The diameters of a mechanical component produced on a certain production line are known from experience to have a normal distribution with mean 97.5mm and standard deviation 4.4mm. find the proportion of components with diameter between 95mm and 105mm. Give your answer to 4 decimal places.
Answers
The diameters of a mechanical component produced on a certain production line are known from experience to have a normal distribution with a mean of 97.5 mm and standard deviation 4.4mm.
We have to determine the proportion of components with diameter between 95mm and 105mm..
Here, mean = μ = 97.5 mm
Standard deviation = σ = 4.4 mm
So, we have to find the probability that X lies between 95mm and 105mm.
P(95 < X < 105) = P(X < 105) - P(X < 95)From the standard normal table, we have Z95 = (95 - 97.5) / 4.4 = -0.56818and Z105 = (105 - 97.5) / 4.4 = 1.70455
Now, we can find P(95 < X < 105) using Z-scores as shown:
P(95 < X < 105) = P(-0.56818 < Z < 1.70455) = P(Z < 1.70455) - P(Z < -0.56818)
By using the standard normal table, we can find these probabilities as:
P(95 < X < 105) = 0.9569 - 0.2839 = 0.673
Therefore, the proportion of components with diameter between 95mm and 105mm is approximately equal to 0.673, or 67.3% when rounded off to one decimal place.
So, the required answer is 0.6730 (4 decimal places).
So, the proportion of components with diameter between 95mm and 105mm is approximately equal to 0.6730.
To know more about standard deviation visit:
https://brainly.com/question/13498201
#SPJ11
Related Questions
write the next term in the sequence. then write a rule for the nth term 9,36,81,144
Answers
The next term in the sequence 9, 36, 81, 144 is 225.
To find a rule for the nth term of the sequence, we can observe that the terms are perfect squares of consecutive positive integers: 3², 6², 9², 12². Therefore, the rule for the nth term is given by:
nth term = (3 + (n-1) * 3)²
Here, n represents the position of the term in the sequence. By substituting the value of n into the rule, we can find the corresponding term. For example, when n = 5, the fifth term is:
(3 + (5-1) * 3)² = (3 + 4 * 3)² = 15² = 225.
So, the rule accurately generates the terms of the sequence.
Learn more about sequence here : brainly.com/question/23857849
#SPJ11
A bag contains seven balls labeled 1 through 7. One ball will be randomly picked.
What is the probability of picking an even number?
Write your answer as a fraction in simplest form.
Answers
Answer:
3/7 not very likely
Step-by-step explanation:
1 2 3 4 5 6 7
4 of the numbers are odd
3 of the numbers are even
Since there are 3 it is 3 out of 7.
3/7
Equations and Inequalities
2x-4=4x-5
Answers
2x−4=4x−5
(2x−4)+(4−4x)=(4x−5)+(4−4x)
2x−4+4−4x=4x−5+4−4x
2x−4x−4+4=4x−4x−5+4
−2x=−1
Answer: x=1/2
2x-4=4x-5
-2x -2x
-4=2x-5
+5 +5
1=2x
2
x= 1/2
Step By Step in words:
Step1: In order to get the x's on both sides, subtract 2x from both sides
Step2 : Now to get the x by itself, do the opposite operation of -5 and add five to both sides
Step 3: Final Step to get the x by itself, do the opposite operation of 2 times x. Divide 2x by 2 and 1 by 2
Which gives you 1/2
I have a bag of 4 cotton candy lollipops 3 cherry 6 butterscotch and 1 orange what is the probability of randomly choosing a cotton candy or orange lilipop
Answers
Answer:
= 1/2
Step-by-step explanation:
From the question: 1 bag contains
4 cotton candy lollipops
3 cherry lollipops
6 butterscotch lollipops
1 orange lollipops
Total number of possible outcomes =
14
The probability of randomly choosing a cotton candy or orange lollipops is calculated as:
P(Cotton candy) + P(Orange)
= 4/14 + 3/14
= 7/14
= 1/2
If
x+1=-5
then
x+3=?
Answers
Answer:-3
x=-5-1
x=-6
x+3
=-6+3
=-3
list 5 values that are solutions to the inequality 3(x+4)<9
Answers
The given inequality will be satisfied by any value of x that is less than -1. Here are five potential remedies. x = -2, x = -2.5, x = -3, x = -1.2,x = -1.8. We can see that each of these values fulfils the given inequality.
What is the inequality formula?When x > Y and a > 0, the result is (x/a) > (y/a), and when x Y and a > 0, the result is (x/a) (y/a). On the other hand, if the inequality sign is reversed, the division of both sides of an inequality by a negative integer results in an equivalent inequality.
