Points B, D, and Fare midpoints of the sides of AACE, EC = 33 and DF = 25. Find AC.

nirvana33 [79]

Your answer is A.

why:

because if the y value changes then your vertical will change. if your x changes than your horizontal will change. if it’s compressed, your x value is less than 1.

8 0

3 years ago

Jamie has a bag containing purple, pink, yellow, and blue marbles. There are a total of 40 marbles in the bag. Jamie randomly se

Ad libitum [116K]

Answer:

1 pink marble

Step-by-step explanation:

If Jamie selected 10 times the pink marble in a total of 420 tries, we can assume that the proportion of pink marble in the total number of marbles is:

10 / 420 = 1/42

So to predict a good number of pink marbles in the total 40 marbles, we just need to multiply the 40 marbles by the proportion found above:

pink marble = 40 * (1/42) = 0.9524

As this number needs to be a whole number, a good assumption is that there is 1 pink marble in the 40 marbles.

8 0

3 years ago

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

Oksana_A [137]

Answer:

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

${n \choose 5 } = \frac{n!}{5!(n-5)!}$

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 ${n \choose 4} .$

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is $4 * {n \choose 4} .$

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is ${n \choose 3} .$

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have ${3 \choose 2 } = 3$ possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of $6 * {n \choose 3}$

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of ${n \choose 2}$ possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

$4 * {n \choose 2}$

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

$n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}$

I hope that works for you!

4 0

3 years ago

One of the fastest recorded speeds of a cheetah is 26.8 m/s. Approximately, what is this speed in kilometers per hour? [1 kilome

ra1l [238]

We know that 1 kilometer = 1,000 meters and that 1 hour = 60 minutes = 3,600 seconds

We have 26.8 meters per second so whats 26.8 meters in kilometers? there is 0.0268 kilometers in 26.8 meters. So now we need to multiply 0.0268 by 3,600 to get 96.48

So your answer would be 96.48 km/h

7 0

3 years ago

On a baseball team, the ages of each of the players are as follows: 21; 21; 22; 23; 24; 24; 25; 25; 28; 29; 29; 31; 32; 33; 33;

Paul [167]

Answer:

Mean = 30.68

Standard deviation = 6.095

Two standard deviations above the mean = 42.87

Step-by-step explanation:

Given the following data :

21; 21; 22; 23; 24; 24; 25; 25; 28; 29; 29; 31; 32; 33; 33; 34; 35; 36; 36; 36; 36; 38; 38; 38; 40

Mean = Σ(x) / n

n = 25

Σ (X) = 767

Mean (m) = 767 / 25

Mean (m) = 30.68

Standard deviation : sqrt[Σ(x - m) / n]

Using a calculator :

Standard deviation = 6.095 ( 2 decimal places)

2 standard deviations above the mean :

Mean + 2(standard deviation)

Mean + 2(6.095)

30.68 + 12.19

= 42.87

6 0

3 years ago