Answer:
12.2%
Step-by-step explanation:
82 · [tex]\frac{100-x}{100}[/tex] = 72 When multiplied by a certain percent we get 72
82(100-x) = 7200
100(A whole as you may say) - *a percent* = the markdown
8200-82x=7200
82x = 1000
x ≈ 12.2
Tell me if you need further explanation
Answer:
12.20%
Step-by-step explanation:
$82 went down to $72.
$82 - $72 = $10
The price went down $10.
Now we find the percent that $10 is of $82.
percent = part/whole * 100%
percent = 10/82 + 100% = 12.195%
Answer: 12.20%
In the parallelogram below, solve for x and y. (Give your answer as a decimal, when necessary)
Answer: x = 15, y = 12.5
Step-by-step explanation:
The sum of the three angle measures of a triangle equals 180ᴼ
Since these triangles are vertical, the measures are congruent.
45 + 60 = 105
180 - 105 = 75
So now we know that 5x = 75ᴼ and 6y = 75ᴼ.
To find x, divide 75 by 5
75 / 5 = 15
x = 15
To find y, divide 75 by 6
75 / 6 = 12.5
y = 12.5
A bus can carry a maximum of 60 passengers. Each row accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry maximum number of passengers. Determine number of rows in the bus and no. Of passengers per row
Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Perform the indicated operation.
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
10) BRAINLIEST & 10+ Points!
Answer:
20Solution,
Complement of 70°
=90°-70°
=20°
hope this helps...
Good luck on your assignment..
Answer:
20°
Step-by-step explanation:
Complement of 70° is 90°-70°= 20°
To determine the complement, subtract the given angle from 90.
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
&
given circleR, how is it known that QS = YT?
(idk the answers i guessed)
Answer:
Step-by-step explanation:
In an isosceles triangle, the base angles are equal. This also means that the length of two sides of the triangle are equal. Looking at triangle ABC, to prove that it is an isosceles triangle, then
Angle CAB = angle CBA
For the second question, to determine how it is known that QS is equivalent to YT, we would recall that the diameter of a circle passes through the center and from one side of the circle to the other side. Assuming R is the center of the circle, then QS and YT are the diameters of the circle and also the diagonals of the rectangle. Thus, the correct option is
The diameters act as diagonals
Which expression represents the phrase 4 times the sum of 9 and 6
A. 4x (9+6)
B.4x 9+6
C.9+ 6x4
D. 9+ (6x4)
Answer:
The answer is option A
4 x ( 9 + 6)
Hope this helps you
The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x.
(i) 6.9
mPQ = 1
(ii) 6.99
mPQ = 2
(iii) 6.999
mPQ = 3
(iv) 6.9999
mPQ = 4
(v) 7.1
mPQ = 5
(vi) 7.01
mPQ = 6
(vii) 7.001
mPQ = 7
(viii) 7.000
mPQ = 8
(b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at
P(7, −2).
m = 9
(c) Using the slope from part (b), find an equation of the tangent line to the curve at
P(7, −2).
The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.
(i) For x = 6.9:
mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)
= 2.22
(ii) For x = 6.99:
mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)
= 2.020
(iii) For x = 6.999:
mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)
= 2.002002
(iv) For x = 6.9999:
mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)
= 2.000200
(v) For x = 7.1:
mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)
= 1.818182
(vi) For x = 7.01:
mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)
= 1.980198
(vii) For x = 7.001:
mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)
= 1.998002
(viii) For x = 7.0001:
mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)
= 1.999800
By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.
Using the point-slope form, we have:
y - y₁ = m(x - x₁)
Substituting the values of P(7, -2), we have:
y - (-2) = 2(x - 7)
y = 2x -16
Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.
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xpress 8/(1 - 2x)2 as a power series by differentiating the equation below. What is the radius of convergence? 4 (1 - 2x) = 4(1 + 2x + 4x2 + 8x3 + ...) = 4 [infinity] Σ n=0 (2x)n SOLUTION Differentiating each side of the equation, we get 8 (1 - 2x)2 = 4(2 + Correct: Your answer is correct. + 24x2 + ...) = 4 [infinity] Σ n=1 Incorrect: Your answer is incorrect. If we wish, we can replace
Recall that for |x| < 1, we have
[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]
Replace x with 2x, multiply 4, and call this function f :
[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]
Take the derivative:
[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]
By the ratio test, the series converges for
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]
or |x| < 1/2, so the radius of convergence is 1/2.
Which is true about all quadratic equations that contain a difference of squares? Only the value of c is a perfect square. Only the value of a is a perfect square. The value b=0. The value |b|=2[tex]\sqrt{a} \sqrt{c}[/tex]
Answer:
b = 0
Step-by-step explanation:
The standard form of a regular quadratic equation is ax² + bx + c and the standard form of the difference of squares is ax² - c. This means that b = 0 because there is no x term.
Find the amount in an account where $500 is invested at 2.5% compounded continuously for period of 10 years
Hi
500 *1.025^10 ≈ 640.04
The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)
Answer:
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Step-by-step explanation:
The equation of the curvature is:
[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]
The parametric componentes of the curve are:
[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]
The first and second derivative associated to each component are determined by differentiation rules:
First derivative
[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]
[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]
Second derivative
[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]
[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]
[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]
[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]
Now, each term is replaced in the the curvature equation:
[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]
And the resulting expression is simplified by algebraic and trigonometric means:
[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]
[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]
[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]
[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]
[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
I NEED HELP PLEASE, THANKS! :)
Answer:
Step-by-step explanation:
Step1 : Verify Sn is valid for n = 1
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface that lies above the disk x2 + y2 ≤ 81
Answer:
A(s) = 255.8857
Step-by-step explanation:
Find the area of the surface correct to four decimal places by expressing the area in terms of a single integral and using your calculator to estimate the integral. The part of the surface z = e^-x^2-y^2 that lies above the disk x2 + y2 ≤ 81.
Given that:
[tex]Z = e^{-x^2-y^2}[/tex]
By applying rule; the partial derivatives with respect to x and y
[tex]\dfrac{\partial z }{\partial x}= -2xe^{-x^2-y^2}[/tex]
[tex]\dfrac{\partial z }{\partial y}= -2ye^{-x^2-y^2}[/tex]
The integral over the general region D with respect to x and y is :
[tex]A(s) = \int \int _D \sqrt{1+(\dfrac{\partial z}{\partial x} )^2 +(\dfrac{\partial z}{\partial y} )^2 }\ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(-2xe^{-x^2-y^2})^2 +(-2ye^{-x^2-y^2})^2 } \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+4x^2({e^{-x^2-y^2})^2 +4y^2({e^{-x^2-y^2}})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)({e^{-x^2-y^2})^2 }} \ dA[/tex]
[tex]A(s) = \int \int _D \sqrt{1+(4x^2+4y^2)e^{-2}({{x^2+y^2}) }} \ dA[/tex]
By relating the equation to cylindrical coordinates
[tex]A(s) = \int \int_D \sqrt{1+4r^2 e^{-2r^2} }. rdA[/tex]
The bounds for integration for the circle within the cylinder [tex]x^2+y^2 =81[/tex] is r =9
[tex]A(s) = \int \limits ^{2 \pi}_{0} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }. dr d\theta[/tex]
[tex]A(s) = {2 \pi} \int \limits^9_0 r \sqrt{1+4r^2 e^{-2r^2} }\ dr[/tex]
Using integral calculator to estimate the integral,we have:
A(s) = 255.8857
what is the gfc of 16 and 8
Answer:
Greatest common factor of 16 and 8 is 8 .....Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
Simplify: 1. (x−1)+(12−7.5x) 2. b−(4−2b)+(3b−1) 3. (2p+1.9)−(7−p)
Answer:
1. -6.5x+11
2. 6b-5
3. 3p-5.1
Step-by-step explanation:
[tex]1. \\(x-1)+(12-7.5x)=\\x-1+12-7.5x=\\x-7.5x-1+12=\\-6.5x-1+12=\\-6.5x+11\\\\2.\\b-(4-2b)+(3b-1)=\\b-4+2b+3b-1=\\b+2b+3b-4-1=\\3b+3b-4-1=\\6b-4-1=\\6b-5\\\\3.\\(2p+1.9)-(7-p)=\\2p+1.9-7+p=\\2p+p+1.9-7=\\3p+1.9-7=\\3p-5.1[/tex]
There are 12 teams, each representing a different country, in a women’s Olympic basketball tournament. In how many ways is it possible for the gold, silver, and bronze medals to be awarded? Use the formula for permutations to find your answer.
Answer:
1320 ways
Step-by-step explanation:
To solve we need to use permutations and factorials. If we wanted to find where they would all place 1-12, we would do 12!
12! is the same as 12x11x10x9x8... etc
But in this problem, we are only looking for the top 3.
We can set up a formula
[tex]\frac{n!}{(n-r)!}[/tex]
N is the number of options that are available and r represents the amount we are choosing
In this case, we have 12 teams so n=12
We are looking for the top 3 so r=3
[tex]\frac{12!}{(12-3)!}[/tex]
[tex]\frac{12!}{9!}[/tex]
We expand the equation and cancel out
[tex]\frac{12x11x10x9x8x7x6x5x4x3x2}{9x8x7x6x5x4x3x2}[/tex]
Notice how both sides can cancel out every number 9 and below
That leaves us with 12x11x10
1320 ways
The possible ways for the gold, silver, and bronze medals to be awarded is 1320
What is permutation?A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Given that, there are 12 teams, each representing a different country, in a women’s Olympic basketball tournament.
We need to find that, in how many ways is it possible for the gold, silver, and bronze medals to be awarded,
Using the concept of permutation, to find the number of ways
ⁿPₓ = n!/(n-x)!
= 12! / (12-3)!
= 12! / 9!
= 1320
Hence, the possible ways for the gold, silver, and bronze medals to be awarded is 1320
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CAN SOMEONE HELP ME ASAP
A. 5
B. 53‾√53
C. 10
D. 103√3
Answer:
n = 5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 30 = n/ 5 sqrt(3)
5 sqrt(3) tan 30 = n
5 sqrt(3) * 1/ sqrt(3) = n
5 = n
The vector matrix[ 27 ]is dilated by a factor of 1.5 and then reflected across the X axis if the resulting matrix is a B then a equals an VE
Correct question:
The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???
Answer:
a = 3
b = 10.5
Step-by-step explanation:
Given:
Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]
Dilation factor = 1.5
Since the vector matrix is dilated by 1.5, we have:
[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]
= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]
Here, we are told the vector is reflected on the x axis.
Therefore,
a = 3
b = 10.5
Answer:
a = 3
b = -10.5
Step-by-step explanation:
got a 100% on PLATO
a.) The perimeter of a rectangular field is 354 m. If the length of the field is 95m, what is its width? b.) The area of a rectangular painting is 8439 cm^2. If the width of the painting is 87cm, what is its length?
Answer:
a) 82
b) 97
Step-by-step explanation:
a) 354 - (95+95)
354 - 190
164
164 ÷ 2 = 82
(82+82+95+95=254)
b) 8439 cm^2 = 87x
8439 cm^2 ÷ 87 = 87x ÷ 87
97 = x
Basic factoring. Please help!
Answer:
-1(3 - y)
Step-by-step explanation:
If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:
-3 + y
So our answer is 2nd Choice.
Solving by fractions
Answer: Step 3
Step-by-step explanation:
x = -9 or 1. She flipped the signs.
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
Step 3
▹ Step-by-Step Explanation
Juliet flipped the signs. The final answer should be (-9, 1)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
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Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
Please help!!!!! I'm on a timerrrrrrrrrrrrrr!
Step-by-step explanation:
6
[tex]6 \sqrt{6} [/tex]
Answer:
6√6is the exact answer
PLEASE ANSWER FAST, THANKS! :)
Answer:
Step-by-step explanation:
k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8
k = 4; 2k + 2 = 2*4 + 2 = 8 +2 = 10
k =5; 2k + 2 = 2*5 +2 = 10+2 = 12
k=6; 2k +2 = 2*6 + 2 = 12+2 = 14
k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16
k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18
∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78
PLEASE HELP! Two complementary angles measure (12x - 18) and (5x +23). What is the measure of the smaller angle? (1) 5 (2) 42 (3) 48 (4) 90
Answer:
5
Step-by-step explanation:
firstly, what are complementry angles.complementary angles are angles that su
m up to 90°
(12x-18)+(5x+23)=90
collecting like terms
12x+5x+23-18=90
17x-5-90=0
17x-95=0
17x=95
divide through by 17
x=5
The measure of the smaller angle when complementary angles are given is 42 degree.
Complementary AnglesWhat are complementary angles?Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.
Calculation for the value of x in the given angles:The first angle of the triangle is (12x - 18).
The measure of the second angle of the triangle is (5x + 23).
As both angles are complementary, their sum would be equal to 90 degree.
(12x - 18) + (5x + 23) = 90
12x - 18 + 5x + 23 = 90
17x = 85
x = 5
Calculation for the angles.Substitute the value of x = 5 in the given angles.
(1) 12x - 18 = 12×5 - 18
= 42 degrees
(2) 5x + 23 = 5×5 +23
= 48 degrees
Therefore, the smaller angle is found to be 42 degrees.
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help asap!! will get branliest.
Answer:
C
Step-by-step explanation:
A reflection is when the original diagram or picture is fliped exactly over the x axis.
HEYA!!
Answer:
Your Answer of the Question is C
if you want to prove it you can do the same thing in real life by drawing a 'W' on a paper and see its reflection on the mirror
HOPE IT MATCHES!!
Please answer this correctly
Answer:
4/5 chance
Step-by-step explanation:
There are 4 numbers that fit the rule, 1, 3, 4, 5, since all of them are either odd or greater than 3. There will be a 4/5 chance of picking one.
Answer:
4/5 is the answer.Step-by-step explanation:
Facts!This is because 5 is odd and greater than 3.
Also. 4 is greater than 3.
After that, the other odd numbers are 1 and 3
So the numbers are 1, 3, 4, and 5.
So 4 out of 5 numbers are counted in the circle.
In this way 4/5 is the answer.
4/5 is the answer.Hope this helped!
Kavitha
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
A company determined that the marginal cost, Upper C prime (x )of producing the xth unit of a product is given by Upper C prime (x )equalsx Superscript 4minus2x. Find the total cost function C, assuming that C(x) is in dollars and that fixed costs are $6000.
Answer:
C(x) = 0.2x^5 - x^2 + 6000
Step-by-step explanation:
Given in the question are restated as follows:
Marginal cos = C'(x) = x^4 - 2x ...................... (1)
Note that marginal cost (C'(x)) refers to the change in the total cost (C(x)) as a result of one more unit increase in the quantity produced. That is, MC refers to the additional cost incurred in order to produce one more unit of a good.
Therefore, TC can be obtained by integrating equation (1) as follows:
C(x) = ∫C'(x) = ∫[x^4 - 2x]dx
C(x) = 1/5x^5 - 2/2x^2 + F ................................ (2)
Where F is the fixed cost. Since the fixed cost is given as $6,000 in the question, we substitute it for F into equation (2) and solve as follows:
C(x) = 0.2x^5 - x^2 + 6000 ......................... (3)
Equation (3) is the total cost function C.