differences between mean and median 1. you're given n = 5 measurements: 0, 7, 1, 1, 4. find the mean, median, and mode. show your work (don't use the calculator; show the calculations.) (2 points)

The GCFs of the given polynomials are 4, 7x² and 1

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

Given are some polynomial, we need to find GCF,

a) 12x²-8x+4

12x² = 2×2×3×x×x

8x = 2×2×2×x

4 = 2×2

GCF = 2×2 = 4

b) 7x⁸-14x⁴+21x²

7x⁸ = 7×x×x×x×x×x×x×x×x

14x⁴ = 7×2×x×x×x×x

21x² = 7×3×x×x

GCF = 7×x×x

GCF = 7x²

c) 17x³+15x²-21x+3

17x³ = 17×x×x×x

15x² = 3×5×x×x

21x = 7×3×x

3 = 3×1

GCF = 1

Hence, the GCFs of the given polynomials are 4, 7x² and 1

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A polynomial is even if each term is an even function. f ( x ) = 2 x 4 − 3 x 2 − 5 f(x)=2x^4-3x^2-5 f(x)=2x4−3x2−5. Odd

What is odd and even polynomial?

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The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an [tex]$m \times n$[/tex] matrix on the left side has n free variables.

An augmented matrix is composed of two parts, the left side and the right side. The left side is an [tex]$m \times n$[/tex] matrix, where m is the number of rows and n is the number of columns. The right side is a column of constants. The number of free variables in an augmented matrix is equal to the number of columns in the left side matrix, which is n.

The number of free variables in an augmented matrix depends on the size of the matrix. An augmented matrix with an[tex]$m \times n$[/tex] matrix on the left side has n free variables.

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The area of the shaded region is equal to sin(2).

The shaded region is a sector of a circle with radius r and central angle 2. To find the area of the shaded region, we first need to find the radius of the circle, which is given by r2 = sin(2). Taking the square root of both sides, we get r = sqrt(sin(2)).

Next, we need to find the area of the sector, which is given by:

A = (r^2 * 2) / 2 = r^2

Substituting r = sqrt(sin(2)), we get:

A = (sqrt(sin(2)))^2 = sin(2)

Therefore, the area of the shaded region is equal to sin(2).

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QUESTION CORRECTION: Find The Area Of The Shaded Region. R² = Sin (2Ф).

We know Ms. Langlois has 26 pencils.

We DO NOT know the amount of pencils that Mr.Cox has, we can use the variable "x" to represent Mr.Cox's number of pencils.

An expression is just an expression, not an equation, so it DOES NOT require a "="

The expression could be represented as 26+x

Check the picture below.

[tex]\textit{Law of Cosines}\\\\ \cfrac{a^2+b^2-c^2}{2ab}=\cos(C)\implies \cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C \\\\[-0.35em] ~\dotfill\\\\ \cos^{-1}\left(\cfrac{21^2+32^2-26^2}{2(21)(32)}\right)=\measuredangle J \implies \cos^{-1}\left(\cfrac{ 789 }{ 1344}\right)=\measuredangle J\implies \boxed{54.1^o\approx \measuredangle J}[/tex]

Make sure your calculator is in Degree mode.

The answer indicates that it will take 2.38 yrs to for population to treble in size.

A population is any large group that has at least one resource is common. People do not make up all populations. Population numbers can include, but aren't limited to, people, animals, groups, organizations, buildings, houses, trucks, farms, and things.

Let's call the population after it has tripled "P_triple". Then:

P(t) = 3P(0) = 3 * 95

P_triple = 285

We want to find the time t such that P(t) = 285, so we'll set the two expressions equal to each other:

95 (1.53)^t = 285

Dividing both sides by 95:

(1.53)^t = 3

Taking the natural logarithm of both sides:

t = log(3) / log(1.53)

Approximating using a calculator:

t = approximately 2.38 years

So it will take approximately 2.38 years for the population to triple in size.

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a. The different sequences possible are 1200.

b. The different sequences have all hip, knee, and shoulder surgeries scheduled consecutively are 720.

c. The different schedules begin and end with knee surgery is 6.

