Find the expected value of the
random variable with the
following probability distribution:
Х
2
3
4
5
6
7
8
9
10
11
12
Р
1/36
1/18
1/12
1/9
5/36
1/6
5/36
1/9
1/12
1/18
1/36
[?]

Answer:

a) 11/100

b) 60 times

Step-by-step explanation:

a)

We want to find the probability that a 3 will be rolled.

Probability = # of favorable outcomes / total # of outcomes.

Here the number of favorable outcomes will be the number of times a 3 was rolled and the total number of outcomes will simply be the # of times that the dice was rolled which can be calculated by finding the sum of the frequencies of each number.

So # of favorable outcomes = 11 ( as the dice was rolled on a 3 11 times.)

And the total number of outcomes would be 100 ( the sum of the frequencies , 12 + 35 + 11 + 23 + 7 + 12 = 100 )

So the probability of rolling a 3 would be 11/100

b)

For this part we want to find the expected times that a 6 would be rolled if we rolled the die 500 more times.

To calculate this we simply find the probability of rolling a 6 and then multiply that by 500.

So again probability = # of favorable outcomes / total # of outcomes.

Here # of favorable outcomes is frequency of rolling a 6 which would be 12 and the total number of outcomes is 100 as we found out during the last part.

So the probability of rolling a 6 is 12/100 or 3/25

We then multiply this by 500 to find the expected number of times a 6 would be rolled if the dice was rolled 500 more times

So our answer = 3/25 × 500 = 60 times

Answer:

The answer is:

Step-by-step explanation:

9, 4.1, 2.6, 7, 8.5

the answer to your question is 36

To determine which option gives a better chance of winning, we need to calculate the expected number of A's and B's in the 1,000 draws and compare it to the conditions for winning in each option.

Let's calculate the expected number of A's and B's:

Number of A's in "ARABIA": 3

Number of B's in "ARABIA": 1

Total number of letters in "ARABIA": 6

Probability of drawing an A: 3/6 = 1/2

Probability of drawing a B: 1/6

Expected number of A's in 1,000 draws: (1/2) * 1,000 = 500

Expected number of B's in 1,000 draws: (1/6) * 1,000 = 166.67

Now let's analyze the conditions for winning in each option:

Option A: You win a dollar if the number of A's among the draws is 10 or more above the expected number (500 + 10 = 510 or more).

Option B: You win a dollar if the number of B's among the draws is 10 or more above the expected number (166.67 + 10 = 176.67 or more).

Comparing the two options:

Option A requires having 510 or more A's out of the 1,000 draws.

Option B requires having 176.67 or more B's out of the 1,000 draws.

Since it is not possible to have a fraction of a letter, the number of B's will always be an integer. Therefore, it is impossible to reach the condition for winning in option B, as there can't be 176.67 B's.

Therefore, the correct answer is:

(i) Option A gives a better chance of winning than option B.

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Using mixture word problem, the antifreeze must be added to 12l of a 40% solution of antifreeze to obtain a 60% solution is 6l.

Mixture word method or mixture word problem is a method in mathematics to solve the problem when creating a mixture of two or more different things. This method will solve the problem for determining the quantity of mixture result.

In the question, we will mixture two antifreeze to obtain 60% solution. First we must know the maximum quantity of pure antifreeze is 100%. So,

(0.4*12) + (1*x) = 0.6*(12+x)

(0.4*12) + 0.1x = (0.6*12) + 0.6x

0.4x = 0.2*12

x = 0.2*30

x = 6

Thus, the pure antifreeze must be added is 6l.

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Answer:

1. 120583

2. 0248182

Step-by-step explanation:

According to the one you gave

Answer:

A. 12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

9 + (1/2)⁴ · 48

Step 2: Evaluate

Millimeters can be converted into centimeters by dividing the value by 10. The solution has been obtained by using the unit conversion.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. For instance, you could use minutes instead of hours to represent time or feet instead of miles to indicate distance. It commonly occurs when measurements are provided in one system of units, such as feet, but are required in a different system, such as chains.

We are required to convert millimeters to centimeters.

We know that 1 centimeter = 10 millimeters

So, for converting millimeters to centimeters, we need to divide the value by 10.

Hence, millimeters can be converted into centimeters by dividing the value by 10.

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Adding a tracking variable to count the number of times a loop executes can be an effective way to measure the answer choice's truthfulness.

Adding a tracking variable to count the number of loop executions can indeed be a useful technique for various purposes. By incrementing the tracking variable within the loop, we can keep track of the number of times the loop body is executed. This information can be valuable in measuring the accuracy or efficiency of the loop and evaluating the truthfulness of an answer choice.

For example, when comparing different algorithms or approaches, counting loop iterations can help determine which solution performs better. It provides a quantitative measure to assess time complexity or resource usage. Additionally, the tracking variable can be used to validate the correctness of a loop by ensuring that the expected number of iterations is reached.

By monitoring the loop execution count, we can gain insights into the behavior of the code, identify potential issues such as infinite loops, and make informed decisions based on the observed results. Hence, adding a tracking variable to count loop executions can be an effective technique to measure the truthfulness or performance of an answer choice in certain scenarios.

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Answer:

A.

Step-by-step explanation:

when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1

Answer:

7 miles per hour

Step-by-step explanation:

3.5 times 2.

Area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

The correct option is b.

The area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

What is Z score: The z-score (aka, standard score) is a dimensionless metric that represents the deviation of a score from the mean in units of the standard deviation.

The formula for computing z-scores is as follows:

Z = (X - μ) / σ

where X is the score,

μ is the mean,

and σ is the standard deviation.

Z-scores can be used to assess the relative position of a score in relation to the distribution's mean and standard deviation.

In this particular question, the Z score of two test scores is 1.2 and 1.5.

To obtain the area between these scores, we have to find the area between each score and the mean in the z-score table, and then subtract the smaller area from the larger area.

First, we need to find the area between 1.2 and 1.5.

We can see the area from the z-score table as P(z < 1.5) - P(z < 1.2).

The following z-score table can be used to find these probabilities:

z-score table

From the table, P(z < 1.5) is equal to 0.9332, and P(z < 1.2) is equal to 0.8849.

Thus, P(1.2 < z < 1.5) = 0.9332 - 0.8849 = 0.0483.

To find the answer to the question, we have to calculate the area between the scores, which is 0.0483 in this case, by finding the area between each score and the mean in the z-score table and then subtracting the smaller area from the larger area.

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Answer:

6 remainder 8

Step-by-step explanation:

It is 7 times can 53 go into 326 by using long division method.

To find the how many times can 53 go into 326.

We use long division method,

by long division method we divide 326 by 53,

326 ÷ 53 = 6.150.

Therefore, appropriate 7 times can 53 go into 326

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The \(17th\) term of the arithmetic sequence is \(81\)

An arithmetic sequence is a sequence of numbers produced by adding a fixed number, called the common difference, to a term in the sequence to get the next term of the sequence.

The formula for calculating the \(nth\) term of a sequence is

\(a_n=a_1+(n-1)d\)

where

\(a_n=\text{the nth term}\\a_1=\text{the first term}\\d=\text{the common difference}\)

from the question

\(n=17\\d=5\\a_1=1\)

from this information, we can calculate the \(17th\) term of the sequence thus

\(a_n=a_1+(n-1)d\\a_{17}=1+(17-1)\times5\\=81\)

so, \(a_n=81\)

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The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

To find out how long each sprinkler was used, we can set up a system of equations. Let's say the Alexander family used their sprinkler for x hours, and the Chen family used their sprinkler for y hours.

From the given information, we know that the water output rate for the Alexander family's sprinkler is 30 liters per hour. Therefore, the total water output from their sprinkler is 30x liters.

Similarly, the water output rate for the Chen family's sprinkler is 40 liters per hour, resulting in a total water output of 40y liters.

Since the combined total water output from both sprinklers is 2250 liters, we can set up the equation 30x + 40y = 2250.

We also know that the families used their sprinklers for a combined total of 65 hours, so we can set up the equation x + y = 65.

Now we can solve this system of equations to find the values of x and y, which represent the number of hours each sprinkler was used.

By solving the equation we get,

The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

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Answer:

3360 quarts in 48 hours and also the rate per day is 1680 quarts

Step-by-step explanation:

Answer: Monomial, binomial,trimonial,  polynomials

Step-by-step explanation:

a) it takes 9.61 seconds for the automobile to overtake the truck. b) The automobile was initially 165.34 meters behind the truck. c) During the overtaking, the speed of the truck is 21.142 m/s, and the speed of the automobile is 33.635 m/s.

To solve this problem, we can use the equations of motion to calculate the time it takes for the automobile to overtake the truck, the initial distance between them, and their speeds during the overtaking.

Let's denote the time it takes for the automobile to overtake the truck as t.

(a) For the truck:

Using the equation of motion s = ut + (1/2)a\(t^{2}\), where s is the distance covered, u is the initial velocity (0 in this case), a is the acceleration (2.2 m/s^2), and t is the time, we can find the distance covered by the truck when the automobile overtakes it.

s_truck = (1/2) * 2.2 * \(t^{2}\)

s_truck = 1.1 *  \(t^{2}\)

For the automobile:

s_automobile = (1/2) * 3.5 * \(t^{2}\)

s_automobile = 1.75 *  \(t^{2}\)

Given that the truck has moved 60 m when the automobile overtakes it, we can set up the equation:

s_truck = s_automobile + 60

1.1 *  \(t^{2}\)  = 1.75 *  \(t^{2}\)  + 60

Simplifying the equation:

0.65 *  \(t^{2}\)  = 60

\(t^{2}\)  = 60 / 0.65

\(t^{2}\)  ≈ 92.3077

t ≈ √92.3077

t ≈ 9.61 seconds

Therefore, it takes approximately 9.61 seconds for the automobile to overtake the truck.

(b) To find the initial distance between the automobile and the truck, we can substitute the value of t into either of the equations:

s_automobile = (1/2) * 3.5 *  \(t^{2}\)

s_automobile = (1/2) * 3.5 * \((9.61)^{2}\)

s_automobile ≈ 165.34 meters

Therefore, the automobile was initially approximately 165.34 meters behind the truck.

(c) To find the speeds of the automobile and the truck during overtaking, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity (0 in this case), a is the acceleration, and t is the time.

For the truck:

v_truck = 0 + 2.2 * 9.61

v_truck ≈ 21.142 m/s

For the automobile:

v_automobile = 0 + 3.5 * 9.61

v_automobile ≈ 33.635 m/s

Therefore, during the overtaking, the speed of the truck is approximately 21.142 m/s, and the speed of the automobile is approximately 33.635 m/s.

Correct Question :

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. Then truck has a constant acceleration of 2.2 m/s2 and the automobile has an acceleration of 3.5 m/s 2. The automobile overtakes the truck when it (truck) has moved 60 m.

(a) How much time does it take to automobile to overtake the truck?

(b) How far was the automobile behind the truck initially?

(c) What is the speed of each during overtaking?

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Answer: 90

Step-by-step explanation: The mean of a data set is equal to the

sum of the set of numbers divided by how many numbers are in the set.

So to find the mean of the data set

shown here, begin by adding the numbers.

Adding the numbers, we get 720.

This will be divided by the number of numbers in the set, or 8.

So we have 720/8 or 90.

So the mean of the data set shown here is 90.

(a) F2(t)/F2(t) is not Galois because it is not a separable extension.

(b)  F1(Ft)/F4(t) is a separable extension of fields and hence Galois.

(c)  F2n (t)/F2n (t) is Galois if and only if n + 1 is finite, i.e., n < ∞.

(a) F2(t)/F2(t) is not Galois because it is not a separable extension. This is because its derivative is 0, meaning that it has a repeated root. Therefore, it does not satisfy the conditions for a Galois extension.

(b) To prove that F1(Ft)/F4(t) is Galois, we need to show that it is both normal and separable.

Normality is straightforward since F1(Ft) is a splitting field over F4(t).

To show that it is separable, we note that the extension is generated by a single element, t, and this element has distinct roots in any algebraic closure of F4.

Therefore, F1(Ft)/F4(t) is a separable extension of fields and hence Galois.

(c) F2n (t)/F2n (t) is Galois if and only if its Galois group is isomorphic to the group of automorphisms of the extension. The Galois group is isomorphic to the group of invertible matrices of size n over F2, which is the general linear group GL(n, F2).GL(n, F2) is a finite group, and hence the extension is Galois if and only if its degree is finite.

The degree of the extension is the dimension of F2n (t) as a vector space over F2n.

This is equal to n + 1, and hence F2n (t)/F2n (t) is Galois if and only if n + 1 is finite, i.e., n < ∞.

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9514 1404 393

Answer:

  3.347 N

Step-by-step explanation:

The vertical component of the dragging force is (120 N)/√2, so the net downward force is the difference between that due to gravity and the upward component of the dragging force.

  (9.8 m/s²)(9 kg) -(120 N)/√2 = 3.347 N

The normal force acting on the log is 3.347 N.

Everything is graphed out and labeled here for ya!

The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°.

By Euclidean geometry we know that squares are quadrilaterals with four sides of equal length and four right angles and triangles are equilateral when its three sides have equal length and three angles with a measure of 60°. In addition, a complete revolution has a measure of 360°.

Finally, we must solve the following equation for the angle QUP:

m∠QUR + m∠QUP + m∠PUT + m∠RUT = 360

60 + m∠QUP + 60 + 90 = 360

m∠QUP + 210 = 360

m∠QUP = 150

The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°. \(\blacksquare\)

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Answer:

Area = B x H + L (sum of sides of triangle)

        = 9 x 12 + 10 (12 + 15 + 9)

        = 108 + 360

        =\(468in^2\)

Either your options are wrong or question is to find lateral surface.

Lateral Surface area = ( a + b + c) x H , where a, b , c are sides of the triangle.

Lateral Surface Area = (12 + 15 + 9) x 10

                                =\(360in^2\)                    

Answer:

The function that best models the given data is;

B. h(t) = -6.73·t² + 14.19·t + 0.83

Step-by-step explanation:

The data in the given table is presented as follows

\(\begin{array}{cccccc}Time, \, t(s)&0&0.5& 1.0 & 1.5& 2.0\\Height, \, h \, (m) & 1.0 & 5.42 & 9.71 & 5.9 & 2.6\end{array}\)

Where;

Time, t(s) is the independent variable

Height, h(m) is the dependent variable

Therefore, we have;

When t = 0, h = 1.0

From the given functions, we have the following table of the result of the function generated with Microsoft Excel

\(\begin{array}{cccccc}\\t & h & A & B & C& D\\0 & 1.0 & 1.22 & 0.83& 0.83& 1.22\\0.5 & 5.42 & 5.26 & 6.2425 & 9.6075 & 10.17\\1 & 9.71 & 4.39 & 8.79 & 21.75 & 24.03 \\ 1.5 & 5.9 & -1.39& 6.9725& 37.2575 &42.8\\2& 2.6 & -12.08 & 2.29 & 56.13 & 66.48\end{array}\)

By comparison, the function that nest models the given data is the function 'B', given as follows;

h(t) = -6.73·t² + 14.19·t + 0.83.

Answer:

Apothem:

radius is the same length as the base/length of each side of the hexagon.

r = 8

use pythagorean theorem to calculate the apothem

\(4^2+a^2=8^2\\\\16+a^2=64\\\\a^2=48\\\\a= 6.928\)

≈ 6.9

Area

\(A = \frac{3\sqrt{3} }{2} *a^2\\\\=\frac{3\sqrt{3} }{2}(6.928)^2\\\\=124.7\)