Answers
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
\(\frac{(-1-3i)(-i)}{8i(-i)}\)
This simplifies to
\(\frac{i+3i^{2} }{-8i^{2} }\)
This further simplifies to
\(\frac{i-3}{8}\)
This can be rewritten as
\(-\frac{3}{8} +\frac{1}{8} i\)
a= -3/8
b= 1/8
Answer:
\( a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \)
Step-by-step explanation:
\( \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ \)
Related Questions
Find the GCF (greatest common factor) of 38 and 16.
Answers
Answer:
2
Step-by-step explanation:
2 is the gcf of 38 and 16 as it is the only greatest number which could be divided by both.
Answer:
2
Step-by-step explanation:
Because 2 is the largest number that both numbers can multiply with the factors, it is the Greatest Common Factor (GCF).
8 x 2 = 16, and 19 x 2 = 38
Hope this helps.
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
!!!!! Due today !!!!!!!
Answers
Answers:
5)
a.Highest- 96
Lowest-52
b.74
c. 70-80
d. 13
e. 7
6)
a. 89%
b. 51%
c. In the morning(89%)
Two companies A and B are offering 70 and 50 products respectively. Company A is offering 40 software products and 30 hardware products. Company B is offering x hardware products and y software products to be determined. If a product is selected at random, what is the probability that (a)This product is a hardware product given that is from company B? (in terms of y) (b)This product is a hardware product given that is from company A? (C) For what values of y will the probability in part (a) be greater than the probability in part (b)?
Answers
The probability that the selected product is a hardware product given that is from company B is x/50.
The probability that the selected product is a hardware product given that is from company A is 3/7.
The value of x must be greater than 21 so that the probability in part (a) is greater than the probability in part (b).
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Company A:
Total product = 70
Software product = 40
Hardware product = 30
Company B:
Total product = 50
Software product = y
Hardware product = x
The probability that the selected product is a hardware product given that is from company B.
= x/50 ____(1)
The probability that the selected product is a hardware product given that is from company A.
= 30/70
= 3/7 _____(2)
From (1 ) and (2) we get,
x/50 > 3/7
x > 3/7 x 50
x > 21
Thus,
The probability that the selected product is a hardware product given that is from company B is x/50.
The probability that the selected product is a hardware product given that is from company A is 3/7.
The value of x must be greater than 21 so that the probability in part (a) is greater than the probability in part (b).
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Nicole will attend a 2-year college, and she is planning her budget.
Answer the following.
(a) Below is an estimate of all her expenses and sources of funding for her 2-year college
education.
For each, select whether it is an expense or a source of funding.
Expense
Funding
Books and supplies:
Savings:
Scholarships:
Housing and food:
Tuition and fees:
Transportation:
$1700
$7800
$10,240
$14,020
$11,660
$2040
$11,600
$6200
$2980
Grants:
Student loans:
Personal expenses:
(b) What is the total of her estimated expenses?
$
0000
0000 1000
X
Answers
a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,
Scholarships, Grants and Student loans.
b. Total estimated expenses are $29,400
(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.
Expense:
Books and supplies: $1700
Housing and food: $14,020
Tuition and fees: $11,660
Transportation: $2040
Personal expenses: $2980
Funding:
Savings: $7800
Scholarships: $10,240
Grants: $11,600
Student loans: $6200
(b) What is the total of her estimated expenses?
To find the total estimated expenses, we need to add up all the expenses mentioned:
$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400
Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.
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6-102. Write an expression for each mat below. 6-102 HW eTool (CPM). Homework Help
Mat A
Mat B
= +1
a. Simplify each mat to determine which expression is greater, if possible.
b. If x = 3, would your answer to part (a) change?
Explain.
c. If x=-2, would your answer change?
Explain.
Answers
As per the comparisons shown in the reference attachment attached thereby along with the question statement, the ride side is greater.
What is comparison?It means the act of comparing : the state of being compared. : change in the form of an adjective or an adverb (as by having -er or -est added or more or most prefixed) to show different levels of quality, quantity, or relation.
here, we have,
As per the questions statement we are provided with a comparison between two parent blocks as shown in the reference attachment attached thereby,
And we are required to determine the which side is greater.
Now, if you observe our reference attachment, we can see two big blocks which are horizontally divided into two equal parts - the upper part having positive magnitude and the lower part having negative magnitude. Furthermore, each of these parts of the bigger parent blocks contains smaller daughter blocks which are available in two different colors - black and white, and these black daughter blocks have a magnitude of (+1) while the white ones have that of (-1).
Now, considering the parent block on the left hand side, we can see that, it contains 4 black blocks and 3 whites, in the positive part, while 2 blacks and 2 whites in the negative part which evaluates to:
[(4 * 1) + {3 * (-1)}] - [(2 * 1) + {2 * (-1)}]
= [{4 + (-3)} - {2 + (-2)}]
= [(4 - 3) - (2 - 2)]
= (1 - 0)
= 1
And considering the parent block on the right hand side, we can see that, it contains 3 black blocks and 2 whites, in the positive part, while 1 black and 3 white blocks in the negative part which evaluates to:
[(3 * 1) + {2 * (-1)}] - [(1 * 1) + {3 * (-1)}]
= [{4 + (-2)} - {1 + (-3)}]
= [(3 - 2) - (1 - 3)]
= [1 - (-2)]
= (1 + 2)
= 3
Since (3 > 1), the right side parent block is greater in magnitude than the left hand side one, as per our concerned comparison.
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Write the equation of this conic section in conic form: 100pts pls
Answers
The equation of the conic section in conic form is (x - 1) = (y + 6)²/4.
To write the equation of the conic section in conic form, we can complete the square to transform the equation into its standard form. Let's start with the given equation:
y² - 4x + 12y + 32 = 0
Rearranging the terms, we have:
y² + 12y - 4x + 32 = 0
To complete the square for the y-terms, we add and subtract the square of half the coefficient of y (which is 6 in this case):
y² + 12y + 36 - 36 - 4x + 32 = 0
Simplifying this, we get:
(y + 6)² - 4x + 4 = 0
Now, rearranging the terms, we have:
(y + 6)² = 4x - 4
Dividing both sides of the equation by 4, we get:
(y + 6)²/4 = x - 1
Finally, we can write the equation in conic form:
(x - 1) = (y + 6)²/4
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The Probable question may be:
Which type of conic section is defined by the equation y²-4x+12y + 32 = 0?
This is an equation of a parabola
Write the equation of this conic section in conic form:
(4x-10) x (3x²)
Find the area of the rectangle
Answers
If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).
How to find the area of rectangle?The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.
Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.
Area of rectangle = length × breadth
= (3x +2) × (4x +10)
simplifying the above equation, we get
= (3x) × (4x +10) + 2(4x +10)
= 12x² + 30x +8x +20
12x² + 38x + 20 = 0
simplifying the above equation, we get
By using quadratic equation, then
\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)
simplifying the above equation, we get
\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)
Separate the solutions, we get
\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)
The solutions to the quadratic equation are:
\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)
The complete question is:
Find the area of rectangle with length (3x+2) units and width (4x+10)units.
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what is the mean for 98,78,84,75,91
Answers
the sum of three consecutive integers is -324
Answers
Answer:
i think it is 3 8 19.
Step-by-step explanation:
Answer:108
Step-by-step explanation:
Marjorie purchased a county government bond with a par value of $3,000 and coupon rate of 3.42% which pays interest quarterly. What will be Marjorie’s quarterly interest payments?
Answers
Step-by-step explanation:
To calculate Marjorie's quarterly interest payments, we need to use the formula:
Quarterly interest payment = (par value x coupon rate) / number of payments per year
Since the bond pays interest quarterly, there are four payments per year. Substituting the given values into the formula, we get:
Quarterly interest payment = ($3,000 x 3.42%) / 4
Quarterly interest payment = ($3,000 x 0.0342) / 4
Quarterly interest payment = $85.50 / 4
Quarterly interest payment = $21.375
Therefore, Marjorie's quarterly interest payments will be $21.375.
Jamel has 2 and 2/5 of string. Jamel needs 1/5 of a foot of string to sew a button to a shirt. What is the greatest amount of buttons he can sew onto the shirt with the rest of the string he has?
Answers
Answer:
12
Step-by-step explanation:
1=5/5 so 2=10/5
add 2/5 to 10/5 to get 12/5
Apollo Cinemas opened at 10 a.m. In the first hour they sold tickets to 240 people. In the second hour 25% more people purchased admission tickets than in the first hour. Each admission ticket cost $12.50. What was the total amount of money paid for all the tickets in the first two hours?
Answers
Answer:
$312.50
Step-by-step explanation:
240 + 25% = 300
300 + 12.50 =
312.50
Solve the system. Estimate the solution first. Enter whole numbers for the estimated solution and improper fractions in simplest form for the algebraic solution.
6x + y = 2
x - 4y = 2
The estimated solution is ( , ).
The algebraic solution is ( , ).
Answers
The solution of the system of equation is as follows:
x = 2 / 5 and y = - 2 / 5.
How to solve system of equation?System of equation can be solved using different method such as elimination method and substitution method.
Let's solve the system of equation by substitution method.
6x + y = 2
x - 4y = 2
Hence,
x = 2 + 4y
substitute the value of x in equation(i)
6(2 + 4y) + y = 2
12 + 24y + y = 2
12 + 25y = 2
25y = 2 - 12
25y = - 10
y = -10 / 25
y = - 2 / 5
Hence, let's find the value of x
6x = 2 - y
6x = 2 + 2 / 5
6x = 10 + 2/ 5
6x = 12 / 5
x = 12 / 5 × 1 /6
x = 12 / 30
x = 2 / 5
Therefore,
x = 2 / 5 and y = - 2 / 5
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let p be a point chosen uniformly at random in the interior of the unit square with vertices at (0, 0),(1, 0),(1, 1), and (0, 1). the probability that the slope of the line determined by p and the point 5 8 , 3 8 is greater than or equal to 1 2 can be written as m n , where m and n are relatively prime positive integers. find m n
Answers
The probability that the slope of the line determined by p and the point (5/8, 3/8) is greater than or equal to 1/2 is 5/8.
Let the coordinates of point p be (x,y). Then, the slope of the line determined by p and the point (5/8, 3/8) is:
(slope) = (y - 3/8)/(x - 5/8)For the slope to be greater than or equal to 1/2, we must have:
(y - 3/8)/(x - 5/8) >= 1/2Solving for y, we get:
y >= (x/2) + 7/16Graphing this inequality on the unit square, we see that the region satisfying this inequality is a trapezoid with vertices (5/8,3/8), (1,1/2), (1,1), and (3/4,1).
The area of this trapezoid is (1/2)*((5/8 - 3/4) + (1 - 5/8) + (1 - 1/2) + (3/8 - 3/16)) = 5/16.
The area of the unit square is 1, so the probability we seek is 5/16.
Hence, the answer is 5/16 written as a fraction in its simplest form, which is 5/16.
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20 POINTS- Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
Marlene surveyed her classmates asking them whether they prefer to vacation during spring break or summer and the type of vacation preferred. The results are shown in the table.
A 4-column table with 5 rows titled Vacation Preferences. Column 1 has entries beach, big city, camping, skiing, total. Column 2 is labeled spring with entries 35, 7, 14, 4, 60. Column 3 is labeled summer with entries 10, 2, 8, 10, 30. Column 4 is labeled total with entries 45, 9, 22, 14, 90.
Complete each statments.
About ____% of the students surveyed prefer a spring camping vacation.
About ____% of the students surveyed prefer a big city vacation.
Answers
Answer:
The answers for edge 2021 is
Step-by-step explanation:
16 and 10
Write the equation of the line that is perpendicular to the graph of 2x+y =5, and y-intercept is 4.
Answers
....................help
Answers
Answer:
A
Step-by-step explanation:
With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.
Helpppp plzzzz what is the measure of /_x
Answers
Answer:
100
Step-by-step explanation:
Will mark brainliest!!! Plz solve for each variable!!!
Answers
Answer:
the answer is
12 = y - 5
y=17
x+2 = 4
x=2
A researcher wishes to estimate the number of households with two cars. A previous study indicates that the proportion of households with two cars is 25%. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 3%?
A) 4.
B) 1132.
C) 1842.
D) 1382.
Answers
foreign direct investment helps improve the economic situation of a recipient country by increasing —- opportunities in the country that the company invests in.
Answers
Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.
When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.
Increased employment opportunities result in more individuals having access to income and improved standards of living.
Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.
Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.
Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.
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Identify the correct compound events from the given options.Tossing a coinRolling a diePicking a fruit from a fruit bagTossing a coin and picking a fruit from a bag
Answers
A compound event is an event that has more than one possible outcomes.
These outcomes may have different probabilities but they are all equally possible
For example, the probability of rolling an even number on a die, then tossing a head on a coin.
or in this case
Tossing a coin and picking a fruit from a bag
use distributive property to rewrite this problem: -2(n-7)
Answers
To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:
a(b + c) = ab + ac
Applying this property to the given expression:
-2(n-7) = -2 * n + (-2) * (-7)
Simplifying further:
-2(n-7) = -2n + 14
Therefore, the rewritten expression is -2n + 14.
Consider a sample with six observations of 15, 16, 12, 8, 6, and 9. Compute the z-scores for each sample observation.
Sample observation. z-scores
15
16
12
8
6
9
Answers
Answer:
1 ; 1.25 ; 0.25 ; - 0.75 ; - 1.25 ;- 0.5
Step-by-step explanation:
Given the sample observations : 15, 16, 12, 8, 6, 9
Zscore for each sample Observation :
Zscore = (x - mean) / standard deviation
(15 + 16 + 12 + 8 + 6 + 9) / 6 = 11
Mean value (m) = 11
Standard deviation (s) = 5
Sqrt[(x - m)^2 / (n - 1)]
[(15-11)^2 + (16-11)^2 + (12-11)^2 + (8-11)^2 + (6-11)^2 + (9-11)^2] / (6 - 1)
= 80/5 = 16
Sqrt(16) = 4
Zscore = (x - mean) / standard deviation
x = 15
Zscore = (15 - 11) / 4 = 1
x = 16
Zscore = (16 - 11) / 4 = 1.25
x = 12
Zscore = (12 - 11) / 4 = 0.25
x = 8
Zscore = (8 - 11) / 4 = - 0.75
x = 6
Zscore = (6 - 11) / 4 = - 1.25
x = 9
Zscore = (9 - 11) / 4 = - 0.5
Quinn bought a bouquet of flowers as a surprise for her grandfather. She had expected it would cost $15 but her prediction was 50% more than the actual cost of the flowers. What was the actual cost of the flowers?
Answers
To find 50% of 15, you multiply. 15*50% equals 7.5.
A 6-pound container of detergent costs $4.38. what is the price per pound?
Answers
Answer:
.73 per pound
Step-by-step explanation:
Take the total cost and divide by the number of pounds
4.38/ 6
.73 per pound
How much food can this container hold 3in 9in
Answers
Answer:
27
Step-by-step explanation:
Answer:
18Πin3
Step-by-step explanation:
How do i solve it with steps pls
Answers
Answer:
Step-by-step explanation:
We know the the total of angles for a triangle is 180 degrees.
So in this case we'd want to set up adding all of our angles and setting them equal to 180
17 + 126 + b = 180
then solve for b
143 + b = 180
b = 37 degrees
So the answer would be 37 degrees for angle b
the depth of water d in a swimming pool increases and decreases by 3% over a one-month period. Match each verbal description of the greatest and least water depths with all equivalent expressions.
Answers
The least water depth and greatest depth will be 0.97d and 1.03d.
How to illustrate the expression?An expression is used to show the relationship between the variables.
In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.
The least water depth will be:
= d - (3% × d)
= d - 0.03d
= 0.97d
The greatest water depth will be:
= d + (3% × d)
= d + 0.03d
= 1.03d
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