Yn+1 = Yn + hf(x,y) e-/Pdx Y₂(x) = Y₁(x) [ fe y²(x) G(x, t)= y₁ (t)y₂(x) − y₁ (x)yz(t) W(t) -SGC G(x, t)f(t)dt L{f(t = a)U(t—a)} = e-as F(s) Yp = L{eat f(t)} = F(s – a) L{f(t)U(t − a)} = e¯ªsL{f(t + a)} as L{t"f(t)} = (−1)ª dºm [F(s)] dsn L{8(t - to)} = e-sto Yn+1 = Yn + hf(x,y) e-/Pdx Y₂(x) = Y₁(x) [ fe y²(x) G(x, t)= y₁ (t)y₂(x) − y₁ (x)yz(t) W(t) -SGC G(x, t)f(t)dt L{f(t = a)U(t—a)} = e-as F(s) Yp = L{eat f(t)} = F(s – a) L{f(t)U(t − a)} = e¯ªsL{f(t + a)} as L{t"f(t)} = (−1)ª dºm [F(s)] dsn L{8(t - to)} = e-sto Solve the following separable equation: (e-2x+y +e-2x) dx - eydy = 0 e = 0 y

For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error decreases as the margin of error increases.

The square root of the variance for the given set of numbers is what the standard deviation examines. It is employed to compute a confidence interval for making judgments (such as accepting or rejecting a hypothesis).

Here, the population standard deviation, and level of significance are the same.

As the margin of error increased.

So, with the increase in the value of the margin of error, there will surely decrease in the value of the sample size

\($$\begin{aligned}&\mathrm{MOE}_\gamma=z_\gamma \times \sqrt{\frac{\sigma^2}{n}}\\&\begin{aligned}\mathrm{MOE} & =\text { margin of error } \\\gamma & =\text { confidence level } \\z_\gamma & =\text { quantile } \\\sigma & =\text { standard deviation } \\n & =\text { sample size }\end{aligned}\end{aligned}$$\)

As the margin of error is in the denominator position in the sample size formula

Hence with an increase in the margin of error sample size decreases.

For more question on margin of error

https://brainly.com/question/24289590

#SPJ4

Step-by-step explanation:

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

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

= 2x-x + 4-2

= 2x - x + 2

They would require more 4 8/22 days to complete the work.

Ann can translate the document in 10days

In 1 day he can translate 1/10 of the document

In 2 days he translates = 2 x 1/10

Ben can translate the same document in 12 days

In 1 day he can translate 1/12

Work left after Ann works for 2 days is 1 - 2/10 = 8/10

When working together they can work in 1 day is= 1/10 + 1/12 = 22/120

They do 22/120 work in 1 day

For 1 work, they require 1/(22/120) = 120/22

for 8/10, they would require (120/22)(8/10) = 96/22 = 4 8/22

Therefore, They would require more 4 8/22 days to complete the work.

To learn more about work refer here

https://brainly.com/question/24900258

#SPJ1

There are 7 students who are studying both programming languages in the given class of 55 freshman.

This can be determined using a Venn diagram.

A Venn diagram is a graphical representation of sets or classes. The diagram shows sets, their elements, and the union, intersection, and complement of these sets.

A set is a collection of distinct objects, considered as an object in its own right. The elements of a set are frequently things of a similar nature, and sets are characterized by a distinctive property.

The size of a set is represented by the number of elements it contains. Let's use the following symbols to represent sets:

A={Elements in set A}

B={Elements in set B}

The intersection of sets A and B is the set of elements that are in both sets A and B. This can be expressed in the following way

n(A∪B) = n(A) + n(B) - n(A⋂B) where n(A⋂B) is known as intersection

The number of students studying both programming languages can be calculated by taking the intersection of the two sets.

We can use this formula to calculate the number of students studying both programming languages

:|A∩B|=|A|+|B|-|A∪B|

Where |A| denotes the number of elements in set  A studying C programming

|B| denotes the number of elements in set B studying Java

|A∪B| denotes the number of elements in the union of sets A and B (total students)

Now we can substitute the given values into the formula as follows

|A∩B|=38+24−55=7

Therefore, there are 7 students studying both programming languages.

Learn more about intersection of sets : https://brainly.com/question/20886002

#SPJ11

In the basis step of the mathematical induction proof for P(n), we show that the equation is true for n = 1. The equation of the inductive hypothesis (IH) is P(k), where k is an arbitrary natural number. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

In the basis step, we substitute n = 1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1. This gives us the equation 1⋅2 = 1+1, which is true.

The inductive hypothesis (IH) is denoted as P(k), where k is an arbitrary natural number. We assume that P(k) is true, meaning that 11⋅2+12⋅3+⋅⋅⋅+1k⋅(k+1)=kk+1 holds.

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true. This involves substituting n = k+1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1 and demonstrating that the equation holds for this value. The specific equation we need to show in the inductive step is 11⋅2+12⋅3+⋅⋅⋅+1(k+1)⋅((k+1)+1)=(k+1)(k+1+1).

Learn more about inductive hypothesis here: brainly.com/question/31703254

#SPJ11

In the basis step, we need to show that the equation P(1) is true. The equation of the inductive hypothesis (IH) is P(k), where k is any natural number greater than or equal to 1. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

To prove the equation P(n): 11⋅2 + 12⋅3 + ... + 1n⋅(n+1) = n(n+1) using mathematical induction, we follow the two-step process.

1. Basis Step:

We start by showing that the equation is true for the base case, which is n = 1:

P(1): 11⋅2 = 1(1+1)

Simplifying, we get: 2 = 2, which is true.

2. Inductive Step:

Assuming that the equation is true for some arbitrary value k, the inductive hypothesis (IH) is:

P(k): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) = k(k+1)

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true:

P(k+1): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) + 1(k+1)⋅((k+1)+1) = (k+1)((k+1)+1)

By adding the (k+1)th term to the sum on the left side and simplifying the right side, we can demonstrate that P(k+1) is true.

Learn more about equation here: brainly.com/question/30130739

#SPJ11

Answer:

(-2, 3)

Step-by-step explanation:

Point (2, -3) becomes:

Answer:

The measure of exterior angle is 6 is 122

Answer:

The building is taller than 12ft is b>12

The box contains more than 11 books is b>11

Answer:

b<11 is The board is shorter than 11 cm

b>11 is The box contains more than 11 books

b<12 is There are fewer than 12 beetles in a jar

b>12 is The building is taller than 12 ft.

Step-by-step explanation:

The total number of ways/ permutation that A occupies first position is 24 ,  A occupies the first position, and B the second is 6 and a appears before b is 10 ways.

What is permutation ?

Permutation is a meeting of objects in an exceedingly definite order. The members or components of sets square measure organized here in an exceedingly sequence or linear order.

Main body:

A) a occupies the first position-

As A is first, and arrange the remaining letters.  letters (B,C,D,E,F) can be arranged as-

4*3*2*1 = 24 ways

B) a occupies the first position, and b the second

As A is first and b is just after it , there are 5 position out of which 2 are taken by A, B in order , so number of ways they can be arranged is

3*2*1 = 6 ways

C) a appears before b

in this part there is no  condition that a appears just before b , so b can be places anywhere after A.

after fixing A at first place , B can be placed at 4 places.

after fixing A at 2nd place , B can be placed at 3 places.

after fixing A at 3rd place , B can be placed at 2 places.

after fixing A at 4th  place , B can be placed at 1 places.

total ways = 4+3+2+1 = 10

Hence the answer to these parts are 24, 6,10

to know more about permutation , visit:

https://brainly.com/question/12468032

#SPJ4

Answer:

Option D

Hope this helps!

to get the equation of any straight line we simply need two points off of it, hmm let's get two from this table

\(\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} 0&4\\ 1&10\\ 2&16\\ 3&22\\ 4&28\\ \cline{1-2} \end{array} \begin{array}{llll} \\ \leftarrow \textit{let's use this point}\\\\ \leftarrow \textit{and this point} \end{array}\)

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{22}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{22}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}}\implies \cfrac{12}{2}\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{6}(x-\stackrel{x_1}{1}) \\\\\\ y-10=6x-6\implies y=6x+4\)

The probability that at least one of the lights is defective is 0.2661 .

in the question ,

it is given that

the total number of bulbs in the pack of new light bulbs is (n) = 5

percent of bulb that did not work is  = 6%

probability that lights did not work is (p) = 0.06

probability that lights work is (q) = 1 - 0.06 = 0.94

let x be the number of defective lights

So ,the probability that at least one of your lights is​ defective

is P(x ≥ 1) = 1 - P(x<1)

= 1 - P(x = 0)

By Binomial Probability

= 1 - ⁿCₓ*(p)ˣ*(q)ⁿ⁻ˣ

= 1 - ⁵C₀*(0.06)⁰*(0.94)⁵⁻⁰

= 1 - 1*1*(0.94)⁵         ...because ⁵C₀ = 1

= 1 - (0.94)⁵

= 1 - 0.7339

= 0.2661

Therefore , The probability that at least one of the lights is defective is 0.2661 .

