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2 years ago

(04.01 MC)

Mathematics

1 answer:

Reil [10]2 years ago

4 0

Answer:

144'

Step-by-step explanation:

Your ratio is 45'/5" or 9:1

9x4"=36'

9x3"=27'

45+36+36+27=144'

I believe this is the same answer as I gave previously.

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If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

As we see, the situation is exactly the same, but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

2 years ago

A zoologist is studying four very closely related feline species. She wishes to compare their gestation periods. An observationa

diamong [38]

Answer:

$p_v= 0.01$

Since the significance level is 0.05 we see that $pv$ so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different, NOT to conclude that the all the means are different.

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Solution to the problem

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}= \mu_D$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C,D$

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have $p=4$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

And in order to test this hypothesis we need to ue an F statistic and for this case the p value calculated is

$p_v= 0.01$

Since the significance level is 0.05 we see that $pv$ so we have enough evidence to reject the null hypothesis. And the best conclusion for this case would be:

b. at least some, but not all, of the gestation periods across all four species are the same

Because is only to identify if AT LEAST one mean is different NOT to conclude that the all the means are different.

8 0

2 years ago

Help me solve for x. the angles they give to you are 138, 78, and 94. please help

Taya2010 [7]

Answer:

x = 8

Step-by-step explanation:

180 = 78 + 94 + x

180 =172 + x

-172 -172

18 = x

7 0

2 years ago

If the least value of n is 5, which inequality best shows all the possible values of n?

Lostsunrise [7]

N is greater than or equal to 5. (n > 5)

5 0

2 years ago

-2(-5x+5) - 3x + 4= -34 solve for x

geniusboy [140]

Answer:

x = -4

Step-by-step explanation:

-2(-5x+5) - 3x + 4= -34

10x - 10 -3x + 4 = -34

7x - 6 = -34

+6 + 6

7x = -28

x = -4

4 0

2 years ago

Read 2 more answers