A ___ is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups

Answer:

Part a) The unit rate of change of d with respect to t is equal to

Part b) The graph of the line corresponding to the attached diagram

Step-by-step explanation:

we know that

The relationship between the variables t and d depicts a proportional change if described in the form or

step 1

Determine the value of k

we have

substitute

so

the resulting linear equation equals

step 2

utilize a graph tool

plot the line

The maximum number of identical dental care bags the dentist can create with the smallest leftover is 1.

The counts of bags are 2, 4, and 3, respectively.

Clarification:

Total tubes of toothpaste = 56

Total packets of floss = 112

Total toothbrushes = 85

Therefore, the greatest number of identical dental care bags the dentist can assemble with minimal leftover for toothbrushes is found by calculating the H.C.F of 56, 112, 85 = 1 ( ∵ as they are coprime to each other )

Given that there is no common factor among 56, 112, and 85, except for the commonality between 56 and 112, which is 56, the remainder of toothbrushes will be 85-56=29.

Thus considering 28,[TAG_24]]

The numbers can be expressed as follows: 56 = 28×2, 112 = 28×4, and 84 = 28×3

Consequently, the dentist can create 28 bags containing all three supplies, with no leftover from toothpaste and floss, but with leftover from toothbrushes as we substitute 84 for 85 to maintain divisibility by 28 for common factor demonstration.

This results in 2 bags for toothpaste, 4 bags for floss, and 3 bags for toothbrushes.

Answer:

                          π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let r denote the radius of the sphere. The volume of the sphere is expressed as

V = (4/3)(π)(r³).

Next, understand that the cube's side length is 2r, hence the cube's volume is

V = (2r)³, which equals 8r³.

The volume of the foam is derived from the cube's volume subtracting that of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to

                          π

V-foam = 4r³( 2 - ----- )

                             3

Let n denote the number of days and C the total cost; Charges by Day and Night kennel, C=15+20n Charges by Home Away from Home; C=5 + 30n The resulting system of equations would be; C=15+20n C=5+30n

Answer:

(1, 3)

Step-by-step explanation:

Provided:

A circle containing these specified points-

(4, 2), (-2, 2), (-1, 4), (1, 1), (1, 3), (2, -3).

A function resembles a mechanism that produces an output for each unique input. Each input must yield a distinct output.

The function's input is characterized as the domain, and the output corresponds to its range.

The domain is indicated by the 'x' coordinate while the range is represented by the 'y' coordinate.

This means the domain serves as the independent variable, and the range is contingent upon the domain’s values.

In this case, a relation or set of points constitutes a function only if every 'x' in the ordered pairs is unique.

Within the described relation, the pairs (1, 1) and (1, 3) share the same input. Thus, removing either one will convert the relation into a function.

Therefore, choosing (1, 3) is the right answer.