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3 years ago

7

The polynomial is a difference squares. Use the formula a^2 -b^2=(a+b)(a-b) to factor completely. 81x^2-49 the value of a is the

value of b is the product of the prime factors is

2 answers:

AnnZ [28]3 years ago

6 0

Answer: $(9x)^{2}-(7)^{2}=(9x-7)(9x+7)$

Step-by-step explanation:

1. By definition you have that the difference of squares is:

$a^{2}-b^{2}=(a+b)(a-b)$

2. Given the polynomial:

$81x^{2}-49$

You can identify that there are two terms whose signs are different and they are perfect squares.

3. Therefore, you have:

$81x^{2}-49=(9x)^{2}-(7)^{2}=(9x-7)(9x+7)$

oksano4ka [1.4K]3 years ago

5 0

Answer:

(9x+7)(9x-7)

Step-by-step explanation:

We have given an expression.

81x²-49

We have to use difference formula which is given in question.

a²-b² =(a+b)(a-b)

We have to write given expression in above formula.

81x²-49 = (9x)²-(7)²

Using given formula , we have

81x²-49 = (9x+7)(9x-7)

Hence, the factors of given expression are (9x-7) and (9x+7).

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A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track

harkovskaia [24]

Answer:

C. 2.0 < t < 2.5

Step-by-step explanation:

time = distance / speed

The circumference of the lake is given by ...

C = πd = 2π miles ≈ 6.28 miles

Then Johanna's time is ...

(6.28 mi)/(3 mi/h) ≈ 2.09 h

This time is in the interval (2, 2.5), so matches choice C.

___

<em>Alternate solution</em>

If we take pi to be 3, then this boils down to ...

2×3/3 = 2 . . . hours

Pi is on the order of 5% more than 3, so her time will be on the order of 5% more than 2 hours, or just above 2, but not as great as 2.5 hours. This sort of estimating can get you to the correct answer without a calculator.

6 0

4 years ago

P2q2+pq–q3–p3 =<br><br> for p=0.5 and q = −0.5<br><br><br> Please help!!!

Aleksandr [31]

In order to answer the question, we simply substitute the value of p and q to the given expression and solve. We do as follows:

<span>P^2q^2+pq–q^3–p^3
</span>0.5^2(-0.5)^2+0.5(-0.5)–(-0.5)^3–(0.5)^3
-3/16 or -0.1875

Hope this answers the question. Have a nice day.

5 0

3 years ago

In a recent year, a poll asked 2362 random adult citizens of a large country how they rated economic conditions. In the poll,

Harman [31]

Answer:

a) The 99% confidence interval is given by (0.198;0.242).

b) Based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

c) $\alpha=0.01$

Step-by-step explanation:

<em>Data given and notation </em>

n=2362 represent the random sample taken

X represent the people who says that they would watch one of the television shows.

$\hat p=\frac{X}{n}=0.22$ estimated proportion of people rated as Excellent/Good economic conditions.

$p_o=0.24$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest) <em> </em>

<em>Concepts and formulas to use </em>

We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:

Null hypothesis: $p=0.24$

Alternative hypothesis: $p \neq 0.24$

When we conduct a proportion test we need to use the z statistic, 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 $p_o$ .

Part a: Test the hypothesis

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10

Condition satisfied.

<em>Calculate the statistic</em>

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

$z=\frac{0.22 -0.24}{\sqrt{\frac{0.24(1-0.24)}{2362}}}=-2.28$

The confidence interval would be given by:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The critical value using $\alpha=0.01$ and $\alpha/2 =0.005$ would be $z_{\alpha/2}=2.58$ . Replacing the values given we have:

$0.22 - (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.198$

$0.22 + (2.58)\sqrt{\frac{0.22(1-0.22)}{2362}}=0.242$

So the 99% confidence interval is given by (0.198;0.242).

Part b

<em>Statistical decision </em>

P value method or p value approach . "This method consists on 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 significance level provided is $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

So based on the p value obtained and using the significance level assumed $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.

Part c

The confidence level assumed was 99%, so then the signficance is given by $\alpha=1-confidence=1-0.99=0.01$

6 0

3 years ago

Please help on the answer with explanation! picture provided

Alisiya [41]

Answer:

B

Step-by-step explanation:

3 0

3 years ago

Need help on my work

Vedmedyk [2.9K]

Could you send a clear image from frobt view

4 0

3 years ago