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3 years ago

6x-9y+45 in slope intercept form

Mathematics

1 answer:

sweet [91]3 years ago

6 0

The answer is: y= 2/3x +5

You might be interested in

Test the hypothesis using the P value approach. Be sure the verify the requirements of the test.

Andreas93 [3]

Answer:

$p_v =2*P(z$

If we compare the p value and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X=380 represent the number of people with some characteristic

$\hat p=\frac{380}{500}=0.76$ estimated proportion of adults that said that it is morally wrong to not report all income on tax returns

$p_o=0.76$ 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)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:

Null hypothesis: $p=0.77$

Alternative hypothesis: $p \neq 0.77$

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 $p_o$ .

<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

$np_o =500*0.77=385>10$

$n(1-p_o)=384*(1-0.77)=115>10$

3) Calculate the statistic

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

$z=\frac{0.76-0.77}{\sqrt{\frac{0.77(1-0.77)}{500}}}=-0.531$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about 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 $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z$

6 0

3 years ago

Does anyone know the answers to these?

dem82 [27]

Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c. The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

3 0

3 years ago

A researcher is interested in whether people are less able to identify emotions correctly when they are extremely tired. It is k

stepan [7]

<h2>Answer with explanation:</h2>

Let $\mu$ be the population mean.

By analyzing the given information, we have the following hypothesis:-

$H_0:\mu\geq81\\\\H_a:\mu$

Since the alternative hypotheses is left tailed so the test is a right-tailed test.

Also, the accuracy ratings of people in the general population are normally distributed.

Given : Sample size : n=51 , since n>30 so we use z-test.

Sample mean : $\overline{x}=79$

Standard deviation : $\sigma=\sqrt{20}\approx4.47$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{79-81}{\dfrac{4.47}{\sqrt{51}}}\\\\\Rightarrow\ z\approx-3.195$

Critical value (one-tailed) corresponds to the given significance level :-

$z_{\alpha}=z_{0.05}=1.645$

Since the observed value of z (-3.195) is less than the critical value (1.645) , so we do not reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to accept that people are less able to identify emotions correctly when they are extremely tired .

3 0

3 years ago

Let V denote the set of ordered triples (x, y, z) and define addition in V as in

icang [17]

Answer:

a) No

b) No

c) No

d) No

Step-by-step explanation:

Remember, a set V wit the operations addition and scalar product is a vector space if the following conditions are valid for all u, v, w∈V and for all scalars c and d:

1. u+v∈V

2. u+v=v+u

3. (u+v)+w=u+(v+w).

4. Exist 0∈V such that u+0=u

5. For each u∈V exist −u∈V such that u+(−u)=0.

6. if c is an escalar and u∈V, then cu∈V

7. c(u+v)=cu+cv

8. (c+d)u=cu+du

9. c(du)=(cd)u

10. 1u=u

let's check each of the properties for the respective operations:

Let $u=(u_1,u_2,u_3), v=(v_1,v_2,v_3)$

Observe that

1. u+v∈V

2. u+v=v+u, because the adittion of reals is conmutative

3. (u+v)+w=u+(v+w). because the adittion of reals is associative

4. $(u_1,u_2,u_3)+(0,0,0)=(u_1+0,u_2+0,u_3+0)=(u_1,u_2,u_3)$

5. $(u_1,u_2,u_3)+(-u_1,-u_2,-u_3)=(0,0,0)$

then regardless of the escalar product, the first five properties are met for a), b), c) and d). Now let's verify that properties 6-10 are met.

6. $c(u_1,u_2,u_3)=(cu_1,u_2,cu_3)\in V$

$c(u+v)=c(u_1+v_1,u_2+v_2,u_3+v_3)=(c(u_1+v_1),u_2+v_2,c(u_3+v_3))\\=(cu_1+cv_1,u_2+v_2,cu_3+cv_3)=c(u_1,u_2,u_3)+c(v_1,v_2,v_3)=cu+cv$

$(c+d)u=(c+d)(u_1,u_2,u_3)=((c+d)u_1,u_2,(c+d)u_3)=\\=(cu_1+du_1,u_2,cu_3+du_3)\neq (cu_1+du_1,2u_2,cu_3+du_3)=cu+du$

Since 8 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product $a(x,y,z)=(ax,y,az)$

b) 6. $c(u_1,u_2,u_3)=(cu_1,0,cu_3)\in V$

$c(u+v)=c(u_1+v_1,u_2+v_2,u_3+v_3)=(c(u_1+v_1),0,c(u_3+v_3))\\=(cu_1+cv_1,0,cu_3+cv_3)=c(u_1,u_2,u_3)+c(v_1,v_2,v_3)=cu+cv$

$(c+d)u=(c+d)(u_1,u_2,u_3)=((c+d)u_1,0,(c+d)u_3)=\\=(cu_1+du_1,0,cu_3+du_3)=(cu_1,0,cu_3)+(du_1,0,du_3) =cu+du$

$c(du)=c(d(u_,u_2,u_3))=c(du_1,0,du_3)=(cdu_1,0,cdu_3)=(cd)u$

$1u=1(u_1,u_2,u3)=(1u_1,0,1u_3)=(u_1,0,u_3)\neq(u_1,u_2,u_3)$

Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product $a(x,y,z)=(ax,0,az)$

c) Observe that $1u=1(u_1,u_2,u3)=(0,0,0)\neq(u_1,u_2,u_3)$

Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product $a(x,y,z)=(0,0,0)$ .

d) Observe that $1u=1(u_1,u_2,u3)=(2*1u_1,2*1u_2,2*1u_3)=(2u_1,2u_2,2u_3)\neq(u_1,u_2,u_3)=u$

Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product $a(x,y,z)=(2ax,2ay,2az)$ .

8 0

3 years ago

In ΔCDE, \text{m}\angle C = (4x-16)^{\circ}m∠C=(4x−16) ∘ , \text{m}\angle D = (6x-1)^{\circ}m∠D=(6x−1) ∘ , and \text{m}\angle E

borishaifa [10]

Answer:

m∠C = 44°

Step-by-step explanation:

In ΔCDE,

m∠C=(4x−16) ∘

m∠D=(6x−1) ∘

m∠E=(4x−13) ∘ .

The sum of angles in a triangle = 180°

Step 1

We solve for x

m∠C + m∠D + m∠E

(4x−16)° + (6x−1)° + (4x−13)° = 180°

4x - 16 + 6x - 1 + 4x - 13 = 180°

4x + 6x + 4x -16 - 1 - 13 = 180°

14x - 30 = 180°

14x = 180+ 30

14x = 210

x = 210/14

x = 15

Step 2

Find m∠C

m∠C = (4x−16)°

m∠C = (4 × 15 - 16)°

m∠C = (60 - 16)°

m∠C = 44°

3 0

3 years ago