Help i dont get this one ASAP

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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The number line will begin at point 8 and point in the negative direction, with the circle darkened.

Inequalities are expression not separated by an equal sign. Given the inequality expression below:

2x-5≤11

Add 5 to both sides

2x-5 + 5≤11 + 5

2x≤16

Divide both sides by 2

2x/2 ≤16/2

x≤8

The number line will start from the point 8 pointing towards the negative direction and the circle shaded.

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The measure of each of the angles are calculated as:

m<1 = 63 degrees.; m<2 = 49 degrees; m<3 = 87 degrees; m<4 = 44 degrees.

The measure of each angle can be calculated as explained below:

m<2 = 49 degrees [based on the vertical angles].

m<1 = 180 - m<2 - 68 [based on the triangle sum theorem]

Plug in the values:

m<1 = 180 - 49 - 68

m<1 = 63 degrees.

m<3 = 180 - 93 [linear pair theorem]

m<3 = 87 degrees.

m<4 = 180 - m<3 - 49 [based on the triangle sum theorem]

Substitute:

m<4 = 180 - 87 - 49

m<4 = 44 degrees.

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The solution to the given differential equation is:ln|1/√(1 - y^2) + y/√(1 - y^2)| = x + C where C is the constant of integration.

To solve the differential equation dy/dx = x/(1 - y^2) by separation of variables, we can rewrite it as:

(1 - y^2) dy = x dx

Now we can separate the variables by bringing all the y-related terms to one side and x-related terms to the other side:

(1 - y^2) dy = x dx

1/(1 - y^2) dy = x dx

Integrating both sides with respect to their respective variables, we get:

∫1/(1 - y^2) dy = ∫x dx

To integrate the left side, we can use partial fraction decomposition or trigonometric substitution. Let's use the latter approach:

Using the substitution y = sin(theta), we have dy = cos(theta) d(theta) and (1 - y^2) = (1 - sin^2(theta)) = cos^2(theta). The integral becomes:

∫1/cos^2(theta) * cos(theta) d(theta) = ∫sec(theta) d(theta) = ln|sec(theta) + tan(theta)| + C

Now, we need to substitute back y = sin(theta):

ln|sec(theta) + tan(theta)| + C = ln|sec(arcsin(y)) + tan(arcsin(y))| + C = ln|1/√(1 - y^2) + y/√(1 - y^2)| + C

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The repeating decimal 11.454545... can be expressed as the ratio of two integers: 1134/99.Simplifying the fraction, if possible, we find that:1134/99 = 114/11Hence, the repeating decimal 11.454545... can be written as the ratio 114/11.

To express the repeating decimal 11.454545... as a ratio of two integers, we can use algebraic manipulation to convert it into a fraction.

Let's denote the repeating decimal as x:

x = 11.454545...

Multiplying x by 100, we get:

100x = 1145.454545...

Subtracting the original equation from the multiplied equation, we have:

100x - x = 1145.454545... - 11.454545...

Simplifying both sides:

99x = 1134

Dividing both sides by 99:

x = 1134/99.

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Answer:

Grandma can make 0.75 batches of cookies with only a half cup of milk.

Step-by-step explanation:

To solve this problem, we can set up a proportion.

[tex]\frac{2}{3}[/tex] = [tex]\frac{0.5}{x}[/tex]

We can use cross products to solve.

3(0.5)=1.5

2(x)=1.5

x=0.75

Therefore, Grandma can make 0.75 batches of cookies with only a half cup of milk.

Hope this helps!

Knowing whether the mean is more than or less than the median can give us information about the skewness of a distribution because the mean and median represent different aspects of the distribution's central tendency.

In a positively skewed distribution, the tail of the distribution extends towards higher values, meaning there are some extreme high values that pull the mean towards the right. In this case, the mean is greater than the median because it is influenced by those high values, shifting the central tendency towards the right.

On the other hand, in a negatively skewed distribution, the tail of the distribution extends towards lower values, indicating the presence of extreme low values that pull the mean towards the left. As a result, the mean is lower than the median because the central tendency is shifted towards the left by those low values.

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Answer:

Use the radioactive decay formula: A = Ao*2^(-t/h), where

A = 722*2^(-17/71)

find 2^(-17/71) with a calc

A = 722*.847076

A = 611.59 kg after 17 hrs

Step-by-step explanation:

Answer:

The formula for the amount of radioactive material remaining after a certain time can be expressed as:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the amount of radioactive material remaining after time t

N₀ is the initial amount of radioactive material

h is the half-life of the material

Substituting the given values, we have:

N(14) = 439 * (1/2)^(14/76)

N(14) = 386.377 kg

Therefore, the amount of radioactive material remaining after 14 hours is 386.377 kg. The answer is option (d).

Step-by-step explanation:

Hello

4/2 + 7/2 - 3/2

= 11/2 - 3/2

= 8/2

= 4

The equation of h(x) in vertex form is: C. h(x) = (x + 1)² + 2.

In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Next, we would create a system of equation by using the data points provided in the table above;

a(-3)² + b(-3) + c = 6

9a - 3b + c = 6     .....equation 1.

a(0)² + b(0) + c = 3

c = 3    .....equation 2.

a(1)² + b(1) + c = 6

a + b + c = 6    .....equation 3.

By solving the system of equations simultaneously, the values of a, b, and c are as follows;

a = 1

b = 2

c = 3

Therefore, the required quadratic function in vertex form is given by;

ax² + bx + c = 0

x² + 2x + 3 = 0

h(x) = x² + 2x + 3

h(x) = (x + 1)² + 2

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The taste test conducted by the local chili Restaurant  of a Single-blind study because the customers do not know the type of chili they are tasting, while the test administrators do know which type of chili is being presented.

In a single-blind study, the participants or subjects do not know which group they are assigned to or what treatment they are receiving, while the experimenter or test administrator knows the type of treatment being given. In this case, the test administrators know which type of chili is being presented to the customers, but the customers are not aware of the type of chili they are tasting.

The use of a single-blind study is appropriate in this case because it helps to reduce the possibility of bias in the results. If the customers knew which type of chili they were tasting, it could influence their preferences based on preconceived notions or expectations. By not knowing the type of chili they are tasting, the customers are more likely to give their unbiased opinions and preferences.

Additionally, the experiment is not a double-blind study because the test administrators are aware of the type of chili that is being presented. In a double-blind study, both the participants and the experimenters are unaware of which group the participants are assigned to or which treatment they are receiving. This helps to reduce the potential for bias from both the participant and experimenter.

the taste test conducted by the local chili restaurant is an example of a single-blind study because the customers do not know the type of chili they are tasting, while the test administrators do know which type of chili is being presented.

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The equivalent expressions of 3(2/3p+3-1/3p-5) is 2p - 6.

By simplifying 3(2/3p+3-1/3p-5), we first have to combine the constants in the parentheses:

2/3p + 3 - 1/3p - 5 = (2/3p - 1/3p) + (3 - 5) = (1/3p) - 2

Substituting this expression back into the original equation, we get:

3(2/3p+3-1/3p-5) = 3[(1/3p) - 2 + 3 - 5]

Simplifying inside the brackets, we have:

3[(1/3p) - 2 + 3 - 5] = 3[(1/3p) - 2 - 2]

Multiplying by 3, we get:

3[(1/3p) - 2 - 2] = (1/p) - 6

Therefore, the equivalent expression of 3(2/3p+3-1/3p-5) is (1/p) - 6.

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The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Here, Parent function is,

⇒ f (x) = x²

And, After translation the function is,

⇒ f (x) = (x + 3)²

Now, We can draw the graph of both function.

Hence, By graph we get;

The correct choice for the transformation of the function f (x) = (x + 3)² from the parent function f (x) = x² is,

⇒ Horizontal translation.

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The distance between points A and B will be 6.71 units.

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

Where we have

A = (0, 0)

B = (6, 3)

This means that the point A is on the origin and point B will be (6, 3).

Then the distance between points A and B will be

D² = (6 - 0)² + (3 - 0)²

D² = 6² + 3²

D² = 36 + 9

D² = 45

D = √45 units

Evaluate

D = 6.71 units

Hence, the distance between points A and B will be 6.71 units.

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a. It will take 392 minutes for just 1 machine to produce same batch.

b. it will take 49 minutes for 8 machines to produce same batch.

a) To get minutes its take for just 1 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 1

Time = 392 / 1

Time = 392 minutes

b. To get minutes its take for just 8 machine, we will use the following formula:

Time = (Number of machines * Original time) / New number of machines

Time = (7 * 56) / 8

Time = 392 / 8

Time = 49 minutes.

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The speed is 3.6 meters per second.

Given that Laura ran 1 km in 4 minutes and 37 seconds.

We know that, 1 km =1000 meters

1 minute =60 seconds

So, 4 minutes and 37 seconds

We know that one minute is equal to sixty seconds

So let us convert four minutes to seconds by multiplying four with sixty seconds

= 4×60 +37

When four is multiplied with sixty we get two hundred forty

= 240+37

= 277 seconds

4 minutes and 37 seconds is equal to two hundred seventy seven seconds.

Now, the formula for speed is distance by time

Speed = Distance/Time

Distance =1000 and time is 277

= 1000/277

= 3.6 meters per second

Therefore, the speed is 3.6 meters per second.

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Laura ran 1 km in 4 minutes and 37 seconds. What was her speed in metres per second (m/s)? If your answer is a decimal, give it to 1 d.p.​

Answer:

reflect the parent function over the y-axis, and translate it 3 unit to the left

The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

       The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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The most appropriate statistical test to determine if there is a difference in history of fracture in the past 5 years between 60-year-old men with normal bone density, those with osteopenia, and those with osteoporosis is the chi-square test for independence.

      The chi-square test for independence is used to determine whether there is a relationship between two categorical variables. In this case, the two variables are bone density (normal, osteopenia, osteoporosis) and history of fracture in the past 5 years (at least once or none). The test determines if there is a significant association between these two variables, and if so, how strong the association is. The null hypothesis is that there is no association between the two variables, while the alternative hypothesis is that there is a significant association. The test calculates a chi-square statistic and a p-value, which is compared to a significance level to determine if the null hypothesis should be rejected.

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The equation of the line in slope intercept form is y = -1/3 x - 6

Note that the Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is defined as the ratio of the rise to the run.

We are Given that the line passes through the points (0, -6) and (-6, -4)

The slope of the line is calculated by the formula given as;

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -4 + 6 ) / ( -6 - 0)

Slope = ( 2 / -6 )

Slope  = -1/3

Thus, the equation of the line in slope-intercept form is

y-y₁ = m(x-x₁)

y + 6 = -1/3(x)

y = -1/3 x - 6

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To find the general solution of the second-order differential equation 5y'' + y' = 0, we can use the method of separation of variables.

Let's assume y = e^(mx), where m is a constant.

Taking the first and second derivatives of y with respect to x, we have:

y' = me^(mx)

y'' = m^2e^(mx)

Substituting these expressions into the differential equation, we get:

5(m^2e^(mx)) + (me^(mx)) = 0

Now, we can factor out e^(mx):

e^(mx) * (5m^2 + m) = 0

For this equation to hold true, either e^(mx) = 0 or 5m^2 + m = 0.

Since e^(mx) is never zero for any real value of x, we focus on the second equation:

5m^2 + m = 0

We can factor out m:

m(5m + 1) = 0

Setting each factor equal to zero, we have two possible solutions:

m = 0 or 5m + 1 = 0, which gives m = -1/5.

Therefore, the general solution of the given second-order differential equation is:

y(x) = C1e^(0x) + C2*e^((-1/5)*x)

Simplifying this expression, we have:

y(x) = C1 + C2*e^(-x/5)

Here, C1 and C2 are arbitrary constants that can be determined based on initial conditions or additional information about the problem.

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Answer:

A - 1/4

Step-by-step explanation: The probability of getting heads on the toss of a coin is 0.25. If we consider all possible outcomes of the toss of two coins as shown, there is only one outcome of the four in which both coins have come up heads, so the probability of getting heads on both coins is 0.25.

They would spend approximately 13.33 hours driving if they plan to cover a total distance of 800 miles at an average speed of 60mph.

To answer this question, we need to use the formula: time = distance/speed. In this case, the distance is 800 miles and the average speed is 60mph. Therefore, the time spent driving can be calculated as:
Time = 800 miles / 60 mph
Simplifying this equation, we get:
Time = 13.33 hours
So, the total time that they would spend driving is 13.33 hours. It's important to note that this is the average time it would take them if they maintained a constant speed of 60mph throughout their journey. However, if they encountered traffic, roadworks, or took any breaks during their trip, the actual time spent driving would be longer than this.
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The solutions to the equation √(2x² - 7) - x = 3 are x = -2 and x = 8 and x = -2 is an extraneous solution

From the question, we have the following parameters that can be used in our computation:

√2x²-7-x=3

Express properly

So, we have

√(2x² - 7) - x = 3

Add x to both sides of the equation

This gives

√(2x² - 7) = x + 3

Take the square roots of both sides

So, we have

2x² - 7 = x² + 6x + 9

So, we have

x²  - 6x - 16 = 0

When solved for x, we have

x = -2 and x = 8

Hence, the solutions to the equation are x = -2 and x = 8 and x = -2 is an extraneous solution

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There are 36, coins of 50c out of a total of 120 coins.

Assume that

Quantity of 50 cent coin = x

Quantity of 20 cent coin = y

Then according to question,

50x + 20y = 3480 ...(i)

Now if the sum of the coins is 120,

x + y = 120  ...(ii)

Now use elimination method,

By 50 x (ii) - (i),

30y = 2520

y = 84  

Now put this value this into (ii);

x = 36

Hence,

Quantity of 50 cent coin = 36

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Answer:

A

Step-by-step explanation:

Hope this helps

For the following examples:

3. Dave's truck has a fuel capacity of 180 US gallons, but it is only one-quarter full, which means he needs 3/4 of 180 gallons = 135 gallons of diesel fuel.

To convert gallons to liters, multiply by 3.78541 (1 gallon = 3.78541 liters).

So Dave needs 135 gallons x 3.78541 liters/gallon = 511.66535 liters of diesel fuel.

The cost of diesel fuel is 94.9 C per liter, so the total cost for Dave to refill his truck is 511.66535 liters x 94.9 C/liter = $485.63.

4. To determine the volume of concrete Greg will need for his driveway, we first convert the dimensions to meters:

20 feet = 6.096 meters, 36 feet = 10.9728 meters, and 4 inches = 0.1016 meters.

Then use the formula for the volume of a rectangular solid: volume = length x width x height.

So the volume of concrete needed for Greg's driveway is 6.096 meters x 10.9728 meters x 0.1016 meters = 6.801 cubic meters.

The cost of the concrete is $135 per cubic meter, so the total cost for the concrete that he will need for his driveway is 6.801 cubic meters x $135/cubic meter = $918.14.

5. The volume of each planting box is 48 inches x 24 inches x 18 inches = 20736 cubic inches.

To convert cubic inches to cubic yards, divide by 46656 (1 cubic yard = 46656 cubic inches).

So each planter box requires 20736 cubic inches / 46656 cubic inches/cubic yard = 0.44444 cubic yards of potting soil.

Susan needs to build 35 planting boxes, so she will need 35 x 0.44444 cubic yards = 15.5554 cubic yards of potting soil.

Holland Growers charges $17 per cubic yard of potting soil, so the cost from them will be 15.5554 cubic yards x $17/cubic yard = $264.45.

Night Growers charges $21.50 per cubic meter of potting soil, which is equivalent to $16.34 per cubic yard (1 cubic meter = 1.30795 cubic yards).

So the cost from Night Growers will be 15.5554 cubic yards x $16.34/cubic yard = $254.36.

Therefore, the total cost of the topsoil she needs from each supplier is $264.45 from Holland Growers and $254.36 from Night Growers.

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Answer:

do it yourself what do you do while teacher is teaching

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=158055.04\\ h=78 \end{cases}\implies 158055.04=\cfrac{\pi r^2(78)}{3} \\\\\\ (3)158055.04=78\pi r^2\implies \cfrac{(3)158055.04}{78\pi }=r^2 \\\\\\ \sqrt{\cfrac{(3)158055.04}{78\pi }}=r\implies \sqrt{\cfrac{(3)158055.04}{78(3.14) }}=r\implies 44=r[/tex]

As per the properties of parallel lines and interior alternate angles postulate, we can prove that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Given that;

Line y || z

i.e. y is parallel to z.

To Prove:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

Since, It is given that the lines y and z are parallel to each other.

m∠5, m∠1 are interior alternate angles because lines y and z are parallel and one line AC cuts them.

So, m∠5 = m∠1  ..... (1)

Similarly,

m∠6, m∠3  are interior alternate angles because lines y and z are parallel and one line AB cuts them.

So, m∠6 = m∠3  ...... (2)

Now, we know that the line y is a straight line and A is one point on it.

Sum of all the angles on one side of a line on a point is always equal to 180 degree .

i.e. ⇒ m ∠1+ m ∠2+ m ∠3 = 180°

Using equations (1) and (2):

We can see that:

⇒ m ∠5+ m ∠2+ m ∠6 = 180°

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