What is the point that divides line DC into a ratio of 1:3, starting from point D C (-120, 83) D (156, -64)

Answer:

x = 95

Step-by-step explanation:

Given that,

The cost of a banquet at Nick's Catering is $215 plus $27.50 per person

The total cost of a banquet was $2827.50

We need to find the number of people invited. Let there are x people. So,

215+27.5x = 2827.50

27.5x = 2827.50 -215

27.5x = 2612.5

x = 95

So, there are 95 people that were invited.

Answer:

option c.

by Pythagoras theorem.

hypotenuse²=height ²+base²

20²=x²+12²

400=x²+144

400-144=x²

256=x²

256½=x

16=x

Answer:

27/30

Step-by-step explanation:

yepyffghhhhgghjj

Answer:

9/10 or 0.9

Step-by-step explanation:

When adding fractions, you look at each of them as an equal number, or a whole.

25+36

91

So, now all we have to do is convert it to it's closest form. (In tenths, since we are adding tenths.)

90

And it would be 9/10, or 0.9

Hope this helps!

Answer:

The distance the hiker must travel is approximately 5.5 miles

Step-by-step explanation:

The distance between the two cell phone towers = 22.5 miles

The distance between the hiker's phone and Tower A = 14.2 miles

The distance between the hiker's phone and Tower B = 10.9 miles

The direction of the highway along which the towers are located = East to west

The direction in which the hiker is travelling to reach the highway quickly = South

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Let 'a', 'b', and 'c', represent the sides of the triangle formed by the imaginary line between the two towers, the hiker's phone and Tower A, and the hiker's hone and tower B respectively, we have;

a = 22.5 miles

b = 14.2 miles

c = 10.9 miles

Therefore, we have;

22.5² = 14.2² + 10.9² - 2 × 14.2 × 10.9 × cos(A)

cos(A) = (22.5² - (14.2² + 10.9²))/( - 2 × 14.2 × 10.9) ≈ -0.6

∠A = arccos(-0.6) ≈ 126.9°

By sine rule, we have;

a/(sin(A)) = b/(sin(B)) = c/(sin(C))

∴ sin(B) = b × sin(A)/a

∴ sin(B) = 14.2×(sin(126.9°))/22.5

∠B = arcsine(14.2×(sin(126.9°))/22.5) ≈ 30.31°

∠C = 180° - (126.9° - 30.31°) = 22.79° See No Evil

The distance the hiker must travel, d = c × sin(B)

∴ d = 10.9 × sin(30.31°) ≈ 5.5

Therefore, the distance the hiker must travel, d ≈ 5.5 miles.

To find the surface area of the parametric surface given by 22 (u,v) = 5r1 (u,v), where r1 (u,v) is a parametric surface with a known surface area of 2, we need to consider the scaling factor of 5. The surface area of the parametric surface given by 22 (u,v) = 5r1 (u,v) is 10.

The surface area of a parametric surface can be calculated using the formula ∬||ru x rv|| dA, where ru and rv are the partial derivatives of the position vector r with respect to u and v, and ||ru x rv|| is the magnitude of their cross product.

When we scale the original parametric surface by a factor of 5, the scaling applies to each component of the position vector, resulting in a scaling factor of 5 for ||ru x rv||. Therefore, the new surface area is 5 times the original surface area, i.e., 5 * 2 = 10.

Thus, the surface area of the parametric surface given by 22 (u,v) = 5r1 (u,v) is 10.

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Answer:

The answer is BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

To travel 1400miles from Seattle to Los Angeles it will take the train 35 hours

A rate is the ratio between two related quantities in different units. For example , the train travels 80 miles in 2hrs . the two quantities that are related here are distance and time

here, we have,

distance in miles and time in hours

the time to travel for 1 mile

= 2/80 = 1/40 miles

for the train to travel 1400 miles , it will take it

1/40× 1400

= 35 hours

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complete question:

There is a train that travels from Seattle, Washington, to Los Angeles, California. In its first 2 hours the train went about 80 miles including stops. At this rate, how longer will it take to travel the 1400 miles from Seattle to Los Angeles?

