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antoniya [11.8K]
3 years ago
11

3x-5<19 Fill in the blanks to show the steps in solving the inequality.

Mathematics
1 answer:
Stels [109]3 years ago
4 0

Answer:

8

Step-by-step explanation:

3x - 5 <19

3x <19 +5

3x <24

x <24 :3

x <8

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Svet_ta [14]

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A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were de
olga2289 [7]

Answer:

Se=1.2

Step-by-step explanation:

The standard error is the standard deviation of a sample population. "It measures the accuracy with which a sample represents a population".

The central limit theorem (CLT) states "that the distribution of sample means approximates a normal distribution, as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population distribution shape"

The sample mean is defined as:

\bar X =\frac{\sum_{i=1}^n x_i}{n}

And the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

Let X denotes the random variable that measures the particular characteristic of interest. Let, X1, X2, …, Xn be the values of the random variable for the n units of the sample.

As the sample size is large,(>30) it can be assumed that the distribution is normal. The standard error of the sample mean X bar is given by:

Se=\frac{\sigma}{\sqrt{n}}

If we replace the values given we have:

Se=\frac{12}{\sqrt{100}}=1.2

So then the distribution for the sample mean \bar X is:

\bar X \sim N(\mu=80,Se=1.2)

5 0
3 years ago
Solve and verify please solve​
RUDIKE [14]

Answer:

Below in bold.

Step-by-step explanation:

I'll solve a few of them to illustrate the method:

a) 5x - (3x - 1) = x - 4

The aim is to get all the 'x' terms to one sides of the '=' and the numbers to the other side:

Distribute the negative over the 3x - 1 in the parentheses:

5x - 3x + 1 = x - 4        ( Note that  -* -1 = + 1)

Now subtract  1 from both sides:

5x - 3x + 1 - 1 = x - 4 - 1

5x - 3x = x - 5

Now subtract x from both sides:

5x - 3x - x = x - x - 5.

2x - x = -5

x = -5.

(b) 3/5 x + 1 = 2/5 - 3x

We first get rid of the fractions by multiplying each term by 5:

5 * 3/5 x + 1*5 = 5 * 2/5 - 5*3x

3x + 5 = 2 - 15x

3x + 15x + 5 = 2 - 15x + 15x        (adding 15x to both sides)

18x + 5 = 2          Subtract 5 from both sides:

18x + 5 - 5 = 2 - 5

18x = -3

Now we divide both sides by 18:

x = -3/18 = -1/6.

g) 0.3(6 + m) = 0.4(8 - m)

0.3 * 6 + 0.3* m = 0.4*8 + 0.4 * -m   ( Distributing the 0.3 and 0.4 over the parentheses)

1.8 + 0.3m = 3.2 - 0.4m        ( recall that + * - = -)

1.8 - 1.8 + 0.3m = 3.2 - 1.8 - 0.4m

0.3m = 1.4 - 0.4m

0.3m + 0.4m = 1.4 - 0.4m + 0.4m

0.7m = 1.4

m = 1/4/0.7

m =  2.

I hope this helps.

5 0
3 years ago
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