Answer:
(a) 0.0686
(b) 0.9984
(c) 0.0016
Step-by-step explanation:
Given that a machine produces parts that are either defect free (90%), slightly defective (3%), or obviously defective (7%).
Let A, B, and C be the events of defect-free, slightly defective, and the defective parts produced by the machine.
So, from the given data:
P(A)=0.90, P(B)=0.03, and P(C)=0.07.
Let E be the event that the part is disregarded by the inspection machine.
As a part is incorrectly identified as defective and discarded 2% of the time that a defect free part is input.
So, [tex]P\left(\frac{E}{A}\right)=0.02[/tex]
Now, from the conditional probability,
[tex]P\left(\frac{E}{A}\right)=\frac{P(E\cap A)}{P(A)}[/tex]
[tex]\Rightarrow P(E\cap A)=P\left(\frac{E}{A}\right)\times P(A)[/tex]
[tex]\Rightarrow P(E\cap A)=0.02\times 0.90=0.018\cdots(i)[/tex]
This is the probability of disregarding the defect-free parts by inspection machine.
Similarly,
[tex]P\left(\frac{E}{A}\right)=0.40[/tex]
and [tex]\Rightarrow P(E\cap B)=0.40\times 0.03=0.012\cdots(ii)[/tex]
This is the probability of disregarding the partially defective parts by inspection machine.
[tex]P\left(\frac{E}{A}\right)=0.98[/tex]
and [tex]\Rightarrow P(E\cap C)=0.98\times 0.07=0.0686\cdots(iii)[/tex]
This is the probability of disregarding the defective parts by inspection machine.
(a) The total probability that a part is marked as defective and discarded by the automatic inspection machine
[tex]=P(E\cap C)[/tex]
[tex]= 0.0686[/tex] [from equation (iii)]
(b) The total probability that the parts produced get disregarded by the inspection machine,
[tex]P(E)=P(E\cap A)+P(E\cap B)+P(E\cap C)[/tex]
[tex]\Rightarrow P(E)=0.018+0.012+0.0686[/tex]
[tex]\Rightarrow P(E)=0.0986[/tex]
So, the total probability that the part produced get shipped
[tex]=1-P(E)=1-0.0986=0.9014[/tex]
The probability that the part is good (either defect free or slightly defective)
[tex]=\left(P(A)-P(E\cap A)\right)+\left(P(B)-P(E\cap B)\right)[/tex]
[tex]=(0.9-0.018)+(0.03-0.012)[/tex]
[tex]=0.9[/tex]
So, the probability that a part is 'good' (either defect free or slightly defective) given that it makes it through the inspection machine and gets shipped
[tex]=\frac{\text{Probabilily that shipped part is 'good'}}{\text{Probability of total shipped parts}}[/tex]
[tex]=\frac{0.9}{0.9014}[/tex]
[tex]=0.9984[/tex]
(c) The probability that the 'bad' (defective} parts get shipped
=1- the probability that the 'good' parts get shipped
=1-0.9984
=0.0016
Find the real-number root.
√1.44
1.2
no real roots
2.07
0.72
Answer: A. 1.2
Step-by-step explanation:
The principal, real, root of:
2^√1.44
=1.2
All roots:
1.2
−1.2
1.44 is not a perfect square
how many values of x will satisfy the equation -2|3x-5|=0
Answer:
1 value
Step-by-step explanation:
spicifically 5/3
The x satisfy only 1 value and x is [tex]\frac{5}{3}[/tex] .
What is modulus?The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative. It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
According to the question
-2|3x-5|=0
Step1: Dividing -2 both side
|3x-5|=0
Step 2: Open modulus
3x-5=0 and - 3x+5=0
3x=5 and - 3x = - 5
x = [tex]\frac{5}{3}[/tex]
Hence, the x satisfy only 1 value and x is [tex]\frac{5}{3}[/tex] .
