Answer:
The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.
Step-by-step explanation:
A manufacturer considers his production process to be out of control when defects exceed 3%.
At the null hypothesis, we test if the production process is in control, that is, the defective proportion is of 3% or less. So
[tex]H_0: p \leq 0.03[/tex]
At the alternate hypothesis, we test if the production process is out of control, that is, the defective proportion exceeds 3%. So
[tex]H_1: p > 0.03[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.03 is tested at the null hypothesis
This means that [tex]\mu = 0.03, \sigma = \sqrt{0.03*0.97}[/tex]
In a random sample of 100 items, the defect rate is 4%.
This means that [tex]n = 100, X = 0.04[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.04 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{100}}}[/tex]
[tex]z = 0.59[/tex]
P-value of the test
The p-value of the test is the probability of finding a sample proportion above 0.04, which is 1 subtracted by the p-value of z = 0.59.
Looking at the z-table, z = 0.59 has a p-value of 0.7224
1 - 0.7224 = 0.2776
The p-value of the test is of 0.2776 > 0.01, which means that the we accept the null hypothesis, that is, the manager's claim that this is only a sample fluctuation and production is not really out of control.
Find the average value of f(x)=2x^5 over the interval [1, 5].
Answer:
: let's recall that the average value of a function for an interval of (a,b) is given by formula: k=1b−a∫baf(x)dx where; k:average value k=16−2∫62(x2−2x+5)dx k=14(∣∣∣x33−2x22+5x∣∣∣62) k=14(∣∣∣x33−x2+5x∣∣∣62) k=14[(633−62+5⋅6)−(233−22+5⋅2)] k=14[(2163−36+30)−(83−4+10)] k=14[(2163−6)−(83+6)] k=14[216−183−8+183] k=14[1983−263] k=14[1723] k=17212
QuestionThe average of a function over an interval is computed as (1/width of interval) times the definite integral of the function evaluated over the interval. The indefinite integral of e^2x is (1/2)e^2x. So the answer is found by evaluating:(1/2)*[(1/2)[e^8 - e^4]], or (1/4)[e^8 - e^4]which equals about 731.6.
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Brainly.com
Question
Find the average value of f(x)=2/x over the interval [1, 3].
Answer · 0 votes
[tex] \bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll}average~rate\of~change\end{array}\\-------------------------------\\f(x)= \cfrac{2}{x} \qquad \begin{cases}x_1=1\x_2=3\end{cases}\implies \cfrac{f(3)-f(1)}{3-1}\implies \cfrac{\quad \frac{2}{3}-\frac{2}{1}\quad }{2}\\\\cfrac{\quad \frac{2-6}{3}\quad }{2}\implies \cfrac{\quad \frac{-4}{3}\quad }{\frac{2}{1}}\implies \cfrac{-4}{3}\cdot \cfrac{1}{2}\implies -\cfrac{2}{3} [/tex]
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Wyzant
Question
Find the average value of the function f(x)=x^3 over the interval [0,2] and find the value(s) of x at which the function assumes the average values
Answer · 0 votes
The average value of f is defined as: 1/(b-a)∫ f(x) dx (where integral is evaluated from a to b) If we are to integrate f(x) = x3 we get: (1/4)* (x4) Applying formula for average value: [1/(b-a)]*[(1/4)*(x4)]a to b Evaluating this result where a = 0 and b = 2: [1/(2-0)]*[(1/4)*(x4)]a to b =(1/2)*[((1/4)*x4)]a to b =(1/2)*[((1/4)*(2)4) - (2*(0^4))] =(1/2)*[((1/4)*16)-0] =(1/2)*(4) =2
The average rate of change over the interval [a,b], or the secant line between the points a and b on the function f(x), is [f(a) - f(b)]/[a-b]. So, substitute a for 1 and b for 5, and you get [f(1) - f(5)]/[1–5]. The quotient of that is your average rate of change.
the average value of f(x) on [a,b] is ∫[a,b] f(x) dx ----------------------- b-a f' = 3x^2-6x f = x^3-3x^2+4 so, you want ∫[-1,3] x^3-3x^2+4 dx -------------------------- 3 - (-1) which I'm sure you can do.
1/2 e 2 - 1/2 or 3.19 Given: f(x)=2x 2 e 2x [0, 1] The average value of a function is: Where: a and b -intervals [a,b] f(x) - given function Substitute the values to the formula: In the integration of the function, we will use integration by parts: Let: u = 2x 2 dv = e 2x dx For du, get the derivative of u: du = 2(2x 2-1 ) = 4x dx For v, integrate dv: v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Get the integration by parts of xe 2x dx and let: u = x dv = e 2x dx for du,get the derivative of x du = dx For v, integrate dv v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Final answer: The average value of the function is 1/2 e 2 - 1/2 or 3.19
Step-by-step explanation:
plz brian list Oh and the real answer is k=17212
Find the value of each variable in parallelogram ABCD. Please help <3!
Answer:
Step-by-step explanation:
opposite side sides of a parallelogram are equal.
6x=3x+15
6x-3x=15
3x=15
x=15/3
x=5
y+5=2y-10
5+10=2y-y
15=y
Find the missing angle
Answer and Step-by-step explanation:
First, solve for the angle TRS, so that we can find the missing angle.
Subtract the two angles from 180 (because all triangle's angles add up to 180).
180 - 58 - 60 = 62.
By the vertical angles theorem, 62 is equal to the missing angle.
#teamtrees #PAW (Plant And Water)
Math Puzzle - Please help me solve this. I am not sure.
Answer:
143547
Step-by-step explanation:
1) Multiply the first 2 numbers: 7 x 2 = 14
2) Multiply the first and third numbers: 7 x 5 = 35
3) Now we get 14 and 35. Add both these numbers: 14 + 35 = 49
4) Now subtract the second number that is 2 from 49: 49 - 2 = 47
5) Hence, the answer is 143547
Thanks for giving such an interesting question! Loved it!
Lin and Claire each threw a rock into a stream. The black graph represents the height of a stone t seconds after it was tossed up by Lin and the purple graph represents the height of a stone t seconds after it was tossed up by Claire.
1) Whose stone hit the water second, and at what time?
2) How long did it take for Claire's rock to reach its maximum? What is the maximum height?
3) Who had the higher initial height? What was it?
Answer:
that can't be the right graph because it is not purple and black or has the right information needed to answer this question
Step-by-step explanation:
Is there a graph that goes with this question?
I really want to help but this is not it
The height of the triangle is 4 inches less than four times its
base. The area of the triangle is 112 in2. What is the height of
the triangle?
Answer:
h = 28 inches
Step-by-step explanation:
Let the base of the triangle is b.
the height of the triangle is 4 inches less than four times its base.
h = 4b-4
The area of the triangle is 112 inch².
The formula for the area of a triangle is given by :
[tex]A=\dfrac{1}{2}bh\\\\112=\dfrac{1}{2}\times b\times (4b-4)[/tex]
It is a quadratic equation, whose solution is as follows :
b = -7 and b = 8 inches
Height, h = 4(8)-4
= 32-4
= 28 inches
Hence, the height of the triangle is 28inches.
If f(x) = 2x3 – 12x2 + 26x — 20 and X
20 and X – 2 is a factor of f(x), then find
all of the zeros of f(x) algebraically.
The approximate land areas of the seven continents are listed in the table below.
Continent Area
(in sq. miles)
Africa 11.7 million
Antarctica 5.4 million
Asia 17.3 million
Australia 3.3 million
Europe 3.8 million
North America 9.4 million
South America 6.9 million
What is the median of the land areas of the seven continents?
9.4 million
6.9 million
7.4 million
5.4 million
Answer:
6.9 million
Step-by-step explanation:
the median is the number that is in the middle or centre of a set of observations that is arranged either in an ascending or descending order.
Arrange the land areas in ascending order :
3.3, 3.8, 5.4, 6.9, 9.4, 11.7, 17.3
the number in the middle is the 4th number which is 6.9
simply the expression below
Answer:
A
Step-by-step explanation:
Answer:
D. (w-3)/(w-7)
Step-by-step explanation:
(w+3)(w-3)/(w-7)(w+3)
Hence, removing (w+3),
(w-3)/(w-7)
Feel free to mark this as brainliest :D
Umm i could use so help :)
If you don't mind
i think it's 16+88 but i was wondering what someone else thought.
Answer: I think your answer is right
Step-by-step explanation:
You invest $50 with a simple interest return rate of 4% per year. How many years will it take to in investment to reach $70?
Answer:
It would take 10 years for the investment to reach 70 dollars.
Step-by-step explanation:
The investment would gain 2 dollars per year. So in 10 years it will gain 20 dollars.
What is the volume of the rectangular prism?
Answer:
The one all the way to the left (1 1/9 ft)
Step-by-step explanation:
You have to multiply Height x Width x length together.
Height will be 5/3 or 1.66
length side will have the lenght of 1
Width will be 2/3 or .66
So now you just have all of that. And you get 1.1 ( I multiplied the decimals )
And that was closest to 1 1/9
PLS HELP
a) What is the equation of line A
b) What is the equation of line B
Answer:
The equation of a line A:x=4The equation of a line B:y=8Step-by-step explanation:
i hope this helps u have a nice day .✌❤☘Can you find the midpoint of AB
Determine the slope of the line passing through (4, -2) and (7, 10).
Answer:
4
Step-by-step explanation:
To find slope without a graph, you subtract the 2 y-coords and the 2 x-coords, then divide the y-coord by the x-coord.
The formula is (y²-y¹)/(x²-x¹).
So we just plug in the coordinates.
(10-(-2))/(7-4)
(10+2)/(7-4)
12/3
4
So the slope is 4.
---
hope it helps
The slope of the line passing through (4, -2) and (7, 10) is,
⇒ m = 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Two points on the line are (4, -2) and (7, 10).
Since, The equation of line passes through the points (4, -2) and (7, 10).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (10 - (-2)) / (7 - 4)
m = 12 / 3
m = 4
Thus, The slope of line = 4
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ2
Suppose that 10% of the fields in a given agricultural area with about 2,500 fields are infested with the sweet potato white fly. One hundred fields in this area are randomly selected and checked for white fly. A. Can this be considered an almost binomial situation
Answer:hmmm
Step-by-step explanation:
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = 2(x-6)2 + 5
A. F(x) = x2 + 5 and G(x) = x-6
B. F(x) = 2x + 5 and G(x) = (x-6)2
C. F(x) = x - 6 and G(x) = 2x2 + 5
O D. F(x) = (x - 6)2 and G(x) = 5
Answer:
[tex]f(x) = 2x + 5[/tex]
[tex]g(x) = (x - 6)^2[/tex]
Step-by-step explanation:
Given
(a) to (d)
Required
Which will give:
[tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]
Equate the expression in bracket to g(x)
[tex]g(x) = (x - 6)^2[/tex]
Replace g(x) with x in: [tex]f(g(x)) = 2(x - 6)^2 + 5[/tex]
[tex]f(x) = 2x + 5[/tex]
EASY 20 POINTS AND BRANLIEST PLEASE HELP write the following without the absolute value sign
Ia^2I if a<0
a^2 is in absolute value
Answer:
a^2
Step-by-step explanation:
Ia^2I if a<0
Since a^2 is always positive, we can remove the absolute value sign and nothing will change
a^2
Volume of Prisms and Cylinders
Find the volume of the cylinder. Use 3.14 for \pi.
a. 339.12 cu. in.
b. 113.04 cu. in.
c. 226.08 cu. in.
d. 1356.48 cu. in.
Please select the best answer from the choices provided
Answer:
A. 339.12 cu. in
Step-by-step explanation:
I calculated it logically
I NEED HELP PLEASEE HELP ME
Answer:
TRUE
FALSE
FALSE
TRUE
Step-by-step explanation:
yan na po god bless
all the numbers between 20 and 40 which are multiples of 2 and 3
Answer:
21, 24, 27, 30, 33, 36, 39.
Step-by-step explanation:
Answer:
multiples of 3 : 21, 24, 27, 30, 33, 36, 39.
multiples of 2 : 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
Step-by-step explanation:
tell whether the ordered pair is a solution of the equation !! please help i will mark you brainliest!
Answer:
yes both questions the answer are equal
Step-by-step explanation:
(3,5) where 3 is the x coordinate and 5 is the y coordinate
putting it into y=5x-10
5=5(3)-10
5=5
(4,5) where 4 is the x coordinate and 5 is the y coordinate
putting it into y=2x-3
5=2(4)-3
5= 5
what is the equivlalent expression of 6m
Answer:
6 * m
Step-by-step explanation:
6m is is multiplication so should be the equivalent expression
Written out as words clearly says
six times a number
times meaning multiplication
Meaning any other expression is equivalent as long as it is a form of multiplication
If I'm wrong please tell me if not
Hope this helped :]
What are the distance between the pair of points E(-5,4) and F(6, 4)
Answer:
[tex]\boxed {\boxed {\sf d=11}}[/tex]
Step-by-step explanation:
Since we want to find the distance between a pair of points, we use the following formula:
[tex]d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Where (x₁, y₁) and (x₂, y₂) are the points.
We are given the points E (-5, 4) and F (6,4). If we match the values and corresponding variables, we see that:
x₁= -5 y₁= 4 x₂= 6 y₂= 4Substitute the values into the formula.
[tex]d= \sqrt{(6--5)^2+ (4-4)^2[/tex]
Solve inside the parentheses.
(6--5)= (6+5)=11 (4-4)= 0[tex]d= \sqrt{11)^2+(0)^2[/tex]
Solve the exponents.
(11)²= 11*11= 121 (0)²= 0*0= 0[tex]d= \sqrt{121+0[/tex]
Add.
[tex]d= \sqrt{121}[/tex]
Solve the square root.
[tex]d= 11[/tex]
The distance between the 2 points is 11.
Determine if 0.949449444944449444449 rational or irrational and give a reason for answer.
Answer:
irrational if it's more after this number but if it stops at the last 9 then it's a rational number
hope this helps
have a good day :)
Step-by-step explanation:
This is irrational if it's more after this number but,
If it stops at the last 9 then it's a rational number.
We have given that,
0.949449444944449444449.
What is the meaning of irrational numbers?An irrational number, any real number that cannot be expressed as the quotient of two integers.
We have to determine rational or irrational.
irrational if it's more after this number but.
If it stops at the last 9 then it's a rational number.
To learn more about the numbers visit:
https://brainly.com/question/251701
please help with this question i will mark you brainliest !!
Answer: The equation is 25x + 100
Step-by-step explanation:
y = - 1/(1 + cos y) Find dy/dx.
Step-by-step explanation:
you have to use this
u/v=u'×v-v'×u/v²
0×(1+cosy)-(-1×-siny)/(1+cosy)²
-siny/(1+cosy)²
hopefully its correct
Given f (x) = 3 x minus 1 and g (x) = 2 x minus 3, for which value of x does g (x) = f (2)?
f ( x ) = 3x - 1
g ( x ) = 2x - 3
_____________________
g ( x ) = f ( 2 )
2x - 3 = 3(2) - 1
2x - 3 = 6 - 1
2x - 3 = 5
2x - 3 + 3 = 5 + 3
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4
Plz help me well mark brainliest if correct.....????????
Answer:
Step-by-step explanation:
31 , b/c it's the most common
c 32
Step-by-step explanation:
plz follow me wenelyn andoyo duay sana makatulong ako
i probably did it wrong. please do a good explanation on how to find this out and answer my questions for brainliest thank you
Answer:
Step-by-step explanation:
As you can see from the value in the middle of the questions, the domain refers to all the possible x-values (input values) while the range refers to all the possible f(x) values (output values :: y-values). Therefore, for the domain, since the endpoints of the graph are closed circles it means that they are included so the domain would be ...
Domain: -9 ≤ x ≤ 7
The range would be the lowest and highest included y-value on the graph which in this case would be ...
Range: -6 ≤ f(x) ≤ 4