We can solve the inequality 3(x+4)<9 as follows:
3(x+4) < 9 (given inequality)
3x + 12 < 9 (distributing the 3)
3x < -3 (subtracting 12 from both sides)
x < -1 (dividing both sides by 3 and changing the direction of the inequality)
So, any value of x that is less than -1 will satisfy the given inequality. Here are five possible solutions:
x = -2
x = -2.5
x = -3
x = -1.2
x = -1.8
To know more about inequality visit:-
https://brainly.com/question/30231190
#SPJ1
(b) Given the matrix D = k 0 0 3 k² k³ 0 kª k³ kº k k k 0 0 0 k¹⁰ Find all possible value(s) of k if det(D) = 1024."
Answers
To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.
Given matrix D:
D = | k 0 0 |
| 3 k² k³ |
| 0 kª k³ kº |
| k k k |
| 0 0 0 |
| k¹⁰ |
The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
- 0(det | 3 k² k³ |
| 0 kª k³ |
| k k k |)
+ 0(det | 3 k² k³ |
| k k k |
| k k k |)
Simplifying further, we have:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
Now, we can calculate the determinant of the 3x3 submatrix:
det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |
This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:
det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº
Now, we can set det(D) equal to 1024 and solve for k:
k⁴+kº = 1024
Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.
Learn more about matrix here
https://brainly.com/question/2456804
#SPJ11
Cycle City charges an initial price of $15 plus $0.75 per hour for bike rentals, which is
represented by the expression 15 +0.75h.
Complete each statement to describe the terms.
The variable h represents ?
The constant 15 represents ?
The variable term 0.75h represents ?
Answers
The constant 15 represents the initial price charged by Cycle City for bike rental.
The variable term 0.75h represents the additional price charged by Cycle City for each hour of bike rental.
Find the distance between the two points rounding to the nearest tenth (if necessary). (-1,8) and (8,5)
Answers
(a)A line through (2,1) meets the curve x²-2x-y=3at A (-2,5)and at B. Find the coordinates of B
(b) A(3,1) lies on the curve (x-1)(y+1)=4. A line through A perpendicular to x+2y=7 meets the curve again at B. Find the coordinates of B.
Answers
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (1 - 5) / (2 - (-2)) = -4/4 = -1
Using the point-slope form of the equation of a line, the equation of the line passing through A and (2,1) is:
y - 5 = -1(x + 2)
y - 5 = -x - 2
y = -x + 3
To find the coordinates of point B, we need to solve the system of equations formed by the equation of the line and the equation of the curve:
x² - 2x - y = 3
y = -x + 3
Substituting the second equation into the first, we get:
x² - 2x - (-x + 3) = 3
x² - x - 6 = 0
Solving for x using the quadratic formula, we get:
x = (1 ± √(1 + 24)) / 2 = 3 or -2
When x = 3, y = -x + 3 = 0, which means that point B is (3,0).
When x = -2, y = -x + 3 = 5, which means that point B is (-2,5).
Therefore, the coordinates of point B are (3,0) and (-2,5).
(b) We know that point A (3,1) lies on the curve (x-1)(y+1)=4.
Substituting x=3 and y=1 into this equation, we get:
(3-1)(1+1) = 4
4 = 4
Therefore, point A satisfies the equation of the curve.
We need to find the equation of the line passing through point A that is perpendicular to the line x+2y=7.
The slope of the line x+2y=7 is:
m = -1/2
The slope of a line perpendicular to this line is the negative reciprocal, which is:
m' = 2
Using the point-slope form of the equation of a line, the equation of the line passing through A(3,1) with slope 2 is:
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5
To find the coordinates of point B, we need to solve the system of equations formed by the equation of the line and the equation of the curve:
(x-1)(y+1) = 4
y = 2x - 5
Substituting the second equation into the first, we get:
(x-1)(2x-4) = 4
2x³ - 6x² + 4x - 5 = 0
We can use numerical methods to solve this cubic equation to get the value of x, and then substitute it back into the equation y = 2x - 5 to get the value of y. One possible solution is:
x ≈ 2.632
y ≈ -0.736
Therefore, the coordinates of point B are approximately (2.632, -0.736).
One of the disadvantages of simulation is that it Group of answer choices Is a trial-and-error approach that may produce different solutions in different runs. Interferes with production systems while the program is being run. Is very limited in the type of probability distribution that can be used. Does not allow for very complex problem solutions. Is not very flexible.
