equation of a line with slope m=−2/5 that contains the point (10,−5).
Answers
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the given values, we get:
y - (-5) = (-2/5)(x - 10)
Simplifying the right side, we get:
y + 5 = (-2/5)x + 4
Subtracting 5 from both sides, we get:
y = (-2/5)x - 1
Therefore, the equation of the line with slope m = -2/5 that contains the point (10,-5) is y = (-2/5)x - 1.
Answer:
y = (-2/5)x+b
Step-by-step explanation:
First plug these into the y=mx+b equation:
-5 = (-2/5)(10)+b.
Then solve for b:
-5 = -4+b
Add 4 to both sides:
-1 =b.
Therefore, the equation of the line is y = (-2/5)x+b. You can also double check this by plugging 10 into the equation we just obtained.
Related Questions
if molly can mow a lawn in 3 hours and her little brother can do it in 6 hours, how many hours will it take to mow the lawn while working together?
Answers
It will take 2 hours for Molly and her little brother to mow the lawn while working together.
Molly can mow a lawn in 3 hours and her little brother can mow the lawn in 6 hours.
The task is to calculate how long it will take to mow the lawn while working together.
When two people work together, their work rates add up, so the total work rate is given by the sum of their individual work rates.
Let M represent the work rate of Molly and B represent the work rate of her little brother.
Then: M = 1/3 (Molly can mow a lawn in 3 hours)B = 1/6 (Little brother can mow a lawn in 6 hours)
When working together, their combined work rate is the sum of their individual work rates.
Hence, their combined work rate is given by: M + B = 1/3 + 1/6 (Adding the work rates of both)
M + B = 1/2 (Adding both fractions, the LCD of the two fractions is 6)
So, the combined work rate of Molly and her brother is 1/2.
This means that they can complete one lawn in 2 hours.
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Suppose that a certain differential equation has two solutions at the point y(t0) = y0. Explain why there could be two solutions to the differential equation without contradicting the existence and uniqueness theorem. How does your answer vary depending on the classification of the differential equation?
Answers
A differential equation can have more than one solution, and it can satisfy the initial conditions as long as it is nonlinear or inhomogeneous, and there is no guarantee that the solution exists and is unique. The solutions to a differential equation are entirely dependent on its classification. If the differential equation is nonlinear or inhomogeneous, the existence and uniqueness theorem does not apply. Thus, two solutions can exist for the same initial conditions.
The existence and uniqueness theorem of a differential equation states that for a given initial condition, there is a unique solution of a differential equation within a given interval. That is, if two solutions agree at a certain point and their derivatives are equal at that point, then they must be identical over their entire interval.
Thus, if a certain differential equation has two solutions at the point y(t0) = y0, it means that the solutions agree at that particular point, but this does not violate the existence and uniqueness theorem because there could be different solutions within different intervals. A differential equation can have two solutions for the same initial condition but in different intervals. Hence, the existence and uniqueness theorem applies only when the differential equation is linear and homogeneous.
That is, the equation must not have any nonlinear terms and the coefficients must not depend on the dependent variable. If the differential equation is nonlinear or inhomogeneous, there is no guarantee that the solution exists and is unique. Therefore, when it comes to the classification of the differential equation, if the differential equation is linear and homogeneous, the existence and uniqueness theorem applies, and two solutions would violate the theorem.
However, if the differential equation is nonlinear or inhomogeneous, the existence and uniqueness theorem does not apply. Thus, two solutions can exist for the same initial conditions.
Therefore, it is crucial to note that the nature of differential equations plays an essential role in the existence of multiple solutions. A differential equation can have more than one solution, and it can satisfy the initial conditions as long as it is nonlinear or inhomogeneous, and there is no guarantee that the solution exists and is unique. The solutions to a differential equation are entirely dependent on its classification.
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imagine an island that is 1 square mile. the island has a population of 1950 people. although the island is not perfectly square, the image below can help us imagine the situation. 1
Answers
ANSWER:
a. 1950 people per square mile
b. The island's area got smaller
c.
\(\frac{1950\text{ people}}{0.5\text{ square mile}}\)STEP-BY-STEP EXPLANATION:
Population density is the average number of people living per unit area. It is calculated by dividing the total number of population of a geographical unit (in this case it is the island) by the total amount of surface.
a.
