The polynomial P(x)=3x^3-5x^2-4x+4 has a factor of (x-2) rewrite P(x) as a product of linear factors

An Article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the

Sergio039 [100]

Answer:

The estimate is $P__{hat}} \pm E = 0.37 \pm 0.0348$

Step-by-step explanation:

From the question we are told that

The sample size is n = 522

The sample proportion of students would like to talk about school is $\r p__{hat}} = 0.37$

Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as

$\alpha = 100 - 90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645$

Generally the margin of error can be mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }$

=> $E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }$

=> $E = 0.0348$

Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is

$P__{hat}} \pm E$

substituting values

$0.37 \pm 0.0348$

5 0

3 years ago

Use the area of a rectangle and the Distributive<br> Property to find each product.<br> 9 X 34

OLga [1]

Answer:

Step-by-step explanation:

Write 34 in tens and units.

34 = 30 + 4

9(30 + 4)

9 * 30 = 270

9* 4 = 36

270 + 36 = 306

After awhile if your practice enough, you can do them in your head.

5 0

2 years ago

Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3). Find the coordinates of G.

Olin [163]

Answer:

Coordinates of G = $(2,0)$

Step-by-step explanation:

Given: Three vertices of parallelogram DEFG are D(-4,-2), E(-3,1) and F(3, 3).

To find: coordinates of G

Solution:

Midpoints of a side joining points $(a,b),\,(c,d)$ are given by $(\frac{a+c}{2},\frac{b+d}{2})$

Diagonals of a parallelogram bisect each other.

So,

Midpoint of DF = Midpoint of EG

Midpoint of DF = $(\frac{-4+3}{2},\frac{-2+3}{2})=(\frac{-1}{2},\frac{1}{2})$

Midpoint of EG = $(\frac{-3+x}{2},\frac{1+y}{2})$

Let coordinates of G be $(x,y)$

Therefore,

$(\frac{-1}{2},\frac{1}{2}) =(\frac{-3+x}{2},\frac{1+y}{2})\\\\\frac{-1}{2}=\frac{-3+x}{2},\,\frac{1}{2}=\frac{1+y}{2}\\\\-1=-3+x,\,1=1+y\\\\x=-1+3,\,y=1-1\\x=2,\,y=0$

So,

Coordinates of G = $(2,0)$

8 0

2 years ago

What is the x intercept of f(x)=x^2+7x+2? And how do you solve it?

Kitty [74]

Answer:

Since that is a quadratic equation, it will have 2 "x" intercepts.

x^2+7x+2

a = 1 b = 7 c = 2

You would solve for "x" using the quadratic formula.

x = [ -b +- sq root (b ^ 2 - 4 a c) ] / 2 a

x = [ -7 +- sq root (7^2 - 4*1*2) ] / 2 * 1

x = [ -7 +- sq root (49 -8) ] / 2

x1 = [-7 + 6.4031242] / 2

x1 = -.29844

x2 = [-7 - 6.4031242] / 2

x2 = -6.7016

Step-by-step explanation:

4 0

3 years ago

The heights of 1/4 sheet cakes baked by a bakery have been normally distributed with a mean of μ = 2.05 inches and a standard de

jasenka [17]

Answer:

1. Null hypothesis: $\mu = 2.05$

Alternative hypothesis: $\mu \neq 2.05$

2. $P(Z>a)=0.025, P(Z$

And the value of a that satisfy this is a=1.96. So our critical regions are: $(-\infty,-1.96), (1.96,\infty)$

3. $z=\frac{2.01-2.05}{\frac{0.12}{\sqrt{9}}}=-1$

4. If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the heights is NOT significant different than 2.05. Using the critical region founded on part 2 we agree with the decision obtained with the p value since -1 is not on the critical zones, so we FAIL to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=2.01$ represent the sample mean

$\sigma=0.12$ represent the standard deviation for the population

$n=9$ sample size

$\mu_o =2.05$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

1) The null and alternative hypotheses should be ?

We need to conduct a hypothesis in order to determine if the mean change from 2.05, the system of hypothesis would be:

Null hypothesis: $\mu = 2.05$

Alternative hypothesis: $\mu \neq 2.05$

2. Using the critical value to set up the decision rule, the decision rule should be?

For this case we need two critical values since we are conducting a two tailed test. We have this equality:

$P(Z>a)=0.025, P(Z$

And the value of a that satisfy this is a=1.96. So our critical regions are: $(-\infty,-1.96), (1.96,\infty)$

3. The test statistic of this test is?

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{2.01-2.05}{\frac{0.12}{\sqrt{9}}}=-1$

4. The conclusion of this test should be

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

$p_v =2*P(Z$

Conclusion

If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the heights is NOT significant different than 2.05. Using the critical region founded on part 2 we agree with the decision obtained with the p value since -1 is not on the critical zones, so we FAIL to reject the null hypothesis.

4 0

2 years ago