Why did the cow give only buttermilk

Answer:

a) The distance covered halfway = 16.49 [m], while the displacement at that point = 10.5 [m]b)

The distance traveled increases

when the child finishes one lap around the track.

Step-by-step explanation:

a)

Distance is a scalar measurement

that indicates how much ground an object has traversed in motion. Contrarily, displacement is a vector measurement which describes how far an object is from its original position after moving.

In this scenario, the child travels halfway around the circular track from point 1 to point 2. We know that the circumference or perimeter of a circle can be calculated as 2*PI*radius. Since the child only covers half the distance, we need to divide the circumference by 2, leading to distance = PI*radius

The halfway distance = (PI)*(5.25) = 16.49 [m]

Considering the definition of displacement, it’s clear that the distance from point 1 to point 2 equals one diameter from the starting point:

The halfway displacement = D = 2*radius = 2(5.25) = 10.5 [m]

b) What occurs to the distance after the child completes one full circuit? The distance will increase since the child covers more ground during the full lap:

• The distance for one circuit = 2*(PI)*radius = 2(PI)(5.25) = 32.99 [m]

32.99 is greater than 16.49, confirming that the distance does indeed increase.

Answer:

a) S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) S={top,bottom,side}

c) S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds),(King of diamonds),(Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

Step-by-step explanation:

The sample space consists of all potential outcomes for each experiment:

a) The sample encompasses the outcomes resulting from tossing a coin (heads or tails) and throwing a die (a number between 1 and 6):

S={(head,1),(head,2),(head,3),(head,4),(head,5),(head,6),(tails,1),(tails,2),(tails,3),(tails,4),(tails,5),(tails,6)}

b) A paper cup can settle in one of three different positions: on its top, bottom, or side:

S={top,bottom,side}

c) The entire set of cards within a standard deck constitutes the sample space:

S={(Ace of diamonds),(Two of diamonds),(Three of diamonds),(Four of diamonds),(Five of diamonds),(Six of diamonds),(Seven of diamonds), (Eight of diamonds),(Nine of diamonds),(Ten of diamonds), (Jack of diamonds), (Queen of diamonds),(King of diamonds),(Ace of hearts),(Two of hearts),(Three of hearts),(Four of hearts),(Five of hearts),(Six of hearts),(Seven of hearts), (Eight of hearts), (Nine of hearts),(Ten of hearts), (Jack of hearts), (Queen of hearts),(King of hearts),(Ace of clubs),(Two of clubs),(Three of clubs),(Four of clubs),(Five of clubs),(Six of clubs),(Seven of clubs), (Eight of clubs), (Nine of clubs),(Ten of clubs), (Jack of clubs),(Queen of clubs),(King of clubs),(Ace of spades),(Two of spades),(Three of spades),(Four of spades),(Five of spades),(Six of spades),(Seven of spades),(Eight of spades), (Nine of spades),(Ten of spades),(Jack of spades),(Queen of spades),(King of spades)}

Response:

Detailed explanation:

a) this situation has a two-tailed test

The critical value is found using the t distribution table.

α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Consulting 0.975 with df 10

The critical value obtained is 2.228

b) α = 1 - 0.95 = 0.05

1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975

Consulting 0.975 with df 20

The critical value obtained is 2.086

c) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Consulting 0.995 with df 20

The critical value obtained is 2.845

d) α = 1 - 0.99 = 0.01

1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995

Consulting 0.995 with df 60

The critical value obtained is 2.660

e) 1 - α = 1 - 0.01 = 0.99

Consulting 0.99 with df 10

The critical value obtained is 2.764

f) 1 - α = 1 - 0.025 = 0.975

Consulting 0.975 with df 5

The critical value obtained is 2.571

We consider all workers as either full-time or part-time. 36 = 24 + 12 If there are 24 or fewer full-time workers, there must be at least 12 part-time workers. (This conclusion is based on the understanding of sums.) You can formulate the inequality in two steps. First, present and resolve an equation for full-time workers in relation to part-time workers. Then, apply the specified limit on full-time workers. This results in an inequality that can be solved for part-time workers. Let f and p represent full-time and part-time positions, respectively. f + p = 36... given f = 36 - p... subtract p to express f in terms of p. f ≤ 24......... given (36 - p) ≤ 24.... substitute for f. This gives your inequality in terms of p. 36 - 24 ≤ p.... rearranging gives p ≥ 12........ this is the solution to the inequality