Answers
The disadvantage of simulation mentioned in the question is that it is a trial-and-error approach that may produce different solutions in different runs.
This variability introduces uncertainty and may make it hard to achieve constant and reliable consequences. Moreover, the execution of simulation programs can interfere with manufacturing structures, inflicting disruptions or delays in real-international operations.
Additionally, simulations regularly have obstacles within the styles of chance distributions they can efficaciously version, potentially proscribing their accuracy and applicability in certain situations. Furthermore, even as simulations are valuable for information and reading structures, they may war to deal with pretty complex problem answers that contain complicated interactions and dependencies.
Lastly, simulations can lack flexibility as they're usually designed for unique purposes and may not easily adapt to converting situations or accommodate unexpected elements.
To know more about simulations,
https://brainly.com/question/27382920
#SPJ4
what number needs to be added to both sides of the equation in order to complete the square? x2+16x=18
Answers
In order to complete the square for the given equation x^2+16x=18, the number added to both sides is 64.
Complete the square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial. To complete the square, add or subtract the same value to both sides. In this case, add the square of half the coefficient of the x -term, (b/2)^2 to both sides of the equation. Hence, the number to add would be (16/2)^2 = 64.
Thus,
x^2+16x + 64 =18 + 64
x^2+16x + 64 =82
x^2+ 2*8x + 64 =82
(x + 8)^2 = 82
Learn more about Complete the square:
https://brainly.com/question/10449635
#SPJ4
what is 60 times 400 equalsssssss
Answers
Answer:
24000 is ur awnser
Step-by-step explanation:
Answer:
24,000
Step-by-step explanation:
A parabola can be represented by the equation y2 = 12x.
Which equation represents the directrix?
O y=-3
O y=3
O X=-3
O x= 3
Answers
Answer:
It's C
X = -3
Step-by-step explanation:
Edge 2022
The equation represents the directrix is x=-3.
the correct option is (C).
what is directrix in parabola?A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.
given: y²=12x
y²=4*3*x
Here a=3
So, x+a=0
x+3=0
x=-3.
Hence, the directrix of parabola is: x=-3
Learn more about directrix here:
https://brainly.com/question/4333610
#SPJ2
Find the missing values in the ratio table. Then write the equivalent ratios in the order they appear in the table. Meters $8$8 $4$4 Minutes $\frac{1}{3}$ 1 3 $\frac{1}{4}$ 1 4 $\frac{5}{12}$ 5 12
Answers
Answer: To fill in the missing values in the ratio table, we can use cross-multiplication.
Starting with the first row, we know that the ratio of meters to minutes is constant, so we can set up the equation:
$88/4 = x/\frac{1}{3}$
where x is the unknown value.
Cross-multiplying, we get:
$88 \cdot \frac{1}{3} = 4x$
Simplifying, we get:
$\frac{88}{3} = x$
So the missing value in the first row is $\frac{88}{3}$.
We can use the same method to fill in the missing values in the second and third rows:
For the second row:
$4/1 = x/1$
$4 = x$
So the missing value is 4.
For the third row:
$88/5 = x/12$
$88 \cdot 12 = 5x$
$x = \frac{88 \cdot 12}{5} = \frac{2112}{5}$
So the missing value is $\frac{2112}{5}$.
Writing the equivalent ratios in the order they appear in the table, we have:
$\frac{88}{4} = \frac{22}{1}$
$\frac{88}{\frac{1}{3}} = 264$
$\frac{4}{1} = 4$
$\frac{\frac{5}{12}}{\frac{1}{4}} = \frac{5}{12} \cdot 4 = \frac{5}{3}$
So the equivalent ratios are:
$22:1, 264:1, 4:1, 5:3$
Step-by-step explanation:
What is the sum of all interior angles of a regular hexagon? A. 120° B. 360° C. 540° D. 720°
Answers
because 120x6 =720
What is the domain of the relation below? A. {-1,0, 1, 3} B. {-2,0, 1, 3) C. -2,-1,0, 1, 2, 3} D. {0, 1, 2, 3)
Answers
Answer:
C
Step-by-step explanation:
a is a 5 5 matrix with two eigenvalues. one eigenspace is three-dimensional, and the other eigenspace is twodimensional. is a diagonalizable? why?
Answers
The required answer is a 5 5 matrix is a diagonalizable.
