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qwelly [4]
3 years ago
15

Can you help me with these questions​

Mathematics
1 answer:
dlinn [17]3 years ago
7 0

Answer:

see below (I hope this helps!)

Step-by-step explanation:

41. √20 = √4 * 5 = √4 * √5 = 2√5

43. The sum of interior angles in a triangle is 180°, therefore, x = 180 - (75 + 64) = 41°.

45. 15 + 5(2x - 3) = 15 + 5(2x) + 5(-3) = 15 + 10x - 15 = 10x

47. Complementary angles have a sum of 90°, therefore, x = 90 - 48 = 42°.

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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
Create write an expression that simplifies to 2a + 14 using the distributive property
geniusboy [140]

Answer:

2 ( a + 7)

Step-by-step explanation:

2a + 14

both 2a and 14 are divisible by 2

2a/a = a

14/2 = 7

2( a + 7) = 2a + 14

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

4 0
3 years ago
Select all the expressions that are equivalent to −5/6 / -1/3
Sindrei [870]

Step-by-step explanation:

We need to find an expression for \dfrac{\dfrac{-5}{6}}{\dfrac{-1}{3}}.

We can solve it as follows.

We know that,

\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times \dfrac{d}{c}

So,

\dfrac{\dfrac{-5}{6}}{\dfrac{-1}{3}}=\dfrac{-5}{6}\times -3\\\\=\dfrac{5}{2}

or

=2\dfrac{1}{2}

Hence, this is the required solution.

3 0
3 years ago
Write an addition equation with a positive addend and negative addend and a resulting sum of -8
Ierofanga [76]
-18 + 10 = -8

------------------------------------
7 0
3 years ago
Triangle QRS is a right triangle.
olasank [31]

Answer:

5.3

Step-by-step explanation:

a² + b² =² c²               the Pythagorean theorem

RQ² + RS² = QS²            Solve RS

6² + RS² = 8²

RS² = 64 -36

RS² = 28

RS = √28                  28 is slightly > 25   and since  √25 =5

RS = 5.3                    actually 5.2915  to a few more significant digits

5 0
3 years ago
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