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3 years ago

8

Simplify completely the quantity 14 times x to the 5th power times y to the 4th power plus 21 times x to the third power times y

to the 2nd power all over 7 times x to the third power times y. 2x8y5 + 3x6y3 2x2y4 + 3xy 2x2y3 + 3y 2x2y3 + 3y2

2 answers:

timofeeve [1]3 years ago

6 0

We have to simplify the given expression:

$\frac{14x^5y^4+21x^3y^2}{7x^3y}$

Dividing the terms of the numerator by the given term of denominator individually, we get

= $\frac{14x^5y^4}{7x^3y}+\frac{21x^3y^2}{7x^3y}$

By using the laws of exponent, $a^m \div a^n = a^{m-n}$ , we get

= $\frac{7 \times 2 x^5y^4} {7x^3y} + \frac{7 \times 3 x^3y^2}{7x^3y}$

= $\frac{2 x^5y^4} {x^3y} + \frac{3 x^3y^2}{x^3y}$

= ${2 x^{5-3}y^{4-1}} + 3 y^{2-1}$

= ${2 x^{2}y^{3}} + 3 y$

Therefore, the simplification of the given expression is ${2 x^{2}y^{3}} + 3 y$ .

So, Option 3 is the correct answer.

kramer3 years ago

5 0

Answer:

2x^2y^3 + 3y

Step-by-step explanation:

Divide the Coefficients Like you would a normal division problem for each term separately. Then subtract the like exponents.

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Answer:

1) Null hypothesis: $p\geq 0.41$

Alternative hypothesis: $p < 0.41$

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And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

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And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

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Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

X represent the people indicated that they watch the late evening news on this local CBS station

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

$p_o=0.41$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v{/tex} represent the p value (variable of interest) Part 1We need to conduct a hypothesis in order to test the claim that 11:00 PM newscast reaches 41 % of the viewing audience in the area: Null hypothesis:[tex]p\geq 0.41$

Alternative hypothesis: $p < 0.41$

Part 2

$\hat p=0.36$ estimated proportion of people indicated that they watch the late evening news on this local CBS station

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$z_{crit}=-2.33$

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

Part 4

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)

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017$

Part 5

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Part 6

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<em>19</em>

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Solution:

$2x-1$ is a factor

$2x - 1 = 0 \Rightarrow x = \frac{1}{2}$ when we put this value of x to the function, it will become 0.

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$\Rightarrow f(\dfrac{1}{2}) =0 =4\times (\dfrac{1}2)^3-8(\dfrac{1}2)^2+\dfrac{a}{2}+b=0\\\Rightarrow \dfrac{1}{2}-2+\dfrac{a}{2}+b=0\\\Rightarrow 1-4+a+2b=0\\\Rightarrow a +2b=3 ......(1)$

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$f(-2) =20$

$\Rightarrow f(-2) =20 =4\times (-2)^3-8(-2)^2-2a+b=20\\\Rightarrow -32-32-2a+b=20\\\Rightarrow -2a+b=84 ...... (2)$

Solving (1) and (2), Multiply equation (1) by 2 and adding to (2):

$5b=6+84\\\Rightarrow b = \dfrac{90}{5} = \bold{18}$

By equation (1):

$a+2(18) = 3\\\Rightarrow a = -33$

So, the equation becomes:

$f(x) =4x^3-8x^2-33x+18$

$\Rightarrow f(1) = 4(1) -8 (1) -33(1) +18 = \bold{19}$

So, when divided by (x-1), remainder will be <em>19</em>.

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