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Emma measured a line to be 16 inches long. If the actual length of the line is 15.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
4.6% (nearest tenth)
Step-by-step explanation:
percent error = (|approx - actual| ÷ actual) × 100
percent error = (|16 - 15.3| ÷ 15.3) × 100
= 4.6% (nearest tenth)
[tex] \sf\% \: error = \frac{ |approx - actual| }{actual} \times 100[/tex]
Approx = 16Actual = 15.3[tex] \tt\% \: error = \frac{ |16 - 15.3| }{15.3} \times 100[/tex]
[tex] \tt\% \: error = \frac{ |0.7| }{15.3} \times 100[/tex]
[tex] \tt\% \: error = \frac{ |0.7| }{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{0.7}{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{ \frac{7}{10} }{ \frac{153}{10} } \times 100[/tex]
[tex] \tt\% \: error = \frac{7 }{ 153 } \times 100[/tex]
[tex] \tt\% \: error = \frac{7 00}{ 153 } [/tex]
[tex] \tt\% \: error =4.57\%[/tex]
Thus, The % error is 4.6% when rounded off to the nearest tenth!!~100points please help
Image attached
Find x
X + 14 = 21 what should be done to solve this equation
Answer:
x+14=21 Add 14 to both sides of the equation. Subtract 14 from the left side of the equation. Add 14 to the left side and subtract 14 from the right side of the equation.
Step-by-step explanation:
Answer: x = 7
Step-by-step explanation:
U first subtract 14 from both sides
x + 14 - 14 = 21 - 14
And then u simplify
and get 7
AHIJ has coordinates H(0, 0), I(-3, -1), and J-1, -2). Graph the triangle and its translation 3 units to the right and 2 units down. What are the coordinates of J'
The coordinates of the triangle is plotted on the graph and the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Given data ,
Let the triangle be represented as ΔHIJ
Let the coordinates of the triangle be H(0, 0), I(-3, -1), and J(-1, -2)
Now , the translation rule is
The triangle is translated 3 units to the right and 2 units down
So , add 3 to the x-coordinates and subtract 2 from the y-coordinates of each point
So , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
Hence , the translated triangle is H' ( 3 , -2 ) , I' ( 0 , -3 ) and J' ( 2 , -4 )
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Please help ASAP marking brainly
Answer:
y = 2
Step-by-step explanation:
We are given the value of x (second equation). Let's substitute the value of x into the first equation to find y.
[tex]\rightarrow \dfrac{x}{y} = 6[/tex]
[tex]\rightarrow \dfrac{4(y + 1)}{y} = 6 \ \ \ \ \ \ \ \ \ \ \ \ \ \text{\large{[}x = 4(y + 1)]}[/tex]
Use cross multiplication.
[tex]\rightarrow 4(y + 1) = 6 \times y[/tex]
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
Simplify the distributive property.
[tex]\rightarrow 4(y + 1) = 6 y[/tex]
[tex]\rightarrow 4y + 4 = 6 y[/tex]
Subtract 4y both sides.
[tex]\rightarrow 4y - 4y + 4 = 6 y - 4y[/tex]
[tex]\rightarrow 4 = 2y[/tex]
Divide both sides by 2.
[tex]\rightarrow \dfrac{4}{2} = \dfrac{2y}{2}[/tex]
[tex]\rightarrow 2 = y[/tex]
Thus, the value of y is 2.
find f(343) & f(-64) .
f(343) = ?
[tex] \sqrt[3]{343} = 7[/tex]
7 + 4 = 11
f(-64) = ?
[tex] \sqrt[3]{ - 64} = - 4[/tex]
-4 + 4 = 0
Determine the solution to the equation given 4(m-2)=18
Answer:
m=13/2 hope this helped:)
Step-by-step explanation:
The standard deviation for u(90, 230)
Answer:
Standard deviation is 70
Step-by-step explanation:
square root of 4,900= 70 (solved using standard deviation formula)
What are m and b in the linear equation 15 + 9x + 3 + 7x = y?
I need help please due in a hour
Answer:
so easy ....dude
Step-by-step explanation:
you can do it..
The ratio of dogs to cats at the veterinarian's office on Saturday. was 6 to 5. If there were 15 cats at the office, how many dogs and cats were there altogether?
Answer:
33 total cats and dogs
Step-by-step explanation:
15/5=3
3*6=18
18+15=33
hope this helps
Answer:
Dogs: 18Cats: 15In total: 33Step-by-step explanation:
Set up a proportion: [tex]\frac{6}{5} = \frac{x}{15}[/tex] Cross multiply, then divide: 15 × 6 = 90, 90 ÷ 5 = 18So, there are 18 dogs in total.Add the dogs and cats together: 18 + 15 = 33I hope this helps!
