Answer:
f(x) = x³ -9x² +28x -30
Step-by-step explanation:
You want a monic polynomial f of least degree with zeros 3 and 3-i.
FactorsFor zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...
f(x) = (x -3)(x -3 +i)(x -3 -i)
f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors
f(x) = x³ -9x² +28x -30
__
Additional comment
When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:
f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)
In one year, assuming Dodgers will recruit more good players from free agent market so it will have two times chance (doubling the chance vs Angels) to win when Dodgers plays against Angels.What is the probability for Dodgers to win four games out of a seven games series?
Assuming the Dodgers sign more quality players from the free agent market in a year, they will have a better chance of winning when they play the Angels. The odds of the Dodgers winning four of a possible seven games in a series are in probability 0.2097.
The probability for the Dodgers to win a game when playing against the Angels is 2/3 (doubling the chance vs Angels).
So the probability for the Dodgers to win a seven game series against the Angels is (2/3)^7. That is, the probability for the Dodgers to win four games out of a seven game series is (2/3)^4.
Therefore, the probability for the Dodgers to win four games out of a seven games series is (2/3)^4 = 0.2097.
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Write an equation that expresses the statement (Use k as the constant of proportionality.)
1- T varies directly as x.
2- w is jointly proportional to y and z
3- x is proportional to s and inversely proportional to t.
4- A is proportional to the square of t and inversely proportional to the cube of y
By using proportionality theorem, the equation that expresses the statement is written as
1) T = kx
2) w = kyz
3) x = ks/t
4) A = kt²/y³
Proportionality
In math, a proportional relationship between a quantity y and a quantity x that has a constant of proportionality k is represented by the equation y = kx.
Given,
Here we have to find the equation that expresses the statement by using the k as the constant of proportionality.
Here we know that the value of the constant of proportionality is k.
Then the equation for the statement are,
1- T varies directly as x. And it can be written based on the constant proportionality,
=> T = kx
2- w is jointly proportional to y and z
Then the statement is written as,
=> w = k x y x z
=> w = kyz
3- x is proportional to s and inversely proportional to t.
Here we have to use the inverse proportional to write the statement,
=> x = k x s x 1/t
=> x = ks/t
4- A is proportional to the square of t and inversely proportional to the cube of y
Here first we have to take the square on t, then we get t² and then have to take cube on y, then we get y³,
then the equation is written as,
=> A = kt²/y³
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Translate the following into a formula:
The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.
The value of the formula will be;
⇒ S = 180 (n - 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''
Now,
Since, The algebraic expression is,
''The sum S of the measures of the angles of a polygon is equal to 180 times the difference of the number of sides n and 2.''
Hence, We can formulate the expression as;
⇒ S = 180 (n - 2)
Thus, The value of the formula is,
⇒ S = 180 (n - 2)
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Use the diagram to answer the both questions.
What is the value of x?
x =
What is the measure of the unknown angle?
Angle =
The value of x is 56 and the value if the unknown angle is 106°
What are angles on a straight line?Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. The law of angle on a straight line states that the sum of angle on a straight line is 180°
This means that (2x-6)°+74= 180
(2x-6)°= 180-74
(2x-6)° = 106
add 6 to both sides
2x= 106+6
2x= 112
x= 112/2
x= 56
therefore the unknown angle = 2(56)-6 = 112-6= 106°
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12 greater than or equal to -x+9 and 6 less than or equal to -x+9
Answer: anything between -3 and 3, inclusive (meaning-3 and 3 are answers)
Step-by-step explanation:
6≤-x+9≤12(-x is just x times 1)
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washery=2−1/2x, y = 0, x 1, x = 2; about the x-axis
The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex] ------------------------------ (1)
Simplifying,
[tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]
⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]
⇒ [tex]\pi (1 + \frac{7}{12})[/tex]
⇒ [tex]\frac{19\pi }{12}[/tex]
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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The standard deviation of returns averages28 percent. The options mature in 5 years and the risk-freerate is 2.36 percent. What is the value of e−Rt?
The value of e⁻ᴿᵗ is 0.8886 for the given the standard deviation of returns averages 28 percent with the options mature in 5 years and the risk-free rate is 2.36 percent.
So, the correct option is option ( C).
Exponential function is characterized by rapid increase (as in size or extent) and an exponential growth rate.
We have given that,
standard deviation of returns averages = 28%
options mature, t = 5 years and
Risk-free rate , R = 2.36 percent.
we have to calculate the value of e−Rt.
Exp(-Rt) = e⁻⁽²·³⁶⁾⁵
use exp(value) function to find the value :
=exp(-5 × 2.36%)
= exp(- 0.118 )
=0.8886
Hence, the the value of e⁻ᴿᵗ is 0.8886.
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Complete question:
I. M. Greedy has been granted options on 500,000 shares. The stock is currently trading at $48 a share and the options are at the money. The standard deviation of returns averages 28 percent. The options mature in 5 years and the risk-free rate is 2.36 percent. What is the value of e-rt?
a) .7087
b) .8476
c) .8886
d) .6087
e) .7952
. A cartographer creates a map using the function
d = 250n where n is the number of inches on the
map and d is the actual distance between the
locations in miles. If the actual distance between
two cities is 1,125 miles, how far apart on the ma
should the cities be?
(A) 0.5 inches
(B) 1.5 inches
(C) 2.5 inches
(D) 4.5 inches
To find the distance between two cities on the map, we can use the formula provided in the question:
d = 250n
where d is the actual distance between the cities in miles, and n is the number of inches on the map. Since we are given that the actual distance between the two cities is 1,125 miles, we can substitute this value for d in the formula above to find the number of inches on the map:
1,125 = 250n
Solving for n, we get:
n = 1,125 / 250 = 4.5 inches
This means that the distance between the two cities on the map should be 4.5 inches, so the correct answer is (D) 4.5 inches.
______ results from the exclusion of certain groups of subject from a population frame. coverage error measurement error sampling error non-response error
Coverage Error results from the exclusion of certain groups of subjects from a population frame. The answer for the given statement is Coverage Error.
What is Coverage Error?Coverage errors come from failure to cover sufficiently all components of the population being studied. Incomplete sampling frames usually result in coverage errors. Coverage errors happen because of the divergences between the target population and the frame.
Coverage error also may happen when not all members of the population of interest have an equal chance of being selected for the survey. For example, if we use e-mail lists or phone lists to build the sample and not all potential respondents are on those e-mail or phone lists.
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1. Helen took four tests, for which her mean score was 26. Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15. What was the corrected mean score?
The corrected mean will be 17.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Helen took four tests, for which her mean score was 26.
Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.
Now,
Since, Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15.
Hence, The correct mean = 26 - (51 - 15)/4
= 26 - 36/4
= 26 - 9
= 17
Thus, The corrected mean will be 17.
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What is 96 = 10(x + 2) +6 ?
Our goal when we solve algebraic equations is always to isolate the variable. We can do this by performing inverse operations on the equation, cancelling out values.
Solving the Question[tex]96 = 10(x + 2) +6[/tex]
⇒ Subtract 6 from both sides:
[tex]90 = 10(x + 2)[/tex]
⇒ Divide both sides by 10:
[tex]9 = x + 2[/tex]
⇒ Subtract 2 from both sides:
[tex]x=7[/tex]
Answer[tex]x=7[/tex]
Answer:
x = 7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable
If f(x)=5x³-2 and g(x)=x+1, find (f - g)(x).
Answer:
5x³ - x - 3
Step-by-step explanation:
(f - g)(x) =
f(x) - g(x) =
5x³-2 - (x+1) = ==> plug in known values
5x³-2 - x - 1 = ==> simplify
5x³ - x - 2 - 1 = 5x³ - x - 3
f(x) = 5x³ - 2
g(x) = x + 1
Therefore, (f - g)(x) = (5x³ - 2) - (x + 1) = 5x³ - x - 3
So, (f - g)(x) = 5x³ - x - 3.
4. Which equation describes the line that
passes through (2, 1) and (0, -5)?
A. Y=1/3x-5
B. Y=3x-5
C. Y=-1/3x-5
D. Y=-3x-5
The equation that describes the line that passes through (2, 1) and (0, -5) is: B. y = 3x - 5.
How to Write the Equation of a Line?To find the equation of a line, find the value of the slope (m) and the y-intercept (b), and plug in the values into y = mx + b.
Given the points:
(2, 1) and (0, -5)
Slope (m) of the line = change in y / change in x = (-5 - 1) / (0 - 2)
Slope (m) = -6/-2
Slope (m) = 3
The y-intercept (b) = -5 (this is because it is the value of y when x = 0).
To write the equation, substitute m = 3 and b = -5 into y = mx + b:
y = 3x - 5
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A karaoke machine regularly costs $163 and is on sale for 25% off. How much is the discount?
$20.38
$40.75
$114.10
$122.25
In the following question, we will count distinct integer solutions to the equation X_1 + X_2 + X_3 + X_4 = 35. How many solutions are there if all the variables must be non-negative? How many solutions are there if all the variables must be positive? How many solutions are there if X_1 greaterthanorequalto 2, X_2 greaterthanorequalto 4, X_3 greaterthanorequalto 0, and X_4 greaterthanorequalto 0? How many solutions are there to the equation X_1 + X_2 + X_3 + X_4 lessthanorequalto 35 in which all the X_i are non-negative?
There are 364 positive variables and 5984 non - negative integers.
An integer is zero (0), a positive integer (1, 2, 3, etc.), or a negative integer with a minus sign (-1, -2, -3, etc.). [1] A negative number is the additive reciprocal of the corresponding positive number. [2] In mathematics languages, sets of integers are often represented by a bold Z or blackboard bold . The integers form the smallest group and smallest ring containing the natural numbers. In algebraic number theory, integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers. In fact, (rational) integers are algebraic integers that are also rational numbers.
Let us take each xi = a₁+1
x₁+x₂+x₃+x₄ = 35
∴a₁+a₂+a₃+a₄ = 31 ,where each ai is non-negative.
Now using the stars and bars method the answer is -
([tex]\left \{ {{31 + 4 - 1} \atop {4 - 1}} \right.[/tex] = [tex]\left \{ {{34} \atop {3}} \right.[/tex]}
= [tex]\frac{34!}{3! * (34 - 3)!}[/tex]
= 5984
A particular solution of this equation corresponds to the placement of 3 addition signs in the 14 spaces between successive ones in a row of 15 ones.
Since, a particular solution of the equation corresponds to the placement of k−1 addition signs in the n−1 spaces between successive ones in a row of n ones, the number of solutions of the equation x₁ + x₂ + x₃ +⋯+xₐ=n in the positive integers is
[tex]\left \{ {{n - 1} \atop {k - 1}} \right.[/tex]}
For instance, placing an addition sign in the fourth, seventh, and twelfth spaces gives
1111+111+11111+111
which corresponds to the solution x₁ = 4, x₂ = 3, x₃ = 5, x₄ = 3.
Hence, the number of such solutions is the number of ways we can select which three of the 14 spaces between successive ones in a row of 15 ones will be filled with addition signs, which is
[tex]\left \{ {{14} \atop {3}} \right.[/tex]}
= [tex]\frac{14!}{3! * (14 - 3)!}[/tex]
= 364
Therefore, there are 364 positive variables and 5984 non - negative integers.
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An accountant used to charge $91.50 per hour, but recently decided to charge 10% less. Now how much does she charge per hour?
Answer:
82.35
Step-by-step explanation:
91.5-(91.5*0.1)=
91.5-9.15=82.35
Find the perimeter in centimeters.
Answer: 210
Step-by-step explanation:
Answer: 210cm
Step-by-step explanation:
This is a parallelogram, the sides opposite of each other are congruent. So we can just add up all the sides 50+50+55+55=210cm.
Evaluate for d = 10, u = 7, e = 3. 2 de
i think its 28 but im not sure
Answer:
32
Step-by-step explanation:
Just plug in the numbers for [ d times e ]
The equation is then [ 10 x 3.2 = ? ]
The answer is 32
A bond has a 6.5 percent annual coupon rate. It will mature in 6 years, and semi-annual coupon payments are made at the end of each year. Present annual yields on similar bonds are 7.5 percent. What should be the current price?
Therefore the answer to this question is the current price will be $991.47
What is interest rate ?The amount of interest due each period is represented by an interest rate, which is expressed in relationship to the amount lent, deposited, or borrowed. How much money is lent or borrowed depends on the amount lent, the interest rate, the frequency of compounding, and the length of time that it is lent, deposited, or borrowed. much interest will be charged overall.
Here,
Given
n=6*2
i/y=7.5/2
pv=?
pmt=75/2
face value=1000
Annualized Interest Payment / Par Value of Bond * 100% =Coupon Rate
65/1000 * 100% =6.5%
and other coupon rate
75/1000*100%=7.5%
Therefore by calculating the given values we get the current price as $991.47
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The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 36 minutes of calls is
$24.24, and the remaining credit after 55 minutes of calls is $21.20. What is the remaining credit after 63 minutes of calls?
The remaining credit after 63 minutes of calls is $19.92.
What is the remaining credit after 63 minutes of calls?From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.
The rate will be:
= (24.24 - 21.20) / (55 - 36)
= 3.04 / 19
= 0.16
The remaining credit after 63 minutes of calls will be:
= $21.20 - ((63 - 55) × $0.16)
= $21.20 - $1.28
= $19.92
The credit is $19.92.
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please help i cant copy and paste it but yea ty
Answer:
a = 2
b = 4
c = 3
d = 4
e = 6
Step-by-step explanation:
When dividing fractions, you flip the fraction on the right; here, we have
1/2 / 3/4 so it is the same as 1/2 * 4/3. From there, we would assign our values, so a =2, b = 4, c =3, d is equal to 1*4, so 4, and e is equal to 2*3, so 6.[tex]1[/tex]
See attached for the question
Check the picture below.
