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allochka39001 [22]
3 years ago
14

Find the following quotient. (5−4i)/(5+4i) Answer in the form (a+bi)/c .

Mathematics
1 answer:
Umnica [9.8K]3 years ago
3 0

Answer:

Step-by-step explanation:

\frac{5-4i}{5+4i}=\frac{(5-4i)*(5-4i)}{(5+4i)*(5-4i)}\\\\

Now numerator is in the form (a - b)² & denominator in the form (a+b)(a - b)

(a -b)² = a² - 2ab + b²

(a + b)(a-b) = a² - b²

\frac{(5-4i)^{2}}{(5)^{2}-(4i)^{2}}=\frac{5^{2}-2*5*4i+(4i)^{2}}{25-16i^{2}}\\\\=\frac{25-40i+16i^{2}}{25-16*(-1)}\\\\=\frac{25-40i+16*(-1)}{25+16}\\\\=\frac{25-40i-16}{41}\\\\=\frac{9-40i}{41}

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What is mn+5m-2+mn+3
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Answer:

mn + 5m - 2 + mn + 3 \\  = 2mn + 5m + 1 \\  =  =  =  =  =  =  =  =  =  =  =

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3 years ago
Last week, a chocolate shop sold 7/12 pounds of white chocolate. It sold 2 1/5 times as much milk chocolate as white chocolate.
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Answer:

5?

Step-by-step explanation:

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6 0
3 years ago
At the end of a party, there are 3 pizzas left over. Each person will eat 2/8 of a pizza. How many people will 3 pizza feed?
Georgia [21]

First, convert 3 into a fraction with denominator 8.

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Then, divide 24/8 pizzas by 2/8 pizzas per 1 person.

(24/8 pizzas)(2/8 pizzas/person)

Dividing by a fraction is the same as multiplying by the reciprocal:

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4 0
3 years ago
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day
kvv77 [185]

The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

<h3>How to calculate the probability distribution?</h3>

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

<h3>Calculation:</h3>

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

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Z - score for X = 156:

Z = (156 - 120)/18

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So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

Learn more about standard normal distribution here:

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5 0
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