The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviation of .009 inch. The nails that are either shorter than 2.98 inches or longer are than 3.02 inches are unusable. What percentage of all the nails produced by this machine are unusable?
Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 3 inches, hence [tex]\mu = 3[/tex].The standard deviation is of 0.009 inches, hence [tex]\sigma = 0.009[/tex].Nails that are more than 0.02 inches from the mean are unusable, hence:
[tex]Z = \frac{0.02}{\sigma}[/tex]
[tex]Z = \frac{0.02}{0.009}[/tex]
[tex]Z = 2.22[/tex]
The proportion is P(|Z| > 2.22), which is 2 multiplied by the p-value of Z = -2.22.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
You can learn more about the normal distribution at https://brainly.com/question/24663213
The ratio of the radii of two circles is 2:3. Find the ratio of their areas. If the area of the bigger circle is 3123 sq. cm, find the area of the smaller circle.
Answer:
Your answer .
Step-by-step explanation:
Help please, 9th grade math.
Answer:
table k
Step-by-step explanation:
4:3 ratio
Can someone please help me with this one? :D ty!
2,000 Sorry That Was I Know #carryonlearning
Examine the function f(x)=log2x.
Which point is the intersection of f(x) and the line y=1?
(1,2)
(12,1)
(2,1)
(1,1)
Answer:
Is the question worded properly?
I find the intersection of the two lines to be (5,1), which is not an answer option.
Step-by-step explanation:
We want the value of x that will produce a value of 1, which will be the point the curve crosses y = 1.
log (10) = 1
Therefore 2x = 1, and x = 5
(5,1)
What is the HCF of 62 and 24 ?
Answer: As you can see when you list out the factors of each number, 2 is the greatest number that 24 and 62 divides into.
Step-by-step explanation:
For a field trip 20 students rode in cars and the rest filled 5 buses. How many students were in each bus if no more than 250 students went on the trip?
Answer:
46 bc 250 -20 =230 and 230÷5= 46
Who wants to help with a math discussion?
The distance between two points, a and b, on a number line is expressed as
|a – b|, where a and b are rational numbers. Think about locating a point halfway between a and b on a number line. How can you find the coordinate for such a point? Develop a formula in terms of a and b that you can use to find the coordinate. Your formula must work for positive and negative values of a and b. Does absolute value play a role in your formula? Why or why not? Under what circumstances might your formula be used in the real world? Explain.
Discuss how you can find the coordinate of a point located other fractional distances from a to b (or from b to a). For example, locate a point three-fourths of the distance from a to b. What kind of calculation is involved?
The distance between two points is the number of units between them.
Halfway points (a) and (b)
To locate a point halfway points (a) and (b), we use the following steps
Calculate the absolute difference between both pointsDivide the absolute difference by 2Add the quotient to the smaller point.Assume the smaller value is (a), the point (P) halfway points (a) and (b) would be
[tex]P = a + \frac{|a - b|}{2}[/tex]
Take for instance, a = 5, and b = 10.
The halfway point would be:
[tex]P = 5 + \frac{|5 - 10|}{2}[/tex]
[tex]P = 5 + \frac{5}{2}[/tex]
[tex]P = 5 + 2.5[/tex]
[tex]P = 7.5[/tex]
The halfway point between 5 and 10 is 7.5
The formula works for negative values, and absolute values are used to return the actual difference between both points
Real world circumstance
The formula can be used to calculate the halfway distance between a school gate and the school library (as an instance)
Fractional distance
To determine the fractional distance, we simply replace the 1/2 in the original formula with the appropriate fraction.
Take for instance, three-fourths from (a) to (b) would be:
[tex]P = a + \frac{3|a - b|}{4}[/tex]
Read more about distance at:
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kam
An object oscillates as it moves along
the x-axis. Its displacement varies with
time according to the equation
x = 3 cos(6pi t + pi/2)
where t is in seconds
What is the frequency of this motion?
The frequency of this motion is 3 Hz
The standard equation of an oscillation is given by:
x = A cos(ωt + Ф)
Where x is displacement, A is amplitude, ω is angular frequency = 2πf and Ф is phase difference.
Given the equation:
x = 3 cos(6πt + π/2)
Hence;
ω = 6π
2πf = 6π
f = 3 Hz
The frequency of this motion is 3 Hz
Find out more about frequency at: https://brainly.com/question/254161
How many points are on this plane?
Answer:
5
Step-by-step explanation:
A,B and C would be the inside of the plane not outside.
4. The original price of a pair of shoes is $80 and they are on sale for $48. What is the percent of discount?
O A 32%
O B. 40%
OC. 60%
O D. 66.7%
Answer:
c
Step-by-step explanation:
80 × percent = 48
percent = 48/80
= 0.6
= 60%
Need help please. High school Geometry
Answer: last one
Step-by-step explanation:
Write the equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form.
Answer:
Step-by-step explanation:
Given:
x1 = -1
x2 = 6
y1 = 2
y2 = 3
Solution:
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( 3 - 2 ) / ( 6 - -1 )
m = 1 / ( 6 + 1 )
m = 1/7
Then,
y - y1 = m ( x - x1 )
y - 2 = 1/7 ( x - -1)
y - 2 = 1/7 ( x + 1 )
y - 2 = 1/7x + 1/7
y = 1/7x + 1/7 + 2
y = 1/7x + 15/7
Which sign makes this number sentence true?
|-56|___ 1561
A)>
B)<
C)=
D) X
The absolute value of -56 is 56
the new sentence is 56____1561
A is not true because 56 is not bigger then 1561 if you count and put on number line
B is very true if you look at A. 56 is smaller than 1516
So, the answer is a
I hope this helped if it's wrong, plz blame me.
Ps.Brainlist would help a lot
Answer:
B
Step-by-step explanation:
The | | around -56 means absolute value or the total of the number, which in this case is 56, therefore 56 is less than 1561.
PLEASE HELP ME!!!!!!!
Answer:
The answer is B
Step-by-step explanation:
The answer would be B because the domain of a function is always all real numbers.
Please find the range of these numbers
Answer:
91 - 74 = 17
Step-by-step explanation:
The range is the difference between the highest and lowest values in a set of numbers.
amplitude of y=-2sin(3x)+6
Answer:
amplitude = 2
Step-by-step explanation:
Given sine in standard form
y = asinbx + c
amplitude = | a | , period = [tex]\frac{2\pi }{b}[/tex] , c is the vertical shift
Given
y = - 2sin(3x) + 6
amplitude = | - 2 | = 2
Solve for x in the equation x2 + 4x-4=8.
O x = -6 or x = 2
X=-2+2/2
O x = -2 or x = 6
O x=2+2V5
[tex] {x}^{2} + 4x - 4 = 8 \\ = > {x}^{2} + 4x - 4 - 8 = 0 \\ = > {x}^{2} + 4x - 12 = 0 \\ = > {x}^{2} + 6x - 2x - 12 = 0 \\ = > x(x + 6) - 2(x + 6) = 0 \\ = > (x - 2)(x + 6) = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 6 [/tex]
Answer:
x = -6 or x = 2
Hope you could get an idea from here.
Doubt clarification - use comment section.
Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
And the accurate root is 3 it can be determined by using rules of the rational root equation.
Given that,Function; [tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
We have to determine,Which of the values shown are potential roots of the given equation?
According to the question,Potential roots of the polynomial are all possible roots of f(x).
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45[/tex]
Using rational root theorem test. We will find all the possible or potential roots of the polynomial.
[tex]\rm p=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 45}[/tex]
[tex]\rm q=\dfrac{All\ the \ positive}{Negative\ factors \ of\ 3}[/tex]
The factor of the term 45 are,
[tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45[/tex]
And The factor of 3 are,
[tex]\pm1, \ \pm3[/tex]
All the possible roots are,
[tex]\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex]
Now check for all the rational roots which are possible for the given function,
[tex]\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0[/tex]
Therefore, x = 3 is the potential root of the given function.
Hence, The potential roots of the function are, [tex]\pm1, \ \pm3, \ \pm5, \ \pm9,\ \pm15, \ \pm45,\ \pm \dfrac{1}{3},\ \pm \dfrac{5}{3}[/tex].
For more details about Potential roots refer to the link given below.
https://brainly.com/question/25873992
Answer: ALL OF THEM
Step-by-step explanation:
Solve the system of equations
2x - 9y =14
x= -6y + 7
Answer: x=
6
7
=1
6
1
≈1.166666667
y=−
9
14
=−1
9
5
≈−1.555555556
Step-by-step explanation:
I need help with this question
Answer:
Option D
Step-by-step explanation:
a^2 + b^2 = c^2
5^2+b^2=9^2
25+b^2=81
b^2=56
b=2√14
here is the next question jj
Answer:
3.7 and east.
Step-by-step explanation:
Answer:
3.7 and east
Hope this helps! Good luck!! :)
Planes A and B intersect. Vertical plane B intersects horizontal plane A at line E D. Line C D is on plane A. Which describes the intersection of planes A and B? line CD line ED point C point D.
The description of the intersection of plane A and plane B is line CD
From the question (see attachment for the diagram of both planes), we have the following highlights
Point C is on plane A and plane BPoint D is on plane A and plane BBoth planes meet at the line that joins points C and D.
Hence, the description of the intersection of plane A and plane B is line CD
Read more about planes and lines at:
https://brainly.com/question/13099718
Answer:
The first answer, CD, is correct.
Edg, 2023
Alg 2 the problem is below please help !!!
Find the area between f(x) = 3x and f(x) = x2 on the interval (0,3]
Answer:
[tex]A=4.5[/tex]
Step-by-step explanation:
The area between two curves over the interval [tex][a,b][/tex] is [tex]A=\int\limits^b_a {f(x)-g(x)} \, dx[/tex] where [tex]f(x)[/tex] is the upper function and [tex]g(x)[/tex] is the lower function.
Therefore:
[tex]A=\int\limits^3_0 {3x-x^2} \, dx[/tex]
[tex]A=\frac{3}{2}x^2-\frac{x^3}{3}\Big|_0^3[/tex]
[tex]A=[\frac{3}{2}(3)^2-\frac{(3)^3}{3}]-[\frac{3}{2}(0)^2-\frac{(0)^3}{3}][/tex]
[tex]A=\frac{3}{2}(9)-\frac{27}{3}[/tex]
[tex]A=\frac{27}{2}-\frac{27}{3}[/tex]
[tex]A=\frac{9}{2}[/tex]
[tex]A=4.5[/tex]
So, the area between [tex]f(x)=3x[/tex] and [tex]g(x)=x^2[/tex] on the interval [tex](0,3][/tex] is [tex]4.5[/tex] square units.
Hey can u help me pls.
Answer:
15 dots
Step-by-step explanation:
formula :: 1/2 x n ( n +1 )
fig 1 ; 1 /2 x 1 ( 1+1 ) = 1 dot
fig 2 :; 1/2 x 2 ( 2+1 ) = 3 dots
......
fig 5 :: 1/2 x 5 ( 5+1 ) = 15 dots
what color is my shirt?? PLEASE HELP I FORGOT
Answer:
um
Step-by-step explanation:
Answer:
Its white! atleast i think its white because your pfp has white clothes on
Sally wants to buy themselves a beautiful, scrumptious, delightful cake but they don't know how money works. If Sally has $50.00, and the cake is $54.99, how much more do they need? literally just made this question off the top of my mind xD
Answer:
$4.99
Step-by-step explanation:
$54.99-$50.00=$4.99
Answer:
Step-by-step explanation:
cake: $54.99
sally money: $50.00
54.99-50= $4.99 lol
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
158, 155, 152, ...
Find the 34th term
The 34th term of the sequence 158, 155, 152 ...... is 59
The sequence is as follows:
158, 155, 152 ......
let
a = first term = 158
d = common difference = 155 - 158 = -3
Using Arithmetic progression formula, let's find the 34th term as follows:
aₙ = a + (n - 1)d
a₃₄ = 158 + (34 - 1)-3
a₃₄ = 158 + (33)(-3)
a₃₄ = 158 - 99
a₃₄ = 59
Therefore, the 34th term of the sequence is 59.
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Sara has a cell phone plan that charges $2 per minute for her long distance calls to Italy. She also has a pay a flat fee of $10 each month to have this plan, no matter how many minutes she talks on the phone. If Sara talks for 20 minutes long distance this month, how much money does she have to pay in total? Show work that supports your response.
Answer:
50
Step-by-step explanation:
she pays 10 in a flat fees and 2 dollars a minute so you multiply the 2 by 20 and add 10