What are the 3 identities?

Answer:

72 square inches

Step-by-step explanation:

A = (1/2)Pa

A = (1/2)(2×8)(9)

A = (1/2)(16)(9) = (1/2)(144)

A = 72 square inches

Given the ODE using Frobenius Method x²y"+x²y¹-2y = 0The Frobenius method is used to obtain the power series solution of a differential equation of the form:

xy″+p(x)y′+q(x)y=0Which is given in your question as: x²y"+x²y¹-2y = 0The general form of the Frobenius solution can be expressed as a power series of the form:y(x)=x^r ∑_(n=0)^(∞) a_n x^n+rwhere 'r' is any arbitrary constant and the 'a_n' coefficients are determined from the recurrence relation.

The Frobenius method consists of substituting this power series into the differential equation and equating the coefficient of the same powers of x to zero. This method can be used to solve any second-order differential equation having a regular singular point.

Therefore, substituting the given equation we get:$$ x^2 y'' + x^2 y' - 2y = 0 $$Let the solution of the given equation be:y(x) = ∑_(n=0)^(∞) a_n x^(n + r)Substituting this in the differential equation, we get:$$ x^2y'' + x^2y' - 2y = \sum_{n=0}^\infty a_n [(n+r)(n+r-1)x^{n+r} + (n+r)x^{n+r} - 2x^{n+r}] $$Equating the coefficient of each power of x to zero, we get:Coefficients of x^(r):$$ r(r-1)a_0 = 0 \Rightarrow r=0,1 $$Coefficients of x^(r + 1):$$ (r+1)r a_1 + (r+1)a_1 - 2a_0 = 0 $$Taking r = 0, we get:a_1 - 2a_0 = 0a_1 = 2a_0

The solution becomes:y_1(x) = a_0 [1 + 2x]Taking r = 1, we get:$$ 6a_2 + 3a_1 - 2a_0 = 0 $$a_2 = (1/6) [2a_0 - 3a_1]Substituting the value of a_1 from above, we get:a_2 = a_0/3The second solution is given by:y_2(x) = a_0 [x^2/3 - 2x/3]Therefore, the required solution of the given ODE using Frobenius method is:y(x) = c_1 y_1(x) + c_2 y_2(x)y(x) = c_1 [1 + 2x] + c_2 [x^2/3 - 2x/3]

Hence, the second and third-degree Legendre polynomials generated and the solution of the given ODE using the Frobenius method is obtained above.

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A plane is also referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Also, two (2) planes intersect at a line.

Collinear points can be defined as three or more points that all lie on the same straight line (single line). Based on the geometric figures shown in the image above, the three collinear points include the following:

A plane should be named by using any three (3) non-collinear points that are located on the plane while making use of an uppercase script letter.

Based on the geometric figure shown in the image attached above, another name for plane W is plane ABC. Also, the intersection of plane ADE and plane W is line AD.

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Answer:

The angle between the two vectors

∝ = 64°

Step-by-step explanation:

Step(i):-

Given that the vectors

                           \(a^{-} = i^{-} - 2j^{-} +5k^{-}\)

          and

                         \(b^{-} = 3i^{-} +j^{-} -2k^{-}\)

\((a^{-} . b^{-} ) = (i^{-} - 2j^{-} +5k^{-} ) . (3 i^{-} + j^{-} - 2k^{-} )\)

           =  3 (i⁻ . i⁻) - 2(j⁻.j⁻) -10(k⁻.k⁻)

          = 3 - 2 -10

          = -9

Step(ii):-

Let '∝' be the angle between the two vectors

                    \(cos\alpha = \frac{a^{-}.b^{-} }{|a||b|}\)

                  \(cos\alpha = \frac{|-9| }{\sqrt{1+4+25}\sqrt{9+1+4} }\)

                 \(cos\alpha = \frac{|-9| }{\sqrt{30}\sqrt{14} }\)

               \(\alpha =cos^{-1} ( \frac{|-9| }{\sqrt{30}\sqrt{14} })\)

              ∝ = cos⁻¹(0.4392) = 63.947

Final answer:-

The angle between the two vectors

               ∝ = cos⁻¹(0.4392) = 63.947

                ∝ = 64°

Answer:

Three cups of oil will be needed

Step-by-step explanation:

Here, we are told that the recipe calls for a 3/4 of a cup of oil per serving

Thus for 2 2/3

What is needed will be 2 2/3 * 3/4

= 8/2 * 3/4 = 24/8 = 3

Answer:

4800 ft²

or

5280 ft²

Step-by-step explanation:

The deck is 48 inches by 4 inches in the drawing.

The scale is 60:1, so the real dimensions are 60 times greater than the drawing dimensions.

Let's calculate the real dimensions and also convert to feet from inches.

length = 48 in. × 60 × (1 ft)/(12 in.) = 240 ft

width = 4 in. × 60 × (1 ft)/(12 in.) = 20 ft

The real dimensions of the deck are 240 ft by 20 ft.

area = length × width

area = 240 ft × 20 ft = 4800 ft²

If the correct drawing width is really 4 2/5 in., then the real area is:

48 in. × 4 2/5 in. × 60 × 60 / 144 ft²/in.² = 5280 ft²

Answer:

$12$ km

Step-by-step explanation:

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The student 3's numeric grade percentage is 95.6%.

