conditional Probability?The likelihood of the preceding event is multiplied by the probability of the subsequent, or conditional, occurrence to determine the conditional probability. Conditional probability examines the likelihood that one event will occur given the likelihood that a related event will occur beforehand.
We have,
Member enjoy dancing, n(D) = 62
Member enjoy hiking, n(H) = 28
Member enjoy dancing or hiking, n(D ∪ H) = 62
Using Conditional probability
n (D ∪ H) = n(D) + n(H) - n (D ∩ H)
75 = 62 + 28 - n (D ∩ H)
75 - 90 = - n (D ∩ H)
n (D ∩ H) = 15
Thus, 15 member enjoy both dancing and hiking.
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Enter your answer and show all the steps that you use to solve this problem in the space provided.
Multiply and simplify if possible.
(3−√5) (7−√5)
Answers
Answer:
To multiply and simplify the expression (3 - √5)(7 - √5), we can use the distributive property of multiplication.
Step 1: Multiply the first terms of each binomial:
(3 - √5)(7 - √5) = 3 * 7
Step 2: Multiply the outer terms of each binomial:
(3 - √5)(7 - √5) = 3 * (-√5)
Step 3: Multiply the inner terms of each binomial:
(3 - √5)(7 - √5) = (-√5) * 7
Step 4: Multiply the last terms of each binomial:
(3 - √5)(7 - √5) = (-√5) * (-√5)
Now, let's simplify each multiplication:
Step 1: Multiply the first terms: 3 * 7 = 21
Step 2: Multiply the outer terms: 3 * (-√5) = -3√5
Step 3: Multiply the inner terms: (-√5) * 7 = -7√5
Step 4: Multiply the last terms: (-√5) * (-√5) = 5
Finally, let's add the simplified multiplications together:
21 + (-3√5) + (-7√5) + 5
Combining like terms, we have:
21 + 5 + (-3√5) + (-7√5) = 26 - 10√5
Therefore, the simplified form of (3 - √5)(7 - √5) is 26 - 10√5.
Step-by-step explanation:
Which expression is equivalent to 6(3h + g) ?
Group of answer choices
9h + g
18h + 6g
9h + 6g
18h + g
Answers
Answer:
18h × 6g is equivalent to 6(3h + g)
because 6 x 3 = 18 and 6 x 1 = 6
Which one of the following is the correct definition for initializing data in a two-dimensional array of three rows and two columns?a) int[][] arr ={{ 1, 1, 1 },{ 2, 2, 2 },};b) int[][] arr ={{ 1, 1 },{ 2, 2 },{ 3, 3 }};c) int[][] arr ={{ 1, 1 }{ 2, 2 }{ 3, 3 }};d) int[][] arr ={{ 1, 1, 1 }{ 2, 2, 2 }{ 3, 3, 3 }};
Answers
for initializing data in a two-dimensional array of three rows and two columns is option b) int[][] arr = {{ 1, 1 },{ 2, 2 },{ 3, 3 }};
what is array?
In mathematics, an array refers to an ordered arrangement or grid of numbers, variables, or objects in rows and columns. Arrays are commonly used to represent data sets or organize information in a structured manner.
Mathematical arrays can have various dimensions. A one-dimensional array is a simple list of elements arranged in a single row or column. For example, [1, 2, 3, 4] is a one-dimensional array with four elements.
A two-dimensional array is a grid-like arrangement of elements with rows and columns. It can be visualized as a table or matrix. For example,
1 2 3
4 5 6
represents a two-dimensional array with two rows and three columns.
Arrays in mathematics are often used for matrix operations, data analysis, and representing geometric shapes or patterns. They provide a structured way to organize and manipulate mathematical data, allowing for efficient calculations and analysis.
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Huilan is 9 years older than Thomas. The sum of their ages is 73 . What is Thomas's age?
Answers
Answer: Thomas is 32
Step-by-step explanation: bada bing badaboom
Answer: thomas is 45, (46 if you have to round up since it’s 45.5 exactly)
Step-by-step explanation: the sum of their ages added together is 73, so you would divide that by 2. to find thomas age as he is 9 years older, you add 9 onto that. hope this helps!
