A sample of 4 different calculators is randomly selected from a group containing 18 that are defective and 35 that have no defects. What is the probability that at least one of the calculators is defective?A. 0.180B. 0.810C. 0.179D. 0.821
Answers
We want the probability of "at least one is defective". Let's call this "D"
D -> "at least one is defective"
So we want P(D).
However, notice that the probability of "at least one is defective" plus the probability of "no on is defective" is 100%.
Let's call "no one is defective" as "N". So:
\(\begin{gathered} P(N)+P(D)=1 \\ P(D)=1-P(N) \end{gathered}\)We do this because it is much easier to calculate P(N).
The probability of "N", "no one is defective", is the probability of picking one of the good ones four times in a row. We have 18 defective and 35 good ones, total of 53. So the probability of picking a good one first is:
\(\frac{35}{53}\)Now, we have 18 defective and 34 good ones, total of 52, so the probability of picking a good one now is:
\(\frac{34}{52}\)The third is:
\(\frac{33}{51}\)And the fourth is:
\(\frac{32}{50}\)The probability of all this happening is P(N), and we can calculate by:
\(P(N)=\frac{35}{53}\cdot\frac{34}{52}\cdot\frac{33}{51}\cdot\frac{32}{50}\approx0.1788\)Now, we can calculate P(D):
\(P(D)=1-P(N)\approx1-0.1788\approx0.821\)So, the probability os at least one of the calculator is defective is 0.821, alternative D.
Related Questions
what is the area of the patio if the yard is 12 feet on each side . PLS HELP
Answers
Answer:
36 ft²
Step-by-step explanation:
1/4(12)²
1/4(144)
36 ft²
The area of the patio if the area of the yard is 12 feet on each side is 36 ft².
What is the area?The area is the total space occupied by the object, and the area of the square is the square of each of its sides.
Given:
The length of each side of the yard, a = 12 ft,
Calculate the area of the yard by following the formula,
A = a²,
Here A is the area,
A = 12²
A = 144 ft²,
The area of the patio = area of yard / 4
The area of patio = 144 / 4
The area of the patio = 36 ft²
Therefore, the area of the patio if the area of the yard is 12 feet on each side is 36 ft².
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Solve for x In the equation x2 - 12x+ 36 = 90
Answers
Answer:
x ≈ 15.49 or -3.49
Step-by-step explanation:
x² - 12x + 36 = 90
x² - 12x - 54 = 0
Quadratic formula:
( -b ± √b² - 4ac ) / 2a
=
( 12 ± √144 + 216 ) / 2
= (12 ± 18.97) / 2
(12 + 18.97) / 2 = 30.97 /2 ≈ 15.49
(12 - 18.97) / 2 = -6.97 / 2 ≈ -3.49
HELP! the student council at woodlands middle school is planning a field trip. they polled randomly selected teachers and students and asked what they want to eat for lunch. the results are shown in the tables below. which of the following statements are true?
Answers
Answer:
c
Step-by-step explanation:
because on the chart is says 19% under burgers for teachers.
Tell me if it is right.
Imena earned $261 last week. If she worked 18 hours and earned the same amount each hour, how much was she paid per hour?
Answers
The amount paid to Imena per hour will be $14.5
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Imena earned $261 last week. She worked 18 hours and earned the same amount each hour.
Imena's earnings for an hour will be calculated as:-
Earning per hour = 261 / 18
Earning per hour = $14.5
Therefore, the amount paid to Imena per hour will be $14.5
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help please!!!!!! Brainliest for correct awnser!! Which of the following is equal to the rational expression when x ≠ 5 or -1? (x-7)(x+1)/(x+1)(x-5)
Answers
Answer:
C
Step-by-step explanation:
I’m am really confused on this question
Answers
Answer:
2x^7
Step-by-step explanation:
add the exponents because they both are x
2x^4*x^3=2x^7
Find a 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1
Answers
A 3rd degree polynomial function with real coefficients satisfying the given condition. 2 and -3 +3i are zeros; leading coefficients is 1, is:
f(x) = x³ + 4x² + 6x - 36
What is polynomial function?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.
we have to find third degree polynomial, so, n = 3
Since 2 is its zero ,so, x - 2 is its factor
As complex zeros occur in conjugate pairs .
So,other factors are (x + (3 + 3i)) and (x + (3 - 3i)) ,
Firstly, we find the product of these two factors:
= x² + 6x + 9 - 9i²
= x² +6x +9 - 9(-1)
= (x² +6x + 18)
Now multiply (x² +6x + 18) with (x - 2) we get f(x):
= (x² +6x + 18) (x - 2)
= x³ - 2x² + 6x² - 12x + 18x - 36
= x³ + 4x² + 6x - 36
Correct option: b
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64 + (5 ÷ 3) - 2^3
help me plz
Answers
Answer:
57.67
Step-by-step explanation:
64+1.67-8
65.67-8
57.67
let sn be the number of successes in n independent bernoulli trials, where the probability of success for each trial is 1/2. evaluate the following limits.
(a) n→[infinity]lim P( 2n− 3n ≤S n ≤ 2n + 3n)
(b)n→[infinity] lim P( 2n− 4n ≤S n ≤ 2n+ 4n)
(c) n→[infinity]lim P(2n−20≤Sn ≤ 2n+20)
Answers
The following limits -
Option a) = 1
Option b) = 0
Option c) = 0
According to the question given,
The probability of success of each trial is = \(\frac{1}{2}\)
Let us consider options a),
n→[infinity]lim P( \(2n - 3n \leq S n \leq 2n + 3n\) ),
We could conclude that if n tends to infinity, the probability of having \(2n - 3n\) successes in n number of trials = the probability of having \(2n - 3n\) successes in n number of trials.Since in the question, the probability of success for each trial is 1/2, so we could say that, \(2n - 3n\) successes = \(2n - 3n\) successesTherefore, the limit is = 1
Taking option b),
We could conclude that if n tends to infinity, the probability of having \(2n - 4n\) successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, \(2n - 4n\) successes = 0Therefore, the limit is = 0
Taking option c),
We could conclude that if n tends to infinity, the probability of having \(2n - 20\) successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, \(2n - 20\) successes = 0Therefore, the limit = 0
Therefore, the following limits are - a) 1, b) 0, c) 0
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Please help someone I’m miserable I’ll pay Lol
Answers
Answer:
7,6 1/2, 5 here are your answers welcome
Will give brainliest if correct
explain reason
Answers
Therefore , the solution of the given problem of parallel lines comes out to be parallel lines stay parallel option C is correct.
What applications do parallel lines have?A parallelogram in Euclidean geometry is essentially a straightforward hexagon with two different groups & equal distances. When both sets of sides evenly share a horizontal path, a particular type of quadrilateral known as a parallelogram is created. There are four distinct types of parallelograms, three of them being incompatible. The four distinct forms are slightly parallelograms, rectangular shapes, squares, and parallelograms.
Here,
C. It is untrue that a line may be translated into two parallel lines.
A line can be translated into another line that runs parallel to the first line, but not into two parallel lines.
Every point on the line is rigidly transformed by a translation, which moves all of the points along the line uniformly and in one direction.
After a translation, parallel lines stay parallel.
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You are given the great circle of a sphere is a length of 25 miles. What is the volume of the sphere
Answers
The volume of the sphere is approximately 3431.82 cubic miles.
To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.
C = 2πr
60 = 2πr
Divide both sides of the equation by 2π:
r = 60 / (2π)
r = 30 / π
Now that we have the radius, we can use the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(30/π)³
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)(27000/π²)
V = (4/3)(27000/9.87) (approximating π to 3.14)
V ≈ 3431.82 cubic miles
Therefore, the volume of the sphere is approximately 3431.82 cubic miles.
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Question
You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?
what are the assymptotes of this equation
Answers
Based on the graph how many bottles will be filled in 80 seconds? 
Answers
Answer:
Below
Step-by-step explanation:
Find unit rate (since it starts at 0,0)
at 45 seconds it is 900 bottles
900 bottles / 45 seconds = 20 bottle / sec
20 bottles / sec * 80 sec = 1600 bottles
The volume of a spherical balloon with radius 3.4 cm is about 165 cm3. Estimate the volume of a similar balloon with radius 17.0 cm.
Answers
we can use the formula of the sphere
\(V=\frac{4}{3}\pi\times r^3\)and replace the value of the new radious
\(\begin{gathered} V=\frac{4}{3}\pi\times(17)^3 \\ \\ V=\frac{4}{3}\pi\times4913 \\ \\ V=\frac{19652}{3}\pi\approx20,579 \end{gathered}\)the volume of the new ballon is 20579 cm3
What is the value of f(6) in the function below?
fx) = 2x
Answers
Answer:
substitute that (6) in X so f(6) = 2(6) which is = 12
The line passing through -1, 4 and 1, 7
Answers
Answer:
6
Step-by-step explanation:
The ratio of the sides of rectangle LMNP to the sides of rectangle TUVW is 1:4. The length of LM is 3.6 in, and the length of UV is 16 in.
What is the difference between the areas of the two rectangles?
A. 226 in2
B. 172.8 in2
C. 211 in2
D. 216 in2
Answers
Counting up on a number line starting at 0 corresponds with what numbers
Answers
Use the working backward method to find the solution of the equation.
6y - 5=7
y=____
Answers
Answer:
y = 2
Step-by-step explanation:
6y - 5 = 7
~Add 5 to both sides
6y = 12
~Divide 6 to both sides
y = 2
Best of Luck!
Answer:
2.16
Step-by-step explanation:
6y - 5 = 7
7 + 5 = 13
6y = 13
6y/6 = 13/6
y = 2.16
5. Si un paquete de 100 hojas iguales mide 1 cm de altura, ¿cuál
es el grosor de una hoja?
Answers
Responder:
0,01 cm
Explicación paso a paso:
Dado que :
Un paquete de 100 hojas iguales = 1cm de alto
Esto significa que el grosor del paquete es de 1 cm de alto.
Dado que las hojas son iguales, el grosor de una sola hoja será:
(Espesor del paquete completo / número de hojas en el paquete)
(1 cm / 100)
= 0,01 cm
Usando proporciones, se encuentra que el grosor de una hoja es de 0.01 cm.
Esto problema é solucionado por proporciones, se utilizando de una regla de três.Hay 100 hojas iguales, al todo midiendo 1 cm de altura. ¿Cuál es la equivalente medida de 1 hoja?La regla de três es dada por:
100 hojas - 1 cm
1 hoja - x cm
Aplicando multiplicación cruzada:
\(100x = 1\)
\(x = \frac{1}{100}\)
\(x = 0.01\)
Por eso, el grosor de una hoja es de 0.01 cm.
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In a given country the average price of a gallon of unleaded gasoline in 1997 was $1.58 in 2010 the average price of 311 find that interpret the average rate and change in the price of a gallon of gasoline per year
Answers
Answer:
$0.51 per year
Step-by-step explanation:
In 3 years the average rate went from $1.58 per gallon to $3.11
The price increase in 3 years = $3.11 - $1.58 = $1.53
Average rate of change = 1.59/3 = $0.51 per year
Write the prime factorization of 38.
Answers
i = $125 r = 6% t = 1
Answers
Answer:
\(\$ 117.92\)
Step-by-step explanation:
Use simple interest formula.
\(I = P (1 + rt)\)
\(125 = P (1 + 0.06(1))\)
\(125 = P (1.06)\)
\(125/1.06=P\)
\(117.924528=P\)
NO LINKS!! Please help me with this Geometry part 7
Answers
The converse statement is; If dana is the queen of England, then Mr. Brown is a rockstar
The inverse statement is; " If Mr. Brown is not a rockstar, then dana is not the queen of England"
The contrapositive statement is; If dana is not the queen of England, then Mr. Brown is not a rockstar.
How to Interpret Conditional Statements?A conditional statement is defined as a statement that can be written in the form “If P then Q,” where P and Q are sentences
We are given the conditional statement;
If Mr. Brown is a rockstar, then dana is the queen of England
To form the converse of the conditional statement, we will interchange the hypothesis and the conclusion. The converse statement of "If it rains, then they cancel school" is expressed as "If they cancel school, then it rains."
Thus, the converse of our statement "If Mr. Brown is a rockstar, then dana is the queen of England." is;
If dana is the queen of England, then Mr. Brown is a rockstar.
To form the inverse statement of the conditional statement, we will take the negation of both the hypothesis and the conclusion. The inverse of “If it rains, then they cancel school” is expressed as “If it does not rain, then they do not cancel school.”
Thus, the inverse of our statement " If Mr. Brown is a rockstar, then dana is the queen of England." is;
" If Mr. Brown is not a rockstar, then dana is not the queen of England"
The contrapositive of our conditional statement is;
If dana is not the queen of England, then Mr. Brown is not a rockstar.
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Question 2 (4 points)
A student rolled two six-sided dice. what is the probability that the first die landed
on a number less than 3 and the second die landed on a number greater than 3?
Answers
Answer:
Step-by-step explanation:
If the values in the table below model a proportional relationship, what is the equation for the function?
Answers
Given:
The table represents a proportional relationship.
To find:
The equation of the function.
Solution:
If y is directly proportional to x, then
\(y\propto x\)
\(y=kx\) ...(i)
where, k is the constant of proportionality.
From the given table it is clear that the function passes through (2,1). So, the equation must be satisfied by the point (2,1).
Putting x=2 and y=1 in (i), we get
\(1=k(2)\)
\(\dfrac{1}{2}=k\)
Putting \(k=\dfrac{1}{2}\), we get
\(y=\dfrac{1}{2}x\)
Therefore, the correct option is A.
If two angles are complementary then the sum of their measures is _______.
(Answer with a number ONLY)
Answers
If the two angles are complementary, then their sum is 90 degrees.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
If the two angles are complementary, then their sum is 90 degrees.
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Line a is parallel to line b. If the
measure of Z7 is 114°, what is the
measure of Z1?
Answers
9514 1404 393
Answer:
114°
Step-by-step explanation:
Alternate exterior angles 1 and 7 are congruent. Angle 1 has the same measure as angle 7.
angle 1 = 114°
The data distribution is ___
Answers
Skewed right
Explanation:
The data is higher on the right
Answer:
skewed left
Step-by-step explanation: