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Masteriza [31]
2 years ago
6

Which expression is equivalent to…

Mathematics
1 answer:
kompoz [17]2 years ago
6 0

Answer:

D

Step-by-step explanation:

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How many solutions does the following equation have?
sergiy2304 [10]

Answer:

choice a

Step-by-step explanation:

6 0
3 years ago
The moats separating people from the animals are 5 m wide for lions and 4 m wide for the elephants. If the lion’s moat is 4 m de
ZanzabumX [31]

Answer:

<em>The elephants' moat should be 3.2 meters deep.</em>

Step-by-step explanation:

Suppose, the depth of the elephants' moat is  x meter.

Width of the lions' moat is 5 meter and width of the elephants' moat is 4 meter.

Given that, the lion’s moat is 4 meter deep.

So, <u>according to the ratio of width and depth</u>, the equation will be.......

\frac{5}{4}=\frac{4}{x}\\ \\ 5x=4*4\\ \\ 5x=16\\ \\ x=\frac{16}{5}=3.2

Thus, the elephants' moat should be 3.2 meters deep.

3 0
3 years ago
Simplest way to multi-step equations...
Bess [88]

Answer: calculator boi

Step-by-step explanation:

4 0
2 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
How to solve 6x&gt;-24 and 9x&lt;54 ?
djverab [1.8K]
6x>-25 and 9x<54the answer (solve x ) you have 6x>-25 so we solve 'x' we say divide by 6 both side then we get { x>-25/6 or x>-4.166} second you have 9x<54 we say divide by 9 each side { x<6 } your answer is { x>-25/6 and x<6 }
7 0
3 years ago
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