1) Explain why Triangle ABD is congruent to triangle CDB
a.) given segment CB is congruent to segment AD and segment CB is parallel to segment AD

The value of particular solution is,

⇒ y (p0 = (4/5)x^(5/2) - (4/15)x^(7/2).

Now, we need to find the Wronskian of the given solutions;

⇒ y₁ = e²ˣ and y₂ = x e⁻²ˣ.

Hence, We get;

⇒ W(y₁, y₂) = |e²ˣ   xe⁻²ˣ|

                 = -2e⁰

                  = -2

Next, we can find the particular solution using the formula:

⇒ y (p) = -y₁ ∫(y₂ g(x)) / W(y₁, y₂) dx + y₂ ∫(y₁ g(x)) / W(y₁, y₂) dx

where g(x) = 8x^(5/2) / (3 - 16x²)

Plugging in the values, we get:

y(p) = -e²ˣ ∫(xe⁻²ˣ 8x^(5/2) / (3 - 16x²)) / -2 dx + xe⁻²ˣ ∫(e²ˣ 8x^(5/2) / (3 - 16x²)) / -2 dx

Simplifying this, we get:

y (p) = (4/5)x^(5/2) - (4/15)x^(7/2)

Therefore, the particular solution is,

⇒ y (p0 = (4/5)x^(5/2) - (4/15)x^(7/2).

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Answer:

\(\large \boxed{\mathrm{(a) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(b) \ One \ solution}} \\ \\ \large \boxed{\mathrm{(c) \ All \ real \ numbers}}\)

Step-by-step explanation:

2x+4(x-1)=2+4x

Expand brackets.

2x+4x-4=2+4x

Combine like terms.

6x-4=2+4x

Subtract 4x from both sides.

Add 4 to both sides.

2x=6

Divide both sides by 2.

x=3 (One solution)

25-x=15-(3x+10)

Distribute negative sign.

25-x=15-3x-10

25-x=-3x+5

Add x and -5 to both sides.

20=-2x

Divide both sides by -2.

-10=x (One solution)

4x=2x+2x+5(x-x)

Solve for brackets.

4x=2x+2x+5(0)

4x=2x+2x

Combine like terms.

4x=4x

Divide both sides by 4.

x=x

All real numbers are solutions. (All real numbers)

Answer:

8n

Step-by-step explanation:

8n is the factor of both 8 and n. in the following question.

Factor ⇒ If a number, that use to divide another number and we get zero as a remainder, the number is called the factor of another number.

In this question, 8n is divided by both 8 and n and also we get zero as a remainder.

Therefore, 8n is the factor of both 8 and n .

We have that  the expression must have 8 and n as integer and variable of the expression

From the Question we are told that

both 8 and n are factors of an expression

It is important to note that for 8 and n to be factors of an expression it must be present in the expression or the expression must have 8 and n as integer and variable of the expression

e.g

x=8+n

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Answer:

answer is

Step-by-step explanation:

Object distance (u) = -100cm  Focal length (f) = 50cm Image distance = v  By lens formula; 1v−1u=1f1v−1u=1f ⇒ 1v−1−100=1501v−1−100=150 ⇒1v=150−11001v=150−1100 ⇒1v=2−1100−11001v=2−1100−1100 v =100cm  Hence the image is formed at 100 cm behind the lens.  Object distance (u) = -100cm  Focal length (f) = -25cm  Image distance = v  By lens formula;Read more on Sarthaks.com - https://www.sarthaks.com/951256/an-object-is-kept-at-a-distance-of-100-cm-from-each-of-the-above-lenses-calculate-the?show=951265#a951265

Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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Answer:

u457sups

Step-by-step explanation:

= 89 - 89b 67 =  80

Answer:

A

Step-by-step explanation:

The correct representation of the language L3 is L1 ∩ L2.

The language L1 represents all strings that contain at least one 1, while the language L2 represents all strings that start with 0. We are tasked with determining the language L3, which consists of strings that start with 0 and contain only 0's.

To determine L3, we need to find the intersection of L1 and L2. The intersection of two languages consists of all the strings that are common to both languages.

In this case, L1 ∩ L2 represents the set of strings that satisfy both conditions: they contain at least one 1 and start with 0. However, L3 is specifically defined as the language where all the characters following the initial 0 are 0's.

So, L1 ∩ L2 would include strings that contain at least one 1 after the initial 0, which doesn't match the requirement of L3. Therefore, L1 ∩ L2 does not represent L3.

On the other hand, L1 ∪ L2 represents the set of strings that either contain at least one 1 or start with 0. This includes strings that satisfy the condition of L3 since L3 allows for strings that start with 0. However, L1 ∪ L2 also includes strings that contain at least one 1, which doesn't match the requirement of L3. Therefore, L1 ∪ L2 does not represent L3 either.

In conclusion, the correct representation of the language L3={x∣x starts with 0 and contains only 0's} is L1 ∩ L2, which means the answer is L1 ∩ L2.

Correct Question :

Consider the following languages over alphabet {0,1}. Let L1={x∣ x contains at least one 1} and L2={x∣x starts with 0}. Which of the following represents the language L3={x∣x starts with 0 and contains only 0 's } ?

L1∩L2

L1∪L2

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Answer:

y/5= x

Step-by-step explanation:

y=5x

divide both sides by 5

y/5=5x/5

five will cancel five so x is left to stand alone

x=y/5

The Implied Equity Risk Premium (ERP) is generally considered a better predictor of future equity risk premium

Implied Equity Risk Premium is derived from the current market prices of stocks and other securities. It represents the difference between the expected rate of return on equities and the risk-free rate of return. Investors' expectations about future returns are embedded in market prices, so the implied ERP reflects the collective wisdom and expectations of market participants. It takes into account current market conditions, investor sentiment, and other relevant factors, making it a forward-looking indicator.

On the other hand, historical geometric average and historical arithmetic average equity risk premium are calculated based on past performance data. While historical averages provide valuable insights into the past behavior of equity risk premium, they may not fully capture the changing dynamics of the market or reflect future expectations.

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Answer:

3x + 3 = -2x + 13 doesn't

Step-by-step explanation:

Answer:

-21

Step-by-step explanation:

3x-5=2

4x 2=2

2x-3=2

add them together you will get -21

A. x and y are both within the same solar system.

7.2 light years= 455336 AU

Answer:

2

3,0

Step-by-step explanation:

The probability that exactly seven of them order sugar cones is 0.27.

Since in this question, we have a fixed number of trials (ten customers) and each trial has only two possible outcomes (sugar cone or not sugar cone), we can solve this question using the binomial distribution.

According to the question the probability of ordering a sugar cone is 0.7 and not ordering is 0.3

The probability mass function for the binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, k is the number of successes(ordering sugar cone), and p is the probability of success.

So, using this formula we get,

P(X=7) = (10 choose 7) * 0.7^7 * 0.3^3 = 0.2668 ≈0.27

Therefore, the probability that exactly seven of the next ten customers will order sugar cones is 0.27.

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To estimate the number of sandwiches the deli manager should anticipate selling when 178 customers visit the deli, we can analyze the given data and approximate it using a linear function.

By observing the table, we notice that the number of sandwiches sold varies with the number of customers. This indicates a relationship between the two variables.

To estimate the number of sandwiches, we can fit a line to the data points and use the linear function to make predictions. Using a statistical software or a spreadsheet, we can perform linear regression analysis to find the equation of the best-fit line. However, since we are limited to text-based interaction, I will provide a general approach.

Let's assume the number of customers is the independent variable (x) and the number of sandwiches is the dependent variable (y). Using the given data points, we can calculate the equation of the line.

After calculating the linear equation, we can substitute the value of 178 for the number of customers (x) into the equation to estimate the number of sandwiches (y).

Please provide the data points for the number of sandwiches sold corresponding to each number of customers so that I can perform the linear regression analysis and provide a more accurate estimate for you.

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The graph illustrates the supply and demand curves on a single graph to represent the equilibrium point in a market. The equilibrium point is where the quantity demanded equals the quantity supplied, resulting in a balance between buyers and sellers.

This point determines the market price and quantity exchanged in the market. The graph demonstrates the interplay between supply and demand, showcasing how changes in these factors can impact the equilibrium point and market outcomes.

The equilibrium point is the intersection of the supply and demand curves on the graph. At this point, the quantity demanded by buyers matches the quantity supplied by sellers. The equilibrium price is determined by the vertical position of the equilibrium point on the graph, while the equilibrium quantity is determined by the horizontal position.

If the market price is above the equilibrium price, there is excess supply, leading to a surplus. Sellers will be motivated to decrease prices to sell their goods, which, in turn, increases the quantity demanded. Conversely, if the market price is below the equilibrium price, there is excess demand, resulting in a shortage. Buyers will be incentivized to bid higher prices, increasing the quantity supplied by sellers.

The equilibrium point represents a state of market balance where the forces of supply and demand are in harmony. It reflects the price and quantity at which both buyers and sellers are satisfied, maximizing the efficiency of resource allocation in the market.

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Answer:

2 ...................

In order to multiply two fractions, we can follow the steps below:

0. find the product between the two numerators; ,(3 * 7 = 21)

1. find the product between the two denominators; ,(10 * 2 = 20)

2. the product of the two fractions will be the result of step 1 (the numerator of the final result), divided by the result of step 2 (the denominator of the final result):

Therefore, the answer is:

To find the arc length, we use the formula L = rθ, where r is the radius of the circle, θ is the central angle of the arc in radians, and L is the arc length.

Arc length refers to the distance covered along the curved portion of a circle or any other curved shape. It is an important concept in geometry and trigonometry and is used to measure the size of circular arcs, the size of angles, and in many other mathematical applications.

To find the arc length, we need to use the formula for the circumference of a circle and the central angle of the arc.

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle.

The central angle of the arc is given in radians and is defined as the angle between two radii that meet at the endpoints of the arc.

To find the arc length, we use the formula

=> L = rθ,

where L is the arc length, r is the radius of the circle, and θ is the central angle of the arc in radians.

To convert the central angle from degrees to radians, we use the formula θ = (π/180) x degrees, where degrees are the central angle in degrees.

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Answer:

14

Step-by-step explanation:

Distance between X and Y = 17 - 5 = 12

\(\dfrac{3}{4} \ of \ 12 = \dfrac{3}{4}*12=3*3=9\)

3/4 of the way from  X to Y = 5 + 9 = 14

Answer:

A linear pair is a adjacent angles formed when two lines

interset.

Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

Answer: Pedro tiene 21 años.

Step-by-step explanation:

Sea x su edad actual.

Dentro de 11 años tendrá (x+11) años.

Hace 13 años fue (x-13)

Por lo tanto (x+11) = ((x-13)(x-13))/2

Multiplica ambos por 2 y Foil.

2x+22 = x*x - 26x + 169 (Lo siento, x*x es x al cuadrado - limitaciones del teclado)

Recoger términos semejantes:

x*x - 28x +147 = 0

Entonces la factorización da:

(x-21)(x-7)=0

Por propiedad del producto cero:

X-21 = 0. X = 21

X-7 = 0. X = 7

Ahora prueba para x = 21.

(21+11) = ((21–13)(21–13))/2

32 = 64/2

entonces tu edad es 21

We cannot have a fraction of a person in the sample, we need to round up to the next whole number, which is 1022.

So, you will need to sample at least 1022 individuals to achieve a 95% confidence level with a margin of error no more than 3%.

This means that the correct answer among the given options is "at least 1068".

To estimate the sample size needed for survey, you can use the formula for sample size calculation in a proportion estimation problem.

The formula is:
\(n = (Z^2 * p * (1-p)) / E^2\)
where:
n = required sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence level)
p = estimated proportion (0.35 in this case)
E = desired margin of error (0.03 in this case)
Now, let's plug the values into the formula:
\(n = (1.96^2 * 0.35 * (1-0.35)) / 0.03^2\)
n = (3.8416 * 0.35 * 0.65) / 0.0009
n = 0.919326 / 0.0009
n ≈ 1021.473.

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It takes 50 seconds to travel the full length at the constant rate R.

Remember the relation between speed, distance and time:

distance = speed*time

Here we know that at a rate R (or speed S, these are equivalent) it moves (1/20) of the total distance D in (2 + 1/2) seconds, then we can write:

R*(2 + 1/2) = (1/20)*D

Now we only need to isolate D on the right side, to do so we need to multiply both sides by 20.

20*R*(2 + 1/2) = D

The time is:

20*(2 + 1/2) seconds

40 + 10 seconds

50 seconds

It takes 50 seconds to travel the full length,

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The answer is C. The set of all symmetric 3 × 3 matrices is a subspace of M33.


To determine if a set of matrices is a subspace of M33, we need to check three conditions:
1. The set contains the zero matrix.
2. The set is closed under addition of its elements.
3. The set is closed under multiplication by other matrices in the set.
In this case, the set of all symmetric 3 × 3 matrices does contain the zero matrix (all diagonal entries are zero), and it is also closed under matrix addition (the sum of two symmetric matrices is also symmetric).

To check the third condition, we need to verify that if we multiply any symmetric matrix by another symmetric matrix, the result is also a symmetric matrix. This is indeed true, since the transpose of a product of matrices is the product of their transposes in reverse order: (AB)^T = B^T A^T. For any symmetric matrix A, we have A^T = A, so (AB)^T = B^T A^T = BA, which is also symmetric if B is symmetric.
Therefore, all three conditions are satisfied, and the set of all symmetric 3 × 3 matrices is indeed a subspace of M33.

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Answer:

\(-4^{15}\)

Step-by-step explanation:

Given expression:

\(\left[(-4)^5\right]^3\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies (-4)^{(5 \times 3)}\)

\(\implies (-4)^{15}\)

\(\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:\)

\(\implies -4^{15}\)

Answer:

6s2

= 6(2)2

= 12 × 12

= 144

: The value of the expression is equal to 144