Simplify the expression. 3 + 4i over 2 + 4i

1 answer:

3 0

$\dfrac{3+4i}{2+4i}=\dfrac{3+4i}{2+4i}\cdot\dfrac{2-4i}{2-4i}=\dfrac{(3)(2)+(3)(-4i)+(4i)(2)+(4i)(-4i)}{2^2-(4i)^2}\\\\=\dfrac{6-12i+8i-16i^2}{4-16i^2}=\dfrac{6-4i-16(-1)}{4-16(-1)}=\dfrac{6-4i+16}{4+16}\\\\=\dfrac{22-4i}{20}=\boxed{\dfrac{11-2i}{10}}=\boxed{\dfrac{11}{10}-\dfrac{1}{5}i}$

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A care care company sells 45in. Upholstery fabric for car restoration. Art bought 7 1/4 yd and 12 9/10 yd for two car projects.

Troyanec [42]

Answer: the number of yards that art bought is 20 3/20 yards

Step-by-step explanation:

Art bought 7 1/4 yd and 12 9/10 yd for two car projects. We would convert both measurements from mixed fraction to improper fraction before adding.

Converting 7 1/4 yd to improper fraction, it becomes 29/4

Converting 12 9/10 yd to improper fraction, it becomes 129/10 yd

Adding both measurements, it becomes

29/4 + 129/10 = (145 + 258)/20 = 403/20yds

Converting to mixed fraction, it becomes

20 3/20 yards

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SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below

kvasek [131]

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

Let $\sigma$ = population standard of the reading and writing section SAT score of the students in this school

So, Null Hypothesis, $H_0$ : $\sigma \leq$ 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, $H_A$ : $\sigma$ > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}