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astraxan [27]
3 years ago
13

Assume that two samples are independent simple random samples selected from normally distributed​ populations, and do not assume

that the population standard deviations are equal. Which distribution is used to test the claim that male king penguins from Marion Island weigh more than female king penguins from Marion​ Island?A. Chi-square
B.t
C.Normal
D.F
Mathematics
1 answer:
Paraphin [41]3 years ago
7 0

Answer:

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t

Step-by-step explanation:

Notation

\bar X_{1} represent the mean for male king penguins

\bar X_{2} represent the mean for the female king penguins

s_{1} represent the sample standard deviation for the sample male

s_{2} represent the sample standard deviation for the sample female

n_{1} sample size for the male penguins

n_{2} sample size for the female penguins

t would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to check if the male king penguins weigh more than female king penguins, the system of hypothesis would be:

Null hypothesis:\mu_{1}=\mu_{2}

Alternative hypothesis:\mu_{1} > \mu_{2}

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t

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Answer:

<h2>0.6 </h2>

Step-by-step explanation:

Each fraction has a equivalent decimal:

\frac{4}{7} = 0.57\\\frac{5}{7} = 0.71\\

So, as you can see, a decimal number between these fraction, could be 0.6, which is equivalent to the fraction \frac{3}{5}

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Step-by-step explanation:

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Which binomial is a factor of 49x^2+84xy+36y^2
sweet-ann [11.9K]

7x + 6y is a binomial that is a factor of given equation

<em><u>Solution:</u></em>

A binomial is a mathematical expression which has only two terms

<em><u>Given expression is:</u></em>

49x^2 + 84xy + 36y^2

We have to find the binomial that is a factor to given expression

Let us find the factors of given equation

49x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}49x^2+84xy+36y^2\mathrm{\:as\:}\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\mathrm{Rewrite\:}49\mathrm{\:as\:}7^2\\\\7^2x^2+84xy+36y^2\\\\\mathrm{Rewrite\:}36\mathrm{\:as\:}6^2\\\\7^2x^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\7^2x^2=\left(7x\right)^2\\\\Therefore,\\\\\left(7x\right)^2+84xy+6^2y^2\\\\\mathrm{Apply\:exponent\:rule}:\quad \:a^mb^m=\left(ab\right)^m\\\\6^2y^2=\left(6y\right)^2\\\\

Therefore\\\\\left(7x\right)^2+84xy+\left(6y\right)^2\\\\\mathrm{Rewrite\:}84xy\mathrm{\:as\:}2\cdot \:7x\cdot \:6y\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2\\\\

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\\\a=7x,\:b=6y\\\\Therefore,\\\\\left(7x\right)^2+2\cdot \:7x\cdot \:6y+\left(6y\right)^2 = \left(7x+6y\right)^2

Thus we get,

49x^2 + 84xy + 36y^2 = (7x+6y)^2\\\\49x^2 + 84xy + 36y^2 =  (7x+6y)(7x+6y)

Thus the binomial which is a factor is 7x + 6y

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Answer:

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4 + 4 + 8 + 8 + 10 + 16 + (50 x 10)

Step-by-step explanation:

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