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kkurt [141]
2 years ago
7

Brent is considering buying a new circular track for his model train. He estimates that the model's circumference is about 3 tim

es the measure of the circle's diameter. With this information, Brent could derive the value of —
Group of answer choices

radius

length

width

area
Mathematics
1 answer:
Dvinal [7]2 years ago
3 0

Answer:

Answer is D or a

Step-by-step explanation:

You might be interested in
Suppose a local manufacturing company claims their production line has a variance of less than 9.0. A quality control engineer d
Alexxx [7]

Answer:

\chi^2 =\frac{35-1}{9} 2.12^2 =16.979

p_v =P(\chi^2

If we compare the p value and the significance level provided we see that p_v so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly lower than 9

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=35 represent the sample size

\alpha=0.01 represent the confidence level  

s =2.12 represent the sample deviation obtained

\sigma_0 =3 represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is lower than 9 and the deviation lower than 3, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 \geq 9

Alternative hypothesis: \sigma^2

Calculate the statistic  

For this test we can use the following statistic:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

\chi^2 =\frac{35-1}{9} 2.12^2 =16.979

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df= n-1= 35-1=34. And since is a left tailed test the p value would be given by:

p_v =P(\chi^2

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(16.979,34,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that p_v so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly lower than 9

6 0
3 years ago
Please...Solve the inequality, and then graph its solution: 5 + 2x - 2 < 12 + 8x - 3x​
andreev551 [17]

Rewrite so

x

is on the left side of the inequality.

12

+

8

x

−

3

x

≥

5

+

2

x

−

2

Subtract

3

x

from

8

x

.

12

+

5

x

≥

5

+

2

x

−

2

Subtract

2

from

5

.

12

+

5

x

≥

2

x

+

3

Move all terms containing

x

to the left side of the inequality.

Tap for more steps...

12

+

3

x

≥

3

Move all terms not containing

x

to the right side of the inequality.

Tap for more steps...

3

x

≥

−

9

Divide each term by

3

and simplify.

Tap for more steps...

x

≥

−

3

The result can be shown in multiple forms.

Inequality Form:

x

≥

−

3

Interval Notation:

[

−

3

,

∞

)

3 0
2 years ago
If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. Find the first term and the 20th term.
Reil [10]

The first term is 2 and the 20th term is 1048576 .

<u>Step-by-step explanation:</u>

Here we have , If the sum of the first 12 terms of a geometric series is 8190 and the common ratio is 2. We need to Find the first term and the 20th term. Let's find out:

We know that Sum of a GP is :

⇒ S_n = \frac{a(r^n-1)}{r-1}

So ,Sum of first 12 terms is :

⇒ S_1_2 = \frac{a(2^{12}-1)}{2-1}

⇒ 8190=a(2^{12}-1)

⇒ \frac{8190}{4095}=a

⇒ a=2

Now , nth term of a GP is

⇒ a_n = ar^{n-1}

So , 20th term is :

⇒ a_2_0 = 2(2)^{20-1}

⇒ a_2_0 = (2)^{20}

⇒ a_2_0 = 1048576

Therefore , the first term is 2 and the 20th term is 1048576 .

8 0
3 years ago
Sequences:
IrinaK [193]

Answer:

A.

  • aₙ = (2n + 3)/4

<u>The first 5 terms:</u>

  • a₁ = (2*1 + 3) / 4 = 5/4
  • a₂ = (2*2 + 3) / 4 = 7/4
  • a₃ = (2*3 + 3)/ 4 = 9/4
  • a₄ = (2*4 + 3) / 4 = 11/4
  • a₅ = (2*5 + 3) / 4 = 13/4

B.

  • aₙ = (n - 3)/(n - 2)

<u>The first 5 terms:</u>

  • a₁ = (1 - 3) / (1 - 2) = 2
  • a₂ = (2 - 3) / (2 - 2) = undefined
  • a₃ = (3 - 3)/ (3 - 2) = 0
  • a₄ = (4 - 3) / (4 - 2) = 1 / 2
  • a₅ = (5 - 3) / (5 - 2) = 2 / 3
7 0
2 years ago
Solve the inequality -2/3m&lt;-4
ycow [4]

Answer:

m > 6

Step-by-step explanation:

-2/3m<-4

-2/3 * m < -4

m > -4 * (-3/2)

m > -2 * -3

m > 6

6 0
2 years ago
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