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3 years ago

Which pair of complex factors results in a real number product? 15(–15i) 3i(1 – 3i) (8 + 20i)(–8 – 20i) (4 + 7i)(4 – 7i)

Mathematics

2 answers:

photoshop1234 [79]3 years ago

6 0

Answer:

(4 + 7i)(4 – 7i)

Step-by-step explanation:

This pair will produce a real answer because they are complex conjugates.

Complex conjugates ( a+bi) (a-bi) when multiplied together form a real number ( a^2 + b^2)

I am Lyosha [343]3 years ago

6 0

Answer:

D. (4+7i)(4-7i)

Step-by-step explanation:

You might be interested in

What is the answer to… 1 > x - 6

Ratling [72]

Answer:

x < 7

Step-by-step explanation:

Flip the equation to make it easier: x - 6 < 1

Move 6 to the other side and change sign: x < 1 + 6

Do simple addition: x < 7

7 0

3 years ago

As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple

zhenek [66]

Answer:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

$P(A)=\frac{Possible outcomes}{Total outcomes}$

For this case if we replace we got:

$P(A) =\frac{23}{56}=0.411$

And using the complemnt rule we got:

$0.411 +P(A')=1$

And solving for P(A') we got:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

4 0

3 years ago

Find the Value of X.

ArbitrLikvidat [17]

Answer:

Step-by-step explanation:

∠ TUL + ∠ LUV = ∠ TUV , substitute values

x + 16 + 11x = 172 , that is

12x + 16 = 172 ( subtract 16 from both sides )

12x = 156 ( divide both sides by 12 )

x = 13 → C

5 0

3 years ago

Using the information regarding the proportion of work time linguists study a new language, choose the correct conclusion for th

Vlada [557]

Answer:

The correct option is B

Step-by-step explanation:

From the question we are told that

The null hypothesis is $H_o : p = 0.10$

The alternative hypothesis is $H_a : p > 0.10$

The p-value is $p-value = 0.09$

The level of significance is $\alpha = 0.025$

From the given values $p-value > \alpha$ so we fail to reject the null hypothesis

So there is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

5 0

3 years ago

Researchers want to determine whether or not there is a difference in systolic blood pressure based on how many hours a person e

VARVARA [1.3K]

Answer:

(1) The between groups degrees of freedom is 2.

(2) TRUE.

(3) The correct option is (a).

Step-by-step explanation:

(1)

The between groups degrees of freedom for the study is:

$\text{df}_{B}=k-1\\=3-1\\=2$

Thus, the between groups degrees of freedom is 2.

(2)

The hypothesis for he one-way ANOVA is:

H₀: All the means are equal.

Hₐ: At least one of the mean is not equal.

The output of the ANOVA test is attached below.

The p-value of the test is 0.00005.

p-value = 0.00005 < α = 0.05

Thus, the result is statistically significant.

The statement is TRUE.

(3)

As the p-value of the test is less than the significance level, the researcher should make the decision to reject the null hypothesis.

The correct option is (a).

6 0

3 years ago