Answer:
∠ U = 12°
Step-by-step explanation:
the inscribed angle RST is half the measure of its intercepted arc RT , then
arc RT = 2 × ∠ RST = 2 × 30° = 60°
the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is
∠ U = [tex]\frac{1}{2}[/tex] ( RS - RT ) = [tex]\frac{1}{2}[/tex] × (84 - 60)° = [tex]\frac{1}{2}[/tex] × 24° = 12°
There are 10 fewer Robins than Cardinals. There are 3 time as many bluebirds than robins. There are 16 cardinals. How many bluebirds there are?
The number of bluebirds is 18.
How many are bluebirds?The following equations can be determined from the question:
10 = c - r equation 1
b = 3r equation 2
Where:
c = number of Cardinals b = number of bluebirds r = number of robinsSubstitute for c in the first equation :
10 = 16 - r
r = 16 - 10
r = 6
Substitute for r in the second equation:
b = 6 x 3
b = 18
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22 is what percent of 145.1?
Answer:
15.161
Step-by-step explanation:
Answer:
31.922
Step-by-step explanation:
Need help with this questions
The angle measures in this problem are given as follows:
42. m < KMN = 101º.
43. m < M = 20º.
How to obtain the angle measures?The angle measures are obtained considering that the sum of the measures of the internal angles of a triangle is of 180º.
Additionally, an angle is also supplementary with it's exterior angle, meaning that the sum of their measures is also of 180º.
Considering the missing angle as y, the equations for item 42 are given as follows:
y + 4x + 81 = 180º.y + 13x + 36 = 180º.Hence:
13x + 36 = 4x + 81
9x = 45
x = 5.
Then the measure of angle KMN is of:
m <KMN = 13 x 5 + 36 = 101º.
For problem 43, the triangles are similar, meaning that they have the same angle measures, which are given as follows:
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A manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item. If the relationship between the number of items sold i and the price per item p is a linear one: Find a formula that gives x in terms of p, 2 = Preview Now use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.
The number of items 125 they will sell if the price per item is $3.50. They will sell 125 items if the price is $3.50.
In the given question, a manufacturing company finds that they can sell 275 items at $2.50 per item and 350 items at $2.00 per item.
If the relationship between the number of items sold i and the price per item p is a linear one then we have to find a formula that gives x in terms of p, x =
Now we have to use the formula to find the number of items they will sell if the price per item is $3.50. They will sell items if the price is $3.50.
Let’s find the slope using
m = {y(2)-y(1)}/{x(2)-x(1),
where
x(1) = 2.5 y(1)=275
x(2) = 2 y(2)=350
m = (350-275)/(2-2.5)
m = 75/(-0.5)
m = -150 is the slope
Point slope form to find the equation:
y - y1 = m(x-x1)
y - 275 = -150(x - 2.5)
y - 275 = -150x + 375
y = -150x + 275 + 375
y = -150x + 650,
But they want to have x = items sold and p = the price
So we have to write the equation where x is in terms of p
x = -150p + 650:
then use the formula to find the number of items they will sell if the price per item is $3.00.
x = -150(3.5) + 650
x = -525 + 650
x = 125 items sold when the price is $3.5
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suppose that as a follow up question you asked all the students who were graduating with stem degrees if they planned on working in academia. out of the 95 students graduating with stem degrees, 9 report they plan on working in academia. build a 95% confidence interval for the true percentage of students graduating with stem degrees that plan on working in academia. make sure to interpret your interval and check any necessary conditions. (hint: make sure to use an appropriate method to do this)
The sample size must be more than 30 and the sample must be chosen at random for this confidence interval to hold true. The sample size in this example is 95, and the students were chosen at random, thus both of these requirements are satisfied.
How do percentages work?Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.
How do you find the percentage?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
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Question
Write a linear function f with f(5)=7 and f(2)=0
f(5) = 7 is another to say a point at (5 , 7)
f(2) = 0 is another to say a point of (2 , 0)
to get the equation of any straight line, we simply need two points off of it, let's use those two above
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{5}}} \implies \cfrac{ -7 }{ -3 } \implies \cfrac{ 7 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{ 7 }{ 3 }}(x-\stackrel{x_1}{5}) \\\\\\ y-7=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }\implies y=\cfrac{ 7 }{ 3 }x-\cfrac{ 35 }{ 3 }+7\implies {\Large \begin{array}{llll} y=\cfrac{ 7 }{ 3 }x-\cfrac{14}{3} \end{array}}[/tex]
For which values of x does the expression square root of x+11 make sense?
Answer:
all values greater than or equal to -11
Step-by-step explanation:
For a square root to be a real number, the value under the square root must be positive. Therefore, all values of x must ensure that the value under the square root remains positive.
Answer:
Any real number x ≥ - 11-------------------------------------------
The square root is defined when the expression under the root is not negative.
It is shown as:
x + 11 ≥ 0 ⇒ x ≥ - 11what is 58388383-776463783
Answer:
Subtract 58388383 - 776463783
