The sum of three consecutive integers is 267. What is the largest integer?

Compression ratio of an ideal autocycle using air as the working fluid = 8  Minimum temperature, T1 = 300 K; maximum temperature, T3 = 1340 K

(a) Heat transfer amount to air during the heating process: The heat transfer amount during the heating process, Qh is given by,Qh = Cp(T3 - T2)Where Cp is the specific heat capacity at constant pressure and T2 is the temperature at the end of the compression stroke. We know that, Compression ratio, r = V1/V2 ...(1)Where V1 and V2 are the volumes of air at the beginning and end of the compression stroke, respectively.In an ideal autocycle, we haveV1/T1 = V2/T2 = V3/T3 ...(2)Where V3 is the volume at the end of the expansion stroke.Substituting the value of V1/V2 from equation (1) in equation (2), we have,T2/T1 = 1/r => T2 = T1/r = 300/8 = 37.5 KAlso, T4/T3 = 1/r => T4 = T3r = 1340 × 8 = 10,720 KFrom the first law of thermodynamics, we have,Qh = Ql + W ...(3)Where Ql is the heat transfer amount during the cooling process, and W is the work done.We know that,W = Cv(T4 - T3) ...(4)

Where Cv is the specific heat capacity at constant volume.Substituting the values of Cp and Cv, we haveCp - Cv = R ...(5)Where R is the gas constant for air.Then,Qh = Cp(T3 - T2) = Cp(T3 - T4/r) ...(6)Ql = Cp(T2 - T1) = Cp(T2 - T1/r) ...(7)Substituting equations (5), (6), and (7) in equation (3), we getCp(T3 - T4/r) = Cp(T2 - T1/r) + R(T4 - T3)Cp(1340 - 1340/8) = Cp(37.5 - 300/8) + R(10,720 - 1340)Cp(1375) = Cp(74.375) + R(9380)Cp = 0.741 kJ/kg KThen,Qh = Cp(T3 - T4/r) = 0.741(1340 - 10,720/8) = 156.4 kJ/kg

(b) Thermal efficiency:The thermal efficiency of the cycle is given by,η = 1 - 1/r^(γ-1) ...(8)Where γ is the ratio of specific heats.Then,γ = Cp/Cv = 1 + 1/0.741 = 2.35Substituting the values of r and γ in equation (8), we getη = 1 - 1/8^(2.35 - 1) = 58.2%

(c) Thermal effect of the Carnot cycle operating in the same temperature range:For a Carnot cycle, the thermal efficiency is given by,ηc = 1 - T1/T3Substituting the values of T1 and T3, we getηc = 1 - 300/1340 = 77.6%Then, the thermal effect of the Carnot cycle is given by,Qc = ηcQh = 0.776 × 156.4 = 121.3 kJ/kgTherefore, the required answers are,(a) Heat transfer amount to air during the heating process = 156.4 kJ/kg(b) Thermal efficiency = 58.2%(c) Thermal effect of the Carnot cycle operating in the same temperature range = 121.3 kJ/kg.

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Answer:

Unit price of roast beef = $6.86

Step-by-step explanation:

Given:

Cost of \(1\frac{3}{4}\) pound package of roast beef = $12

Find:

Unit price of roast beef

Computation:

Unit price of roast beef  = Cost of 1 pound package of roast beef

\(1\frac{3}{4}\) pound package of roast beef = 7 / 4 = 1.75 pound package of roast beef

Cost of 1 pound package of roast beef = Total cost / Total mass

Cost of 1 pound package of roast beef = 12 / 1.75

Cost of 1 pound package of roast beef = 6.857

Unit price of roast beef = $6.86

The number of miles per gallon to the nearest tenth is; 50.9 miles per gallon

We are given;

Distance driven by Bill = 519 miles

Amount of gas in gallons used by Bill for that distance = 10.2 gallons

Thus;

Number of miles per gallon is gotten by dividing the number of miles by the number of gallons used. Thus;

Number of miles per gallon = 519/10.2

Number of miles per gallon = 50.9 miles per gallon

Thus we can conclude that the number of miles per gallon to the nearest tenth.

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Answer:  The correct answer is x = 19 / 5

Step-by-step explanation:

Solve the equation

5x + 3 = 22

Subtract 3 from both sides

5x + 3 − 3 = 22 − 3

5x = 19

Divide both sides by 5

5x/5 = 19/5

x = 19 / 5

The most responsible choice for Nick regarding his birthday money would be option C, which is to use all the money to pay down his credit card debt.

This is because credit card debt  generally comes with high- interest rates, and it can be  grueling  to pay off the debt if the interest keeps adding up. By using the$ 500 to pay down his credit card debt, Nick can reduce the  quantum he owes and, as a result, pay  lower interest in the long run.   Options A and D suggest  unyoking the  plutocrat between paying down debt and investing/ saving, which may not be the stylish choice given Nick's current  fiscal situation.

Option B suggests putting all the  plutocrat into a savings  regard with a lower interest rate, which would not be as effective in reducing his credit card debt. thus, option C is the most responsible choice for Nick.

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Answer:

Step-by-step explanation:

Hello

(fog)(x)=f(g(x))=10(x-6)/10+6=x-6+6=x

(gof)(x)=(10x-6+6)/10=10x/10=x

So YES the functions are inverse

hope this helps

The prediction of the value of the dependent variable outside the experimental region is called

extrapolation. So, the option(a) is right one.

A dependent variable is defined as the variable which is tested and measured in a scientific experiment. It is always depends on other variables. That's why it is called dependent variable and other variable is independent variable. Because it is a variable so it's value always change according to situation. So, there are two processes for predicting the values of dependent variable. These are defined as below :

Hence, the prediction of the value of the dependent variable outside the experimental region is known as extrapolation.

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Answer:

D

Step-by-step explanation:

Step 1(Base step) − It proves that a statement is true for the initial value.

Step 2(Inductive step) − It proves that if the statement is true for n=k, then it is also true for n=k+1.

Answer:
Just in simple words, brainless is basically a search engine but gives you answers easier and way quicker. You can use this to answer some questions of yours like math question or just anything. Also you can give answers to people who have  questions on certain topics.

Answer:

5.5 gallons

Step-by-step explanation:

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Answer:

9/40

Step-by-step explanation:

He needs 5/8, he already has 2/5, so still needed is 5/8-2/5.

To add or subtract fractions, the denominators must be equal.

Simplest approach is to multiply them. 8 times 5 is 40, so 40 is the new denominator we need for both fractions.

So first we convert 5/8 to 25/40.

Then we convert 2/5 to 16/40.

Now we can subtract them:

25/40 - 16/40 = 9/40.

9/40 cannot be simplified so this is the final answer.

There are some basic rules you need to know to work with fractions. If above work is too fast, comment below for deeper explanation.

The assumption of y being 1, it would take approximately 210.03 feet to stop a car going 100 mph.

To determine the stopping distance of a car going 100 mph, we can use the given equation d=0.03y^2 +2.1v, where d represents the stopping distance in feet and v represents the speed in mph.

Plugging in the value of v as 100 mph into the equation, we get:
d = 0.03y^2 + 2.1(100)
d = 0.03y^2 + 210

To find the value of d, we need to know the value of y, which represents the friction between the tires and the road. Unfortunately, the question does not provide this information. Hence, we cannot accurately determine the distance required to stop the car going 100 mph without knowing the value of y.

However, if we assume a reasonable value for y, we can calculate an approximate stopping distance. Let's say we assume y to be 1, then the equation becomes:
d = 0.03(1)^2 + 210
d = 0.03 + 210
d = 210.03

However, it's important to note that this value may vary depending on the actual value of y, which is not given.

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The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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Given information:The random variable X has a binomial distribution with n = 5 and p = 0.3.Want to find: The probability that X is less than or equal to 1 i.e. P(X ≤ 1).

Solution:Given, the random variable X has a binomial distribution with n = 5 and p = 0.3.The probability mass function (pmf) of the binomial distribution is given by\(;P(X = x) = nCx * p^x * (1-p)^(n-x),\) where;n = 5, the number of trials.p = 0.3, the probability of success.x = 0, 1, 2, 3, 4 and 5.

The required probability is to find P(X ≤ 1).P(X ≤ 1) = P(X = 0) + P(X = 1)Putting the values;\(P(X = 0) = 5C0 * 0.3^0 * 0.7^5= 0.16807 P(X = 1) = 5C1 * 0.3^1 * 0.7^4= 0.36015 Therefore, P(X ≤ 1) = P(X = 0) + P(X = 1)= 0.16807 + 0.36015= 0.52822\)Therefore, the probability that X is less than or equal to 1 i.e. P(X ≤ 1) is 0.52822 (approx) when n = 5 and p = 0.3.

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As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

If there is a low supply and a high demand, there is an increase in price and vice versa.

Last 2012, there was a virus which infected millions of chicken. It was known as Avian influenza or bird flu. It resulted to scarcity of eggs.

As the law of supply and demand states, there is an effect on the price of a product depending on its availability.

For example we can use water. If a product becomes scarce its price would increase due to supply in demand.

If drinkable water became scarce its price would be greatly increased to its need and being in extreme demand.

In short,  if there is a low supply and a high demand, there is an increase in price and vice versa.

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If the radius of the semi-circle is 38 m. Then the area of the training field will be 11,908.459 square meters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 97 m long and 76 m wide.

Then the radius of the semi-circle will be

2r = 76

 r = 38 m

Then the area of the training field will be

Area = area of rectangle + 2 x area of semi-circle

Area = 97 x 76 + 2 x (1/2) x π x 38²

Area = 7372 + 4536.459

Area = 11908.459 square m

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Answer:

y = 2.95 * x (it has to be 20 characters, but the answer is shorter than that)

Answer:

The answer would be 50.

Step-by-step explanation:

The fraction, David used 13/8 cups of blueberries for the pancakes.

Let's solve it step-by-step using the given information.

1. David has 3 1/2 cups of blueberries.
2. He uses 1/4 cup for a breakfast smoothie.
3. He uses 1/2 of the remaining blueberries for pancakes.

Step 1: Calculate the remaining blueberries after making the smoothie.
3 1/2 - 1/4 = (7/2) - (1/4)

To subtract the fractions, they need a common denominator, which in this case is 4.

(7/2) * (2/2) - (1/4) = (14/4) - (1/4) = 13/4 cups

Step 2: Calculate the amount of blueberries used for the pancakes.
David uses 1/2 of the remaining blueberries for the pancakes, so:

(13/4) * (1/2) = 13/8 cups

David uses 13/8 cups of blueberries for the pancakes.

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If you apply the law of detachment to the conditional "if you have a square, then you have a rectangle," you can conclude that if you have a square, you must also have a rectangle.

This is because the law of detachment states that if a conditional statement is true and the antecedent (the "if" clause) is also true, then the consequent (the "then" clause) must also be true.

In this case, the conditional "if you have a square, then you have a rectangle" is true because all squares are rectangles (since a rectangle is defined as a geometric figure with four straight sides and four right angles). Therefore, if you have a square, you can conclude that you also have a rectangle.

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Answer:

360°

Step-by-step explanation:

The sum of the exterior angles of any polygon = 360°

The price of a 1940 movie ticket in today's dollars, which was option (e) $4.64.

To determine the price of a 1940 movie ticket in today's dollars, we need to adjust the price using the CPI. The CPI in 1940 was 14, while the CPI today is 260. The formula for adjusting the price for inflation is:

Adjusted Price = Price in Year T1 x CPI in Year T2 / CPI in Year T1

Where T1 is the base year and T2 is the target year.

In this case, the base year is 1940, and the target year is today. Therefore, we can calculate the adjusted price of the 1940 movie ticket as follows:

Adjusted Price = $0.25 x 260 / 14

Adjusted Price = $4.64

Therefore, the price of a 1940 movie ticket in today's dollars is $4.64.

Then the correct option is (e).

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Answer:

Last one is correct

Step-by-step explanation:

Answer:

R'=(-3,6)

Q'=(-3,-3)

S'=(7,6)

T'=(7,-3)

Answer:

see explanation

Step-by-step explanation:

A translation of 7 units right means adding 7 to the x- coordinate. The y- coordinate remains unchanged, then

Q (- 10, - 3 ) → Q' (- 10 + 7, - 3 ) → Q' (- 3, - 3 )

R (- 10, 6 ) → R' (- 10 + 7, 6 ) → R' (- 3, 6 )

S (0, 6 ) → S' (0 + 7, 6 ) → S' (7, 6 )

T (0, - 3 ) → T' (0 + 7, - 3 ) → T' (7, - 3 )

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

I think B, but not sure.......

Step-by-step explanation:

Answer:

The solution will be "x = 2 and x = -1".

Step-by-step explanation:

The given equation is:

⇒  \(2^{2x+2}\times 5^{x-1}=8^x\times 5^{2x}\)

On solving "\(8^x\)", we get

⇒  \(2^{2x+2}\times 5^{x-1}=(2^3)^x\times 5^{2x}\)

As we know, if the base are same then their powers will be added together.

⇒  \(2x+2=3x\) ...(equation 1)

⇒  \(x-1=2x\) ...(equation 2)

From equation 1, we get

⇒  \(2=3x-2x\)

⇒  \(2=x \ i.e., x =2\)

From equation 2, we get

⇒  \(-1=2x-x\)

⇒  \(-1=x \ i.e., x=-1\)

So that the correct answer will be "x = 2" and "x = -1".

Let h be height of building

then In ΔABC

AB/BC =tan60degree

h/100 = root 3

h= 100 root 3

PLEASE MARK BRAINLIST!!

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The required angle of elevation of the building is 16.7°.

Given that,
what is the angle of elevation to a building 1000 m away that is 300 m high is to be determined.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
The angle of the elevation is given as,
TanФ = 300/1000
Ф = tan⁻¹(3/10)
Ф = 16.7°

Thus, the required angle of elevation of the building is 16.7°.

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