Therefore:
\(Density=\frac{1950\text{ people}}{1\text{ square mile}}=1950\text{ people per square miles}\)b.
Since the size of the island is halved without losing any people, we can conclude that the area has become smaller.
Therefore:
The island's area got smaller
c.
Since it is half the area, the new density would be:
\(Density=\frac{1950\text{ people}}{0.5\text{ square mile}}\)Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.s = 31.3, t = 13.3
Answers
The value of sin(θ) is approximately 0.921 and the value of cos(θ) is approximately 0.391.
To find the value of each variable using sine and cosine, we need to set up a right triangle with the given information. Let's label the sides of the triangle as follows:
s = 31.3 (opposite side)t = 13.3 (adjacent side)h (hypotenuse)Using the Pythagorean theorem, we can find the length of the hypotenuse:
h2 = s2 + t2
h2 = 31.32 + 13.32
h2 = 979.69 + 176.89
h2 = 1156.58
h = √1156.58
h ≈ 34.0
Now that we know the length of the hypotenuse, we can use sine and cosine to find the values of the variables:
sin(θ) = s / h
sin(θ) = 31.3 / 34.0
sin(θ) ≈ 0.921
cos(θ) = t / h
cos(θ) = 13.3 / 34.0
cos(θ) ≈ 0.391
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10) Alayah's puppy weighed 12 lbs. when they brought it home from the Humane Society.
Over the past 6 months, the puppy gained the same amount of weight each month and
now weighs 36 lbs. How much weight was gained each month?
Answer Statement:
Answers
24+12 = 36
Line l passes through the points (-8, 8) and (-4, 0). Write the equation of the image of
after a dilation with a scale factor of 1, centered at the origin.
Write your answer in slope-intercept form.
y =
Answers
Find the absolute maximum and absolute minimum of the function z=f(x,y)=5x 2
−20x+5y 2
−20y on the domain D:x 2
+y 2
≤121 (Use symbolic notation and fractions where needed.) absolute min: absolute max:
Answers
The absolute minimum of the function z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y on the domain D: x^2 + y^2 ≤ 121 is achieved at the point (-11, 0), and the absolute maximum is achieved at the point (11, 0).
To find the absolute maximum and absolute minimum of the function \(z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y\) on the domain \(D: x^2 + y^2 \leq 121\), we need to consider the critical points and boundary of the domain.
First, we find the critical points by taking the partial derivatives of \(f\) with respect to \(x\) and \(y\) and setting them equal to zero:
\(\frac{\partial f}{\partial x} = 10x - 20 = 0\),
\(\frac{\partial f}{\partial y} = 10y - 20 = 0\).
Solving these equations, we get the critical point \((2, 2)\).
Next, we examine the boundary of the domain \(D: x^2 + y^2 \leq 121\), which is a circle centered at the origin with radius 11. We can parameterize the boundary as \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\), where \(r = 11\) and \(0 \leq \theta \leq 2\pi\).
Substituting these parameterizations into \(f(x, y)\), we obtain \(z = g(\theta) = 5(11\cos(\theta))^2 - 20(11\cos(\theta)) + 5(11\sin(\theta))^2 - 20(11\sin(\theta))\).
To find the absolute maximum and minimum on the boundary, we need to find the critical points of \(g(\theta)\). We take the derivative of \(g(\theta)\) with respect to \(\theta\) and set it equal to zero:
\(\frac{dg}{d\theta} = -220\cos(\theta) + 110\sin(\theta) = 0\).
Simplifying this equation, we get \(\tan(\theta) = \frac{220}{110} = 2\).
Thus, the critical points on the boundary occur at \(\theta = \arctan(2)\) and \(\theta = \arctan(2) + \pi\).
Now, we evaluate the function \(f(x, y)\) at the critical points and compare them to determine the absolute maximum and minimum.
At the critical point \((2, 2)\), we have \(f(2, 2) = 5(2)^2 - 20(2) + 5(2)^2 - 20(2) = -40\).
At the critical points on the boundary, we have \(z = f(11\cos(\theta), 11\sin(\theta))\).
Evaluating \(f\) at \(\theta = \arctan(2)\), we get \(f(11\cos(\arctan(2)), 11\sin(\arctan(2)))\).
