Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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!!GIVING BRAINLISET!! HELP IF ANYONE CAN
SOLVE THIS FOR ME 1-7 JUST ANSWERS
The solution to the given polynomial in their degree are:
5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - TrinomialPolynomial5m²p³ + 6 - binomial5q^-4 + 6q - binomial7ab + 6b² - 2a³ - Trinomial2a + 4a³ - 5a² - 1
= 4a³ - 5a² + 2a - 1
The leading coefficient is 4a³
4z - 2z² - 5z⁴
= -5z⁴ - 2z² + 4z
The leading coefficient is -5z⁴
(-3d² - 8 + 2d) + (4d - 12 + d²)
= -3d² - 8 + 2d + 4d - 12 + d²
= -2d² + 6d - 20
(y + 5) + (2y + 4y² - 2)
= y + 5 + 2y + 4y² - 2
= 4y² + 3y + 3
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A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.
The distance d is 9 ft and the height is 12ft.
How to find the distance and the height?
Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.
The height is one cathetus and the distance is the other catheti.
Let's define:
h = heightd = distance.hypotenuse = 15ftWe know that the height of the tower is 3 ft larger than the distance, then:
h = d + 3ft
Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Then:
[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]
Now we can solve this equation for d:
[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]
Then the solutions are:
[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]
We only take the positive solution:
d = (-3ft + 21ft)/2 = 9ft
And the height is 3 ft more than that, so:
h = 9ft + 3ft = 12ft
The distance d is 9 ft and the height is 12ft.
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Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 99%, sample size 10.
Answer:
1.894
3.169
2.064
3.690
Step-by-step explanation: 90% ; sample size = 8
Degree of freedom, df = n - 1
t(1 - α/2, 7) = t0.05, 7 = 1.894
Select the two values of x that are roots of this equation x^2-5x+2=0
The roots of the equation is x = 4.56 OR x = 0.44
Quadratic equationFrom the question, we are to determine the roots of the given equation
The given equation is
x² -5x +2 = 0
Using the formula method,
[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]
In the given equation,
a = 1, b = -5, c = 2
Putting the values into the formula,
[tex]x =\frac{-(-5) \pm \sqrt{(-5)^{2}-4(1)(2) } }{2(1)}[/tex]
[tex]x =\frac{5 \pm \sqrt{25-8} }{2}[/tex]
[tex]x =\frac{5 \pm \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + \sqrt{17} }{2}[/tex] OR [tex]x =\frac{5 - \sqrt{17} }{2}[/tex]
[tex]x =\frac{5 + 4.12}{2}[/tex] OR [tex]x =\frac{5 - 4.12}{2}[/tex]
[tex]x =\frac{9.12}{2}[/tex] OR [tex]x =\frac{0.88}{2}[/tex]
x = 4.56 OR x = 0.44
Hence, the roots of the equation is x = 4.56 OR x = 0.44
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Question
n⃗ =⟨−2, −1⟩ and D=[−4423].
What is D⋅n⃗ ?
Enter your answer as a vector by filling in the boxes.
The dot product of the D⋅n is 32.
According to the statement
We have given the value of n vector and d matrix and we have to find the dot product of these.
So, For this purpose,
The given values:
n = {-2,-1} and D = [−4423].
The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers, and returns a single number.
So, The d matrix become
[tex]D = \left[\begin{array}{cc}-4&4&\\2&3&\\\end{array}\right][/tex]
Now solve it with the help of multiplication then the matrix become
D = (-12, -8)
and n = {-2,-1}
Now multiply both terms with the dot product.
So, the dot product of the both terms will become
D.n = 24 +8
Then
The output of the dot product of both terms is 32.
So, The dot product of the D⋅n is 32.
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8(x-1) >12-2x
O A. x>-/
X>
3
OB. x>7
OC. x>-5
O D. x>¹
3
Answer: x>2
Step-by-step explanation:
[tex]8(x-1) > 12-2x\\\\8x-8 > 12-2x\\\\10x-8 > 12\\\\10x > 20\\\\x > 2[/tex]
the sum of the measures of three angles is 200. these measures are in the ration 3:5:12. Find the measure of the three angles.
Answer:
30, 50, and 120
Step-by-step explanation:
3/20 × 200 = 30
5/20 × 200 = 50
12/20 × 200 = 120
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
Given that:
The sum of the measures of three angles = 200.
Let the ratios be x.
The ratio of first angle be 3x
The ratio of second angle be 5x
The ratio of third angle be 12x
According to the question,
3x+ 5x+ 12x = 200
20x = 200
Divide both sides by x
x = 200/20
x = 10
The ratio of first angle be 3x = 3(10) = 30 degrees
The ratio of second angle be 5x = 5(10) = 50 degrees
The ratio of third angle be 12x = 12(10) = 120 degrees
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
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-11r is greater than or less than -20
I need some help on this question
Using slopes, the table that could represent Relationship B is the second table.
What is the slope of a relationship?The slope of a relationship is given by the change in y divided by the change in x.
For relationship A, we have points (2,3) and (4,6), hence the slope is:
mA = (6 - 3)/(4 - 2) = 3/2 = 1.5.
Then, the slopes in the table are given as follows:
m = (8.4 - 6.3)/(4 - 3) = 2.1 > mA, hence the first table cannot be representation B.m = (4.5 - 2.25)/(6 - 3) = 0.75 < mA, hence the second table could represent Relationship B.m = (7.2 - 5.4)/(4 - 3) = 1.8 > mA, hence the third table cannot be representation B.m = (9.6 - 4.8)/(6 - 3) = 1.6 > mA, hence the fourth table cannot be representation B.More can be learned about slopes at https://brainly.com/question/24674549
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The sum of two numbers is 42. The greater number is equal to 5 times the smaller number. Find the numbers.
Answer:
35 and 7
Step-by-step explanation:
5x + 1x =42
6x=42
x=7
Answer:
Greater number: 35
Smaller number: 7
Step-by-step explanation:
1) Set up system of equations.
Let x = greater number
Let y = smaller number
----------------------------------------------
x + y = 42
x = 5y
2) Solve them using elimination or substitution.
x + y = 42
x - 5y = 0
----------------
6y = 42
y = 42/6
y = 7
3) Substitute the found answer into one of the two equations to find the value of x.
x = 5(7)
x = 35
Therefore, the greater number is 35, and the smaller number is 7.
Find the interest rate for a principal of $6514 and charged $45415 in interest for 15 years.
Answer:
the answer is 46.47937775048613
your restaurant serves 50 bowls of French onion soup daily and each serving has 8 ounces of onion per portion. Do you think it would be better to purchase whole onions at $1.99 per pound, and cut them yourself, or purchase pre-sliced onions at $2.99 per pound?
I would be better to purchase whole onions at $1.99 per pound, and cut them yourself
Optimization of costNumber of bowls = 50
Weight of each bowl = 8
Total weight of the onion soup = 8 x 50 = 400 ounces
Note that:
1 pound = 16 ounces
Total weight in pounds = 400/16
Total weight in pounds = 25 pounds
If you buy the whole onions and purchase at $1.99 per pound
Total cost = 25 x 1.99 = $49.75
If you purchase pre-sliced onions at $2.99 per pound
Total cost = 25 x $2.99 = $74.75
Since it is cheaper to purchase whole onions at $1.99 per pound, it is the better choice
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1. Quadratics.
The path of the longest shot put by the Women's track team at Sun Devil U is modeled by h(x) = -0.017x² + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground. (Both x and h(x) are measured in feet.)
a. 4 points. Determine h(24). Round your answer to 2 decimal places. Then explain what your answer means in the context of the problem. ("In the context of the problem" means "in terms of the shot put's horizontal distance from the start and in terms of the height of the shot put above the ground.")
b. 4 points. Determine the numerical value of the vertical intercept and explain what this means in the context of the problem.
c. 4 points. Determine the numerical values of the vertex coordinates and explain what they mean in the context of the problem.
d. 4 points. How far from the start did the shot put strike the ground? Round your answer to 2 decimal places.
h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.
What is the value of h(24)?Given,
h(x) = -0.017x² + 1.08x + 5.8
Put h = 24,
h(24) = -0.017(24)² + 1.08(24) + 5.8
h(24) = -9.792 + 25.92 + 5.8
h(24) = 21.93
The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.
What is the value of the vertical intercept?Vertical intercept, x = 0
h(0) = -0.017(0)² + 1.08(0) + 5.8
h(0) = 5.8
The height of the shot put above the ground is 5.8 feet at the start.
What is the values of the vertex coordinates?vertex coordinates,
(h,k) = [(-b/2a),-(b²- 4ac)/4a]
(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]
(h,k) = [(1.08/0.034),(1.5608)/0.068)]
(h,k) = (31.76,22.95)
The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.
How far from the start did the shot put strike the ground?Put h(x) = 0,
-0.017x² + 1.08x + 5.8 = 0
Use quadratic formula for solving x,
x = (-b±√b²- 4ac)/2a
Here a = -0.017, b=1.08, c=5.8
x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)
x = [-1.08±√1.5608]/-0.034
x = [-1.08-1.2493]/-0.034 and x = [-1.08+1.2493]/-0.034
x = 68.509 and x = - 4.98
Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²
= √73.49²
= 73.49 feet
Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.
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If a cylinder has a volume of 300 m3 and a radius of 5 m, what is its height (in meters)? (Round your answer to two decimal places.)
also second question:
The diameter is 6 feet 6 inches. The height is 12 feet 3 inches. Determine the surface area (in square feet) and volume (in cubic feet) of the following. (Round your answers to one decimal place.)
The height of the cylinder is 3.82 m
2. The surface area is 316.5 ft²
The volume is 406.5 ft³
Calculating volume of a cylinderThe volume of a cylinder is given by the formula,
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
V = 300 m³
r = 5 m
h = ?
Putting the parameters into the formula, we get
300 = π × 5² × h
300 = π × 25× h
∴ h = 300/25π
h = 3.82 m
Hence, the height of the cylinder is 3.82 m
2.
Diameter = 6 feet 6 inches = 6.5 feet
∴ Radius = 3.25 feet
Height = 12 feet 3 inches = 12.25 feet
Surface area of a cylinder is given by
Surface area = 2πr(r + h)
Where r is the radius
and h is the height
Surface area = 2π×3.25(3.25 + 12.25)
Surface area = 316.5 ft²
For the volume
V = πr²h
V = π × 3.25² × 12.25
V = 406.5 ft³
Hence, the volume is 406.5 ft³
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You can build two triangles that have the same side lengths but are not
congruent.
A. True
B. False
Answer: False .
Step-by-step explanation: mark me brainliest
Answer:
false because l don't know
Solving for the area.
Area
1/2(sum of parallel sides)height1/2(50+65)(30)1/2(115)(30)15(115)1150+5751725ft²Answer:
1725 ft²
Step-by-step explanation:
The formula to find the area of a trapezoid is :
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30
Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30
Area = [tex]\frac{1}{2}[/tex] × 3450
Area = 1725 ft²
Click to select points on the graph.
104
-10
-8
The solution is
-6
-4
-2
8
6
4
2
-2
4
6
-8
-104
2
4
y = -2x + 1
6
8
10
ha
Answer: [tex](-2, 5)[/tex]
Step-by-step explanation:
The graphs are shown in the attached image.
The solution is where they intersect.
The solution to the system of equations is x = -2 and y = 5.
i.e
The solution is = (-2, 5)
We have,
To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."
So, you'll have:
(-7/2)x - 2 = -2x + 1
Now, let's solve for x:
Step 1:
Get rid of the fractions by multiplying both sides by 2:
2 * ((-7/2)x - 2) = 2 * (-2x + 1)
This simplifies to:
-7x - 4 = -4x + 2
Step 2:
Isolate the x terms on one side of the equation.
Let's move the -4x to the left side by adding 4x to both sides:
-7x - 4 + 4x = -4x + 4x + 2
This simplifies to:
-3x - 4 = 2
Step 3:
Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:
-3x - 4 + 4 = 2 + 4
This simplifies to:
-3x = 6
Step 4:
Finally, solve for x by dividing both sides by -3:
x = 6 / -3
x = -2
Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.
Let's use the first equation y = (-7/2)x - 2:
y = (-7/2) * (-2) - 2
y = 7 - 2
y = 5
Thus,
The solution to the system of equations is x = -2 and y = 5.
i.e
(-2, 5)
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For many years organize crime rent a number game that is now run illegally by minis states government the player select a three digit number from 0 to 999 there are 1000 such members a bet of two dollars is placed on a number say number 115 if the number is selected the player wins $700 if any other number is selected the player wins nothing find the expected value for this game and describe what it means
Using a discrete distribution, the expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the situation described in this problem, the distribution for the earnings is given as follows:
P(X = 700) = 1/1000.P(X = -2) = 999/1000.Hence the expected value is given as follows:
[tex]E(X) = 700\frac{1}{1000} - 2\frac{999}{1000} = \frac{700 - 2(999)}{1000} = -1.298[/tex]
The expected value for this game is of -$1.298, which means that each time he plays, he is expected to lose $1.298.
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Which of the following is a radical equation?
x StartRoot 3 EndRoot = 13
x + StartRoot 3 EndRoot = 13
StartRoot x EndRoot + 3 = 13
x + 3 = StartRoot 13 EndRoot
Using it's concept, a radical equation is given as follows:
[tex]\sqrt{x} + 3 = 13[/tex].
What is a radical equation?A radical equation is an equation in which the variable is inside the radical.
Hence, among the equations given, the radical equation is:
[tex]\sqrt{x} + 3 = 13[/tex].
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Answer:
C
Step-by-step explanation:
took edge test and got 100
You randomly select an integer from 0 to 9 (inclusively) and then randomly select and integer from 0 to 7 what is the probability of selecting a 2 both times
Reason:
Set A = {0,1,2,3,4,5,6,7,8,9}
Set B = {0,1,2,3,4,5,6,7}
The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.
The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.
Multiply those fractions mentioned (1/10)*(1/8) = 1/80
This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.
3. Make a conjecture about the sum of two even numbers based on the following pattern:
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
and so on.
The conjecture we can use is that the sum of all even numbers is an even number.
How to write Mathematical Conjectures?We are given the sum of two even numbers as follows;
12 = 4 + 8
26 = 6 + 20
48 = 16 + 32
72 = 24 + 48
88 = 36 x 52
From the above, we see that they are all even numbers and as such the conjecture we can use is that the sum of all even numbers is an even number.
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How much should be invested now at an interest rate of 6.5% per year, compounded continuously, to have $1500 in two years?
Do not round any intermediate computations, and round your answer to the nearest cent.
If necessary, refer to the list of financial formulas.
Answer:
$1317.14
Step-by-step explanation:
compounded continuously formula is A=Pe^rt
given that you want to have $1500 in 2 years while the rate is 6.5%, you have A, r, and t of the formula and you are just looking for the P.
plugging everything in...
1500=P (e)^2x0.065
P=1500/1.139
P=1317.14
The function y=f(x is graphed below. What is the average rate of change of the function f(x)on the interval 0≤x≤5?
[tex]m = \frac{f(5) - f(0)}{5 - 0} [/tex]
[tex]m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4[/tex]
Step-by-step explanation:
the average rate of change is
(f(high interval end) - f(low interval end))/(high interval end - low interval end)
in our case here
(f(5) - f(0)) / (5 - 0)
(-10 - 10) / 5 = -20/5 = -4
Arnez Company’s annual accounting period ends on December 31. The following information concerns the adjusting entries to be recorded as of that date. The Office Supplies account started the year with a $3,850 balance. During the year, the company purchased supplies for $15,901, which was added to the Office Supplies account. The inventory of supplies available at December 31 totaled $3,388. The Prepaid Insurance account had a $27,744 debit balance at December 31 before adjusting for the costs of any expired coverage for the year. An analysis of prepaid insurance shows that $20,004 of unexpired insurance coverage remains at year-end. The company has 15 employees, who earn a total of $1,800 in salaries each working day. They are paid each Monday for their work in the five-day workweek ending on the previous Friday. Assume that December 31 is a Tuesday, and all 15 employees worked the first two days of that week. Because New Year’s Day is a paid holiday, they will be paid salaries for five full days on Monday, January 6 of next year. The company purchased a building at the beginning of this year. It cost $725,000 and is expected to have a $45,000 salvage value at the end of its predicted 25-year life. Annual depreciation is $27,200. Since the company is not large enough to occupy the entire building it owns, it rented space to a tenant at $3,400 per month, starting on November 1. The rent was paid on time on November 1, and the amount received was credited to Rent Revenue. However, the tenant has not paid the December rent. The company has worked out an agreement with the tenant, who has promised to pay both December and January rent in full on January 31. On November 1, the company rented space to another tenant for $3,080 per month. The tenant paid five months' rent in advance on that date. The payment was recorded with a credit to the Unearned Revenue account. Assume no other adjusting entries are made during the year. Required: 1. Use the information to prepare adjusting entries as of December 31. 2. Prepare journal entries to record the first subsequent cash transaction in January of the next year for parts c and e.
1. The preparation of the adjusting entries as of December 31 for Arnez Company is as follows:
Adjusting Journal Entries:1. Debit Office Supplies Expenses $16,363
Credit Office Supplies $16.363
2. Debit Insurance Expenses $7,740
Credit Prepaid Insurance $7,740
3. Debit Salaries Expenses $54,000
Credit Salaries Payable $54,000
4. Debit Rent Receivable $3,400
Credit Rent Revenue $3,400
5. Debit Unearned Rent Revenue $6,160
Credit Rent Revenue $6,160
2. The preparation of the journal entries to record the first subsequent cash transactions in January of the next year for Arnez Company is as follows:
Journal Entries:Debit Salaries Payable $54,000
Credit Cash $54,000
Debit Cash $6,800
Credit Rent Receivable $3,400
Credit Rent Revenue $3,400
Adjusting Transaction Analysis:1. Office Supplies Expenses $16,363 Office Supplies $16.363 ($3,850 + $15,901 - $3,388)
2. Insurance Expenses $7,740 Prepaid Insurance $7,740 ($27,744 - $20,004)
3. Salaries Expenses $54,000 Salaries Payable $54,000 ($1,800 x 15 x 2)
4. Rent Receivable $3,400 Rent Revenue $3,400
5. Unearned Rent Revenue $6,160 Rent Revenue $6,160 ($3,080 x 2)
January Transactions:Salaries Payable $54,000 Cash $54,000
Cash $6,800 Rent Receivable $3,400 Rent Revenue $3,400
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Which of the following has the least steep graph?
Which figures demonstrate a translation?
The two bottom graphs demonstrate translations.
Which figures demonstrate a translation?
We will have a translation only if:
The size of the figure does not change (like in option 1, which we can discard).If the "direction" of the figure does not change, like in option 2, where you can see that there is a reflection.The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.
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The graph of f(x) = x3 − 7x − 6 is shown.
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6?
x = −6
x = −2, −1
x = −2, −1, 3
x = −6, −2, −1, 3
In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.
What are the roots of a cubic equation according to a graph?
In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.
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solve the equation: z^ +4z+20+iz(a+1)=0 Where A is constant, has complex conjuget root. if one of roots this quadratic is z=B+2i?
The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.
How to estimate complex conjugate roots?
If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to
[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]
From the z and constant terms, we have
[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]
From the second equation, we get
[tex]B^2 = 16[/tex]
B = ± 4
Then 4+(A+1)i = ± 8
(A + 1)i = 4 or (A + 1)i = -12
Since [tex]$\frac{1}{i} = -i[/tex], we have
[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]
A+1 = -4i or A+1 = 12i
A = -1-4i or A = -1+12i
Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.
To learn more about complex conjugate roots refer to:
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In a survey of 320 college graduates, 36% reported that they stayed on their first full-time job less than 1 year. If 15 of those subjects are randomly selected without replacement for a follow-up survey, find the probability that exactly 5 of them stayed on their job for less than one-year.
Name the variables in the context of the problem.
State the requirements for binomial distribution for this problem.
Use the long formula above to find P(x)
Using the binomial distribution, there is a 0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, there is a fixed number of independent trials, each with only two possible outcomes, hence the binomial distribution is used. The values of the parameters are:
n = 15, p = 0.36.
The probability is P(X = 5), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.36)^{5}.(0.64)^{10} = 0.2094[/tex]
0.2094 = 20.94% probability that exactly 5 of them stayed on their job for less than one-year.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Determine whether the graph is bipartite.
The graph isn't bipartite because it isn't possible to assign either Blue or Red to each vertex, without having connected vertices with the same color.
What is the bipartite graph theorem?The bipartite graph theorem states that a graph is considered to be bipartite only if it's possible to assign either Blue or Red to all the vertex, such that no two (2) connected vertices would have the same color.
By critically observing the image after assigning the colors to each vertices (see attachment), we can logically deduce that the graph isn't bipartite because it isn't possible to assign either Blue or Red to all the vertex, without having connected vertices with the same color.
Read more on bipartite graph here: brainly.com/textbook-solutions/q-exercises-2-1-25-determine-graph-bipartite-useful
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