Using probability and binomial distribution, we determined that the probability of exactly 5 out of 40 machines not working is approximately 0.18. The probability that all machines are working is around 0.024, and the probability that at least one machine is working is almost certain, approximately 1.
To address this problem, we will use the concepts of probability and the binomial distribution.
Calculating the Probabilities:
Let’s denote the probability of a single machine not working as p = 0.12. The probability of a single machine working is q = 1 - p = 0.88.
1. Probability that exactly 5 out of 40 machines are not working
We can use the binomial distribution formula:
P(X = 5) = C(40, 5) * p^5 * q^(40-5)
Where C(40, 5) is the number of combinations of 40 machines taken 5 at a time.
C(40, 5) = 40! / [5!(40-5)!] = 658,008
Therefore:
P(X = 5) = 658,008 * (0.12)^5 * (0.88)^35 ≈ 0.18 (using a calculator for binomial probability)
2. Probability that all 40 machines are working
This can be found by raising the probability of one machine working to the power of 40:
P(all working) = q^40 = 0.88^40 ≈ 0.024
3. Probability that at least one machine is working
The easiest way to calculate this is to find the complement of the probability that none are working and subtract it from 1:
P(none working) = p^40 = (0.12)^40 ≈ 9.0949 x 10^-38 (which is extremely close to 0)
P(at least one working) = 1 - P(none working) ≈ 1 - 0 = 1
Final answer: A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is _0.18_ , the probability that all would be working is_0.024_, and the probability that at least one machine would be working is_1_.
Complete question:
A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is ____ , the probability that all would be working is____, and the probability that at least one machine would be working is______
If you were to pick 40 machines randomly, the probability that 5 would not be working is 0.186 , the probability that all would be working is 0.011, and the probability that at least one machine would be working is 0.989.
This problem involves probability calculations for a company that has 200 machines, each with a 12% chance of not working. Let's break down the calculations step-by-step:
1. Probability that 5 out of 40 machines are not working:
This can be modeled using the binomial distribution. The binomial formula is:
[tex]P(X = k) = C(n, k) \times p^k \times (1-p)^{(n-k)[/tex]
where:
n = number of trials (40 machines)k = number of successes (5 machines not working)p = probability of success (0.12)C(n, k) = binomial coefficient (number of ways to choose k successes in n trials)For our problem, it becomes:
P(X = 5) = C(40, 5) × (0.12)⁵ × (0.88)³⁵
= 0.186
2. Probability that all 40 machines are working:
This is calculated using the complement probability as follows:
P(All working) = (0.88)⁴⁰
≈ 0.011
3. Probability that at least one machine is working:
This can be calculated using the complement rule:
P(At least one working) = 1 - P(None working)
= 1 - (0.88)⁴⁰
≈ 0.989
The graph of a function, f(x), is plotted on the coordinate plane. Select the function that would move the graph of the function to the right of the coordinate plane.
a.f(x+6)
b.f(x)+4
c.f(x-3)+1
d.f(x)-3
Correct option:
c.f(x-3)+1
Explanation:From the options we have either vertical or horizontal shift. So, for this type of transformation we have:
For any real positive number [tex]c[/tex], vertical and horizontal shift in the graph [tex]y=f(x)[/tex] are expressed as follows:
[tex]\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)[/tex]
From these rules, we know that:
[tex]f(x-3)+1[/tex]
would move the graph of the function to the right of the coordinate plane because of [tex]f(x-3)[/tex]. In other words, the transformation is as follows:
[tex]f(x-3)+1[/tex] shifts the graph of [tex]f(x)[/tex] three units to the right and one unit up
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Which of the following digits might composite numbers greater than 10 have in the ones place? Select all that apply.
1
2
3
4
The digits which a composite number greater than 10 might have include; 1, 2 ,3 and 4.
According to the question;
We are required to determine which of the digits a composite number greater than 10 might have in the ones place.The number 10 has two place values namely;
1 is in the tens place0 is in the ones place.In essence, any composite number greater than 10 can have either of 1, 2, 3 and 4 in the ones place.
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It takes b minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 3 same-size bathtubs?
Write your answer as an expression.
Answer:
3b
Step-by-step explanation:
Since it takes b minutes to fill one bathtub, then it will take 3 times b minutes to fill all three bathtubs.
Answer:
3 times b
Step-by-step explanation:
find the value of x to the nearest tenth
Answer:
20.8
Step-by-step explanation:
Using Pythagorean theorem, you can find 1/2 of x.
12²= 6² +1/2x²
From this we find 1/2 x is ≈ 10.4
Then x itself would be 2 times that, resulting in 20.8, that is your answer
Which action describes an aspect of technological design?
