Answers
The non-real complex number is \(\frac{8}{3} + \sqrt{-\frac{7}{3}}\).
We have,
To find a non-real complex number,
What is not a real number?
Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i.
A non-real complex number is an imaginary number containing negative numbers in the root.
Here,
\(\frac{8}{3} + \sqrt{-\frac{7}{3}}\)
In this option, it includes the negative term that is in the root so this is imaginary, therefore, the answer is "Option B".
Hence, the non-real complex number is \(\frac{8}{3} + \sqrt{-\frac{7}{3}}\).
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Related Questions
Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
Answers
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
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Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
What is the equation of the line shown in this graph?
у
5
4
3
(-2,2)
2
1
-5
-4
-3 -2
-1 0
1
2.
3
4
5
-1
-27
(-2,-3)
-3
-4
Answers
Answer: (1,-4)
Step-by-step explanation:ssghvssd5633
Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
Answers
Answer:
1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean
2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?
The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.
So
Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.
2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
We have that:
\(\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000\)
This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
\(Z = \frac{164000 - 168000}{4000}\)
\(Z = -1\)
\(Z = -1\) has a pvalue of 0.1587
15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Find value of x in trapezoid
Answers
Answer:
x = 1
Step-by-step explanation:
You want to know the value of x in the trapezoid with adjacent angles (43x+2)° and 135°.
Supplementary anglesThe two marked angles can be considered "consecutive interior angles" where a transversal crosses parallel lines. As such, they are supplementary.
(43x +2)° +135° = 180°
43x = 43 . . . . . . . . . . . . . . divide by °, subtract 137
x = 1 . . . . . . . . . . . . . . . divide by 43
The value of x is 1.
__
Additional comment
Given that the figure is a trapezoid, we have to assume that the top and bottom horizontal lines are the parallel bases.
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using division to determine which of the following numbers are factors of 35
1
2
3
5
7
35
so which are factors and which are not
Answers
Answer:
Factors:
1, 5, 7, 35
Non-Factors:
2, 3
Step-by-step explanation:
Given that ABCDEF, solve for x.
A. 3
B. 2
OC. 6
D. 4
Answers
The value of side length x (DF) in the triangle is 4.
What is the value of x?The figures in the image is that of two similar triangle.
Triangle ABC is similar to triangle DEF.
From the diagram:
Leg 1 of the smaller triangle DE = 5
Leg 2 of the smaller triangle DF = x
Leg 1 of the larger triangle AB = 30
Leg 2 of the larger triangle AC = 24
To find the value of x, we take the ratio of the sides of the two triangle since they similar:
Hence:
Leg DE : Leg DF = Leg AB : Leg AC
Plug in the values:
5 : x = 30 : 24
5/x = 30/24
Cross multiplying, we get:
30x = 5 × 24
30x = 120
x = 120/30
x = 4
Therefore, the value of x is 4.
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Suppose that y varies directly with x, and y= --27 when x= --3 .
A) write a direction variation equation that relates x and y.
B) Find Y when x= 5
Answers
Answer:
A) y=9x
B) y=45 when x=5
Step-by-step explanation:
Part A
\(y=kx\\-27=k(-3)\\-27=-3k\\9=k\\y=9x\)
Part B
\(y=9(5)\\y=45\)
An organization is contemplating the implementation of a drug test as part of screening potential employees. The drug test is not 100% effective, i.e., it occasionally classifies drug users as nonusers and vice-versa. Assume that the null hypothesis for the test is that a job candidate is not a drug user. Which of the following would be a Type II error?
a. A false positive (concluding the job candidate is a drug user when he or she is not)
b. A true positive (concluding the job candidate is a drug user when he or she indeed is)
c. A false negative (concluding the job candidate is not a drug user when he or she indeed is)
d. A true negative (concluding the job candidate is not a drug user when he or she is not)
e. There cannot be a Type Il error in this kind of drug testing.
Answers
Answer:
(c) A false negative (concluding the job candidate is not a drug user when he or she indeed is)
Step-by-step explanation:
First, we need to determine if it is possible for type II error to occur or not.
In analysis, type 2 error occurs when the stated null hypothesis is false.
The given null hypothesis here is "a job candidate is not a drug user" which indicates false. This means that option (e) cannot be the solution.
Having established that there is a possibility for an occurrence of type II error.
Next, is to determine the error.
Type II error implies false negative; hence, options (a), (b) and (d) cannot be the solution.
(c) is correct.
Identify the pattern in the list of numbers. Then use this pattern to find the next number.
