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1 year ago

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Mathematics

1 answer:

blagie [28]1 year ago

6 0

What is the question?

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A regular hexagon rotates counterclockwise around its center. It turns through angles greater than 0° and less or equal to 360°.

Sonja [21]

there are 6 sides to a hexagon

360/6 = 60 degrees

so it will map onto itself at 60, 120, 180, 240, 300 & 360

there are 6 different angles

6 0

2 years ago

A prticular type of tennis racket comes in a midsize versionand an oversize version. sixty percent of all customers at acertain

svetlana [45]

Answer:

a) P(x≥6)=0.633

b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).

c) P(x≤7)=0.8328

Step-by-step explanation:

a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).

The number of trials is n=10, as they select 10 randomly customers.

We have to calculate the probability that at least 6 out of 10 prefer the oversize version.

This can be calculated using the binomial expression:

$P(x\geq6)=\sum_{k=6}^{10}P(k)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\geq6)=0.2508+0.215+0.1209+0.0403+0.006=0.633$

b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:

$\sigma=\sqrt{np(1-p)}=\sqrt{10*0.6*0.4}=\sqrt{2.4}=1.55$

The mean of this distribution is:

$\mu=np=10*0.6=6$

As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.

$LL=\mu-\sigma=6-1.55=4.45\approx4\\\\UL=\mu+\sigma=6+1.55=7.55\approx8$

The probability of having between 4 and 8 customers choosing the oversize version is:

$P(4\leq x\leq 8)=\sum_{k=4}^8P(k)=P(4)+P(5)+P(6)+P(7)+P(8)\\\\\\P(x=4) = \binom{10}{4} p^{4}q^{6}=210*0.1296*0.0041=0.1115\\\\P(x=5) = \binom{10}{5} p^{5}q^{5}=252*0.0778*0.0102=0.2007\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\\\P(4\leq x\leq 8)=0.1115+0.2007+0.2508+0.215+0.1209=0.8989$

c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.

Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.

$P(x\leq7)=1-\sum_{k=8}^{10}P(k)=1-(P(8)+P(9)+P(10))\\\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\leq 7)=1-(0.1209+0.0403+0.006)=1-0.1672=0.8328$

7 0

1 year ago

In a certain country, a letter up to 1 ounce requires postage in the amount of $0.42, and each additional ounce (or fraction of

kati45 [8]

The answer is $7.14 is wunt josiah pay

8 0

2 years ago

Read 2 more answers

Suppose a system has two modules, A and B, that function independently. Module A fails with probability 0.24 and Module B fails

DiKsa [7]

Answer:

Idk idk idk idk idk idk idk idk

4 0

2 years ago

18.) The cost of textbooks for a school increases with the average class size. Identify the independent and dependent quantity i

son4ous [18]

The independent quantity is the average class size and the dependent quantity is the cost ⇒ c

Step-by-step explanation:

Lets revise the meaning of dependent and independent variables

The dependent variable is the one that depends on the value of some other number
The dependent variable is the output value and the independent variable is the input value
Ex: if y = 2x + 3, x is the input and y is the out put, then is independent variable and y is dependent variable

∵ The cost of the textbook increases with the average class size

- The cost of the textbooks depends on the average of the

class size

∴ The input is the average class size

∴ The output is the cost of the textbooks

∵ The input variable is independent variable

∵ The output variable is dependent variable

∴ The average of the class size is independent

∴ The cost of the textbooks is dependent

The independent quantity is the average class size and the dependent quantity is the cost

Learn more:

You can learn more about the word problems in brainly.com/question/13174281

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8 0

1 year ago