Explanation,
Yes, the matrix a is diagonalizable. This is because if a 5x5 matrix has two eigenvalues, and one eigenspace is three-dimensional while the other is two-dimensional, then the matrix is guaranteed to be diagonalizable. This is because the sum of the dimensions of the One eigenspace is three-dimensional, and the other eigenspace is two-dimensional. A matrix is diagonalizable if the sum of the dimensions of its eigenspaces is equal to the size of the matrix. In this case, the dimensions of the eigenspaces are 3 and 2, which add up to 5. Since the size of the matrix A is also 5 the sum of the dimensions of the eigenspaces is equal to the size of the matrix. Therefore, matrix A is diagonalizable. must equal the size of the matrix , and because the eigenvectors associated with each eigenvalue form a linearly independent set, it is possible to diagonalize the matrix using those eigenvectors. Therefore, a is diagonalizable because the dimensions of its eigenspaces add up to 5 and its eigenvectors are linearly independent.
The study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices.
To know more about eigenvectors. Click on the link.
https://brainly.com/question/31306935
rotate the triangle below: A(5,3) B(8,10) C(11,3) angle of rotation is 180 centre origin direction is anti- clock wise
Answers
Answer:
see explanation
Step-by-step explanation:
Under a rotation ( clockwise or anticlockwise ) about the origin of 180°
a point (x, y ) → (- y, - x ), thus
A(5, 3 ) → A'(- 3, - 5 )
B(8, 10 ) → B'(- 10, - 8 )
C(11, 3 ) → C'(- 3, - 11 )
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
Answers
The number of subscribers they must sample to obtain this interval is: b) 385.
How to find the sample?
95% confidence interval for z-score is 1.96
Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample
zσ = Z-score
ME = margin of error
Let plug in the formula
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore the correct option is B.
The complete question is:
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?
a) 1537
b) 385
c) 192
d) 10
learn more about of interval here
https://brainly.com/question/29567414
#SPJ4
Need help ASAP!!!!!!
Answers
Answer:
Step-by-step explanation:
1) (x+2)(x+2)=-x-2
\(x^{2}\) +2x +2x +4+=-x-2
\(x^{2}\)+4x+4+x+2
\(x^{2}\)+5x+6
2) \(x^{2}\) +4x +12 -16x +24=0
\(x^{2}\) -12x+36=0
3) (x-4)(x+1)
x=4 and/or x=-1
4) (x-5)(x-6)
x=5 and/or x=6
5) (x-7)(x+2)
x=7 and/or x=-2
6) \(x^{2}\)+3x-10=0
(x-5)(x+2)
x=5 and/or x=2
7) \(x^{2}\)+x-20
(x-5)(x+4)
x=5 and/or x=-4
One country has 12 stone bridges and 20 steel bridges. What is the ratio of ? A. Stone bridges to steel bridges. B. Steel bridges to stone bridges. C total bridges to steel bridges.
Answers
Answer:
A. Stone bridges to steel bridges=
12 : 20
6 : 10
3 : 5
answer = 3 : 5
B. Steel bridges to Stone bridges
20 : 12
10 : 6
5 : 3
answer = 5 : 3
Total bridges = 20+12=32
C. Total bridges to steel bridges
32 : 20
16 : 10
8 : 5
answer = 8 : 5
Answer:
A (Stone to Steel bridges)= 3:5
B (Steel to Stone bridges)= 5:3
C (Total bridges to steel bridges)= 8:5
Step-by-step explanation:
A: Stone to steel bridges is
12:20
You can simplify that by dividing by 4 on both numbers:
3:5
So the ratio of stone to steel bridges is 3:5
B: Steel to stone bridges is
20:12
You can simplify that by dividing by 4 on both numbers:
5:3
So the ratio of stone to steel bridges is 5:3
C: Total bridges to steel bridges is
What is the total number of bridges?
20+12=32
32:20
You can simplify that by dividing 4 on both numbers:
8:5
So the ratio of the total number of bridges to steel bridges is 8:5
Hope this helps!
a cable tv receiving dish is in the shape of a paraboloid of revolution. find the location of the receiver, which is placed at the focus, if the dish is 6 feet across at its opening and 2 feet deep.
Answers
the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).To find the location of the receiver, we first need to determine the equation of the paraboloid.
The standard equation for a paraboloid of revolution with a vertical axis is:
z = \((x^2 + y^2)\)/(4f)
Where:
z is the height at any point (x, y) on the paraboloid.
x and y are the horizontal coordinates of the point.
f is the focal length of the paraboloid, which is half the depth of the dish.
In this case, the dish is 6 feet across at its opening, so the diameter is 6 feet and the radius is 3 feet. Therefore, the maximum value of x and y is 3 feet. The depth of the dish is given as 2 feet.
