A metallic split ring has a target internal diameter of 50 mm, but records show that the diameters are normally distributed
with mean 50 mm and standard deviation 0.07 mm.
An acceptable diameter is one within the range 49.93 mm to 50.07 mm. What proportion of the output is unacceptable?
Round your answer to four decimal places.
Answers
The proportion of the output that is unacceptable is; 0.32
How to use empirical rule of statistics?The empirical rule of statistics is also called the 68 - 95 - 99.7 rule, and it states that states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations of the mean, and 99.7% will occur within three standard deviations of the mean.
We are told that the target diameter is 50 mm.
Mean; μ = 50 mm
Standard deviation; σ = 0.07 mm
An acceptable diameter is one within the range 49.93 mm to 50.07 mm. Thus;
50 ± x(0.07) = (49.93, 50.07)
Thus;
50 - 0.07x = 49.93
0.07x = 50 - 49.93
x = 0.07/0.07
x = 1
Thus, the proportion that is acceptable is 68% or 0.68.
Proportion unacceptable = 1 - 0.68 = 0.32
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Related Questions
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Answers
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
Find the quotient of z₁ by z2. Express your answer in
trigonometric
form.
² - 3 (0 (4) + (*))
Z₁ cos
+/sin
Z₂
²2 = 7 (cos(377)+
COS
8
O A. 7 (cos (577) + i sin (5/77))
8
B.
21(cos(577)+isin (577))
8
OC. 21 cos
21(cos(-7)+ i sin(-77))
O D. 7 (cos(-7) + + sin(-7))
i
+/sin
37T
8
Answers
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.
Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.
We have:
z₁ = 7(cos(577°) + i sin(577°))
Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.
From the given information, we have:
z₂ = 21(cos(-7°) + i sin(-77°))
To find the quotient, we divide z₁ by z₂:
z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]
Substituting the given values, we have:
z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]
= (7/21) * [cos(584°) + i sin(584°)]
The quotient of z₁ by z₂ in trigonometric form is:
7/21 * (cos(584°) + i sin(584°))
Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.
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an inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. the company has evidence that 0.9% of the items its line produce is nonconforming. (a) what is the probability that an item selected for inspection is classified as defective? (5pt) (b) if an item selected at random is classified as defective, what is the probability that it is indeed nonconforming? (5pt) (c) if an item selected at random is classified as non-defective, what is the probability that it is indeed good? (5pt)
Answers
The probability of an item selected for inspection is classified and the defective is 0.01485.
Denote the events as follows:
A₁ = an item that is produced by the company and is defective.
A₂ = an item produced by the company that is not defective.
X is an item that is classified as defective by an inspector.
Given:
P (X|A₁) = 0.99
P (X|A₂) = 0.005
P (A₁) = 0.01
P (A₂) = 1 - P (A₁)
P (A₂) = 1 - 0.01 = 0.99
The law of total probability defines that:
P(B)=P(B|A).P(A)+P(B|C).P(C)
By using this law we can compute the probability that it is selected for inspection that is classified as defective as follows:
P(X)=P(X|A₁).P(A₁)+P(X|A₂).P(A₂)
So, the probability that an item selected for inspection is classified as defective is 0.01485.
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What is the difference between heat and temperature?
How does a thermometer measure temperature?
When, if at all, does heat transfer stop?
Exit Ticket
What type of heat transfer occurs when eggs fry in a pan?
What type of heat transfer occurs when you roast a marshmallow by holding it over a campfire?
What type of food in which convection helps the cooking process? Explain your answer
When you touch a picnic table, your hand gets warmer. Explain how energy conservation applies to this situation
please answer these i give brainliest
Answers
Answer:
heat is hot and tempture is all
Collect like terms
−
8
d
2
−
3
d
2
Answers
Answer:
8,2,2,3
d,d,
HOPE THIS HELPS
Answer:
5d²
Step-by-step explanation:
Given
8d² - 3d² ← collect like terms by subtracting the coefficients, that is
(8 - 3)d²
= 5d²
alg 2 - transformations of functions. need asap
(brainliest + 15 pts)
Answers
Answer:
\(y = f(x - 1) + 2\)
Step-by-step explanation:
Let's say that the dotted graph is y.
