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4 years ago

Determine the value of n in the equation (n – 4) – 3 = 3 – (2n + 3).

2 answers:

8 0

(N-4)-3=3-(2n+3)
•distribute the negative symbol into the parentheses on the right side of the equation and combine like terms. This would leave you with n-7= -2n. Bring the variables to the left and numbers to the right.
3n= 7
•divide 3 from both sides of the equation
N= 7/3 or N= 2.3

nlexa [21]4 years ago

3 0

Since the equation is (n-4)-3 = 3 - (2n+3):

By distributive property:
n-4-3 = 3 -2n -3

Variables on the right side, while constants on the left side:
n+2n = 3
3n = 3

Divide both sides by 3:
n = 3/3
n = 1

Therefore, the value of n in the expression is 1.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

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3 years ago

Harold uses the binomial theorem to expand the binomial (3x^5 - 1/9y^3)^4

riadik2000 [5.3K]

<h3><em>The complete question:</em></h3>

<u><em> </em></u><u>Harold uses the binomial theorem to expand the binomial </u> $(3x^5 -\dfrac{1}{9}y^3)^4$ <u />

<u>(a) What is the sum in summation notation that he uses to express the expansion? </u>

<u>(b) Write the simplified terms of the expansion.</u>

Answer:

(a). $(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}( -\dfrac{1}{9}y^3)^k $$$

(b). $(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561}$

Step-by-step explanation:

(a).

The binomial theorem says

$(x+y)^n=$$\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k $$$

For our binomial this gives

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}x^{4-k}y^k $$}$

(b).

We simplify the terms of the expansion and get:

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}y^k $$= \binom{4}{0}(3x^5)^{4-0}(-\dfrac{1}{9}y^3 )^0+\binom{4}{1}(3x^5)^{4-1}(-\dfrac{1}{9}y^3 )^1+\\\\\binom{4}{2}(3x^5)^{4-2}(-\dfrac{1}{9}y^3 )^2+\binom{4}{3}(3x^5)^{4-3}(-\dfrac{1}{9}y^3 )^3+\binom{4}{4}(3x^5)^{4-4}(-\dfrac{1}{9}y^3 )^4$

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}(-\frac{1}{9}y^3 )^k $$= (3x^5)^{4}+4(3x^5)^{3}(-\frac{1}{9}y^3 )+6(3x^5)^{2}(-\frac{1}{9}y^3 )^2+\\\\4(3x^5)(-\frac{1}{9}y^3 )^3+(-\frac{1}{9}y^3 )^4$

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561} }$

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3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines

borishaifa [10]

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 220 engines and the mean pressure was 5.4 pounds/square inch (psi), the level of significance for the hypothesis test is 0.05. This is further explained below.

<h3>What is the level of significance?</h3>

Generally, the level of significance is simply defined as statistical analysis, the significance level is defined as the likelihood of rejecting the null hypothesis when it is correct.

In conclusion, The average pressure throughout testing on 220 engines was 5.4 psi, and the significance threshold for the hypothesis test was set at 0.05.