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2 years ago

Create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

Mathematics

1 answer:

damaskus [11]2 years ago

6 0

Answer:

Step-by-step explanation:

Two cases arise to obtain the median.

Case (1): Sample size (n) is odd

First, arrange the data in ascending order. Then, the median is the middle value and lies at the ${\left( {\frac{{n + 1}}{2}} \right)^{{\rm{th}}}}$ position.

Case (2): Sample size (n) is even

First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on and positions.

Formula for mean is, where is the sum of all observations and n is the total number of observations.

(1)

Use the below process to create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.

1.Select the 5 ordered numbers with middle value 7.

2.Adjust the remaining 4 numbers other than 7 to get mean 10 without changing the order of the numbers.

Based on the process to select the 5 ordered numbers with middle value 7 and change the other ordered numbers to get the mean value 10.

(2)

The product of the mean and the total number of observations is obtained. Then, the sum of four observations is subtracted from the product.

Here, the first four numbers are (5, 6, 7, 8).

The last number by using mean 10 is,

$\begin{array}{c}\\\bar x = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\10 = \frac{{5 + 6 + 7 + 8 + a}}{5}\\\\50 = 26 + a\\\\a = 50 - 26\\=24\end{array}$

The last number is 24.

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A set of speakers costs $22 and songs cost $1.25 each. The sales tax rate is 7.5%. The expression 0.075(22 + 1.25s) can be used

kykrilka [37]

Answer:

1.65 + 0.09s

Step-by-step explanation:

Given that :

Cost of speaker = $22

Cost per song = $1.25

Sales tax rate = 7.5%

Expression to obtain the amount of sales tax on entire purchase : 0.075(22 + 1.25s)

Expanding the expression :

0.075(22 + 1.25s)

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Rounding to the nearest hundredth :

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1 year ago

What are the x- and y- coordinates of point E, which partitions the directed line segment from J to K into a ratio of 1:4? (–13,

Lana71 [14]

I added a screenshot of the complete question.

Answer:

(-7, -1)

Explanation:

The formulas given to calculated the x and y coordinates are as follows:

$x = (\frac{m}{m+n})(x_{2}-x_{1}) + x_{1}\\\\y = (\frac{m}{m+n})(y_{2}-y_{1}) + y_{1}$

Let's define the variables used:

(x₁ , y₁) are the coordinates of the first point while (x₂ , y₂) are the coordinates of the second point.

We are given that the segment is directed from J to K, therefore:

First point is J ..........> (x₁ , y₁) is (-15, -5)

Second point is K ....> (x₂ , y₂) is (25, 15)

m and n defined the portion of the partitioned segment (JE : EK). It is given that this ratio is 1:4. Therefore:

m = 1 and n = 4

Finally, let's substitute with these variables in the equations as follows:

$x = (\frac{1}{1+4})(25-(-15)) + (-15) = -7\\\\y = (\frac{1}{1+4})(15-(-5)) + (-5) = -1$

Based on the above, the coordinates of point E are (-7, -1)

Hope this helps :)

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