Answer:

x = -2

Step-by-step explanation:

y = -4

2x -3y = 8

Substitute the first equation into the second equation

2x - 3(-4) = 8

2x +12 = 8

Subtract 12 from each side

2x+12-12 = 8-12

2x = -4

Divide by 2

2x/2 = -4/2

x = -2

Answer:

4.1 inches

I would appreciate Brainliest, but no worries.

Answer:

6

Step-by-step explanation:

the formula for the sphere's volume is [tex]\frac{4}{3} *\pi *r^3[/tex]

so when you set that equal to 288[tex]\pi[/tex], you get 6 as the radius

Answer:

20 boys

Step-by-step explanation:

If there are 4 boys for every 3 girls, multiply both numbers by 5 (3*5 = 15) to find the number of boys.

Answer:

20

Step-by-step explanation:

4/3 = ?/15

multiply both sides by 15

15*4/3 = ?

? = 20

Given that f, g ∈ L’[a, b], we need to prove the Cauchy-Schwarz inequality, |(f, g)| = ||$|| . ||$||.

The Cauchy-Schwarz inequality for inner product in L’[a, b] states that for all f, g ∈ L’[a, b],|(f, g)| ≤ ||$|| . ||$||Proof: Consider a function Q(t) = (f + tg, f + tg) for any real number t. Then, by using the rules of inner product, we can expand this expression and obtain a quadratic polynomial in t.$$Q(t) = (f + tg, f + tg) = (f, f) + t(f, g) + t(g, f) + t^2(g, g)$$$$ = (f, f) + 2t(f, g) + t^2(g, g)$$. Now, Q(t) > 0 because Q(t) is a sum of squares. So, Q(t) is a quadratic polynomial that can have at most one real root since Q(t) > 0 for all t ∈ R.

To find the discriminant of Q(t), we need to solve the equation Q(t) = 0.$$(f, f) + 2t(f, g) + t^2(g, g) = 0$$.

The discriminant of Q(t) is:$$D = (f, g)^2 - (f, f)(g, g)$$

Since Q(t) > 0 for all t ∈ R, the discriminant D ≤ 0.$$D = (f, g)^2 - (f, f)(g, g) ≤ 0$$$$\Right arrow (f, g)^2 ≤ (f, f)(g, g)$$$$\Right arrow |(f, g)| ≤ ||$|| . ||$||$$

Thus, |(f, g)| = ||$|| . ||$||, which proves the Cauchy-Schwarz inequality. Therefore, the given statement is true.

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a. The decomposition into cycles is (2 5 6 3 4).

b. The decomposition into transpositions is (2 5)(5 6)(6 3)(3 4).

c. The permutation is even.

We have,

To decompose the given permutation into cycles, we start with the first element and follow its path:

Starting with 2, we see that it goes to 5.

5 goes to 6.

6 goes to 3.

3 goes to 4.

Finally, 4 goes back to 2, completing the cycle.

The cycle can be represented as (2 5 6 3 4).

To decompose the permutation into transpositions, we consider each adjacent pair of elements and write them as separate transpositions:

(2 5)(5 6)(6 3)(3 4)

Now, we can observe that the permutation has a total of four transpositions.

To determine if the permutation is even or odd, we need to count the number of transpositions.

In this case, there are four transpositions, which means the permutation is even since the number of transpositions is even.

Therefore,

a. The decomposition into cycles is (2 5 6 3 4).

b. The decomposition into transpositions is (2 5)(5 6)(6 3)(3 4).

c. The permutation is even.

