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3241004551 [841]
3 years ago
8

What is the fourth term of the binomial expansion for (3x-2y)6

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
7 0
One way is to just expand it by using binomial theorem
or to use pascal's triangle

ok so

to find the nth term of a binomial, (a-b). where the binomial is to the r power you do
n-1=k

rCk times (a)^{r-k}(-b)^k
and rCk=\frac{r!}{k!(r-k)!}

so

4th term
4-1=3
6 is exponent

6C3(3x)^{6-3}(-2y)^3=
( \frac{6!}{3!(6-3)!} )((3x)^3(-8y^3)=
( \frac{6*5*4}{1*2*3} )(27x^3)(-8y^3)=
(20)(27)(-8)(x^3)(y^3)=-4320x^3y^3



the 4th term is -4320x^3y^3

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The test statistic of zequals2.32 is obtained when testing the claim that pgreater than0.3. a. Identify the hypothesis test as b
Sonja [21]

Answer:

a) We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:p \leq 0.3  

Alternative hypothesis:p > 0.3  

Right tailed test

b) p_v =P(z>2.32)=0.0102  

c) So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

Step-by-step explanation:

Part a: Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion p is greatr than 0.3, so then the system of hypothesis are.:  

Null hypothesis:p \leq 0.3  

Alternative hypothesis:p > 0.3  

Right tailed test

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

For this case the statistic is given by z_{calc}= 2.32

Part b: Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(z>2.32)=0.0102  

Part c

So the p value obtained was a very low value and using the significance level given \alpha=0.1 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is higher than 0.3

6 0
3 years ago
What is 10√94 simplified. Its not 98 or its decimal form.
slavikrds [6]

Answer:

hi

Step-by-step explanation:

i think 96(probably)

have a nice day

3 0
2 years ago
If m∠BAC = 98°, what is m∠BDC?
Leviafan [203]
I believe it's also 98 degrees, because the are symmetrical.
5 0
3 years ago
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The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. Find an equiva
kolezko [41]

Answer:

Now if the high and low monthly average temperatures satisfy the inequality, then the , monthly averages are always within 22 degrees of 43°F.

Step-by-step explanation:

The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location.

The inequality expression is given as:

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now this expression could also be expressed as:

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Now if the high and low monthly average temperatures satisfy the inequality, then the , monthly averages are always within 22 degrees of 43°F.

( As the difference is 22 degrees to the left and right)

5 0
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Aaron is making jam using strawberries and raspberries. He made 1/2 a jar of strawberry jam. If he made 1/3 as much raspberry ja
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Answer:

2/6 more.

Step-by-step explanation:

You need to find a common denominator. In this case it was 6.

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