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guajiro [1.7K]
3 years ago
8

Answer the following questions using what you've learned from this unit. Write your answers in the

Mathematics
1 answer:
sesenic [268]3 years ago
8 0

Answer:

x=-3

Step-by-step explanation:

5(x - 4) + 3x - 9x = 6 - (2x + 5) + 8x

(remove parentheses)

5x-20+3x-9x=6-2x-5+8x

(collect like terms and calculate)

-x-20=1+6x

(move the terms)

-x-6x=1+20

(collect like terms and calculate)

-7x=21

(divide both sides)

x=-3

(your answer :))

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HELP ME WITH THIS QUESTION PLEASE
lara [203]

Answer:

  • 0.79

Step-by-step explanation:

all you really need to do is multiply your decimal (15.8) by your percent (5) so, you problem would look like 15.8(.05) (note it is .<em>0</em>5 because there need to be 2 decimal places) so, your answer is .79

6 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
A.<br> B.<br> C.<br> D.<br> Whats the answer
icang [17]
I think it’s c not so sure tho
3 0
3 years ago
Read 2 more answers
Which is the answer. A B C D?
Harlamova29_29 [7]

Answer:

A) T'(-2,3), U'(0,5), V'(-1,0)

5 0
3 years ago
The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a stand
erastovalidia [21]

Answer:

z=0.524

And if we solve for a we got

a=5 +0.524*2=6.048 \approx 6.05 min

Step-by-step explanation:

Let X the random variable that represent the lenght time it takes to find a parking space at 9AM of a population, and for this case we know the distribution for X is given by:

X \sim N(5,2)  

Where \mu=5 and \sigma=2

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.3   (a)

P(X   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.7 of the area on the left and 0.3 of the area on the right it's z=0.524

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.524

And if we solve for a we got

a=5 +0.524*2=6.048 \approx 6.05 min

3 0
3 years ago
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