(a) To find the number of different sequences, we can use the permutation formula n!/(n-r)!

where n is the total number of surgeries and r is the number of surgeries of each type that we need to schedule.

For knee surgeries, n = 5 (total surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 5!/(5-3)! = 5!/(2!) = 54 = 20.

Similarly, the number of different sequences for hip surgeries is 5!/(5-2)! = 5!/(3!) = 54*3 = 60.

Hence, the total number of different sequences is 20 * 60 = 1200.

(b) To find the number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively, we first need to find the number of sequences for each type of surgery.

For knee surgeries, n = 3 (number of knee surgeries) and r = 3 (number of knee surgeries), so the number of different sequences for knee surgeries is 3!/(3-3)! = 3!/(0!) = 3! = 6.

Similarly, the number of different sequences for hip surgeries is 2!/(2-2)! = 2!/(0!) = 2! = 2.

For shoulder surgeries, the number of different sequences is 5!

Hence, the total number of different sequences with all hip, knee, and shoulder surgeries scheduled consecutively is 6 * 2 * 5! = 720.

(c) In order to find the number of different schedules that begin and end with knee surgery, we first need to find the number of sequences for the middle surgeries.

There are 2 hip surgeries and 2 knee surgeries left to schedule, so the number of different sequences for these surgeries is (2+2-1)!/(2!2!) = 3!/(2!1!) = 3.

Hence, the total number of different schedules that begin and end with a knee surgery is 3 * 2 * 1 = 6.

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The complete question is -

A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.

(a) How many different sequences are possible?

(b) How many different sequences have all hip, knee, and shoulder surgeries scheduled consecutively?

(c) How many different schedules begin and end with knee surgery?

$20 more money the band members need to raise.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totaled in an accident is irreparably damaged.

Here, we have

Given: Band members are selling magazines to raise $150 for a school dance.

= 150 - (25 + 45 + 10 +25 + 15 + 10)

= 150 - 130

= 20

Hence, $20 more money the band members need to raise.

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Answer:

A. The graph of the stock value would start at a low point on the left side of the graph and gradually increase in value as it moves to the right. The line representing the stock value would start to level off and then suddenly drop, representing the quick decrease in value. The line would then level off again and stay the same for the rest of the day.

B. If the stock gradually decreased during the middle of the day, the line on the graph would start at a high point, gradually decrease in value, and then level off.

Answer: Option D

Step-by-step explanation: Given: -2x + 14 + 10x = 34

-2x + 10x + 14 = 34

8x + 14 = 34

8x = 34 - 14

8x = 20

divide both sides by 8

8x/8 = 20/8

x = 5/2

Answer:

To solve this problem, we can use a system of equations. Let x be the number of shoes sold at $66.95 and y be the number of shoes sold at $84.95. We know that:

x + y = 240 (because 240 pairs of shoes were sold in total)

66.95x + 84.95y = 17,652 (because this is the total amount of money earned from shoe sales)

To find the number of each type of shoe sold, we can use substitution method, by solving one equation for one variable and substituting that expression into the other equation.

We can solve the first equation for y:

y = 240 - x

Then we can substitute this expression into the second equation and solve for x:

66.95x + 84.95(240 - x) = 17,652

66.95x + 21,068 - 84.95x = 17,652

-18x = -3,416

x = 176

So, 176 pairs of shoes were sold at $66.95. To find the number of shoes sold at $84.95, we can substitute this value of x into the first equation:

y = 240 - 176 = 64

So, 64 pairs of shoes were sold at $84.95.

In conclusion, we can recover the information and the manager can know that 176 pairs of shoes were sold at $66.95 and 64 pairs of shoes were sold at $84.95.

The number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

The number of monic polynomials of degree n in Fp[x] is pⁿ. In this case, "monic" means that the coefficient of xⁿ is 1.

In Fp[x], there are p possible values for the coefficient of each power of x, from x⁰ to xⁿ. Hence, there are pⁿ possible polynomials of degree n.

The number of polynomials that do not take on the value 0 for x ∈ Fp is pⁿ - 1 because if a polynomial is zero for all values of x in Fp, then it must be the zero polynomial. The zero polynomial is not counted because it is not monic, as it has a coefficient of 0 for the xⁿ term.