Similarly, evaluating \(f\) at \(\theta = \arctan(2) + \pi\), we get \(f(11\cos(\arctan(2) + \pi), 11\sin(\arctan(2) + \pi))\).
Comparing the values of \(f\) at the critical points and the critical point \((2, 2)\), we can determine the absolute maximum and minimum.
In summary, the absolute minimum of the function \(z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y\) on the domain \(
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Rectangle pqrs is folded along the line pr. The ratio of the area of rectangle pqrs to the new area of the figure is 11:7. The area of the shaded part is 68cm find the are of rectangle pqrs
Answers
Rectangle pqrs is folded along the line pr. The ratio of the area of rectangle pqrs to the new area of the figure is 11:7, the area of rectangle pqrs is 106.8 cm².
Let the area of the rectangle be x
therefore, we already know that x/68 = 11/7 as the area of the shaded part is 68cm and the ratio of the area of rectangle pqrs to the new area of the figure is 11:7.
x = 11/7 × 68
x = 11 × 9.71428
x = 11 × 9.71
x = 106.81 cm² or we can round it off as 106.8 cm²
Rectangle pqrs is folded along the line pr. The ratio of the area of rectangle pqrs to the new area of the figure is 11:7. The area of the shaded part is 68cm, the area of rectangle pqrs is 106.8 cm².
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ten plus 8 to the third power divided by 16
Answers
Answer: 42
Step-by-step explanation:
10+8^3/10
Exponets first
8^3=512
Then Divide
512/16=32
Finally add
32+10=42
Use Order of Operations
A researcher is investigating the effect of sleep deprivation on learning. She recruits 30 participants and randomly assigns half to a "no sleep" group and half to a "regular sleep" group. The "no sleep" group are required to stay up all night and report to a testing room at 2PM the following day. The "regular sleep" group are instructed to have a normal night's sleep and report to the testing room at 9AM the following day. Unfortunately, a water pipe broke outside the testing room window and there was noisy construction crew working the whole day of testing. Which of the following statements is true?
a. The study may be affected by a situational variable.
b. The construction noise may contribute to variability in test scores.
C. The study has a confounding variable. The groups differ in the time they are to report to the testing room.
d. All of these are true.
Answers
The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
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which example describes the scientific method?
Answers
The correct steps that best describe the scientific method are:
The scientific method has five basic steps, plus one feedback step:
Make an observation.Ask a question.Form a hypothesis, or testable explanation.Make a prediction based on the hypothesis.Test the prediction.Iterate: use the results to make new hypotheses or predictions.What is the Scientific Method?The scientific method is a systematic approach to scientific inquiry that involves a series of steps used to investigate, test, and understand natural phenomena
The process of the scientific method involves making conjectures (hypotheses), deriving predictions from them as logical consequences, and then carrying out experiments or empirical observations based on those predictions.
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let p(n) be the statement that 13 23 33 ... n3 = (n(n +1)2)^2 for the positive integer n. we will have completed the basis step of the proof if we show that (Check all that apply.) (You must provide an answer before moving to the next part.) Check All That Apply O P(1) is true. O P(O) is true. O P(1) -> P2) is true. O 1^3 + 2^3 + ... + n^3 = { n(n+1)^2} is true for n=1 1^3 + 2^3 + ... + n^3 = { n(n+1)^2} is true for some integer n.
Answers
To complete the basis step of the proof for p(n), we need to show that P(1) is true.
This means substituting n=1 into the equation 1³ + 2³ + ... + n³ = { n(n+1)²) and verifying that it holds true. In this case, we get 1³ = 1(1+1)², which simplifies to 1 = 1. Therefore, P(1) is true.
The statement p(n) represents an equation that we need to prove for all positive integers n.
To start a proof by induction, we need to establish the basis step by showing that the equation holds true for the first value of n, which in this case is n=1. By checking that P(1) is true, we can establish a strong foundation for the rest of the proof.