The given question is incomplete , the complete question is

You purchased a​ five-pack of new light bulbs that were recalled because ​6% of the lights did not work. What is the probability that at least one of your lights is​ defective ?

Learn more about Probability here

https://brainly.com/question/28788900

#SPJ4

Answer:

x = 7

Step-by-step explanation:

7^2 or 7*7 = 49

The force between gently tossing a ball to your friend and throwing it at them as hard as you can are significantly different. When you gently toss a ball to your friend, the force exerted on the ball is relatively low.

This is because you are not applying much acceleration to the ball as it moves towards your friend. However, when you throw the ball at them as hard as you can, the force exerted on the ball is much higher. This is because you are applying a greater amount of acceleration to the ball, which results in a greater force being exerted.
In physics, force is defined as the product of mass and acceleration. When you throw the ball with greater acceleration, you are applying a greater force to the ball. This can be explained by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force applied to it, and inversely proportional to its mass.
Overall, the difference in force between gently tossing a ball and throwing it as hard as you can is significant. The latter involves a much greater force being exerted on the ball, due to the higher acceleration applied to it.

To know more about force visit:

https://brainly.com/question/30507236

#SPJ11

The error between the exponential function e^x and its third degree Taylor polynomial p3(x) = 1 + x + (x^2)/2 + (x^3)/6 can be computed by subtracting p3(x) from e^x. The error depends on the value of x and can be determined using the Taylor series remainder formula.

1. The error is generally smaller for values of x closer to zero, as the Taylor series approximation becomes more accurate near the expansion point. As x increases, the error tends to grow, indicating that the approximation becomes less accurate further away from the expansion point.

2. To compute the error ex−p3(x) for various values of x, we subtract the Taylor polynomial p3(x) from the exponential function e^x. The third degree Taylor polynomial is given by p3(x) = 1 + x + (x^2)/2 + (x^3)/6. Subtracting p3(x) from e^x gives us the error term ex−p3(x).

3. The error between the approximation and the actual value depends on the value of x. The Taylor series approximation becomes more accurate as x approaches zero, as the higher degree terms in the polynomial become relatively smaller compared to the lower degree terms. Thus, for values of x close to zero, the error is relatively small.

4. However, as x increases, the error tends to grow. This is because the Taylor series approximation is centered around the expansion point (in this case, x = 0), and as we move further away from the expansion point, the approximation becomes less accurate. Higher degree terms in the Taylor polynomial become relatively larger and contribute more to the error.

5. In conclusion, the error ex−p3(x) between the exponential function and its third degree Taylor polynomial depends on the value of x. The error is generally smaller for values of x closer to zero and tends to increase as x moves further away from the expansion point.

Learn more about Taylor polynomial here: brainly.com/question/30481013

#SPJ11

The side of the square equals half the minor axis of the ellipse.

To show that the side of the square is half the minor axis of the ellipse, we must prove that the angles of the ellipses and the squares are congruent. To do this, we must first draw in the diagonals of the square, which will form two additional isosceles triangles.

Since the ellipses are perpendicular, the angles of the ellipses and the squares will be the same. Since the angles of the isosceles triangles are equal, the side of the square must be equal to half of the minor axis of the ellipse. Therefore, the side of the square is equal to half of the minor axis of the ellipse.

For more questions like Minor axis click the link below:

https://brainly.com/question/29054958

#SPJ4

The area of the shaded face of the cylinder is 1,520 mm².

We can see that the shaded area of the cylinder is circular in shape.

This means that we can find the area of the shaded area by finding the area of the circle.

The radius of the circle is given as 22 mm.

The formula for finding the area of a circle is given as:

Area = πr²

= 3.14 × 22 × 22

= 1,519.76

≈ 1520 mm²

Therefore, we have found the area of the shaded face of the cylinder to be 1,520 mm².

Learn more about the area of a circle here: https://brainly.com/question/14068861

#SPJ4

Disclaimer: The question was incomplete, the complete question is attached below.

The measure of the angle of the triangle is ∠A = 51.3178°

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides are

AB = 24 units

AC = 15 units

Now , from the trigonometric relations , we get

cos θ = adjacent / hypotenuse

So , cos θ = 15 / 24

cos θ = 0.625

Taking inverse on both sides , we get

θ = cos⁻¹ ( 0.625 )

θ = 51.3178°

Hence , the measure of angle ∠A = 51.3178°

To learn more about trigonometric relations click :

https://brainly.com/question/14746686

#SPJ2

(a) The probability of ending up with two hits is approximately 0.1406.

(b) The probability of ending up with no hits is approximately 0.4219.

(c) The probability of ending up with exactly three hits is approximately 0.0156.

(d) The probability of ending up with at most one hit is approximately 0.8438.

To solve the given problem, we need to use the concept of binomial probability since each at-bat is independent and has the same probability of a hit. We'll use the batting average of 0.250 to calculate the probabilities.

The probability of a hit is given by the batting average, which is 0.250.

(a) To find the probability that she ends up with two hits:

Using the binomial probability formula, the probability of getting exactly two hits in three at-bats can be calculated as follows:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (1 - 0.250)^(^3^ -^ 2^)\)

Calculating the values:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (0.750)^1\)

P(X = 2) = 3 * 0.0625 * 0.750

P(X = 2) ≈ 0.1406

Therefore, the probability that she ends up with two hits is approximately 0.1406.

(b) To find the probability that she ends up with no hits:

Using the same binomial probability formula, the probability of getting no hits in three at-bats can be calculated as follows:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (1 - 0.250)^(^3^ -^ 0^)\)

Calculating the values:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (0.750)^3\)

P(X = 0) = 1 * 1 * 0.4219

P(X = 0) ≈ 0.4219

Therefore, the probability that she ends up with no hits is approximately 0.4219.

(c) To find the probability that she ends up with exactly three hits:

Using the same binomial probability formula, the probability of getting three hits in three at-bats can be calculated as follows:

P(X = 3) = (3 choose 3) \(* (0.250)^3 * (1 - 0.250)^(^3^ -^ 3^)\)

Calculating the values:

P(X = 3) = (3 choose 3) *\((0.250)^3 * (0.750)^0\)

P(X = 3) = 1 * 0.0156 * 1

P(X = 3) ≈ 0.0156

Therefore, the probability that she ends up with exactly three hits is approximately 0.0156.

(d) To find the probability that she ends up with at most one hit:

We can find this probability by calculating the sum of the probabilities of getting 0 hits and 1 hit.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Substituting the calculated values:

P(X ≤ 1) ≈ 0.4219 + P(X = 1)

To calculate P(X = 1), we can use the binomial probability formula as before:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^(^3^-^1^)\)

Calculating the values:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^2\)

P(X = 1) = 3 * 0.250 * 0.5625

P(X = 1) ≈ 0.4219

Substituting back into the equation:

P(X ≤ 1)

≈ 0.4219 + 0.4219

P(X ≤ 1) ≈ 0.8438

Therefore, the probability that she ends up with at most one hit is approximately 0.8438.

For more such information on: probability

https://brainly.com/question/30390037

#SPJ8

Answer:

hope it helps plz mark me brainliest!

Step-by-step explanation:

4x² - 3, x less than/equal to 0

Step-by-step explanation:

y = (-1/2)[(x+3)^½]

(x+3)^½ = -2y

Square both sides,

(x+3) = (-2y)²

x+3 = 4y²

x = 4y²-3

Interswitch x and y

Inverse is 4x²-3

Domain of inverse is the range of f.

The range of f is less than/equal to 0

Because at x = -3, f(x) = 0

For x > -3, f(x) is negative

Domain of inverse is x less than/equal to 0

Answer:

P = 91/990

Step-by-step explanation:

first red marble:    \(\frac{14}{45}\)

second red marble: \(\frac{13}{44}\)

The probability

\(P=(\frac{14}{45})(\frac{13}{44} )=\frac{(14)(13)}{(45)(44)} =\frac{182}{1980} =\frac{91}{990}\)

Hope this helps

Answer:

5 meters per second

Step-by-step explanation:

First you must find the slope of the graph. Take the rise/run of the function. The graph starts at 8500 meters and goes down to 7500 meters in 200 seconds. the difference between the change in meters is 1000 meters and the change in seconds is 200 seconds. That is 1000/200. This can be simplified to 5/1 which is 5 meters per second.

Answer: 5 meters per second.

Step-by-step explanation:

(A) It was at 8000m at 100 seconds.

(B) It was at 7000m at 300 seconds.

Difference in altitude = 8000m - 7000m = 1000m

Difference in time = 300s - 100s = 200s

\(\frac{1000m}{200s} =5m/s\)

Answer:

p = - 14

Step-by-step explanation:

Using the rules of exponents

\(a^{m}\) ÷ \(a^{n}\) = \(a^{(m-n)}\)

\((a^{m}) ^{n}\) = \(a^{mn}\)

Note 81 = 9² and 729 = 9³

Given

\((81)^{-4}\) ÷ \((729)^{2-p}\)

= \((9^{2}) ^{-4}\) ÷ \((9^{3}) ^{2-p}\)

= \(9^{-8}\) ÷ \(9^{6-3p}\)

= \(9^{-8-(6-3p)}\)

= \(9^{-8-6+3p}\)

= \(9^{3p-14}\)

Thus

\(9^{3p-14}\) = \(9^{4p}\)

Since bases on both sides are equal then equate the exponents

4p = 3p - 14 ( subtract 3p from both sides )

p = - 14

The simplified form of the given expression is (x-7)/3x.

The given expression is (2x²-8x-42)/6x² ÷ (x²-9)/(x²-3x)

Here, (x²-4x-21)/3x² ÷ (x-3)(x+3)/x(x-3)

= (x²-4x-21)/3x² ÷ (x+3)/x

= (x²-4x-21)/3x² × x/(x+3)

= (x²-4x-21)/3x × 1/(x+3)

= (x²-4x-21)/3x(x+3)

= (x²-7x+3x-21)/3x(x+3)

= [x(x-7)+3(x-7)]/3x(x+3)

= (x-7)(x+3)/3x(x+3)

= (x-7)/3x

Therefore, the simplified form of the given expression is (x-7)/3x.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ1

Step-by-step explanation:

x + x + 3 = 48

2x = 48 - 3

2x = 45

x = 45/2

Answer:

x = 45/2

Step-by-step explanation:

x+x+1+2 = 48

combine like terms

2x + 3 = 48

2x - 3 = -3

     2x = 45

  2x/2 = 45/2

       x = 45/2

The probability of getting a sum of 4 when rolling two 4-sided dice is 3/16.

Expressed as a percentage, the probability is approximately 18.75%.

To determine the probability of obtaining a sum of 4 when rolling two 4-sided dice,

Count the number of favorable outcomes (combinations that add up to 4) and divide it by the total number of possible outcomes.

Let's consider all the possible outcomes when rolling two 4-sided dice,

1+1 = 2

1+2 = 3

1+3 = 4

1+4 = 5

2+1 = 3

2+2 = 4

2+3 = 5

2+4 = 6

3+1 = 4

3+2 = 5

3+3 = 6

3+4 = 7

4+1 = 5

4+2 = 6

4+3 = 7

4+4 = 8

Out of the 16 possible outcomes, we can see that there are 3 favorable outcomes (1+3, 2+2, and 3+1) that sum up to 4.

The probability of obtaining a sum of 4 when rolling two 4-sided dice is 3/16.

Expressed as a percentage, this probability is (3/16) × 100 ≈ 18.75%.

Therefore, the probability of getting a sum of 4 when rolling two 4-sided dice is 3/16 and as a percentage it is approximately 18.75%.

Learn more about probability here

brainly.com/question/10094983

#SPJ4

In monthly sales would mr. gonzalez need to have $100000

Mr. Gonzalez earns his living as a salary plus commission employee, then his annual earnings can be represented by

Monthly earnings=a+bx

Where a =his annual salary (fixed),

b = the percentage of sales commission and

X =represents the volume of sales made each year.

Therefore When  Mr. Gonzalez annual salary is $18,000 and makes a commission of 4%, his annual sales that will enable him earn an annual salary of $60,000 will be equal to

$60000 = $18000 + 0.04X

$60000 - $18000 = 0.04X

$48000 = 0.04X

0.04X = $1200000

X = $48000/0.04=12000000

X=$12000000

Therefore, his monthly sales is given by his  earnings divided evenly each month is equal to

$1200000/12=$100000

So the option c is correct.

To learn mpre about the earning visit:

https://brainly.com/question/25793394

Answer:c

Step-by-step explanation: