Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: 6 (Multiplicity 2); 3i
Enter the expanded polynomial. Let a represent the leading coefficient.
f(x) = a( )

the population will reach 1500 after about 30.1 days.

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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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:

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°.

The probability that the winner will pull out at least one $100 bill is 7/36, or 19.4%.

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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The value of x in the equation is 2.10.

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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An equation of the image of the line after dilation is -30x - 20y = -8.

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:

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.

The unit sales of product A at the monthly break-even point is 193,750 units.

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 four translation rules are defined as follows:

Comparing the equivalent vertices, the translations are given as follows:

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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

Check the picture below.

~(~(P&~Q)v(R&~S)) transformation of this statment into NNF is ((~P v Q) & (~R v S))

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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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]

The estimated rating of chips whose cost is $1.10 is 2.25.

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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Answer:

MN and ML are on the same straight line.

Answer:

17.023413

Step-by-step explanation:17.023413

The correlation coefficient between the minutes the actor appeared shirtless in a film and the film's opening weekend gross is 0.75.

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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The angle that is supplementary to the angle DEA is angle DEC

From the question, we have the following parameters that can be used in our computation:

Also 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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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]

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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For the remaining set of garments, the average per day that they need to be completed would be = 126 sets/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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Group work and group discussion are discouraged is a factor that does not fit into the environment for doing mathematics

The 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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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

The statement on theoretical probabilities is True.

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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Answer:

Step-by-step explanation:

[tex]6/2 ( 1 + 2 ) = 3(3) = 9[/tex]

The measure of ∠LPN is 57°.

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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Answer:

Give me a sec

Step-by-step explanation:

The values of x in the isosceles trapezoids x = 32, x = 10.9 and x = 41

An 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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Answer:

The area of right-angled triangle is 30 cm².

Step-by-step explanation:

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 :

[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]

[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.

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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