A study was conducted to see the differences between oxygen consumption rates for male runners from a college who had been trained by two different methods, one involving continuous training for a period of time each day and the other involving intermittent training of about the same overall duration. The means, standard deviations, and sample sizes are shown in the following table. Continuous training n₁ = 15 Intermittent training n₂=7 x₁ = 46.28 s₁=6.3 x₂ = 42.34 $₂=7.8 If the measurements are assumed to come from normally distributed populations with equal variances, estimate the difference between the population means, with confidence coefficient 0.95, and interpret.

Answer:

Step-by-step explanation:

1.  Not sure...

2. $ 1.44

3. $ 3.70

4. $11 per ticket

After considering the given data we conclude the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products and  the quotient q(x) is [tex]x^2 - x,[/tex] and the remainder r(x) is [tex]3x^2 + 8x + 5,[/tex]

To evaluate the product h(x) of the two polynomials f(x) and g(x) manually, we can apply a table [tex]T_3[/tex] to show line by line how each term is computed.
The table possess columns for the term from f(x), the term from g(x), and the product of the two terms. The rows of the table will correspond to the different powers of x, starting from [tex]x^0[/tex].
For instance , to compute the constant term of h(x), we need to multiply the constant terms of f(x) and g(x). The constant term of f(x) is 5, and the constant term of g(x) is 4, so the constant term of h(x) is 54 = 20.
Similarly, to compute the x term of h(x), we need to multiply the x term of f(x) (which is 4) by the constant term of g(x) (which is 4), and add it to the constant term of f(x) (which is 5) multiplied by the x term of g(x) (which is 2).
Therefore, the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products.

To evaluate the quotient q(x) and remainder r(x) when f(x) is divided by g(x), we can use polynomial long division.
We apply division the highest degree term of f(x) by the highest degree term of g(x) to get the first term of q(x).
Then we multiply g(x) by this term of q(x) and subtract the result from f(x) to get the first remainder. We repeat this process with the next highest degree term of the remainder until the degree of the remainder is less than the degree of g(x).
The coefficients of the terms in q(x) are the quotients obtained in each step of the division, and the coefficients of the terms in the remainder are the final remainder obtained after all the steps of the division.
For instance , to compute the quotient q(x) and remainder r(x) when [tex]f(x) = x^4 + 2x^3 + 3x^2 + 4x + 5[/tex] is divided by [tex]g(x) = x^2 + 2x + 4,[/tex]
we first divide [tex]x^4[/tex] by [tex]x^2[/tex] to get [tex]x^2[/tex] as the first term of q(x).
We then multiply g(x) by [tex]x^2[/tex] to get [tex]x^4 + 2x^3 + 4x^2,[/tex] and subtract this from f(x) to get[tex]-x^3 - x^2 + 4x + 5[/tex] as the first remainder.
We then divide [tex]-x^3[/tex] by [tex]x^2[/tex] to get -x as the second term of q(x).
We multiply g(x) by -x to get[tex]-x^3 - 2x^2 - 4x[/tex], and subtract this from the first remainder to get [tex]3x^2 + 8x + 5[/tex]as the final remainder.
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The given integral is: $$\int (-2x^2 + 500)dx$$

To solve the above integral, we integrate both terms separately. Using the integral formulas, $$\int x^n dx= \frac{x^{n+1}}{n+1}+ C$$$$\int kf(x)dx= k\int f(x)dx$$

where C is a constant of integration and k is a constant.

The integral $\int -2x^2 dx$ is:\begin{align*} \int -2x^2 dx &= -2\int x^2 dx\\&= -2\times \frac{x^{2+1}} {2+1} + C\\&= -\frac {2}{3}x^3+ C\end{align*}

The integral $\int 500 dx$ is:\begin{align*}\int 500 dx &= 500\int dx\\&= 500\times x + C\\&= 500x + C\end{align*}

Thus, the integral $\int (-2x^2 + 500) dx$ is:\begin{align*}\int (-2x^2 + 500) dx &= \int -2x^2 dx + \int 500 dx\\&= (-\frac {2}{3}x^3+ C_1) + (500x + C_2)\\&= -\frac {2}{3}x^3+ 500x + C\end{align*}

where C is a constant of integration and $C=C_1+C_2$.

