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3 years ago

Using the expansion for the binomial: ( x^3 − y^4 )^9 :The coefficient for the 6th term is

Mathematics

1 answer:

Lelechka [254]3 years ago

8 0

Answer:

-126

Step-by-step explanation:

For the binomial expression $(a-b)^{n}$ the coefficient of $(r+1)^{th}$ term is given by ${n \choose r} \times -1^{(r)}$ .

We have to find the coefficient of 6th term in the binomial expansion of

$(x^{3}-y^{4})^{9}$ .

Hence n=9 and r=5

The coefficient of 6th term = ${9 \choose 5} \times (-1)^{5}$

= $-{9 \choose 5}$

= -126

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Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experime

Citrus2011 [14]

Answer:

There is enough evidence to say that the true average heat output of persons with the syndrmoe differs from the true average heat output of non-sufferers.

Step-by-step explanation:

We have to perform a hypothesis test on the difference between means.

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a: \mu_1-\mu_2$

μ1: mean heat output for subjects with the syndrome.

μ2: mean heat output for non-sufferers.

We will use a significance level of 0.05.

The difference between sample means is:

$M_d=\bar x_1-\bar x_2=0.63-2.09=-1.46$

The standard error is

$s_{M_d}=\sqrt{\sigma_1^2/n_1+\sigma_2^2/n_2}=\sqrt{0.3^2/9+0.5^2/9}=\sqrt{ 0.038 } \\\\ s_{M_d}=0.194$

The t-statistic is

$t=\dfrac{M_d}{s_{M_d}}=\dfrac{-1.46}{0.194}=-7.52$

The degrees of freedom are

$df=n_1+n_2-2=9+9-2=16$

The critical value for a left tailed test at a significance level of 0.05 and 16 degrees of freedom is t=-1.746.

The t-statistic is below the critical value, so it lies in the rejection region.

The null hypothesis is rejected.

There is enough evidence to say that the true average heat output of persons with the syndrmoe differs from the true average heat output of non-sufferers.

5 0

3 years ago

A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his exper

steposvetlana [31]

The population of the bacteria after 8 hours is 1639 bacteria.

An exponential function is given by:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the population of bacteria after x hours.

Given that he starts his experiment with 500 bacteria, hence

a = 500

The bacteria grow at a rate of 16% per hour, hence: