R+5/mn=p solve for m

Answer:

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)   reflects across the x-axis

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)     translates 5 units downward

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)    reflects across the y-axis

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)    translates 7 units to the right

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this instance, the vertices share the same x-coordinates while their y-coordinates are opposites, indicating a reflection across the x-axis.

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case, the x-coordinates of the vertices remain constant, while the y-coordinates of EFGH are reduced by 5 units, indicative of a downward translation of 5 units.

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

Here, the vertices share the same y-coordinates while the x-coordinates are opposites, representing a reflection across the y-axis.

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

For this case, the y-coordinates for EFGH remain the same while the x-coordinates have increased by 7 units, showing a rightward translation of 7 units.

The total number of casts possible, assuming each actor can fill any of the four distinct roles, and ensuring at least one of sir Ian or Patrick is included, is given as 6,840. The methodology involves calculating the total permutations of four roles from twelve actors and subtracting the permutations that exclude both sir Ian and Patrick.

Answer:

Correct choice: a. The null hypothesis is rejected.

Step-by-step explanation:

Utilizing a statistical hypothesis test for comparing means can help ascertain if the average duration that families in Gotham have lived in their homes is shorter than that of families in Metropolis.

The hypothesis is:

H₀: The average duration of residence for families in Gotham is not shorter than that of families in Metropolis, meaning μ₁ ≥ μ₂.

Hₐ: The average duration of residence for families in Gotham is shorter than that of families in Metropolis, meaning μ₁ < μ₂.

Provided:

Assuming the significance level of the test is α = 0.10.

The calculated statistic is:

Here, s refers to the pooled standard deviation.

Calculate s as follows:

Determine the value of the test statistic as follows:

The result for the test statistic is -5.654.

The critical value for the test is,

*Refer to a t-table for the necessary value.

*The negative value denotes that this is a left-tailed test.

*Since the table lacks an entry for 248 degrees of freedom, use the closest larger value available.

Decision rule:

If the test statistic is lower than the critical value, the null hypothesis is dismissed.

Test statistic = -5.654 < Critical t = -1.282.

Therefore, the null hypothesis is rejected.

The equation simplifies to x + 3y = 15. Best wishes!

Answer:

Step-by-step explanation:

The full exercise is included.

The attached image shows that the box takes the shape of a rectangular prism.

To calculate the volume of a rectangular prism, use this formula:

Here, "l" represents length, "w" represents width, and "h" symbolizes height.

Each side of the cubes measures 1 centimeter. Thus, multiplying the number of cubes along each dimension of the box by 1 centimeter yields the box's length, width, and height:

Next, substitute the length, width, and height of the box into the earlier formula:

Finally, by calculating, it is determined that the volume of the box equals: