Answer:
Simple Interest : $ 4400
Step-by-step explanation:
We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.
We can use the simple interest formula here, or :
I = P × r × t,
Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.
Simple Interest : 10000 × 0.055 × 8 = $4400.00
Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.
The simple interest earned on the amount is $4,400
Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.
Simple Interest = principal x time x interest rate
principal = amount borrowed = $10,000
time = 8 years
Interest rate = 5.5%
10,000 x 0.055 x 8 = $4,400
To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults
Simple math! What is the issue with my work? I got it wrong.
Answer:
x = 6
Step-by-step explanation:
In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.
The final value of x will be 6.
[tex] PQ^2 + QO^2 = PO^2 \\
x^2 + 8^2 = (4+x)^2 \\
x^2 + 64 = 16 + 8x + x^2 \\
64 = 16 + 8x \\
64 - 16 = 8x \\
48 = 8x \\
6 = x\\[/tex]
Which equation does the graph of the systems of equations solve? (1 point) 2 linear graphs. They intersect at negative 1, 1
Answer:
3x +4 = -2x -1
Step-by-step explanation:
The line that goes up to the right has a y-intercept of +4. This is where it crosses the y-axis. It's slope (rise/run) is 3/1 = 3, so its equation in slope-intercept form is ...
y = mx +b . . . . where m is the slope, b is the y-intercept
y = 3x +4
The other line has a negative slope and a y-intercept of -1. The slope of that line is rise/run = -2/1 = -2, so its equation is ...
y = -2x -1
__
The solution point will have the x-coordinate that is the solution of the equation ...
y = y
3x +4 = -2x -1 . . . . . . substituting the above expressions for y.
A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean.
Answer:
38.911≤p≤41.089
Step-by-step explanation:
The formula for calculating confidence interval for a population mean us as shown below;
CI = xbar ± Z×S/√N where;
xbar is the sample mean = 40
Z is the z score at 95% confidence interval = 1.96
S is the standard deviation = 5
N is the sample size = 81
Substituting this parameters in the formula we have;
CI = 40±1.96×5/√81
CI = 40±(1.96×5/9)
CI = 40±(1.96×0.556)
CI = 40±1.089
CI = (40-1.089, 40+1.089)
CI = (38.911, 41.089)
The 95% confidence interval for the population mean is 38.911≤p≤41.089
Answer:
38.9 ≤ U ≤ 41.1
Step-by-step explanation:
Mean, m = 40; standard deviation, α = 5; Confidence limit, U = 95% or 0.95
N = 81
The standard error, α(m) = α/√(N) = 5/√81 =5/9
Using table: 0.95 = 0.0379
Z(0.95) = 2 - 0.0379 = 1.9621 or 1.96
Hence, confidence interval = { m - 1.96(α/√N) ≤ U ≤ m +1.96(α/√N)}
But, 1.96(α/√N) = 1.96 X 5/9 = 1.96 X 0.56 = 1.1
(40 - 1.1 ≤ U ≤ 40 + 1.1)
∴ the confidence interval = 38.9 ≤ U ≤ 41.1
Height of a tree increases by 2.5 feet each growing season. Quadratic, linear or exponential?
Answer:
Linear
Step-by-step explanation:
Given
Height of a tree grows by 2.5 feet
Required
Determine the type of relationship
Take for instance, the height of the tree at year 1 is x
At year 2, it will be x + 2 * 1
At year 3, it will be x + 2 * 2
At year 4, it will be x + 2 * 3
Following same pattern
At year n, it will be x + 2 *(n - 1)
Hence, growth rate = x + 2(n -1)
From the list of given options, the correct answer is Linear because the derived formula above is an example of a linear equation
Determine the volume of a sphere with a diameter of 70 mm. Question 13 options: A) 21,714.7 mm3 B) 3,216.9 mm3 C) 100,024 mm3 D) 179,594.4 mm3
Answer:
The answer is option D
Step-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]
where r is the radius
From the question to calculate the radius we use the formula
radius = diameter / 2
diameter =70mm
radius = 70/2 = 35 mm
So the volume of the sphere is
[tex]V = \frac{4}{3} \pi \times {35}^{3} [/tex]
[tex]V = \frac{171500\pi}{3} [/tex]
We have the final answer as
Volume = 179,594.4 mm³Hope this helps you
Given the number of trials and the probability of success, determine the probability indicated: a. n = 15, p = 0.4, find P(4 successes) b. n = 12, p = 0.2, find P(2 failures) c. n = 20, p = 0.05, find P(at least 3 successes)
Answer:
A)0.126775 B)0.000004325376 C) 0.07548
Step-by-step explanation:
Given the following :
A.) a. n = 15, p = 0.4, find P(4 successes)
a = number of trials p=probability of success
P(4 successes) = P(x = 4)
USING:
nCx * p^x * (1-p)^(n-x)
15C4 * 0.4^4 * (1-0.4)^(15-4)
1365 * 0.0256 * 0.00362797056
= 0.126775
B)
b. n = 12, p = 0.2, find P(2 failures),
P(2 failures) = P(12 - 2) = p(10 success)
USING:
nCx * p^x * (1-p)^(n-x)
12C10 * 0.2^10 * (1-0.2)^(12-10)
66 * 0.0000001024 * 0.64
= 0.000004325376
C) n = 20, p = 0.05, find P(at least 3 successes)
P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)
To avoid complicated calculations, we can use the online binomial probability distribution calculator :
P(X≥ 3) = 0.07548
determine x in the following equation 2x - 4 = 10
Answer:
7
Step-by-step explanation:
10+4 = 14
14/2 = 7
x = 7
Study the table. Which best describes the function represented by the data in the table?
Answer:
linear with a common first difference of 2
Step-by-step explanation:
On the face of it, you can reject answers that ascribe a common ratio to a linear or quadratic function. (A common ratio is characteristic of an exponential function.)
You can also reject the answer that ascribes a common first difference to a quadratic function. (A quadratic function has a common second difference.)
After you reject the nonsense answers, there is only one remaining choice. It is also the correct one:
linear with a common first difference of 2
_____
The ratio of change in y to change in x is ...
(0 -(-2))/(-2 -(-3)) = 2
(4 -0)/(0 -(-2)) = 2
(12 -4)/(4 -0) = 2
That is, y increases by 2 when x increases by 1. The common first difference is 2.
The check_time function checks for the time format of a 12-hour clock, as follows: the hour is between 1 and 12, with no leading zero, followed by a colon, then minutes between 00 and 59, then an optional space, and then AM or PM, in upper or lower case. Fill in the regular expression to do that. How many of the concepts that you just learned can you use here
Answer:
Following are the correct code to this question:
import re#import package for regular expression
def check_time(text):#defining a method check_time that accepts string value
p = r'(1[012]|[1-9]):[0-5][0-9][ ]{0,1}?(am|pm|AM|PM)'#defining string variable p that stores values
val = re.search(p, text)#defining val variable that check serachs p and text variable values
return val!= None#use return keyword to return val value
print(check_time("12:45pm"))#defining print method that calls method by input value
print(check_time("9:59 AM")) #defining print method that calls method by input value
print(check_time("6:60 am")) #defining print method that calls method by input value
print(check_time("five o'clock"))#defining print method that calls method by input value
Output:
True
True
False
False
Step-by-step explanation:
In the above-given program, some data is missing that is code file so, the correct code can be defined as follows:
In the above-given method, that is "check time" it uses 12-hour time format validation, that is tested by coding the regex and all the value validates in the "val" variables, that can be defined as follows:
In the first step, its values should be in 1,2,3, ... 10,11,12 In the second step, it values in Between hour and minutes, and there will be a colon. In the third step, the minutes variable should take the double-digit, that will be like 00,01 .... 59. In the last step, one space becomes permitted after an hour: a minute or no space for am or pm value.
Help please!!! Thank you
Answer:
5/7
Step-by-step explanation:
There are a couple ways to solve this. One would be by finding the least common denominator for each one with 2/3, subtracting, and seeing what is left over. Another way is converting to decimals.
2/3=0.666666
————————-
7/8=0.875
8/9=0.88888
4/5=0.8
5/7=0.7143
They are all greater than 2/3 (0.6666666), but 5/7 is the closest, so would have the least waste.
There are $400$ pages in Sheila's favorite book. The average number of words per page in the book is $300$. If she types at an average rate of $40$ words per minute, how many hours will it take to type the $400$ pages of the book?
Answer:
50hours
Step-by-step explanation:
Given that there are 400 pages in Sheila's favorite book.
The average number of words per page in the book is 300
She types an average rate of 40words per minute.
So to type 400pages of the book
Total number of words in the pages = 400×300 = 120000 words
Typing rate : 40words ------- 1minute
120000 words ----------- x minutes
Hence we have 40 × X mins = 120000 × 1min
Make X the subject
40X = 120000minutes
X = 120000/40
X = 3000minutes
Since 60minutes = 1hour
3000minutes = 3000minutes/60
= 50hours
Hence it took her 50hours to type 400pages
Solution:
The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.
Answer:
27/35
Step-by-step explanation:
We use combination to solve for this
C(n, r), =nCr = n!/r!(n - r)!
From the question, we are told that:
Four couples are at a party. Four of the eight people are randomly selected to win a prize.
Four couples = 8 people.
= 8C4 = 8!/4! (8 - 4)!
= 70
No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)
This can happen in 4 ways
[4C1 × 3C2 ] × 4=
[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways
= 4 × 3 × 4 ways
= 48
The probability that both of the members of at least one couple win prizes
48 + 4C2/ 8C4
4C2 = 4!/2!(4 - 2) !
= 6
8C4 = 8C4 = 8!/4! (8 - 4)!
= 70
48 + 6/ 70
= 54/70
= 27/35
Therefore, the probability that both of the members of at least one couple win prizes is 27/35.
The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.
Given :
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize.The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:
Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.
Step 2 - According to the given data, the total number of people is 8.
Step 3 - So, the probability that both of the members of at least one couple win prizes is:
[tex]\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P =\dfrac{48+ 6}{70}[/tex]
[tex]\rm P = \dfrac{27}{35}[/tex]
So, the probability that both of the members of at least one couple win prizes is 27/35.
For more information, refer to the link given below:
https://brainly.com/question/795909
Hey market sales six cans of food for every seven boxes of food the market sold a total of 26 cans and boxes today how many of each kind did the market sale
Answer:
It sold 14 cans boxes of food and 12 cans of food.
Step-by-step explanation:
The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.
Let the no. of sets of food boxes be x.
According to the question,
6x+7x=26
13x=26
x=26/13
x=2
No. of food cans =6x=6×2=12 cans
No. of food boxes=7x=7×2=14 boxes
Please mark brainliest ,if it is truly the best ! Thank you!
Evaluate 2/3 + 1/3 + 1/6 + …
Answer:
7/6
Step-by-step explanation:
The LCD of these three fractions is 6; the denominators 3, 3 and 6 divide evenly into 6.
Therefore we have:
4/6 + 2/6 + 1/6 = 7/6
1+2x=6x+11 PLS HELP URGENT
Answer:
x = -5/2
Step-by-step explanation:
1+2x=6x+11
Subtract 2x from each side
1+2x-2x=6x-2x+11
1 = 4x+11
Subtract 11 from each side
1-11 = 4x
-10 =4x
Divide by 4
-10/4 = 4x/4
-5/2 =x
Answer:
[tex]\boxed{x=-\frac{5}{2}}\\[/tex]
Step-by-step explanation:
To begin, get the variable on one side of the equation - preferably the left for standard solution notation (for this equation, it is easier to place it on the right side to avoid negative values). Do this by subtracting 2x from both sides of the equation. Then, subtract 11. Finally, divide by 4 and get the answer in terms of x.
1 + 2x = 6x + 11
1 = 4x + 11
-10 = 4x
[tex]\boxed{x=-\frac{5}{2}}[/tex]
PLS HELP :Find all the missing elements:
Answer:
[tex]\large \boxed{\mathrm{34.2}}[/tex]
Step-by-step explanation:
[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]
[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]
[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]
There are 9 students at the math club picnic. If 3 students are drinking punch and 6 are drinking lemonade, what fraction are drinking lemonade
A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:
Answer:
Student t-distribution.
Step-by-step explanation:
In this scenario, a test is being conducted to test the difference between two population "means" using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the student t-distribution.
In Statistics and probability, a student t-distribution can be defined as the probability distribution which can be used to estimate population parameters when the population variance is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.
A student t-distribution has a similar curve with the normal distribution curve, except that it is fatter and a little bit shorter.
The following data represents the age of 30 lottery winners.
22 26 27 27 31 34
36 42 43 44 48 49
52 53 55 56 57 60
65 65 66 67 69 72
75 77 78 78 79 87
Complete the frequency distribution for the data.
Age Frequency
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Answer:
Step-by-step explanation:
This is an example of a frequency distribution for a class interval. In order to complete the frequency distribution, we will count the number of data occurring in each group, and write that number as the frequency for that group. This is done as shown below:
Age Frequency ages in class
20-29 4 22, 26, 27, 27
30-39 3 31, 34, 36
40-49 5 42, 43, 44, 48, 49
50-59 5 52, 53, 55, 56, 57
60-69 6 60, 56, 65, 66, 67, 69
70-79 6 72, 75, 77, 78, 78, 79
80-89 1 87
Total 30
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty students plan to participate in track and cross country; six students in cross country and basketball; and eight students in track and basketball. Twelve students plan to participate in all three sports. A total of thirty students plan to participate in basketball, and a total of forty students plan to participate in cross country. Ten students don't plan to participate in any of the three sports. How many students plan to just participate in cross country? 2 4 40 30
Answer:
40
Step-by-step explanation:
In the question only lies the answer:
"and a total of forty students plan to participate in cross country."
Answer:
2
Step-by-step explanation:
2
Given log32≈0.631 and log37≈1.771, what is log314
Answer:
the log to the base 3 of 14 is 2.402
Step-by-step explanation:
You must find a way to indicate that 3 is the base; you cannot run this '3' together with 2, 7 or 14.
Example:
log to the base 3 of 2 = 0.631
log to the base 3 of 7 = 1.771
Note that 2 times 7 is 14. Thus, to obtain the log to the base 3 of 14, we must ADD the two logs shown above:
0.631
+1.771
----------
2.402
Thus, the log to the base 3 of 14 is 2.402.
Check: Does 3^2.402 = 14? YES
According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?
Answer:
The probability is [tex]P(x < 13) = 0.8732[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.70
The sample size is [tex]n = 15[/tex]
Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )
The probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.70[/tex]
[tex]q = 0.30[/tex]
The probability that fewer than 13 have vcrs is mathematically represented as
[tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]
=> [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]
Here [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means 15 combination 13 and the value is 105 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means 15 combination 14 and the value is 15 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means 15 combination 15 and the value is 1 (obtained from calculator)
So
[tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]
substituting values
[tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]
[tex]P(x < 13) = 0.8732[/tex]
What is nine thousandths as a decimal
Answer:
Nine thousandths = 0.009
Step-by-step explanation:
thousandths = 1/1000 = 0.001
nine thousandths = 9/1000 = 0.009
Answer:
.009
Step-by-step explanation:
9 thousandths as a decimal is 9/1000. Which is the same 0.009
In the Cash Now lottery game there are 8 finalists who submitted entry tickets on time. From these 8 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousand dollars, and the third prize is ten thousand dollars. Determine the total number of different ways in which the winners can be drawn. (Assume that the tickets are not replaced after they are drawn.)
Answer:
The number of ways is [tex]\left n} \atop {}} \right. P_r = 336[/tex]
Step-by-step explanation:
From the question we are told that
The number of tickets are [tex]n = 8[/tex]
The number of finalist are [tex]r =3[/tex]
Generally the number of way by which this winners can be drawn and arrange in the order of [tex]1^{st} , \ 2nd , \ 3rd[/tex] is mathematically represented as
[tex]\left n} \atop {}} \right. P_r = \frac{n\ !}{(n-r) !}[/tex]
substituting values
[tex]\left n} \atop {}} \right. P_r = \frac{ 8!}{(8-3) !}[/tex]
[tex]\left n} \atop {}} \right. P_r = \frac{ 8* 7*6*5*4*3*2*1}{ 5*4*3*2*1}[/tex]
[tex]\left n} \atop {}} \right. P_r = 336[/tex]
Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x) =20x^2+40x+600 dollars.
Required:
a. At what rate was the property tax increasing with respect to time in 2008?
b. By how much did the tax change between the years 2008 and 2012?
Answer:
a) 40 dollars
b) 480 dollars
Step-by-step explanation:
Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0
T'(x) = 2(20)x¹ + 40x° + 0
T'(x) = 40x+40
At x = 0,
T'(0) = 40(0)+40
T'(0) = 40
Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).
b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)
Given T(x) =20x²+40x+600
T(4) =20(4)²+40(4)+600
T(4) = 320+160+600
T(4) = 1080 dollars
Also T(0) =20(0)²+40(0)+600
T(0) = 0+0+600
T(0)= 600 dollars
T(4) - T(0) = 1080 - 600
T(4) - T(0) = 480 dollars
Hence, the tax has changed by $480 between 2008 and 2012
Complete the table of values for y=-x^2+2x+1
X -3, -2, -1,0,1,2,3,4,5
Y -14,7, ,1, -2 -14
Answer:
see the attachment
Step-by-step explanation:
When you have a number of function evaluations to do, it is convenient to let a graphing calculator or spreadsheet do them. That avoids the tedium and the mistakes in arithmetic.
Here's your completed table.
Find the minimum sample size n needed to estimate for the given values of c, , and E. c, , and E Assume that a preliminary sample has at least 30 members.
Answer:
hello your question is incomplete below is the complete question
Find the minimum sample size n needed to estimate μ For the given values of c, σ, and E. c=0.98, σ=6.5, and E=22 Assume that a preliminary sample has at least 30 members.
Answer : 48
Step-by-step explanation:
Given data:
E = 2.2,
std ( σ ) = 6.5
c ( level of confidence ) = 0.98
To find the minimum sample size
we have to first obtain the value of [tex]Z_{a/2}[/tex]
note : a can be found using this relation :
( 1 - a ) = 0.98 ----- equation 1
a = 1 - 0.98 = 0.02
hence: a/2 = 0.01
This means that P( Z ≤ z ) = 0.99 the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33
P( Z ≤ 2.33 ) = 0.99
To obtain the sample size n
[tex]n = (\frac{std*z}{E} )^{2}[/tex]
n = [tex](\frac{6.5*2.33}{2.2} )^2[/tex] = (6.88409)^2
Therefore n ≈ 48
If SSR is 2592 and SSE is 608, then A. the standard error would be large. B. the coefficient of determination is .23. C. the slope is likely to be insignificant. D. the coefficient of determination is .81.
Answer:
D. the coefficient of determination is .81.
Step-by-step explanation:
SST = SSE + SSR
where
SST is the summation of square total
SSE is the summation of squared error estimate = 608
SSR is the summation of square of residual = 2593
with these in mind we put the values into the formula
= 2592 + 608
=3200
Coefficient of determination = SSR/SST
= 2592/3200
= 0.81
Therefore option D is the correct answer to the question.
what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:
Step-by-step explanation:
Lets, turn this into words and use order of operations, First, we look for multiplication and division.
the sum of one fourth of 5 times of 8 and 10 gets you 1/4(5*8) + 10 = 20
what is the number if 4 is subtracted from the sum
20 - 4 = 16
Express the product of z1 and z2 in standard form given that [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + isin(\frac{2\pi }{5})][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2}) + isin(\frac{-\pi }{2})][/tex]
Answer:
Solution : 5.244 - 16.140i
Step-by-step explanation:
If we want to express the two as a product, we would have the following expression.
[tex]-6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right]\cdot 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Now we have two trivial identities that we can apply here,
( 1 ) cos(- π / 2) = 0,
( 2 ) sin(- π / 2) = - 1
Substituting them,
= [tex]-6\cdot \:2\sqrt{2}\left(0-i\right)\left(\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right)[/tex]
= [tex]-12\sqrt{2}\sin \left(\frac{2\pi }{5}\right)+12\sqrt{2}\cos \left(\frac{2\pi }{5}\right)i[/tex]
Again we have another two identities we can apply,
( 1 ) sin(x) = cos(π / 2 - x )
( 2 ) cos(x) = sin(π / 2 - x )
[tex]\sin \left(\frac{2\pi }{5}\right)=\cos \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]
[tex]\cos \left(\frac{2\pi }{5}\right)=\sin \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex]
Substitute,
[tex]-12\sqrt{2}(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}) + 12\sqrt{2}(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4})[/tex]
= [tex]-6\sqrt{5+\sqrt{5}}+6\sqrt{3-\sqrt{5}} i[/tex]
= [tex]-16.13996 + 5.24419i[/tex]
= [tex]5.24419i - 16.13996[/tex]
As you can see option d is the correct answer. 5.24419 is rounded to 5.244, and 16.13996 is rounded to 16.14.
