The probabilities for this problem are given as follows:
P(X > 31) = 0.1635 = 16.35%.P(X < 8) = 0.0026 = 0.26%.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the commute times are given as follows:
[tex]\mu = 25, \sigma = 6.1[/tex]
The probability that the time is more than 31 minutes is one subtracted by the p-value of Z when X = 31, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (31 - 25)/6.1
Z = 0.98
Z = 0.98 has a p-value of 0.8365.
1 - 0.8365 = 0.1635 = 16.35%.
The probability that the time is less than 8 minutes is the p-value of Z when X = 8, hence:
Z = (8 - 25)/6.1
Z = -2.79
Z = -2.79 has a p-value of 0.0026.
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The current population of a small city is 48500 people. Due to a loss of jobs, the population is decreasing by an average of 325 people per year. How many years (from now) will it take for the population to decrease to 46875 people?
It takes 5 years for the population to decrease to 46785 from the current population of 48500 of a small city whose population is decreasing by an average of 325 people per year.
What is the equation for the given statement?It is given that,
Current population = 48500 people
Rate of decrease = 325 per year
Number of years = x
decreased population after x years = 46785
Then, the equation is
46785 = 48500 - 325x
Calculation:On simplifying the obtained equation, we get
46785 = 48500 - 325x
⇒ 325x = 48500 - 46785 = 1625
⇒ x = 1625/325 = 5 years
So, the people become 46785 after 5 years.
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Evaluate lim x approaches 0^+ x/|x|
Answer:
The answer of the limit is 1.
LMNO is a parallelogram. If NM\ =\ x+32\ and\ OL=2x+22,\NM = x+32 and OL=2x+22, find the value of x and then find NM and OL
Answer:
the value of x is 10
Step-by-step explanation:
Since LMNO is a parallelogram, the opposite sides are parallel and have the same length. This means that NO and LM have the same length, which we can call y. We can write the following equations to represent the given information:
NM = x + 32
OL = 2x + 22
NO = y
LM = y
Since NO and LM have the same length, we can set their lengths equal to each other to find the value of y:
x + 32 = y
2x + 22 = y
We can solve this system of equations by setting the two equations equal to each other and solving for x:
x + 32 = 2x + 22
-x = -10
x = 10
Substituting the value of x back into the equations for NM and OL, we find that:
NM = 10 + 32 = 42
OL = 2(10) + 22 = 32
Therefore, the value of x is 10, and the lengths of NM and OL are 42 and 32.
9) Joshua threw a ball that traveled on a parabolic path and then landed on the ground. Its flight is modeled
by the equation, h(t) = -5t² + 20t+ 0.4, where time, t, is in seconds and height, h, is in meters.
a) Determine the maximum height reached by the ball.
b) How long did it take to reach maximum height?
c) When will the ball hit the ground?
Answer:
a) The maximum height reached by the ball can be found by taking the derivative of the given equation, setting it equal to 0, and solving for t. We have:
h'(t) = -10t + 20 = 0
Solving for t, we get t = 2. Substituting this value into the original equation, we get:
h(2) = -5(2)² + 20(2) + 0.4 = -10 + 40 + 0.4 = 30.4
Thus, the maximum height reached by the ball is 30.4 meters.
b) The time it takes to reach the maximum height can be found by setting the derivative of the given equation equal to 0 and solving for t, as we did in part (a). In this case, we get t = 2, so it takes 2 seconds for the ball to reach its maximum height.
c) The time at which the ball hits the ground can be found by setting the original equation equal to 0 and solving for t. We have:
h(t) = -5t² + 20t + 0.4 = 0
Solving for t, we get:
-5t² + 20t + 0.4 = 0
This quadratic equation has two solutions, which can be found using the quadratic formula:
t = (-20 ± √(20² - 4(-5)(0.4))) / (2(-5))
= (-20 ± √(400 + 0.8)) / -10
= (20 ± √400.8) / -10
= (-20 ± 20.28) / -10
= -10 ± 10.14
Thus, the ball hits the ground at t = -10 + 10.14 = 0.14 seconds, or at t = -10 - 10.14 = -20.14 seconds. Since the time must be positive, we can conclude that the ball hits the ground at 0.14 seconds.
Haylee selects 10 small businesses at random from her state's directory. Let BBBB be the number of businesses she selects that have websites What type of variable is B? Binomial Geometric Neither
From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
What is binomial variable ?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).
This distribution is used in probability theory and statistics.
A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.
The popular binomial test of statistical significance is based on the binomial distribution.
A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.
Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
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Brian sped up from 68 mph to 80 mph. What was his percent change?
The percent change in the speed of Brian is found as 15%.
Describe the term percent change?The percentage difference between such a final and starting value is known as percent change. Divide the value differences by the starting value to calculate the percent change.The outcome is known as the rate of change, sometimes known as the percentage change, and is expressed in percent (with absolute numbers, it's merely a difference).For the stated question-
Initial speed = 68 mph
Final speed = 80 mph.
Difference = Final speed - Initial speed
Difference = 80 - 68
Difference = 12 mph
Percent change = Difference/Initial speed x 100
Percent change = 12/80 x 100
Percent change = 15%
Thus, the percent change in the speed of Brian is found as 15%.
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
Determine the solution/s to the following quadratic equation. Type "NONE" in any unused blank.
y = x² + 14x + 49
Answer:
Step-by-step explanation:i'm pretty sure that y=x^2+14x+49=625.
Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . The graph represents the situation . How many dogs was Becca walking by the end of the third month?
The graph shows that Becca walks five dogs at the end of the third month.
How many dogs are there in the third month?
We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.
We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . We would now read off the graph to know the number of dogs that he walks after three months.
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15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be
a. 1.96.
b. 3.
c. 1.67.
d. 2.5.
The investment multiplier must be 2.5 i.e.Option (d).
What is an Investment multiplier?
The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.
Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}
where MPC is the marginal propensity to consume
Given, MPC = 0.6
Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times
Hence, the investment multiplier is 2.5 i.e.Option (d).
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ecall that one of the ten parts of the definition of a vector space says that if is a vector space, then there exists a vector in such that for all in hceggg
This means that for any vector v in the vector space V, there is a vector 0 in V such that v + 0 = v.
This is known as the identity property, and it states that adding 0 to any vector in V does not change the original vector. The identity property is an essential part of the definition of a vector space.
In general, a vector space is a set of objects called vectors that can be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.
A vector space is a set V together with two operations that satisfy the eight axioms listed below.
Closure under addition. For all vectors u and v in V, the vector u + v is also in V.Closure under scalar multiplication. For all vectors u in V and all scalars c, the vector cu is also in V.Associativity of addition. For all vectors u, v, and w in V, (u + v) + w = u + (v + w).Commutativity of addition. For all vectors u and v in V, u + v = v + u.Existence of an additive identity. There exists a vector 0 in V such that for all vectors u in V, 0 + u = u + 0 = u.Existence of additive inverses. For every vector u in V, there exists a vector -u in V such that u + (-u) = (-u) + u = 0.Compatibility of scalar multiplication with field multiplication. For all vectors u and v in V and all scalars c and d, (c + d)u = cu + du and c(dv) = (cd)v.Compatibility of scalar multiplication with field addition. For all vectors u and v in V and all scalars c and d, c(u + v) = cu + cv.To learn more about vectors, visit:
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Question 17
Suppose that the given statement is true.
If Stacie likes pizza, then Amir likes soda.
Which statement must also be true?
O If Amir likes soda, then Stacie likes pizza.
O If Stacie likes pizza, then Amir does not like soda.
If Stacie does not like pizza, then Amir does not like soda.
O If Amir does not like soda, then Stacie does not like pizza.
The conditional statement that must also be true is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
What is a conditional statement?A conditional statement has the format defined as follows:
p -> q.
It is read as follows:
If p then q.
In which:
p is the hypothesis.q is the conclusion.The statement in this problem is given as follows:
If Stacie likes pizza, then Amir likes soda.
Then the parameters are given as follows:
p: Stacie likes pizza.q: Amir likes soda.When the conditional statement is true, the inverse statement must also be true, that is:
~p -> ~q.
The symbol ~ represents negation.
Thus the inverse statement is given as follows:
If Stacie does not like pizza, then Amir does not like soda.
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what is the circumference
The circumference is 12.56
A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A(0, 0), B(3, 8), and C(6,0).
One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
The triangle ABC is an isosceles triangle because AB = BC = √73
How to prove that the triangle is an isosceles triangle?From the question, we have the following parameters that can be used in our computation:
A(0, 0), B(3, 8), and C(6,0).
An isosceles triangle is any triangle that has two of its sides to be equal
So, we start by calculating the lengths of the sides using the distance equation represented as follows
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
AB = √[(0 - 3)² + (0 - 8)²]
AB = √73
AC = √[(0 - 6)² + (0 - 0)²]
AC = 6
BC = √[(3 - 6)² + (8 - 0)²]
BC = √73
Because AB = BC = √73, then the triangle is an isosceles triangle
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I took a number, wrote a 9 to the right of it, and added the new number to double the original number. The sum is 633. What is the original number?
The original number is, if The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number is 52.
What is the number?An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers.
Given:
The sum is 633 and wrote a 9 to the right of it, and added the new number to double the original number,
Assume the original number is x then, according to the condition,
10x + 9 + 2x = 633
12x = 633 - 9
x = 624 / 12
x = 52
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Outback Outfitters sells recreational equipment. One of the company’s products, a small camp stove, sells for $50 per unit. Variable expenses are $32 per stove, and fixed expenses associated with the stove total $108,000 per month. Required: 1. What is the break-even point in unit sales and in dollar sales? 2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher or a lower break-even point? Why? (Assume that the fixed expenses remain unchanged.) 3. At present, the company is selling 8,000 stoves per month. The sales manager is convinced that a 10% reduction in the selling price would result in a 25% increase in monthly sales of stoves. Prepare two contribution format income statements, one under present operating conditions, and one as operations would appear after the proposed changes. Show both total and per unit data on your statements. 4. Refer to the data in (3) above. How many stoves would have to be sold at the new selling price to attain a target profit of $35,000 per month?
The break-even point in unit sales for Outback Outfitters is 4,200 units.
What is the break-even analysis?= Fixed Cost/Contribution margin per unit
= $176,400/$42
= 4,200 units.
The break-even point in sales dollars for Outback Outfitters is $588,000.
= $176,400/30%
= $588,000
If the variable expenses per stove increase as a percentage of the selling price, it will result in a higher break-even point.
Two Contribution format income statements:
Current Proposed
Sales units 16,000 20,000
Sales revenue $2,240,000 $2,100,000
Variable cost $1,568,000 $1,960,000 ($98 x 20,000)
Contribution margin $672,000 $140,000
Fixed expenses 176,400 $176,400
Net income (loss) $495,600 ($36,400)
Sales units per month = 16,000
Selling price per unit = $105 ($140 x 1 - 10%)
New sales units per month = 20,000 (16,000 x 1.25)
Variable expenses per unit = $98
Contribution margin per unit = $7 ($105 - $98)
Contribution margin ratio = 6.67%
The number of stoves to be sold at the new selling price to attain a target profit of $80,000 per month is 36,629 units.
= ($176,400 + $80,000)/$7
=36,629 units.
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|x+9|=|-x-9|
How do I solve this equation and graph it?
The value of x is :
x≤ -9 or x > -9
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
|x+9|=|-x-9|
Both the sides have absolute symbols, consider as below:
x+9 = -x-9
=> 2x = -9 - 9 = -18
=> 2x = -18
=> x= -9
This means, x≤ -9 or x > -9
For graph:
consider as below:
y = |x+9|
y = |-x-9|
graph them without absolute symbols
consider upper v shaped graph. ignore downward v shaped graph
By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).
By plotting and joining those points, we get the graph as shown in the attachment.
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In triangle ABC, m∠B = (14x − 22)° and the measure of the exterior angle to ∠B is (6x − 18)°. Find m∠B.
After solving the equation, the value obtained for m ∠B will be equal to 132°.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The inside angle plus the external angle add up to 180°.
So,
m ∠B = (14x − 22)°
14x - 22° + 6x - 18° = 180°
14x + 6x - 22° - 18° = 180°
20x - 40° = 180°
20x = 180° + 40°
20x = 220°
x = 220° / 20
x = 11°
Now, let's find m∠B.
m ∠B = (14x − 22)°
Put x = 11° in above equation,
m ∠B = (14(11) − 22)°
m ∠B = 154° - 22°
m ∠B = 132°.
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Erin has a balance of $1,123.72 in her check register. On her statement, the balance of her account is $879.87.
Not reported on the bank statement are deposits of $62.42, $21, and $61.14. There are outstanding checks in the
amount of $60.24 and $50.24 and an ATM withdrawal of $40. After Erin reconciles her check register with her
statement, what entry does she need to make in her register?
Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.
The sum of three numbers is 96. The first number is 6 less than the second. The third number is 4 times the second. What are the numbers?
Step-by-step explanation:
x = second number
first number = x - 6
third number = 4x
x - 6 + x + 4x = 96
6x - 6 = 96
6x = 102
x = 102/6 = 17
first number = x - 6 = 17 - 6 = 11
second number = x = 17
third number = 4x = 4×17 = 68
2. How do you know from the equation that a line is vertical or horizontal?
Vertical lines have the form x = a, where a stands for the common x-coordinate of all points, while horizontal lines have the form y = b, where b denotes the y-intercept. Horizontal lines run left to right.
Explain about the equation?The link between two expressions on either side of the sign is represented by a mathematical equation. One variable and an equal sign are typically present. For instance, 2x – 4 = 2.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
Expressions that equal one another are the building blocks of an equation. The equation 4x2+3x = 22. A formula is an equation that has at least two variables and depicts the relationship between them.
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Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have
a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be
between 64 inches and 77 inches.
Make sure you are rounding z-scores properly to two places.
Part A: Find the two z-scores for women who meet this height requirement z =
and z=
I
(larger value)
For Blank 1
Part B: Using the z-scores from part A, find the proportion of women who meet the height requirement. Give this answer as a
decimal.
Z=
(smaller value)
Part C: Find the two z-scores for men who meet this height requirement z =
(larger value)
Part D: Using the z-scores from part C, find the proportion of men who meet the height requirement. Give this answer as a
decimal.
QUESTION 2
(smaller value) and
Part E: If the height requirement were changed to exclude only the shortest 1% of women and tallest 1% of men, what are the
new heights? The short value would be
in inches and the tall value would be
in inches. Please give these two values rounded properly to one decimal place.
Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.
What is meant by normal distribution curve?A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.
In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.
According to the normal distribution curve:
"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.
Area from a value (Use to compute p from Z)
Value from an area (Use to compute Z for confidence intervals)
Let the parameters be
Mean 64
Standard deviation 2.75
Above 1.96
Below 1.96
Between 64 and 69.5
Outside -1.96 and 1.96
Area (probability) 0.4772
And that value is 95 % of the whole data
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Nadine's Nursery sells St. Augustine grass seeds for $10 per lbs. and Zoysia grass seeds for $15 per lbs. Nancy wants to buy 20 ;bs. of grass seeds and wants to pay an average of $12 per lbs. How much of each type should she get?
The quantity of each type that Nadine should get would be= 96 of St. Augustine grass seeds and 144 of Zoysia grass seeds.
What is an average cost ?An average cost is defined as the total cost of production divided by the total number of units produced.
The cost of St. Augustine grass seeds per lbs = $10
The cost of Zoysia grass seeds per Ibs = $15
The quantity of seed Nadine wants to buy = 20
The average amount the Nadine want to pay per Ibs = $12
That is the total money available for the grass seeds = 20 × 12 = 240
To find the number of each grass seed she can buy the following is carried out;
10 + 15 = 25 ( Total cost for both grass seed)
The number of St. Augustine grass seeds she can buy ;
= 10/25 × 240
= 2400/25
= 96
The number of Zoysia grass seeds she can buy;
= 15/25 × 240
= 3600/25
= 144.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answer:
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Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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Decide which of the two given prices is the better deal. You can buy laundry product in a 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08 .
A) not enough information
B) 24-ounce bottle for $4.08
C) equal value
D) 30-ounce bottle for $6.00
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.
We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08. The unit price for each bottle will be: The bottle having the lower price will be:-
30-ounce bottle = $6.00
One ounce bottle = 30 / 6.00 = $5.00
and
24-ounce bottle = $4.08
One ounce bottle = $24/ 4.08 = $5.88
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
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Lines DE and AB intersect at point C.
What is the value of x?
A.12
B.25
C.38
D.05
Answer:
B
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25°
A ball is dropped from a height of 80 ft. The elasticity of this ball is such that it rebounds three-fourths of the distance it has fallen. How high does the ball rebound on the fifth bounce? Find a formula for how high the ball rebounds on the nth bounce.
Formula for how high the ball rebounds on the nth bounce is 80 (3/4)ⁿ ft and the rebound on 5th bounce is 14.24 ft.
It is given that the ball is dropped from 80 ft and it rebounds (3/4)th of the height it has fallen.
Firstly , using logic ,
The height reached by the ball on its 1st rebound = 80(3/4) = 60 ft
Similarly , calculating on it's 2nd rebound = 60(3/4) = 45 ft
and on 3rd rebound = 45(3/4) ft.
This forms a sequence , known as GP (Geometric Progression).
A Geometric Progression in mathematics, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Hence , here the first term : a = 60 ft
and common ratio is : r = 3/4
the general term for rebound on nth bounce
= 60 * (3/4)ⁿ⁻¹ = 80 (3/4)ⁿ ft
Using the above expression , the rebound on 5th bounce = 60 * (3/4)⁵ = 14.24 ft.
To know more about Geometric Progression, go to
brainly.com/question/4853032
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(2-2i)(3+3i)
56 points ]
Answer:
12
Step-by-step explanation:
Answer : 12
Step-by-step explanation:
The method that i used here was FOIL
(2 - 2i)(3 + 3i)
2x3=6
2x3i=6i
-2ix3=-6i
-2ix3i=-6i^2
6 + 6i - 6i - 6i^2
6-6i^2
i^2 is also known as (-1)
6 - 6(-1)
6 + 6
= 12
