Answer:
Step-by-step explanation:
The polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be formed as follows:
Since the zero 6 has a multiplicity of 2, it appears twice in the factored form of f(x), i.e., (x-6)(x-6) = (x-6)^2.
The other zero is 3i, which means its complex conjugate, -3i, is also a zero. Therefore, the factored form of f(x) can be written as:
(x-6)^2(x-3i)(x+3i)
Expanding this expression, we get:
f(x) = (x-6)^2(x^2 + 9)
Multiplying this out, we get:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324
Therefore, the polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be written as:
f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324.
The garment factory plans to make 690 sets of garments. It has been done for 5 days, with an average of 75 sets per day. The rest needs to be completed in 2.5 days, how many sets are done on average per day (step-by-step answer)
For the remaining set of garments, the average per day that they need to be completed would be = 126 sets/day.
How to calculate the average set made per day?The quantity of garments planned to be made by the factory = 690sets.
The rate of coverage for 5 days = 75sets/day.
That is for 5 days the number of garments covered = 75×5 = 375
The remaining sets = 690-375 = 315
The average per day to cover the remaining sets of garment = 315/2.5 = 126 sets/day
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Please help, ASAP! This is for a College Algebra Class, No wrong answer.
The value of x in the equation is 2.10.
How to solve exponential equation?The exponential equation above can be solved as follows:
[tex]8^{\frac{4}{x} } = 53[/tex]
Therefore, let's log both sides
log [tex]8^{\frac{4}{x} }[/tex] = log 53
Hence,
4 / x log 8 = log 53
divide both sides by log 8
4 / x = log 53 / log 8
4 / x = 1.7242758696 / 0.90308998699
4 / x = 1.9092439208
cross multiply
1.902x = 4
x = 4 / 1.902
x = 2.09511837419
Therefore,
x = 2.10
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Pleaseeeee helppp meeee
Subtracting 8 times the first row to the second row we will get the matrix.
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
How to get a zero in row 2, column 1?To get that, you will need to take row 2 and subtract 8 times row 1, then the values of each column will be:
Remember that the rows are the horizontal vectors and the columns are the vertical ones.
8 - 8*1 = 0
-3 - 8*10 = -83
65 - 8*-23 = 249
Then the new matrix will be:
[tex]\left[\begin{array}{ccc}1&10&-23\\0&-83&249\end{array}\right][/tex]
That is the matrix with a zero in row 2, column 1.
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Supplementary angles
The angle that is supplementary to the angle DEA is angle DEC
Finding the angle that is supplementary to the angle DEAFrom the question, we have the following parameters that can be used in our computation:
The lines HF and CAThe transversal line GEAlso from the question, we have
Angle = DEA
As a general rule;
Two angles are said to be supplementary if their sum add up tp 180 degrees
This means that the angles are on a straight line
The angle are on the same straight line with ange DEA is DEC
Hence, the angle is angle DEC
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what is an equation of the image of the line after dilation
An equation of the image of the line after dilation is -30x - 20y = -8.
What is scale factor?In Mathematics and Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object based on a specific scale factor of 5 is given by this mathematical expression:
(x, y) → (kx, ky)
Where:
x and y represents the data points.k represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (kx, ky)
(x, y) → (5(-6x), 5(-4y)) = -30x - 20y = -8.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
reduce to lowest terms 4x^y^3/-8x^2y
Answer:
x^(y^3-1) / -2xy
Step-by-step explanation:
4x^y^3 = 4x^(y^3)
-8x^2y = -8x^2y^1
= 4x^(y^3) / -8x^2y^1
= (4x^(y^3) / 4xy) / (-8x^2y^1 / 4xy)
= x^(y^3-1) / -2xy
Answer:
Step-by-step explanation:
Please help me
Decide the type of transformation and state the rule
The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.Comparing the equivalent vertices, the translations are given as follows:
5 units right: x -> x + 5.3 units up: y -> y + 3.More can be learned about translation at brainly.com/question/29209050
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The price of an item has been reduced by 25%. The original price was $35
Correct
The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of
dollars. The summary output for the regression model is given below.
df
SS
Regression 1 16.54127801
Residual 6 5.641280047
Total 7
22.18255806
ANOVA
MS
F
16.54127801 17.59311136
0.94021334
Significance F
0.005721150
Step 1 of 3: What is the coefficient of determination for this model, R2? Round your answer to four decimal places.
Answer:
17.023413
Step-by-step explanation:17.023413
answer and explain in detail
Answer:
The area of right-angled triangle is 30 cm².
