A project can be completed by 5 workers in 24 days. How many workers are needed to finish the project in 15 days? The time to complete a project is inversely proportional to number of people who are doing the project.

The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

3/8

Step-by-step explanation:

The answer would be 3/8 because if you take 7/8 and subtract 1/2 from the height of the cat after finding equivelent denominators you'd get 7/8. hope I helped :)

Answer:

its 3/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

10 minutes

if it took her 16 minutes to read 8 pages then that means it takes her 2 minutes to read one page. 2 times 5 is 10

Answer:

Step-by-step explanation:

It would be ten. Because it took her 16 minutes to read 8 pages and 8 pages times 2 minutes each page = 16 minutes, so 5 pages times 2 minutes each page = 10

Hey there! I'm happy to help!

AREA

To find the area of a parallelogram, you multiply the base by the height.

12(6)=72

The area is 72 square centimeters.

PERIMETER

The two diagonal sides are 8 cm and the two bases are 12 cm.

8+8+12+12=40

The perimeter is 40 cm.

Have a wonderful day! :D

The constant of proportionality is 20.

What is constant of proportionality?

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Given,

the recipe uses 5 cups of strawberries per 1/4 cup of sugar.

And let constant of proportionality is k.

that is

5 α 1/4

5 = k1/4

k = 5(4)

k = 20

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Answer:

no because it just reaches one class, not the student body

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

4 [4,8,12,16,20,24,28,32,36,40,...]

9 [9,18,27,36,45,54,...}

36 for both

3/4 (x 9 on top and bottom) = 27/36

7/9 = 28/36

Answer:

(3,2)

Step-by-step explanation:

the other three ordered pairs do not lie in the shaded region

72 x 12 = 864

864 x 156 = 134,784

in the capacity of the year, 134784 people have been carried on the train

merry christmas:)

In the word problem,  the train has carried 134,784 people in that year.

To calculate the total number of people carried by the train in a year, we need to find the number of people carried in a single trip and then multiply it by the total number of trips made in a year.

Each coach can seat exactly 72 people, and there are 12 coaches on the train. So, in a single trip, the train can carry:

72 (people per coach) * 12 (number of coaches) = 864 people

Now, the train made 156 trips in full capacity in a year. So, the total number of people carried in that time would be:

156 (trips) * 864 (people per trip) = 134,784 people

Therefore, the train has carried 134,784 people in that year.

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Step-by-step explanation:

the correct answer is option a 6a-7

Answer:

A

Step-by-step explanation:

What makes it a function?

If an x is unique but y can be duplicated

A is correct because the x are unique

B is incorrect because 3 is used twice

C is incorrect because -5 and -10 is used twice

D is incorrect because 20 is used twice

The 8 pints of juice Luna has and the amount Michael has which  is a multiple of the mixed fraction 2 3/4 and the amount Luna has indicates;

A) The amount of juice Michael has is 22 pint of juice

B) Michael has 14 more pint of juice than Luna

A fraction is a number that represents a part of an amount, and which can be represented by the quantity of the part over the quantity of the whole, with a division line in between the quantities.

Part of the question, obtained from a similar question on the internet includes;

Michael has 2 3/4 has many pints of Juice as Luna

A) The amount of juice Michael has obtained from the multiple of the amount of juice Luna has, which is 2 3/4 is therefore;

Michael has 2 3/4 × 8 pints of juice = 8 × 11/4 pint = 22 pint of juice

B) The amount of juice Michael has than Luna, ΔV is therefore;

ΔV = 22 pint - 8 pint = 14 pint

Michael has 14 more pint of juice than Luna

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Answer: 3:45

Step-by-step explanation:

Answer:

True.

Explanation:

When solving equations with unknowns on both sides, it is generally recommended to first deal with the variable terms before dealing with the constant terms. This involves simplifying the equation by combining like terms and isolating the variable on one side of the equation. Once the variable is isolated, you can then solve for its value.\(\)

Answer:

528cm³

Explanation:

The shape is a square pyramid, so we must use the equation of it, which is 1/3Bh.

In order to find B, base, you need to multiply the Length and Width of the Square, in this case, 12×12=144cm

The height of the shape is 11cm, as the picture states.

Then put the values into the equation and multiply to solve.

(1/3)(144)(11) = 528cm³

The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F

from the question, we have the following parameters that can be used in our computation:

Yeast thrives between 90°F to 95°F

For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range

Using the above as a guide, we have the following:

T < 90°F or T > 95°F.

Where

T = Temperature

Hence, the inequality is T < 90°F or T > 95°F.

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Answer:

I think you copied this wrong

Step-by-step explanation:

Most likely g = 2

Therefore (2) + 6(11)

2+66=68

Answer: 24

Step-by-step explanation:

Answer:

hmmmmmmmmmmmmmmmmm

Step-by-step explanation:

egfrggggggdfgd

djdgg

gfhdst

Answer:

\(\underline{\boxed{\sf -38}}\)

Step-by-step explanation:

\(\sf 35+(-1)+(-64)+(-8)\)

Subtract 1 from 35= 34

\(\sf 34-64-8\)

Subtract 64 - 34= -30

\(\sf -30-8\)

Subtract 8 - 30 = -38

\(\sf -38\) ← Answer

To show that the product of the sample observations is a sufficient statistic for θ > 0 in the case of a random sample taken from a gamma distribution with parameters α = θ and β = 6, we can use the factorization theorem for sufficient statistics.

Let's denote the random sample as X₁, X₂, ..., Xₙ, where each Xi is an independent and identically distributed random variable following a gamma distribution with parameters α = θ and β = 6.

The probability density function (pdf) of a gamma distribution with parameters α and β is given by:

f(x; α, β) = (1 / (β^α * Γ(α))) * (x^(α - 1)) * exp(-x / β)

where Γ(α) is the gamma function.

The joint pdf of the random sample can be expressed as:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * (x₁ * x₂ * ... * xₙ)^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β)

By the factorization theorem, the product of the sample observations, denoted as T = x₁ * x₂ * ... * xₙ, is a sufficient statistic for θ if we can express the joint pdf as the product of two functions, one depending on the sample observations T and the other on the parameter θ.

Let's rewrite the joint pdf in terms of T:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β)

Now, we can separate the terms depending on T and θ:

f(x₁, x₂, ..., xₙ; α, β) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) * exp(-(x₁ + x₂ + ... + xₙ) / β) = g(T; α) * h(x₁, x₂, ..., xₙ; β)

Here, we can observe that g(T; α) = (1 / (β^(nα) * Γ(α)^n)) * T^(α - 1) depends only on T and α, and h(x₁, x₂, ..., xₙ; β) = exp(-(x₁ + x₂ + ... + xₙ) / β) depends only on the sample observations and β.

Therefore, we have successfully factorized the joint pdf into two functions, one depending on T and α, and the other depending on the sample observations and β. This confirms that the product of the sample observations T = x₁ * x₂ * ... * xₙ is a sufficient statistic for the parameter θ when the random sample is taken from a gamma distribution with parameters α = θ and β = 6.

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-The first one is

6 pounds

-The second one is

14

-The third one is

$172.20

i just took it on ~e d g e n u i t y~

Answer:

-The first one is

6 pounds

-The second one is

14

-The third one is

$172.20

i just took it on ~e d g e n u i t y~

Step-by-step explanation:

Answer:

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14

Step-by-step explanation:

If the circle has a center at (8,9), the equation for this circle is:

\((x-8)^2 + (y - 9)^2 = r^2\)

All concentric circles have the same center, so their equations need to have the same left side of the equation above.

-> x2 + y2 = 25

This circle has a center at (0,0), so it's not concentric to our circle.

-> (x – 8)² + (y – 9)² = 3

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y – 9)² = 14

This circle has a center at (8,9), so it's concentric to our circle.

-> (x – 8)² + (y + 9)² = 3

This circle has a center at (8,-9), so it's not concentric to our circle.

-> (x + 8)² + (y + 9)² = 25

This circle has a center at (-8,-9), so it's not concentric to our circle.

-> (x + 9)² + (y + 8)² = 3

This circle has a center at (-8,-9), so it's not concentric to our circle.

Correct options:

(x – 8)² + (y – 9)² = 3

(x – 8)² + (y – 9)² = 14

Answer:

B. (x – 8)² + (y – 9)² = 3

C.(x – 8)² + (y – 9)² = 14

Step-by-step explanation:

edg 2020

The equation of the line from the given figure is y=-7.

We need to find the equation of the line from the given figure.

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x and y to form an algebraic equation, which is referred to as an equation of a line.

From the given figure, we can see that the line is passing through the point (0, -7).

The slope (m) of the line is 0.

Put m=0 and (0, -7) in y=mx+c and simplify.

That is, -7=c

Now, substitute c=-7 in y=mx+c.

Thus, y=-7

Therefore, the equation of the line from the given figure is y=-7.

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Answer:

There are 6 * 6 = 36 total outcomes from throwing 2 dice. Of those, there is only 1 that will give you a sum less than 3 (1 + 1) so the answer is 1 / 36.

The equation which governs Kyle's Wages, W are :

Kyle's hourly pay = $10

Hourly pay if h ≤ 40

Then there will be no extra hours worked ;

W = 10h

Pay for extra hours, hours greater than 40

If h > 40

Extra hours will be paid at 1.5times the normal hourly rate :

W = (40 × 10) + 1.5 * 10(h - 40)

W = 400 + 15(h - 40)

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The correct answer is:

The results of the ANOVA indicate that both Kia and Honda have significantly better gas mileage than Ford.

Given is an information about,
Least Squares Means

Adjustment for Multiple Comparisons: Tukey-Kramer

We need to identify the correct answer from the options given.

So, from the table we can conclude that "the results of the ANOVA indicate that both Kia and Honda have significantly better gas mileage than Ford."

This can be inferred from the comparison of LSMEAN numbers in the table.

The LSMEAN number for Ford is 1, for Honda it is 2, and for Kia it is 3. Comparing the values in the table, we can see that the Pr > t values for the comparisons between Ford and both Honda and Kia are less than the significance level (0.05).

This indicates that there are significant differences in gas mileage between Ford and both Honda and Kia, suggesting that both Honda and Kia have significantly better gas mileage than Ford.

Hence the correct option is 4th.

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Complete question is attached.

We can use the Comparison Test to determine the convergence of the given series:

Since 0 ≤ cos^2(n) ≤ 1 for all n, we have:

0 ≤ cos^2(n) / (n^5 + 1) ≤ 1 / (n^5)

The series ∑(n=1 to ∞) 1 / (n^5) is a convergent p-series with p = 5, so by the Comparison Test, the given series is also convergent.

Therefore, the series ∑(n=1 to ∞) cos^2(n) / (n^5 + 1) is convergent.

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