It is important to understand that integral equations also arise from problems in differential equations. (a) For example, write the initial value problem dx = f(t, x), x(to) = xo dt as an integral equation and indicate what kind of equation it is. (b) Show that an initial value problem d²x dt² = f(t, x), x(to) = xo, x'(to) = x₁ involving a second order differential equation can be transformed into a Volterra integral equation

The complete proofs with all the reasons and statements; have been enumerated below

The image showing the given triangle is missing and so i have attached it.

From the attached image, we can deduce that;

Statement 1; AB * BE = CB * BD

Reason 1; Given

Statement 2; CB/BE = AB/BD

Reason 2; Property of Cross Multiplication

Statement 3; ∠ABC ≅ ∠DBE

Reason 3; Vertical Angles

Statement 4; ΔABC ~ ΔDBE

Reason 4; SAS property of similarity

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Answer: $45

Step-by-step explanation:

Let the original price be x.

Since there was a discount of 20%, it means the person bought the frying pan at (100% - 20%) = 80% of the original price. This can then be formed into an equation as:

80% × x = $36

0.8 × x = $36

0.8x = $36

x = $36/0.8

x = $45

The original price was $45

Answer:

4x - 2y can be simplified as 2(2x - y)

Answer:

2

Step-by-step explanation:

The Intial value, also know as the y-intercept, is where the line crosses line y.

Therefore, looking at the graph, your initial value is 2.

Answer:

17x

Step-by-step explanation:

so first 2x is 2 x x = 2x

then +10 =12x then 5 + x = 5x so 5x + 12x = 17x

Answer:

1: x = 6

2: There is no solution. Sorry. (because the ending equation will be 0 = 7)

3: I can't see the other part of the equation, I need to see what the fraction is in order to solve it. If you can retake the picture, I can edit my response :)

Step-by-step explanation:

#1: 3(x-1) is pretty much just 3x-3. Simple.

Now, your equation becomes 3x-3 = 2x+9.

Arrange them so that the like terms are together.

Since you will be taking the 2x from 2x+9 over to the other side, it becomes 3x-2x-3 = 9.

Now, bring the 3 over to the side with the 9.

x = 6.

#2: Same as before, -2(x+1) is (-2x) - 2.

So, -2x-2 = -2x+5.

As I said before, you need to group the like terms together.

-2x and -2x go together, and -2 and 5 go together.

-2x+2x=5+2

0=7.

There is no solution.

#3: Like the other two, 4(x-1) is 4x-4. As for the other part, I cannot see the fraction before (x-8).

Given: What should be done to both sides of the equation in order to solve y - 4.5 = 12.2?

To Find: What should be done on both side of equation.

Solution:

Step1 : Add 4.5 both sides so that +4.5 gets eliminated from LHS ,

=> y-4.5+4.5=12.2+4.5

=> y = 16.7

Hence the value of y is 16.7.

To need to solve the equation we need to add 4.5 on both sides and the value of y will be 16.7.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In other words, the equation must be constrained with some constraints.

As per the given equation,

y - 4.5 = 12.2

Add 4.5 on both sides of the equation,

y - 4.5 + 4.5 = 12.2 + 4.5

y = 16.7

Hence "To need to solve the equation we need to add 4.5 on both sides and the value of y will be 16.7".

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Answer:

15 pizzas.

Step-by-step explanation:

The rate is 3 pizzas for every 7 people. If there are 35 people at the party (7 times 5), the amount of pizzas you should buy is 15 pizzas (3 times 5). Hope I  explained that well (^^'')

The statement "W is a subspace of P2" is true, as W satisfies the conditions for being a subspace: closure under addition and scalar multiplication, and containing the zero vector.

The statement "W is a subspace of P2" is true.

To show that W is a subspace, we need to verify the three conditions for subspace:

W is closed under addition: For any two polynomials p(x) = a + 2x + bx^2 and q(x) = c + 2x + dx^2 in W, their sum p(x) + q(x) = (a + c) + 4x + (b + d)x^2 is also in W. Therefore, W is closed under addition.

W is closed under scalar multiplication: For any polynomial p(x) = a + 2x + bx^2 in W and any scalar k, the scalar multiple kp(x) = ka + 2kx + kbx^2 is also in W. Therefore, W is closed under scalar multiplication.

W contains the zero vector: The zero polynomial 0 = 0 + 0x + 0x^2 is in W since a = b = 0. Therefore, W contains the zero vector.

Since W satisfies all three conditions for subspace, it is indeed a subspace of P2.

Hence, the statement "W is a subspace of P2" is true.

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Answer: i don’t know what that is

Step-by-step explanation:

Answer:

>

Step-by-step explanation:

sqrt{17} > sqrt{11}

Answer: >

Step-by-step explanation: the square root of 17 is going to be larger than the square root of 11. since you add 3 to both equations, that is all you have to worry about.

Answer:

1/6

Step-by-step explanation:

there is only one side in which there is 3 out of total six sides so 1/6

Answer:

I think the correct answer is....... The measure of center for table 1 is 61, 62, 58, and 57 inches. The most kids had the same number of inches in this category.

I'm not 100% sure so try at your own risk

Have a great day!

The center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

Measures of center of data set is also "a way of describing data set. The two most widely used measures of the center is mean and median".

Mean is the process of "adding all values and then divided by total number of values".

Median is the "process of arranging data value in ascending or descending order and then divided data set into two if 'n' is odd then middle  point is the median or if 'n' is even then sum of two mid value and then divided by two".

Mode can be one, "two or more in the given data set. The number or data point which have more frequency is taken as mode".

According to the question,

Measures of center is the most appropriate for the data in Table 1 (Height) in Task 1.

Heights in inches                       Frequency

         55                                             1

          57                                              3

          58                                             3

          59                                              2

          60                                              1

          61                                               3

          62                                              3

          63                                              2

          64                                              2

          65                                              2

          66                                              1

           67                                              1

Total number of frequency = N = 1+3++3+2+1+3+3+2+2+2+1+1 =24. Number of siblings n =12

Mean = ∑(Height of inches × Frequency of height)/Total number of frequency.

= [tex]\frac{(55*1+57*3+58*3+59*2+60*1+61*3+62*3+63*2+64*2+65*1+66*1+67*1)}{24}[/tex]

= [tex]\frac{1399}{24}[/tex]

= 58.29.

Mean of heights of siblings are 58.29

Median of the height of 24 siblings are sum of 61 and 62 divided by 2.

= [tex]\frac{61+62}{2}[/tex]                           [since 'n' is odd]

=61.5.  

Median of the height of 24 siblings are 61.5.

Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

Hence, the center of measures of table 1 height (task1) are Mean of heights of siblings are 58.29. Median of the height of 24 siblings are 61.5. Mode of the height 24 siblings 57,58,61,62 are the heights in inches.

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Nia's original class average was 89%. After increasing it by 3%, she now has a 92% in her math class.

1. Let's assume Nia's original class average was X.

2. She increased her class average by 3%, which can be represented as X + (3/100)X.

3. According to the question, X + (3/100)X = 92.

4. Simplifying the equation, we have (103/100)X = 92.

5. To find X, we divide both sides of the equation by (103/100): X = (92 * 100) / 103.

6. Calculating the value, X ≈ 89.32.

7. Therefore, Nia's original class average was approximately 89.32%.

8. After increasing it by 3%, her new class average is 89.32% + (3/100) * 89.32% ≈ 92%.

Note: The values have been rounded for simplicity.

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Answer:

|-2| = 2

Step-by-step explanation:

Answer:

[tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] will change

[tex]\angle ABC[/tex] equal [tex]\angle ADC[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

What happens when AC changes

(a) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are formed from points A and C. So, a change in AC will result to a change in the measures of [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex].

(b) [tex]\angle ABC[/tex] and [tex]\angle ADC[/tex] are in the same segment, meaning that they will always have the same measure

Answer:

For two fractions to be proportional, they must be equivalent. 32=1.5 and 188=2.25 , so these fractions are not proportional.

Step-by-step explanation:

Answer:

5 hours and 24 minutes

Step-by-step explanation:

sorry if im wrong

Answer:

5.4 hours

Step-by-step explanation:

I'm not 100 percent sure

hope this helped ;)

The t-statistic of the slope coefficient is -19 is the answer.

Suppose a regression was run between y and one x variable.

The coefficient of the x variable (slope coefficient) was -0.76.

The associated standard error of the slope coefficient was 0.04, and p value of the slope coefficient was 0.

The t stat of the slope coefficient is -19.

To find the t-statistic value, divide the slope coefficient by the standard error.

This is given as t = slope / SE.

We have the values of the slope and the SE in the problem.

Substitute these values to get the t-statistic.t = -0.76 / 0.04 = -19

From this calculation, we can see that the t-statistic of the slope coefficient is -19.

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Answer:

y=2x+4

Step-by-step explanation:

y=2x+4

Answer:

y = 2x + 4

Step-by-step explanation:

The formula for the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is where the line passes through the y-axis, which would be (0,4), which is positive. To find the slope, find where the line passes through a point, and then count how many units there are till the next point. For this example, you could start from the y-intercept, (0, 4) and to get to the next point, you will go up 2 units, and the right 1 unit. This means that the slope is 2/1 (because it's rise over run) which is the same as 2. So just plug it into the equation, and you get y = 2x + 4.

I hope this helped! :)

Answer:

Step-by-step explanation:

3

For the sequence of functions fr : [0,1] → R defined recursively by fo(x) = 1, fn(x) = Vxfn-1(x), n > 1, the sequence converges on [0, 1] and the convergence is uniform.

First, we need to show that the sequence is pointwise convergent. To do that, we take an arbitrary x ∈ [0,1] and use induction on n to prove that fn(x) is convergent.

Let A = sup{f1(x), 1}

Since f1(x) = √x ≤ 1, there exists a decreasing sequence (an) such that f1(x) ≤ an ≤ 1 for all n.

Noting that an → √A (since an is decreasing and bounded below), we have:

fn(x) = √x*fn-1(x) ≤ √A * fn-1(x)

Now, by induction, we have:

f2(x) ≤ √A * f1(x) ≤ √A * a1 ≤ √Afn(x) ≤ √A * fn-1(x) ≤ √A * an-1 ≤ A for all n.

So, by the squeeze theorem, fn(x) is convergent and since this holds for all x, the sequence is pointwise convergent.

We need to show that the sequence is uniformly convergent on [0,1].

Let ε > 0 be arbitrary and let N be such that |an - A| < ε/2 for all n > N.

Let M be such that 1/M < ε/2.

We want to show that |fn(x) - A| < ε for all x ∈ [0,1] and all n > N.

If n ≤ N, then we can write:

|fn(x) - A| ≤ |f

n(x) - an| + |an - A| < ε for all x ∈ [0,1].

So, assume n > N. Then we have:

|fn(x) - A| = |fn(x) - an + an - A| ≤ |fn(x) - an| + |an - A| < ε/2 + ε/2 = ε for all x ∈ [0,1] by the definition of N and M.

Therefore, the sequence is uniformly convergent on [0,1].

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The joint PMF, marginal PMFs, and conditional PMF can be determined for the maximum and minimum outcomes when flipping a biased coin twice. The joint PMF describes the probabilities of different combinations of maximum and minimum outcomes, while the marginal PMFs represent the probabilities of individual outcomes.

The conditional PMF shows the probability of one outcome given another. Detailed calculations and explanations are required to provide a complete answer.
(a) To find the joint PMF px,y(x,y), we need to consider all possible outcomes of flipping the coin twice. Since X represents the maximum outcome and Y represents the minimum outcome, we can determine the probabilities for each combination of X and Y. For example, if X = 1 and Y = 0, it means that the first flip was a tail and the second flip was a head. The joint PMF will assign probabilities to all possible combinations of X and Y.
(b) The marginal PMFs px(x) and py(y) represent the probabilities of individual outcomes for X and Y, respectively. To find px(x), we sum up the probabilities of all combinations where X takes the value x. Similarly, to find py(y), we sum up the probabilities of all combinations where Y takes the value y.
(c) The conditional PMF Pxy(x|y) provides the probability of X taking a certain value given that Y has a specific value. It can be obtained by dividing the joint PMF px,y(x,y) by the marginal PMF py(y) for each y value.
To provide a more detailed answer with calculations and sketches, specific values for p, the probability of a head, are needed.

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Answer:

26 , 10 , 3

Step-by-step explanation:

Any number larger than 2 will work.

Answer: hello your question is incomplete below is the missing part

Based on your simulation, what is the average amount of error you expect to see in the sample proportions in this situation?

answer : 0.0458

Step-by-step explanation:

In 2005 - 2007 : 30% of all current smokers started smoking before the age of 16

n ( sample size ) = 100 smokers

The average amount of error expected can be calculated as

[tex]\sqrt{pq/n}[/tex]  = [tex]\sqrt{0.3*0.7/100}[/tex] = 0.0458

where : p = 0.3

             q = 0.7

              n = 100

Temperature is an average measure of the kinetic energy of particles of matter.

Temperature can be in negative degrees.

The temperature at the end of the day is -3°F.

Temperature is an average measure of the kinetic energy of particles of matter.

The Celsius scale is generally used for measuring most temperatures.

The Fahrenheit (°F) temperature scale is also used.

We have,

The temperature at the beginning of the day = 6°F

The temperature drop by the end of the day = 9°F

Temperature can also be in negative degrees.

The temperature at the end of the day:

= 6°F - 9°F
= -3°F

Thus the temperature at the end of the day is -3°F.

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Answer:

d = 83

Step-by-step explanation:

Answer:

d=83°

Step-by-step explanation:

the sum of the inner angles is equal to 360°

so

127+67+d+d=360

194+2d=360

2d=166

d=83°

Answer:

graph is shown

Step-by-step explanation:

slope: -1/3

y intercept: (0,-17/3)

Answer: 6773.27

Step-by-step explanation: volume formula for the cone is pie(radius)^2(height/3) just plug in your information into the formula and viola