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HELPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEE
(1/4) + (1/2) =
Answers
Answer:
.75
Step-by-step explanation:
(1/4)+(1/2)= (3/4)
PLZZZ HELP!! Which expressions are equivalent to -6+4q+(-6q) Choose all answers that apply:
Answers
Answer: IT IS: A
Step-by-step explanation:
math duh
Answer:
the answer : None of them above
Step-by-step explanation:
the true answer is -6-2q
Select whether the equation has a solution or not? Square root 4x =2 square root 2x-3
Answers
Answer:yes
Step-by-step explanation:
don't ask i searched it up
What is the solution to n/4 = -12.4?
n = 3.1
n = -3.1
n = 49.6
n = -49.6
Answers
Answer:
n= -49.6
Step-by-step explanation:
49.6 i did this test and got it right
Evaluate the given integral by changing to polar coordinates. 49 − x2 − y2 darwhere r = (x, y) | x2 y2 ≤ 49, x ≥ 0
Answers
The value of the integral is 343π/3 by changing to polar coordinates. √(49 − x2 − y2) dA where r = (x, y) | x2 y2 ≤ 49, x ≥ 0
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have the integral:
\(\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA\)
Where, r = (x, y) | x2 y2 ≤ 49, x ≥ 0
The polar coordinate will be:
x = rcosθ
y = rsinθ
Where x²+y²= r²
Put the value of x and y in the integral, and the limits will be:
r²≤49 or 0≤r≤7, -π/2≤θ≤π/2 ( since x ≥0)
dA = rdrdθ
\(\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA = \int\limits^{\dfrac{\pi}{2}}_{\dfrac{-\pi}{2}} \int\limits^7_0 {\sqrt{49-r^2]} \, rdrd\theta\)
After solving the double integration, we will get:
\(\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA = \dfrac{343}{3} \pi\)
Thus, the value of the integral is 343π/3 by changing to polar coordinates. √(49 − x2 − y2) dA where r = (x, y) | x2 y2 ≤ 49, x ≥ 0
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simplify the expression 10(7+7g)+4
Answers
Answer:
70g+74
Step-by-step explanation:
Answer:
= 70g + 74
Step-by-step explanation:
10 (7 + 7g) + 4
= 10(7g + 7) + 4
= 70 + 70g + 4
= 70g + 74
PLEASEEEEE HELPPP !!!!!!!!
JKL and KMN are shown below.
Which statement is true?
Answers
Answer:
SIMILAR
Step-by-step explanation:
The lines are parallel to each other, and one of the angles are 90 degrees. That is the only info that you get. You need to be able to make sure that another angle besides the 90 degrees is similar. The lines are parallel to each other, meaning that the other two angles should be equal in measure. See, if the angle in the second triangle gets bigger, the lines wouldn't be parallel, would they?
The manager would like to know the probability of a stockout during replenishment lead-time. in other words, what is the probability that demand during lead-time will exceed 25 gallons?
Answers
The probability that demand during this period will exceed 25 gallons depends on the distribution of demand.
To calculate the probability of a stockout during the replenishment lead-time, we need to consider the distribution of demand during this period. If the demand follows a known probability distribution, such as the normal distribution, we can use statistical methods to estimate the probability.
First, we need to determine the parameters of the distribution, such as the mean and standard deviation of the demand during the lead-time. Once we have these parameters, we can calculate the probability of demand exceeding 25 gallons using the cumulative distribution function (CDF) of the chosen distribution.
For example, if the demand during lead-time follows a normal distribution with a mean of 20 gallons and a standard deviation of 5 gallons, we can use the normal distribution table or statistical software to find the probability of demand exceeding 25 gallons.
Alternatively, if we have historical data on demand during lead-time, we can use that data to estimate the probability. We can calculate the proportion of instances where the demand exceeded 25 gallons and use this as an estimate of the probability of a stockout during the lead-time.
Overall, the probability of a stockout during replenishment lead-time depends on the distribution of demand and can be determined using statistical techniques or historical data.
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Scheduling classes in three periods expressed using SAT. About Suppose a school has three periods (called 1, 2, and 3) during which a class can be scheduled. For each class, there are three variables. For example, for class A, there are variables XA1, XA2, and XA3. Setting ХА2-1 represents scheduling class A during period 2.
(a) Give a Boolean expression that evaluates to 1 if and only if A is scheduled in at least one of the three periods.
(b) Give a Boolean expression that evaluates to 1 if and only if A is not scheduled in more than one period.
(c) Give a Boolean expression that evaluates to 1 if and only if A and B are not scheduled in the same period.
