Other variables or phenomena that may have caused the independent and dependent variables to be related in the sample is a

The domain of a function are the values for which the function is defined or in the other words, it is the set of all possile values that the function accepts.

Therefore:

Answer:

slope = - 3

Step-by-step explanation:

\(slope, m = \frac{y_2 - y_1}{x_2 - x_ 1}\)    ,    \([ \ (x_ 1 , y_ 1 ) = ( -3 , 3 ) , \ (x_2 , y _ 2 ) = ( - 5 , 9 ) \ ]\)

\(slope = \frac{9 - 3}{-4 - ( -3 )} = \frac{6}{-5 + 3} = \frac{6}{-2} = -3\)

There are 6 subgroups of order 7 in Z/28Z. To find them, you need to identify which elements of Z/28Z generate a group of order 7.

These elements are 1, 7, 13, 19, 25, and 27. Each element creates a subgroup of order 7. These subgroups are:

1) {1, 7, 13, 19, 25, 27, 28}
2) {1, 7, 13, 19, 25, 27}
3) {1, 7, 13, 19, 25}
4) {1, 7, 13, 19}
5) {1, 7, 13}
6) {1, 7}

To know more about subgroups  refer here:

https://brainly.com/question/30865357#

#SPJ11

It will take 2.2 hours for the two trains to meet.

We can find the time taken by the two trains to meet by using the formula,

large Time=Distance/Speed

Let's consider the time taken by the two trains to meet be "t".The distance between two trains = 418 miles.

Now, the first train is traveling at a speed of 85 mph and the second train is traveling at a speed of 105 mph.

Let's calculate the distance covered by both the trains in time "t".The distance covered by the first train in time "t"=85t.

The distance covered by the second train in time "t"=105t.

So, the total distance covered by both the trains in time "t" is,

Distance covered = 85t+105t=190t.

But we know the distance between the two trains is 418 miles.

Therefore,190t = 418

Now, solve for "t"t = 418/190t = 2.2 hours

Therefore, the two trains will meet in 2.2 hours.

To know more about speed: https://brainly.com/question/13943409

#SPJ11

To find the value of k given the equation (xk)^2 = x^2 - 2xk^2 for all values of x, we can solve for k by manipulating the equation.

Let's start by expanding the left side of the equation:

(xk)^2 = x^2k^2

Now, we can rewrite the equation as:

x^2k^2 = x^2 - 2xk^2

Next, we can simplify the equation by moving all terms to one side:

x^2k^2 - x^2 + 2xk^2 = 0

Now, we can factor out common terms:

x^2(k^2 - 1) + 2xk^2 = 0

Since this equation should hold for all values of x, we can set the coefficients of the terms equal to zero:

k^2 - 1 = 0

2k^2 = 0

From the first equation, we have:

k^2 = 1

Taking the square root of both sides, we get two possible values for k:

k = 1 or k = -1

However, when we substitute these values back into the original equation, we find that k = 1 satisfies the equation while k = -1 does not.

Therefore, the value of k that satisfies the equation (xk)^2 = x^2 - 2xk^2 for all values of x is k = 1.

To learn more about equation refer below

https://brainly.com/question/12396626

#SPJ11

Answer:

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)\)

Step-by-step explanation:

 \(x^3 - 10x^2 -53x - 42\)

The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42

Using trial and error method we will find the first root of the polynomial.

1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42

     1 - 10 - 53 - 42  ≠ 0

   Therefore 1 is not a root

-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42

      - 1 - 10 + 53 - 42

       53 - 53 = 0

Therefore - 1 is a root of the polynomial.

Therefore ( x + 1) is a factor.

Now by long division or by using synthetic division we can find other factors.

Synthetic Division :

                             -1 | 1      -10       -53      - 42

                                | 0     - 1          11          42

                                |______________________

                                  1      - 11       - 42        0

Therefore ,

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)\)  ------ ( 1 )

Next further factorize x² - 11x - 42

   x² - 11x - 42

= x² -  14x + 3x - 42

=x(x - 14) + 3 (x - 14)

=(x + 3 )(x - 14)

Therefore ,

\(x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)\)

The one that has the most circles in a group :D

a) The simple interest for the loan is $927.19.

b) The total amount that Jax will have to pay at the end of 30 months is $9,427.19.

a) To calculate the simple interest for the loan, we can use the formula:

Simple Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the annual interest rate, and Time is the duration of the loan in years.

Since the loan is for 30 months, which is equivalent to 2.5 years, we can substitute the given values:

Simple Interest = 8,500 x 0.0435 x 2.5 = $927.19

b) To determine the total amount that Jax will have to pay at the end of 30 months, we need to add the simple interest to the original amount borrowed. The total amount can be calculated using the formula:

Total Amount = Principal + Simple Interest

Substituting the given values:

Total Amount = 8,500 + 927.19 = $9,427.19

In summary, Jax will have to pay $927.19 in simple interest and a total of $9,427.19 at the end of 30 months to repay the 8,500 loan with an annual simple interest rate of 4.35%.

To learn more about interest click on,

https://brainly.com/question/31709159

#SPJ1

At the moment when the radius is 12 inches, the balloon is inflating at a rate of 20 cubic inches per second.

To determine the rate at which the radius is changing, we can use the formula for the volume of a sphere, which is given by \(V = \left(\frac{4}{3}\right)\pi r^3\), where V is the volume and r is the radius.

Taking the derivative of both sides with respect to time t, we get \(\frac{dV}{dt} = 4\pi r^2\left(\frac{dr}{dt}\right)\), where \(\frac{dV}{dt}\) represents the rate of change of volume with respect to time and \(\frac{dr}{dt}\) represents the rate of change of radius with respect to time.

Given that \(\frac{dV}{dt} = 20\) cubic inches per second, we can substitute this value into the equation and solve for \(\frac{dr}{dt}\) when r = 12 inches:

\(20 = 4\pi (12)^2 \left(\frac{dr}{dt}\right)\)

Simplifying the equation:

\(20 = 576\pi \left(\frac{dr}{dt}\right)\)

Dividing both sides by 576π:

\(\left(\frac{dr}{dt}\right) = \frac{20}{576\pi}\)

Therefore, the rate at which the radius is changing when the radius is 12 inches is approximately \(\frac{20}{576\pi}\) inches per second.

To know more about Equation visit-

brainly.com/question/14686792

#SPJ11

Answer:

D

Step-by-step explanation:

You are given the two sides and the abgle inbetween.

The correct relationship between Student's t-distribution and the standard normal distribution is option B: as the sample size approaches infinity, the Student's t-distribution approaches the standard normal distribution.

The sample mean's estimation of the population mean is less precise and the sample mean's distribution is more erratic when the sample size is small. Because the distribution of t-values is more skewed as a result, the student's t-distribution has thicker tails than the traditional normal distribution.

The sample mean's distribution, however, narrows as sample size increases, making it a more precise reflection of the population mean. The student's t-distribution resembles the traditional normal distribution as a result of the narrowing of the t-value distribution.

For the ordinary normal distribution to accurately approximate the student's t-distribution in practice, a sample size of 30 or more is frequently thought to be sufficient.

To know more about T-distribution, refer:

https://brainly.com/question/16994704

#SPJ4

Correct question:

what is the relationship between student's t distribution and the standard normal distribution?

student's t will approach to standard normal distribution as the sample size approachs 0.

student's t will approach to standard normal distribution as the sample size approachs infinite

standard normal distribution will approach to student's t distribution as the sample size approachs 0

standard normal distribution will approach to student's t distribution as the sample size approachs infinite.

Answer:

x = 3

Step-by-step explanation:

you need to set them equal to each other since all sides of a square are the same.

5(4x-3) = 5x+30

distribute

20x - 15 = 5x + 30

combine like terms

15x = 45

divide

3

Answer:

2080.50 = 970.50 - 74p

Step-by-step explanation:

........

The probability that the second person chosen will also be a boy is roughly 0.872, or 87.2%.

Since the first person chosen is a boy, there are now 12 boys and 15 girls left in the class. We want to find the probability that the second person chosen is also a boy.

The probability of choosing a boy for the first selection is 13/28. Then, for the second selection, there are now 12 boys and 27 students left, so the probability of choosing a boy is 12/27.

Using conditional probability, we can calculate the probability that the second person chosen is also a boy given that the first person chosen is a boy:

P(Second person is a boy | First person is a boy) = P(Both are boys) / P(First person is a boy)

P(Second person is a boy | First person is a boy) = (12/27) / (13/28)

P(Second person is a boy | First person is a boy) ≈ 0.872

Therefore, the probability that the second person chosen is also a boy given that the first person chosen is a boy is approximately 0.872 or 87.2%.

To learn more about probability refer to:

brainly.com/question/30034780

#SPJ4

Answer:

370

Step-by-step explanation:

can i get brainliest

The measure of the angle B in the triangle is 51.34 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.

The angle of a right triangle can be found using trigonometric ratios as follows:

tan B = opposite / adjacent

tan B = 25 / 20

B = tan⁻¹ 5 / 4

B = tan⁻¹ 1.25

B = 51.3401917459

Therefore,

B = 51.34 degrees

learn more on triangle here: https://brainly.com/question/13337013

#SPJ1

Answer:

B. 700+200

Step-by-step explanation:

691+208=899

A. 600+200=700

B.700+200=900

C.700+300=1000

D.900+200=1100

B is closest to 899

Answer:

700+200

Step-by-step explanation:

we round these numbers to the closest hundreds by looking at the tenth place

5 or more we round up

4 or less we let it rest and round down

691 since it is 9 in the tenths place we round up to 700

208 since the tenths place is 0 we round down to get 200

700+200 is the answer hopes this helps please mark brainliest

Answer:

32y³

Step-by-step explanation:

a) The surface integral of the given vector field F over the unit cube S is given by:

∫∫∫ S F(x, y, z) n · dS = ∫∫∫ S x²yzi - xy²zj n · dS

where n is the unit normal vector to the surface element pointing outward.

To evaluate this surface integral, we need to break up the unit cube into infinitesimal cubes, each of which has a surface element dS = x²y dz. The normal vector to this surface element is given by n = (0,0,1).

Substituting this into the surface integral, we get:

∫∫∫ S x²yzi - xy²zj n · dS = ∫∫∫ [x²yzi - xy²zj] (0,0,1) · (x²y dz)

Now, we can evaluate this surface integral using the triple integral formula:

∫∫∫ S f(x, y, z) dS = ∫∫∫ [y²(0, 1, 0) - x²(0, 1, 0)] + [z²(0, 1, 0) - x²(0, 1, 0)] + [x²(0, 1, 0) - y²(0, 1, 0)] dS

Simplifying this expression, we get:

∫∫∫ S x²yzi - xy²zj n · dS = ∫[x²y²(1, 1, 0) - x²(1, 1, 0)] + [z²(1, 1, 0) - x²(1, 1, 0)] dS

where dS is the infinitesimal surface area element.

b) To evaluate the surface integral using a volume integral, we need to use Gauss's theorem, which states that:

∫∫∫ S F · dS = ∫[∫∫ F dV - ∫∫ n · d(F · dV) dS] dV

where F is the vector field, dS is the surface element, dV is the infinitesimal volume element, and n is the unit normal vector to the surface element pointing outward.

Substituting the given vector field F = x²yzi - xy²zj, we get:

∫∫∫ S x²yzi - xy²zj n · dS = ∫[∫[x²y²(1, 1, 0) - x²(1, 1, 0)] + [z²(1, 1, 0) - x²(1, 1, 0)] dV - ∫[x²y²(1, 1, 0) - x²(1, 1, 0)] n · (1, 1, 0) dS]

The first integral is zero because the volume integral is taken over the entire volume of the unit cube, which is symmetric with respect to the x-axis, y-axis, and z-axis.

The second integral is given by:

∫[z²(1, 1, 0) - x²(1, 1, 0)] n · (1, 1, 0) dS

Using the normal vector n = (0,0,1), we can simplify this integral as:

∫[z²(1, 1, 0) - x²(1, 1, 0)] n · (1, 1, 0) dS = ∫[0 - 0] (1, 1, 0) · (1, 1, 0) dS = 0

Therefore, the surface integral using a volume integral is also zero.

c) The given vector field F is conservative if and only if it can be written as the gradient of a scalar function. In other words, F = ∇φ for some scalar function φ.

Substituting F = x²yzi - xy²zj into this equation, we get:

x²yzi - xy²zj = ∇²φ

Using the product rule for the Laplacian operator, we get:

∇²φ = 2xy(∇y · ∇x) + 2z(∇x · ∇x)

Substituting the given expression for F, we get:

∇²φ = 2xy(x²y + y²z) + 2z(x²z)

Comparing this to the given expression for F, we can see that it is indeed the gradient of a scalar function φ, which is given by:

φ = 1/2 (x²y + y²z) + 1/2 (x²z)

Therefore, F is conservative.

Learn more about Surface integral visit : brainly.com/question/28171028

#SPJ11

The false statement is (a) P( A^c n B^c)=P(A^c) P(B^c). The probability of the intersection of complements is generally not equal to the product of individual complements.

The misleading assertion including p, and the erratic occasions An and B is (a) P( A^c n B^c)=P(A^c) P(B^c).

This assertion is bogus in light of the fact that by and large, the likelihood of the convergence of the supplements of two occasions, A^c and B^c, isn't equivalent to the result of their singular supplements.

For instance, assume we flip a fair coin. Let A be the occasion of getting heads and B be the occasion of getting tails. Then, P(A) = P(B) = 1/2, so P(A^c) = P(B^c) = 1/2. In any case, A^c and B^c are a similar occasion (getting heads or tails, separately), so P(A^c n B^c) = P(A^c) = 1/2. Then again, P(A^c) P(B^c) = (1/2)(1/2) = 1/4, which isn't equivalent to P(A^c n B^c).

Consequently, proclamation (a) is misleading.

To learn more about probability, refer:

https://brainly.com/question/30629927

#SPJ4

Answer:

Answers = a , c, d, e

Step-by-step explanation:

Absolute value of -8 = 8

Find the absolute values of the other numbers

The other numbers have to be less than 8 or else they are less than -8

Absolute value of 2.6 = 2.6 .   2.6<8

Absolute value of -10 = 10 .     10 >8 .      not correct

Absolute value of -2 = 2 .         2<8

Absolute value of 4 = 4 .           4<8

Absolute value of 1/4 = 1/4 .       1/4<8

Absolute value of -8.5 = 8.5 .     8.5>8 .   not correct

About Absolute Value:

Absolute value is the distance from 0 on the number line.

The number 5 is 5 units from 0

The number -5 is also 5 units from the 0, except from the opposite side

Absolute value states that negative numbers have a positive absolute value and a positive number has a positive absolute value.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

1/2×2/3×3/4=6/24

=1/4

Answer:

12 because 12 to the power of two will be 12 x 12 = 144, and 35 x 35 = 1225 which is b and 37 x 37 = 1369 which is c and is the answer so..  144 + 1225 = 1369. SO 12 would fit!

Based on the question above, the patient pays $600 and the insurance company pays $2400.

To calculate how much the patient pays, we first need to calculate how much the insurance pays. We can do this by taking the total cost of the treatment ($3000) and multiplying it by the percentage that the insurance pays:

(90% = 0.9).

$3000 x 0.9 = $2700

This means that the insurance pays $2700 of the cost of the treatment. But we also need to subtract the $300 deductible from this amount.

$2700 - $300

= $2400

So the insurance pays $2400 for the medical treatment.

To find out how much the patient pays, we can subtract the amount paid by the insurance from the total cost of the treatment:

$3000 - $2400

= $600

Therefore, the  mathematics involved in solving this problem is very straightforward. We used basic arithmetic operations such as multiplication and subtraction to find the amounts paid by the insurance company and the patient.

Learn more about arithmetic operations from

https://brainly.com/question/20628271
#SPJ1

Answer:

Step-by-step explanation:

You want the proportion and its solution that represents the question, "25% of what number is 9?"

The problem statement is telling us the ratio of 9 to w is 25%:

  \(\dfrac{9}{w}=\dfrac{25}{100}\\\\9\times100=25\times w\qquad\text{multiply by $100w$}\\\\w=\dfrac{9\times100}{25}=36\qquad\text{divide by 25}\)

The number is 36.

__

Additional comment

We like to write these problems using the exact relation given:

  "25% of w is 9"

  0.25w = 9 . . . . . . . . . . . using math symbols

  w = 9/0.25 = 36 . . . . . . solve this one-step equation

The "cross multiplication" step used above inevitably results in multiplying the variable by a number, then dividing by that number. That seems unnecessary.