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2 years ago

10

Mrs. Dryson is dividing her collection of 52 glass bears into groups of equal numbers. She has 1 bear left over. How many groups

did Mrs. Dryson make?

1 answer:

Zepler [3.9K]2 years ago

3 0

It was probably 20 idk

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A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago

How long is bob's journey from aberystwyth to shrewsbury

steposvetlana [31]

Answer: bob will take a while

Step-by-step explanation:

4 0

2 years ago

A student wants to determine if pennies are really fair when flipped, meaning equally likely to land heads up or tails up. He fl

Verdich [7]

Answer:

For this case we want to determine if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: $p=0.5$

Alternative hypothesis: $p \neq 0.5$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to determine if pennies are really fair when flipped, meaning equally likely to land head up or tails, so then the correct system of hypothesis are:

Null hypothesis: $p=0.5$

Alternative hypothesis: $p \neq 0.5$

7 0

2 years ago

The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is (x

DaniilM [7]

We have the following equation:
x2 + y2 + 42x + 38y - 47 = 0
We rewrite the equation:
x2 + 42x + y2 + 38y - 47 = 0
x2 + 42x + y2 + 38y = 47
Rewriting we have:
x2 + 42x + (42/2) ^ 2 + y2 + 38y + (38/2) ^ 2 = 47 + (42/2) ^ 2 + (38/2) ^ 2
x2 + 42x + 441 + y2 + 38y + 361 = 47 + 441 + 361
Rewriting we have:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
The center of the circle is:
(x, y) = (-21, -19)
The radio is:
r = root (849)
r = (849) ^ 2

A circle of the same radius is given by:
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
Let's check:
x ^ 2 - 50x + y ^ 2 - 30y + 1 = 0
x ^ 2 - 50x + y ^ 2 - 30y = - 1
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + (-30/2) ^ 2 + (-50/2) ^ 2
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + 225 + 625
(x-25) ^ 2 + (y-15) ^ 2 = 849
Answer:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
(x, y) = (-21, -19)
r = (849) ^ 2
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0

5 0

2 years ago

Children under 10 years and older people over 65 years receive a discount on movie tickets. Let x represent the age of a person

mr_godi [17]

0<x<10

x>65

0<x<10 or x>65

4 0

2 years ago