O building a telescope to look deeper into space
O creating a collection of mosquitoes that cause disease
o observing Doppler radar as a storm approaches
O designing an experiment to measure the heat of a volcano
Answer: A)
Step-by-step explanation: This is correct because a telescope is a piece of technology use to look further into space
A class is going on a trip to a museum. It costs $750 to rent a bus. Each ticket to the museum costs $12 Write an algebraic expression that represents the cost of the trip for people. Then evaluate this expression for 37
people
The total cost of trip for 37 people will be $1194.
Step-by-step explanation:
Given,
Rent of bus = $750
Cost of one ticket = $12
Let,
x be the number of people.
T be the total cost of the trip for people.
According to given statement;
Total cost = Rent of bus + (Cost of one ticket * number of people)
[tex]T=750+12x[/tex]
For 37 people, x=37
[tex]T=750+12(37)\\T=750+444\\T=\$1194[/tex]
The total cost of trip for 37 people will be $1194.
Keywords: linear expression, addition
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please help me with these, oh sweet jesus
Answer:
77. [tex]\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x[/tex]Proved
78. [tex]\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex] Proved
79. [tex]\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x[/tex] Proved.
80. [tex]\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x[/tex] Proved.
Step-by-step explanation:
77. Left hand side
= [tex]\cot^{6} x[/tex]
= [tex]\cot^{4} x \times \cot^{2} x[/tex]
= [tex]\cot^{4}x [\csc^{2}x - 1][/tex]
{Since we know, [tex]\csc^{2} x - \cot^{2}x = 1[/tex]}
= [tex]\cot^{4} x \csc^{2}x - \cot^{4} x[/tex]
= Right hand side (Proved)
78. Left hand side
= [tex]\sec^{4}x \tan^{2} x[/tex]
= [tex]\sec^{2} x [1 + \tan^{2}x] \tan^{2} x[/tex]
{Since [tex]\sec^{2}x - \tan^{2}x = 1[/tex]}
= [tex]\sec^{2}x [\tan^{2}x + \tan^{4}x ][/tex]
= Right hand side (Proved)
79. Left hand side
= [tex]\cos^{3} x\sin^{2} x[/tex]
= [tex]\cos x[1 - \sin^{2} x] \sin^{2} x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex][\sin^{2}x - \sin^{4}x] \cos x[/tex]
= Right hand side
80. Left hand side
= [tex]\sin^{4}x - \cos^{4}x[/tex]
= [tex][\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x[/tex]
{Since [tex]\sin^{2}x + \cos^{2} x = 1[/tex]}
= [tex]1 - 2\cos^{2} x[1 - \cos^{2}x ][/tex]
= [tex]1 - 2\cos^{2}x + 2 \cos^{4} x[/tex]
= Right hand side. (Proved)
Ashots height changed from 150 cm to 165 cm during the last year. By what percent did Ashot become taller?
150 cm ......... 100 %
165 cm ...............x %
x = 165×100/150 = 16500/150 = 110 %
Answer:
10%
Step-by-step explanation:
Subtract 150 from 165, which gives 15.
Then, do 15/150 = 0.1
Convert decimal to percent by moving the decimal point two spaces back. 0.1 becomes 10%.
Which of the following are true of linear functions? Select all that apply.
There is exactly one output for each input.
The graph of a linear function is a straight line.
Alinear function can cross the y-axis in two places
Alinear function has a constant rate of change.
Alinear function must cross the x-axis
Answer:
There is exactly one output for each input.
The graph of a linear function is a straight line.
A linear function has a constant rate of change.
Step-by-step explanation:
Answer:
A,B,D
Step-by-step explanation:
i took the assignment and quiz on ed2020
Point D (-1,5) is reflected across the x-axis which statements about D are true
Answer:
When a point is reflected across the x axis, it has the same x axis but the y axis is multiplied by -1. Think about the x axis as a mirror and the point is projected across the x axis.
Hence the x coordinate is -1 and the y coordinate is -5.
Step-by-step explanation:
Answer:
the first option
Step-by-step explanation:
the x coordinate is -1
what is 2/9+1/3= i need it for for my homework
Answer:
5/9
Step-by-step explanation:
Answer:
5/9
Step-by-step explanation:
Now we need to make our denominators match.
9 goes into 3 evenly, so we only need to multiply one term to get a common denominator.
Multiply 1 by 3, and get 3, then we multiply 3 by 3 and get 9.
Since our denominators match, we can add the numerators.
2 + 3 = 5
That gives us the sum, which is
5/9
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! Here's the final answer to 2/9 + 1/3
EFGH is a parallelogram. Find the measure of FG.
