Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree​ 4; zeros: -2-5i; 4 multiplicity 2

Answer:

1. Circumference of a circle = 2πr or πd (r=radius and d=diameter)

2. Perimeter = 74 feet

3. 2π*5 = 10π

4. π*20 = 20π

Step-by-step explanation:

1. Diameter is equal to radius*2.

2. 25+25+12+12=74

3. Substitute 5 for r in the formula.

4. Substitute 20 for d in the second formula.

A control chart is a visual representation of the various states in a process. The answer is b. True. Control charts are used in quality control and process improvement to monitor and analyze the performance of a process over time.

b. True. A control chart is a graphical tool used to monitor the performance of a process over time. It is a visual representation of the data collected from the process and helps in identifying any patterns or trends that may occur. The chart typically consists of a central line representing the average or target value, and upper and lower control limits representing the acceptable range of values for the process. The data is plotted on the chart, and any points that fall outside the control limits indicate a process that is out of control and may require further investigation. Control charts are commonly used in industries such as manufacturing, healthcare, and finance to ensure that processes are running smoothly and to identify any potential issues early on. Overall, control charts provide a powerful way to monitor and manage processes in a systematic manner.

They help to identify trends, patterns, and variations that may indicate potential issues, allowing for timely corrective actions to be taken.

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From the triangle he value of x is given as 13 units

Trigonometrical ratio of angles is a measure used to determine the sign of an angle. It can be calculated by finding the quadrant in which the angle (n ∙ 90° + θ) or (n ∙ 90° - θ) lies

The ratios are given as SOH CAH TOA

Where

S = sine = opposite/Hypothenuse

C = cosine = Adjacent/Hypothenuse

T = Tangent = Opposite/Adjacent

Tan 59 = x/7.7

x = 7.7 * tan59

Finding the value of tan59

x = 7.7 * 1.6643

x = 12.82 units

In conclusion, the value of x = 13 units

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Mr. Singh had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers. The total number of stickers that there were originally on each sheet is 24.

Let the number of stickers on one sheet be 'a'

So, the number of stickers on three sheets = 3a

Number of stickers given from each sheet = 20

So, total number of stickers given from three sheets = 3 × 20 = 60

Number of stickers left with Mr. Singh = 12

Therefore,

3a - 60 = 12

3a = 12 + 60 = 72

a = 72/3

a = 24

So, the total number of stickers that were there originally on the sheet is 24 and Mr. Singh had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers.

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Answer:

m=n + x/p

multiply through by the LCM

which gives

mp=np+x

group like terms and you'll get

mp - np= x

Answer:

A and D are true statements.

Explanation:

A: Vertical angles are always congruent. This is a property of vertical angles; they are opposite angles formed by the intersection of two lines and are always congruent.

D: All right angles are congruent. This is a property of right angles, which are defined as angles that measure 90 degrees. All right angles have the same measure, so they are congruent to each other.

B: When a pair of lines are cut by a transversal, the corresponding angles are not always congruent. Corresponding angles are only congruent if the lines are parallel.

C: Inscribed angles that intercept the same arc are not always congruent. The measure of an inscribed angle is half the measure of its intercepted arc, so inscribed angles that intercept the same arc will only be congruent if the arcs have the same measure.

The curved surface area of cylinder is,

⇒ 90π m²

We have to given that;

the height of the right cylinder is twice it’s diameter.

Hence, We get;

Diameter = 12 / 2 = 6 m

So, Radius = 6 / 2 = 3 m

So, Lateral surface area of cylinder is,

⇒ 2πrh

⇒ 2π × 3 × 12

⇒ 72π m

And, Curved surface area is,

⇒ 2πr²

⇒ 2π × 3²

⇒ 18π m

Thus, The curved surface area is,

⇒ 72π + 18π

⇒ 90π m²

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There is need to save $3,166.79 each month to build up a 5-month emergency fund over an 18-month period.

To calculate how much you need to save each month to build up a 5-month emergency fund over an 18-month period, follow these steps:

Step 1: Determine your monthly gross income:

Divide your gross annual income by the number of months in a year.

Monthly Gross Income = Gross Annual Income / 12 months

Monthly Gross Income = $52,800 / 12

Monthly Gross Income = $4,400

Step 2: Calculate your monthly savings goal:

Multiply your monthly gross income by the saving percentage allocated for the emergency fund in the 20-50-30 budget model.

Monthly Savings Goal = Monthly Gross Income x Savings Percentage

Monthly Savings Goal = $4,400 * 20%

Monthly Savings Goal = $4,400 * 0.20

Monthly Savings Goal = $880

Step 3: Determine the number of months to save:

Divide the desired number of months to build the emergency fund by the total saving period.

Number of Months to Save = Desired Number of Months / Total Saving Period

Number of Months to Save = 5 months / 18 months

Number of Months to Save = 5 / 18

Number of Months to Save = 0.2778

Step 4: Calculate the monthly saving amount needed:

Divide the monthly savings goal by the number of months to save.

Monthly Saving Amount = Monthly Savings Goal / Number of Months to Save

Monthly Saving Amount = $880 / 0.2778

Monthly Saving Amount ≈ $3,166.79

Therefore, you need to save $3,166.79 each month to build up a 5-month emergency fund over an 18-month period.

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The period of the function f(x) = -2 sin⁡x is 2π. So to summarize, the amplitude of the function is -2 and the period is 2π.

The general form of a sinusoidal function is f(x) = A sin(Bx - C) + D, where A is the amplitude, B determines the period, C is the phase shift, and D is the vertical shift.
For the function f(x) = -2 sin⁡x, we can see that the amplitude (A) is -2, since the coefficient of the sin function is -2. The amplitude represents the maximum distance the graph oscillates above and below the midline, so in this case, the graph oscillates between y = -2 and y = 2.
To find the period (B), we can use the formula T = 2π/B, where T is the period and B is the coefficient of x in the sin function. In this case, B = 1, so T = 2π/1 = 2π.

Therefore, the period of the function f(x) = -2 sin⁡x is 2π. So to summarize, the amplitude of the function is -2 and the period is 2π.

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a) The exact circumference of the circle is given as follows: 20π yd.

b) The approximate circumference of the circle is given as follows: 62.8 yd.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The radius for the circle in this problem is given as follows:

r = 10 yd.

Hence the circumference of the circle is given as follows:

C = 2π x 10

C = 20π yd.

For the approximation, we consider π = 3.14, hence:

C = 20 x 3.14

C = 62.8 yd.

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If p and n are positive integers and p > n. 0, 1, 5, 6, 9, and 11 are the remainders when p² - n² is divided by 15.

To find the remainder whilst (p² - n²) is split with the aid of 15, we are able to think of the expression p² - n² the usage of the distinction of squares method.

The distinction of squares formula states that a² - b² can be factored as (a + b)(a - b).

Applying this method to p² - n²;

p² - n² = (p + n)(p - n)

Now, we recognize that p and n are positive integers and p > n. This way that p + n and p - n are both advantageous integers.

To locate the remainder whilst (p^2 - n^2) is split through 15, we will take a look at the remainders of (p + n) and (p - n) when divided with the aid of 15.

Let's don't forget the viable remainders when dividing an integer by means of 15:

zero, 1, 2, 3, 4, five, 6, 7, eight, 9, 10, 11, 12, 13, 14

Since p + n and p - n are both high-quality integers, the feasible remainders when dividing them by way of 15 could be:

zero, 1, 2, three, 4, 5, 6, 7, eight, 9, 10, eleven, 12, thirteen, 14

Now, permits take into account the viable products of (p + n) and (p - n) while the remainder is multiplied:

0 * 0 = 0

1 * 14 = 14

2 * 13 = 26 (that's equal to eleven modulo 15)

3 * 12 = 36 (that's equal to six modulo 15)

4 * eleven = 44 (that's equivalent to fourteen modulo 15)

5 * 10 = 50 (which is equivalent to five modulo 15)

6 * 9 = 54 (that is equivalent to nine modulo 15)

7 * eight = 56 (that's equal to 11 modulo 15)

8 * 7 = 56 (that is equivalent to eleven modulo 15)

9 * 6 = 54 (that's equal to nine modulo 15)

10 * 5 = 50 (which is equivalent to 5 modulo 15)

11 * 4 = 44 (that's equivalent to fourteen modulo 15)

12 * 3 = 36 (that is equal to 6 modulo 15)

13 * 2 = 26 (that's equivalent to 11 modulo 15)

14 * 1 = 14

From the above merchandise, we will see that (p + n)(p - n) will have remainders of zero, 1, five, 6, 9, and eleven when divided via 15.

Therefore, the feasible remainders whilst () is split through 15 are 0, 1, 5, 6, nine, and 11.

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If the tax rate at this restaurant is 9. 5% and some other person’s sales tax is $5. 69 then their subtotal is $65.58

Here, some other person’s sales tax is $5. 69

Consider that for the amount of 'p' dollars, the sales tax is 9. 5% is $5. 69

Here, the tax rate at this restaurant is 9.5%

This means, 9.5 percent of m dollars is $5. 69

Using percentage formula,

m × (9.5 / 100) = 5. 69

m × 9.5 = 5. 69× 100

m × 9.5 = 569

m = 59.89 dollars

So, their subtotal would be,

m + sales tax

= 59.89 + 5. 69

= 65.58 dollars

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Answer:

  the rule for repeated denominator factors applies

Step-by-step explanation:

You want to know why is there not a separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function.

The rule for repeated denominator factors is that there is a fraction in the partial fraction sum for each power of the denominator factor up to its greatest power.

  A(x)/B(x)^n = a1(x)/B(x) + a2(x)/B(x)^2 + a3(x)/B(x)^3 + ... +an(x)/B(x)^n

This rule applies to cubic factors as well as factors of any other power.

__

Additional comment

The attached calculator display shows an example of a repeated factor.

<95141404393>

There is no separate rule in the partial fraction decomposition key idea for what to do if you have a cubic function in the denominator of a rational function because the general method can be applied to any rational function regardless of the degree of the denominator.

Partial fraction decomposition is the process of decomposing a rational function to a sum of simpler fractions. It is a technique used in the integration and simplification of algebraic expressions. The partial fraction decomposition key idea is a method for separating a rational function into its parts so that it can be more easily manipulated.

1: Factorize the denominator of the rational function into linear factors.

2: Write the partial fraction decomposition of the function as a sum of simpler fractions, with each term having a denominator that matches the factors.

3: Determine the unknown coefficients by equating the coefficients of like terms in the original function and its partial fraction decomposition.

The degree of the denominator does not affect the general method of partial fraction decomposition.

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Answer:

b

Step-by-step explanation:

Standford form is highest exponent to lowest

The length of C'A' is 10 units.

Triangle ABC is dilated by the rule Dy, 5/4

CA = 8

The length of C'A' will be determined by using the formula of scale factor

Scale factor = Dimensions of new figure/ Dimensions of original figure

So, Scale factor = C'A' / CA

(5/4) x CA = C'A'

C'A' = (5/ 4) x 8

C'A' = 10 units

Thus, the length of C'A' is 10 units.

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Answer:

10

Step-by-step explanation:

Edge 2023

The null hypothesis in a chi-square test for goodness of fit involves frequencies for the entire population, not just proportions or frequencies for the sample. c.

In a chi-square test for goodness of fit, the null hypothesis specifies the expected frequencies or counts for different categories in the entire population being studied.

The test compares the observed frequencies in the sample to the expected frequencies under the null hypothesis to determine if there is a significant difference between the observed and expected distributions.

The chi-square test for goodness of fit assesses whether the observed frequencies in the sample deviate significantly from the expected frequencies specified by the null hypothesis for the entire population. The test evaluates if the observed data supports or contradicts the null hypothesis, which assumes that the observed frequencies follow a specific distribution or proportions.

The null hypothesis in a chi-square test for goodness of fit defines the predicted frequencies or counts for various categories in the total population under investigation.

The test determines if there is a significant discrepancy between the observed and predicted distributions by comparing the observed frequencies in the sample to the anticipated frequencies under the null hypothesis.

The chi-square test for goodness of fit determines if the sample's observed frequencies differ noticeably from the null hypotheses' predicted frequencies for the overall population.

The null hypothesis, which holds that the observed frequencies follow a particular distribution or proportions, is assumed in the test, and it is determined if the observed data supports or refutes it.

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Answer:

The answer is down below

Step-by-step explanation:

y=x²-3x-1

y=mx+c=x²-6x+4-(x²-3x-1)

y=3x+3

where slope=3

y-intercept =3

To estimate the chance of getting 12 heads and 13 tails when a coin is tossed 25 times, we can use the binomial probability formula.

The binomial probability formula is given by:

P(x) = (nCx) * p^x * q^(n-x)

Where:

P(x) is the probability of getting x successes,

n is the total number of trials,

x is the number of desired successes,

p is the probability of success on a single trial,

q is the probability of failure on a single trial, which is equal to 1 - p,

and (nCx) is the number of combinations of n items taken x at a time.

In this case, n = 25, x = 12 (number of heads), p = 0.5 (since the coin is fair), and q = 1 - p = 0.5.

Using the binomial probability formula, we can calculate the probability of getting 12 heads and 13 tails as:

P(12 heads) = (25C12) * (0.5^12) * (0.5^13)

Calculating this expression will give us the estimated chance of getting 12 heads and 13 tails when a coin is tossed 25 times.

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The scale factor is 10.

Given that are two triangles which are similar, we need to find the scale factors,

Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.

For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively.

Hence, we can use the scale factor to get the dimensions of the changed figures.

The scale factor (k) = ratio of the corresponding sides,

So,

k = XY / VU

k = 60 / 6

k = 10

Hence the scale factor is 10.

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Step-by-step explanation:

If t and w are inversely proportional, it means that as one variable increases, the other variable will decrease by the same factor. In this case, we have the equation t = 4/w, which means that if we multiply w by a certain factor, t will be divided by the same factor.

If we multiply w by 6, the new value of w will be 6 times the original value:

w' = 6w

To find the new value of t, we can substitute w' into the equation:

t' = 4/w'

t' = 4/(6w)

t' = 2/3w

So we see that t has been divided by 6/1 = 6. Therefore, the value of t will decrease by a factor of 6 if the value of w is multiplied by 6.

The amplitude of the function is 2, and the period is 2π.

To find the amplitude and period of the function f(x) = -2 sin(x), we can use the standard form of a sine function:

f(x) = A * sin(Bx)

where A represents the amplitude and B represents the reciprocal of the period.

Comparing this with the given function f(x) = -2 sin(x), we can see that A = -2.

Now let's find the period of the function:

The general formula for the period of a sine function is given by:

Period = 2π / |B|

In our case, B = 1, so the period is:

Period = 2π / |1| = 2π

Therefore, the amplitude of the function is 2, and the period is 2π.

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Answer:

----------------------

We need to determine the total number of outcomes and the number of favorable outcomes.

Total outcomes:

Favorable outcomes:

To find the probability, divide the number of favorable outcomes by the total number of outcomes:

The matching choice is C.

The final value of the investment after 8 years is approximately $2,346.09.

We can use the formula for compound interest to find the final value of the investment:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = 2000, r = 0.02 (2% expressed as a decimal), n = 4 (compounded quarterly), and t = 8.

Plugging in these values, we get:

A = P(1 + r/n)^(nt)

A = 2,000.00(1 + 0.02/4)(4)(8)

A = 2,000.00(1 + 0.005)(32)

A = $2,346.09

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When the pressure is 2.6 g/m² then the depth is 3.9 m.

Given that the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.

We need to find the depth if the pressure is 2.6 g/m².

So, here we will use the concept of proportionality,

Let the unknown depth be x,

So,

320 / 480 = 2.6 / x

2 / 3 = 2.6 / x

2x = 7.8

x = 3.9

Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.

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The Shannon index value for an area in which only a single species is present is zero. This is because the Shannon index takes into account both species richness (the number of different species present) and evenness (the relative abundance of each species).

The Shannon Diversity Index (H') is used to measure the diversity of species in a given area and is calculated as H' = -Σ(pi)ln(pi), where pi is the proportion of individuals belonging to the i-th species. In an area where only a single species is present, pi would equal 1, meaning that there is no variation in species and only one species is observed.

Therefore, ln(pi) would be 0, and the entire summation would be equal to 0. As a result, the Shannon Diversity Index for an area with only one species would be 0, indicating no diversity in the community.

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The experimental probability of a randomly selected student planning to take auto shop can be found by dividing the number of students.

Who plan to take auto shop (8) by the total number of students surveyed (16):  p(auto shop) = 8/16
Simplifying this fraction, we get: p(auto shop) = 1/2
Therefore, the experimental probability that a randomly selected student plans to take auto shop is 1/2 or 0.5 (as a decimal).

The experimental probability that a randomly selected student plans to take auto shop can be calculated as follows:
P(auto shop) = (number of students planning to take auto shop) / (total number of students surveyed)
P(auto shop) = 8 / 16
By simplifying the fraction, we get: P(auto shop) = 1/2
So, the experimental probability that a randomly selected student plans to take auto shop is 1/2.

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The height of the cylinder whose area is given would be =7.6cm.

To calculate the height of a cylinder, the formula for the area of cylinder should be used and it is given below as follows;

Surface area of cylinder = 2πr²+2πhr

This can also be written as = 2πr(h+r)

surface area = 54cm²

h+r = 9cm

r = ?

54 = 2×2.14×r(9)

54 = 38.52r

r = 54/38.52

r = 1.4

h = 9-1.4 = 7.6cm

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Answer:

41

Step-by-step explanation:

Use the Pythagorean Theorem to find the hypotenuse.

[tex]a^{2} +b^{2} =c^{2}[/tex]

Plug in the values.

[tex]40^{2} +9^{2} =c^{2}[/tex]

Simplify.

[tex]1600+81=c^{2}[/tex]

Add.

[tex]1681=c^{2}[/tex]

Take the square root of both sides.

[tex]\sqrt{1681}=\sqrt{ c^{2}[/tex]

41=c