So, the number of monic polynomials of degree n in Fp[x] that do not take on the value 0 for x ∈ Fp is pⁿ - 1.

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The compound experiment is the probability of heads on a coin and 4 on a number cube which is P = ( 1/12 )

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability be represented as P

Now , the equation will be

a)

The probability of heads on a coin and 4 on a number cube

Now , the probability of tossing a heads on a coin = 1/2

The probability of rolling a 4 on number cube = 1/6

So , the compound probability P = ( 1/2 ) ( 1/6 )

On simplifying the equation , we get

P = 1/12

b)

The probability of 3 on a six spaced spinner

The value of P = 1/6

c)

The probability of rolling a 6 on a number cube

The value of P = 1/6

d)

The probability of drawing a King from a regular deck of cards

The value of P = 4/52

On simplifying the equation , we get

The value of P = 1/13

Hence , the compound probability is P = 1/12

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Answer:

(x+2)(x−5)(x−4)

Step-by-step explanation: These are the possible roots of the polynomial function. ± 1 , ± 40 , ± 2 , ± 20 , ± 4 , ± 10 , ± 5 , ± 8 Substitute − 2 and simplify the expression. In this case, the expression is equal to 0 so − 2 is a root of the polynomial. Tap for more steps... 0 Since − 2 is a known root, divide the polynomial by x + 2 to find the quotient polynomial. This polynomial can then be used to find the remaining roots. x 3 − 7 x 2 + 2 x + 40 x + 2 Divide x 3 − 7 x 2 + 2 x + 40 by x + 2 . Tap for more steps... x 2 − 9 x + 20 Write x 3 − 7 x 2 + 2 x + 40 as a set of factors. ( x + 2 ) ( x 2 − 9 x + 20 )

The definite integral of x * ln(x) from [tex]x = e^{1/8} \ to \ x = \frac{e^{-1/6}}{2}[/tex]

To find the definite integral of x * ln(x) from x = [tex]e^{(1/8)}[/tex] to x = [tex]e^{(1/6)[/tex] it can be evaluated using integration by substitution.

Let u = ln(x), then du/dx = 1/x and dx = [tex]e^u du[/tex]. The integral becomes:

[tex]\int e^{(1/8)} e^{(1/6) }x \ ln(x) dx = \int e^{(1/8)} e^{(1/6)} e^u u du[/tex]

= [[tex]e^{(2u)[/tex]/2] evaluated at u = ln([tex]e^{(1/6)[/tex]) and u = ln([tex]e^{(1/8)}[/tex]), which gives the final result:

[e[tex]^{(2u)[/tex]/2] evaluated at u = 1/6 - 1/8 = -1/12

[tex]= e^{(-2/12)}/2 = e^{(-1/6)}/2[/tex]

The integral is a mathematical concept that refers to the sum of the values of a function over a specific interval or region. It is a tool used to calculate the area under a curve or the total change in a quantity over a given interval.

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given two positive numbers a and b such that b < a. it turns out that a/b is the same as the ratio (a+ b)/a=b/(a-b)

Integers are a set of counting numbers (positive and negative), along with zero, that can be written without a fractional component. As mentioned above, an integer can be either positive, negative or zero.

All natural numbers are also integers that start from 1 and end at infinity.

All whole numbers are also integers, starting from 0 and ending at infinity.

We have two positive numbers a and b and b less a . the ratio of a and b is the same of (a+b)/a .

a:b=(a+b):a

[tex]a^2=b(a+b)\\[/tex]

(a+b)(a-b)=ab

(a+b):a=b:(a-b)

The ratio of a/b = b:(a+b).

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The final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.

Considering the triangle formed by the ship ∆ABC where A, B and C are the points for; the port, where the ship changes its course, and its final bearing. The final distance "a" of the port from the ship is calculated with cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

a² = 40² + 70² - 2(40)(70)cos82°

a² = 1600 + 4900 - 5600cos82°

a² = 5720.63 {take square root of both sides}

a = 75.63

For the triangle ABC, by sine rule;

a/sinA = b/sinB = c/sinC

75.63/sin82° = 70/sinC

C = sin⁻¹(70 × sin82°/75.63) {by cross multiplication}

C = 66.43

angle C = 60 + 6.43 {60° is an alternate angle with angle 30° at the point B where the ship chenged course and 6.43° is a complementary angle at the 3rd quadrant of point C}

The final bearing of the port from the ship is calculated as;

180° + (90 - 6.43)° = 263.57°

Therefore, the final distance of the port from the ship is 75.63 km and the final bearing of the port from the ship is 263.57° using cosine and sine rules.

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The declaration won't work because the animation name property is missing.

Declaration : linear 5s 3 alternate-reverse

The absence of the animation name attribute prevents the declaration from functioning.

The name of the animation A CSS attribute specifies the names of one or more keyframes at-rules that describe the animation to be applied to an element.

Several keyframe at-rules are supplied as a list of names separated by commas. No properties are animated if the provided name does not match any keyframe at-rule. When setting all animation properties at once, it is frequently convenient to use the shortcut property animation.

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The radius sign () with a little three (3) above it, followed by the number, can be used to represent a number's cube root. For instance, 8's cube root is represented by the symbol 8.

The number that remains the same after being multiplied twice by itself is known as a number's cube root. It can be written as the radical sign () followed by the number and a little three (3) above it. For instance, 8's cube root is represented by the symbol 8. When 8 is multiplied by itself twice (8 x 8 x 8), the result is 8; this is known as "the cube root of 8." In a similar way, 27's cube root can be expressed as 27, which, when multiplied by itself twice, also equals 27. Exponential expressions can also be used to represent cube roots. Because 8's cube root is expressed as 23, the result of multiplying 8 by itself three times (2 x 2 x 2) is also 8. Similarly, 33 can be used to represent the cube root of 27.

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two angles in the triangle are 60°, so the last one must be 60°, since all must add up to 180°, that means the triangle is equilateral

[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3}~ ~~ units^2[/tex]

Answer:

C.

Step-by-step explanation:

It is an equilateral triangle.

DB = 6, AB = 12, DC = height

[tex]DC=\sqrt{(CB)^{2}- (DB)^{2} } =\sqrt{144-36} =\sqrt{108}=\sqrt{(36)(3)} =6\sqrt{3}[/tex]

[tex]A=\frac{(DC)(AC)}{2} =\frac{(6\sqrt{3})(12) }{2} =\frac{72\sqrt{3} }{2} =36\sqrt{3}[/tex]

Hope this helps

Answer:

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

Step-by-step explanation:

cos^2(x) - sin^2(x) = sin(x) can be rewritten as cos^2(x) = sin^2(x) + sin(x)

Using the identity sin^2(x) + cos^2(x) = 1, we can simplify the equation as

cos^2(x) = 1 - cos^2(x) + sin(x)

Solving for cos^2(x), we get

cos^2(x) = (1 + sin(x))/2

Therefore, cos(x) = sqrt((1 + sin(x))/2) or cos(x) = -sqrt((1 + sin(x))/2)

To find the possible values of x, we need to find the values of sin(x) that satisfy this equation.

For the domain [0, 2pi), the range of sin(x) is [-1, 1], so we have:

cos(x) = sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

cos(x) = -sqrt((1 + sin(x))/2) for -1 <= sin(x) < 1

So, the solution is

x = arccos(sqrt((1 + sin(x))/2)) + 2npi or x = pi - arccos(sqrt((1 + sin(x))/2)) + 2npi

where n is an integer.

A hallway having 1000 doors at the end of the process the doors which are open are all the factors of 24 i.e, 24,48,72,96,120,144...

A hallway has 1000 doors named 1 from 1000

So he opens all the doors of the hallway so all the doors are opened.

He decides to close every other door starting with door number 2 so 1st door is open and from 2nd door every alternate door is opened so factor of 2 is all close,

2, 4, 6, 8, 10, 12, 14, 16, 18, 20..................1000.

Then he decides to close very open door and open every close door from door three so,

3 is open it will be closed

6 was close so open

9 was open so it will be close

12 was close the it is open

so on 15,21, 27,33......999 will all be closed,

and all 18, 24, 30.....will be all open

then he walks down the hall and changes every fourth door starting with door 4

so 4 will be open so on

4, 8, 16,20, 28,32, 36,40........so on 1000 will all be open

and 12,24,48,60.............will be closed.

So all the door with factor of 12 i.e.12,24,36,48,60,72...will closed.

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To purchase all the paint, it will cost £ 186.89.

-Following are the formulas for calculating the trapezium's area:

[tex]& A=\frac{1}{2}(a+b) h \\[/tex]

[tex]& a \| b \text { dimensions } \\[/tex]

[tex]& \therefore A=\frac{1}{2}(16+10) \times 7.6 \\[/tex]

[tex]& =98.8 \mathrm{~m}^2[/tex]

-Since 1 litre of paint covers an area of 1.9 sq m, we divide the area of the trapezium by this and multiply by the cost per litre to get the overall cost:

[tex]$& \text { Paint Used }=\frac{\text { Area }}{\text { Paint } / m^2} \\[/tex]

[tex]$& =\frac{98.8}{1.9} \\[/tex]

[tex]$& =52 \text { litres }[/tex]

-We are given that each 5 I tin of paint costs $£ 16.99$. We therefore divide the paint used by 5 and multiply by $£ 16.99$ :

[tex]$& =\frac{52}{5} \\[/tex]

[tex]$& =10.4-. > 11 \text { tins } \\[/tex]

[tex]$& \text { Cost }=11 \times 16.99 \\[/tex]

= £ 186.89

Hence, it will cost £ 186.89 to buy all the paint

Paint is only bought in 5 I tins. Hence, any fractional bit will necessitate the purchase of the whole 5 I tin

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The statement [1,5] = { 1, 2, 3, 4, 5 is False.

In mathematics, there are two ways of representing a set of elements: by using curly braces {} or square brackets []. The curly braces {} are commonly used to represent sets, while square brackets [] are used to represent lists or arrays.

[1,5] is a list, which means it is ordered and has duplicates allowed. On the other hand, {1,5} is a set, which means it is unordered and has no duplicates allowed.

Therefore, [1,5] is not equal to {1, 2, 3, 4, 5} because the former is a list of two elements, while the latter is a set of five distinct elements.

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Introduction:

Probability is a measure of the likelihood that a given event will occur. In this scenario, the event of interest is the fuel tank being empty, given the observation that the battery is flat. Evaluating the probability of this event involves finding the relationship between the fuel tank and the battery, and using this information to calculate the probability that the fuel tank is empty.

Detailed explanation:

To evaluate the probability of the fuel tank being empty given the observation that the battery is flat, we need to use Bayes' theorem. Bayes' theorem states that the probability of event A given event B can be calculated as follows:

P(A|B) = P(B|A) * P(A) / P(B)

Where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the probability of event A, and P(B) is the probability of event B.

In this scenario, event A is the fuel tank being empty, and event B is the battery being flat. To calculate the probability of the fuel tank being empty given the battery is flat, we need to find the values of P(B|A), P(A), and P(B).

Suppose we have the following information:

P(A) = 0.1 (the probability that the fuel tank is empty)

P(B|A) = 0.8 (the probability that the battery is flat given that the fuel tank is empty)

P(B) = 0.05 (the probability that the battery is flat)

Using these values, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B) = 0.8 * 0.1 / 0.05 = 0.16

This means that the probability that the fuel tank is empty given the battery is flat is 0.16.

In conclusion, the probability that the fuel tank is empty given that the battery is flat is lower than the probability that the fuel tank is empty, which was 0.1. This suggests that having a flat battery decreases the likelihood that the fuel tank is empty.

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Mr. Estes paid $136,000 for the SUV after the discount was applied.

Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.

We have the formula,

Selling price = (1 - markdown rate) Original price

Here,

Markdown percentage = 15%

Markdown rate = 15/100 = 0.15

Original price of the car = $160,000

Selling price = (1 - 0.15) × 160,000

                     = 0.85 × 160,000

                     = 136,000

Hence the selling price of the car is $136,000.

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Answer:

Step-by-step explanation: