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masya89 [10]
3 years ago
8

Solve the inequality. |3x + 6| x > 2 C. –2 < x < 2 D. –6 < x < 2

Mathematics
1 answer:
iren [92.7K]3 years ago
8 0

Answer:

-6 < x < 2

Step-by-step explanation:

hope this helps :)

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The Ohio Department of Agriculture tested 203 fuel samples across the state
Rus_ich [418]

Answer:

\hat p = \frac{14}{105}= 0.133

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:  

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

If we replace the values obtained we got:

0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475

0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185

The 99% confidence interval would be given by (0.0475;0.2185)

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The proportion estimated would be:

\hat p = \frac{14}{105}= 0.133

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:  

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

If we replace the values obtained we got:

0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475

0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185

The 99% confidence interval would be given by (0.0475;0.2185)

3 0
3 years ago
Read 2 more answers
Trình bày ứng dụng của vi phân toàn phần trong việc tính xấp xỉ giá trị của một hàm số hai biến. Cho ví dụ.
Anastaziya [24]
Can you translate this to English
6 0
3 years ago
Find the slope of the line that passes through (4, 6) and (2, 3).
Verizon [17]
The slope is 3/2

To find the slope, you have to use the slope formula

y2-y1/x2-x1

6-3/4-2

3/2

So the slope is 3/2
3 0
3 years ago
The manufacturer offers a $125 rebate on photocopiers purchases before january 1. what is the nest cost of a $1,475 photocopier
Yuri [45]

Answer:

The net cost of the photocopier before january 1 is <u>$1350.</u>

Step-by-step explanation:

Given:

The manufacturer offers a $125 rebate on photocopiers purchases before january 1.

Now, to find the net cost of $1,475 photocopier before january 1.

Amount of rebate before January 1 = $125.

Cost of photocopier = $1,475.

So, to get the net cost of $1475 photocopier before january 1 we subtract the rebate from it:

\$1475-\$125

=\$1350.

Therefore, the net cost of the photocopier before january 1 is $1350.

6 0
3 years ago
2) Dada a equação x2 – 4x – 12, faça o que se pede.
alexandr1967 [171]

Answer:

a) x1 = 6 and x2 = -2

b) -2

Step-by-step explanation:

a)

To find the roots of the quadratic equation, we can use the Bhaskara's formula:

Delta = b^2 - 4ac

Delta = (-4)^2 - 4*1*(-12) = 64

sqrt(Delta) = 8

x1 = (-b + sqrt(Delta)) / 2a

x1 = (4 + 8) / 2

x1 = 6

x2 = (-b - sqrt(Delta)) / 2a

x2 = (4 - 8) / 2

x2 = -2

b)

The roots are 6 and -2, so the smaller root is -2

4 0
3 years ago
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