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frutty [35]
3 years ago
7

Find the LCM of k^2 + 3k + 2 and 2k^2 + 14k + 20.

Mathematics
1 answer:
Airida [17]3 years ago
3 0

Answer:

  C.  2(k +2)(k +5)(k +1)

Step-by-step explanation:

The LCM will be the product of unique factors.

  (k^2 + 3k + 2)=(k+1)(k+2)\\(2k^2 + 14k + 20)=2(k+2)(k+5)

The unique factors are 2, (k+1), (k+2), (k+5), so the LCM is their product:

  2(k+1)(k+2)(k+5) . . . . matches choice C

You might be interested in
In a study of the accuracy of fast food drive-through orders, McDonald’s had 33 orders that were not accurate among 362 orders o
melomori [17]

Answer:

A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B. Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

C. z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558  

D. z_{\alpha/2}=-1.96  z_{1-\alpha/2}=1.96

E. Fail to the reject the null hypothesis

F. So the p value obtained was a very high 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 true proportion of inaccurate orders is not significantly different from 0.1.  

Step-by-step explanation:

Data given and notation

n=362 represent the random sample taken

X=33 represent the number of orders not accurate

\hat p=\frac{33}{363}=0.0912 estimated proportion of orders not accurate

p_o=0.10 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)  

A: Write the claim as a mathematical statement involving the population proportion p

We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B: State the null (H0) and alternative (H1) hypotheses

Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

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.

C: Find the test statistic

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

z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558  

D: Find the critical value(s)

Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:

z_{\alpha/2}=-1.96  z_{1-\alpha/2}=1.96

P value

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  

E: Would you Reject or Fail to Reject the null (H0) hypothesis.

Fail to the reject the null hypothesis

F: Write the conclusion of the test.

So the p value obtained was a very high 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 true proportion of inaccurate orders is not significantly different from 0.1.  

6 0
3 years ago
PLZ HELP
Agata [3.3K]

Answer:

\frac{5x^{2} }{12}

Step-by-step explanation:

Given: Height: x

          Base: \frac{5x}{6}

Now, finding the area of triangle.

Formula; Area of triangle= \frac{1}{2} \times base\times height

⇒ Area of triangle= \frac{1}{2}\times \frac{5x}{6} \times x

⇒ Area of triangle= \frac{5x^{2} }{12}

Hence, area of triangle= \frac{5x^{2} }{12}

4 0
3 years ago
Someone please help ASAP will give brainliest
iren [92.7K]

Your answer is B Hope I helped :)

7 0
3 years ago
Hitung jarak di antara titik P(7, 1) dengan titik Q(7, 8) ​
MaRussiya [10]

Answer:

7 units

Step-by-step explanation:

Distance between 2 points

=\sqrt{(y1 - y2)^{2}  + (x1 - x2) {}^{2} }

Thus, distance PQ

=\sqrt{(8 - 1)^{2}  + (7 - 7)^{2} }  \\ = \sqrt{7^{2} }  \\  = 7

Or you could simply take 8-1= 7 since both points have the same x-coordinate. Thus, PQ is a vertical line and the distance between them is due to the difference in their y-coordinate.

5 0
3 years ago
Help ? Plz forgot the steps (3z+9)(z-4)
Dafna11 [192]
It's a binomial times a binomial, so you FOIL
First multiply the First numbers
3z*z = 3z(^2)
Then multiply Outers:
3z* -4  = -12z 
Nest, Inners:
9*z = 9z
Finally, the Lasts: 
-4*9 = -36
Then, throw it all together in descending order, starting with the variable of highest degree to lowest:
3z^2 - 12z + 9z - 36
Last of all, simplify coefficients with like terms and you're good to go:
3z^2 - 3z - 36
Hope this helps!
3 0
3 years ago
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