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ANSWER : D

EXPLANATION : 81 > 13 is true

(a) Math2 is not an unbiased estimator of μ. (b)Math1 has a variance of

σ[tex]^{2}[/tex] and Math2 has a variance of  5σ[tex]^2[/tex]/8

(a) Neither of the estimators, Math1 or Math2, is an unbiased estimator of μ. An unbiased estimator should have an expected value equal to the parameter being estimated, in this case, μ.

For Math1,

the expected value is

E[Math1] = E[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]

= (E[[tex]X_{1}[/tex]] + E[[tex]X_{2}[/tex]]) / 2

= μ/2 + μ/2 = μ,

which means Math1 is an unbiased estimator of μ.

For Math2,

the expected value is

E[Math2] = E[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]

= (E[[tex]X_{1}[/tex]] + 3E[[tex]X_{2}[/tex]]) / 4

= μ/4 + 3μ/4

= (μ + 3μ) / 4

= 4μ/4

= μ/2.

(b) To calculate the variances of the estimators, we'll use the property that the variance of a sum of independent random variables is the sum of their variances.

For Math1,

the variance is Var[Math1]

= Var[([tex]X_{1}[/tex] + [tex]X_{2}[/tex]) / 2]

= (Var[[tex]X_{1}[/tex]] + Var[[tex]X_{2}[/tex]]) / 4

= σ[tex]^2[/tex]/2 + σ[tex]^2[/tex]/2

= σ[tex]^2[/tex]

For Math2,

the variance is Var[Math2]

= Var[([tex]X_{1}[/tex] + [tex]3X_{2}[/tex]) / 4]

= (Var[[tex]X_{1}[/tex]] + 9Var[[tex]X_{1}[/tex]]) / 16

= σ[tex]^2[/tex]/4 + 9σ[tex]^2[/tex]/16

= 5σ[tex]^2[/tex]/8

Math1 has a variance of σ[tex]^2[/tex]

and Math2 has a variance of 5σ[tex]^2[/tex]/8

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In counseling and psychotherapy groups, member-to-member contact outside of the group often results in subgroups and hidden agendas

According to various research studies on Personal relationships among specialty group members, such as counseling and psychotherapy groups, which was concluded that member-to-member contact outside of the group often results in SUBGROUP and HIDDEN AGENDAS.

However, Most of the time, which can lead to damaging situations.

Therefore it is considered a sensible strategy to prevent the formation of such subgroups.

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Step-by-step explanation:

you're multiple times a day po

Answer:

uhh i don't know the answer sorry

Step-by-step explanation:

ummm i Don't know

Answer:

not a function becuz 2 repeats its self twice

Step-by-step explanation:

Answer:

You are welcome

Step-by-step explanation:

The Surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.

The surface area of a cylinder, we need to consider the lateral surface area and the area of the two circular bases.

The lateral surface area of a cylinder can be determined by multiplying the height of the cylinder by the circumference of its base. The formula for the lateral surface area (A) of a cylinder is given by A = 2πrh, where r is the radius and h is the height of the cylinder.

In this case, the height of the cylinder is 8 ft and the radius is 4 ft. Therefore, the lateral surface area can be calculated as follows:

A = 2π(4 ft)(8 ft)

A = 64π ft²

The area of each circular base can be calculated using the formula for the area of a circle, which is A = πr². In this case, the radius is 4 ft. Therefore, the area of each circular base is:

A_base = π(4 ft)²

A_base = 16π ft²

Since a cylinder has two circular bases, the total area of the two bases is:

A_bases = 2(16π ft²)

A_bases = 32π ft²

the total surface area, we sum the lateral surface area and the area of the two bases:

Total surface area = Lateral surface area + Area of bases

Total surface area = 64π ft² + 32π ft²

Total surface area = 96π ft²

Now, let's calculate the numerical value of the surface area:

Total surface area ≈ 96(3.14) ft²

Total surface area ≈ 301.44 ft²

Therefore, the surface area of the given cylinder, with a height of 8 ft and a radius of 4 ft, is approximately 301.44 square feet.

In conclusion, the surface area of the cylinder with a height of 8 ft and a radius of 4 ft is approximately 301.44 square feet.

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Answer:

6*(61^2) and 61^3

Step-by-step explanation:

If the squares have a side length of 61 (assuming this is a cube) our surface area is 6*(61^2) because each side is a square and there are six sides.

As for the volume, we have 61^3.

Hope this was helpful.

~cloud

Answer:

x-intercept: (-1,0)

y-intercept: (0,3)

Vertex: (-2,-1)

Step-by-step explanation:

Answer:

7m ^1÷2

Step-by-step explanation:

see attached joint

hope it helps

Answer:

( 21 x X ) + 1

Step-by-step explanation:

the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.

To find three numbers whose sum is 21 and whose sum of squares is a minimum, we can use a mathematical technique called optimization. Let's denote the three numbers as x, y, and z.

We need to minimize the sum of squares, which can be expressed as the function f(x, y, z) = x² + y² + z²

Given the constraint that the sum of the three numbers is 21, we have the equation x + y + z = 21.

To find the minimum value of f(x, y, z), we can use the method of Lagrange multipliers, which involves solving a system of equations.

First, let's define a Lagrange multiplier, λ, and set up the following equations:

1. ∂f/∂x = 2x + λ = 0

2. ∂f/∂y = 2y + λ = 0

3. ∂f/∂z = 2z + λ = 0

4. Constraint equation: x + y + z = 21

Solving equations 1, 2, and 3 for x, y, and z, respectively, we get:

x = -λ/2

y = -λ/2

z = -λ/2

Substituting these values into the constraint equation, we have:

-λ/2 - λ/2 - λ/2 = 21

-3λ/2 = 21

λ = -14

Substituting λ = -14 back into the expressions for x, y, and z, we get:

x = 7

y = 7

z = 7

Therefore, the three numbers whose sum is 21 and whose sum of squares is a minimum are 7, 7, and 7.

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Answer:

A x<1125

Step-by-step explanation:

Answer:

34.78

Step-by-step explanation:

8/23

The given differential equation d⁴y/dx⁴ - a⁴y = 0 models the deformation of a cylindrical shaft rotating with angular velocity ω. The function y(x) represents the deformation of the cylinder.

To solve the differential equation, we can assume a solution of the form y(x) = A*cos(ax) + B*sin(ax), where A and B are constants to be determined, and 'a' is a parameter related to the properties of the cylinder.

Taking the fourth derivative of y(x) and substituting it into the differential equation, we have:

d⁴y/dx⁴ = -a⁴(A*cos(ax) + B*sin(ax))

Substituting the fourth derivative and y(x) into the differential equation, we get:

-a⁴(A*cos(ax) + B*sin(ax)) - a⁴(A*cos(ax) + B*sin(ax)) = 0

Simplifying the equation, we have:

-2a⁴(A*cos(ax) + B*sin(ax)) = 0

Since the equation must hold for all x, the coefficient of each term (cos(ax) and sin(ax)) must be zero:

-2a⁴A = 0   (coefficient of cos(ax))

-2a⁴B = 0   (coefficient of sin(ax))

From these equations, we find that A = 0 and B = 0, which implies that the only solution is the trivial solution y(x) = 0.

Therefore, the solution to the differential equation d⁴y/dx⁴ - a⁴y = 0 is y(x) = 0.

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The probability that he hits the hare within his first 4 shots is 0.8789.

Probability of success for the first shot = P1 = 12 Probability of missing the first shot = 1 – P1 = 1 – 12 = 12  Probability of

success for the second shot, given that the first shot missed = P2 = 14Hence, the probability that he hits the hare within

his first 2 shots is:P1 + (1 – P1)P2= 12+(12)×(14)= 12+16= 38(2) The probability that he hits the hare within his first 3 shots is

most nearly (a) 1 (b) 0.9 (c) 0.8 (d) 0.7We have to find the probability of hitting the hare within his first 3 shots. Probability

of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability of success for the

second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given that the first two

shots missed = P3 = 18Hence, the probability that he hits the hare within his first 3 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 –

P2)P3= 12+(12)×(14)+(12)×(34)×(18)= 12+16+18×(12)= 1316= 0.8125(3) The probability that he hits the hare within his first 4

shots is most nearly (a) 0.9 (b) 0.7 (c)1 (d) 0.8We have to find the probability of hitting the hare within his first 4

shots. Probability of success for the first shot = P1 = 12Probability of missing the first shot = 1 – P1 = 1 – 12 = 12Probability

of success for the second shot, given that the first shot missed = P2 = 14Probability of success for the third shot, given

that the first two shots missed = P3 = 18 Probability of success for the fourth shot, given that the first three shots missed

= P4 = 116Hence, the probability that he hits the hare within his first 4 shots is:P1 + (1 – P1)P2 + (1 – P1)(1 – P2)P3 + (1 – P1)

(1 – P2)(1 – P3)P4= 12+(12)×(14)+(12)×(34)×(18)+(12)×(34)×(78)×(116)= 12+16+18×(12)+18×(78)×(116)= 7892= 0.8789

Therefore, the answer is (d) 0.8.

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(a) To argue that P(T < ∞) = 1, where T is the first time the walk visits 0 or N, we can consider each time the walk visits 1 before time T.

Suppose the walk visits 1 for the first time at time k < T. At this point, the random walk is in a state where it can either hit 0 before N or hit N before 0.

Let's define a new random variable Y, which represents the number of steps needed for the walk to hit either 0 or N starting from state 1. Y follows a geometric distribution with parameter p since the steps are +1 with probability p and -1 with probability q = 1 - p.

Now, we can compare the random variable T and Y. If T < ∞, it means that the walk has hit either 0 or N before reaching time T. Since T is finite, it implies that the walk has hit 1 before time T. Therefore, we can say that T ≥ Y.

By the properties of the geometric distribution, we know that P(Y = ∞) = 0. This means that there is a non-zero probability of hitting either 0 or N starting from state 1. Therefore, P(T < ∞) = 1, as the walk is guaranteed to eventually hit either 0 or N.

(b) To find P(J|So = n), where So = n, we need to determine the probability of hitting N before hitting 0 starting from state n.

Recall that the probability of hitting N before 0 starting from state 1 is given by (g/p)^(N-1), as shown in the Optional Stopping Theorem formula. In our case, since the walk starts at state n, we need to adjust the formula accordingly.

The probability of hitting N before 0 starting from state n can be calculated as P(J|So = n) = (g/p)^(N-n).

This probability takes into account the number of steps required to reach N starting from state n. It represents the likelihood of hitting the jackpot (N) before going bust (0) when the walk starts at state n.

It's worth noting that this probability depends on the values of p, q, and N.

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Answer:

x = 5 ; z = 70

Step-by-step explanation:

Vertical angles have the same degree measure

(13x + 45) = 110

13x + 45 = 110

      -45     -45

13x = 65

/13     /13

x = 5

Complementary angles add up to 180°

110 + z = 180

-110         -110

z = 70

Answer:

X = 5º

Z = 70º

Step-by-step explanation:

So we know that vertical angles are congruent. So what we do to figure out x is set the equation equal to 110º because we are given that. And then we solve for x.

(13x + 45) = 110

13x + 45 = 110

      -45      -45

----------------------

13x = 65

÷13     ÷13

---------------

x = 5

Now, we plug x into the equation. (13x5 + 45) = 110 so we know that x = 5

Now, we also know that a straight line equals 180º so what we do is subtract 110 from 180.

180 - 110= 70º

z = 70º

Answer:

24 or 12

Step-by-step explanation:

Multiplication