Answer:
FG = 47
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent, thus
EH = FG, that is
5z - 18 = 3z + 8 ( subtract 3z from both sides )
2z - 18 = 8 ( add 18 to both sides )
2z = 26 ( divide both sides by 2 )
z = 13
Hence
FG = 3z + 8 = (3 × 13) + 8 = 39 + 8 = 47
Based on the property of a parallelogram, the measure of FG is: 47.
Opposite Sides of a ParallelogramBased on the properties of a parallelogram, the opposite sides of a parallelogram are equal in length.
Therefore:
EH = FG
Substitute5z - 18 = 3z + 8
Combine like terms5z - 3z = 18 + 8
2z = 26
Divide both sides by 2z = 13
FG = 3z + 8
Plug in the value of zFG = 3(13) + 8
FG = 47
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The ratio of pears to green apples is 1:3 how many pears are there
Answer:
There is 1 pear for every green apple! So in this ratio there would be 1 pear!
Step-by-step explanation:
-viridiancat4, an 8th grader! :)
A 12 pound turkey takes about 180 minutes to cook. How many hours would it take to cook a 20 pound turkey?
These are ratios, which are technically equal to each other. So, you can set up the problem like this:
12/180=20/x
180*20=3600
3600/12=300
So, it would take 300 minutes.
The required time consumed to cook 20 pounds of turkey is 300 minutes.
Given that,
A 12-pound turkey takes about 180 minutes to cook.
To determine how many hours would it take to cook a 20-pound turkey.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the rate of change?The rate of change is defined as the change in value with the rest of the time is called rate of change.
A 12-pound turkey takes about 180 minutes to cook.
rate of cooking = 180 / 12 = 15 minute per pound of turkey
Time consumed to cook 20 pounds of turkey = 20 * 15 = 300 minutes
Thus, the required time consumed to cook 20 pounds of turkey is 300 minutes.
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in a group of 84 kids 3/7 brought their lunches of those who bought their lunches 9 got a slice of pizza. what fraction of the students who bought their lunches got a slice of pizza?
Answer:
3/16
Step-by-step explanation:
4/7 of 84 = 48 kids
9/48 = 3/16
Answer:
9/36=1/4
Step-by-step explanation:
3/7x84=36
Ans: 9/36=1/4
Which of the following pairs are alternate interior angles?
A.6 and 7
B.2 and 7
C.5 and 2
D.5 and 4
Every time Liliana bakes a batch of brownies,
she uses 3/4 cup of chocolate. If she has 12/8
cup(s) of chocolate remaining, how many
batches of brownies can Liliana make? Input
your answer as a whole number.
Answer:
2
Step-by-step explanation:
12/8 is equal to 6/4.
6 divided by 3 is 2.
Answer:
2 batches of brownies
Step-by-step explanation:
3/4 = (3x2)/(4x2) = 6/8
(12/8) / (6/8) =
(12/8) x (8/6) =
12/6 =
2
The sum of two numbers is 89. Three times the smaller
number is 71 more than the larger. Find the numbers.
Answer:
The numbers are 40 and 49
Step-by-step explanation:
Smaller number = x
Larger number = y
Let's write our system of equations:
x + y = 89
3x = y + 71
***************************
x = 89 - y
Substituting x in the 2nd equation and solving for y:
3 (89 - y) = y + 71
267 - 3y = y + 71
-3y - y = 71 - 267 (Like terms)
-4y = - 196
y = -196/-4
y = 49
Solving for x in the 1st equation:
x + y = 89
x + 49 = 89
x = 89 - 49
x = 40
The numbers are 40 and 49
A golf ball, thrown upwards, rises at a speed of v metres per second.
The ball reaches a maximum height of h metres.
h is proportional to the square of v.
When v = 20, h = 8
Work out the maximum height reached by the golf ball when v = 35
Answer:24.5
Step-by-step explanation:
Formula:
H=KV²
8=K×20²(400)
=8/400
=0.02
H=0.02×35²
=24.5
Answer:
The maximum height reached by the golf ball when v = 35 is 24.5 meters.
Step-by-step explanation:
Given : A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres. h is proportional to the square of v. When v = 20, h = 8.
To find : Work out the maximum height reached by the golf ball when v = 35 ?
Solution :
h is proportional to the square of v i.e. [tex]h\propto v^2[/tex]
[tex]h=kv^2[/tex]
Where, k is the constant of proportionality
When v = 20, h = 8,
[tex]8=k(20)^2[/tex]
[tex]8=400k[/tex]
[tex]k=\frac{8}{400}[/tex]
[tex]k=0.02[/tex]
The equation became [tex]h=0.02v^2[/tex].
Now, when v = 35 the value of h is
[tex]h=0.02(35)^2[/tex]
[tex]h=0.02\times 1225[/tex]
[tex]h=24.5[/tex]
Therefore, the maximum height reached by the golf ball when v = 35 is 24.5 meters.
Jackson has let out 50 meter of kite string when he observes that his kite is directly above a point on the ground 30 meters away from him, how high is the kite?
The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.
(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)
Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]
(positive root since length is a non-negative quantity).
We have |AC| = length of the kite's string = 50 meters
|AB| = distance of the observer from the point directly above which the kite is flying = 30 meters
Thus, we get the height of the kite from the ground as:
[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]
Thus, the height of the kite from the ground is 40 meters approximately.
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A bag contains 10 red, 9 white, 8 yellow and 2 blue marbles. How many marbles must be taken out from the bag so that there will be 4 marbles of the same colour?
Answer:25
Step-by-step explanation:
10 plus 9+4+2 will give you 21 and it will have 4 yellow ones left
-2.2-(-4x-2)=-(-x-3.1)
Answer: x=1.1
Step-by-step explanation:
-2.2 - (-4x - 2) = - (-x - 3.1)
-2.2 + 4x + 2 = x + 3.1
-0.2 + 4x = x + 3.1
+0.2 + 0.2
4x = x + 3.3
-x -x
3x = 3.3
/3 /3
x = 1.1
hope this helps!
Help me with A and B. And gave me the answer and how you got to the answer.
Answer:
the answer is 12m + 4
Step-by-step explanation:
you do the distributive property which is 3*2m and then 3*4 and you get 6m+12 and then you do it again which you do 2*3m and then 2*-4 and you get 6m-8 and then you get 6m+12+6m-8 and you just add your like terms to get 12+4
hope this helped
A portion of a daycare has been set aside for toddlers under 2. The dimensions are shown. A scale drawing of the room is 1.5 cm tall. How wide is the scale drawing?
Answer:
2.4 cm.
Step-by-step explanation:
See the given diagram of two similar triangles one with actual dimensions and the other drawn on paper with a certain scale.
The ratio of corresponding sides of two similar triangles is always the same.
Now, 1.5 cm on the drawing is equivalent to 2.5 m i.e. 250 cm. in actual dimension.
So, 4 m i.e. 400 cm in actual dimension will be equivalent to [tex]\frac{1.5}{250} \times 400 = 2.4[/tex] cm. in the drawing. (Answer)
Which of the following statement are false?
A) 5/9 can be shown as equivalent to an improper fraction.
B) 8/2 can be simplified as a whole number.
C) 1 1/3 can be shown as equivalent to an improper fraction.
D) 6/7 can be shown as equivalent to a proper fraction.
Answer:
A
Step-by-step explanation:
Because 5/9 is an example of a proper fraction. In order to be an improper fraction, the numerator needs to be larger than the denominator. 8/2 can be simplified as 4 and 4 is a whole number. 11/3=3 2/3 is an example of improper fraction. 6/7, again, this is another example of a proper fraction.
What is 4 divided by 3/5
4 divided by 3/5
pretend that 4 has a denominator which is 1
4/1 divided by 3/5
when dividing always flip over the second fraction
4/1*5/3
multiply the numerators together
4*5=20
multiply the denominators together
1*3=3
answer:
20/3 or 6 2/3
Four more than twice a number is less than negative twelve. Find all numbers that make this statement true.
Answer:
x<-8
Step-by-step explanation:
four more than twice a number = 4+2X
is less than negative twelve = <-12
4+2X<-12
(4-4)+2X< -12-4
2x<-16
X<-8
To find the numbers that make the statement true, we need to solve the equation 2x + 4 < -12 for x. Any number less than -8 will make the statement true.
Explanation:To find the numbers that make the statement true, we need to translate the given sentence into a mathematical equation. Let's denote the unknown number as 'x'. The sentence 'Four more than twice a number is less than negative twelve' can be written as 2x + 4 < -12. Now, we can solve this equation for x:
Subtracting 4 from both sides, we get 2x < -16.
Dividing both sides by 2, we have x < -8.
Therefore, any number less than -8 will make the statement true.
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Barry's house has 4 windows that he is planning to replace to improve energy efficiency. The width of each window is between 3.3 and 3.7 ft, and the length of each window is between 3.7 and 4.1 ft. Barry estimates the area of all 4 windows to be 62 sq ft. Is this a reasonable estimate?
A.
No, the estimate should be lower.
B.
No, the estimate should be higher.
C.
Yes, the estimate given is reasonable.
Answer:
B)No, the estimate should be higher
Answer:
no the estimate should be lower
the sum of 2fifteens and 10 fifteens
Answer:4/5
Step-by-step explanation:
2/15 + 10/15=12/15=4/5
easy right?
Six friends went out to dinner. Each person ordered the same meal, which was $15.85. The friends left a combine tip of $14. What was the total of the bill and the tip?
Answer:
$77.40
Step-by-step explanation: