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2 years ago

Multiply Conjugates Using the Product of Conjugates Pattern

Mathematics

1 answer:

weeeeeb [17]2 years ago

5 0

Answer:

The product is the difference of squares is $\left(xy-9\right)\left(xy+9\right)={{x}^2}{{y}^2}-81$

Step-by-step explanation:

Explanation

The given expression is (x y-9)(x y+9).
We have to multiply the given expression.
Square the first term xy. Square the last term 9 .

$\begin{aligned}&(x y-9)(x y+9)=(x y)^{2}-(9)^{2} \\&(x y-9)(x y+9)=x^{2} y^{2}-81\end{aligned}$

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A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week

Levart [38]

Answer:

99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].

Step-by-step explanation:

We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.

Of the 250 employed individuals surveyed, 41 responded that they did work at home at least once per week.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of individuals who work at home at least once per week = $\frac{41}{250}$ = 0.164

n = sample of individuals surveyed = 250

<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<em>99% confidence interval for p</em> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.164-2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ , $0.164+2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ ]

= [0.104 , 0.224]

Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].

7 0

3 years ago

Plz help I need to know how many bags of snacks they bought in all

spin [16.1K]

Answer:

7x - 2

Step-by-step explanation:

let x be the number of bags of chips, then

3x is the number of bags of pretzels ← 3 times the number of bags of chips

3x - 2 is the number of bags of nachos ← 2 less than bags of pretzels

total snacks bought = x + 3x + 3x - 2 = 7x - 2

6 0

3 years ago

Please help!!!!!!!!!!

juin [17]

A: -3.25 or -13/4,b:-13/4?????

8 0

3 years ago

PLEASE HELP ASAP!! WORDED QUADRATIC QUESTIONS!!!

Roman55 [17]

Answer:

x² - 5x = 14

x = -2 or x = 7

Step-by-step explanation:

x² - 5x = 14

x² - 5x - 14 = 0

(x+2)(x-7) = 0

x = -2 or x = 7

4 0

2 years ago

Why is it important to know the different properties of three-dimensional figures

IgorLugansk [536]

A two-dimensional shape has length and width. A three-dimensional solid shape also has depth. Three-dimensional shapes, by their nature, have an inside and an outside, separated by a surface. All physical items, things you can touch, are three-dimensional.

4 0

3 years ago