The value of Y is not independent of the value of X, and so X and Y are not independent.
Let X be a random variable with EXP <∞ and let Y = [X]. Since X has a Lebesgue density symmetric about 0, we know that E[X] = 0. Therefore, E[XY] = E[X[X]] = E[X²] = Var[X] + E[X]² = Var[X].
Since X and Y are uncorrelated, we have E[XY] - E[X]E[Y] = 0, which implies that E[XY] = E[X]E[Y] = 0*E[Y] = 0. Therefore, X and Y are uncorrelated.
However, X and Y are not independent because the value of Y depends on the value of X. For example, if X = 1.5, then Y = 1, but if X = -1.5, then Y = -2. Therefore, the value of Y is not independent of the value of X, and so X and Y are not independent.
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Perform long division, please clearly show work of remainders
and arrows, where numbers pass down.
Thanks
1. 32.156 / 100
2. 174.787 / 0.01
There are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
To perform long division, we need to follow these steps:
Set up the long division problem with the dividend on the inside and the divisor on the outside of the division symbol.
Determine how many times the divisor can go into the first digit or group of digits of the dividend.
Write the result above the division symbol and multiply it by the divisor.
Subtract the result from the first digit or group of digits of the dividend.
Bring down the next digit or group of digits from the dividend and repeat the process until there are no more digits to bring down.
The final result is the quotient with any remainders.
For the first problem, 32.156 / 100, we can set it up like this:
```
100 | 32.156
```
Since 100 cannot go into 32, we need to bring down the next group of digits, which is 156. Now we have:
```
100 | 3215.6
```
100 can go into 3215 a total of 32 times, so we write 32 above the division symbol and multiply it by 100:
```
32
100 | 3215.6
-3200
-----
15.6
```
Now we bring down the next group of digits, which is 6:
```
32.1
100 | 3215.6
-3200
-----
156
```
100 can go into 156 a total of 1 time, so we write 1 above the division symbol and multiply it by 100:
```
32.16
100 | 3215.6
-3200
-----
156
-100
-----
56
```
Since there are no more digits to bring down, we are left with a remainder of 56. So the final result is 32.156 with a remainder of 56.
For the second problem, 174.787 / 0.01, we can set it up like this:
```
0.01 | 174.787
```
Since 0.01 cannot go into 174, we need to bring down the next group of digits, which is 787. Now we have:
```
0.01 | 17478.7
```
0.01 can go into 17478 a total of 1747800 times, so we write 1747800 above the division symbol and multiply it by 0.01:
```
1747800
0.01 | 17478.7
-17478
-----
0.7
```
Since there are no more digits to bring down, we are left with a remainder of 0.7. So the final result is 1747800 with a remainder of 0.7.
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Does someone mind helping me with this problem? Thank you!
The amount we would have after 40 years will be $8183.27
What is an exponential growth?Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given that, an amount increasing exponentially every two years and with a rate of 15% and the amount is $500, we need to find the amount we would have after 40 years.
Since, the amount is increasing exponentially every two years, therefore,
T = 40 / 2 = 20 years
A = P(1+0.15)²⁰
A = 500(1+0.15)²⁰
A = 500(1.15)²⁰
A = 8183.27
Hence, the amount we would have after 40 years will be $8183.27
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O is the center of the regular decagon below. Find its perimeter. Round to the nearest tenth if necessary. 6 O
By answering the above question, we may infer that So the perimeter of the regular decagon is approximately 38.2 units (rounded to the nearest tenth).
what is decagon?In geometry, a decagon is either a decagon or not. There are 144° of inner angles total in a simple decagon. A regular decagon that self-intersects is known as a decagram. A polygon with 10 sides, ten internal angles, and ten vertices is called a decagon. Geometry may contain the form known as a decagon. It also has ten horns and ten horns. A dodecagon is a polygon with twelve sides. Some unusual types of dodecagons are shown in the photographs above. Particularly, a regular dodecagon has angles that are equally placed around a circle and sides that are of the same length.
Each interior angle of a regular decagon measures:
[tex]$$(n-2)\times180^\circ/n = (10-2)\times180^\circ/10 = 144^\circ$$\\$$\cos(72^\circ) = \frac{x}{2y}$$[/tex]
Solving for x, we get:
[tex]$$x = 2y\cos(72^\circ)$$[/tex]
We can use the fact that[tex]$\cos(72^\circ) = \frac{1+\sqrt{5}}{4}$[/tex](which can be derived using the golden ratio) to get:
[tex]$$x = 2y\cos(72^\circ) = 2y\cdot\frac{1+\sqrt{5}}{4} = \frac{y}{2}(1+\sqrt{5})$$\\$$R = \frac{x}{2\sin(180^\circ/10)} = \frac{x}{2\sin(36^\circ)}$$\\[/tex]
We can use this formula to find[tex]$y$:[/tex]
[tex]$$y = R = \frac{x}{2\sin(36^\circ)} = \frac{x}{2\sin(\frac{1}{2}\times72^\circ)} = \frac{x}{2\cos(72^\circ/2)}$$[/tex]
We can use the half-angle identity [tex]$\cos(\theta/2) = \sqrt{\frac{1+\cos(\theta)}{2}}$ to simplify this expression:[/tex]
[tex]$$y = \frac{x}{2\cos(72^\circ/2)} = \frac{x}{2\sqrt{\frac{1+\cos(72^\circ)}{2}}} = \frac{x}{2\sqrt{\frac{1+\frac{1+\sqrt{5}}{4}}{2}}} = \frac{x}{2\sqrt{\frac{3+\sqrt{5}}{4}}} = \frac{x}{\sqrt{3+\sqrt{5}}}$$[/tex]
Putting it all together, we have:
[tex]$$\text{Perimeter} = 10x = 10\cdot\frac{y}{2}(1+\sqrt{5}) = 5\sqrt{10+2\sqrt{5}}\approx 38.2$$[/tex]
So the perimeter of the regular decagon is approximately 38.2 units (rounded to the nearest tenth).
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\[ \begin{array}{l} n=4 \\ -1,4, \text { and } 3+2 i \text { are zeros; } \\ f(1)=-144 \end{array} \] \[ f(x)= \] (Type an expression using \( x \) as the variable. Simplify your answer.)
Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \]
To find the expression for \( f(x) \), we need to use the fact that the zeros of a polynomial are the values of \( x \) that make the polynomial equal to zero. This means that if \( -1, 4, \) and \( 3+2i \) are zeros of \( f(x) \), then the factors of \( f(x) \) are \[ (x+1)(x-4)(x-(3+2i))(x-(3-2i)) \] Now, we can simplify the last two factors by multiplying them together: \[ (x-3-2i)(x-3+2i) = (x-3)^2 - (2i)^2 = x^2 - 6x + 9 - 4i^2 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13 \] So, the expression for \( f(x) \) is \[ f(x) = (x+1)(x-4)(x^2 - 6x + 13) \] Now, we can use the fact that \( f(1) = -144 \) to find the value of the leading coefficient of \( f(x) \). Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \] This is the final answer.
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A standard deck of cards contains 52 cards. One card is selected from the deck.
(a) Compute the probability of randomly selecting a diamond or heart
(b) Compute the probability of randomly selecting a diamond or heart or spade
(c) Compute the probability of randomly selecting a seven or a heart
The probabilities are:
(a) P(diamond or heart) = 0.5
(b) P(diamond or heart or spade) = 0.75
(c) P(seven or heart) ≈ 0.308.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
(a) To compute the probability of randomly selecting a diamond or heart from a standard deck of 52 cards, we need to count the number of diamond cards and heart cards in the deck. There are 13 diamond cards and 13 heart cards, so the total number of cards that are either diamonds or hearts is 13 + 13 = 26. Therefore, the probability of randomly selecting a diamond or heart is:
P(diamond or heart) = number of diamond cards + number of heart cards / total number of cards
P(diamond or heart) = 26/52
P(diamond or heart) = 1/2
P(diamond or heart) = 0.5
(b) To compute the probability of randomly selecting a diamond or heart or spade from a standard deck of 52 cards, we need to count the number of cards that belong to any of these three suits. There are 13 diamond cards, 13 heart cards, and 13 spade cards in the deck, so the total number of cards that are either diamonds, hearts, or spades is 13 + 13 + 13 = 39. Therefore, the probability of randomly selecting a diamond or heart or spade is:
P(diamond or heart or spade) = number of diamond cards + number of heart cards + number of spade cards / total number of cards
P(diamond or heart or spade) = 39/52
P(diamond or heart or spade) = 3/4
P(diamond or heart or spade) = 0.75
(c) To compute the probability of randomly selecting a seven or a heart from a standard deck of 52 cards, we need to count the number of seven cards and the number of heart cards in the deck. There are 4 seven cards and 13 heart cards, but we need to be careful not to double-count the seven of hearts. Therefore, the total number of cards that are either sevens or hearts is 4 + 12 = 16. Therefore, the probability of randomly selecting a seven or a heart is:
P(seven or heart) = number of seven cards + number of heart cards - number of seven of hearts / total number of cards
P(seven or heart) = 16/52
P(seven or heart) = 4/13
P(seven or heart) ≈ 0.308
Hence, The probabilities are:
(a) P(diamond or heart) = 0.5
(b) P(diamond or heart or spade) = 0.75
(c) P(seven or heart) ≈ 0.308.
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HELP ME PLS ANYBODY
ITS DUE TODAY AND I NEED HELP ASAP
Answer:
1. around 4.86 or 4.9 for the nearest tenth
2. 17 months
Step-by-step explanation:
1. (1.7×10^6)/(3.5×10^5) = (1.7/3.5)×(10^6/10^5) = 0.4857×10 = 4.857
Therefore, 1.7×10^6 is about 4.857 times as great as 3.5×10^5.
2. start by finding out how much Erica still owes after the down payment:
Total cost - Down payment = $1,867 - $320 = $1,547
divide the amount still owed by the monthly payment to find out how many months Erica will be paying:
$1,547 ÷ $91 per month = 17 months (rounded up)
Therefore, Erica will be paying for the bike for 17 months
A consumer price analyst claims that prices for liquid crystal display (LCD) computer monitors have a mean of $ 170 and a standard deviation of $ 53.
1. What is the probability that a randomly selected LCD computer monitor costs less than $ 180? Assume here that the prices are normally distributed.
2. You randomly selected 9 LCD compute monitors. What is the probability that their mean cost is less than $ 180? Assume here that the prices are normally distributed
3. You randomly selected 36 LCD compute monitors. What is the probability that their mean cost is less than $ 180?
1. The probability of getting a z-score of 0.189 or less is 0.5753.
2. The probability of getting a z-score of 1.13 or less is 0.8708.
3. The probability of getting a z-score of 3.02 or less is 0.9982.
What is Normally distributed data:Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.
In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.
Here we have
The mean price for liquid crystal display (LCD) computer monitors is $ 170 and the standard deviation is $ 53.
Find the z-score associated with $ 180 using the formula:
z = (x - μ) / σ
where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.
z = (180 - 170) / 53
z = 0.189
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.
To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.
The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.
Now we need to find the z-score associated with $ 180 using the formula:
z = (x - μ) / σ/√n
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
z = (180 - 170) / (53 / √9)
z = 1.13
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.
To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:
z = (x - μ) / σ/√n
z = (180 - 170) / (53 / √36)
z = 3.02
Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.
Therefore,
1. The probability of getting a z-score of 0.189 or less is 0.5753.
2. The probability of getting a z-score of 1.13 or less is 0.8708.
3. The probability of getting a z-score of 3.02 or less is 0.9982.
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elect all expressions that represent a correct solution to the equation 6(x + 4) = 20.
A. (20-4) +6
D.
B. (20-4)
C. 20-6-4
206-4
E.
(20-24)
F. (20-24) +6
The correct solution to the equation is (20 - 24)/6
How to determine the correct solutionFrom the question, we have the following parameters that can be used in our computation:
6(x + 4) = 20.
There are many different expressions that can represent a correct solution to an equation
These expression depends on the specific equation and context.
Open the bracketss
So, we have
6x + 24 = 20
Collect the like terms
6x = 20 - 24
Divide both sides by 6
So, we have the following representation
x = (20 - 24)/6
Hence, the correct expression in the equation solution is (20 - 24)/6
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Suppose that you have the following looping root motion character animations:
IDLE – an idle pose (5s duration)
WALK_1 – a straight walking loop of relaxed pace, starting with left foot forward, a right step, and then ending with left foot forward (1s duration)
WALK_2 – the same as WALK_1 but sped up to a fast walking pace (0.75s duration)
SPRINT_1 – a straight sprinting loop, starting with the left foot forward, a right step, and then ending with the left foot forward (0.5s duration)
SPRINT_2 – a slight right turn sprinting loop, starting with the right foot forward, a left step, and then ending with right foot forward (0.5s duration)
Now consider an animation created by blending 50 percent of each animation of the pairs that follow. The animation timelines are normalized and aligned during blending (similar to Unity blendtrees). What is the result?
The result of blending 50 percent of each animation of the pairs that follow will be a new animation that combines the features of both animations. This is known as "root motion blending" and is used to create smooth transitions between different animations.
The new animation will have a duration that is the average of the two animations being blended (for example, blending IDLE and WALK_1 will result in a 3s duration animation) and will include features from both animations. For example, blending WALK_1 and WALK_2 will result in a walking animation that is at a pace between relaxed and fast. Similarly, blending SPRINT_1 and SPRINT_2 will result in a sprinting animation that includes both a straight sprint and a slight right turn. The root motion of the new animation will be the average of the root motions of the two animations being blended.
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in 2002, there was about 150 wolves yellowstone national park. From 2002 to 2003, the wolf population increased by 16%. then from 2003 to 2005 it decreased by 32%.
The response to the given question would be that Therefore, after equation growing to 174 in 2003, the wolf population in Yellowstone National Park dropped from 150 in 2002 to 118.32 in 2005.
What is equation?When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.
beginning with a wolf population of 150 in 2002:
The number of wolves grew by 16% in 2003. We may multiply the initial population by 1.16 (100% + 16% = 116%) to determine the increase:
150 times 1.16 is 174 wolves.
There was a 32% decline in the wolf population between 2003 and 2005. We may multiply the population in 2003 by 0.68 (100% - 32% = 68%) to determine the decline:
174 times 0.68 equals 118.32 wolves (rounded to two decimal places)
Therefore, after growing to 174 in 2003, the wolf population in Yellowstone National Park dropped from 150 in 2002 to 118.32 in 2005.
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the coordinates of the vertices of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) . The coordinates of the vertices of △R′S′T′ are R′(3, −3) , S′(3, −1) , and T′(−1, −4) . What is the sequence of transformations that maps △RST to △R′S′T′?
The sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.
What is the sequence of transformation?
In mathematics, a sequence of transformations refers to a series of geometric transformations performed on a shape to create a new shape. These transformations can include translations, rotations, reflections, and dilations.
The sequence of transformations is the order in which the transformations are performed. The order matters because different sequences of transformations can lead to different final shapes.
For example, to transform a triangle into a new position, we might first perform a translation to move the triangle to a new location, then perform a rotation to change its orientation, and finally perform a reflection to flip the triangle across a line. The sequence of transformations in this case is translation-rotation-reflection.
Sequences of transformations are used in geometry to analyze and describe shapes and to solve problems related to symmetry, congruence, and similarity. They are also used in computer graphics and animation to create 2D and 3D shapes that can be moved and transformed on a screen.
To map △RST to △R′S′T′, we need to perform a sequence of transformations that includes translations, rotations, reflections, and/or dilations. Here's one possible sequence of transformations:
Translation: We can translate △RST by 6 units to the right and 2 units down to get a new triangle that has R at (3, -3), S at (5, -3), and T at (2, -7).
Reflection: We can reflect the translated triangle across the y-axis to get a new triangle that has R′ at (-3, -3), S′ at (-5, -3), and T′ at (-2, -7).
Rotation: We can rotate the reflected triangle 90 degrees counterclockwise about the origin to get a new triangle that has R′ at (3, -3), S′ at (3, -1), and T′ at (-1, -4).
Therefore, the sequence of transformations that maps △RST to △R′S′T′ is a translation of 6 units to the right and 2 units down, followed by a reflection across the y-axis, and finally a rotation of 90 degrees counterclockwise about the origin.
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Use the properties of kites to answer the questions.
a. If AB = 8x-2, and AD = 6x+4, solve for AD.
b. If mPlease show your work.
The values of the length and angle are;
AD = 22 units
m < ADC = 106 degrees
How to determine the valuesThe properties of a kite are given as;
It has one pair of opposite angles that are equalThe shorter diagonal forms two equal isosceles trianglesThe longer diagonal forms two equal or congruent trianglesThe diagonals are perpendicular to each otherIt has two adjacent and equal sidesFrom the information given, we have that;
AB = 8x - 2
AD = 6x + 4
Equate the sides
8x - 2 = 6x + 4
collect like terms
2x = 6
x = 3
AD = 22 units
Also,
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
collect like terms
-3x = -24x
x = 8
m < ADC = 106 degrees
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Answer: AD = 22 units
Step-by-step explanation:
m < ADC = 106 degrees
AB = 8x - 2
AD = 6x + 4
Equate any sides
8x - 2 = 6x + 4
Collect terms
2x = 6
x = 3
AD = 22 units
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
Collect terms
-3x = -24x
x = 8
m < ADC = 106 degrees
find the range of the function f(x)
Answer:
62
Step-by-step explanation:
x2 a 4 - 91
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A bus covers a certain distance in 3hours 20 minutes ata n average speed of 45km/h.How long will it take to cover the some distance at a speed of 36km/h?
Answer:
Let's first convert the time taken to cover the distance at 45 km/h into minutes:
3 hours and 20 minutes = 3 x 60 + 20 = 200 minutes
The distance covered by the bus at 45 km/h is:
distance = speed x time
distance = 45 km/h x 200 minutes
distance = 9000/60 km
distance = 150 km
Now, let's use the distance and the new speed of 36 km/h to calculate the time it would take to cover the same distance:
distance = speed x time
150 km = 36 km/h x time
time = distance / speed
time = 150 km / 36 km/h
time = 4.1667 hours or 4 hours and 10 minutes (rounded to the nearest minute)
Therefore, it would take approximately 4 hours and 10 minutes to cover the same distance at a speed of 36 km/h.
d. The height of the ball is represe x is time in seconds. Rewrite the -1(-6x^(2)+4x+2)
The height of the ball is represented by the equation -1(-6x^(2)+4x+2), where x is time in seconds.
We can rewrite this equation by distributing the -1 and simplifying.
First, we distribute the -1 to each term inside the parentheses:
-1(-6x^(2)+4x+2) = 6x^(2) - 4x - 2
Now, we can simplify by combining like terms:
6x^(2) - 4x - 2 = 6x^(2) - 4x - 2
Therefore, the rewritten equation for the height of the ball is:
h = 6x^(2) - 4x - 2
This equation shows the relationship between the height of the ball (h) and the time in seconds (x). As time increases, the height of the ball changes according to the equation.
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9.9=3.1 - 3.4x solve for x
Answer:
x = -2.
Step-by-step explanation:
9.9 = 3.1 - 3.4x
9.9 - 3.1 = -3.4x
6.8 = -3.4
6.8 /-3.4 = -3.4/-3.4
-2 = x
dennis invested £1000 for 4 years into a savings account. he recieved 5% per annum compound interest. calculate the total interest he earned over 4 years
help me please a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
the solution is: population in 2015 will be 40,115,896
What is exponential?The exponential function is an illustration of a mathematical function that may be used to identify if something is increasing or decreasing exponentially. An exponential function employs exponents, as suggested by its name.
But, you should be aware that an exponential function does not have a constant base and a variable exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
the median population change in California from 2000 to 2009 in percentage terms.
Given that there are 9 years, add up all the percentages, and then divide by 9.
1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93/9 = 1.3567%
From 2009 through 2015, there were six different time periods.
In the future, 37,000,000 x (1 + 0.013567) x 6 = 40,115,896.06
Hence, the solution is: population in 2015 will be 40,115,896
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To be on the safe side, three detectors were installed in a factory room to make sure that if there was a fire, at least one of them would signal a warning. The company that manufactured the smoke detectors indicated that, based on their testing, the probability that any one of the smoke detectors will work correctly is 0.75 (meaning that it works 75% of the time in the long run). This also means that there is a 25% chance that if there is smoke or a fire, the detector will not work! What is the probability that if there was smoke in the factory, none of the 3 detectors would work? Does this probability indicate a safety problem for the factory? Explain.
PLEASE HELP MEEEE!!
The probability that none of the 3 detectors would work if there was smoke in the factory is 0.25³, or 0.015625 (1.56%).
What is Probability?Probability is a branch of mathematics that deals with the likelihood of certain outcomes or events occurring. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event that is certain to occur has a probability of 1, while an event that is impossible to occur has a probability of 0. The probability of an event occurring can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
This probability indicates that the factory does have a safety problem, as there is a 1.56% chance that none of the smoke detectors would sound an alarm if there was smoke present. This presents a significant risk to the factory, as it could lead to an undetected fire that may cause damage to the facility or put employees in danger.
The company should look into ways to reduce the risk of the smoke detectors not working. One way to do this would be to increase the number of smoke detectors in the factory room, as the more detectors there are, the lower the probability that none of them will work. The company could also consider using more reliable smoke detectors that have a higher probability of working correctly when needed. Ultimately, the company should seek to reduce the risk of none of the detectors working by taking steps to increase the probability that at least one of them will sound an alarm in the event of smoke or a fire.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e}. If A = {1,
2, a, e} and B = {1, 2, 3, 4, a, b, c}, find the following.
(c) n(A ∪ Bc)
(d) n(Ac ∩ Bc)
The answers are n(A ∪ Bc) = 10 and n(Ac ∩ Bc) = 6.
To solve this question we need knowledge of set theory, union and intersection.
(c) To find n(A ∪ Bc), we first need to find the complement of B, which is Bc = {5, 6, 7, 8, 9, d, e}. Now, we can find the union of A and Bc, which is A ∪ Bc = {1, 2, a, e, 5, 6, 7, 8, 9, d}. The number of elements in this set is n(A ∪ Bc) = 10.
(d) To find n(Ac ∩ Bc), we first need to find the complement of A, which is Ac = {3, 4, 5, 6, 7, 8, 9, b, c, d}. Now, we can find the intersection of Ac and Bc, which is Ac ∩ Bc = {5, 6, 7, 8, 9, d}. The number of elements in this set is n(Ac ∩ Bc) = 6.
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Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.
Step-by-step explanation:
Refer to pic..........
A full bottle of cordial holds 800 m/ of cordial. A full bottle of cordial is mixed with water to make a drink to take onto a court for a tennis match. When mixed, the drink is put into a container. (c) What is the minimum capacity, in litres, of the container? 1000 m/= 1 litre
Answer:
We are not given the ratio of cordial to water used in the mixture, so we can assume that the entire bottle of cordial is mixed with water to make the drink.
Since the bottle of cordial holds 800 ml of cordial, the total volume of the mixture would be 800 ml + volume of water added. Let's call the volume of water added x.
Therefore, the total volume of the drink would be 800 ml + x.
We are asked to find the minimum capacity of the container in liters, so we need to convert the total volume of the drink from milliliters to liters:
800 ml + x = (800 + x)/1000 liters
Now we can set up an inequality to find the minimum value of x that would make the total volume of the drink at least 1 liter:
800 ml + x ≥ 1000 ml
Simplifying this inequality, we get:
x ≥ 200 ml
Therefore, the minimum volume of water that needs to be added to the cordial to make a drink with a total volume of at least 1 liter is 200 ml.
So the minimum capacity of the container would be:
800 ml + 200 ml = 1000 ml = 1 liter
Therefore, the minimum capacity of the container in liters would be 1 liter.
Step-by-step explanation:
Write an explicit formula for � � a n , the � th n th term of the sequence 7 , 35 , 175
The explicit formula for the nth term of the sequence 7, 35, 175 is:
[tex]a_n = 7 * 5^{n-1}[/tex]
What is the geometric sequence?
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number called the common ratio. The general formula for a geometric sequence is:
a, ar, ar², ar³, ...
where a is the first term and r is the common ratio.
To find the explicit formula for the sequence 7, 35, 175, we need to identify the pattern in the sequence.
Notice that each term is obtained by multiplying the previous term by 5. Specifically, the first term (7) is multiplied by 5 to get the second term (35), and the second term is multiplied by 5 to get the third term (175).
So, the sequence is a geometric sequence with a common ratio of 5.
To find the explicit formula for a_n, we can use the formula:
[tex]a_n = a_1 * r^{n-1}[/tex]
where a1 is the first term, r is the common ratio, and n is the term we want to find.
In this case, a1 = 7 and r = 5.
Substituting these values into the formula, we get:
[tex]a_n = 7 * 5^{n-1}[/tex]
Therefore, the explicit formula for the nth term of the sequence 7, 35, 175 is:
[tex]a_n = 7 * 5^{n-1}[/tex]
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How many can a mother, a father aed Their 3 kids be seated in ao row, suce that P=n
There are 120 different ways to arrange a mother, a father, and their 3 kids in a row.
There are several ways to arrange a mother, a father, and their 3 kids in a row. One way is to use the permutation formula, which is given by:
P = n! / (n - r)!
Where n is the total number of items and r is the number of items to choose from. In this case, n = 5 (mother, father, and 3 kids) and r = 5 (since we are choosing all 5 items).
Plugging in the values into the formula, we get:
P = 5! / (5 - 5)!
P = 5! / 0!
P = 120 / 1
P = 120
Therefore, there are 120 different ways to arrange a mother, a father, and their 3 kids in a row.
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What is (x^(2)+8x+16)/(x^(2)-4x-32) in simplest form? State any restrictions on the variable.
The simplest form of the expression (x^(2)+8x+16)/(x^(2)-4x-32) is (x+4)/(x-8) with restrictions x≠8 and x≠-4.
The expression (x^(2)+8x+16)/(x^(2)-4x-32) can be simplified by factoring the numerator and denominator.
First, we can factor the numerator:
(x^(2)+8x+16) = (x+4)(x+4)
Next, we can factor the denominator:
(x^(2)-4x-32) = (x-8)(x+4)
Now, we can simplify the expression by canceling out the common factor of (x+4):
(x+4)(x+4)/(x-8)(x+4) = (x+4)/(x-8)
Therefore, the simplest form of the expression is (x+4)/(x-8).
However, there are restrictions on the variable x. The denominator of the expression cannot equal zero, so we must find the values of x that make the denominator zero and exclude them from the domain of the expression.
To find the restrictions, we set the denominator equal to zero and solve for x:
(x-8)(x+4) = 0
This gives us two solutions:
x = 8
x = -4
Therefore, the restrictions on the variable are x≠8 and x≠-4.
In conclusion, the simplest form of the expression (x^(2)+8x+16)/(x^(2)-4x-32) is (x+4)/(x-8) with restrictions x≠8 and x≠-4.
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please help asap and explain how u got the answer
Answer:
90 degrees clockwise rotation
Step-by-step explanation:
The way to do this is by looking at your transformation rules, where you will find that in a 90 degree clockwise rotation you take your original X and Y, swap them, and make Y negative (y, -x).
To find this, pick any two points from each rectangle (Each point must have the same letter) and compare them:
Example:
Q is at (4, 2) and Q' is at (2,-4). When comparing the two points you will find that X and Y have been swapped, and Y is now negative. This matches the 90 degree clockwise rotation rule
how to do this problem
a. The scale factor is 2.
b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.
What is the Scale factor:A scale factor is a number that is used to resize, a geometric figure. When a figure is scaled, all of its dimensions are multiplied by the scale factor.
The resulting figure is similar to the original figure, but it may be larger or smaller, depending on the value of the scale factor.
Here we have
ABCD ∼ FGHJ
Since both figures are similar
The ratio of the corresponding sides will be equal
a. Scale factor = AB/FG = 8m/ 4m = 2
b. Calculating JF, HJ, and GH
As we know the ratio of the corresponding sides is equal
=> AB/FG = BC/GH = CD/HJ = AD/JF
From the figure,
=> 8 m /4 m = 26 m/GH = 8 m/HJ = 16/JF
=> 26 m/GH = 8 m/HJ = 16/JF = 2
=> 26 m/GH = 2
=> GH = 13 m
=> 8 m/HJ = 2
=> HJ = 4
=> 16/JF = 2
=> JF = 8 m
Therefore,
a. The scale factor is 2.
b. The lengths of GH, HJ, and JF are 13 m, 4 m, and 8 m respectively.
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Select the correct slope and y-intercept for the following linear equation:
y=2x+7
The correct slope and y-intercept for the linear equation y=2x+7 are 2 and 7, respectively.
What is y-intercept?The y-intercept of a graph is the point where the graph crosses the y-axis. It is written as (0, b), where b is the y-intercept. The y-intercept is the value of y when x is equal to zero. It can be used to determine the equation of a line when two points on the line are known.
The slope of a linear equation is the coefficient of the x variable, which is 2 in this case. The y-intercept is the constant term, which is 7 in this case.
So, the slope is 2 and the y-intercept is 7.
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I need help with this problem please and thank you also with work shown please
The circumcenter of the triangle formed by the vertices is found as (2 , 5).
Explain about the circumcenter?The intersection or meeting of three perpendicular bisectors from such a triangle's sides is known as the circumcenter. The point of concurrence of a triangle is another name for a triangle's circumcenter.
Given points are,
A = (-2, 5),
B = (2, 1),
C = (5, 5)
We must solve either two bisector equations then determine the intersection locations in order to determine the circumcenter.
Mid point of AB = [(-2 + 2)/2, (5 + 1)/2] = (0,3)
Slope of AB = [(1 - 5)/(2 + 2)] = -1
The negative reciprocal of a given slope is the slope of the bisector.
Hence, the perpendicular bisector's slope equals 1.
Formula of AB with coordinates (0, 3) and slope (1),
(y – 3) = 1(x – 0)
x – y = -3 eq…(1)
Similarly, for AC
Mid point of AC = [(-2 + 5)/2, (5 + 5)/2] = (1.5, 5)
Slope of AC = [(5-5)/(5+2)] = 0
The negative reciprocal of a given slope is the slope of the bisector.
Hence, the perpendicular bisector's slope equals 0
Equation of AC at coordinates (1.5,5) and slope (0),
(y – 5) = 0(x – 1.5)
y = 5 ....eq 2
Solve eq (1) and (2),
x – y = -3
x - 5 = -3
x = 2
Thus, the circumcenter of the triangle formed by the vertices is found as (2 , 5).
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Please help meeeeeeeeee
The answer of the given question based on the Equation is given the solution to the given equation is n = 21/4.
What is Quadratic equation?A quadratic equation is type of equation in an algebra that involves variable (usually represented by x) that raised to the second power (i.e., squared). The general form of the quadratic equation are given,
[tex]ax^2+bx+c = 0[/tex]
The highest power of variable is 2, hence , name "quadratic".
To solve this equation, we can start by simplifying each of the terms on both sides of the equation:
3n + √(n² + 8) + 3√(n² + 8) - √(n² + 8) = 8
Combining like terms, we get:
3n + 3√(n² + 8) = 8
Subtracting 3√(n² + 8) from both sides, we get:
3n = 8 - 3√(n² + 8)
Dividing both sides by 3, we get:
n = (8/3) - (√(n² + 8)/3)
Now, we can rearrange this equation to isolate the radical term on one side of the equation:
√(n² + 8)/3 = (8/3) - n
by Squaring both the sides of equation, we get:
n² + 8 = 64/9 - (16n/3) + n²
Simplifying this equation, we get:
16n/3 = 56/9
Dividing both sides by 16/3, we get:
n = 21/4
Therefore, the solution to the given equation is n = 21/4.
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