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Semmy [17]
2 years ago
11

Which step do the constructions of a regular hexagon, a square, and an equilateral triangle inscribed in a circle all have in

Mathematics
1 answer:
irga5000 [103]2 years ago
3 0

Answer:

a

Step-by-step explanation:

took the test

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"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0
3 years ago
If A ABC ~ ARST and m 2 A = 42°, m 2 C = 60°,<br> find the measure of &lt; S.
Free_Kalibri [48]

Answer:

78

Step-by-step explanation:

∠A + ∠B + ∠C = 180   { Angle sum property of triangle}

42 + ∠B + 60 = 180

∠B + 102 = 180

∠B = 180 - 102 = 78

In similar triangles, corresponding angles are congruent.

∠S ≅ ∠B

∠S = 78°

7 0
2 years ago
Triangle IHJ is similar to triangle RST.<br> What is the length of side _<br> RT
solmaris [256]
6 mm

Set up a proportion of 12/9=8/x. Cross multiply and this gives us 12x=72. Now divide both sides by 12 and you get 6.
3 0
2 years ago
A calculator may be used for this question. The energy saving from recycling one glass bottle will power the oven Adam uses to c
evablogger [386]
The one above is right.
5 0
2 years ago
Use the substitution methods to solve the system of equations. Choose the correct ordered pair. y=7x+8 y=x+20
krek1111 [17]

Answer:

d

Step-by-step explanation:

Solution by substitution method

y=7x+8

∴y-7x=8

and y=x+20

∴y-x=20

Suppose,

-7x+y=8→(1)

and -x+y=20→(2)

Taking equation (1), we have

-7x+y=8

⇒y=7x+8→(3)

Putting y=7x+8 in equation (2), we get

-x + 7x + 8 = 20

6x = 20-8

6x = 12

x= 12 / 6

x = 2

substitute for x in equation (3)

y = 7(x) + 8

y = 7(2) + 8

y = 22

4 0
2 years ago
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