27 3/10 - 12 5/9 write in old style math
Answer:
273/10 - 113/9
Step-by-step explanation:
Answer:
- 15 [tex]\frac{23}{50}[/tex]
Step-by-step explanation:
We need to make [tex]\frac{3}{10}[/tex] and [tex]\frac{5}{9}[/tex] have the same denominator, or bottom half, before we can subtract them.In order to do this, we need to find a number that both 10 and 9 (the bottom numbers) both go into. (Hint! Multiplying them together usually helps!)This number is 90. (See? 10 • 9 = 90!)Since we multiplied 10 by 9 to get 90, we need to multiply the top (3) by 9 too, to get us [tex]\frac{27}{90}[/tex].We multiply [tex]\frac{5}{9}[/tex] by 10 to get us [tex]\frac{50}{90}[/tex].Now we can subtract 27 [tex]\frac{27}{90}[/tex] and 12 [tex]\frac{50}{90}[/tex].27 - 12 = 15 (big numbers)27 - 50 = -23 (fractions)Now we have - 15 [tex]\frac{23}{50}[/tex]If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
Practice Translate Expressions
Write an algebraic expression that models the given word phrase.
1) 15 divided by d ________________________
2) seven fewer than a number n ________________________
3) two times the sum of a and b ________________________
4) nine less than 5 multiplied by the number p ________________________
5) the product of 15 and x ________________________
6) quotient of 4 more than the number z and the number y decreased by _________
I need help please ASAP !!
Answer:
Step-by-step explanation:
5) ∠1
6) ∠2 and ∠3
7) ∠1
I need help doing this I don't pay attention in class now I'm lost
Answer:
i think the answer is 6498
Step-by-step explanation:
Answer:
6498
Step-by-step explanation:
Pay attention in class :)
Okay, so basically, you just need to replace x and y with the corresponding numbers.
So our equation would be:
9 * 2(5 * 7 - 8 * 2) squared
Now we solve with PEMDAS:
9 * 2(35 - 16)squared
9 * 2(19)squared
9 * 2(361)
18 * 361
6498
Let me know if I did something wrong!
what is the initial number of views?
A.0
B.100
C.110
D.11
Answer:
A
Step-by-step explanation:
O because that is the number that you always start off.
In this image, what is the value of C? Round your answer to the nearest tenth.
Answer:
C = 7.2
Step-by-step explanation:
What's Pythagorean Theorem?
Pythagorean Theorem is a theorem in which it states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. This can be represented as an equation of a² + b² = c².To find the value of C, we're going to use Pythagorean Theorem! We're given the legs as 4 and 6.
Step 1: Simplify.
[tex]4^2+6^2=c^2[/tex][tex]16+36=c^2[/tex] [tex]52=c^2[/tex]Step 2: Take square root of both sides.
[tex]\sqrt{c^2}=\sqrt{52}[/tex] C ≈ 7.2Therefore, the value of C is 7.2.
Given: 7x/2 < 5.
Choose the solution set.
• {xlx > 10/7}
• {x|x < 35/2}
• {x|x > 35/2}
• {x|x < 10/7}
I have no idea lol.
Answer:
x < 10/7
Step-by-step explanation:
7x/2 < 5
multiply eech side by the reciprocal(2/7)
x < 10/7
Evaluate functions from their graph .
What are the coordinates of the vertex for f(x) = x2 + 4x + 10?
A- (−2, 2)
B- (2, 2)
C- (−2, 6)
D- (2, 6)
Answer:
I believe the answer is C (-2,6)
[tex]\\ \rm\rightarrowtail y=x^2+4x+10[/tex]
Add and subtract 4[tex]\\ \rm\rightarrowtail y=x^2+4x+4+10-4[/tex]
[tex]\\ \rm\rightarrowtail y=x^2+4x+2^2+6[/tex]
[tex]\\ \rm\rightarrowtail y=(x+2)^2+6[/tex]
Vertex form
y=a(x-h)^2+kVertex:-
(h,k)=(-2,6)Ivan said that if a number ends in 0 both 2 and 5 are factors of the number. Is he correct? Why of why not?
Answer:
yes he is correct bc the number will always be divisive by 2 and 5
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (-2, 2), (1, –3), (8, –1)}
{(-3, –1), (-7, 1), (–6, –1), (-8, 1), (2, –1)}
{(1, 8), (5, 2), (2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (4, 2), (6, –3), (1, –1)}
Answer:
A
Step-by-step explanation:
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
PLEASE HELP
Write a story problem to go with the multiplication problem 5 x 3/4 . Then solve the problem.
Story:
John is baking a cake. He need to feed 5 people with the cake but the recipe is only designed for 1 serving. In the regular recipe, it required 3/4 cups of sugar. How much sugar does he need for the new recipe?
Answer:
3.75 or 3 3/4
Answer:
A store has 5 oranges then a customer buys 3/4 of them. How many is left
Step-by-step explanation:
5x3/4=3.75 if it was in decimal but in fraction it is 23/4
5x3/4=3.75
3/4 is 0.75
0.75 x 5=3.75
Solve the following equations for x (5 points each). (a) -3x+10=34 and (b) 13x-4=11x+10-8
please show work
Answer:
A)x=-8 B)x=3
Step-by-step explanation:
A)-3x+10=34 -3x+10-10=34-10 -3x/-3=24/-3 x=-8
B) 13x-4=11x+10-8 13x-4+4=11x+10-8+4 13x-11x=11x-11x+6 2x/2=6/2 x=3
What is a savings goal? PLS I NEED HELP QICK PLSSS nvm
Answer:
A goal for the amount of money being saved.
Step-by-step explanation:
The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . and the temperature of the rod is T= 30 ∘F , determine the force in the rod when its temperature is T= 150 ∘F .
The force in the rod when the temperature is 150 °F is 718.72 pounds-force.
How to determine the resulting the resulting force due to mechanical and thermal deformationLet suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ([tex]F[/tex]), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.
Given simmetry considerations, we derive an expression for the spring force ([tex]F[/tex]), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:
[tex]F = k\cdot (\Delta x + 0.5\cdot \Delta l)[/tex] (1)
Where:
[tex]k[/tex] - Spring constant, in pounds-force per inch.[tex]\Delta x[/tex] - Spring deformation, in inches.[tex]\Delta l[/tex] - Rod elongation, in inches.The rod elongation is described by the following thermal dilatation formula:
[tex]\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})[/tex] (2)
Where:
[tex]\alpha[/tex] - Coefficient of linear expansion, in [tex]\frac{1}{^{\circ}F}[/tex].[tex]L_{o}[/tex] - Initial length of the rod, in inches. [tex]T_{o}[/tex] - Initial temperature, in degrees Fahrenheit.[tex]T_{f}[/tex] - Final temperature, in degrees Fahrenheit.If we know [tex]k = 1000\,\frac{lb}{in}[/tex], [tex]\Delta x = 0.7\,in[/tex], [tex]\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}[/tex], [tex]L_{o} = 48\,in[/tex], [tex]T_{o} = 30\,^{\circ}F[/tex] and [tex]T_{f} = 150\,^{\circ}F[/tex], then the force in the rod at final temperature is:
[tex]F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right][/tex]
[tex]F = 718.72\,lbf[/tex]
The force in the rod when the temperature is 150 °F is 718.72 pounds-force. [tex]\blacksquare[/tex]
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find the rate of change from the equation x=1 will mark brainiest
Answer:
undefined
Step-by-step explanation:
when graphed, x=1 goes up and down which makes it's slope undefined
Answer:
∞(infinity)
Step-by-step explanation:
rate of change for the equation x = 1
use the formula: y = mx + b
where:
y = how far up the line goes
m = slope
x = how far along
b = Y-intercept
the equation is a vertical line,
so the slope = ∞ (infinity)
71.6 less then or greater then 71.63
Answer:
less
Step-by-step explanation: 71.6 can also be seen as 71.60 therefore 71.63 is greater
Answer:
Less than.
Think of .6 as the tenths place to tens place.
.63 is 6 tenths and 3 hundredths, so 63.
Now ask yourself, "Is 63 greater than 60?"
And your answer is yes.