Determine if the two triangles are congruent. If they are, state how you know.

A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hos

Lady_Fox [76]

Null hypothesis: $p = 0.81$

Alternative hypothesis: $p \ne 0.81$

The null is based on a recent study that 81% of the population (in this case senior citizens) takes at least one medication. The alternative hypothesis is basically the flip of the claim made in the null.

If Amelia wanted to know if the percentage was less than 81%, then the alternative would be p < 0.81

If Amelia wanted to know if the percentage was larger than 81%, then the alternative would be p > 0.81

However, she wants to know if the percentage is 81%.

5 0

3 years ago

A rubber ball is dropped from the top of a hole. Exactly 20 seconds later, the sound of the rubber ball hitting bottom is heard.

gayaneshka [121]

9514 1404 393

Answer:

4192.9 ft

Step-by-step explanation:

We assume your falling-distance formula is supposed to be ...

s = 16t²

So, the time required to fall distance s is ...

t = √(s/16) = (1/4)√s

The time required for sound to travel distance s is ...

s = 1100t

t = s/1100

Then the sum of the time for the ball to fall and the time for the sound to travel back is ...

(1/4)√s + s/1100 = 20

275√s = 22000 -s . . . . . multiply by 1100 and subtract s

75625s = s^2 -44000s +484,000,000 . . . square both sides

s^2 -119,625s +484,000,000 = 0 . . . . put in standard form

s ≈ (1/2)(119,625 ±√12,374,140,625) = {4192.943, 115432.057}

Only the smaller of these two solutions makes any sense in this problem.

The hole is about 4192.9 feet deep.

_____

<em>Additional comment</em>

The distance equation for the falling object presumes a vacuum. The sound transmission presumes the presence of air, so the question setup is self-contradictory.

7 0

3 years ago

A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.

kondor19780726 [428]

Answer:

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

Step-by-step explanation:

The kittens are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.

This means that $N = 8 + 10 = 18$

We want 3 boys, so $k = 8$

The director is going to choose 8 of these kittens at random to be in the commercial.

This means that $n = 8$

What is the probability that the director chooses 3 boy kittens and 5 girl kittens?

This is P(X = 3).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 3) = h(3,18,8,8) = \frac{C_{8,3}*C_{10,5}}{C_{18,8}} = 0.323$

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

3 0

3 years ago

Yesterday, Mary had n baseball cards. Today, she got 8 more. Using , write an expression for the total number of baseball cards

Oksana_A [137]

Answer:

n + 8 =

Step-by-step explanation:

Yesturday she had n

plus the 8 she got today

the equation is

n+8=?

3 0

3 years ago

Read 2 more answers

What is 2/3 multiplied by 3/4 simplified? I need step by step to get answer.

Masteriza [31]

You start with the top number of each fraction and multiply them. So 2x3=6. Next you take the bottom number and multiply. So 3x4=12. That would give you a fraction of 6/12. 6 is half of 12 so 6/12 simplified is equal to 1/2. Hope this helps!

3 0

4 years ago