Given the differential equation:
dy/dx -xy = -2 (x2 ex – y2)
with the initial condition y(0) = 1, find the values of y corresponding to the values of x0+0.2 and x0+0.4 correct to four decimal places using Heun's method.

The answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

To calculate the sperm concentration using a Neubauer counting chamber, we can use the following formula:

Sperm concentration = (number of sperm counted ÷ number of counting squares) ÷ dilution factor

In this case, we have:

Number of sperm counted = 54

Number of counting squares = 5

Dilution factor = 1:20

First, we need to calculate the total volume of the diluted sperm sample that was loaded onto the counting chamber. To do this, we can use the following formula:

Total volume = volume of loaded sample ÷ dilution factor

Since the dilution factor is 1:20, this means that the volume of loaded sample is 1/20th of the total volume. The total volume depends on the depth of the chamber and is usually 0.1 mL (or 100 μL) for a standard Neubauer counting chamber. Therefore:

Total volume = 0.1 mL ÷ 20 = 0.005 mL

Next, we can calculate the sperm concentration using the formula above:

Sperm concentration = (54 ÷ 5) ÷ 1/20

Sperm concentration = 54 ÷ 5 × 20

Sperm concentration = 54 ÷ 100

Sperm concentration = 0.54 million/cc

Therefore, the answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

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Your question is incomplete, but probably the complete question is :

Using a 1:20 dilution and the 5 RBC counting squares of the Neubauer counting chamber, an average of 54 sperm is counted. The sperm concentration is:

A. 54,000/cc

B. 54,000,000/mL

C. 108,000/cc

D. 108,000,000/mL

To calculate the amount Briana saved by purchasing a backpack with a sales promotion, we need to find the difference in prices between the two backpacks after applying the respective discounts.

For the first backpack that originally costs $45 with a sales promotion of 20% off:

Discounted price = $45 - (20% * $45) = $45 - $9 = $36

For the second backpack that originally costs $42 with a sales promotion of 10% off:

Discounted price = $42 - (10% * $42) = $42 - $4.2 = $37.8

Now we can calculate the savings:

Amount saved = Original price - Discounted price

Amount saved = $42 - $37.8 = $4.2

Therefore, Briana saved $4.2 by purchasing the backpack that cost $45 with a 20% off promotion instead of the backpack that cost $42 with a 10% off promotion.

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The value of base in the given right angle triangle is x which equal to 12√3. Trigonometry is used to find the value in the given figure.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of an angle in a triangle. That means that these trig functions provide the relationship between the angles and sides of a triangle. The fundamental trigonometric operations are sine, cosine, tangent, cotangent, secant, and cosecant. 

sin A = perpendicular/hypotenuse : sin (<BAC) = BC/ AC

put AC = 24,

<BAC = 30⁰

put it in above,

sin( 30⁰) = BC/24  : BC = 12

by using Pythagoras theorem : AB² + BC² = AC²

by putting the value, AB = x, BC = 12

x² + 12² = 24²

x = 12√3

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The answer is C: \(h = \frac{2A}{b}\)

Starting with the given formula for the area, A = 1/2hb, the first step is to isolate h by using the multiplicative inverse of b, which is \(\frac{1}{b}\) on both sides of the equation:

\(A(\frac{1}{b}) = \frac{1}{2}hb* (\frac{1}{b})\)

The result will be:

\(\frac{A}{b} = \frac{1}{2}h\)

The last step is to use the multiplicative inverse of \(\frac{1}{2}\), which is 2 or \(\frac{2}{1}\) to further isolate the variable h :

\(\frac{A}{b} (\frac{2}{1}) = (\frac{2}{1}) \frac{1}{2} h\)

The formula for h will be:

\(h = \frac{2A}{b}\)  which is the option C in your question.

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

Answer:

x=-2\(\sqrt{x} 22 -9\)

Step-by-step explanation:

Answer: s = 16

2(s - 10) = 12

distribute the 2

2s - 20 = 12

add 20 to both sides

2s = 32

divide both sides by 2

s = 16

you can then check your work by putting in the 16

2 (16-10) = 12

2 (6) = 12

12 = 12

The lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

The lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

Given an ellipse with center (0,0) that has the equation

\($\frac{x^2}{225}+\frac{y^2}{400}=1$\),

find the directrices.