Step-by-step explanation:
Given : Here we given that the base and hypotenuse of triangle 12 cm and 13 cm respectively.To Find : We have to find the area of right-angled triangle but before we will find the height of the triangle.Solution :By using Pythagoras Theorem we will find the hypotenuse of triangle :
[tex] \sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
Substituting all the given values in the formula to find hypotenuse :
Hypotenuse = 13 cmBase = 12 cm[tex]\sf{\longrightarrow{{(Hypotenuse)}^{2} = {(Height)}^{2} + {(Base)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{{(13)}^{2} = {(Height)}^{2} + {(12)}^{2}}}[/tex]
[tex]\sf{\longrightarrow{(13 \times 13) = {(Height)}^{2} + {(12 \times 12)}}}[/tex]
[tex]\sf{\longrightarrow{(169) = {(Height)}^{2} + {(144)}}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 169 - 144}}[/tex]
[tex]\sf{\longrightarrow{{(Height)}^{2} = 25}}[/tex]
[tex]\sf{\longrightarrow{{(Height)} = \sqrt{25}}}[/tex]
[tex]\sf{\longrightarrow{\underline{\underline{\red{(Height) = 5 \: cm}}}}}[/tex]
Hence, the height of triangle is 5 cm.
[tex]\begin{gathered} \end{gathered}[/tex]
Now, calculating the area of right-angled triangle by substituting all the given values in the formula :
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
b (Base) = 12 cmh (Height) = 5 cm[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2}bh}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times b \times h}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = \dfrac{1}{2} \times 12\times 5}}[/tex]
[tex]\dashrightarrow{\sf{Area_{(\triangle)} = 6\times 5}}[/tex]
[tex]\dashrightarrow{\sf{\underline{\underline{\pink{Area_{(\triangle)} =30 \: {cm}^{2}}}}}}[/tex]
Hence, the area of triangle is 30 cm².
—————————————————URGENT!! Please help
The correlation coefficient between the minutes the actor appeared shirtless in a film and the film's opening weekend gross is 0.75.
How to write the linear regression equation and determine the correlation coefficient?In this scenario, the minutes shirtless (x) would be plotted on the x-axis of the scatter plot while the open weekend gross (y) would be plotted on the x-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the relationship between the minutes shirtless (x) and the open weekend gross (y), an equation for the linear regression is given by:
y = 10.83 + 0.86x
Correlation coefficient, r = 0.7488571925 ≈ 0.75
In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is approximately greater than 0.7;
0.7＜|r| ≤ 1 (strong correlation)
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For questions 4 – 7, find the value of x.
The values of x in the isosceles trapezoids x = 32, x = 10.9 and x = 41
Calculating the values of x in the figuresAn isosceles trapezoid is a four-sided geometric shape that has two parallel sides and two non-parallel sides that are of equal length.
The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs and the angles in the same base are equal in measure
Using the above as a guide, we have the following:
2x + 14 = 78
x = 32
2 * (6x +32 + 4x + 39) = 360
x = 10.9
4x = 164
x = 41
The last details are not clear
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the temperature at noon was 10degree Celsius above 0 . if it decreases at the rate 2 degree Celsius per hour till midnight , at time the temperature would be 8 degree Celsius below zero ? what would be the temperature at mid-night?
Answer:
Time at which temperature will be -8 degrees Celsius = 21 00 (24 hour clock) or 9pm (12 hour clock)
Temperature at midnight = - 14°C
Step-by-step explanation:
The pic
Need help will give brainliest and 5 stars!
Looking for x and y intercepts, the hole and vertical asymptote.
Check the picture below.
At a local college 29 of the male students are smokers and 262 are non smokers. Of the female students, 40 are smokers and 360 are non smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
We have,
Let's first find the probability of selecting a male smoker and then the probability of selecting a female smoker.
P(Male smoker) = Number of male smokers / Total number of male students
P(Male smoker) = 29 / (29 + 262)
P(Male smoker) = 0.10
Similarly, the probability of selecting a female smoker is:
P(Female smoker) = Number of female smokers / Total number of female students
P(Female smoker) = 40 / (40 + 360)
P(Female smoker) = 0.10
Now, we can find the probability of selecting both a male smoker and a female smoker by multiplying the probabilities:
P(Both smokers) = P(Male smoker) x P(Female smoker)
P(Both smokers) = 0.10 x 0.10
P(Both smokers) = 0.01
Therefore,
The probability that both a male student and a female student from the college are smokers is 0.01 or 1%.
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What is the unit sales of product A at the monthly break even point?
The unit sales of product A at the monthly break-even point is 193,750 units.
What is the unit sales of product A at the monthly break even point?To determine the unit sales of product A at the monthly break-even point, we need to calculate the total contribution margin that covers the monthly fixed costs of $387,500.
Given that the unit contribution margin for product A is $2 and the unit selling price for product A is $5, we can calculate the contribution margin ratio for product A as follows:
Contribution Margin Ratio for Product A:
= (Unit Contribution Margin for Product A) / (Unit Selling Price for Product A)
= $2 / $5
= 0.4
40%
Now, let's consider the sales ratios given in the problem statement. It states that the company sells two units of A for each unit of B, and three units of B for each unit of C. This means that the sales ratio for product A to product B is 2:1, and the sales ratio for product B to product C is 3:1.
Let's assume that the unit sales of product A at the monthly break-even point is "x". Then, the unit sales of product B would be "2x" (based on the sales ratio of 2:1 between A and B), and the unit sales of product C would be "6x" (based on the sales ratio of 3:1 between B and C).
The total contribution margin for product A at the monthly break-even point can be calculated as follows:
Total Contribution Margin for Product A = (Unit Contribution Margin for Product A) * (Unit Sales of Product A at Break-Even Point)
= $2 * x
Since the monthly fixed costs are $387,500, we can set up the equation for the break-even point as follows:
Total Contribution Margin for Product A = Monthly Fixed Costs
$2 * x = $387,500
Now we can solve for x, the unit sales of product A at the monthly break-even point:
$2 * x = $387,500
x = $387,500 / $2
x = 193,750
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the expression 30 x squared - 100x - 60 and (5x-20) (6x+3) define the same function f. Which expression makes it easier to find f of 0
PLEASE SOLVE THIS....I WILL GIVE BRAINLIEST!!!
Answer:
Give me a sec
Step-by-step explanation:
Find the volume of the prism. Round your answer to the nearest tenth, if necessary.
cm³
18 cm
8 cm
16 cm
Answer: 2304.0 cm³
Step-by-step explanation: V = length x width x height
V = 18 cm x 8 cm x 16 cm
V = 2304 cm³
Need to solve some questions can you Help me?
2nd Question
6 ÷ 2 ( 1 + 2 ) = ?
Answer:
Step-by-step explanation:
[tex]6/2 ( 1 + 2 ) = 3(3) = 9[/tex]
For the rotation -757°, find the coterminal angle from 0° ≤ 0 < 360°, the
quadrant, and the reference angle.
To find the coterminal angle for a rotation of -757°, we can add or subtract multiples of 360° until we find an angle between 0° and 360° that is coterminal with -757°.
Adding 360° multiple times:
-757° + 360° = -397° (not coterminal)
-397° + 360° = -37° (not coterminal)
-37° + 360° = 323°
Therefore, the coterminal angle for -757° is 323°.
To find the quadrant in which 323° lies, we can note that 323° is between 270° and 360°, which means it lies in the fourth quadrant.
To find the reference angle for 323°, we can subtract 360° from 323° until we get an angle between 0° and 90°:
323° - 360° = -37° (not in the correct range)
-37° + 360° = 323°
So the reference angle for 323° is 37°.
Help is my work right?
Answer:
32[tex]a^{35}[/tex]
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](2a^3a^4)^{5}[/tex]
= (2[tex]a^{(3+4)}[/tex] )^5
= [tex](2a^7)^{5}[/tex]
raise each term inside the parenthesis to power 5
= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]
= 32[tex]a^{35}[/tex]
Answer:
32[tex]a^{35}[/tex]
Step-by-step explanation:
using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
[tex](2a^3a^4)^{5}[/tex]
= (2[tex]a^{(3+4)}[/tex] )^5
= [tex](2a^7)^{5}[/tex]
raise each term inside the parenthesis to power 5
= [tex]2^{5}[/tex] × [tex]a^{7(5)}[/tex]
= 32[tex]a^{35}[/tex]
In settings where we can assume that each possible outcome is equally likely to occur we are
using theoretical probabilities. We do this when we expect a coin to have the same chance of
landing on heads as it does on tails. We also do this when we assume that if we roll a six sided
die each possible number has the same chance of landing up.
The statement on theoretical probabilities is True.
What is theoretical probability ?Theoretical probabilities, referred to as classical probabilities, are utilized when we can suppose that each conceivable result has an equal chance of happening.
Typically, this is observed in games of luck like tossing a coin or rolling dice, where the chances of every possible outcome are equivalent. Such scenarios permit one to use probability principles and determine the probability of each outcome transpiring.
For instance, with fair coins, it's reasonable to assert that there's an even likelihood for heads or tails, setting both probabilities at 1/2.
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The size P of a certain insect population at time t (in days) obeys the function P = 700e0.03t, After how many days will the population reach 1500?
the population will reach 1500 after about 30.1 days.
After how many days will the population reach 1500?We can solve for the time t by setting P = 1500 and solving for t:
1500 = 700[tex]e^{(0.03t)}[/tex]
Divide both sides by 700:
2.14 = [tex]e^{(0.03t)}[/tex]
Take the natural logarithm of both sides:
ln(2.14) = ln([tex]e^{(0.03t)}[/tex])
Using the logarithm property that ln([tex]e^{x}[/tex]) = x, we can simplify to:
ln(2.14) = 0.03t
Divide both sides by 0.03:
t = ln(2.14)/0.03
Using a calculator, we get:
t ≈ 30.1 days
Therefore, the population will reach 1500 after about 30.1 days.
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Based on this equation, estimate the rating of chips whose cost is $1.10.
Round your answer to the nearest hundredth.
The estimated rating of chips whose cost is $1.10 is 2.25.
Estimating the rating of chips whose cost is $1.10.From the question, we have the following parameters that can be used in our computation:
y = 2.5x - 0.5
To estimate the rating of chips whose cost is $1.10, we can substitute x = 1.10 into the equation y = 2.5x - 0.5 and solve for y.
y = 2.5x - 0.5
y = 2.5(1.10) - 0.5
y = 2.75 - 0.5
y = 2.25
Therefore, the estimated rating of chips whose cost is $1.10 is 2.25. Rounded to the nearest hundredth, it is 2.25.
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Find the measure of
The measure of ∠LPN is 57°.
What is arc?An arc is a segment of a circle in geometry that is typically defined by two endpoints and the arc itself, which is the collection of all points on the circle that are situated between the two endpoints.
The subtendency of an arc can be measured by measuring its central angle.
Since angles inscribed in the same arc are congruent, we have:
m(arc LP) = m(arc NP) = 102° + 144° = 246°
Now, using the fact that the sum of the measures of the arcs of a circle is 360°, we have:
m(arc LM) + m(arc LP) + m(arc NP) + m(arc MN) = 360°
Substituting the known values, we get:
m(arc LM) + 246° + m(arc MN) = 360°
Simplifying, we have:
m(arc LM) + m(arc MN) = 114°
But angles inscribed in the same arc are congruent, so we have:
m(∠LPN) = (m(arc LM) + m(arc MN))/2
Substituting the value we found for m(arc LM) + m(arc MN), we get:
m(∠LPN) = 114°/2 = 57°
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The following describes a classroom environment for doing mathematics ". Which one does not fit
Group work and group discussion are discouraged is a factor that does not fit into the environment for doing mathematics
How is the environment for doing mathematicsThe mathematics scope can differ contingent upon a person's exact circumstances in addition to their individual preferences. As a whole, however, math is customarily studied and exercised within tranquil and absorbed settings that allow for intensive thought processes. A few typical conundrums for executing mathematics tasks encompass:
Libraries: Many mathematicians affectionately flock to libraries for their serene environment furthermore the availability of learning materials and related informational sources. University-focused facilities usually brag extensive selections of mathematics books as well as magazines.
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nangle
In order to justify your general statement above (to give a reason why it is true), construct the angles A, B
and C of triangle 1 around point M as in the diagram below.
H
Are [MN] and [ML] on the same straight line?
Answer:
MN and ML are on the same straight line.
The winner of a contest will be blindfolded and then allowed to reach into a hat containing 29 $1 bills and 7 $100 bills. The winner can remove 4 bills from the hat and keep the money. Find the probability that the winner will pull out at least 1 $100 bill. (See Example 5 in this section. Round your answer to the nearest tenth of a percent.)
The probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
What is probability?The probability of an event occurring is determined by the number of favorable outcomes divided by the total number of possible outcomes.
In this problem, the favorable outcome is that the winner will pull out at least one $100 bill, while the total number of possible outcomes is the number of ways to select 4 bills from the hat, which is 36.
Thus, the probability of the winner pulling out at least one $100 bill is calculated by dividing the favorable outcome by the total number of possible outcomes.
Since there are 7 $100 bills in the hat, the favorable outcome is 7. The total number of possible outcomes is 36, which is calculated by using the formula nCr, where n is the total number of objects and r is the number of objects selected.
In this case, n = 36 and r = 4, so the equation is 36C4.
Thus, the probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.
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I am in need of this to be answered~
Transform this sentence into NNF:
~(~(P&~Q)v(R&~S))
Please answer, step by step to the answer.
Thank you!
~(~(P&~Q)v(R&~S)) transformation of this statment into NNF is ((~P v Q) & (~R v S))
How to transform the statement by using NNF?The transformations used to turn the given sentence into NNF:
Using the equivalence, remove the implication: p → q ≡ ~p ∨ q
≡ (((P&~Q)) & ~(R&~S))
Use De Morgan's law: ~(p ∨ q) ≡ ~p & ~q, and ~(p & q) ≡ ~p ∨ ~q
≡ ((~P v Q) & (~R v S))
Elimination by double negation:~~p ≡ p
≡ ((~P v Q) & (~R v S))
The resulting sentence, ~(~(P&~Q)v(R&~S)) is in NNF (Negation Normal Form), which limits negations to atomic propositions (P, Q, R, S) and logical connectives ¬, ∧, and ∨.
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