Pascal wants to find the sum of the measures of the interior angles of a polygon that has n sides. How could he do this?

Answer:  The filled truth table for p ∨ q is shown below.

Step-by-step explanation:  We are given to fill the truth table for the p ∨ q.

We know that

If any one of p or q is true, then  p ∨ q is also true. And it is false, only when both p and q are false.

The filled truth table is as follows :

p                  q                     p ∨ q

T                  T                        T

T                  F                        T

F                  T                        T

F                  F                        F

Thus, a0 = T, a1 = T, a2 = T  and  a3 = F.

O stands for Offer another idea.

Option B is the correct answer.

Abbreviations are shortened versions of words or phrases that are commonly used in written or spoken language.

They are created by taking the first letter (or sometimes multiple letters) of each word in a phrase and using them to form a shorter, more compact version of the phrase.

For example:

"ASAP" is an abbreviation for "as soon as possible" and "FYI" is an abbreviation for "for your information".

Abbreviations are often used to save time and space in writing and are common in fields such as science, medicine, and technology where complex terms and phrases are frequently used.

We have,

The "O" in the S.T.O.P. method of refusal stands for "Offer another idea."

Thus,

O stands for Offer another idea.

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Answer: 825.

Step-by-step explanation:

Answer:

The total cost of the meal, rounded to the nearest cent, is approximately $82.30.

Explanation:

First, let's calculate the discount amount:

Discount = 15% of $78.38

         = 0.15 * 78.38

         ≈ $11.76

Now, let's find the discounted meal cost:

Discounted meal cost = Original meal cost - Discount

                    = $78.38 - $11.76

                    ≈ $66.62

Next, let's calculate the tip amount based on the original meal cost:

Tip = 20% of $78.38

   = 0.20 * 78.38

   ≈ $15.68

Now, let's find the total cost of the meal, including the discounted amount and the tip:

Total cost = Discounted meal cost + Tip

          ≈ $66.62 + $15.68

          ≈ $82.30

So, the total cost of the meal, rounded to the nearest cent, is approximately $82.30.

Final answer:

During the power stage of a four-cycle gas engine, both the intake and exhaust valves are closed, allowing the air-fuel mixture to expand and exert force on the piston, converting fuel's chemical energy into mechanical work.

Explanation:

The question concerns the position of the intake and exhaust valves during the power stage of a four-cycle gas engine, specifically within the context of the Otto cycle. During the power stroke, the intake valves are closed to allow the air-fuel mixture, which was ignited at the beginning of this stage, to expand without escaping. Meanwhile, the exhaust valves also remain closed to ensure that the expanding gases exert maximum force on the piston, driving it down.

This process converts the chemical potential energy of the fuel into mechanical work. The exhaust valve opens only after the completion of the power stroke, during the exhaust stage, to expel the combustion products and prepare the engine for the next cycle.

Answer:  Affect extremely.

Step-by-step explanation:

When a data set contains extreme values also known as outliers , then mean gets affected extremely.

For example : We have a data set with values : 1 , 2, 1,2,1, 2, 12

Here , 12 is much larger than the rest of the data values.

Mean of data : [tex]\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]

[tex]=\dfrac{1 +2+ 1+2+1+2+12}{8}=\dfrac{21}{8}=2.625[/tex]

Mean excluding outlier :

[tex]=\dfrac{1 +2+1+2+1+2}{7}=\dfrac{9}{7}=1.28571428571\approx1.29[/tex]

We can see that with outlier the mean is way higher than the mean of the rest of the values.

Hence, When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will get affected.

Answer: +2

Step-by-step explanation: When you're doing a problem like [tex]\frac{12}{2 + 4}[/tex], it's important to understand that a division bar has the same effect on a problem as a set of parentheses in that it groups terms together.

So this 2 + 4 can be thought of as being inside a set of parentheses just like it is in the original problem. Remember from your order of operations that before you do anything else, you must simplify what's inside the set of parentheses.

So the first thing we do here is add 2 + 4 to get 6 and this problem simplifies to [tex]\frac{12}{6}[/tex]. Now we can divide 12 by 6 which gives us +2.

For 99% confidence level, the interval will be (0.4582, 0.5818).

It can be interpreted as "45.82% to 58.18% of US adult will get information from twitter with a confidence of 99%".

Given information:

52% or 0.52 fraction of US adult twitter users get at least some news on twitter. It is the sample population in fractions.

The standard error is 2.4% or 0.024 fraction.

Normal distribution may be used to model the sample proportion.

Now, for 99% confidence level, the interval for the fraction of US adult who get some news on twitter will be,

[tex]I=\texttt{sample population}\pm 2.575\times \texttt{standard error}\\I=0.52\pm 2.575\times0.024\\I=0.52\pm 0.0618\\I=(0.4582, 0.5818)[/tex]

Therefore, for 99% confidence level, the interval will be (0.4582, 0.5818).

It can be interpreted as "45.82% to 58.18% of US adult will get information from twitter with a confidence of 99%".

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The rate of return built into the annuity is approximately 4.38%, calculated using the present value formula and solving for [tex]\( r \).[/tex]

To determine the rate of return built into the annuity, we set the present value of the annuity equal to the lump sum option.

The present value formula for an annuity is used, equating the lump sum amount of $13,800,000 to the present value of the annuity.

The formula is:

[tex]\[ 13,800,000 = 1,050,000 \times \frac{1 - (1 + r)^{-20}}{r} \][/tex]

Solving this equation for [tex]\( r \)[/tex], the annual interest rate (rate of return), requires numerical methods or a financial calculator.

Using trial and error or a financial calculator, we find that [tex]\( r \)[/tex] is approximately 4.38%.

This implies that the annuity offers a rate of return of 4.38% per year over the 20-year period, making it equivalent to receiving $13,800,000 today. Thus, the correct answer is option (b) 4.38%.

The problem primarily involves the calculation and understanding of the concepts of perimeter and area in Mathematics. Given the length is 3 ft longer than the width, and the perimeter of the rectangle is 26 feet, first, we find that the width is 5 feet and the length is 8 feet. The area is thus, 40 square feet.

To solve this problem, we need to understand the formula for the perimeter of a rectangle, which is 2l + 2w, where 'l' stands for length and 'w' for width. Also, the area of a rectangle is calculated by l*w. The problem states that the length is 3 ft longer than the width and that the perimeter is 26 feet. Firstly, we can express the length as 'w + 3' and substitute into the perimeter formula:

2(w + 3) + 2w = 26

After simplifying, we get the width equals to 5 feet. Substituting 5 for width, we get the length as 8 feet, because length is 3 feet longer than the width. Then, the area of the rectangle can be calculated by multiplying the width by the length:

Area = l * w = 8 ft * 5 ft = 40 square feet

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x = number of pounds

5x<30

x<30/5

 so she can buy X<6 pounds

Answer:

The possible numbers of pounds she will buy is less than 6.

Step-by-step explanation:

Given : Donna buys candy that costs $5 per pound. She will spend less than $30 on candy.

To find : What are the possible numbers of pounds she will buy?

Solution :

Let x be the number of pounds.

Donna buys candy that costs $5 per pound.

i.e. cost of x candy is $5x.

She will spend less than $30 on candy.

i.e. [tex]5x<30[/tex]

Solve the inequality,

[tex]x<\frac{30}{5}[/tex]

[tex]x<6[/tex]

The possible numbers of pounds she will buy is less than 6.

The equations we can create is based from this equation:

time = volume of pool / rate

Drain A: time = 108 gal / (2 gal / min) = 54 min

Drain B: time = 108 gal / (5 gal / min) = 21.6 min

Answer: 9 times

Step-by-step explanation:

Let the total number students be x.

Then the number of students liked cookies and cream = 18% of x= 0.18 x

The number of strawberry = 2% of x = 0.02 x

Clearly, 0.18 x> 0.02 x

The number of times more students prefer cookies and cream than prefer strawberry =[tex]=\frac{0.18x}{0.02x}=9[/tex]

Hence, The students prefer 9 times cookies and cream than prefer strawberry.

To solve this problem, we have to use the formula:

P = 1 - e^(-λx)

where λ = 0.01382, and x is the  distance

A. when x = 100

(P < or equal to 100) = 1 - e^(-0.01382 * 100)

(P < or equal to 100) = 0.75 

B. when x = 200
(P < or equal to 200) = 1 - e^(-0.01382 * 200)
(P < or equal to 200) = 0.94

C. when 100 < x < 200
P (100 < x < 200) = P ((x < 100) + P(x > 200)) 
P (100 < x < 200) = 0.75 + (1 – 0.94)

P (100 < x < 200) = 0.81 

Final answer:

The probabilities for a banner-tailed kangaroo rat to move at most 100 m, at most 200 m, and between 100 and 200 m are 0.7487, 0.9389, and 0.1903 respectively, when rounded to four decimal places.

Explanation:

The question deals with exponential distribution, which is a type of continuous probability distribution often used to model the time or space between events in a Poisson process. Given that the parameter λ (lambda) for the banner-tailed kangaroo rats is 0.01382, the mean (μ) can be calculated as the reciprocal of λ, so μ = 1/λ. In this case, μ = 1/0.01382. The cumulative distribution function (CDF) for an exponential distribution is  [tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex]

To find the probability that the distance is at most 100 m, we use the CDF:

[tex]P(X \leq 100) = 1 - e^{-(0.01382)(100)} = 1 - e^{-1.382} \approx 1 - 0.25132 = 0.74868[/tex]

For the distance at most 200 m:

[tex]P(X \leq 200) = 1 - e^{-(0.01382)(200)} = 1 - e^{-2.764} \approx 0.93894[/tex]

To find the probability that the distance is between 100 m and 200 m, we subtract the probability of being at most 100 m from the probability of being at most 200 m:

P(100 < X ≤ 200) = P(X ≤ 200) - P(X ≤ 100) = 0.93894 - 0.74868 = 0.19026

So, the probabilities are approximately 0.7487 for at most 100 m, 0.9389 for at most 200 m, and 0.1903 for between 100 and 200 m, when rounded to four decimal places.

Final answer:

Pascal's Triangle demonstrates a pattern where the second term in each row relates to the row number raised to a specific power, with the power increasing by one as you move down the rows.

Explanation:

Pascal's Triangle is a mathematical concept that shows a triangular array of binomial coefficients. Each number in the triangle is the sum of the two directly above it.

The relationship between the row number and the second term in each row is that the second term in each row corresponds to the row number raised to the power of 1. For example, in the 3rd row, the second term is the row number (3) raised to the power of 1, which is 3.

As you move down the rows of Pascal's Triangle, the power to which you raise the row number to get the second term of each row increases by one. This pattern continues throughout the triangle.

Penny can arrange the 25 dimes into three piles in 6 different ways.

Penny has 25 dimes and wants to arrange them into three piles, with an odd number of dimes in each pile. In order to do this, let's consider the possible combinations:

Possible combinations:
1. Pile A: 1 dime, Pile B: 1 dime, Pile C: 23 dimes
2. Pile A: 1 dime, Pile B: 3 dimes, Pile C: 21 dimes
3. Pile A: 1 dime, Pile B: 5 dimes, Pile C: 19 dimes
4. Pile A: 1 dime, Pile B: 7 dimes, Pile C: 17 dimes
5. Pile A: 1 dime, Pile B: 9 dimes, Pile C: 15 dimes
6. Pile A: 1 dime, Pile B: 11 dimes, Pile C: 13 dimes

Therefore, Penny can arrange the dimes into three piles in 6 different ways.

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