See f(3) = 0 or (3,0). Let's call that the point of interest. Notice that our point of interest has to move to the right by 1 unit to get to the dotted graph. so
\(y = f(x - 1)\)
And it has to go up by two units so
\(y = f(x - 2) + 2\)
9x + 18 - 5x = 2 + 4x
Answers
Answer:
There are no solutions
Step-by-step explanation:
9x+18−5x=2+4x
Step 1: Simplify both sides of the equation.
9x+18−5x=2+4x
9x+18+−5x=2+4x
(9x+−5x)+(18)=4x+2(Combine Like Terms)
4x+18=4x+2
4x+18=4x+2
Step 2: Subtract 4x from both sides.
4x+18−4x=4x+2−4x
18=2
Step 3: Subtract 18 from both sides.
18−18=2−18
0=−16
Answer:
There aren't any values of x that would make the equation true.
NO SOLUTION
Hope this helped <3
Let S be the universal set, where:
S= {1, 2, 3,..., 18, 19, 20}
Let sets A and B be subsets of S, where:
Answers
Answer:
Step-by-step explanation:
Therefore, the height of the tower is approximately 121.4 meters.
1) Which of the following relations are functions?
Answers
The relation which is a function among the given answer choices are Choices A and D.
Which among the given answer choices represent a function?It follows from the task content that the answer choices which represent a function be identified as required.
By definition, a function is a relation in which case, no one input value is assigned more than one output.
On this note, for Choice A; all input values have only one output value assigned to them and for Choice D; the graph represents a quadratic function in which case, each input value, x is assigned only one output value, y.
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David's overtime rate is $20. This week, he worked 3 overtime hours. How much will he get paid for overtime?
A. $30
B.$45
C$60
Answers
Answer:
$60
Step-by-step explanation:
3x20=60
PLS HELP FOR BRAINLIEST
Answers
Answer:
He used 15 quarters and 3 dimes.
Step-by-step explanation: Hope this helps and if you want more of an explanation feel free to ask <33
Answer:
q = 15, d = 3
Step-by-step explanation:
0.25q + 0.1d = 4.05
q + 0.4d = 16.20
q + d = 18 (--subtract this equation from the one above)
-0.6d = -1.8
d = -1.8/-0.6=3
q + 3 = 18
q = 15
Translate to an equation please.
four less than thirteen times a number is equal to that number added to eight
Answers
Hi
let call "a number" X.
then we have: 4-13X = X + 8 ..
13x-x = 8+ 4
12x= 12
X= 1
how do - 1 3/4 and - 1 1/4 compare. choose the symbol
Answers
-1/2 is negative, we know that -1 3/4 is less than -1 1/4.
What is denominator ?
In a fraction, the denominator is the bottom number that represents the total number of equal parts into which a whole is divided. It indicates the number of equal parts that make up a single unit or the whole. For example, in the fraction 3/4, the denominator is 4, which means the whole is divided into 4 equal parts and we are considering 3 of those parts.
The denominator of a fraction plays an important role in determining the size of the parts being considered. A larger denominator means the parts are smaller, while a smaller denominator means the parts are larger. For instance, 1/2 represents larger parts than 1/4 since the denominator of 2 means the whole is divided into 2 equal parts, while the denominator of 4 means the whole is divided into 4 equal parts.
According to the question:
To compare -1 3/4 and -1 1/4, we need to first convert both numbers to the same format. We can do this by finding a common denominator for the fractions and then subtracting the whole numbers.
-1 3/4 can be written as -7/4, and -1 1/4 can be written as -5/4.
Now we can see that -7/4 is less than -5/4, because -7/4 is further to the left on the number line than -5/4. Therefore, we can use the "less than" symbol to compare them:
-1 3/4 < -1 1/4
Alternatively, we can subtract the two numbers to get:
-1 3/4 - (-1 1/4) = -7/4 + 5/4 = -2/4 = -1/2
Since -1/2 is negative, we know that -1 3/4 is less than -1 1/4.
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elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).
Answers
Help with this trig identities problems.
1) Given csc Φ = 7/3 and cot Φ = - (2√10)/(3), find sec Φ.
2) Given that sec β = 6/5 and sin β > 0, find tan β and sin β.
Answers
Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.