The final grade for the students is calculated based on the test scores and the class project score.

The test is worth 80% and the project is worth 20% of the grade. To calculate the final grade percentage, the individual percentages of test and project are computed, then added together.

The result cannot exceed 100%.Let us calculate the weighted test score for student 3.

There were three tests each worth 100 points. The scores of student 3 are 91, 78, and 83.

We have to add up the test scores; then divide by the total number of test points and then multiply by the weighted percentage.

The weighted test score is:(91+78+83)/300 * 80% = 76.6%

We can now calculate the percentage for the project. Student 3 received a grade of 95%.

Therefore, the percentage for the project is: 95% * 20% = 19%.

Now, we add the weighted test score to the weighted project score to find the final grade for student 3. 76.6% + 19% = 95.6%.

Therefore, The final grade of student 3 is 95.6%

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9514 1404 393

Answer:

  7x

Step-by-step explanation:

We can factor out x and simplify.

  4x +3x = x(4 +3) = 7x

The approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.019

We can use the normal distribution to approximate the probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average.

To do this, we have to standardize the variable by subtracting the mean and dividing by the standard deviation.

In this case, X = (50 - 37) / hours = 1.83

We know that for a standard normal distribution, the probability of X being less than a certain value can be found using a standard normal table or a calculator with a built-in standard normal cumulative distribution function (CDF).

Now, we will use the cumulative distribution function to find the probability of less than 10 out of 200 working more than 50 hours a week on average. Using a standard normal table or calculator, we can find the probability of having X < -2.04.

P(X < -2.04) = 0.0188

So the approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.0188 which rounding it off to the third decimal place we get 0.019.

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Elijah read: x

Harper read: x + 2 , then

Harper read 5 books this summer

Answer: A. = 37,38,39,41,43,47,52,54

Step-by-step explanation:

The numbers to the left represent the tens place, and each number on the right represents a different ones place value (according to key.)

Therefore, we find a chronological list of numbers, such as:

37,38,39,41,43,47,52,54

This list is the answer Choice of A.

Hope this Helped!

8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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Answer:

7.616

Step-by-step explanation:

Hope this helps.

Answer:

7.61

Step-by-step explanation:

Answer: \(\Large\boxed{y-1=\frac{4}{5} (x+2)}\)

Step-by-step explanation:

Given the requirement for function

Point-slope form : y - y₁ = m (x - x₁)

Given information

m = 4/5

Point = (x₁, y₁) = (-2, 1)

Substitute values into the function form

y - y₁ = m (x - x₁)

y - (1) = (4/5) (x - (-2))

Simplify the function

\(\Large\boxed{y-1=\frac{4}{5} (x+2)}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1/4x^2 + 7x + 49

Step-by-step explanation:

Use binomial theorem (a + b)^2 = a^2 + 2ab + b^2 to expand (1/2x + 7)^2

To show that T s(T, P) = (co + bT) - b(T - T.) (T - T.) 210,P(T - T.) - Avqap and that the reversible and adiabatic curves must appear cup-shaped in the T-P plane, we can follow the steps below:

1. Start with the definition of entropy change for an ideal gas: ds = C/T dT - R/T dP.

2. Since we are choosing s(To, 0) = 0 as the reference entropy, we can integrate the entropy change from To to T and 0 to P to get:
∫ds = ∫(C/T)dT - ∫(R/T)dP = ∫(C/T)dT - R ln(P/Po).
Here, Po is the reference pressure.

3. Integrating the first term gives us:
∫(C/T)dT = C ln(T/To).

4. Plugging this back into the equation, we have:
∫ds = C ln(T/To) - R ln(P/Po).

5. Now, we can rewrite the equation as:
s(T, P) - s(To, Po) = C ln(T/To) - R ln(P/Po).
Since we chose s(To, 0) = 0, s(To, Po) = 0 as well.

6. Simplifying the equation, we get:
s(T, P) = C ln(T/To) - R ln(P/Po).

7. Applying the ideal gas law, PV = nRT, we can express P in terms of T:
P = nRT/V.

8. Substituting this expression into the equation, we get:
s(T, P) = C ln(T/To) - R ln((nRT/V)/Po).

9. Rearranging the equation, we have:
s(T, P) = C ln(T/To) - R ln(nRT/V) + R ln(Po).

10. Recognizing that nR/V = c, where c is the heat capacity per unit volume, we can simplify the equation to:
s(T, P) = C ln(T/To) - R ln(cT) + R ln(Po).

11. Using the relation co = C - R ln(cT), we can rewrite the equation as:
s(T, P) = co + bT - b(T - To)ln(P/Po).
Here, b = R/c.

