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svetlana [45]
3 years ago
8

Juwan collects 36 pieces of candy while trick-or-treating. He eats one-third of them and gives a fourth of whats left away. How

many candies does he still have?
Mathematics
1 answer:
Nady [450]3 years ago
6 0

Answer:

18 candies.

Step-by-step explanation:

Given:

Juwan collects 36 pieces of candy while trick-or-treating.

He eats one-third of them and gives a fourth of whats left away.

<u>Question asked:</u>

How many candies does he still have?

<u>Solution:</u>

Total candies collected by Juwan = 36

Candies eaten by Juwan = \frac{1}{3} \ of \ 36=\frac{1}{3} \times36=12\ candies

Remaining candies = 36 - 12 = 24

Candies given by her = \frac{1}{4}\ of\ 24= \frac{1}{4}\times24=6\ candies

Remaining candies = 24 - 6 = 18 Candies.

Thus, he still have 18 candies.

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A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over th
baherus [9]

Answer:

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which 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)!}

And p is the probability of X happening.

In this problem we have that:

p = 0.553, n = 10

If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:

This is

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.553)^{0}.(0.447)^{10} = 0.0003

P(X = 1) = C_{10,1}.(0.553)^{1}.(0.447)^{9} = 0.0039

P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219

P(X = 3) = C_{10,3}.(0.553)^{3}.(0.447)^{7} = 0.0724

P(X = 4) = C_{10,4}.(0.553)^{4}.(0.447)^{6} = 0.1567

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0003 + 0.0039 + 0.0219 + 0.0724 + 0.1567 = 0.2552

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

3 0
3 years ago
The area of a playground is 204 yd^2 the width of thr playground is 5 yd longer that its length what the length and the width of
morpeh [17]
W= width= L+5
L= length
Area= 204

Area= LW
204 square yards= LW
substitute w=L+5 for w
204= (L)(L+5)
204= L^2 + 5L
subtract 204 from both sides
0= L^2 + 5L - 204
factor
0= (L+17)(L-12)

0= L+17
-17= L

0= L-12
12 yards= L


WIDTH
Since the area cannot be a negative number, we'll use L=12 to find the width.

w=L+5
w=12+5
w=17 yards


CHECK:
204=(12)(17)
204=204


ANSWER: The length is 12 yards and the width is 17 yards.

Hope this helps! :)
6 0
4 years ago
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