Answers
The Boolean expression for A being scheduled in at least one of the three periods is XA1 OR XA2 OR XA3.
The Boolean expression for A not being scheduled in more than one period is (XA1 XOR XA2) AND (XA2 XOR XA3) AND (XA3 XOR XA1).
The Boolean expression for A and B not being scheduled in the same period is (XA1 XOR XB1) AND (XA2 XOR XB2) AND (XA3 XOR XB3).
(a) To evaluate whether class A is scheduled in at least one of the three periods, we use the OR operator between the three variables: XA1 OR XA2 OR XA3. If at least one of these variables is true, the expression will evaluate to true (1), meaning that class A is scheduled in at least one period.
(b) To ensure that class A is not scheduled in more than one period, we use the XOR (exclusive OR) operator between all possible pairs of variables.
If two variables are true (1) at the same time, the expression will evaluate to false (0), meaning that class A is not scheduled in more than one period. We need to use the AND operator between all three pairs of XOR expressions to ensure that they are all true.
(c) To ensure that class A and class B are not scheduled in the same period, we use the XOR operator between the corresponding variables for each class:
XA1 XOR XB1, XA2 XOR XB2, and XA3 XOR XB3.
If any of these expressions evaluate to true (1), it means that class A and class B are not scheduled in the same period. We need to use the AND operator between all three expressions to ensure that they are all true.
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The Brandywine Dance Team is buying equipment and T-shirts. The equipment costs $356 and the T-shirts cost $12 each. The team spent a total of $644
Answers
The number of T-shirts bought by the Brandywine Dance Team is 24.
How is the number of T-shirts determined?The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.
First, the cost of the equipment is subtracted from the total cost spent by the team. The remainder refers to the cost of the T-shirts. Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.
Data and Calculations:The total amount spent = $644
The cost of the equipment = $356
The remainder after the equipment = $288 ($644 - $356)
Unit cost of T-shirts = $12
The number of T-shirts bought = 24 ($288/$12)
Thus, the Brandywine Dance Team bought 24 T-shirts.
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Question Completion:How many T-shirts were purchased by the Team?
How do you simplify 8z • 6z
Answers
Answer:
its really simple
Step-by-step explanation:
since you dont know z you would just multiply them so you would get 48z
but since you dont know what z is i believe its 48z^2 or just 48z
Please help, due soon. Use the information provided to write the standard form equation of each circle
Answers
Answer:
D
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( where r is the radius ) , then
x² + y² = (\(\sqrt{249}\) )² , that is
x² + y² = 249 → D
Enrique's company pays Salim to advertise on Salim's Website. Salim's Website earns $15 per month plus $0.05 every time a visitor clicks on the advertisement. What is the least number of clicks per month that Salim needs in order to earn $50 per month or more?
Answers
Answer:
2000
Step-by-step explanation:
Salim will need to get 2000 clicks in order to get $50 per month or more.
First: 5 cents goes into one dollar 20 times.
Second: You multiply 20 times 50. This is how you get 2000. There is your answer.
Salim needs at least 700 clicks per month in order to earn $50 per month or more
A linear equation is in the form:
y = mx + b;
where y, x is variable, m is the rate of change and b is the y intercept.
Let y represent the total pay Salim earns and x represent the number of clicks.
Salim's Website earns $15 per month plus $0.05 every time a visitor clicks, hence:
y = 0.05x + 15
To earn for than $50 per month:
0.05x + 15 > 50
0.05x > 35
x > 700
Salim needs at least 700 clicks per month in order to earn $50 per month or more
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Lisa bought 4 feet of gold braid at a price of 5.75 per yard. what was the total price of the amount of gold braid she bought
Answers
Use the table of values to calculate the linear correlation coefficient r.
х
-20
3
-7
10
6
у
-81
-9
6
-5
r= 0.968
r=0.781
r=0.625
r=0.756
Would someone pls show steps to solving this
Answers
The linear correlation coefficient (r) using the given table of values is approximately 0.968, indicating a strong positive correlation between x and y values. so, the correct option is A.
