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melomori [17]
3 years ago
9

A diagonal divides a square into two isosceles right triangles

Mathematics
1 answer:
boyakko [2]3 years ago
6 0

Answer:

always true I think hope it helps

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Which of the following functions is graphed below?
Irina18 [472]

Answer:

fat bit

fat old ugly

Step-by-step explanation:

5 0
3 years ago
Write an expression that is equivalent to -2/5(15 - 20d +50)<br> Explain please!:)
valina [46]

Answer:

-26 + 4/5d

Step-by-step explanation:

-2/5 ( 15 - 2d + 50)

= -2/5 ( 65 - 2d)

= -2/5 * 65 - (-2/5) * 2d

= -26 - (-4/5d)

= -26 + 4/5d

3 0
3 years ago
"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
Please help me<br> Sooo confused!!!
SashulF [63]
Well let's say x = -1000
That's what I would do
8 0
3 years ago
Read 2 more answers
| x - 1 | = 5x + 10<br> Check for extraneous solutions.
Ronch [10]
[x-1]=5x+10

We have two equations:
1) x-1=5x+10

x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4

2) x-1=-(5x+10)

x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2

we have two  possible solutions:
solution₁;       x=-11/4
solution₂:       x=-3/2

we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4  - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4  + 10
[-15/4]=(-55+40) /4
15/4≠-15/4   This solution don´t work.

2) x=-3/2
[x-1]=5x+10
[-3/2  - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2  + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.

Therefore:

Answer: x=-3/2.
8 0
3 years ago
Read 2 more answers
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