12. Finally, simplifying the equation, we get:
s(T, P) = (co + bT) - b(T - To)ln(P/Po).

13. The reversible and adiabatic curves in the T-P plane appear cup-shaped because the second term, b(T - To)ln(P/Po), has a negative coefficient (-b) for the temperature difference (T - To). As a result, the entropy change becomes negative as temperature decreases, leading to the cup-shaped curves.

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There is no statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis and value of p in which p-value = 0.5893.

H0: There is no difference in Mr. Goodman’s evaluations and the History Department’s

H- There is a significant difference between Mr. Goodman’s evaluations and the History Department’s

Applying the chi-square test:

            relative  observed  expected        residual                      Chisquare

Cat frequency(p) Oi        Ei=total x p  R2i=(Oi-Ei)/√Ei    R2i=(Oi-Ei)2/Ei

1's         0.100          11.000        12.500           -0.42                         0.180

2's        0.150         14.000         18.750           -1.10                         1.203

3's       0.340         47.000       42.500            0.69                       0.476

4's       0.410          53.000       51.250            0.24                         0.060

total     1.000         125              125                                               1.9196

Through the attached file as well as shown above we get the value of X2 equal to 1.9196.

Test statistic X2 = 1.9196.

P value through Chi-Square Distribution table = 0.5893

No, it can't be concluded that there is a statistically significant difference between Mr. Goodman’s evaluations and the History Department’s as we fail to reject the null hypothesis.

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

a.The probability that Xˉ is less than 49 is 0.0228.b.The probability that X is above 50.9 is 0.0359.c.The probability that X is above 50.9 is 0.0359.d.There is a 35% chance that Xˉ is above 50.01925.

a. What is the probability that Xˉ is less than 49 ?The given μ=50 and σ=5. We have a sample of n=100. The Central Limit Theorem states that the sampling distribution of the sample mean is normal, mean μ and standard deviation σ/sqrt(n).

So the mean of the sampling distribution of the sample mean is 50 and the standard deviation is 5/10=0.5. To find P( X <49) we need to standardize the variable.  z=(x-μ)/σz=(49-50)/0.5=-2P( X <49)= P(z < -2)P(z < -2)= 0.0228Therefore, the probability that Xˉ is less than 49 is 0.0228.

b.Using the mean of the sampling distribution of the sample mean 50 and the standard deviation 0.5, let’s calculate the standardized z-scores for 49 and 51.5. z1=(49-50)/0.5=-2 and z2=(51.5-50)/0.5=1P(49< X <51.5)=P(-250.9)= P(z > 1.8)P(z > 1.8)= 0.0359.

c.Therefore, the probability that X is above 50.9 is 0.0359.

d.We want to find the value of Xˉ such that P(Xˉ > x) = 0.35.Using the standard normal distribution table, the z-score that corresponds to 0.35 is 0.385. Therefore,0.385 = (x - μ) / (σ/√n)0.385 = (x - 50) / (0.5/10)We can solve for x.0.385 = 20(x - 50)0.385/20 = x - 50x = 50 + 0.01925x = 50.01925Therefore, there is a 35% chance that Xˉ is above 50.01925.

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The error in the set of instructions can be resolved by rearranging the steps so they are in sequential order. The Option A is correct.

The most effective solution would be to rearrange the steps so they follow a logical order.

For example, the steps could be rearranged as follows:

Therefore, by doing this would make the instructions clearer and easier to follow. The Option A is correct.

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Answer:

When you buy more expensive items or buildings it will raise your intrest so thats the difference look in between the two.

Step-by-step explanation:

Good luck on the rest of the quiz

The value of "m" represents the length of side G F in the kite F G H K. The value of "m" is 3.5. Given that sides G F and F K are congruent, we can conclude that their lengths are equal.

We are given that the length of side G H is 5 m 1 and the length of side H K is 3 m 7.

To find the value of "m," we need to find the length of side G F.

Since G F and F K are congruent, we can set up an equation:

5 m 1 = 3 m 7

To solve for "m," we need to subtract 3 m from both sides of the equation:

5 m - 3 m = 3 m - 3 m + 7

This simplifies to:

2 m = 7

Now, we can solve for "m" by dividing both sides of the equation by 2:

m = 7 ÷ 2

m = 3.5

Therefore, the value of "m" is 3.5.

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Answer:

the answer is negative 2

roots = {-2, -6}

Factors: (x + 6) and (x + 2)

Answer:

\(9n - 12 \rightarrow \frac{1}{3} (9n - 12) \\ = \frac{3}{3} (3n - 4) \\ l = 3n - 4\)

The perimeter of an equilateral triangle is 9n - 12. Write an expression to represent the length of each side.

\( = \frac{9n-12}{3} \\ = \frac{3(3n - 4)}{3} \\ = 3n - 4\)

The length of each side of the triangle is 3n-4.

Hope it helps!!

The markers identified when identifying significant digits include:

Significant digits in mathematics refers to digits that  are meaningful in mathematical calculations. This implies that their position and the quantity alters the value of the number. The particular digit and the position determines whether the digit is significant or not.

Instances of digits with their locations that are significant are:

These instances results to significant digits while the instances below the digits are insignificant:

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