Unit 3: Relations and Functions
Homework 1: Relations,domain,range,and functions
Answers
The values of Relations, domain, range, and functions are calculated below.
What are the Relations, domain, range, and functions?
The domain of a function or relation is the set of all possible independent values the relation can take. It is the collection of all possible inputs. The range of a function or relation is the set of all possible dependent values the relation can produce from the domain values.
Domain - Set of x-values
Range - Set of y-values
3). Since, x values vary from x = -6 to x = 5,
The domain of the graph = [-6, 5]
Since, y-values vary from y = -2 to y = 3
Range of the graph = [-2, 3]
4).
The domain of the graph = [-3, 3]
Range of the graph = [-6, 5]
5).
Domain of the graph = (-∞, ∞)
Range of the graph = (-∞, ∞)
6).
Domain of the graph = (-∞, 4]
Range of the graph = (-∞, ∞)
7).
Domain of the graph = (-∞, ∞)
Range of the graph = [-1, 5]
8)
The domain of the graph = [-1, 5)
Range of the graph = [-3, 3)
Hence, the values of Relations, domain, range, and functions are calculated above.
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Related Questions
Plz help me ASAP ;-;
Answers
Answer:
The person who answered it first is correct
Step-by-step explanation:
If $1 is 3% and $2 is 7% and w1 is 0.1, beta of the portfolio is
Answers
The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.
The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.
To calculate the beta of the portfolio, we use the following formula:
β(portfolio) = (w1 * β1) + (w2 * β2) + ...
In this case, the portfolio contains two assets, so the formula becomes:
β(portfolio) = (w1 * β1) + (w2 * β2)
Substituting the given values:
β(portfolio) = (0.1 * 3%) + (0.9 * 7%)
β(portfolio) = 0.3% + 6.3%
β(portfolio) = 6.6%
Therefore, the beta of the portfolio is 6.6%.
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10. A line has equation y=3kx−2k and a curve has equation y=x 2
−kx+2, where k is a constant. a) Find the set of values of k for which the line and curve meet at two distinet points. b) For cach of two particular values of k, the line is a tangent to the curve. Show that these two tangents meet on the x-axis. 11. The equation x 2
+px+q=0, where p and q are constants, has roots −3 and 5 . a) Find the values of p and q. b) Using these values of p and q, find the value of the constant r for which the equation x 2
+px+q+r=0 has equal roots. 12. A curve has equation y=x 2
−4x+4 and a line has the equation y=mx, where m is a constant. a) For the case where m=1, the curve and the line intersect at the point A and B. b) Find the coordinates of the mid-point of AB. c) Find the non-zero value of m for which the line is the tangent to the curve, and find the coordinates of the point where the tangent touches the curve. Answer: 1. ( 2
1
,0) 9. a) 25−(x−5) 2
2. a) (3x− 2
5
) 2
− 4
25
b) (5,25) b) − 3
1
3
10. a) k>1,k<− 2
1
Answers
a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.
To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:
x^2 - kx + 2 = 3kx - 2k
Rearranging, we get:
x^2 - (3k + k)x + 2k + 2 = 0
For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:
(3k + k)^2 - 4(2k + 2) > 0
Simplifying, we get:
5k^2 - 8k - 8 > 0
Using the quadratic formula, we can find the roots of this inequality:
\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)
Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.
b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:
2x - 4 = m
3k = m
Substituting the first equation into the second, we get:
3k = 2x - 4
Solving for x, we get:
x = (3/2)k + (2/3)
Substituting this value of x into the equation of the curve, we get:
y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2
Simplifying, we get:
y = (9/4)k^2 + (8/9) - (5/3)k
For this equation to have a double root, the discriminant must be zero:
(-5/3)^2 - 4(9/4)(8/9) = 0
Simplifying, we get:
25/9 - 8/3 = 0
Therefore, the constant term is 8/3. Solving for k, we get:
(9/4)k^2 - (5/3)k + 8/3 = 0
Using the quadratic formula, we get:
\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)
Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:
For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1
For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3
Therefore, the two tangents meet on the x-axis at x = 2.
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Solve the following absolute value equation
Answers
Answer:
\( |x - 8| + 1 = 11\)
\( |x - 8| = 10\)
x - 8 = 10 or x - 8 = -10
x = 18 or x = -2
\(|x-8|+1 = 11\)
Move 1 to the right side:\(|x-8| = 10\)
Apply absolute rule: if |w| = a, a > 0 then w = a OR w = - a\(x-8 = -10\) OR \(x-8 = 10\)
Add 8 to both sides.\(x=-2\) OR \(x = 18\)
Which answers are equal to the expression below? Check all that apply
Answers
Answer:
A, B, D, E, F
Step-by-step explanation:
what is the square root of 39 divided by 5 multiplied by 10?
i dont think people realize how much strength it takes to pull your own self out of a dark place mentally. So if you have done that today or any day i am proud of you :)
Answers
2 square root 39 or 12.49
Determine the correct METRIC length of the cockroach in this image.
A 1.0 in
B 2.5 cm
C 7.5 cm
D 3.0 in
Answers
Answer:
B
Step-by-step explanation:
7.5cm - 5cm = 2.5cm
So it is B :)
Solve for p.
7/p = 8/9
Answers
Answer: p = 63/8
Step-by-step explanation:
first, we determine the defined range.
7/p = 8/9, p is not equal to 0.
then, we cross multiply.
63 = 8p
then, we divide both sides.
p = 63/8
anna charges $45 for the bracelets she sells at her boutique. it cost her $16 to make the bracelets. which is closest to the percent markup cost
Answers
The closest percent markup cost to the bracelets Anna sells is 181%.
To determine the percent markup cost for the bracelets Anna sells, we need to calculate the difference between the selling price and the cost price, and then express it as a percentage of the cost price.
The selling price of the bracelets is $45, and the cost price is $16.
Markup = Selling Price - Cost Price
= $45 - $16
= $29
Now, to calculate the percent markup cost, we divide the markup by the cost price and multiply by 100:
Percent Markup Cost = (Markup / Cost Price) \(\times\) 100
= ($29 / $16) \(\times\) 100
= 181.25
Rounded to the nearest whole number, the percent markup cost is approximately 181%.
Therefore, the closest percent markup cost to the bracelets Anna sells is 181%.
This means that Anna is charging customers approximately 181% more than what it cost her to make the bracelets.
The markup cost represents the additional amount she adds to cover expenses, overhead, and to make a profit.
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As a new year's resolution, jimmy has agreed to pay off his 4 credit cards and completely eliminate his credit card debt within the next 12 months. listed below are the balances and annual percentage rates for jimmy's credit cards. in order to pay his credit card debt off in the next 12 months, what will jimmy's total minimum credit card payment be?
Answers
The percentage shows that the value of Jimmy's total minimum credit card payment will be $411.25.
How to compute the minimum value?From the complete information, the balances and annual percentage rates for Jimmy's credit cards are given.
Therefore, the minimum amount for the credit card will be $411.25. This will be necessary to pay his credit card debt off in the next 12 months.
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For items 7-10, use the figure shown. Find the coordinates of the specified vertex after the given sequence of transformations.
Quadrilateral Q R S T plotted on a coordinate plane with vertices at, Q, (1, 3), R, (3, negative 3), S, (zero, negative 2), and T, (negative 2, 1).
a translation 2 units right, then a reflection across x = 0
Q' = ( , )
Answers
The coordinates of the specified vertex after the given sequence of transformations is given by;
Q' = (3, -3).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:
Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)
In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:
(x, y) → (x, -y)
Coordinate Q' (3, 3) → (3, -3).
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What is the domain? I need help on this problem
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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x ≥ -6
How to determine the domain of the functionFrom the question, we have the following parameters that can be used in our computation:
\(f(x) = \sqrt{\frac{1}{3}x + 2\)
Set the radicand greater than or equal to 0
So, we have
1/3x + 2 ≥ 0
Next, we have
1/3x ≥ -2
So, we have
x ≥ -6
Hence, the domain of the function is (d) x ≥ -6
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What is the measure of arc CD?
Answers
Answer:
80 deegree CD .................
What will this expression look like after distribution?
3 (1/3x + 2)
O 3x + 6
O x + 5
O 1/3x + 2
O x + 6
Answers
An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
Answers
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:\((3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2\)
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences \(= \sqrt{48.36 / 4}\)
Solving gives:
The standard deviation of the differences \(= \sqrt{2.09}\)
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
\(t = (2.2 - 0) / (3.47 / \sqrt5)\)
Substituting \(\sqrt 5 = 2.236\)
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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Will’s meal of grilled chicken strips and carrots contained a total of 333 calories. The bag of grilled chicken strips contained x servings of 110 calories each. The bag of carrots contained y servings of 29 calories each. Which equation written in standard form represents the number of servings of chicken strips and carrots that Will may have eaten?
110y = –29x + 333
29x + 110y = 333
29y = –110x + 333
110x + 29y = 333
Answers
Answer:
correct answer is 110x + 29y = 333
Step-by-step explanation:
Deshaun bought 6 bags of sugar for his restaurant. Each bag weighed 6.9 kilograms. How many kilograms of sugar did he buy total?
Answers
Answer:
41.4 kgs
Step-by-step explanation:
Take the number of bags times the weight of each bag
6 * 6.9
41.4 kgs
Answer:
41.4 kilograms of sugar
Step-by-step explanation:
its 41.4 kilograms of sugar because you take the 6 bags and multiply that by the 6.9
If the sum of the three different numbers is 54, what is the largest number?
(1) The largest number is twice the smallest number.
(2) The sum of the two smaller numbers is 30.
Answers
Main answer:
If the sum of the three different numbers is 54, what is the largest number, the largest number is 36.
Let's call the three numbers x, y, and z, where z is the largest number. We know that x + y + z = 54.
From statement (1), we know that z = 2x.
From statement (2), we know that x + y = 30, or y = 30 - x.
Substituting these expressions into the equation x + y + z = 54, we get:
x + (30 - x) + 2x = 54
Simplifying this equation, we get:
3x + 30 = 54
3x = 24
x = 8
Substituting x = 8 into the expressions for y and z, we get:
y = 30 - x = 22
z = 2x = 16
Therefore, the largest number is 36 (which is twice 8).
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The point P(1, 0) lies on the curve y = sin(14pi/x)
If Q is the point (x, (14pi/x)) find the slope of the secant line PQ (correct to four decimal places) for the following values of x.
(i) 2
(ii) 1.5
(iii) 1.4
(iv) 1.3
(v) 1.2
(vi) 1.1
(vii) 0.5
(viii) 0.6
(ix) 0.7
(x) 0.8
(xi) 0.9
Answers
The slopes of the secant lines are listed below:
Case I: m = 0
Case II: m = - √3 (aprox. 1.7321)
Case III: m = 0
Case IV: m = 2.2103
Case V: m = 5√3 / 2 (approx. 4.3301)
Case VI: m = 7.5570
Case VII: m = 0
Case VIII: m = - √3 (aprox. 1.7321)
Case IX: m = 0
Case X: m = 5
Case XI: m = - 9.8480
How to determine the determine the slope of a secant line
In this problem we find eleven cases of two pairs of points lying on a sinusoidal curve, each of which we need to determine the slope of the secant line by means of the following formula:
m = [f(a) - f(b)] / (b - a)
Where the definition of the sinusoidal function is f(x) = sin (14π / x).
Now we proceed to determine the slope of each secant line:
Case I
m = [f(2) - f(1)] / (2 - 1)
m = (0 - 0)
m = 0
Case II
m = [f(1.5) - f(1)] / (1.5 - 1)
m = (- √3 / 2 - 0) / 0.5
m = - √3 (aprox. 1.7321)
Case III
m = [f(1.4) - f(1)] / (1.4 - 1)
m = (0 - 0) / 0.4
m = 0
Case IV
m = [f(1.3) - f(1)] / (1.3 - 1)
m = (0.6631 - 0) / 0.3
m = 2.2103
Case V
m = [f(1.2) - f(1)] / (1.2 - 1)
m = (√3 / 2 - 0) / 0.2
m = 5√3 / 2 (approx. 4.3301)
Case VI
m = [f(1.1) - f(1)] / (1.1 - 1)
m = (0.7557 - 0) / 0.1
m = 7.5570
Case VII
m = [f(0.5) - f(1)] / (0.5 - 1)
m = (0 - 0) / (- 0.5)
m = 0
Case VIII
m = [f(0.6) - f(1)] / (0.6 - 1)
m = (- √3 / 2 - 0) / (- 0. 4)
m = - √3 (aprox. 1.7321)
Case IX
m = [f(0.7) - f(1)] / (0.7 - 1)
m = (0 - 0) / (- 0. 3)
m = 0
Case X
m = [f(0.8) - f(1)] / (0.8 - 1)
m = (- 1 - 0) / (- 0.2)
m = 5
Case XI
m = [f(0.9) - f(1)] / (0.9 - 1)
m = (- 0.9848 - 0) / (- 0.1)
m = - 9.8480
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Solve the quadratic equation numerically (using tables of x- and y- values). (x +2) (x + 3) = 12
Answers
sorry bro i let my brother try to solve random problems on here
Answer:
\(x=-6,\: x=1\)
Step-by-step explanation:
\((x+2)(x+3)=12\\\\x^2+5x+6=12\\\\x^2+5x-6=0\\\\(x+6)(x-1)=0\\\\x=-6,\: x=1\)
Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2
Answers
The quadratic function y = -7x² represents the trajectory of one of the water balloons. Since it is a quadratic function, it forms a parabola. The coefficient of x², -7, determines the shape of the parabola.
Since the coefficient is negative, the parabola opens downwards.
The x-axis represents time, and the y-axis represents the height of the water balloon. The vertex of the parabola is the highest point the water balloon reaches before falling back down. To find the vertex, we can use the formula
x = -b/2a.
In this case,
b = 0 and a = -7.
Thus, x = 0.
So, the water balloon reaches its highest point at x = 0.
Plugging this value into the equation, we find that y = 0.
Therefore, the water balloon starts at the ground, reaches its highest point at x = 0, and then falls back down.
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Since the quadratic functions for the two water balloons are identical, the collision happens at all moments. The water balloons collide at every height and time, forming a continuous collision.
The quadratic function \(y = -7x^2\) represents the height (y) of a water balloon at different moments (x). When two water balloons collide, it means their heights are equal at that particular moment. To find when the collision occurs, we can set the two quadratic functions equal to each other:
\(-7x^2 = -7x^2\)
By simplifying and rearranging, we get:
0 = 0
This equation is always true, which means the water balloons collide at every moment. In other words, they collide continuously throughout their trajectory.
In conclusion, since the quadratic functions for the two water balloons are identical, the collision happens at all moments. The water balloons collide at every height and time, forming a continuous collision.
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Please help! (Also show work)
Tutorials :D
Answers
The five-number summary is:
Minimum: 9
First Quartile: 16.5
Median: 25.5
Third Quartile: 39
Maximum: 51
3. Range = 42
4. Interquartile range = 22.5
How to Find the Five-number Summary of a Data?Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:
1. The numbers in ordered from the smallest to the largest would be:
9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51
2. The five-number summary for the lengths in minutes would be:
Minimum value: this is the smallest lengths, which is 9First Quartile (Q1): this is the middle of the first half of the data set of the lengths in minutes, which is 16.5.Median: the median is the center of the data distribution which is 25.5.Third Quartile: this is the middle of the second half of the data set of the lengths in minutes, which is 39.Maximum: this is the largest length in minutes, which is, 51.3. Range of the data = max - min = 51 - 9 = 42
4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5
Interquartile range for the data set = 22.5
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Which is the image of the figure below after a 90° clockwise rotation about Point P?
Answers
Check below, please.
1) In this case, we've got here to rotate this figure in a clockwise way about point P.
2) So, this rotation about point P is going to flip this quadrilateral up. And P' will be on the lower left of this image.
3) Thus, the image that represents this transformation is on the alternative:
∠3 and ∠6 are _______ angles
Answers
Alternate interior angles are congruent. so ∠3 = ∠6 -------> by alternate interior angles.
________________
Hope this makes sense!
-Lexi
Need answer PLS will give brainiest
Answers
Answer:
n=-6
Step-by-step explanation:
cuantas veces cabe 12 en 77?
Answers
Answer:
6.4166
Step-by-step explanation:
77/12 = 6.41666666667
will mark brainliest helpppp
Answers
Answer is B. The base of the pyramid is 16 square inches and the other sides add up to 40. 40+16=56
a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 411 gram setting. based on a 19 bag sample where the mean is 437 grams and the varicance is 441, is there sufficent evidence at the 0.025 level that the bags are underfilled?
Answers
Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .
In the given question, we shall check the bag is underfilled at given level or not .
We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :
H₀ : u = 411 : the bags are not underfilled
Hₜ : u < 411 : the bags are underfilled
Check it now using statistic Z-test and the test Statistic formula is given by
= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .
From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21
Including all of the above variables in formula
Z = (437-411)/21/√19
= 26/21/√19
= 5.395
This is right -tail test in statistic Z -test
P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )
The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025
P- value >α , this implies that Null hypothesis is not Rejected .
There is sufficient evidence to suggest that bag is not underfilled.
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Evaluate the expression with it’s given values. 3x/y ; x = 4, y = 12
Answers
The expression with its given values. 3x/y ; x = 4, y = 12 is 1
Given expression= 3x/y
x= 4 and y= 12
putting the values of x and y in the given expression,
3*4/12 = 1
The answer for the given expression is 1.
What is an Expression?
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cone frustum the first-octant portion of the cone z = 2x2 y2>2 between the planes z = 0 and z = 3
Answers
The volume of the cone frustum is 4.19 cubic units.
How to find the volume of the cone frustum?To find the volume of the cone frustum, we can use the formula:
\(V = (1/3)\pi h(R^2 + Rr + r^2)\)
where h is the height of the frustum, R and r are the radii of the top and bottom bases, respectively.
In this case, the frustum is given by the inequality\(z = 2x^2 + y^2 < 2\) and is bounded by the planes z = 0 and z = 3. This means that the height of the frustum is h = 3 - 0 = 3.
To find the radii R and r, we need to find the intersection of the cone \(z = 2x^2 + y^2\) and the plane z = 2. Substituting z = 2 into the cone equation, we get:
\(2 = 2x^2 + y^2\)
This is the equation of an ellipse in the xy-plane with major axis along the x-axis and minor axis along the y-axis.
To find the radii, we can use the standard form of the ellipse:
\((x/a)^2 + (y/b)^2 = 1\)
where a and b are the semi-major and semi-minor axes, respectively. Comparing this with the equation of the ellipse above, we get:
\(a^2 = 1/2\) and \(b^2 = 2\)
Therefore, the radii are R = √(1/2) and r = √2.
Substituting these values into the formula for the volume, we get:
V = (1/3)π(3)(1/2 + √2/2 + 2)
Simplifying this expression, we get:
V = (π/3)(√2 + 5)
Therefore, the volume of the cone frustum is approximately 4.19 cubic units.
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