Please help me
I will mark brainliest!!
Answers
Answer:
it is x3
Step-by-step explanation:
there you go
/ Evaluate the following integrals: a) St12 /sinx cos® x dx b) Stanx sec* x dx c) S y sin (y2) cos? (yl)dy
Answers
a) `∫(sin(x)cos(θ))^12dx`The given integral is,`∫(sin(x)cos(θ))^12dx`We know that
`sin^2x + cos^2x = 1`Let `sinx = t` and `cosx dx = dt`Also, let `θ = φ`Now, the integral becomes:`∫t^12dt`After integration, we get:`= (t^13)/13 + C`Hence, `∫(sin(x)cos(θ))^12dx = (sin^13(x)cos^13(θ))/13 + C`
b) `∫tan(x)sec^2(x)dx`The given integral is,`∫tan(x)sec^2(x)dx`We know that,`
d/dx(tan(x)) = sec^2(x)`Thus, the integral can be written as:`∫tan(x)sec^2(x)dx = ∫tan(x) d(tan(x)) = (tan^2(x))/2 + C`Therefore, `∫tan(x)sec^2(x)dx = (tan^2(x))/2 + C`
c) `∫y sin(y^2)cos(y) dy`Let `y^2 = u`Thus,
`2y dy = du`The integral can be written as:`∫(1/2) sin(u) du`After integration, we get:`-(1/2)cos(u) + C`Substituting back the value of u, we get:`-(1/2)cos(y^2) + C`Therefore, `∫y sin(y^2)cos(y) dy = -(1/2)cos(y^2) + C`
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Hey loves!!! Can any of you lovely people help me with my math?
Answers
Answer:
SAA or AAS
Step-by-step explanation:
∠BAC = ∠BCA Given
∠BDA = 90° and ∠BDC = 90° Given
∠BDA = ∠BDC All 90° angles are congruent
BD = DB Reflexive property
ΔADB = ΔCDB SAA
Which graph shows the solution to the system of linear inequalities?
Answers
Answer:
Send q picture of the graphs so I can help
Step-by-step explanation:
need pictures of graph
Let f x be odd and g(x) is an even function if f(3)=2 and g(-1)=-3 find f(g(1))
Answers
the value of the given function f(g(1)) is 2 , fog is an even function
A function f is even if the equation f(x)=f(x) f (x) = f ( x) holds for every x and x in the domain of f. An even function has a graph that is geometrically symmetric with respect to the y-axis, which means that even after reflection about the y-axis, the graph does not change.
f is even (given)
∴f(−x)=f(x)
g is odd (given)
∴g(−x)=−g(x)
So,
According to question,
fog=f[g(x)]=f(y) Let [g(x)]=y
and also,
fog=f[g(−x)] ∵g(x) is odd
=f[−g(x)]
=f(−y)
=f(y)
⇒fog(x)=fog(−x)
∴fog is an even function
f(g(1)) = f(g(1)) = f(3) = 2
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Find the measure of the angle between the two vectors.
7) u = (6,-2)
v=(8,-8)
9) u=(2,6)
v = (-5, -8)
8) u = (-2,3)
v=(4,-6)
10) u =(-9, 4)
v = (-7, -1)
Answers
Answer:
Step-by-step explanation:
Which of the following correlation coefficients indicates the strongest relationship between two variables? a.−1.0 b. 0.80 c.0.1 d.−0.45
Answers
The correlation coefficient that indicates the strongest relationship between two variables is a. -1.0.
The correlation coefficient is a numerical measure that quantifies the relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.
In this case, a correlation coefficient of -1.0 represents a perfect negative correlation, meaning that the two variables have a strong, linear relationship where as one variable increases, the other decreases in a perfectly predictable manner. This indicates a very strong and consistent inverse relationship between the variables.
In comparison, a correlation coefficient of 0.80 indicates a strong positive correlation, but it is not as strong as a perfect negative correlation of -1.0. A correlation coefficient of 0.1 suggests a weak positive correlation, while a correlation coefficient of -0.45 indicates a moderate negative correlation.