2,4,6,10,16,26,___
Answers
Answer:
42
Step-by-step explanation:
2,4,6,10,16,26,___
The pattern is adding the previous two numbers to get the next number
2+4 = 6
4+6 = 10
6+10 = 16
10+16 = 26
16+26 =42
4+2=6
6+4=10
10+6=16
16+10=26
26+16=42
Pattern: you add each number to the previous one, then you get the next one
What are the examples of ASA congruence?
Answers
ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.
What does a congruence mean in mathematics?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.
Describe ASA congruence through an example.
ASA (Angle-Side- Angle)
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
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Situation:A9 gram sample of a substance that'sused for drug research has a k-value of0.1459.N-Noe-ktNo-initial mass (at time t = 0)N-mass at time tk= a positive constant that depends onthe substance itself and on the unitsused to measure timet-time, in daysFind the substance's half-life, in days.Round your answer to the nearest tenth.
Answers
Given:
Initial value = 9 grams
k-value = 0.1459
Let's find the substance's half-life in days.
Apply the formula:
\(N=N_0e^{-kt}\)The half-life of a substance can be expressed as:
\(\begin{gathered} \frac{N_0}{2}=N_0e^{-kt} \\ \\ \frac{1}{2}=e^{-kt} \end{gathered}\)Plug in 0.1459 for k and solve for t.
We have:
\(\begin{gathered} \frac{1}{2}=e^{-0.1459t} \\ \\ \end{gathered}\)Take the natural logarithm of both sides:
\(\begin{gathered} ln(\frac{1}{2})=-0.1459t\text{ ln\lparen e\rparen} \\ \\ −0.693147=-0.1459t \\ \\ t=\frac{−0.693147}{-0.1459} \\ \\ t=4.75\approx4.8\text{ days} \end{gathered}\)Therefore, the substance's half-life in days is 4.8 days.
ANSWER:
4.8 days
some similarities and differences of xy plane and the complex plane
Answers
The difference between the xy plane and the complex plane is that in the first one we are representing an ordered pair (that is, two numbers) while in the complex plane we are representing only one number (but this number can be decomposed in an real part and an imaginary part).
Now, they are similar in that the construction is the same, that is, they are both made of two perpendicular lines that we call axis, the intersection is called the origin and is represented by the zero in each set.
Gina read 120 pages in 4 days. Which reading rate is equivalent?
Answers
Answer:
Gina reads 30 pages per day.
Step-by-step explanation:
120 / 4 = 30
I hate to ask, but please give me Brainliest. I need it to level up <3.
Answer:
Gina reads 30 pages per day.
Step-by-step explanation:
Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?
Answers
Complete Question:
Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters. This year he wants to make the garden three times as long and two times as wide.
Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.
How many more meters of fencing is needed for this year’s garden than last year’s?
Answer:
26 meters of fencing needed
Step-by-step explanation:
Given
Last Year:
\(Width = 5m\)
\(Area = 20m^2\)
This Year:
\(Length = 3\ times\ longer\)
\(Width = 2\ times\ wider\)
Required
Determine how many more meters is needed
Represent last year's length of Fence with L and last year's width with W
First, we need to calculate L
\(Area = L * W\)
Where
\(Area = 20m^2\)
\(W = 5m\)
\(20m^2 = L * 5m\)
Divide both sides by 5m
\(\frac{20m^2}{5m} = \frac{L * 5m}{5m}\)
\(\frac{20m^2}{5m} = L\)
\(L = \frac{20m^2}{5m}\)
\(L = 4m\)
So, we have that:
For Last Year
\(Length = 4m\) and \(Width = 5m\)
For this year:
\(Length = 3\ times\ longer\)
\(Length = 3 * 4m\)
\(Length = 12m\)
\(Width = 2\ times\ wider\)
\(Width = 2 * 5m\)
\(Width = 10m\)
So, for this year, we have:
\(Length = 12m\) and \(Width = 10m\)
Next, we calculate perimeter of fencing in both years.
\(Perimeter = 2 * (Length + Width)\)
Last Year:
\(Perimeter = 2 * (4m + 5m)\)
\(Perimeter = 2 * 9m\)
\(Perimeter = 18m\)
This Year:
\(Perimeter = 2 * (12m + 10m)\)
\(Perimeter = 2 * 22m\)
\(Perimeter = 44m\)
To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.
\(Difference = 44m - 18m\)
\(Difference = 26m\)
Hence, there are 26 meters of fencing needed
Order from greatest to least : 3.5, 3.05, 3.55, 3.555
Answers
Answer:
Step-by-step explanation:
3.05, 3.5,3.55,3.555
Refers to the use of communication messages that demonstrate confidence, dominance, and forcefulness to achieve personal goals
Answers
The term that refers to the use of communication messages that demonstrate confidence, dominance, and forcefulness to achieve personal goals is "assertiveness".
Assertiveness is a communication style that involves expressing one's opinions, needs, and feelings in a clear and respectful manner, while also respecting the opinions, needs, and feelings of others. It involves standing up for oneself and being confident in one's abilities, while also being open to feedback and willing to compromise when necessary. Assertiveness can be an effective communication style in many situations, as it allows individuals to communicate their needs and achieve their goals while also maintaining positive relationships with others.
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Select all of the ordered pairs below that satisfy the linear inequality y < 2x + 2.
Answers
We will determine the ordered pairs that satisfy the inequality as follows:
*(-3, -6):
\(-6<2(-3)+2\Rightarrow-6<-4\)This is true, so the first ordered pair satisfies it.
*(3, 9):
\(9<2(3)+2\Rightarrow9<8\)This is false, so the second ordered pair does not satisfy the inequality.
*(-1, -2):
\(-2<2(-1)+2\Rightarrow-2<0\)This is true, so the third ordered pair satisfies it.
*(2, 4):
\(4<2(2)+2\Rightarrow4<6\)This is true, so the fourth ordered pair satisfies it.
*(-2, 1):
\(1<2(-2)+2\Rightarrow1<-2\)This is false, so the fifth ordered pair does not satisfy the inequality.
*(0, 2):
\(2<2(0)+2\Rightarrow2<2\)This is false, so the sixth ordered pair does not satisfy the inequaltity.
Write the exponential function y = 22(1.35)' in the form y = aekt.
(a) Once you have rewritten the formula, give k accurate to at least four decimal places.
k%3D
help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and
continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing
decay the negative rate is implied).
(b) The annual? rate is
% per year (round to the nearest 0.01%).
Answers
Answer:
y = 22·e^(0.3001t), growingannual rate: 35%continuous rate: 30.01%Step-by-step explanation:
When an exponential function is in the form ...
y = ab^t
the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...
b = 1 +r
In the alternate form, this can be written ...
y = a·e^(kt)
Comparing the forms, we see that ...
b = e^k ⇒ k = ln(b)
__
(a)y = 22·1.35^t
k = ln(1.35) ≈ 0.3001
y = 22·e^(0.3001t)
The growth factor is greater than 1, so the function is growing.
__
(b)The annual growth rate is ...
r = 1.35 -1 = 0.35 = 35.00%
__
(c)The continuous growth rate is ...
k = 0.3001 = 30.01%
Eight increased by 5 times a number is 24. Express the statement as an algebraic equation
Answers
Answer:
8+5x=24
Step-by-step explanation:
hope this helps
. Read the paragraph and choose a sentence that describes it best. On the way across the Aegean Sea, Caesar was kidnapped by pirates and held prisoner. He maintained an attitude of superiority throughout his captivity. The pirates demanded a ransom of 20 talents of silver, but he insisted that they ask for 50. After the ransom was paid, Caesar raised a fleet, pursued and captured the pirates, before imprisoning them. He had them crucified on his own authority, as he had promised while in captivity—a promise that the pirates had taken as a joke.
a) Caesar was a vane man who thought 20 talents is too little of a ransom
b) Caesar was very brave and kept to his word to kill the pirates
c) Pirates didn’t believe Caesar will kill them because he was their prisoner
d) The pirates didn’t kill Caesar not only because he was promised to be paid for, but because he made them respect him
Answers
The sentence that best describes the paragraph is: "The pirates didn't believe Caesar would kill them because he was their prisoner." So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.
The paragraph recounts the events of Caesar's kidnapping by pirates while crossing the Aegean Sea. Despite being held captive, Caesar maintained an attitude of superiority. The pirates demanded a ransom of 20 talents of silver, but Caesar insisted they ask for 50. This indicates that Caesar saw himself as more valuable than the initial ransom amount suggested by the pirates.
After the ransom was paid, Caesar did not forget the pirates' actions. He raised a fleet, pursued the pirates, and captured them. The sentence implies that the pirates didn't believe Caesar would actually kill them because he was their prisoner and they likely saw his promises as mere jest.
However, Caesar, true to his word, had the pirates crucified on his own authority.
This sequence of events highlights Caesar's determination, strategic thinking, and his ability to command respect even in dire circumstances. Despite being initially taken prisoner, he managed to turn the tables on the pirates, assert his authority, and exact his revenge. So, the correct option is c) Pirates didn’t believe Caesar will kill them because he was their prisoner.
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Ann thought of a number, n . She multiplied it by 5 and then added 7. Then she told Jim the result, r
Start with the formula you wrote in part (b). Use it to write another formula that could help Jim find Ann’s number, n as soon as he is given the result, r
Answers
The formula that could help Jim find Ann’s number, n as soon as he is given the result, r is n = (r - 7) / 5.
How to write formula?Formula 1;
Let the unknown number Ann thought of = n
(n × 5) + 7 = r
5n + 7 = r
If Jim is given Ann's number n if given the results, r
This means Jim will make Ann's number n the subject of the formula;
5n + 7 = r
Subtract 7 from both sides
5n = r - 7
divide both sides by 5
n = (r - 7) / 5
Therefore, the formula written in terms of n is n = (r - 7) / 5
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The function f(x) = x3 – 8x2 + x + 42 has zeros located at 7, –2, 3. Verify the zeros of f(x) and explain how you verified them. Describe the end behavior of the function.
Answers
Answer:
zeros are {-2, 3, 7} as verified by graphingend behavior: f(x) tends toward infinity with the same sign as xStep-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
ZerosThe attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
End behaviorThe leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
x → -∞; f(x) → -∞x → ∞; f(x) → ∞__
Additional comment
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
Bryce made a scale drawing of a shopping center. The scale of the drawing was
1 inch : 4 feet. A bakery in the shopping center is 10 inches in the drawing. How wide is the
actual bakery?
Answers
Answer:
I'm pretty sure the answer is 40.
Step-by-step explanation:
1:4 meaning
1-10 inches
10 x 4 equals 40ft.
Because of the scale being 1:4 .
It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
mentum
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Privacy Policy California Priv
Mar 10
11:
Answers
Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
simplify (5x^3+7x-8)+(2x^3-5x^2-x+3)
Answers
Answer:
Step-by-step explanation:
A ladder of length (2x+6) feet is positioned x feet from a wall. If the ladder reaches a height of (2x+4) feet along the wall. Find the longest leg.
A. 10ft
B. 24ft
C. 26ft
D. 13cm
Answers
Using the Pythagoras theorem, the longest leg has the length of 24 feet.
Given that,
A ladder of length (2x+6) feet is positioned x feet from a wall.
Height of the ladder = (2x + 6) feet
Distance of ladder from the wall = x feet
Height of the wall that the ladder is placed = (2x + 4) feet
These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.
Longest leg is (2x + 4) feet
Using the Pythagoras theorem,
(2x + 6)² = (2x + 4)² + x²
4x² + 24x + 36 = 4x² + 16x + 16 + x²
4x² + 24x + 36 = 5x² + 16x + 16
x² - 8x - 20 = 0
(x - 10) (x + 2) = 0
x = 10 or x = -2
x = 2 is not possible.
So x = 10
Longest leg = 2x + 4 = 20 + 4 = 24 feet
Hence the length of the longest leg is 24 feet.
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through how many degrees does the hour hand of a clock move in 10 hours
Answers
Answer:
120 degrees move in 10 hours
not sure need help please
Answers
Answer:
it should be A. because the lead broke her arm immediately. causing her to spike her preformances
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
Because it shows that after the 1st week, into the 2nd week, it shows an increase of 9 performances.
Pls graph and answer!
Answers
Answer:
Closed bracket “ ] “
at -5 facing the left then fill in the graph from -5 to -10
It’s facing left because -5 is greater than -x-4
Answer:
x ≥ 1
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
−x ≤ −1
Divide each term in −x ≤ −1 by −1 and simplify.
x ≥ 1
Hope this helps! :)
At CVS, the tax paid was $2.45, which was 7% of the cost. What was the cost of the items purch
ased?
Answers
'Percentage' is obtained by multiplying 2.45 by - 7%.
- 7% × 2.45 =
(- 7 ÷ 100) × 2.45 =
(- 7 × 2.45) ÷ 100 =
- 17.15 ÷ 100 =
- 0.1715 ≈
- 0.17;
How do we check the result?If - 7% × 2.45 = - 0.1715 =>
Divide - 0.1715 by 2.45...
... And see if we get as a result: - 7%.
Note:100/100 = 100 ÷ 100 = 100% = 1
Multiply a number by the fraction 100/100,
... and its value doesn't change.
n/100 = n%, any number.