To calculate the linear correlation coefficient (r) using the given table of values, follow these steps
Calculate the mean (average) of both the x-values (X) and y-values (Y).
x-values: -20, 3, -7, 10, 6
Mean of x-values (X) = (-20 + 3 + (-7) + 10 + 6) / 5 = -8/5
y-values: -81, -9, 6, -5
Mean of y-values (Y) = (-81 + (-9) + 6 + (-5)) / 4 = -89/4
Calculate the difference between each x-value and the mean of x (x - X), and the difference between each y-value and the mean of y (y - Y).
x - X: -20 - (-8/5), 3 - (-8/5), -7 - (-8/5), 10 - (-8/5), 6 - (-8/5)
y - Y: -81 - (-89/4), -9 - (-89/4), 6 - (-89/4), -5 - (-89/4)
Simplify these differences
x - X: (-92/5), (43/5), (-27/5), (58/5), (46/5)
y - Y: (-305/4), (305/4), (425/4), (305/4)
Calculate the product of (x - X) and (y - Y) for each pair of values, and sum up these products.
(-92/5) * (-305/4) + (43/5) * (305/4) + (-27/5) * (425/4) + (58/5) * (305/4) + (46/5) * (305/4) = 12168/25
Calculate the standard deviation of x-values (σx) and y-values (σy).
σx = √[(Σ(x - X)²) / (n - 1)]
σy = √[(Σ(y - Y)²) / (n - 1)]
Σ(x - X)² = ((-92/5)² + (43/5)² + (-27/5)² + (58/5)² + (46/5)²) = 14008/25
Σ(y - Y)² = ((-305/4)² + (305/4)² + (425/4)² + (305/4)²) = 183625/16
σx = √[(14008/25) / (5 - 1)] = √(3502/25) = √(14008/100) = √140.08 ≈ 11.83
σy = √[(183625/16) / (4 - 1)] = √(61208.33/16) = √(3825.52) ≈ 61.91
Calculate the correlation coefficient (r)
r = Σ((x - X)(y - Y)) / (σx * σy)
r = (12168/25) / (11.83 * 61.91)
r ≈ 0.968
Therefore, the linear correlation coefficient (r) is approximately 0.968. so, the correct answer is A.
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--The given question is incomplete, the complete question is given below " Use the table of values to calculate the linear correlation coefficient r.
х -20 3 -7 10 6
у -81 -9 6 -5
choose the correct answer
a, r= 0.968
b, r=0.781
c, r=0.625
d, r=0.756
Would someone pls show steps to solving this "--
people attend a party. Each person shakes hands with at most other people. What is the maximum possible number of handshakes, assuming that any two people can shake hands at most once
Answers
The maximum possible number of handshakes at the party can be calculated using the formula n(n-1)/2, where n is the number of people attending. This formula is derived from the fact that each person can shake hands with every other person except themselves.
Let's assume that there are n people attending the party. In order to maximize the number of handshakes, we want each person to shake hands with every other person except themselves.
Now, let's consider the first person. They can shake hands with (n-1) other people, as they cannot shake hands with themselves. Similarly, the second person can shake hands with (n-1) other people, but they have already shaken hands with the first person, so they can only shake hands with (n-1)-1 = (n-2) remaining people.
Following this pattern, the third person can shake hands with (n-1)-2 = (n-3) people, the fourth person can shake hands with (n-1)-3 = (n-4) people, and so on. The last person, the nth person, can shake hands with (n-1)-(n-2) = 1 person.
By summing up the number of handshakes for each person, we get (n-1) + (n-2) + (n-3) + ... + 1, which is the sum of the first (n-1) natural numbers. This sum can be calculated using the formula n(n-1)/2.
Therefore, the maximum possible number of handshakes at the party is n(n-1)/2.
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Create ABC by drawing AC. AC represents the foreman’s line of sight to the top of the landfill. What is m
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Where the above is given, the required angle m∠BAC = 45°.
In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC
What is triangle?The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°
According to conditions angle b = 90°
The sum of angles of a triangle= 180°
That is a + b + c = 180
Therefore, c = a
a = (180 - b)/2
= (180 - 90) / 2
= 90 / 2
= 45°
Hence, the required angle m∠BAC = 45°
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?
when an item is marked up by a certain percent and then marked down by the same percent, is the sale price equal to the price before the markup and markdown?
Answers
Answer: yes it is
Step-by-step explanation: