The expression that represents the area of the patio is 37.5 + 12.5x. To find the area of the patio, we need to multiply the length and width of the patio. From the given plan, we can see that the length of the patio is 3 feet and the width is x feet. Therefore, the area of the patio would be 3x square feet.
However, the question states that Yolanda wants to use both brick and wood for the flooring. So, we need to add the areas of the brick and wood flooring. The area of the brick flooring is 37.5 square feet (given in the plan) and the area of the wood flooring is 12.5x square feet (also given in the plan). Therefore, the total area of the patio would be 37.5 + 12.5x square feet. The other expressions do not accurately represent the area of the patio.
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find x if 4/7 f(2x+6)=4
No links please- will be re ported
Will give Brainliest
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
\(x=\frac{7}{2f} -3\)
My gratitude attitude - THANKS!
Find the slope and the equation of the tangent line to the graph of the function at the given value of x. y=x 4
−10x 2
+9;x=1 The slope of the tangent line is (Simplify your answer.) The equation of the tangent line is
The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.
The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.
Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:
dy/dx = 4x^3 - 20x
To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:
dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16
Therefore, the slope of the tangent line is -16.
To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:
y - y(1) = -16(x - 1)
Expanding the equation and simplifying, we have:
y - y(1) = -16x + 16
Rearranging the equation, we obtain the equation of the tangent line:
y = -16x + (y(1) + 16)
To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.
In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.
The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.
To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.
Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).
The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.
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3. A phone company set the following rate schedule for an m-minute
call from any of its pay phones.
c(m) =
=
0.70
0.70+ 0.24(m - 6)
0.70+ 0.24([m-6] + 1)
when m≤ 6
when m > 6 and m is an integer
when m> 6 and m is not an integer
a. What is the cost of a call that is under six minutes?
b. What is the cost of a 14-minute call?
c. What is the cost of a
1912-m
9-minute call?
The obtained answers for the given piecewise function are:
(a) The cost of a call that is under six minutes is 0.70 (m < 6)
(b) The cost of a 14-minute call is 2.62 (m > 6; m is an integer)
(c) The cost of a 9 1/2 minute call is 1.66 (m > 6; m is not an integer)
What is a piecewise function?A piecewise function is given by different functions at different intervals.
Calculation:It is given that,
phone company set the following rate schedule for an m-minute call from any of its pay phones.
C(m) = 0. 70 when m ≤ 6
= 0.70 + 0.24(m - 6) when m > 6 and m is an integer
= 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer
(a) The cost of a call that is under six minutes:
Since m < 6, the cost is C(m) = 0.76
Thus, the cost of a call that is under six minutes is 0.76
(b) The cost of a 14-minute call:
Since 14 > 6, the cost is C(m) = 0.70 + 0.24(m - 6) when m > 6 and m is an integer.
C(14) = 0.70 + 0.24(14 - 6)
= 0.70 + 0.24(8)
= 0.70 + 1.92
= 2.62
Thus, the cost of a 14-minute call is 2.62.
(c) The cost of a 9 1/2 minute call:
9 1/2 = 19/2 = 9.5
Since 9.5 > 6, the cost is C(m) = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer.
C(9.5) = 0.70 + 0.24([9.5 - 6] + 1)
= 0.70 + 0.24([3.5] + 1)
Since we know that if [x] is a function then its domain is R and the range is Z(integer)
So, [3.5] = 3(is an integer)
Then,
C(9.5) = 0.70 + 0.24(3 + 1)
= 0.70 + 0.96
= 1.66
Therefore, the cost of a 9 1/2 minute call is 1.66.
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find f(s). ℒ (4t 1) (t − 1)
\(f(s) = ℒ{(4t+1)(t-1)} = 8/s^3 - 3/s^2 - 1/s\) by using laplace transform for the function.
A mathematical technique for studying linear, time-invariant systems is the Laplace transform. It transforms a time-domain function into a frequency-domain function, making it simpler to analyse the behaviour of the system.
The transform is defined as the function's integral times an exponential that decays, with the integral being assessed from 0 to infinity. The Laplace transform can convert a differential equation into an algebraic equation, which can subsequently be solved more quickly, making it useful for solving differential equations.
Along with other disciplines, the Laplace transform has uses in signal processing, electrical engineering, and control theory. It is an effective technique for deconstructing complicated systems and comprehending their evolution.
To find f(s), we first need to apply the Laplace transform to the function (4t+1)(t-1), denoted by ℒ{(4t+1)(t-1)}. Using the linearity property of the Laplace transform, we can split this into two separate transforms:
\(ℒ{(4t+1)(t-1)} = ℒ{4t^2 - 3t - 1} = 4ℒ{t^2} - 3ℒ{t} - ℒ{1}\)
Next, we use the table of Laplace transforms to find the transforms of each term:
\(ℒ{t^n} = n!/s^(n+1)\) for any integer n greater than or equal to 0
\(ℒ{1} = 1/s\)
Using these formulas, we get:
\(ℒ{t^2} = 2!/s^3 = 2/(s^3)\\ℒ{t} = 1!/s^2 = 1/s^2\\ℒ{1} = 1/s\)
Substituting these results back into the original equation, we get:
\(ℒ{(4t+1)(t-1)} = 4(2/(s^3)) - 3(1/s^2) - (1/s)\\= 8/s^3 - 3/s^2 - 1/s\)
Therefore, \(f(s) = ℒ{(4t+1)(t-1)} = 8/s^3 - 3/s^2 - 1/s\).
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if alpha and beta are zeroes of x2-3x+q. what is the value of q, if 2 alpha+3 beta=15
The value of q is -27.
Recall Vieta's Formulas, which state that for a quadratic equation \(ax^2\) + bx + c = 0 with zeroes alpha and beta, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.
In our equation \(x^2\) - 3x + q, the sum of the zeroes alpha and beta is -(-3)/1 = 3.
We are given that 2 alpha + 3 beta = 15. Substitute alpha = (15 - 3 beta)/2 into the equation.
Replace the value of alpha in the sum of zeroes equation: (15 - 3 beta)/2 + beta = 3.
Simplify the equation by multiplying both sides by 2: 15 - 3 beta + 2 beta = 6.
Combine like terms: 15 - beta = 6.
Subtract 15 from both sides: -beta = -9.
Multiply both sides by -1 to solve for beta: beta = 9.
Substitute the value of beta into the sum of zeroes equation: alpha = (15 - 3 * 9)/2 = -3.
Since we have the values of alpha and beta, we can find q using the product of the zeroes formula: q = alpha * beta = -3 * 9 = -27.
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In a telephone poll, 18 people said they like shopping and 27 people said they do not like shopping. What is the ratio of the number of people who like shopping to the number of people who do not like shopping?
Write your answer as a fraction. Use a slash ( / ) to separate the numerator and denominator.
Answer:
2/3
Step-by-step explanation:
18/27 simplified is 2/3
how many terms does the sequence, 2, 5, 8, …, 332 have?
As per the details given, the sequence 2, 5, 8, …, 332 has 111 terms.
The formula for the nth term of an arithmetic series can be used to find the number of terms in the given sequence:
nth term = a + (n - 1) * d
Here,
nth term is the value of the term at position n
a is the first term of the sequence
n is the position of the term
d is the common difference between consecutive terms
In this case, the first term (a) is 2, and the common difference (d) is 3, as each term increases by 3.
We need to find the value of n when the nth term is 332. Plugging the values into the formula:
332 = 2 + (n - 1) * 3
Simplifying the equation:
330 = (n - 1) * 3
Dividing both sides by 3:
110 = n - 1
n = 111
Therefore, the sequence has 111 terms.
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Heather and Carlos each improved their yards by planting grass sod and geraniums. They bought their supplies from the same store. Heather spent $171 on 14ft^2 of grass sod and 5 geraniums. Carlos spent $117 on 6ft^2 of grass sod and 7 geraniums. Find the cost of one ft^2 of grass sod and the cost of one geranium.
Answer:
The cost of one ft^2 of grass sod = $9
the cost of one geranium= $9
Step-by-step explanation:
Hi, to answer this question we have to write a cost equation for each one:
Heather : 14x+5y =171
Carlos: 6x+7y=117
Where x is the cost of one ft^2 of grass sod and y is the cost of one geranium.
Multiplying Heather's equation by 7, Carlos' equation by 5, and subtracting Carlos' cost to Heather's cost:
98x+35y=1,197
-
30x+35y=585
____________
68x=612
Solving for x:
x = 612/68
x=$9 per ft2
Replacing x=9 on any equation:
6(9)+7y=117
54+7y=117
7y=117-54
7y=63
y=63/7
y=$9
a is the point with coordinates (4,6)
b is the point with coordinates (d,21)
the graident of line AB is 3
what is the value of d
Answer:
d = 9
Step-by-step explanation:
Calculate the slope of ab then equate to 3.
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (4, 6) and (x₂, y₂ ) = (d, 21)
m = \(\frac{21-6}{d-4}\) = \(\frac{15}{d-4}\) = 3 ( multiply both sides by d - 4 )
3(d - 4) = 15 ( divide both sides by 3 )
d - 4 = 5 ( add 4 to both sides )
d = 9
Use the explicit formula,
b
∫ f(x) dx = lim f (a+k (b-a)/n)(b-a/n), to evaluate the definite integral. a
b
∫ (3x^2 - 2x + 6) dx 1 Set up the explicit formula by substituting the lower and upper limits for a and b.
n
lim Σ (7+ 8k/n + 12k^2/n^2) (2/n)
n→[infinity] k=1
Evaluate the definite integral as the limit of Riemann sums
n
lim Σ [3(1+ 2k/n)^2 - 2 (1+ 2k/n) + 6] (2/n) = ____
n→[infinity] k=1
The value of b∫ (3x^2 - 2x + 6) dx a islim [3(1+k/n)^2-2(1+k/n)+6] (2/n)n→[infinity] k=1.
b∫ f(x) dx = lim f (a+k (b-a)/n)(b-a/n) is the explicit formula used to evaluate the definite integral. To evaluate the definite integral, follow the below steps:Step 1: Set up the explicit formula by substituting the lower and upper limits for a and b.nlim Σ (7+ 8k/n + 12k^2/n^2) (2/n)n→[infinity] k=1Substitute a and b in the formula:
lim f(a+k (b-a)/n)(b-a/n)lim f (a+k/n(b-a))(b-a/n)The given integral isb∫ (3x^2 - 2x + 6) dx a Substituting a = 1, b = 2, and f(x) = 3x^2 - 2x + 6 in the explicit formula, we get lim f (a+k/n(b-a))(b-a/n)lim [3(1+k/n)^2-2(1+k/n)+6] (2/n)n→[infinity] k=1
Therefore, the value of b∫ (3x^2 - 2x + 6) dx a islim [3(1+k/n)^2-2(1+k/n)+6] (2/n)n→[infinity] k=1.
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O'Reilly's Restaurant has advertised an opening for a cashier. The hours listed are Monday, Tuesday, and Friday from 4 to 10 p.m. The job pays $7.58 an hour.
How much is this per week?
$181.92
$136.44
$113.70
$45.48
Answer:
45.48
Step-by-step explanation:
The money earned on Monday, Tuesday, and Friday from 4 to 10 p.m. is $181.92. Therefore, the correct answer is option A.
Given that, the job pays $7.58 an hour.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Total number hours on Monday, Tuesday, and Friday from 4 to 10 p.m. is 24 hours.
Total money per week = Total number of hours × The pay per an hour
= 24×7.58
= $181.92
Therefore, the correct answer is option A.
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Only the smartest person can help me with Algebra 2! Answer how many you can!
Part 3
Using the concepts of domain and range of functions, we have that:
10. The range is y ≥ 2.
11. The domain is all real numbers, the range is y ≤ 3, and it is a function.
12. The domain is (-4,3], and the range is (-5,5).
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is represented by the values of x.The range of a function is the set that contains all the values of the output. In a graph, it is represented by the values of y.Hence, for these problems:
10. The range is y ≥ 2.
11. The domain is all real numbers, the range is y ≤ 3, and it is a function.
12. The domain is (-4,3], and the range is (-5,5).
In item 11, we have that it is a function because it has no vertically aligned points, that is, each value of x is associated with only one value of y.
In item 12, the open intervals are due to the open circles at the extremes of the domain and the range on the graph.
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I need the values of A and B
Answer:
b=12 degrees and a = 168 degrees
Step-by-step explanation:
B is between A and E. AB=52 and AE=116.
What is BE?
Answer:
BE=64
Step-by-step explanation:
AE=116 and AB= 52
subtract 52 from 116 116-52= 64
hope this helps!
help me, cause I'm tuck
Answer:
The answer would be 1.33 x \(10^{4}\)
Step-by-step
1.28 x \(10^{4}\) = 12800
5 x \(10^{2}\) = 500
12800 + 500 = 13300
13300 = 1.33 x \(10^{4}\) in scientific notation
Hope this helps:)
Sorry, I got the wrong answer earlier but I fixed it:)
7. Find the length of HP.
12
P
9
H
Step-by-step explanation:
hope it is helpful to you
Answer and Step-by-step explanation:
To find the length of HP, we must use the Pythagorean Theorem.
This theorem helps us solve for the sides of any right triangle.
The equation for the Pythagorean Theorem is:
\(a^{2}+ b^{2} = c^{2}\), in which a and b are the legs, while c is the hypotenuse.
Let's plug in our values into the equation to find the length of HP.
We will use the variable x to represent HP.
\(9^{2}+ 12^{2} = x^{2} \\\\\\Square.the.9.and.the.12.\\\\\\81 + 144 = x^2\\\\\\Add.\\\\\\225 = x^2\\\\\\Square.both.sides.\\\\\\\sqrt{225} = \sqrt{x^2} \\\\\\15 = x = HP\)
So, we get our answer to be 15.
The length of HP is 15.
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find the equation of the horizontal line passing through the point (-5 3)
The equation of a horizontal line is y = constant, where the constant is the y-coordinate of any point on the line.
In this case, the line passes through the point (-5,3), so the equation is y = 3. The equation of a horizontal line is in the form y = k, where k is a constant. In this case, the horizontal line passes through the point (-5, 3). Since the y-coordinate of the point is 3, the equation of the horizontal line is simply y = 3. This line remains at a constant height of 3 units along the y-axis, regardless of the x-coordinate. The equation of a horizontal line is y = constant, where the constant is the y-coordinate of any point on the line. In this case, the line passes through the point (-5,3), so the equation is y = 3.
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A sari-sari store sells two types of detergent powder. One type(a) cost php 9. 00 and the other type(b) cost php 7. 0. They want to raise at least php 180. 00 for detergents. How many pieces of each detergent must be sold to achieve her goal?
Sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.
Determine the number of pieces of type (a) detergent.
9.00 x x = 180.00
Divide both sides by 9.00:
x = 20 pieces
Determine the number of pieces of type (b) detergent.
7.00 x y = 180.00
Divide both sides by 7.00:
y = 25.71
Since we cannot sell partial pieces, the number of pieces of type (b) detergent must be rounded up to 26 pieces.
Therefore, the sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.
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i forgot how to do this. ill give u a brainliest
Answer:
Possible answers could be that you have 400 adults and no children, or you could have 100 children and 340 adults.
.7. (10 Points each; 20 points in total) Given that x[n] has Fourier transform X(ejw), express the Fourier transforms of the following signal in terms of X(ejw). (a) x1 [n] = x[n – 1] + x[-1 – n] (b) x2[n] = x*[-n] * x[n + 1]
(a) The Fourier transform of x1[n] = x[n - 1] + x[-1 - n] is X1(\(e^{jw}\)) = \(e^{jw}\)X(\(e^{jw}\)) + X(\(e^{-jw}\)). (b) The Fourier transform of x2[n] = x*[-n] * x[n + 1] is X2(\(e^{jw}\)) = X*(\(e^{-jw}\)) * \(e^{jw}\)X(\(e^{jw}\)).
(a) To find the Fourier transform of x1[n] = x[n - 1] + x[-1 - n], we can express it in terms of X(\(e^{jw}\)).
Using the time-shifting property of the Fourier transform, we have:
x1[n] = x[n - 1] + x[-1 - n]
X1(\(e^{jw}\)) = \(e^{jw}\)X(\(e^{jw}\)) + X(\(e^{-jw}\))
(b) To find the Fourier transform of x2[n] = x*[-n] * x[n + 1], we can also express it in terms of X(\(e^{jw}\)).
Using the time-reversal and time-shifting properties of the Fourier transform, we have:
x2[n] = x*[-n] * x[n + 1]
X2(\(e^{jw}\)) = X*(\(e^{-jw}\)) * \(e^{jw}\)X(\(e^{jw}\))
In both cases, the Fourier transforms of the given signals can be expressed in terms of X(\(e^{jw}\)), the Fourier transform of x[n].
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Write an equation to show the total length of the bandages if they are placed end-to-end
There is an image attached btw
The equation that can be written to show the total length of the bandages if they are placed end-to-end is expressed as: 2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3).
How to Write an Equation for the Total Length?In the image given above that shows a line plot for the set of data representing the length of bandages, we have:
Two 1¼ = 2(5/4)
One 1 2/4 = 6/4
Three 1¾ = 3(7/4)
Four 2 = 4(2)
Six 3 = 6(3)
Thus, the equation that will represent the total length of the bandages can be expressed as:
2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3)
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Opposite value of 59
This is actually pretty simple, so i think you should catch on fast, so basically, the opposite of 59 is -59. so basically, just add a negative on there and your all set. If its negative, switch it to positive. Hope it helped!
What evidence is needed to prove two triangles are similar by the SSS similarity theorem?
Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.
So, ∠P = ∠E and ∠Q = ∠F.
Hence, we can write: DP/DE = DQ/DF= PQ/EF.
The above expression is written as
DP/DE = DQ/DF=BC/EF.
It means that PQ = BC.
Hence, the triangle ABC is congruent to the triangle DPQ.
(i.e) ∆ ABC ≅ ∆ DPQ.
Thus, by using the AAA criterion for similarity of the triangle, we can say that
∠A = ∠D, ∠B = ∠E and ∠C = ∠F.
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a certain phone company charges $4.50 for the first five minutes of an international phone call. additional time is charged at $.50 per minute. how much would a customer be charged for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day?
A customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.
Charge for first 5 charged = $ 4.50
Charge for additional time = $ 0.50 per minute
Starting time = 9:35 p.m.
End time = 11:15 p.m.
Total minutes = 100 minutes
Total charge = 4.50 + (95 x 0.50)
= 4.50 + 47.50
= 52.00
Hence, a customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.
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anyone wanna do my summer school work for me on edge it's really hard and in order for me to go to 8th grade I have to get a 60 as my relative grade so please help its english and math
Answer:
I could probably help since I am going to be a junior and will be graduating this year by December
1 is 25, percent of what number
Answer:
Step-by-step explanation:
0.25
Answer:4
Step-by-step explanation:
Consider the function f(x,y)=x2y+y3−75yf(x,y)=x2y+y3−75y.ff has ? a maximum a minimum a saddle some other critical point no critical point at (0,0)(0,0).ff has ? a maximum a minimum a saddle some other critical point no critical point at (0,−5)(0,−5).ff has ? a maximum a minimum a saddle some other critical point no critical point at (53–√,0)(53,0).ff has ? a maximum a minimum a saddle some other critical point no critical point at (0,5)(0,5).ff has ? a maximum a minimum a saddle some other critical point no critical point at (−53–√,0)(−53,0).
at (-5√3, 0), we have another critical point.
To determine the nature of critical points for the function f(x, y) = x^2y + y^3 - 75y, we need to find the critical points by finding where the partial derivatives with respect to x and y are both zero.
Critical point at (0, 0):
Calculate the partial derivatives:
∂f/∂x = 2xy
∂f/∂y = x^2 + 3y^2 - 75
At (0, 0), both partial derivatives are zero:
∂f/∂x = 0 -> 2xy = 0 -> x = 0
∂f/∂y = 0 -> x^2 + 3y^2 - 75 = 0
Substituting x = 0 into the second equation:
0 + 3y^2 - 75 = 0
3y^2 = 75
y^2 = 25
y = ±5
Therefore, at (0, 0), we have a critical point.
Critical point at (0, -5):
Substituting x = 0 and y = -5 into the function:
f(0, -5) = (0)^2(-5) + (-5)^3 - 75(-5)
= 0 + (-125) + 375
= 250
Therefore, at (0, -5), we have another critical point.
Critical point at (5√3, 0):
Substituting x = 5√3 and y = 0 into the function:
f(5√3, 0) = (5√3)^2(0) + (0)^3 - 75(0)
= 0 + 0 + 0
= 0
Therefore, at (5√3, 0), we have another critical point.
Critical point at (0, 5):
Substituting x = 0 and y = 5 into the function:
f(0, 5) = (0)^2(5) + (5)^3 - 75(5)
= 0 + 125 + 375
= 500
Therefore, at (0, 5), we have another critical point.
Critical point at (-5√3, 0):
Substituting x = -5√3 and y = 0 into the function:
f(-5√3, 0) = (-5√3)^2(0) + (0)^3 - 75(0)
= 0 + 0 + 0
= 0
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To pass an online class a student must answer 75% of questions correcrtly on a final exam. If there are 60 quesrtions on the exam, how many questions must a student answer correctly to pass
Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45
Step-by-step explanation:
No of questions= 60,
Answers to be given= 75%
then no of questions to pass the exam= No of questions*Answers to be given in percentage
=60*75/100\
=45
please help. worth 25 points!!!
Answer:
the 8 oz because 0.32375<0.33<0.355625<0.3715625
Step-by-step explanation:
Select the acceptable conclusions to a hypothesis test. a The value of the test statistic lies in the nonrejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. b The value of the test statistic does not lie in the rejection region. Therefore, we accept the null hypothesis. c The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true. d The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. e The value of the test statistic does not lie in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is true. f The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
The acceptable conclusions to a hypothesis test are option a, c, d, f.
What is hypothesis test?
Hypothesis Testing is a way of statistical analysis in which a person can put his assumptions about a population parameter to the test. It usually used to estimate the relationship between two statistical variables.
By the property of hypothesis test the following can be stated.
⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.
⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
Hence the correct options are a, c, d, f.
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