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2 years ago

Simplify (2-7i)+(3+9i) step by step

Mathematics

2 answers:

Mariana [72]2 years ago

5 0

Answer:

first identify the like terms;

(2-7i)+(3+9i)

(2+3-7i+9i)

5+2i

gayaneshka [121]2 years ago

3 0

Answer:

5 + 2i

Step-by-step explanation:

1) Remove parentheses

2 - 7i + 3 + 9i

2) Collect like terms

(2 + 3) + (-7i + 9i)

3) Simplify

5 + 2i

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P(perfect square | odd)

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2 years ago

Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given t

SVEN [57.7K]

Answer:

The minimum sample size required is 207.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

The margin of error of this confidence interval is:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}$

Given:

$MOE=3\\\sigma=29\\z_{\alpha /2}=z_{0.01/2}=z_{0.05}=2.576$

*Use a z-table for the critical value.

Compute the value of n as follows:

$MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207$

Thus, the minimum sample size required is 207.

3 0

3 years ago

What is the solution to this equation? -2(2 - 4m) = 6(m + 3)

serg [7]

Answer:

m = 11

Step-by-step explanation:

-2(2 - 4m) = 6(m + 3)

Divide both sides by -2.

2 - 4m = -3(m + 3)

Distribute -3 on the left side.

2 - 4m = -3m - 9

Add 3m to both sides.

2 - m = -9

Subtract 2 from both sides.

-m = -11

Divide both sides by -1.

m = 11

6 0

3 years ago

naveed makes 6.5litres of soup,correst to the nearest 0.5 litre he serves portions of his soup in 330ml cups correct to the near

Karolina [17]

Answer:

Number of Cups = 19

Step-by-step explanation:

Given

Size of Soup = 6.5 litres

SIze of cup = 330 ml

Required

Number of Cups.

First, it'll be assumed that the size of cups are uniform (the same).

The number of cups needed is calculated by dividing the size of soup by the size of the cup;

Number of Cup = Size of Soup/Size of Cup

Number of Cup = 6.5 litres/ 330 ml

Convert units;

1 litres = 1000 ml

So,

6.5 litres = 6.5 * 1,000 ml

6.5 litres = 6,500 ml

So,

Number of Cups = 6500 ml/330 ml

Number of Cups = 19.696969697

From the solution above, Naveed will definitely be able to serve 19 cups. The remaining fractional part won't fill a cup;

Hence, Number of Cups = 19

3 0

3 years ago