If E and F are events with P(E)=0.326, P(F)=0.298, and P(E∩F)= 0.191 , calculate P(F∣E)=? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your final answer to four decimal places.

Answer:

6

Step-by-step explanation:

Terms are what is separated by addition and subtraction.

the matrix K for the given system is:

K = [k1 + k2   -k2]

     [-k2        k2 + k3]

And it is symmetric.

To calculate the matrix K for the given system, we need to determine the values of k1, k2, and k3 based on the system equation:

[m1   0 ] [x₁(t)] + [k1 + k2   -k2 ][x₁(t)] = [0]

[   ]x(t) + [   ]x(t) = [   ]

[0   m2] [x₂(t)]   [ -k2   k2 + k3][x₂(t)]   [0]

From the equation, we can see that the coefficients of the x₁(t) terms form the diagonal elements of the matrix K, and the coefficients of the x₂(t) terms form the off-diagonal elements.

Therefore, the matrix K is:

K = [k1 + k2   -k2]

   [-k2        k2 + k3]

To verify that K is symmetric, we compare its transpose with the original matrix K.

The transpose of K is:

K^T = [k1 + k2  -k2]

      [-k2         k2 + k3]

We can observe that K is equal to its transpose K^T, which means the matrix K is symmetric.

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The type of armored cable listed under UL 4 with permitted conductor sizes of 14 AWG through 1 AWG only is Type AC Cable.

Type AC Cable is also known as armored cable or BX cable, and it is a type of electrical wiring that consists of two or more insulated conductors that are wrapped in a flexible metal sheath. The metal sheath provides protection against physical damage and also serves as a grounding conductor.

UL 4 is a standard for Armored Cable and it covers various types of armored cables, including Type AC cable. UL 4 specifies the construction, performance, and testing requirements for armored cables. It also includes requirements for the thickness and composition of the metal sheath, as well as the thickness and type of insulation on the conductors.

In summary, Type AC Cable is the type of armored cable that is listed under UL 4 and has permitted conductor sizes of 14 AWG through 1 AWG only.

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Answer:

Step-by-step explanation:

-Start by distributing the 2, -2(3m+1/2).

-Getting -6m-1, your equation should look like -40-6m-1=7m-2

-Combine -40 and -1 to get -41, and then add the -6m to the other side.

-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.

-Now, we have -39=13m. divide both sides by 13 to get m=-3.

If the population size is 500, then the standard error of the sample mean is approximately 0.447.

The standard error of the sample mean is a measure of how much the sample mean differs from the true population mean on average. The formula for calculating the standard error of the sample mean is:

SE=σ/√n

where σ is the standard deviation of the population, n is the sample size.

Using the given values, we can calculate the standard error of the sample mean as follows:

σ = 10

n = 50

SE = σ/√n = 10/√50 = 1.41

When the population size is very large relative to the sample size (n), the standard error of the sample mean can be approximated as:

SE=σ/√N

where N is the population size.

Using the given values, we can calculate the approximate standard error of the sample mean as follows:

N = 500

σ = 10

SE = σ/√N = 10/√500 = 0.447

Thus, the standard error of the sample mean, when the population size is 500, is approximately 0.447.

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You would need to save approximately $14,666.67 each month to accomplish your goal of building up a 5-month emergency fund over an 18-month period of time.

To accomplish your goal of building up a 5-month emergency fund over an 18-month period of time using the 20-50-30 budget model, you would need to save a certain amount each month.
First, let's calculate the total amount needed for the emergency fund. Since you want to have a 5-month fund, multiply your gross annual income by 5:
$52,800 x 5 = $264,000
Next, divide the total amount needed by the number of months you have to save:
$264,000 / 18 = $14,666.67
Therefore, you would need to save approximately $14,666.67 each month to accomplish your goal of building up a 5-month emergency fund over an 18-month period of time.

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Since numbers can be repeated and any number from 0 to 9 can be used for each digit, we have 10 options for each digit of the 7-digit phone number.

To calculate the total number of permutations, we multiply the number of options for each digit together:

Total number of permutations = 10^7

This is because for each of the 7 digits, we have 10 options (0-9) and we multiply these options together.

Calculating the value, we have:

Total number of permutations = 10^7 = 10,000,000

Therefore, there are 10,000,000 permutations of a 7-digit phone number under the given conditions.

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Notice that the intersecton of both inequality is located approximately at the point (150,50). This means that there are at least 100 more feet of quarter inch pipe than half inch pipe, and since the combined cost is represented by the inequality

then, it must not cost more than 800. Therefore, the correct option is a)

The least cοmmοn denοminatοr οf the fractiοn is 24.

Part οf a whοle is a fractiοn. The quantity is written as a quοtient in mathematics, where the numeratοr and denοminatοr are divided. Each is an integer in a simple fractiοn. Whether it is in the numeratοr οr denοminatοr, a cοmplex fractiοn cοntains a fractiοn. The numeratοr and denοminatοr οf a cοrrect fractiοn are οppοsite each οther.

Here the given fractiοn is \($\frac{11}{8}\ \text{and}\ \frac{7}{12}\).

We knοw that Least cοmmοn denοminatiοn οf the fractiοn is lοwest cοmmοn multiple. Then, factοrs οf the denοminatοr

8 = 2*2*2

12=2*2*3

Nοw LCD = 2*2*2*3 = 24.

Hence the least cοmmοn denοminatοr οf the fractiοn is 24.4.

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The unit rate of bananas is $2.25 per pound.

What is the meaning of unit rate?

Unit Rate = Ratio between two separate quantities with different units. = a:b. = a/b. This formula can be used to determine the rate of any two given quantities, such as a and b.

Given that the cost of 2/3 pound of bananas is $1.50.

If the number of pound of bananas increase then the cost of bananas will be increase.

So the relation between amount of banana is directly proportion with the cost.

Therefore,

Amount of bananas/ cost of bananas = Amount of bananas/ cost of bananas

(2/3)/1.50 = 1/x

2/4.50 = 1/x

x = 4.50/2

x = 2.25

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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Answer:

7a - 1

Step-by-step explanation:

Subtract the numbers

+

2

+

7

+

4

−

8

a+2a+{\color{#c92786}{7}}+4a{\color{#c92786}{-8}}

a+2a+7+4a−8

+

2

−

1

+

4

SOLUTION

The shape is a parallelogram

The consecutive angle of a parallelogram is supplementary that is added up to 180 degree

Hence we have

Therefore the right option is D

The unit normal vector of the function f(x,y)=x^3 at point P(5,3,125) is ⟨1, 0, 0⟩.

To find a unit normal vector at point P(5,3,125) for the function f(x,y) = x^3, we need to find the gradient vector of f and normalize it to obtain a unit vector.

The gradient of f is given by

∇f = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ = ⟨3x^2, 0, 0⟩

At point P(5,3,125), the gradient vector is

∇f(P) = ⟨75, 0, 0⟩

To obtain a unit normal vector, we need to normalize ∇f(P) by dividing it by its magnitude

||∇f(P)|| = √(75^2 + 0^2 + 0^2) = 75

So the unit normal vector at point P is

n = ∇f(P) / ||∇f(P)|| = ⟨75/75, 0/75, 0/75⟩ = ⟨1, 0, 0⟩

Therefore, the unit normal vector for the function at the point P is ⟨1, 0, 0⟩.

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Answer:

Step-by-step explanation:

first, you have to find the equation of the perpendicular bisector of this given line.  

to do that, you need the slope of the perpendicular line and one point.

Step 1: find the slope of the given line segment. We have the two end points (10, 15) and (-20, 5), so the slope is m=(15-5)/(10-(-20))=1/3

the slope of the perpendicular line is the negative reciprocal of the slope of the given line, m=-3/1=-3  

step 2: find the middle point: x=(-20+10)/2=-5, y=(15+5)/2=10      (-5, 10)

so the equation of the perpendicular line in point-slope form is (y-10)=-3(x+5)

now plug in all the given coordinates to the equation to see which pair fits:

(-8, 19): 19-10=9, -3(-8+5)=9, so yes, (-8, 19) is on the perpendicular line.  

try the other pairs, you will find that (1,-8) and (-5, 10) fit the equation too. (-5,10) happens to be the midpoint.

Answer:

It's A, B, and D.

Explanation:

A-(−8, 19)

B-(1, −8)

D-(−5, 10)

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Water vapor is an important component of the Earth's atmosphere, and it plays a crucial role in regulating the climate. water vapor makes up about 0-4% of the Earth's atmosphere by volume . So the correct option is A.

It is a greenhouse gas, which means that it can trap heat in the atmosphere and contribute to global warming. The amount of water vapor in the atmosphere can vary depending on location, temperature, and weather conditions. On average, water vapor makes up about 0-4% of the Earth's atmosphere by volume. This may seem like a small amount, but it has a significant impact on weather patterns and climate. As temperatures rise due to climate change, the amount of water vapor in the atmosphere is expected to increase, which could have further impacts on global climate.

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The probability of throwing an odd number with a normal dice is 1/2

When rolling a normal six-sided B, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Out of these six numbers, three of them (1, 3, and 5) are odd numbers. Thus, there are three favorable outcomes (odd numbers) out of a total of six possible outcomes.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes. In this case, the probability of throwing an odd number is 3/6, which simplifies to 1/2.

This means that there is a 50% chance of rolling an odd number with a normal six-sided die. In other words, if you roll the die many times, you can expect that approximately half of the outcomes will be odd numbers.

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The 99% lower confidence bound for the true average ultimate tensile strength is 134.09.

To calculate the 99% lower confidence bound for the true average ultimate tensile strength, we need to use the formula:

Lower confidence bound = sample mean - (critical value * (sample standard deviation / √(sample size)))

First, we need to determine the critical value for a 99% confidence level. Using a t-distribution table with 152 degrees of freedom (sample size - 1), we find a critical value of -2.602.

Plugging in the values, we get:

Lower confidence bound = 135.39 - (-2.602 * (4.59 / √(153)))

Lower confidence bound = 134.09

In simpler terms, we can say that we are 99% confident that the true average ultimate tensile strength is at least 134.09 or higher based on our sample data.

This means that if we were to take many different samples of the same size and calculate the lower confidence bound for each sample, we would expect 99% of them to contain the true average ultimate tensile strength value.

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Answer:

a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.

b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:

Additional amount owed = Taxes owed - Amount withheld

= $4,576 - $4,323

= $253

Therefore, the person would owe an additional $253.

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Answer:

Experimental study

Step-by-step explanation:

The most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the absence of seasonal variations.

The tilt of Earth's axis is what causes the change in seasons as different parts of the planet receive varying amounts of sunlight throughout the year. If Earth's axis were to become perpendicular to the line between the Sun and Earth, the planet would no longer experience these seasonal variations. This means that the climate would become more consistent throughout the year, with less temperature variation between different regions. Without the tilt, the equator would receive the same amount of sunlight year-round, leading to a relatively stable climate with minimal temperature fluctuations. The regions closer to the poles, which currently experience more pronounced seasons, would see a reduction in temperature extremes.

Additionally, the absence of a tilted axis would also affect the length of daylight hours. Currently, as Earth orbits the Sun, different parts of the planet experience longer or shorter days. However, with a perpendicular axis, there would be equal amounts of daylight and darkness across all latitudes throughout the year. This would have significant implications for ecosystems, as organisms rely on daylight and darkness cues for various biological processes such as migration, reproduction, and growth.

Overall, the most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the loss of seasonal variations and the establishment of a more consistent climate throughout the year, with equal daylight hours across all latitudes.

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The expression for the length of the sail is x = 7( tan 50° ).

According to the given question.

The sail of a boat is in the shape of a right triangle.

And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.

Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side

And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.  

So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.

Let the length of the sail be x meters.

Now, in the given right angled triangle

We can say that

tan A = Opposite side/Adjacent side

⇒ tan 50° = x/7

⇒ x = 7( tan 50° )

Hence, the expression for the length of the sail is x = 7( tan 50° ).

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a) Since E is closed, its complement F\ E is contained in F, so the intersection of {U_i1, U_i2, ..., U_in} with E is still a finite subcover of E. Thus, E is compact.

b) The union of all these finite subcovers is a finite subcover of {U_i} that covers K, showing that K is compact.

(a) To show that E is compact, we need to show that any open cover of E has a finite subcover. Let {U_i} be an open cover of E. Since E is closed in F, its complement F\E is open in F. Thus, {U_i} and F\ E together form an open cover of F. Since F is compact, there exists a finite subcover {U_i1, U_i2, ..., U_in, F\ E}. Since E is closed, its complement F\ E is contained in F, so the intersection of {U_i1, U_i2, ..., U_in} with E is still a finite subcover of E. Thus, E is compact.

(b) Let K1, K2, ..., Kn be a finite collection of compact subsets of S. Let {U_i} be an open cover of their union K= K1∪ K2 ∪ ... ∪ Kn. Then each Ki is contained in K, so {U_i} is also an open cover of each Ki. Since each Ki is compact, there exists a finite subcover {U_i1, U_i2, ..., U_ik_i} of {U_i} for each Ki. Thus, we have a finite collection of sets {U_i1, U_i2, ..., U_ik_1}, {U_i1, U_i2, ..., U_ik_2}, ..., {U_i1, U_i2, ..., U_ik_n} that covers K1, K2, ..., Kn respectively. The union of all these finite subcovers is a finite subcover of {U_i} that covers K, showing that K is compact.

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The smallest value of n for which the nth term of the geometric sequence with first term 3/4 and second term 15 is divisible by one .

We want to find the smallest value of n for which the nth term of the sequence is divisible by one million. In other words, we want to find the smallest value of n such that 10^6 divides the nth term of the sequence. We can rewrite this condition as (3/4)(20)^(n-1) = k*10^6, where k is an integer. Dividing both sides by 10^6 and simplifying, we get (3/4)(2/5)^(n-1) = k/125. We want to find the smallest value of n such that k/125 is an integer. Since 3 and 125 are relatively prime, k must be a multiple of 125 for k/125 to be an integer.

Therefore, we can write k = 125m, where m is an integer. Substituting this into the previous equation and simplifying, we get (2/5)^(n-1) = (4/15)m. Taking the logarithm of both sides, we get (n-1)log(2/5) = log(4/15) + log(m). Since log(2/5) is negative, we can divide both sides by log(2/5) and change the direction of the inequality to get n-1 >= (-1/log(2/5))(log(4/15) + log(m)).

Therefore, the smallest value of n for which the nth term of the sequence is divisible by one million is the smallest integer greater than or equal to (-1/log(2/5))(log(4/15) + log(m)) + 1. We want to choose m so that this expression is minimized. Since log(4/15) is negative and log(m) is non-negative, the smallest value of the expression is achieved when log(m) = 0, which corresponds to m = 1. Therefore, the smallest value of n for which the nth term of the sequence is divisible by one million is the smallest integer greater than or equal to (-1/log(2/5))(log(4/15) + log(1)) + 1, which simplifies to 24.

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Less workers = more hours

OR the answer might be worded as

More workers = less hours

Answer:

.899

Step-by-step explanation:

The solution to the problem using laws of exponents is: (3^(5/12))/(4^(1/6)

Some of the laws of exponents are as follows:

- When multiplying by like bases, keep the same bases and add exponents.

- When you raise the base to the power of 1 to another power, keep the base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

We are given the expression as:

\((\frac{3^{\frac{1}{2} } }{4^{\frac{1}{5} } })^{\frac{5}{6} }\)

Applying the laws of exponents gives us:

\(\frac{(3^{\frac{1}{2} * \frac{5}{6}})}{(4^{\frac{1}{5} * \frac{5}{6}})}\)

= (3^(5/12))/(4^(1/6)

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