Solution: The standard equation of an ellipse with center (0,0) is

\($\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$\)

Where 'a' is the semi-major axis and 'b' is the semi-minor axis. Comparing this equation with

\($\frac{x^2}{225}+\frac{y^2}{400}=1$\)

gives us: a=15 and b=20.

The distance between the center and each focus is given by the relation:

\($c=\sqrt{a^2-b^2}$\)

Where 'c' is the distance between the center and each focus.

Substituting the values of 'a' and 'b' gives:

\($c=\sqrt{15^2-20^2}$ = $\sqrt{-175}$ = $i\sqrt{175}$\)

The directrices are on the major axis. The distance between the center and each directrix is

\($d=\frac{a^2}{c}$\).

Substituting the value of 'a' and 'c' gives:

\(d=\frac{15^2}{i\sqrt{175}}$ $=$ $\frac{225}{i\sqrt{175}}$\)

\($= \frac{15\sqrt{7}}{7}i$\)

Therefore, the equations of the directrices are \($x=-\frac{15\sqrt{7}}{7}$\) and \($x=\frac{15\sqrt{7}}{7}$\)

Round to the nearest tenth, the answer is -6.6 and 10.6 respectively. Thus, the lines that represent the approximate directrices of the ellipse are x = -6.6 and x = 10.6.

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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The car was driven 105 miles.

What is rent?

An agreement where a fee is paid for the temporary use of a good, service, or property owned by another is known as renting, sometimes known as hiring, or letting.

In the given example the cost function is, c = 15 + 2m

Where, c is the total cost and m is the number of miles car driven.

The total cost was $225.

So, plug c = $225 in the above equation.

225 = 15 + 2m

210 = 2m

   m = 105

Therefore, the car was driven 105 miles.

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Answer:

??

Step-by-step explanation:

If that truly is homework I'd email your teacher.

Answer:

a leg of something

a piece of watch

or a piece of clothing

Step-by-step explanation:

Answer:

\(\frac{25}{114}\) or 0.219

Step-by-step explanation:

No. of tankers drawn= 342

No. of tankers which didn't have spills= 267

No. of tankers which had spills= 342-267

                                                  = 75

Proportion of oil tankers that had spills= \(\frac{75}{342}\)

Proportion as fraction= \(\frac{25}{114}\)

Proportion as decimal= 0.219

From these data, it is difficult to draw any meaningful conclusions about which waiters and waitresses earn larger tips.

The data only measure the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of the 50 restaurants during a 1-week period, which does not provide a large enough sample size to draw any meaningful conclusions. In order to draw more reliable conclusions, a larger, more comprehensive study should be conducted that measures the tips for multiple waiters and waitresses from each restaurant over a longer period of time.

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Answer:

3.45 m

Step-by-step explanation:

as we know that

1cm=100m

Divide by 100

345/100=3.45 m

Approximate height to the statue's actual height of 120 feet, 3 inches from heel to top of head is 123.75 feet.

To estimate the height of the statue, the student can use the method of similar triangles. Since the length of the statue's right arm is 45 feet and the length of the student's right arm is 2 feet, the ratio of the lengths of the arms is 45/2 = 22.5. If we assume that the ratio of the heights of the statue and the student is also 22.5, then the height of the statue can be estimated as:

height of statue = height of student x ratio of heights

height of statue = 5.5 x 22.5

height of statue = 123.75 feet

This estimated height of the statue is close to the actual height of 120 feet, 3 inches. It should be noted that this method of estimation assumes that the ratio of the heights of the statue and the student is the same as the ratio of the lengths of their arms. This may not be completely accurate, as the proportions of the statue and the student may be different.

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Answer

5.9

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms

Answer:

Below.

Step-by-step explanation:

False for all isosceles triangles except:

This is only true for a 45-45-90 triangle.

Answer:

(a) Set of rational numbers

(b) \(\pi + (-\pi) = 0\)

Step-by-step explanation:

Solving (a): Set that is closed under subtraction

The solution to this is rational numbers.

For a set of number to be closed under subtraction, the following condition must be true

\(a -b = c\)

Where

a, b, c are of the same set.

The above is only true for rational numbers.

e.g.

\(1 - 2 = -1\)

\(5 - 5 = 0\)

\(\frac{1}{2} - \frac{1}{4} = \frac{1}{2}\)

\(4 - 2 = 2\)

The operations and the result in the above samples are rational numbers.

Solving (b): Choice not close under addition[See attachment for options]

As stated in (a)

For a set of number to be closed under subtraction, the following condition must be true

\(a -b = c\)

Where

a, b, c are of the same set.

In the given options (a) to (d), only

\(\pi + (-\pi) = 0\) is not close under addition because:

\(\pi\) is irrational while \(0\) is rational

In other words, they belong to different set

Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

Answer:

D. x = 5 or x = 10

Step-by-step explanation:

Simplifying the expression further may not be possible without knowing the specific value of y. Therefore, the variance of x depends on the value of y within the given interval [10,000, 20,000].

To calculate the variance of the amount of gas sold during a week (denoted by x), we need to use the properties of uniform distributions.

Given that y, the amount of gas stocked at the beginning of the week, follows a uniform distribution over the interval [10,000, 20,000], we can find the probability density function (pdf) of y, which is denoted as f(y).

Since y is uniformly distributed, the pdf f(y) is constant over the interval [10,000, 20,000], and 0 outside that interval. Therefore, f(y) is given by:

f(y) = 1 / (20,000 - 10,000) = 1 / 10,000 for 10,000 ≤ y ≤ 20,000

Now, let's find the cumulative distribution function (CDF) of y, denoted as F(y). The CDF gives the probability that y is less than or equal to a given value. For a uniform distribution, the CDF is a linear function.

For y in the interval [10,000, 20,000], the CDF F(y) can be expressed as:

F(y) = (y - 10,000) / (20,000 - 10,000) = (y - 10,000) / 10,000 for 10,000 ≤ y ≤ 20,000

Now, let's find the probability density function (pdf) of x, denoted as g(x).

Since x is uniformly distributed over the interval [10,000, y], the pdf g(x) is given by:

g(x) = 1 / (y - 10,000) for 10,000 ≤ x ≤ y

To calculate the variance of x, we need to find the mean (μ) and the second moment (E[x^2]) of x.

The mean of x, denoted as μ, is given by the integral of x times the pdf g(x) over the interval [10,000, y]:

μ = ∫(x * g(x)) dx (from x = 10,000 to x = y)

Substituting the expression for g(x), we have:

μ = ∫(x * (1 / (y - 10,000))) dx (from x = 10,000 to x = y)

μ = (1 / (y - 10,000)) * ∫(x) dx (from x = 10,000 to x = y)

μ = (1 / (y - 10,000)) * (x^2 / 2) (from x = 10,000 to x = y)

μ = (1 / (y - 10,000)) * ((y^2 - 10,000^2) / 2)

μ = (1 / (y - 10,000)) * (y^2 - 100,000,000) / 2

μ = (y^2 - 100,000,000) / (2 * (y - 10,000))

Next, let's calculate the second moment E[x^2] of x.

The second moment E[x^2] is given by the integral of x^2 times the pdf g(x) over the interval [10,000, y]:

E[x^2] = ∫(x^2 * g(x)) dx (from x = 10,000 to x = y)

Substituting the expression for g(x), we have:

E[x^2] = ∫(x^2 * (1 / (y - 10,000))) dx (from x = 10,000 to x = y)

E[x^2] = (1 / (y - 10,000)) * ∫(x^2) dx (from x = 10,000 to x = y)

E[x^2] = (1 / (y - 10,000)) * (x^3 / 3) (from x = 10,000 to x = y)

E[x^2] = (1 / (y - 10,000)) * ((y^3 - 10,000^3) / 3)

E[x^2] = (y^3 - 1,000,000,000,000) / (3 * (y - 10,000))

Finally, we can calculate the variance of x using the formula:

Var(x) = E[x^2] - μ^2

Substituting the expressions for E[x^2] and μ, we have:

Var(x) = (y^3 - 1,000,000,000,000) / (3 * (y - 10,000)) - [(y^2 - 100,000,000) / (2 * (y - 10,000))]^2

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Step-by-step explanation:

Simplify the expression

The values of k for which A is diagonalizable are the values that satisfy either k = λ or (7-λ)(u-λ) - 5k = 0 and have two linearly independent eigenvectors associated with λ. The eigenvectors can be found by solving the system (A-λI)x = 0 for each eigenvalue λ.

The eigenvalues of A are the solutions to the characteristic equation det(A-λI) = 0, where I is the identity matrix and det denotes the determinant.

We have:

det(A-λI) = det

|7-λ   5   0 |
| 5   k-λ  k |
| 0    k   u-λ|

Expanding along the first row, we get:

det(A-λI) = (7-λ) det

| k-λ  k |
|  k  u-λ|

- 5 det

| 5  k |
| 0 u-λ|

= (7-λ)(k-λ)(u-λ) - 5(k-λ)k

Setting this equal to 0 and factoring out (k-λ), we get:

(k-λ)[(7-λ)(u-λ) - 5k] = 0

Either k = λ or (7-λ)(u-λ) - 5k = 0.

If k = λ, then A has at least one eigenvalue of multiplicity 2. To be diagonalizable, it must have two linearly independent eigenvectors associated with this eigenvalue.

If (7-λ)(u-λ) - 5k = 0, then λ is an eigenvalue with algebraic multiplicity 2. To be diagonalizable, it must have two linearly independent eigenvectors associated with it.

Therefore, the values of k for which A is diagonalizable are the values that satisfy either k = λ or (7-λ)(u-λ) - 5k = 0 and have two linearly independent eigenvectors associated with λ.

The eigenvectors can be found by solving the system (A-λI)x = 0 for each eigenvalue λ.

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Answer:

42 tablespoons

Step-by-step explanation:

a tablespoon is 1/2 a fluid ounce.

so, 21x2= 42

The equation of the conic in standard form is (x + 1)² + (y - 4)² = 16.

Here, we have,

In this problem we find the equation of the conic in general form, that is, an equation of the form:

A · x² + B · x + C · y² + D · y + E = 0

Where A, B, C, D, E are real coefficients.

And we are asked to find the standard form of the previous formula and this can be found by completing the square:

x² + 2 · x + y² - 8 · y + 1 = 0

(x² + 2 · x) + (y² - 8 · y) = - 1

(x² + 2 · x + 1) + (y² - 8 · y + 16) = 16

(x + 1)² + (y - 4)² = 16

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complete question:

Translate the following conic from standard form to graphing form

x ^ 2 + 2x + u ^ 2 - 8y + 1 = 0

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is 18%.

To find the percent of the total area between two z-scores, we need to calculate the area under the standard normal curve between those two z-scores.

Using a standard normal distribution table or a statistical software, we can find the area to the left of each z-score and subtract the smaller area from the larger area to find the area between the z-scores.

For z = -1.5, the area to the left of z = -1.5 is approximately 0.0668.

For z = -0.7, the area to the left of z = -0.7 is approximately 0.2420.

The area between z = -1.5 and z = -0.7 is:

Area between z = -1.5 and z = -0.7 = Area to the left of z = -0.7 - Area to the left of z = -1.5

= 0.2420 - 0.0668

= 0.1752

To convert this area to a percentage, we multiply by 100:

Percentage of the total area between z = -1.5 and z = -0.7 = 0.1752 * 100 ≈ 17.52%

Rounding to the nearest integer, the percent of the total area between z = -1.5 and z = -0.7 is 18%.

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is approximately 18%.

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Answer:

a juice bo has 20% more juice than the original package. the original package holds 12 ounces.

first find what 100% of 12 is. 12 obvi. then divide 12 by 10 to get what 10% is. 10% of 12 is 1.2 so multiply 1.2 by 2 which is 2.4, and thats 20% of 12.

now add 2.4 to 12, and you get 14.4, how much the new juice box holds