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Snowcat [4.5K]
2 years ago
6

Solve for x 3:21=x:16

Mathematics
2 answers:
gayaneshka [121]2 years ago
8 0

Answer:

16/7 =x

Step-by-step explanation:

We can use ratios to solve

3           x

-----  = ---------

21            16

Using cross products

3*16 = x *21

48 = 21x

Divide by 21

48/21 = x

16/7 =x

ehidna [41]2 years ago
5 0

Given:  3:21 = x:16

Find: The value of the unknown variable, x

Solution: The first step that we should take is to convert the ratios into a fraction so we can then easily cross multiply, isolate the unknown variable, and simplify the expression.

<u>Convert to fractions</u>

  • 3:21=x:16
  • \frac{3}{21}=\frac{x}{16}

<u>Cross multiply</u>

  • 3(16) = 21(x)
  • 48 = 21x

<u>Divide both sides by 21</u>

  • \frac{48}{21} = \frac{21x}{21}
  • \frac{48}{21} = x

<u>Simplify the expression</u>

  • \frac{48/3}{21/3} = x
  • \frac{16}{7} = x

Therefore, the final answer would be that the unknown would be equal to 16/7 in the ratio expression that was provided in the problem statement.

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The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than av
34kurt

Answer:

Probability that the 50 randomly selected laptops will have a mean replacement time of 3.1 years or less is 0.0092.

Yes. The probability of this data is unlikely to have occurred by chance alone.

Step-by-step explanation:

We are given that the replacement times for the model laptop of concern are normally distributed with a mean of 3.3 years and a standard deviation of 0.6 years.

He then randomly selects records on 50 laptops sold in the past and finds that the mean replacement time is 3.1 years.

<em>Let M = sample mean replacement time</em>

The z-score probability distribution for sample mean is given by;

            Z = \frac{ M-\mu}{\frac{\sigma}{\sqrt{n} } }} }  ~ N(0,1)

where, \mu = population mean replacement time = 3.3 years

            \sigma = standard deviation = 0.6 years

            n = sample of laptops = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, Probability that the 50 randomly selected laptops will have a mean replacement time of 3.1 years or less is given by = P(M \leq 3.1 years)

 P(M \leq 3.1 years) = P( \frac{ M-\mu}{\frac{\sigma}{\sqrt{n} } }} } \leq \frac{ 3.1-3.3}{\frac{0.6}{\sqrt{50} } }} } ) = P(Z \leq -2.357) = 1 - P(Z \leq 2.357)

                                                           = 1 - 0.99078 = <u>0.0092</u>  or  0.92%          

<em>So, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.357 in the z table which will lie between x = 2.35 and x = 2.36 which has an area of 0.99078.</em>

Hence, the required probability is 0.0092 or 0.92%.

Now, based on the result above; <u>Yes, the computer store has been given laptops of lower than average quality</u> because the probability of this data is unlikely to have occurred by chance alone as the probability of happening the given event is very low as 0.92%.

8 0
3 years ago
Fine the average of these numbers, 8,12,13,15
GarryVolchara [31]

Answer:

12

Step-by-step explanation:

The average is calculated as

average = \frac{sum}{count} = \frac{8+12+13+15}{4} = \frac{48}{4} = 12

8 0
3 years ago
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There is 5 times the amount of cookie dough to peanut butter
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myrzilka [38]
No. A cube is a 3D figure and polygon is a 2D one.
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Can I have some help with these? Thanks.
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The x^2 over the x is like subtracting x from x^2, so the new equation would be 9-x/-3. You divide 9 by -3 to get the final answer of -3-x, or -x-3, which is E.
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3 years ago
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