Therefore, out of the given options, the correlation coefficient of -1.0 represents the strongest relationship between two variables.
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SAADEDDIN Pastry makes two types of sweets: A and B. Each unit of sweet A requires 6 units of ingredient Z and each unit of sweet B requires 3 units of ingredient Z. Baking time per unit of sweet B is twice that of sweet A. If all the available baking time is dedicated to sweet B alone, 6 units of sweet B can be produced. 36 unites of ingredient Z and 12 units of baking time are available. Each unit of sweet A can be sold for SR8, and each unit of sweet B can be sold for SR2. a. Formulate an LP to maximize their revenue. b. Solve the LP in part a using the graphical solution (i.e., draw all the constraints, mark on the graph ALL the corner points, indicate the feasible region, draw the objective function and find it's direction, determine the optimal solution).
Answers
SAADEDDIN Pastry produces two types of sweets, A and B. Sweet A requires 6 units of ingredient Z, while sweet B requires 3 units of ingredient Z. The baking time per unit of sweet B is twice that of sweet A. The available resources include 36 units of ingredient Z and 12 units of baking time. Sweet A can be sold for SR8 per unit, and sweet B can be sold for SR2 per unit. The goal is to formulate a linear programming (LP) model to maximize revenue.
To formulate the LP model, let's define the decision variables:
- Let x represent the number of units of sweet A to produce.
- Let y represent the number of units of sweet B to produce.
The objective is to maximize revenue, which can be expressed as:
Maximize Z = 8x + 2y
Subject to the following constraints:
6x + 3y ≤ 36 (a constraint on ingredient Z)
x + 2y ≤ 12 (a constraint on baking time)
x ≥ 0 (non-negativity constraint for sweet A)
y ≥ 0 (non-negativity constraint for sweet B)
By graphing the feasible region determined by the constraints and evaluating the objective function at the corner points of the feasible region, the optimal solution can be obtained. The coordinates of the corner points represent different combinations of sweet A and sweet B that satisfy the constraints.
By solving the LP model using graphical analysis, SAADEDDIN Pastry can determine the optimal number of units of sweet A and sweet B to produce in order to maximize revenue while staying within the available resources of ingredient Z and baking time.
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Is triangle ABC obtuse-angled?.
Answers
Is a triangle an obtuse angle?
No, a triangle cannot have both obtuse and right angles, as the sum of the three angles cannot exceed 180 degrees. How do you know if a triangle is obtuse? We can easily identify an obtuse triangle by looking at its angles. If any angle measures more than 90°, that triangle is an obtuse triangle.
In 1997 researchers at Texas A&M University estimated the operating costs of cotton gin plans of various sizes. A quadratic model of cost (in thousands of dollars) for the largest plants was found to be very similar to: C(a) 0. 028q? + 22.3q + 368 where q is the annual quanity of bales (in thousands) produced by the plant: Revenue was estimated at S66 per bale of cotton: Find the following (but be cautious and play close attention to the units): A) The Marginal Cost function: MC(9) 0.056q 22.3 B) The Marginal Revenue function: MR(q) 66 C) The Marginal Profit function: MP(q) D) The Marginal Profits for q 390 thousand units: MP(390) (see Part E for units)
Answers
The marginal profits for q = 390 thousand units is $21.86. To find the marginal cost function (MC), we need to take the derivative of the cost function (C) with respect to q.
Given: C(a) = 0.028q^2 + 22.3q + 368. Taking the derivative: MC(q) = dC/dq = 0.056q + 22.3. So, the marginal cost function is MC(q) = 0.056q + 22.3. To find the marginal revenue function (MR), we are given that the revenue per bale of cotton is $66. Since revenue is directly proportional to the number of bales produced (q), the marginal revenue function is simply the constant $66: MR(q) = 66.
To find the marginal profit function (MP), we subtract the marginal cost function from the marginal revenue function: MP(q) = MR(q) - MC(q) = 66 - (0.056q + 22.3) = -0.056q + 43.7. So, the marginal profit function is MP(q) = -0.056q + 43.7. Finally, to find the marginal profits for q = 390 thousand units, we substitute q = 390 into the marginal profit function: MP(390) = -0.056(390) + 43.7 = -21.84 + 43.7 = 21.86. Therefore, the marginal profits for q = 390 thousand units is $21.86.
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H. e. l. p MeEe
plss
Answers
Step-by-step explanation:
here you go hope it helps you
what hypothesis test should be used to test straight h subscript 1 italic colon italic space italic space sigma to the power of italic 2 subscript italic 1 over sigma to the power of italic 2 subscript italic 2 italic space italic space italic greater than italic space italic 1 one-sample test of means one-sample test of proportions one-sample test of variances two-sample test of means (independent samples) two-sample test of means (paired samples) two-sample test of proportions two-sample test of variances
Answers
An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
What is Hypothesis?In a scientific setting, a hypothesis (plural: hypotheses) is a tested claim regarding the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed. The hypothesis is a succinct statement of the researcher's expectation of the study's findings, which may or may not be confirmed by the results, in a scientific experiment or study. The scientific method's fundamental step is hypothesis testing.It is customary to refer to the researcher's prediction as the alternative hypothesis and any other result as the null hypothesis, or, more simply put, the opposite of what was anticipated. (However, the words are switched around if researchers are speculating that there won't be any difference or change, for instance, that the occurrence of one variable won't rise or fall in concert with thehence,sample test of means one-sample test of proportions one-sample test of variances two-sample test of means (independent samples) two-sample test of means (paired samples) two-sample test of proportions two-sample test of variances.
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student x pushes a 10-n box with a force of 2 n. at the same time, student y pushes the same box with a force of 6 n, but in the opposite direction. which would most likely occur? (ignore friction.)
Answers
how do you solve this pls help!!!
Answers
Answer:
y = 1
x = -0.75
Step-by-step explanation:
The alternate angles theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles are equal.
21y - 1 = 4x + 23
21y - 24 = 4x
5.25y - 6 = x
21y - 1 = 4x + 23
21y = 4x + 24
y = 4/21(5.25 - 6) + 1.14
y = 1 - 1.14 + 1.14
y = 1
5.25(1) - 6 = x
-0.75 = x
Someone plz help me
Answers
Answer:
13
------
28
I think that's the answer
Write each equation in slope-intercept form.
9.-10x + 2y = 12
12. 6x-3y=-18
10. 4y + 12x = 16
13.-2x-8y = 24
11. -5x + 15y = -30
14. -4x-10y = -7
Answers
Answer:
Step-by-step explanation:
2
if the msbetween is lower than your mswithin, the f value will be ______.
Answers
If the MSbetween (Mean Square Between) is lower than the MSwithin (Mean Square Within), the F value will be less than 1.
The F value is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). It is used in analysis of variance (ANOVA) to test for significant differences among group means. The F value follows an F-distribution, and its magnitude determines the statistical significance of the differences between groups.
When the MSbetween is lower than the MSwithin, it indicates that the variability between groups is smaller compared to the variability within groups. This suggests that the differences observed among the group means are not substantial or meaningful. In other words, there is more similarity within the groups than between them.
Since the F value is calculated as the ratio of MSbetween to MSwithin, if the numerator (MSbetween) is smaller than the denominator (MSwithin), the F value will be less than 1.
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geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 microgram of 206pb for 1.000 microgram of 238u present. approximately how old is the sample? yrs
Answers
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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What is the product?
(-6a^3b+ 2ab^2)(5a^2- 2ab^2-b)
A. -30a + 12ab2 +6ab+
10a2b2-4ab" - 2ab2
B. -30a5b+ 12ab + 16ab2-4a²b4-2ab3
C. 30a5b-12ab +4ab2-4a2b4-2ab
D. 30ab- 12ab2- 6ab+ 10a2b2- 4ab4 - 2ab2
Answers
Answer:
-30a^5b + 12a^4b^3 + 16a^3b^2 - 4a^2b^4 - 2 ab^3
Step-by-step explanation: