Dean has worn a white shirt on 6 of the last 18 days. What is the experimental probability that Dean will wear a white shirt tomorrow?
Write your answer as a fraction or whole number.

Using the 18 rules of inference to derive the conclusion of the following symbolized argument is G ⊃ (A · L)

In order to derive the conclusion using the 18 rules of inference, we can follow these steps:

Start with the premises:

G ⊃ A

G ⊃ L

Apply the rule of hypothetical syllogism (HS) to premises 1 and 2:

3. G ⊃ (A · L)

Therefore, the conclusion of the given argument is G ⊃ (A · L).

In conclusion, using the 18 rules of inference to derive the conclusion of the following symbolized argument is G ⊃ (A · L).

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Using the 18 rules of inference, we can derive the conclusion of the symbolized argument: 1) G ⊃ A, 2) G ⊃ L / G ⊃ (A · L).

To derive the conclusion G ⊃ (A · L) from the premises G ⊃ A and G ⊃ L, we can utilize the rules of inference.

Assume G (Assumption),

Apply Modus Ponens to premise 1 and assumption G: A.

Apply Modus Ponens to premise 2 and assumption G: L.

Apply Conjunction Introduction to A and L: (A · L).

Apply Conditional Introduction to the assumption G and the derived (A · L): G ⊃ (A · L).

By utilizing the rules of inference, we have successfully derived the conclusion G ⊃ (A · L) from the given premises G ⊃ A and G ⊃ L. This demonstrates the logical validity of the argument, showing that the conclusion follows from the premises using valid reasoning.

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2, 12, 72, 432, 2592..-3, -12, -48, -192, -768..2, 4, 16, 256, 65536..1, 2, 7, 23, 76..1, 1, 4, 36, 1152..1, 2, 0, 3, 6

(1) For the sequence defined by the recurrence relation an = 6an−1, with a0 = 2, the first five terms are: a0 = 2, a1 = 6a0 = 12, a2 = 6a1 = 72, a3 = 6a2 = 432, a4 = 6a3 = 2592.

(2) For the sequence defined by the recurrence relation an = 2nan−1, with a0 = -3, the first five terms are: a0 = -3, a1 = 2na0 = 6, a2 = 2na1 = 24, a3 = 2na2 = 96, a4 = 2na3 = 384.

(3) For the sequence defined by the recurrence relation an = a^2n−1, with a1 = 2, the first five terms are: a1 = 2, a2 = a^2a1 = 4, a3 = a^2a2 = 16, a4 = a^2a3 = 256, a5 = a^2a4 = 65536.

(4) For the sequence defined by the recurrence relation an = an−1 + 3an−2, with a0 = 1 and a1 = 2, the first five terms are: a0 = 1, a1 = 2, a2 = a1 + 3a0 = 5, a3 = a2 + 3a1 = 17, a4 = a3 + 3a2 = 56.

(5) For the sequence defined by the recurrence relation an = nan−1 + n^2an−2, with a0 = 1 and a1 = 1, the first five terms are: a0 = 1, a1 = 1, a2 = 2a1 + 2a0 = 4, a3 = 3a2 + 3^2a1 = 33, a4 = 4a3 + 4^2a2 = 416.

(6) For the sequence defined by the recurrence relation an = an−1 + an−3, with a0 = 1, a1 = 2, and a2 = 0, the first five terms are: a0 = 1, a1 = 2, a2 = 0, a3 = a2 + a0 = 1, a4 = a3 + a1 = 3.

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Step-by-step explanation:

hope it helps.

Answer:

x = 30, 150, 210, 330 degrees.

Step-by-step explanation:

(sin x)^2 = 1/4

sin x = +/- √1/4

sin x = +/- /2

In the first quadrant  x =  angle whose sine is 1/2 = 30 degrees.

There is also a solution in the other 3 quadrants.

In second quadrant  where sine = 1/2  , x = 180-30 = 150 degrees,

In 3rd and 4th where sine x = -1/2 the angles are 210 and 330 degrees.

Answer:8.24

Step-by-step explanation:

Answer:

2/15 or 0.13

Step-by-step explanation:

Answer:

0.13328

Step-by-step explanation:

it's easier to write in that form

Answer:

Option C represents an exponential function

Step-by-step explanation:

Generally, we have an exponential function in the form ;

y = a.b^x

Where in fact, a is not 0

In this case, let us have a as 1 and b as 2

So we have;

for x = -1

y = 2^-1 = 1/2

for x = 0

y = 2^0 = 1

for x = 1

y = 2^1 = 2

for x = 2

y = 2^2 = 4

So the correct choice here is the third option

The probability that less than or equal to 5 of the 10 independent customers will take more than 3 minutes to check out their groceries is approximately 0.9245.

To calculate this probability, we can use the binomial probability formula. Let's denote X as the number of customers taking more than 3 minutes to check out. We want to find P(X ≤ 5) when n = 10 (number of trials) and p (probability of success) is not given explicitly.

Step 1: Determine the probability of success (p).

Since the probability of each customer taking more than 3 minutes is not provided, we need to make an assumption or use historical data. Let's assume that the probability of a customer taking more than 3 minutes is 0.2.

Step 2: Calculate the probability of X ≤ 5.

Using the binomial probability formula, we can calculate the cumulative probability:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

P(X ≤ 5) = C(10, 0) * p^0 * (1 - p)^(10 - 0) + C(10, 1) * p^1 * (1 - p)^(10 - 1) + C(10, 2) * p^2 * (1 - p)^(10 - 2) + C(10, 3) * p^3 * (1 - p)^(10 - 3) + C(10, 4) * p^4 * (1 - p)^(10 - 4) + C(10, 5) * p^5 * (1 - p)^(10 - 5)

Substituting p = 0.2 into the formula and performing the calculations:

P(X ≤ 5) ≈ 0.1074 + 0.2686 + 0.3020 + 0.2013 + 0.0889 + 0.0246

P(X ≤ 5) ≈ 0.9928

Rounding this probability to the nearest hundredth/second decimal place, we get approximately 0.99. However, the question asks for the probability that less than or equal to 5 customers take more than 3 minutes, so we subtract the probability of all 10 customers taking more than 3 minutes from 1:

P(X ≤ 5) = 1 - P(X = 10)

P(X ≤ 5) ≈ 1 - 0.9928

P(X ≤ 5) ≈ 0.0072

Therefore, the probability that less than or equal to 5 customers out of 10 will take more than 3 minutes to check out their groceries is approximately 0.0072 or 0.72%.

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The general solution to the given differential equation, \(xy^2y' = 2x^3 + y^3\), can be expressed as y(x) = ±\((x^4/4 + C)^(1/3)\), where C is an arbitrary constant.

In the first paragraph, the general solution is summarized as y(x) = ±(x^4/4 + C)^(1/3), where C is an arbitrary constant.

To explain further, we can solve the differential equation step by step. Rearranging the equation, we have \(y^2y' = (2x^3 + y^3) / x\). Separating the variables, we get \(y^2 dy = (2x^3 + y^3) / x\)dx. Integrating both sides, we obtain the integral \(∫y^2 dy = ∫(2x^3 + y^3) / x dx\).

The integral on the left side can be solved as (1/3)y^3 + K1, where K1 is the constant of integration. The integral on the right side can be simplified as \(2∫x^2 dx + ∫y^3/x dx\). Evaluating the integrals, we get \((1/3)y^3 + K1\) = \((2/3)x^3 + ∫y^3/x dx + K2\), where K2 is another constant of integration.

Now, let's focus on evaluating the integral ∫y^3/x dx. This integral can be solved using a substitution or integration by parts. Once the integral is evaluated, we substitute it back into the equation. Simplifying the equation further, we arrive at \((1/3)y^3 - ∫y^3/x dx = (2/3)x^3 + C\), where C = K1 - K2 is the combined constant of integration.

Finally, solving for y(x), we have y(x) = \(±(3(2x^3 + C))^(1/3)\), which simplifies to y(x) = \(±(x^4/4 + C)^(1/3)\) after further simplification. Thus, the general solution to the given differential equation is y(x) =\(±(x^4/4 + C)^(1/3)\), where C is an arbitrary constant.

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The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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After answering the provided question, we can conclude that there are two possible outcomes for a homogeneous system of linear equations: either there are several solutions or there is only one, trivial solution.

A mathematical equation is a formula that joins two statements and indicates equality with the equal symbol (=). In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the relationship between the two sentences on either side of a letter. There is frequently only one variable, which also serves as the symbol. For example, 2x - 4 = 2.

For a homogeneous system of linear equations, there are two possible outcomes: either there are several solutions or there is just one, trivial solution. There are three possible outcomes for a non-homogeneous system: either there is only one (unique) solution, several solutions, or no solutions at all.

homogeneous system of linear equations example =  \(2x-3y=\\\) and \(-4x+6y=0\)

non-homogeneous system of linear equations example = \(4x-2y+6z=8\) and \(x+y-3z =\)\(-1\)

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9514 1404 393

Answer:

  (c)  31°

Step-by-step explanation:

Angles 1 and 2 are congruent. Each is half the sum of the subtended arcs:

  ∠1 = ∠2 = (37° +25°)/2 = 31°

Answer:

C. 31°

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

If you're asking for the probability that the coin is heads and the die is even. Hope this helps :)

1/3*1/2= 1/6

Answer:

The answer is 1/6

Step-by-step explanation:

This is because the dice has 6 sides so the possibility of getting a even is 1/6

The interval of convergence for the given power series is (2, 8).

To find the interval of convergence for the given power series. We have the power series:

∑(n=2 to ∞) ((x-5)ⁿ)/(3ⁿ)

To find the interval of convergence, we'll use the Ratio Test. For the Ratio Test, we need to compute the limit:

L = lim (n → ∞) |(a_(n+1)/a_n)|

For our series, a_n = ((x-5)ⁿ)/(3ⁿ). Therefore, a_(n+1) = ((x-5)(n+1))/(3(n+1)). Now, let's compute the ratio:

|(a_(n+1)/a_n)| = |(((x-5)(n+1))/(3(n+1))) / (((x-5)ⁿ)/(3ⁿ))|

Simplify the expression:

|(a_(n+1)/a_n)| = |(x-5)/3|

The series converges if L < 1. So we have:

|(x-5)/3| < 1

Now, we'll solve for x to find the interval of convergence:

-1 < (x-5)/3 < 1

Multiply each term by 3:

-3 < x-5 < 3

Add 5 to each term:

2 < x < 8

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Answer:

I believe it's true, but I'm not super sure.

Step-by-step explanation:

Eli is a loan officer. he determines his clients’ eligibility for loans and for good interest rates by using their credit scores, the evaluation of his applicants based on their mean and median credit scores will give Dirk the highest mean score, but Valerie has the highest median score.

Generally, The mean is computed by summing all of the scores and then dividing by the number of scores contributed.

In conclusion, with the given data  Roy 750 792 661 Dirk 771 707 755 Haley 643 642 770 Valerie 646 773 762, Dirk has the highest mean score, but Valerie has the highest median score.

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B1. the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.

B2. The bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.

B3. The probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.

B4. The probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.

B5. The bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.

B1. To find the percentage of time the bottle contains less than 36 oz when the machine is set at 37 oz, we need to calculate the probability that a random bottle will have a volume less than 36 oz.

Using the normal distribution, we can calculate the z-score (standardized score) for 36 oz using the formula:

z = (x - μ) / σ

where x is the desired value (36 oz), μ is the mean of the process (37 oz), and σ is the standard deviation (1.2 oz).

z = (36 - 37) / 1.2

z ≈ -0.833

Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.

P(X < 36) = P(Z < -0.833) ≈ 0.2033

Therefore, the bottle would contain less than 36 oz approximately 20.33% of the time when the machine is set at 37 oz.

B2. To find the percentage of time the bottles will overflow when the machine is set at 38 oz, we need to calculate the probability that a random bottle will have a volume greater than 40 oz.

Using the normal distribution, we can calculate the z-score for 40 oz using the formula mentioned earlier:

z = (x - μ) / σ

z = (40 - 38) / 1.2

z ≈ 1.67

Using a standard normal distribution table or a statistical calculator, we can find the cumulative probability associated with this z-score.

P(X > 40) = P(Z > 1.67) ≈ 0.0475

Therefore, the bottles will overflow approximately 4.75% of the time when the machine is set at 38 oz.

B3. To find the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz, we can use the complement rule and subtract the probability that none of the bottles overflow.

The probability of no overflow in a single bottle is given by:

P(X ≤ 38) = P(Z ≤ (38 - 38) / 1.2) = P(Z ≤ 0) ≈ 0.5

Therefore, the probability of no overflow in 10 bottles is:

P(no overflow in 10 bottles) = (0.5)¹⁰ ≈ 0.00098

The probability that at least one bottle will overflow is the complement of no overflow:

P(at least one overflow in 10 bottles) = 1 - P(no overflow in 10 bottles) ≈ 1 - 0.00098 ≈ 0.999

Therefore, the probability that at least one bottle will overflow out of 10 bottles filled when the machine is set at 38 oz is approximately 99.9%.

B4. To find the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz, we can use the binomial distribution formula:

P(X = k) = (nCk) * \(p^k * (1 - p)^{(n - k)\)

where n is the number of trials (15), k is the desired number of successes (3), p is the probability of success (probability of overflow), and (nCk) is the number of combinations.

Using the probability of overflow calculated in B2:

p = 0.0475

The number of combinations for selecting 3 out of 15 bottles is given by:

15C3 = 15! / (3! * (15 - 3)!) = 455

Plugging the values into the binomial distribution formula:

P(X = 3) = 455 * (0.0475)³ * (1 - 0.0475)¹² ≈ 0.250

Therefore, the probability that exactly 3 bottles will overflow out of 15 bottles filled when the machine is set at 38 oz is approximately 25.0%.

B5. To determine the required size of the bottle to avoid overflowing 99.8% of the time when the machine is set at 38 oz, we need to find the z-score corresponding to a cumulative probability of 0.998.

Using a standard normal distribution table or a statistical calculator, we find the z-score for a cumulative probability of 0.998 to be approximately 2.33.

Using the formula mentioned earlier:

z = (x - μ) / σ

Substituting the known values:

2.33 = (x - 38) / 1.2

Solving for x:

x - 38 = 2.33 * 1.2

x - 38 ≈ 2.796

x ≈ 40.796

Therefore, the bottle would need to be approximately 40.796 oz or larger to avoid overflowing 99.8% of the time when the machine is set at 38 oz.

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Answer:

∠ 2 = ∠ 4 = 83°

Step-by-step explanation:

∠ 2 and ∠ 5 are same- side interior angles and sum to 180° , that is

∠ 2 + 97° = 180° ( subtract 97° from both sides )

∠ 2 = 83°

∠ 2 and ∠ 4 are vertical angles and are congruent, then

∠ 4 = 83°

Answer:

.41 cents

Step-by-step explanation:

divide it by 6

Answer:

I think it is $0.41

As the degrees of freedom (DF) increase, the t distribution approaches the normal distribution. Therefore, the correct answer option is: C. normal distribution.

The degrees of freedom (DF) in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses because they are the maximum number of logically independent numerical values (data points) in the final calculation of a statistical problem.

A normal distribution is sometimes referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.

In this context, we can reasonably infer and logically deduce that the t-distribution generally approaches the normal distribution as the degrees of freedom (DF) increase.

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The length of the loan in months is 12 months.

To find the length of the loan in months, we first need to calculate the total amount of interest paid on the loan.
The formula for simple interest is:
Interest = Principal x Rate x Time
Where:
- Principal = $500
- Rate = 13% per year = 0.13
- Time = the length of the loan in years
We want to find the length of the loan in months, so we need to convert the interest rate and loan length accordingly.
First, let's calculate the interest paid:
Interest = $500 x 0.13 x Time
$65 = $500 x 0.13 x Time
Simplifying:
Time = $65 / ($500 x 0.13)
Time = 1.00 years
Now we need to convert 1 year into months:
12 months = 1 year
1 month = 1/12 year
So the length of the loan in months is:
Time = 1.00 years x 12 months/year
Time = 12 months
Therefore, the length of the loan in months is 12 months.

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Answer:

A im pretty sure :)

Step-by-step explanation:

Answer:

4/11

Step-by-step explanation:

7/11-3/11

=>(7-3)/11

=>4/11

The cumulative distribution function (CDF) for the given random variable is plotted. To find probabilities, we calculate P[X≤2], P[X=0], P[X<0], and P[2<X≤3] using the CDF formula and integrating the probability density function (PDF) in the corresponding ranges.

a. The CDF is defined as F_X(x) = 0 for x < 0 and F_X(x) = 1 - (1/4)e^(-2x) for x ≥ 0. Plotting the CDF will show a step function that starts at 0 for x < 0 and approaches 1 as x increases.

b. i. P[X≤2] can be calculated by substituting x = 2 into the CDF: P[X≤2] = F_X(2) = 1 - (1/4)e^(-2*2) = 1 - (1/4)e^(-4).

  ii. P[X=0] represents the probability of the random variable taking the value 0. Since the given CDF is continuous, P[X=0] = P[X≤0] - P[X<0] = F_X(0) - lim(x→0-)F_X(x) = 1 - 0 = 1.

  iii. P[X<0] can be calculated by substituting x = 0 into the CDF: P[X<0] = F_X(0) = 0.

  iv. P[2<X≤3] can be obtained by subtracting P[X≤2] from P[X≤3]: P[2<X≤3] = P[X≤3] - P[X≤2] = F_X(3) - F_X(2) = (1 - (1/4)e^(-2*3)) - (1 - (1/4)e^(-2*2)).

These calculations provide the probabilities based on the given CDF for the specified ranges of the random variable X.

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Answer:

144 is the second power of 12

Step-by-step explanation:

Here, we want to get the power of 12 that 144 is

Mathematically;

144 = 12^2

What this mean is that we have to raise 12 to 2 to get 144

Thus, our answer is that 144 is the 2nd power of 12

Solution :-

2x - 9y = -1

2x = 9y - 1

x = 9y - 1 / 2 _________ (1)

Now, substitute it here!

-4x - 3y = - 19

-4 (9y - 1 /2) - 3y = -19

(-36y + 4 - 6y / 2) = -19

(-42y + 4 / 2) = -19

-42y + 4 = -38

-42y = -38 - 4

-42y = -42

y = 1

Value of x :

Substituting the value of y that is 1 in this equation. x = 9y - 1 / 2

x = 9(1) - 1 / 2

x = 9 - 1 / 2

x = 8 / 2

x = 4

In metric conversion 17000 g is converted to kilograms as 17 kg.

7) We know that, 1 kg =1000 g

So, 17000 g = 17000/1000 = 17 kg

8) 18 kg = 18×1000 = 18000 g

9) 1 gram = 1000 mg

4,200 mg = 4200/1000

= 4.2 g

10) 0.276 g

= 0.276×1000 = 276 mg

11) 4.08 kg

= 4.08×1000

= 4080 g

12) 43 mg

= 43/1000

= 0.043 g

Therefore, in metric conversion 17000 g is converted to kilograms as 17 kg.

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