Therefore, the exact value of the integral is $-\frac {2}{3}x^3+ 500x + C$.

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Answer:

Mean and IQR

Step-by-step explanation:

The measure of centre gives the central or the measure which gives the best mid term of a distribution. Based in the details of the box plot, the median is the value which divides the box in the box plot.

For company A:

Range = 25 to 80 with a median value at 30 ; this means the median does not give a good centre measure of the distribution ad it is very close to the minimum value. This goes for the Company B plot too; with values ranging from (35 to 90) and the median designated at 40.

Hence, the mean will be the best measure of centre rather Than the median in this case.

For the variability, the interquartile range would best suit the distribution. With the lower quartile and upper quartile both having reasonable width to the minimum and maximum value of the distribution.

Answer:

B

Step-by-step explanation:

Answer:

1. 0=0

2. x= -3

3. 14=0

Step-by-step explanation:

I tried I'm sorry if it's wrong

Answer:

#1

#2

#3

#4

Answer:

2:40

Step-by-step explanation:

Add 85 minutes to 45 minutes and then add that to 12:30

Answer:

1350 m³

Step-by-step explanation:

To find the volume of a rectangular prism, we have to multiply its length, width, and height together.

The dimensions of this prism are 9, 10, and 15.

9 · 10 · 15 = 1350

The volume is 1350 meters³.

I hope this helps ^^

Answer:

y=9

Step-by-step explanation:

12/y=4/3

3×12/y=3×4/3

36/y=4

y×36/y= 4×y

36=4y

36/4=4y/4

9=y

9514 1404 393

Answer:

  (d)  (-3, 1)

Step-by-step explanation:

We assume a typo in the problem statement, and that the equations are supposed to be ...

  [tex]2x -3y = -9\\-x +3y = 6[/tex]

Adding the two equations gives ...

  x = -3

Substituting for x in the second equation gives ...

  3 +3y = 6

  1 + y = 2 . . . . divide by 3

  y = 1 . . . . . . . subtract 1

The solution is (x, y) = (-3, 1).

Answer:

2 and 5

Step-by-step explanation:

2×5 = 10 or visa versa

10 ÷5=2

10 ÷2 =5

Answer:

quadratic equation

Step-by-step explanation:

Answer:

the equation shown here is a quadratic equation

Answer:

The 16ᵗʰ term of this sequence is 82

Step-by-step explanation:

Here,

First Term = a₁ = 9

Common Difference = (d) = 2

Now, For 16ᵗʰ term, n = 16

aₙ = a + (n - 1)d

a₁₆ = 7 + (16 - 1) × 2

a₁₆ = 7 + 15 × 5

a₁₆ = 7 + 75

a₁₆ = 82

Thus, The 16ᵗʰ term of this sequence is 82

-TheUnknownScientist

Answer:

Write abt a poem you like or something

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

To find the area of a triangle, multipy the base and height of a triangle, then divide it in half

8x9=72/2=36

Answer:

It would be D

Step-by-step explanation:

Answer:

The circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Step-by-step explanation:

2r=d

2(8)=d

16=d

C=πd

C=π16

So, the circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Answer:

50.2654

Step-by-step explanation:

Answer:

I was unable to see this link. Sorry.

Step-by-step explanation:

Answer:

Where is the number I need to round to?

(Please don't give me a bad rating i'm trying to help :) )

The sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:

2, 3, 2, -12, -88, -432, ...

To define the sequence {aₙ}, given a₀ = 2, a₁ = 3, and the recursive formula aₙ = 6aₙ₋₁ - 8aₙ₋₂, we can calculate the subsequent terms of the sequence.

Using the given initial conditions, we have:

a₀ = 2

a₁ = 3

To find a₂, we substitute n = 2 into the recursive formula:

a₂ = 6a₁ - 8a₀

   = 6(3) - 8(2)

   = 18 - 16

   = 2

To find a₃, we substitute n = 3 into the recursive formula:

a₃ = 6a₂ - 8a₁

   = 6(2) - 8(3)

   = 12 - 24

   = -12

Continuing this process, we can find the subsequent terms of the sequence:

a₄ = 6a₃ - 8a₂

   = 6(-12) - 8(2)

   = -72 - 16

   = -88

a₅ = 6a₄ - 8a₃

   = 6(-88) - 8(-12)

   = -528 + 96

   = -432

and so on.

Therefore, the sequence {aₙ} defined by a₀ = 2, a₁ = 3, and aₙ = 6aₙ₋₁ - 8aₙ₋₂ produces the terms:

2, 3, 2, -12, -88, -432, ...

Please note that if you need the general formula for the nth term of the sequence, it may require a different approach as the given recursive formula is not a linear recurrence relation with constant coefficients.

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(a) Let X and Y be the arrival times of buses A and B respectively, it is given that buses A and B are independent and hence X and Y are independent random variables.

Therefore, X and Y are also degenerate at c.

Since a person arrives at the bus stop at time 0, the arrival times of buses A and B cannot be negative

i.e., X, Y ≥ 0.

Also, both buses cannot arrive at time 0

i.e., P(X = 0, Y = 0) = 0.

Now, suppose that X and Y are not degenerate. T

hen, their joint distribution function is given by:

F(X, Y) = P(X ≤ x, Y ≤ y) > 0, for some x, y ≥ 0.

Using the independence of X and Y, we get:

F(X, Y) = P(X ≤ x)P(Y ≤ y) > 0,

for some x, y ≥ 0.

Since P(XY = 0) = 0,

we have XY ≠ 0 and

hence P(XY = c) > 0,

for some c ≠ 0.

Now, for a fixed ε > 0,

let Bε = {(x, y) : |xy - c| < ε}.

Then, P((X, Y) ∈ Bε) > 0.

Similarly, let B'ε = {(x, y) : x < ε} and

B''ε = {(x, y) : y < ε}.

Then, P((X, Y) ∈ B'ε) > 0

and P((X, Y) ∈ B''ε) > 0.

Now, we have:

Bε ⊆ B'ε ∪ B''ε and (X, Y) ∈ B'ε

if and only if X < ε and (X, Y) ∈ B''ε

if and only if Y < ε.So,

using the union bound and taking ε small enough, we get:

P(X < ε) + P(Y < ε) > P((X, Y) ∈ Bε) > 0.

This contradicts the assumption that P(X = 0, Y = 0) = 0.

Therefore, X and Y must be degenerate.

Now, we will show that if XY is degenerate at c ≠ 0

i.e., P(XY = c) = 1,

then X and Y are also degenerate at the same point.

To see this, note that for any Borel sets A, B ⊆ R, we have:

P(X ∈ A, Y ∈ B) = P(XY ∈ A × B) = P(XY = c)

= 1, if (c ∈ A × B) or (c is an isolated point of A × B).

Therefore, X and Y are also degenerate at c.

This completes the proof of the required statement.

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Answer:

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Step-by-step explanation:

When performing polynomial regression, it is advisable to use the smallest degree that provides a good fit.

Polynomial regression involves fitting a polynomial function to a set of data points. The degree of the polynomial represents the highest power of the independent variable in the equation.

By using the smallest degree that provides a good fit, we aim to strike a balance between model complexity and overfitting.

Using a smaller degree helps prevent overfitting, which occurs when a model becomes too complex and captures noise or random fluctuations in the data. Overfitting leads to poor generalization, meaning the model may perform well on the training data but poorly on new, unseen data.

By using the smallest degree that provides a good fit, we minimize the risk of overfitting and ensure that the model captures the underlying trend in the data without incorporating unnecessary complexity.

This approach helps create a more robust and reliable model for making predictions on new data.

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Answer:

i dont know do it yourself chump

Step-by-step explanation:

Answer:

----------------------

DC is the radius and its length is:

DC is the perpendicular bisector of EF.  Hence the half of the segment EF is the leg of a right triangle with the hypotenuse of EC = DC = 70 and other leg of 50 units.

Using the Pythagorean theorem, find the length of EF: