X follows a binomial distribution with n = 2000 and p = 0.0015. The chance that the batch contains no faulty flashlights is 0.8805 percent. The likelihood of one faulty flashlight in the batch is 1.5307. X has a standard deviation of 1.0708. The likelihood of more than two faulty flashlights in the batch is 0.0388.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Here,
(a) X has a binomial distribution with parameters n = 2000 and p = 0.0015. The binomial distribution is a discrete probability distribution that describes the number of successes in n independent Bernoulli trials, each with success probability p.
(b) The expected value (mean) of X is given by E(X) = n * p = 2000 * 0.0015 = 3. The standard deviation of X is given by sqrt(n * p * (1 - p)) = sqrt(2000 * 0.0015 * 0.9985) = 1.0708.
(c) The probability that the batch contains no defective flashlights is given by P(X = 0) = (2000 choose 0) * 0.0015^0 * (0.9985)^2000 = 0.8805. The probability that the batch contains one defective flashlight is given by P(X = 1) = (2000 choose 1) * 0.0015^1 * (0.9985)^1999 = 1.5307. The probability that the batch contains more than two defective flashlights is given by P(X > 2) = 1 - P(X <= 2) = 1 - P(X = 0) - P(X = 1) - P(X = 2) = 0.0388.
X has a binomial distribution with parameters n = 2000 and p = 0.0015. The probability that the batch contains no defective flashlights is 0.8805.The probability that the batch contains one defective flashlight is 1.5307. The standard deviation of X is 1.0708. The probability that the batch contains more than two defective flashlights is 0.0388.
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find the 20th term of the A.p 3,6,9
Answer:
60
Step-by-step explanation:
1=3
2=6
3=9
The relation is Y=3X
Y20 = 3X20=60
WILL MARK BRAINIEST!!!
An artist is creating various sizes of stained-glass pieces to fit over windows that have a ratio 3:2 between the height and width. That means that the height of the glass portion can be represented as 3x and the width can be represented as 2x. The wooden trim adds 7 inches to the width and 8 inches to the height.
A: Using the length and width of the window what is the area of the glass portion? Show and explain your work.
B: What is the length and width, of the window and the pane? Show and explain your work.
C: Using the length and width you calculated from Part B, what is the area of the window and the pane? Show and explain your work.
D: What is the area of just the wooden pane? Show and explain work.
A. The area of the glass portion is 6x². B. Length of window and pane is 3x + 8 inches, and Width is 2x + 7 inches. C. Area of the window and pane is 6x² + 23x + 56. D. Area of the wooden pane is 23x + 56 inches².
A: The area of the glass portion can be found by multiplying the length and width of the glass.
Given that the height of the glass portion can be represented as 3x and the width can be represented as 2x, we have:
Area of glass portion = 3x × 2x = 6x²
B: To find the length and width of the window and the pane, we must add the wooden trim to the height and width of the glass portion. The wooden trim adds 7 inches to the width and 8 inches to the height, so we have:
Length of window and pane = 3x + 8 = 3x + 8 inches
Width of window and pane = 2x + 7 = 2x + 7 inches
C: Using the length and width from Part B, we can calculate the area of the window and the pane by multiplying the length and width:
Area of window and pane = (3x + 8) × (2x + 7) = 6x² + 23x + 56
D: To find the area of just the wooden pane, we subtract the area of the glass portion from the area of the window and the pane:
Area of wooden pane = Area of window and pane - Area of glass portion = 6x² + 23x + 56 - 6x² = 23x + 56 inches²
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Help and show work pls I’ll mark brainlist
f(x) = x + 4. q(x) = 12x1
Solve for: 1(g(-3))
The value of the composite function f(g(-3) is -32
What is the value of h(1)?From the question, we have the following parameters that can be used in our computation:
f(x) = x + 4. q(x) = 12x
The above are individual functions
This means that
f(g(x)) = 12x + 4
For f(g(-3)), we have
f(g(x)) = 12 * -3 + 4
Evaluate
f(g(x)) = -32
Hence, the value of the composite function is -32
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Health and safety guidelines set the highest sound intensity level in the workplace to 90. 0 db. One workshop with 32 similar machines produces a sound intensity level of 92. 0 db. How many of them must be shut down to bring the workshop into compliance with the guidelines?.
The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.
A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.
Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.
It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.
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The value of a painting increases by 32 percent every year. If the painting
was purchased 2 years ago for $12,430, how much is it worth today?
The painting is worth $22,225.62 today.
Compound interest is computed on the principal as well as the interest accumulated over the preceding period. It differs from simple interest in that interest is not added to the principal when computing interest for the next month.
Compound annual growth rate (CAGR) is the average yearly growth rate of an investment over a time period greater than one year. It is one of the most reliable methods for calculating and determining returns for individual assets, investment portfolios, and anything else whose value might grow or decline over time.
The formula to calculate the increase in the value of the painting is:
value_today = value_yesterday * (1 + 0.32)^number_of_years
Plugging in the given values:
value_today = $12,430 * (1 + 0.32)^2 = $12,430 * 1.32^2
= $12,430 * 1.7984
= $22,225.62
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Solve the system by substitution. -3x+3=y -x+3y=29
Answer: x = −2, y= 9
Step-by-step explanation:
Solving for X
-3x+3=y
-x+3y=29
Plug the top equation into the bottom one
-x+3(-3x+3)=29
Distribute
-x - 9x + 9 = 29
combine like terms
-10x + 9 = 29
-10x = 20
Divide the x
x = -2
Solving for Y:
Plug the value x into any of the equations'
-3(-2) + 3 = y
Distribute
6 + 3 = y
y = 9
To check if that is right, plug x into the other equation
-(-2) + 3y = 29
Distribute and combine like terms
2 + 3 y = 29
3y = 27
y = 9
What is 80 Inches in Feet?
When 80 inches is converted to feet it will be 6.66667 feet.
How to convert inches to feet?Divide 80 by 12 to convert 80 inches to feet. Using a calculator or long division, we can calculate that 80 inches equals 6.66667 feet. As a result, 80 inches equals 6.66 feet. It is important to note that inches and feet are both length units, so when you convert between the two, you are essentially moving the decimal point in the number two places to the left or right depending on which unit you are converting to. To convert inches to feet, divide the number of inches by 12, because a foot is 12 inches long. Similarly, to convert feet to inches, multiply the number of feet by 12, because there are 12 inches in a foot.Therefore, 80 inches equals 6.66667 feet, and inches to feet can be converted by dividing the number of inches by 12.To learn more about inches refer to :
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three point charges are located at the corners of an equilateral triangle
At the four corners of an equilateral triangle are three point charges.
Due to the fact that three charges do not cancel one another out with Colombian force, the system can never reach equilibrium.
A subatomic particle's electric charge causes it to experience a force when it is in an electric and magnetic field.
What does the phrase "charge" actually mean?Electric charge is the property of matter that causes it to experience a force when subjected to an electromagnetic field. Protons and electrons most typically carry positive and negative charges, which are the two forms of electric charges. Energy is created by charge movement.
The most frequent charge carriers for positive and negative electric charges, respectively, are protons and electrons. The coulomb (C) is the standard unit of electric charge used by the International System of Units (ISO) (SI).
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Complete question -
Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic force are acting
Select the correct conversion factor for each step in the following roadmap for a substance with a density of 1 g/mL.
volume (L) ----> volume (mL) ----> mass (g)
The complete conversion roadmap is: Volume (L) ----> volume (mL) ----> mass (g): 1 L * 1000 mL/L = 1000 mL * 1 g/mL = 1000 g
To convert the volume from liters to milliliters, we use the conversion factor of 1000 mL/L. This means that for every 1 liter, there are 1000 milliliters.
Volume (L) ----> volume (mL): 1 L * 1000 mL/L = 1000 mL
To convert volume to mass, we use the density of the substance, which is 1 g/mL. This means that for every 1 milliliter of the substance, it has a mass of 1 gram.
Volume (mL) ----> mass (g): 1000 mL * 1 g/mL = 1000 g
Therefore, the complete conversion roadmap is:
Volume (L) ----> volume (mL) ----> mass (g): 1 L * 1000 mL/L = 1000 mL * 1 g/mL = 1000 g
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Nvm I’ll just fail lol
Answer: probably greater than 3 1/2 inches, since bumper stickers are usually wider than they are tall
Step-by-step explanation:
estimate the solutions of the equation f(x) = −1. (enter your answers as a comma-separated list.)
We can use graphical or numerical methods to estimate the solutions os equations by finding the x-values at which the graph of f(x) intersects the x-axis at y = -1.
What is the equation?We must identify the values of x that cause f(x) to equal -1 in order to estimate the solutions to the equation f(x) = -1.
It is challenging to identify the precise solutions of the equation without knowing the precise shape of the function f. (x). However, by locating the x-values where the graph of f(x) intersects the x-axis at y = -1, we can use graphic or numerical techniques to approximate the solutions. Based on the degree, there are three primary sorts of equations. linear, cubic, and quadratic equations.
How are equations solved?Equation Solving: A General Principle
On each side of the equation, merge like terms and remove parentheses.
You can use either addition or subtraction to separate the variable word.
Use multiplication or division to find the solution for a variable.
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Charlotte works in a department store selling clothing. She makes a guaranteed salary of $500 per week, but is paid a commission on top of her base salary equal to 30% of her total sales for the week. How much would Charlotte make in a week in which she made $1575 in sales? How much would Charlotte make in a week if she made
x
x dollars in sales?
Answer:
Below
Step-by-step explanation:
Her base salary (500) for the week PLUS her comission (.3 * 1575)
totals 972.50 dollars
Hamid has gained weight. He now weighs 88kg which is 10% higher than his normal weight. What is Hamids normal weight?
If Hamid's current weight is 88kg and it is 10% higher than his normal weight, then we can use the following formula to find his normal weight:
Normal weight = Current weight / (1 + 10%)
10% of Hamid's weight is 0.10 * 88kg = 8.8kg
So, Normal weight = 88kg / (1 + 8.8kg) = 88kg / 1.10 = 80kg
Therefore, Hamid's normal weight is 80kg.
What is the length of WY?
The length of WY is 4.9.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
From two triangles the proportional sides are
11.1/5.55=8/4=9.8/WY
2=2=9.8/WY
So 2=9.8/WY
WY=9.8/2
WY=4.9
Hence, the length of WY is 4.9.
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Which quantity is proportional to 8⁄12?
Check all that are true.
16⁄36
12⁄16
24⁄36
2⁄3
18⁄24
The quantities that are proportional to 8⁄12 are 24 / 36 and 2 / 3.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that the fraction is 8 / 12. The equivalent expression will be calculated as:-
8 / 12 = 2 / 3
16⁄36 = 4 / 9
12⁄16 = 3 / 4
24⁄36 = 2 / 3
2⁄3 = 2 / 3
18⁄24 = 3 / 4
The equivalent expressions will be 8 / 12 = 24 / 36 = 2 / 3.
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Someone help me plss
The value of y when x = 45 using the given table is; y = (6/√2) + 4
How to solve function tables?The equation that represents the table is;
y = a cos x° + b
At x = 0, y = 10. Thus;
10 = acos 0 + b
cos 0 = 1
Thus;
10 = a + b ------(1)
At x = 60, y = 7
Thus;
7 = a cos 60° + b
cos 60 = 0.5
Thus;
7 = 0.5a + b -----(2)
Subtract eq 2 from eq 1 to get;
3 = 0.5a
a = 3/0.5
a = 6
b = 10 - 6
b = 4
Thus, the equation is;
y = 6cos x° + 4
At x = 45. we have;
y = 6cos 45° + 4
y = (6/√2) + 4
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Two year ago, a car wa valued at $24,000. Thi year, the value of the car i $23,160. What wa the percent decreae in the value of the car?
A car was worth $24,000 two years ago. The automobile is worth $23,160 this year. 3.5% of the value of the car has decreased.
How to calculate percent?The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage. An enormous, red percentage symbol with a black outline. If you multiply two percentages that are fractions of 100 or decimals, you can find the percentage of another percentage. Calculating, for instance, 50% of 40% results in (50/100) x (40/100) = 0.50 x 0.40 = 0.20 = 20/100 = 20%. As we can see, it provides us with the exact same response as the first approach: 2/5 as a percentage equals 40%. A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed.24,000 - 23,160 = 840
840/24,000 = 0.035
Simplifying the above equation, we get,
0.035 = 3.5%
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Calculate the values of a that satisfy the
equation
2(4x + 8 - x²) = 9x + 7
Give each of your answers to 3 s.f.
The values of x in the equation is x = -2.39 and x = 1.89
How to determine the value of x in the equationFrom the question, we have the following parameters that can be used in our computation:
2(4x + 8 - x²) = 9x + 7
Open brackets
This gives
8x + 16 - 2x² = 9x + 7
Evaluate the like terms
2x² + x - 9 = 0
Using a graphing calculator, we have the following values
x = -2.386 and x = 1.886
Approximate
x = -2.39 and x = 1.89
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60 is 5 times as great as 12 write the equation
5x = 60
Step-by-step explanation:Let x be the value of 12. Then, 5 times as great as 12 is 5x.
So, the equation can be written as:
5x = 60
If you wish to undo this:To isolate x, we can divide both sides of the equation by 5:
x = 60/5
⬇️
x = 12
How to Find a 5 Number Summary:____
Put the numbers in ascending order from smallest to largest, the minimum is the smallest number in the list, The maximum is the largest number in the list, The median is found in the middle of the list and the lower quartile is the median of the first half of the data.
What is meant by number?A number is a numerical unit of measurement and labelling in mathematics.
The natural numbers 1, 2, 3, 4, and so on are the first examples.
Number words are a linguistic way to express numbers.
More commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.
Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.
The Hindu-Arabic numeral system, which enables the depiction of any number using a combination of ten basic numeric symbols, is the most widely used system of numeration.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
please help me and give all steps to it
Answer:
24501.42 m³
Step-by-step explanation:
You want the volume of a cylinder that is 34 m in diameter and 27 m high.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
where r is the radius, half the diameter, and h is the height.
Use the given values in the formula and do the arithmetic. The volume is about ...
24501.42 m³
__
Additional comment
The answer shown has 7 significant figures. The value used for π has 3 significant figures, so any figures in the answer after the first 3 are incorrect. When a more accurate value of π is used, the answer rounds to 24513.85 m³.
select the expression that is equivilant to (3d^4)^2
The expression that is equivilant to (3d^4)^2 is 9d^8
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
(3d^4)^2
Remove the bracket
So, we have the following representation
3^2 * d^(4*2)
Evaluate the exponents
9 * d^8
So, we have
9d^8
Hence, the expression is 9d^8
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a boat travling at an average speed of 30 miles per hour. how far will the boat travle in 2 seconds
Answer:
The boat traveling at 30 miles per hour will travel 30 * (2/3600) = 0.05 miles in 2 seconds.
Step-by-step explanation:
Here's a step-by-step explanation to find the distance traveled by the boat in 2 seconds:
Start with the speed of the boat, which is given as 30 miles per hour.
To find the distance traveled in 2 seconds, we need to convert the speed from miles per hour to miles per second.
To convert from miles per hour to miles per second, divide the speed by 3600 (since there are 3600 seconds in an hour).
30 / 3600 = 0.008333333 (miles per second)
Multiply the speed in miles per second by the time in seconds to find the distance traveled.
0.008333333 * 2 = 0.016666666 miles
So the boat will travel 0.016666666 miles in 2 seconds, or approximately 0.05 miles.
Angle bisectors split the sides of a triangle into a1, a2, b1, b2, c1, and c2. a1 = 11/3 a2= 22/3 b1 = 143/12. Find the perimeter
The perimeter of the triangle which has a bisector that splits a triangle into 6 sides would be = 47½
What is a bisector?A bisector is defined as the line that divides a shape into two equal parts.
The perimeter of triangle is the sum total of all the sides of the triangle. That is;
perimeter = a1 + a2 + b1 + b2 + c1 + c2
But the value of only 3 sides which is exactly half of the perimeter where given;
= 11/3+22/3+153/12
= 44+ 88+ 153/12
= 285/12
Therefore perimeter
= 285/12 + 285/12
= 570/12
= 47½
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B-1. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places. )
The value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
The value of the test statistic in this case is the percentage of drivers under the age of 18 who still use a cell phone while driving. The test statistic is calculated using the following formula:
Test Statistic = (Number of Drivers under 18 using Cell Phone)/ (Total Number of Drivers under 18) x 100
For this case, the test statistic is calculated as follows:
Test Statistic = (150/200) x 100 = 75.00
Therefore, the value of the test statistic in this case is 75.00. This suggests that 75% of drivers under the age of 18 still use a cell phone while driving.
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Andre ran 5 1/2 laps of a track in 8 minutes at a constant speed. It took Andre x minutes to run each lap. Select all the equations that represent this equation
Here, we don't know the exact values for the speed or the lap length, so we need to use symbols in the equation i.e., x= 8 / (5.5 / lap length × speed ).
There are a couple of ways to approach this problem, but one common method is to use the formula: distance = speed x time.
To find the time it took Andre to run each lap, we need to find the distance he covered in 8 minutes and then divide that by the number of laps. Here are the equations:
1. Distance = 5.5 laps x lap length
2. Distance = speed x 8 minutes
3. x = (5.5 x lap length) / (speed x 8)
4. x = 8 / (5.5 / lap length x speed)
Note that we don't know the exact values for the speed or the lap length, so we need to use symbols in the equations.
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Solve the equation for x.
−0.24x − 16.4 = 1.96
x = −60.2
x = 60.2
x = −76.5
x = 76.5
Answer:
254
Step-by-step explanation:
i think it is correct
Answer:
-76.5
Step-by-step explanation:
see image attached for sol
If co A = 1/2 then what i the poitive value of co 1/2 B,in implet radical form with a rational denominator?
The answer is cos(B/2) = 2√5 / 5
Half angle formula of cosine: cos B/2 = ±√[(1 + cos B) / 2]
Given: The positive value of cos 1/2 B in the simplest radical form with a rational denominator, if cos B = 3/5:
Regarding applying the cosine half-angle formula:
cos²(B/2) = (1 + cos B) / 2
put value of cos B =3/5 (given)
cos²(B/2) = (1 + 3/5) / 2
on simplifying
cos²(B/2) = (8/5) / 2
cos²(B/2) = 4/5
on taking under root we get
cos(B/2) = 2/√5
use a rational denominator and the simplest radical form hence, cos(B/2) = 2√5 / 5
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let a = r − {1} and define f : a → a by f (x) = x x − 1 for all x ∈ a. (a) prove that f is bijective. (b) determine f −1. (c) determine f ◦ f ◦ f
(b) The value of f^(-1) is g.
(c) The value of f ◦ f ◦ f = f ◦ (f ◦ f) is f((f ◦ f)(x)) = f((x * (x-1))*((x * (x-1)) - 1)).
According to the question
(a) To prove that f is bijective, we need to show that it is both injective (one-to-one) and surjective (onto).
Injectivity: Let x, y ∈ a such that f(x) = f(y). Then, x * (x-1) = y * (y-1). Multiplying both sides by x-1, we get x = y, meaning that f is injective.
Surjectivity: Let z ∈ a. Then, z = z * (z-1) / (z-1), which means that there exists an x ∈ a such that f(x) = z. This shows that f is surjective.
Therefore, f is bijective.
(b) To find the inverse of f, we need to find a function g: a → a such that f(g(x)) = x and g(f(x)) = x for all x ∈ a.
Consider the function g: a → a defined by g(x) = x / (x-1) for all x ∈ a.
Let x ∈ a. Then, f(g(x)) = f(x / (x-1)) = (x / (x-1)) * ((x / (x-1)) - 1) = x. Similarly, g(f(x)) = g(x * (x-1)) = x * (x-1) / (x * (x-1) - 1) = x. This shows that f and g are inverses.
Therefore, f^(-1) = g.
(c) To find f ◦ f ◦ f, we first evaluate f ◦ f and then evaluate f of the result.
Let x ∈ a. Then, (f ◦ f)(x) = f(f(x)) = f(x * (x-1)) = (x * (x-1)) * ((x * (x-1)) - 1). Hence, f ◦ f ◦ f = f ◦ (f ◦ f) = f((f ◦ f)(x)) = f((x * (x-1)) * ((x * (x-1)) - 1)).
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27.3=3/4y
y=?
Can you please help me?
Answer: 36.4
Step-by-step explanation:
27.3= (3/4)y
divide both sides by 3/4 to isolate the y
27.3/(3/4)= 36.4
To double-check, plug in 36.4 to y; should get you 27.3