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3 years ago

What is the value of the expression given below (8-3i) - (8-3i)(8+8i)

Mathematics

1 answer:

vazorg [7]3 years ago

8 0

At first let's multiply the second terms of the given expression. So,

(8-3i)(8+8i) = 8*8 +8*8i - 3i*8 -3i*8i

= 64 + 64i -24i -24i^2 (By multiplying)

= 64 +40i -24*(-1) (Adding the like terms and i^2=1)

=64 +40i +24 (Since (-24)*(-1)= +24)

= 88+40i (Adding the like terms).

Now the original equation is :

(8-3i) - (8-3i)(8+8i) = (8-3i)-(88+40i)

=8 - 3i -88 -40i

=(8-88)-3i -40i (By grouping the like terms)

=-80 -43i (Combine the like terms).

So, the value of the given expression is -80 -43i.

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The measure of the angle formed by two intersecting perpendicular lines is 90° true or false

Alexandra [31]

It is true. Perpendicular lines are what we call to two lines that intersect together forming a right angle or an angle measuring 90 degrees. You can easily determine this if you see a horizontal and a vertical line intersect together.

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4 years ago

A journalist reported that the average amount of time that a French person spends eating lunch at a restaurant is 22 minutes. Pe

maw [93]

Answer:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Step-by-step explanation:

Data given

American: 21,17,17,20,25,16,20,16 (Sample 1)

French: 24,18,20,28,18,29,17 (Sample 2)

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2 \neq 0$

Our notation on this case :

$n_1 =8$ represent the sample size for group 1

$n_2 =7$ represent the sample size for group 2

$\bar X_1 =19$ represent the sample mean for the group 1

$\bar X_2 =22$ represent the sample mean for the group 2

$s_1=3.117$ represent the sample standard deviation for group 1

$s_2=5.0$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$S^2_p =\frac{(8-1)(3.117)^2 +(7 -1)(5.0)^2}{8 +7 -2}=16.770$

And the deviation would be just the square root of the variance:

$S_p=4.095$

And now we can calculate the statistic:

$t=\frac{19 -22)-(0)}{4.095\sqrt{\frac{1}{8}+\frac{1}{7}}}=-1.416$

Now we can calculate the degrees of freedom given by:

$df=8+7-2=13$

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{13}$

So with the p value obtained and using the significance level assumed $\alpha=0.1$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance we don't have significant differences between the two means.

3 0

3 years ago

the temperature on saturday was 4 degrees Fahrenheit F the temperature on sunday was 9 degrees warmer than the temperature on sa

Naddika [18.5K]

Saturday(x)= 4° Fahrenheit
Sunday(y)= x+9
your answer is: 13 degrees Fahrenheit

6 0

4 years ago

Read 2 more answers

Find the length of the third side to the nearest tenth.

malfutka [58]

Answer:

The answer to your question is b = 9.5

Step-by-step explanation:

Data

hypotenuse = 10

leg 1 = 3

Process

1.- To solve this problem use the Pythagorean theorem.

c² = a² + b²

c = hypotenuse = 10

a = 3

b = x

2.- Solve for b

b² = c² - a²

3.- Substitution

b² = 10² - 3²

4.- Simplification

b² = 100 - 9

b² = 91

5.- Result

b = 9.5

5 0

3 years ago

Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D'E'F’G’H’I’

frez [133]

Answer:

The answer is " $\bold{(x,y)\longrightarrow (x-8, y-7)}$ ".

Step-by-step explanation:

In the given question some data is missing. so, the correct answer to this can be explained in the following example:

In the given example, point D is also known as the coordinates in the (2, 5), and in the coordination of the D prime (D') and after translation its co-ordinates value is (-6, -2). Since the very first choice is only accurate as:

⇒2-8 = -6

⇒ 5-7 = -2

It can try certain things too and see why this alone is the correct translation.

7 0

3 years ago