Using these values, we can solve for the focal length:
2 = \((3^2 + 3^2)\)/(4f)
2 = 18/(4f)
f = 18/8 = 9/4 = 2.25 feet
Now that we have the value of f, we can find the location of the receiver, which is placed at the focus of the paraboloid. The focus is located at (0, 0, f).
Therefore, the receiver is located at (0, 0, 2.25 feet) or (0, 0, 27 inches).
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
Please help me, I don’t understand
Polynomial: x4 + 2x³ - 3x² + x - 4; Divisor: x² + x + 1
Answers
Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible.
Answers
We can conclude that the figure is not a rectangle but a square with sides as 28 m
What is Area ?Area ia the total enclosed portion by any ahape, we can calculate area in most basic case by integrating the described portion.
Let P = perimeter, A = area
As provided above, a = xy and
As the formula to solve for the perimeter of a rectangle is given as P = 2x + 2y. Using the given 112m, we can solve the perimeter using the formula:
112 = 2x + 2y
56 = x + y
Expressing it in single terms on one side,
x = 56-y or y = 56-x
Then solve the given perimeter in terms of y using the formula below:
A = (56-y) (y)
Derivative of area A = 56-y^2 to get the value of y.
dA / dy = 56-2y = 0
y = 56/2
y = 28
To find x, substitute the finded value of y in the equation x = 56 - y.
x = 56 - 28
Therefore, x = 28.
We can conclude that the figure is not a rectangle but a square.
To know more about Area, visit:
https://brainly.com/question/27683633
#SPJ4
THE SEVEN APPLEWOMEN
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?
Answers
Answer:
The amount each took home was 20 unit currency.
Step-by-step explanation:
The given parameters are
The number of apples with each of the seven apple women = 20, 40, 80, 100, 120, and 140
The number of apples each woman has can be written in the following formula obtained online which is a series formula
a·n + (n - 1), (a + b)·n + (n - 2), (a + 2·b)·n + (n - 3), (a + 3·b)·n + (n - 4), (a + 4·b)·n + (n - 5), (a + 5·b)·n + (n - 6), (a + 6·b)·n + (n - 7)
Which gives;
a·n + (n - 1) = 20
(a + b)·n + (n - 2)=40
(a + 2·b)·n + (n - 3) = 60
(a + 3·b)·n + (n - 4) = 80
(a + 4·b)·n + (n - 5) = 100
(a + 5·b)·n + (n - 6) = 120
(a + 6·b)·n + (n - 7) = 140
Solving the above system, we get
n = 7, a = 2, b = 3
Which gives
2×7 + 6 = 20
5×7 + 5=40
8×7 + 4 = 60
11×7 + 3 = 80
14×7 + 2 = 100
17×7 + 1 = 120
20×7 + 0 = 140
Whereby all the women sold the apples for the same sum price, based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount taking home by each of them given as follows;
2×1 + 6×3 = 20
5×1 + 5×3=20
8×1 + 4×3 = 20
11×1 + 3×3 = 20
14×1 + 2×3 = 20
17×1 + 1×3 = 20
20×1 = 20
Therefore, the amount each took home was 20 unit currency.
What are the solutions of y=x^2+5x-7
Answers
Answer:
You have two variables, and only one condition. It means you have infinite solutions of the form \((t; t^2+5t-7)\). Technically correct, probably not what you want to know.
If you wanted to know if and where the RHS crosses the x axis, the points are the solution to
\(x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)\)
If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation \(x=-\frac52\).
can someone help please
Answers
Answer:
1.6
Step-by-step explanation:
I need the answer for this pls help me!!!!
DONT PUT THE LINK THAT EVERYONE IS PUTTING BECAUSE THAT LINK IT DOESN’T WORK FOR ME
Answers
Answer:
Well Ima put the link, hope it works!
jkjk
The answer here is 240 in^3
Step-by-step explanation:
Well You have a triangular prism which all you need is the base. The base cna be found by finding the area of the surface triangle.
Triangle area formula: 1/2(bh)
Well base is 4 height is 10, 4*10=40. 40/2= 20
Now the heighth given or (h) is 12. TO find the volume jsut multiply the height by the base
20*12=240
Plus don’t click the links, their viruses.
help me with this please and thank you
Answers
Answer:
12.56
Step-by-step explanation:
d = 2r = 2(2 m) = 4 m
C = πd = 3.14 × 4 m = 12.56 m
Answer:
C=12.56 m
Step-by-step explanation:
The radius is 2 m. To find the circumference, you need d, which is the diameter.
The diameter of a circle is 2 times the radius.
d=2*2=4
Now use the formula to find the circumference
C=3.14*4=12.56