To reverse the order of integration, we need to rewrite the limits of integration in terms of the other variable.
The value of the given integral by reversing the order of integration is (5/12)([tex]e^{24}[/tex] - 1).
The given integral is ∫∫ [tex]5e^{(2x)}[/tex] dx dy, where the limits of x are from 0 to 4 and the limits of y are from 0 to 3y.
To integrate with respect to y first, we need to express the limits of y in terms of x.
From the limits of y given, we have 0 ≤ y ≤ 3y, which simplifies to 0 ≤ y.
Now we need to find the upper limit of y. To do this, we set the expression for the upper limit equal to the constant 12, which is the upper limit of x.
So we have 3y = 12, which gives y = 4.
Thus, the limits of integration become ∫∫ [tex]5e^{(2x)}[/tex] dy dx, where the limits of y are from 0 to 4 and the limits of x are from 0 to 3y.
Now we can integrate with respect to y:
∫∫ [tex]5e^{(2x)}[/tex] dy dx = ∫ 0^4 ∫ 0^(3y) [tex]\int\limits^4_0 \int\limits^{(3y)}_0 5e^{(2x)} dx dy[/tex]
= [tex]\int\limits^4_0 [5/2 e^{(2x)}]_0^{(3y)} dy[/tex]
= [tex]\int\limits^4_0 [5/2 (e^{(6y)} - 1)] dy[/tex]
= [tex][5/12 (e^{(6y)} - 1)]_0^4[/tex]
= [tex](5/12)(e^{24} - 1)[/tex]
Note that the order of integration can be reversed if the integrand is continuous on a rectangular region that contains the original region of integration.
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a water tank can be filled by two pipes working together in 2 hours. one of the pipes can fill the tank in 3 hours less than the other pipe. how long does each pipe take to fill the tank on its own?
Let's denote the time it takes for the slower pipe to fill the tank on its own as $x$ hours. Then, the faster pipe takes $x-3$ hours to fill the tank on its own. We can use the formula for the rate of work to set up an equation: $r_1 + r_2 = \frac{1}{2}$, where $r_1$ and $r_2$ are the rates of work for each pipe.
We can express the rate of work in terms of the time it takes for each pipe to fill the tank on its own: $r_1 = \frac{1}{x}$ and $r_2 = \frac{1}{x-3}$. Substituting these expressions into the equation above and solving for $x$, we obtain $x=2$. Therefore, the slower pipe takes 2 hours to fill the tank on its own, and the faster pipe takes $2-3=-1$ hour, which doesn't make physical sense. This means there is an error in the problem statement.
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Indicate below whether the equation in the box is true or false?
Answer: False
Step-by-step explanation: :)
what is the value of the correlation coefficient between daily ice cream sales and maximum daily temperature
The correlation coefficient between daily ice cream sales and maximum daily temperature is a measure of the strength and direction of the linear relationship between these two variables.
To calculate the correlation coefficient, we need a sample of paired data that includes daily ice cream sales and the corresponding maximum daily temperature.
We can use a statistical software or a calculator to calculate the correlation coefficient. In this case, the correlation coefficient between maximum daily temperature and daily ice cream sales is 0.934, which indicates a strong positive linear relationship between these two variables.
This means that as the maximum daily temperature increases, the daily ice cream sales also tend to increase. Conversely, as the maximum daily temperature decreases, the daily ice cream sales tend to decrease as well.
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Sum of angles in a
triangle
Task
Suppose ABC is a triangle in the plane as pictured below:
Suppose M is the midpoint of AC and N is the midpoint
of BC.
a. Draw the rotation of AABC by 180 degrees about M,
labeling the image of B as B'.
b. Draw the rotation of AABC by 180 degrees about N,
labeling the image of A as A'.
c. Explain why B', C, and A' are collinear.
d. Deduce that m(ZA) + m(ZB) + m(ZC) = 180.
I
Answer:
B
Step-by-step explanation:
it should be B
This list shows the ingredients needed to make 8 pancakes
240g plain flower
2 eggs
600ml milk
Dan wants to make 12 pancakes. How much of each ingredient will he need?
Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.
To make 12 pancakes, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk.
We can use proportions to figure out how much of each ingredient Dan will need. If 240g of plain flour, 2 eggs, and 600ml of milk are enough to make 8 pancakes, then we can set up the following ratios:
Plain flour: 240g/8 pancakes = x/12 pancakes
Eggs: 2/8 pancakes = y/12 pancakes
Milk: 600ml/8 pancakes = z/12 pancakes
Solving for x, y, and z in each of these ratios, we get x = 360g of plain flour, y = 3 eggs, and z = 900ml of milk. Therefore, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.
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Find the specified areas for a Upper N left-parenthesis 0 comma 1 right-parenthesis density. (a) The area below z equals 1.04 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001 (b) The area above z equals -1.4 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001 (c) The area between z equals 1.1 and z equals 2.1 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001
The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.
To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:
1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).
The area below z=1.04 is approximately 0.851, rounded to three decimal places.
(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:
1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.
The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.
(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:
1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.
The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.
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22. Kalani met her friend at a park for a
18
8
morning run. The function er
f(x) = -x-10| + 5 models their un
distance from Kalani's apartment, in
miles, x minutes after they started
running. Graph the function in the
context of the situation.
vlags
The graph of the function f(x) = |-x - 10| + 5 in the context of the situation is added as an attachment
Graphing the function in the context of the situation.From the question, we have the following parameters that can be used in our computation:
The function f(x) = |-x - 10| + 5
Where
f(x) = distance from Kalani's apartmentx = minutes after they started runningUsing the above as a guide, we have the following:
We plot the minutes on the x-axis and the distance on the y-axis
The graph of the function is added as an attachment
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Complete question
Kalani met her friend at a park for a morning run. The function f(x) = |-x - 10| + 5 models their run distance from Kalani's apartment, in miles, x minutes after they started running. Graph the function in the context of the situation.
evaluate c f · dr. f(x, y) = xi yj c: r(t) = (5t 2)i tj, 0 ≤ t ≤ 1
Thus, the value of c f · dr. f(x, y) = xi yj c: r(t) = (5t 2)i tj, 0 ≤ t ≤ 1 is found as 2c using the vector function.
To evaluate c f · dr, we first need to find the vector function of f evaluated along the path r.
Using the given function f(x, y) = xi yj and the path r(t) = (5t^2)i + tj, we can substitute for x and y to get:
f(r(t)) = (5t^2)i * (t)j = 5t^3i + 5tj
Next, we need to find the differential of the path dr, which is:
dr = (10t)i + j dt
Now we can evaluate the dot product of c f and dr:
c f · dr = ∫c f · dr = ∫(c)(5t^3i + 5tj) · (10t)i + j dt, where c is a constant
= ∫(50c t^4) dt + ∫(5c t) dt
= 10c/5 t^5 + 5c/2 t^2 + C
Evaluating this from 0 to 1, we get:
c f · dr = 10c/5(1)^5 + 5c/2(1)^2 - 10c/5(0)^5 - 5c/2(0)^2
= 2c + 0
= 2c
Therefore, the value of c f · dr is 2c.
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given that p(a ∩ d)=2/5, find p(~ (a ∩ d)).
The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.
The symbol "∩" represents the intersection of two events.
For example, "a ∩ d" means the event where both "a" and "d" occur together.
The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.
Now, onto the question.
We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.
We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.
To find this probability, we need to use some basic probability rules.
One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).
In other words, p(E) = 1 - p(~E).
So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)
Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5
Simplifying this gives:
p(~ (a ∩ d)) = 3/5
Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.
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solve the inequality
2c + 1 >7
—-
3
Answer:
c > 9
Step-by-step explanation:
[tex]\frac{2c}{3} +1 > 7[/tex]
To solve this, first subtract 1 from both sides
[tex]\frac{2c}{3} +1 > 7\\\frac{2c}{3} > 6[/tex]
multiply both sides by 3
2c > 18
divide both sides by 2
c > 9
Hope this helps! :)
Answer:
c > 9
Step-by-step explanation:
Determine the Standard Deviation of a Variable from Raw Data Identify the given statement as either true or false. The standard deviation can be negative. (This is a reading assessment question Be certain of your answer because you only get one attempt on this question.) Choose the correct answer below False True
The given statement is false. The standard deviation is a measure of the spread of data from its mean value. It is always a positive value or zero, but it cannot be negative.
If the standard deviation is zero, it means that all the data values are the same, and there is no variability. However, if the standard deviation is small, it means that the data points are close to the mean value, while a large standard deviation indicates that the data points are widely spread out from the mean. Therefore, it is important to understand that the standard deviation cannot be negative and should always be interpreted as a positive value or zero.
The given statement is: "The standard deviation can be negative." To determine whether this statement is true or false, let's briefly review the concept of standard deviation.
Standard deviation is a measure of the dispersion or spread of a set of values in a dataset. It is calculated using the square root of the variance, which is the average of the squared differences from the mean.
Since variance involves squaring the differences, it will always be a positive value or zero. Consequently, when taking the square root of a positive value or zero, the result will never be negative.
Therefore, the correct answer to the statement "The standard deviation can be negative" is False. Standard deviation cannot be negative as it represents the dispersion of values in a dataset.
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if 81% of scheduled flights actually take place and cancellations are independent events, what is the probability that 3 seperate will all take place?
Assuming that cancellations are independent events, we can use the binomial distribution to find the probability that exactly 3 of the scheduled flights take place.
Let X be the number of flights that take place out of 3 scheduled flights. Then, X follows a binomial distribution with n=3 and p=0.81. The probability mass function of X is given by:
P(X=k) = (3 choose k) * (0.81)^k * (0.19)^(3-k)
where (3 choose k) is the binomial coefficient "3 choose k".
To find the probability that all 3 flights take place, we need to compute P(X=3):
P(X=3) = (3 choose 3) * (0.81)^3 * (0.19)^(0) = (1)(0.81)^3(1) = 0.531441
Therefore, the probability that all 3 scheduled flights will take place is approximately 0.531.
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two circles that share the same center have radii $10$ meters and $20$ meters. an aardvark runs along the path shown, starting at $a$ and ending at $k$. the aardvark runs meters. what is
the aardvark runs $10\sqrt{3} + 30$ meters.Since the circles have the same center, we can connect points $B$ and $C$ to the center of the circles to form radii of length $10$ and $20$ meters.
We can also draw a line segment connecting points $A$ and $K$ to form a straight line that intersects the two radii at points $D$ and $E$, respectively.
Using the Pythagorean theorem, we can find the length of $DE$ as follows:
$DE = \sqrt{AE^2 - AD^2}$
where $AE = 20$ meters and $AD = 10$ meters. Thus,
$DE = \sqrt{20^2 - 10^2} = 10\sqrt{3}$ meters.
We know that the aardvark runs along the path from $A$ to $D$, along the radius of the smaller circle, then along the path from $D$ to $E$, along the segment connecting the two radii, and finally along the path from $E$ to $K$, along the radius of the larger circle. Therefore, the total distance the aardvark runs is:
$AD + DE + EK = 10 + 10\sqrt{3} + 20 = 10\sqrt{3} + 30$ meters.
Thus, the aardvark runs $10\sqrt{3} + 30$ meters.
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i need the derivative of this please?!
The differentiation for the given function is f'(x)=[tex]12/x^2+8/x^5[/tex]
Power Rule of Differentiation states that if x is a variable raised to power n, then the derivative of x raised to the power n is represented by
[tex]\frac{d}{dx}x^n = n.x^n^-^1[/tex]
The given function is f(x) = [tex]-12/x-2/x^4[/tex]
Using the differentiation rule for the given function it can be written as
[tex]\frac{d}{dx}(-12/x-2/x^4) = -12(-1.x^-^1^-^1)-2(-4.x^-^4^-^1)[/tex]
f'(x)=[tex]12/x^2+8/x^5[/tex]
Hence, the answer is [tex]12/x^2+8/x^5[/tex]
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barney and betty break into a parking meter with in dimes and quarters in it (legal disclaimer: don't do this), and agree that barney will get all the dimes, and betty will get all the quarters. (barney isn't terribly bright.) barney ends up with five more coins than betty. how much money did each get?
Fr the solution of Linear equations, the dollars earned by barney and betty are equal to $1.471428571 and $2.428571428 respectively.
We have barney and betty break into a parking meter. Amount of money from dimes and quarters = $3.90
Let the number of dimes and quarters collected by Barney and betty be x and y respectively. According to seniror,
x = y + 5 --(1)
Also, from unit conversion, 1 quarters
= 0.25 dollar and 1 dimes are worth the same as 0.1 dollar. So,
(number of dimes × value of 1 dimes in dollars ) + (number of quaters × value of 1 quaters in dollars )
=> 0.1 x + 0.25 y = $3.90
Multiple both sides by 100, we result
10x + 25 y = 390 --(2)
Now, we have two linear equations and we have to solve these for determining the values of x and y
Using Substitution method, Substitute value of x from equation(1) to equation(2),
=> 10( y + 5) + 25y = 390
=> 10y + 50 + 25y = 390
=> 35y = 340
=>[tex] y = \frac{ 340}{35}[/tex]
= 9.71428571429
from equation (1), x = 9.71428571429 + 5
= 14.7142857143.
So, money get by barney= 9.71428571429 × 0.25 = $2.428571428
and for betty = 14.71 × 0.1 = $1.471428571
Hence, required values are 2.428571428 dollars and 1.471428571 dollars.
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Complete question:
Barney and Betty break into a parking meter with $3.90 in dimes and quarters in it (legal disclaimer: don't do this), and agree that Barney will get all the dimes, and Betty will get all the quarters. (Barney isn't terribly bright.) barney ends up with five more coins than betty. how much money did each get?. oo
a force of 1 pounds is required to hold a spring stretched 0.2 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 0.6 feet beyond its natural length?
To stretch a spring from its natural length to 0.6 feet beyond its natural length, a work of 0.36 foot-pounds is required.
The work done in stretching a spring is equal to the area under the force-extension graph. Since the force required to hold the spring stretched 0.2 feet beyond its natural length is 1 pound, we can assume that the force required to stretch the spring from its natural length to 0.6 feet beyond its natural length is directly proportional to the extension. Therefore, the force required to stretch the spring 0.4 feet beyond its natural length is 2 pounds.
To calculate the work done in stretching the spring from 0.2 feet beyond its natural length to 0.6 feet beyond its natural length, we can use the formula for work:
Work = Force x Distance
Since the force required to stretch the spring 0.4 feet beyond its natural length is 2 pounds, and the distance over which the force is applied is 0.4 feet, the work done is:
Work = 2 x 0.4 = 0.8 foot-pounds
Therefore, the work done in stretching the spring from its natural length to 0.6 feet beyond its natural length is:
0.8 - 0.2 = 0.6 foot-pounds.
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ellen makes cookies and sells them at the local farmers' market. today, she is going to make batches of her famous cardamom cookies. she has a jar with 2 fluid ounces of cardamom, and her recipe calls for 1 4/5 tablespoons, or 3/10 of a fluid ounce, of cardamom in each batch. how many batches can ellen make with all of her cardamom?
Ellen can make a maximum of 6 batches of Cardamom cookies with her 2 fluid ounces of cardamom.
Ellen has 2 fluid ounces of cardamom in a jar. Her recipe requires 3/10 of a fluid ounce of cardamom for each batch of cardamom cookies.
We can use division to find the number of batches of cardamom cookies that Ellen can make with all of her cardamom:
2 fluid ounces ÷ (3/10 fluid ounce per batch) = (2/1) ÷ (3/10)
= (2/1) x (10/3)
= 20/3
= 6 2/3
Therefore, Ellen can make 6 batches of cardamom cookies with her 2 fluid ounces of cardamom, with 2/3 of a batch remaining.
Since she cannot make a fraction of a batch, Ellen can make a maximum of 6 batches of cardamom cookies with her 2 fluid ounces of cardamom.
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An expression is given.
8x³ - 2x - 5x+7
Determine the BEST description of the given parts of the expression. Select each word ONLY ONCE for each part of the expression.
-5
82³
74
Term
O
O
O
Coefficient
O
O
O
©2023 Illuminate Education TM, Inc.
Constant.
O
8x³ is a term
-5 is a coefficient
+ 7 is a constant
What are algebraic expressions?
Algebraic expressions are defined as expressions that are made up of terms, variables, constants, factors and coefficients.
These algebraic expressions are also composed of arithmetic or mathematical operations.
These operations are;
AdditionDivisionBracketParenthesesSubtractionMultiplicationFrom the information given, we have that the algebraic expression is;
8x³ - 2x - 5x+7
We have that;
8x³ is a term
-2x is a term
-5 is a coefficient
+ 7 is a constant
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y is proportional to the square of (x-7) when x=12, y=2 Find y when x=17
Y is proportional to square of (X-7), when Y = 2 , X = 12 .
to make an equation we need to remove proportionality and so we multiply Y with an variable.
Let that variable be 'p'.
So according to the question,
Yp = (X-7)² (from this we will find p)
putting all the known values
2p= (12-7)²
2p = 5 * 5
p = 25/2
Now, using the same equation we will find Y , when X= 17.
Y * 25/2 = ( 17- 7)²
Y * 25/2 = 10 * 10
Y = 100 * 2 / 25
Y = 8
Step-by-step explanation:
y=(x-7)^2k....... equation 1
2=(12-7)^2xk
where k is constant
2=(5)^2k
2=(5x5)k
2=25k
*Divide both sides by coefficient of k*
2/25=25/25k
k=2/25
y=(17-7)^2 x2/25..... equation 2
y=(10)^2x2/25
y=(10x10) x2/25
y=100x2/25
y=200/25
y=8
These lists provide information about two jobs. 2 lists provide information about 2 jobs. job a pays 35,000 dollars per year, has 10 paid days off per year, and has no benefits. job b pays 31,000 dollars per year, has 15 paid days off per year, and provides medical and dental insurance. which statement best compares the two jobs? job a has a lower salary than job b, but the benefits make job a a more attractive pay package. job b has a lower salary than job a, but the benefits make job b a more attractive pay package. job a has a higher salary than job b plus benefits that make job a a more attractive pay package. job b has a higher salary than job a plus benefits that make job b a more attractive pay package.
Job B has a lower salary than Job A, but the benefits make Job B a more attractive pay package.
When comparing the two jobs, it's important to consider not just the salary but also the benefits and paid time off. While Job A offers a higher salary than Job B, it doesn't come with any benefits. On the other hand, Job B has a lower salary but provides medical and dental insurance as well as more paid time off. Depending on the individual's priorities and circumstances, they may value either a higher salary or better benefits and work-life balance. Therefore, Job B could be considered more attractive to some people because of its benefits package, despite the lower salary.
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Krystal is comparing two internet service plans plan 1 costs $134. 97 every 3 months. If Krystal plans to stay with one service plan for 1 year, which should she choose? How much will she save?
Krystal should choose Plan 1 as it will save her $180 over the course of a year.
Plan 1 costs $134.97 every 3 months, which means it costs Krystal $134.97/3 = $44.99 per month.
If Krystal plans to stay with one service plan for 1 year (12 months), then she would pay 12 * $44.99 = $539.88 for Plan 1.
To compare this to Plan 2, we need to know the cost of Plan 2. Let's say Plan 2 costs $59.99 per month. Then for one year, Krystal would pay 12 * $59.99 = $719.88 for Plan 2.
Comparing the two plans, Krystal should choose Plan 1 as it will save her $719.88 - $539.88 = $180 over the course of a year.
Note that the exact amount Krystal would save depends on the cost of Plan 2, which was not given in the problem. But the method for comparing the two plans is the same regardless of the actual cost of Plan 2.
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suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. what is the probability that they all come up heads?
The probability that all four coins come up heads is 1/16 or approximately 0.0625.
The probability of flipping a head on a single coin is 1/2. Since each coin is flipped independently, the probability of all four coins coming up heads can be calculated by multiplying the probability of getting heads on each coin.
That is,
P(all heads) = P(heads on penny) × P(heads on nickel) × P(heads on dime) × P(heads on quarter)
Each of these probabilities is 1/2 since each coin has two possible outcomes – heads or tails – and they are equally likely to occur.
Thus,
P(all heads) = (1/2) × (1/2) × (1/2) × (1/2) = 1/16
This means that if we were to flip these four coins many times, on average we would expect to see all four coins come up heads about once in every 16 flips. It is important to note that the probability of all four coins coming up heads is independent of any previous flips – the coins do not "remember" whether they landed heads or tails on previous flips.
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f(x)=1/2x-7/2 and g(x)=2x+14
Answer:
(-11.667, -9.333)
Step-by-step explanation:
were you looking for the intersection? that's what i just found. have a great day and thx for your inquiry.
Using the notation of the previous problem, prove that for sets A, B, C, D ∈ P(X). AΔB = CΔD <---> AΔC = BΔD.
To prove that AΔB = CΔD if and only if AΔC = BΔD, we need to show two implications:
If AΔB = CΔD, then AΔC = BΔD
If AΔC = BΔD, then AΔB = CΔD
Let's start with implication 1:
Suppose AΔB = CΔD. This means that every element that is in A or B, but not both, is also in C or D, but not both. Similarly, every element that is in C or D, but not both, is also in A or B, but not both.
Now consider AΔC. This is the set of elements that are in A or C, but not both. We can split this set into two parts: (i) the elements that are in A but not in C, and (ii) the elements that are in C but not in A.
For part (i), we know that these elements are either in B or not in B, because if an element is in A but not in C, it must be in B (since B is the set of elements that are in A but not in AΔB). Similarly, for part (ii), we know that these elements are either in D or not in D.
Therefore, we can write AΔC = (A∩B')∪(C∩D').
Similarly, we can write BΔD = (B∩A')∪(D∩C').
Now, since AΔB = CΔD, we have that (A∩B')∪(C∩D') = (B∩A')∪(D∩C'). Rearranging this equation, we get (A∩C')∪(C∩A') = (B∩D')∪(D∩B'). This means that AΔC = BΔD, which proves implication 1.
Now let's move on to implication 2:
Suppose AΔC = BΔD. This means that every element that is in A or C, but not both, is also in B or D, but not both. Similarly, every element that is in B or D, but not both, is also in A or C, but not both.
Now consider AΔB. This is the set of elements that are in A or B, but not both. We can split this set into two parts: (i) the elements that are in A but not in B, and (ii) the elements that are in B but not in A.
For part (i), we know that these elements are either in C or not in C, because if an element is in A but not in B, it must be in C (since C is the set of elements that are in A but not in AΔC). Similarly, for part (ii), we know that these elements are either in D or not in D.
Therefore, we can write AΔB = (A∩C')∪(B∩D').
Similarly, we can write CΔD = (C∩A')∪(D∩B').
Now, since AΔC = BΔD, we have that (A∩C')∪(B∩D') = (C∩A')∪(D∩B'). Rearranging this equation, we get (A∩D')
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The notation p(zless than
a. The probability that a standard normal random variable is less than a b. The probability that a standard normal random variable is greater than a
c. The probability that a standard normal random variable is equal to a d. The probability that a standard normal random variable is not equal to a
The notation p(z < a) represents the probability that a standard normal random variable is less than a. This can be found using a standard normal distribution table or a calculator that provides a normal distribution function.
The probability that a standard normal random variable is less than a can also be expressed as P(Z < a), where Z is a standard normal random variable.
The probability that a standard normal random variable is greater than a can be found using the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Therefore, P(Z > a) = 1 - P(Z < a).
The probability that a standard normal random variable is equal to a is zero, as the standard normal distribution is continuous and has an infinite number of possible values.
The probability that a standard normal random variable is not equal to a can be found using the complement rule again. P(Z ≠ a) = 1 - P(Z = a), where P(Z = a) = 0 (as mentioned above). Therefore, P(Z ≠ a) = 1.
Let's break down each part of your question and provide an explanation for each term:
a. The notation p(z < a) refers to the probability that a standard normal random variable (Z) is less than a certain value (a). In a standard normal distribution (with a mean of 0 and standard deviation of 1), this represents the area under the curve to the left of the value 'a'. To find this probability, you can refer to a standard normal table or use a calculator with a normal distribution function.
b. The probability that a standard normal random variable is greater than a (p(z > a)) can be calculated by subtracting the probability that the variable is less than a from 1 (since the total probability is always 1): p(z > a) = 1 - p(z < a).
c. In a continuous probability distribution like the standard normal distribution, the probability that a standard normal random variable is equal to a specific value (p(z = a)) is always 0. This is because there are an infinite number of possible values, and the probability associated with each individual value is negligible.
d. The probability that a standard normal random variable is not equal to a (p(z ≠ a)) is essentially the complement of the probability that it is equal to a. Since p(z = a) is 0 in a continuous distribution, the probability that the variable is not equal to a is 1: p(z ≠ a) = 1.
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you have started your position as transportation director in a small town called mountainside village. there is only one road in and out of town. today you can expect at peak traffic to see 35 cars per hour and the drive along the road with no traffic is 1 minute. assuming poisson arrival and exponential drive times, what is the current utilization of the road?
From exponential distribution of drive time, the current utilization of the road, in small town and only one road in and out of town is equals to the 05833 or 58 33%.
If i started my position as transportation director in a small town called mountainside. To calculate the current utilization of the road, we have to use the formula, Utilization = Arrival rate x Drive time
Let's consider, Poisson arrival and exponential drive times, then
Arrival rate = λ = 35 cars per hour
Drive time = [tex]\frac{ q}{ μ} = \frac{ 1}{60 } hours [/tex] (since the drive time is 1 minute)
Therefore, from above formula of Utilization = 35 cars per hour x (0.0166 hours)
Utilization = 0.5833 or 58.33%
So, the current utilization value is 58.33%.
Thus, the current utilization of the road is
05833 or 58 33%
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Find the volume of a sphere with a radius of 8 cm.
Answer:
Step-by-step explanation
The formula for the Volume of the sphere is
[tex]v= 4/3*\pi *r^{3}[/tex]
where r⇒radius of the sphere.
According to the question,
radius(r)=8cm
now,
volume(v)=4/3×π×r³
=4/3×π×8³ cm³
=4/3×512×π cm³
=2048/3×π cm³
∴The volume of a sphere with a radius of 8 cm is 2048π/3 cm³.
During a survey, 38% of students said they liked the sports offered at the school. If 217 student said they did not like the sports offered, how many students were surveyed?
Answer:
If 38% of students said they liked the sports offered at the school, 62% of students said they did not like the sports offered at the school.
.62s = 217, so s = 350 students
Dans chaque expression , identifier un facteur commun à chaque terme.
a.4×x+4×7
b.x²+2x
c.7x-7
d.3x-9
e.10x+20
f.9x²-6x
Merci
The discount rate is kept ________ the federal funds rate because the Fed prefers that ________. A) below; banks borrow reserves from each other B) below; banks borrow reserves from the Fed C) above; banks borrow reserves from each other D) above; banks borrow reserves from the Fed
The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other in order to maintain a stable and competitive interbank lending market.
The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other. So, the correct answer is option C) above; banks borrow reserves from each other. This is because the Federal Reserve wants to encourage banks to borrow from each other in the open market, which promotes stability and liquidity within the banking system.
This helps to ensure that banks have access to necessary funds and can lend to customers at reasonable rates. Therefore, option D is incorrect and the correct answer is A) below; banks borrow reserves from each other.
The discount rate is kept above the federal funds rate because the Fed prefers that banks borrow reserves from each other.
So, the correct answer is option C) above; banks borrow reserves from each other. This is because the Federal Reserve wants to encourage banks to borrow from each other in the open market, which promotes stability and liquidity within the banking system.
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