1. We can start by using the Pythagorean identity to find the values of sin Φ:
\(sin^2\) Φ + \(cos^2\) Φ = 1
Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:
1/(7/3) = sin Φ
sin Φ = 3/7
Next, we can use the fact that cot Φ = cos Φ/sin Φ:
cot Φ = cos Φ/(3/7) = - (2√10)/(3)
Simplifying this expression, we get:
cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7
Finally, we can use the fact that sec Φ = 1/cos Φ:
sec Φ = 1/(- 2√10/7) = -7/(2√10)
2. We can use the fact that sec β = 1/cos β to find the value of cos β:
sec β = 6/5
cos β = 5/6
Next, we can use the Pythagorean identity to find the value of sin β:
\(sin^2\) β + \(cos^2\) β = 1
sin β = √(1 - \(cos^2\) β) = √(1 - 25/36) = √(11/36) = √11/6
Finally, we can use the fact that tan β = sin β/cos β:
tan β = (√11/6)/(5/6) = √11/5
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a box being pushed at a force of 125 newtons
is this a vector or a scalar quantity? and why?
Answers
Answer:
force is a vector quantity because we can't add it using simple algebra
it's direction dependent
however in this case
specific direction is not given
though it's mentioned it is pushed
so
force is a vector quantity
Graph the inequality. y is less than negative one fourth times x minus 3 The graph shows a solid line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading above the line. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative, 3 with shading above the line. The graph shows a solid line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.
Answers
A graph of the inequality "y is less than negative one fourth times x minus 3" is: D. The graph shows a dashed line passing through the point negative 12 comma 0 and 0 comma negative 3, with shading below the line.
How to determine the required ordered pair?In order to determine the ordered pair that is included in the solution to this linear inequality, we would first of all translate the word problem into an algebraic equation as follows;
y is less than negative one-fourth times x minus 3 ⇒ y < -x/4 - 3.
Next, we would use an online graphing calculator to graphically solve the linear inequality. Therefore, the required solution for the given linear inequality is the shaded area below the dashed line, which is given by the ordered pairs (−12, 0) and (0, -3).
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Answer:
it’s D dotted line with shading below
Step-by-step explanation:
i got it on my quiz
Write a recursive formula for
Answers
Answer:
\(a(1) = 144\)
\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)
\(a(n) = - \frac{1}{6} a(n - 1)\)
Which of the following expressions is equivalent to 45 - 165n?
Select all that apply.
A. 3(15 - 165n)
B. 5(9 -33n)
C. 15(5 - 33n)
D. 9(5 - 33n)
E. 15(3 - 11n)
Answers
Answer:
E
Step-by-step explanation:
45-165n
15(3-11n)
basically
45/15=3. 165/15=11
Given the individual rates of workers, to find the combined rate of all the individuals working together you must
the individual rates.
Fill in the blank
Answers
To find the combined rate of all the individuals working together, you must add the individual rates.
How to calculate combined rate of individuals working together?When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.
This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.
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the decimal form of a fraction is called a what
Answers
Answer:
Hello Adam here!
Step-by-step explanation:
The numbers that are represented by decimal numerals are the decimal fractions (sometimes called decimal numbers), that is, the rational numbers that may be expressed as a fraction whose denominator is a power of ten.
Hope This Helps From, Adam :)
Rewrite the sum, difference,product of logs
log(5x - 3y)
Answers
Rewriting the logarithm expression log(5x - 3y) is log(-3y + 5x)
Rewriting the logarithm expressionFrom the question, we have the following parameters that can be used in our computation:
log(5x - 3y)
The expression in the bracket of the logarithm expression is 5x - 3y
This expression can be rewritten as
5x - 3y = -3y + 5x
So, we can substitute -3y + 5x for 5x - 3y in the logarithm expression
using the above as a guide, we have the following:
log(5x - 3y) = log(-3y + 5x)
Hence, the solution is log(-3y + 5x)
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geometry again, help please because I’m really bad at it
Answers
===========================================================
Explanation:
UV is the midsegment, so it's parallel to ST and it's half as long
Phrased another way: ST is twice as long compared to UV
ST = 2*UV
8x-28 = 2*(2x-2)
8x-28 = 4x-4
8x-4x = -4+28
4x = 24
x = 24/4
x = 6
We can now find the length of each segment mentioned.
ST = 8x - 28 = 8*6 - 28 = 20UV = 2x-2 = 2*6-2 = 10This shows UV is half as long compared to ST, or ST is twice as long compared to UV. This confirms our answer.
Which system of inequalities is graphed?
Second part please help
Answers
Answer:
Step-by-step explanation:
If f(x) = x + 1 and g(x) = 2x - 7, which expression is equivalent to [fog|(3)?
Answers
Answer and Step-by-step explanation:
First, we plug in the value of 3 for x in g(x), then we plug the answer os g(x) into the value of x in f(x).
g(3) = 2(3) - 7
Multiply 2 by 3, then subtract 7.
g(3) = 6 - 7
g(3) = -1
Now, we plug -1 for x in f(x).
f(g(3)) = f(-1) = -1 + 1
f(-1) = 0
The value of f(g(3)) is 0.
#teamtrees #PAW (Plant And Water)
Which measurement is the same for Charles and Jermod?
median
Orange
Olower quartile
Oupper quartile
These dot plots show how many minutes Charles and Jermod spent on homework per day
for three weeks.
15 20 25 30
40 45 50 55 60
Charles's Homework (minutes per day)
15 20 25 30 35 40 45 50 55 60
Jermod's Homework (minutes per day)
Which measurement is the same for Charles and Jermod?
Answers
The measurement is the same for Charles and Jermod are lower quartile and upper quartile. Therefore, options C and D are the correct answer.
From the given dot plot.
The number of minutes Charles spent on homework.
15, 15, 20, 20, 25, 30, 30, 30, 30, 30, 45, 50, 55, 60, 60.
Here, lower quartile = 20
Upper quartile = 50
Median = 30
Range = 60-15
= 45
The number of minutes Jermod spent on homework.
15, 15, 15, 20, 20, 30, 35, 45, 45, 45, 50, 50, 55, 55.
Here, lower quartile = 20
Upper quartile = 50
Median = 45
Range = 55-15
= 40
Therefore, options C and D are the correct answer.
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I need help on this formative
The graph of the parent quadratic
function is f(x) = x2.
How does that graph transform to the function below?
g(x)=-(x-6)^2
Narrower
Wider
Reflected across the x-axis
Translated / Shifted Up
Translated / Shifted Down
Translated / Shifted Left
Translated / Shifted Right
Answers
Answer:
Reflected across the x-axisTranslated / Shifted RightStep-by-step explanation:
You want the transformation that get you from f(x) = x² to g(x) = -(x -6)².
TransformationThe attachment shows both functions.
The leading minus sign causes the graph to be reflected across the x-axis.
Replacing x with (x -6) causes the graph to be shifted right (translated) 6 units.
__
Additional comment
If there were any horizontal or vertical scaling, the graph would become wider or narrower. There is no scaling here, so the graph retains its original width.
Vertical expansion by a factor of k would make the graph narrower for k > 1:
g(x) = kx²
Horizontal expansion by a factor of k would make the graph wider for k > 1.
g(x) = (x/k)²
Polygons and their Angles
Answers
a. The measure of the interior angle is 162 degrees
b, The sum of the interior angle is 3240 degrees
c. The measure of the exterior angle is 18 degrees
How to determine the valueTo determine the value of the angles, we have that;
The formula for calculating the sum of the interior angles of a polygon is:
(n -2)180
Where , 'n' is the number of the sides of the polygon.
a. (n-2)180/n
3240/20
Divide the values
162 degrees
b. the sum of the interior angles would be;
(20-2)180
subtract the values
18(180) = 3240 degrees
c. the measure of an exterior angle is calculated as;
360/n
Substitute the value
360/20 = 18 degrees
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HELP PLEASEEEEEEE!!!!!
Answers
The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
What are similar shapesSimilar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.
Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:
the measure of angle Z is equal to 65°
the side EF corresponds to JK and side FG corresponds to KL, so:
8/20 = 11/x
x = (11 × 20)/8 {cross multiplication}
x = 27.5
the side EF corresponds to JK and EH corresponds to JM, so:
8/20 = y/30
y = (30 × 8)/20 {cross multiplication}
y = 12
Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12
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Johnny uses a wheelbarrow to move planting soil to a delivery truck. The volume of planting soil that fits in the wheelbarrow measures
2
2 feet by
3
3 feet by
1.5
1.5 feet. The delivery truck measures
11
11 feet by
8
8 feet and is
6
6 feet tall. Johnny puts planting soil in the delivery truck until the truck is
70
70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is
70
70% full?
Answers
The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.
What is the volume of a solid?The volume of a solid is the three dimensional space the solid occupies.
The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;
Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³
Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³
70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³
The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0
The number of times Johnny needs to use the wheelbarrow is about 41 times
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