Please someone help meeee

What is the solution set of [1/x-2]<-2

slavikrds [6]

Step-by-step explanation:

$1 \div (x - 2) + 2 < 0$

$(1 + 2x - 4) \div ( x- 2) < 0$

$(2x - 3) \div (x - 2) < 0$

Hence

You have to put:

$2x - 3 > 0$

And

$x - 2 > 0$

Which results in:

$x > 3 \div 2$

And

$x > 2$

The solution is:

$3 \div 2 < x < 2$

7 0

3 years ago

Given the data

Alexus [3.1K]

Answer:

(a) Mean = 1.6244 (b) Median = 1.65

(c) Mode = 1.35 (d) Range = 1.39

(e) Standard deviation = 0.3325

(f) Variance = 0.1106

(g) Coefficient of variation = 20.47%.

Step-by-step explanation:

The mean (μ) of a data set is the average value of the data set. The formula to compute mean is:

$\mu=\frac{1}{n}\sum X_{i}$

The median (m) is a quantity in statistics that points out where the mid-value of a data set is. In case of, odd number of data-values, the median is given by,

$Median=(\frac{n+1}{2})^{th}\ obs.$

The mode (M) of a data set is the value that appears most often.

The range of a data-set is the difference between the maximum and minimum values in the data-set.

$Range=Max.-Min.$

The standard deviation of a data set is a numerical value that represents the amount of variation between the observed values.

$SD=\sqrt{\frac{1}{n-1}\sum (X_{i}-\mu)^{2}}$

The variance is the square of the standard deviation.

$Var=\frac{1}{n-1}\sum (X_{i}-\mu)^{2}$

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is,

$CV=\frac{\sigma}{\mu}\times 100\%$

Consider the data set provided.

(a)

Compute the mean as follows:

$\mu=\frac{1}{n}\sum X_{i}=\frac{1}{25}\times 40.61=1.6244$

Thus, the mean of the data is 1.6244.

(b)

Compute the median as follows:

Arrange the data in ascending order as follows:

0.9 , 1.05 , 1.27 , 1.3 , 1.32 , 1.35 , 1.35 , 1.42 , 1.47 , 1.47 , 1.55 , 1.63 , 1.65 ,

1.66 , 1.71 , 1.74 , 1.78 , 1.82 , 1.85 , 1.92 , 1.95 , 1.96 , 2.06 , 2.14 , 2.29

$Median=(\frac{n+1}{2})^{th}\ obs.=(\frac{25+1}{2})^{th}\ obs.=13^{th}\ obs.=1.65$

Thus, the median of the data set is 1.65.

(c)

Compute the mode as follows:

Consider the data arranged in ascending order above.

0.9 , 1.05 , 1.27 , 1.3 , 1.32 , 1.35 , 1.35 , 1.42 , 1.47 , 1.47 , 1.55 , 1.63 , 1.65 ,

1.66 , 1.71 , 1.74 , 1.78 , 1.82 , 1.85 , 1.92 , 1.95 , 1.96 , 2.06 , 2.14 , 2.29

The value 1.35 repeats twice and none of the other values repeat themselves.

Thus, the mode of the data set is 1.35.

(d)

Compute the range as follows:

$Range=Max.-Min.\\=2.29-0.90\\=1.39$

Thus, the range of the data set is 1.39.

(e)

Compute the standard deviation as follows:

$SD=\sqrt{\frac{1}{n-1}\sum (X_{i}-\mu)^{2}}=\sqrt{\frac{1}{25-1}\sum (X_{i}-1.6244)^{2}}=0.3325$

Thus, the standard deviation is 0.3325.

(f)

Compute the variance as follows:

$Var=(SD)^{2}=(0.3325)^{2}=0.1106$

Thus, the variance is 0.1106.

(g)

Compute the coefficient of variation as follows:

$CV=\frac{\sigma}{\mu}\times 100\%=\frac{0.3325}{1.6244}\times 100\%=20.47\%$

Thus, the coefficient of variation is 20.47%.

The histogram is attached below.

5 0

3 years ago

PLEASE HELP MY TEST IS DUE IN 13 MINS!!! AREA OF A TRIANGLE: TRIANGLE IS SIDEWAYS, 15 M ON THE LONG SIDE OF THE TRIANGLE AND 2M

Alisiya [41]

Answer:

7.5m²

Step-by-step explanation:

A=½b×l

A=½×7.5×2

A=7.5m²

4 0

3 years ago

The two figures are similar. write the similarity. justify your answer.

scoray [572]

Answer:

The corresponding sides are in proportion. so they are similar triangles.

8 0

4 years ago

Daniel works at an electronics store, and he claims that the popularity of a television (measured in number of sales) is inverse

Rom4ik [11]

We are given that popularity of television is inversely proportional to its cost.

let us say popularity of television is represented by "P" and cost of television by "T".

We will use a constant "k" to convert the proportionality sign to equal to (=) sign.

Thus forming the equation :

$P= \frac{k}{T}$

We are given that 15 customers buy a television that cost $1500.

plugging P=15 and T=1500, finding k,

$15= \frac{k}{1500}$

k=15*1500 = 22500

Next we have to find how many customers would buy a television that costs $2500, so here k=22500 and T=2500, plugging this in the equation we have ,

$P= \frac{22500}{2500}$

P=9

So there will be 9 customers that buy a television which costs $2500.

7 0

3 years ago

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