Find the average in this list of numbers: -20, 15, 30, -45

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

4x^3+x^2-20x-5

Step-by-step explanation:

f(x)=4x+1 and g(x)=x^2-5

(fg)(x) = f(x) *g(x)

         = (4x+1) *(x^2-5)

FOILing

First 4x*x^2 = 4x^3

outer 4x*-5 = -20x

inner 1 * x^2 = x^2

last 1 * -5 = -5

Add them together

         = 4x^3 -20x+x^2-5

Put the terms in order from greatest power to least power

         =4x^3+x^2-20x-5

Answer:

the answer for your question is 1200pi

Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

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a) There are 450 3-digit even numbers.

b)There are 225 3-digit numbers with an odd sum of digits.

c)there are 4,500 5-digit even numbers that remain the same when their digits are reversed.

a) To determine the number of 3-digit even numbers, we need to consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and third digits, we have 10 choices each (0 to 9) since they can be any digit.

Since the number needs to be even, the last digit must be one of {0, 2, 4, 6, 8}. Therefore, there are 5 choices for the last digit.

To find the total number of 3-digit even numbers, we multiply the number of choices for each digit: 9 * 10 * 5 = 450.

Therefore, there are 450 3-digit even numbers.

b) To determine the number of 3-digit numbers with an odd sum of digits, we can consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and third digits, we have 10 choices each (0 to 9) since they can be any digit.

To ensure odd sum of digits, we can have one of the following combinations:- Odd + Odd + Odd = Odd

- Odd + Even + Odd = Odd

- Even + Odd + Odd = Odd

Therefore, the possible combinations for the sum of the second and third digits are: {1, 3, 5, 7, 9}.

For the first digit, there are no restrictions, so we have 9 choices.

For the second and third digits, we have 5 choices each (from the set {1, 3, 5, 7, 9}).

To find the total number of 3-digit numbers with an odd sum of digits, we multiply the number of choices for each digit: 9 * 5 * 5 = 225.

Therefore, there are 225 3-digit numbers with an odd sum of digits.

c) To determine the number of 5-digit even numbers that remain the same when their digits are reversed, we need to consider the choices for each digit.

For the first digit, we have 9 choices (1 to 9) since the number cannot start with 0.

For the second and fourth digits, we have 10 choices each (0 to 9) since they can be any digit.

For the third digit, since it needs to remain the same when reversed, it must be an even digit. Therefore, we have 5 choices (0, 2, 4, 6, 8) for the third digit.

For the fifth digit, it must be the same as the first digit to ensure the number remains the same when reversed. Therefore, there is only 1 choice the fifth digit.

To find the total number of 5-digit even numbers that remain the same when their digits are reversed, we multiply the number of choices for each digit: 9 * 10 * 5 * 10 * 1 = 4,500.

Therefore, there are 4,500 5-digit even numbers that remain the same when their digits are reversed.

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Answer:

9/4

Step-by-step explanation:

2 1/4 = 4x2+1/4 = 9/4

The population density varies across the regions, with Region A having the highest density and Region B having the lowest density.

The table is given as follows:

                     Population       Area (km²)

Region A:        20,178              521

Region B:        1,200              451

Region C:       13,475              395

Region D:        6,980              426

To calculate population density, we divide the population by the area:

Region A: Population density = 20,178 / 521 ≈ 38.72 people/km²

Region B: Population density = 1,200 / 451 ≈ 2.66 people/km²

Region C: Population density = 13,475 / 395 ≈ 34.11 people/km²

Region D: Population density = 6,980 / 426 ≈ 16.38 people/km²

Based on these calculations, we can conclude the following about the population density:

Region A has the highest population density with approximately 38.72 people/km².

Region C has the second-highest population density with approximately 34.11 people/km².

Region D has a lower population density compared to Region A and Region C, with approximately 16.38 people/km².

Region B has the lowest population density with approximately 2.66 people/km².

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Answer:

Hello Mate! Ans : Yes, number x = 9.688888...... is rational number.

The polar coordinates for point A (-2, 5) are

\((r, \theta) = (\sqrt{2^2 + 5^2}, \tan^{-1}\left(\frac{5}{-2}\right)) \\\\\approx (5.39, 112.62^\circ).\)

The polar coordinates for point B (1, -8) are

\((r, \theta) = (\sqrt{1^2 + (-8)^2}, \tan^{-1}\left(\frac{-8}{1}\right)) \\\\\approx (8.06, -81.87^\circ).\)

To convert cartesian coordinates to polar coordinates, we need to determine the distance from the origin (r) and the angle (θ) the point makes with the positive x-axis.

For point A (-2, 5):

1. Calculate the distance from the origin using the distance formula:

\(r = \sqrt{(-2)^2 + 5^2} \\\\= \sqrt{4 + 25} \\\\= \sqrt{29} \\\\\approx 5.39.\)

2. Calculate the angle θ using the arctangent function:

\(\theta = \tan^{-1}\left(\frac{5}{-2}\right) \\\\\approx 112.62^\circ.\)

For point B (1, -8):

1. Calculate the distance from the origin:

\(r = \sqrt{1^2 + (-8)^2} \\\\= \sqrt{1 + 64} \\\\= \sqrt{65} \\\\\approx 8.06."\)

2. Calculate the angle θ:

\(\theta = \tan^{-1}\left(\frac{-8}{1}\right) \\\\\approx -81.87^\circ.\)

Since the point is in a different quadrant, we report the angle as negative. To convert it to a positive angle, we can add 360°:

\(-81.87^\circ + 360^\circ \approx 278.13^\circ.\)

Thus, the polar coordinates for point A are approximately (5.39, 112.62°) and for point B are approximately (8.06, 278.13°).

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According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.

The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.

Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.

The derivative of y with respect to x is given by:

dy/dx = 1.05

This means that for each additional minute purchased, the cost will increase by $1.05.

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Answer: 2

Step-by-step explanation:

5-(6-3)

5-(3)

2

Answer:

2

Step-by-step explanation:

First you need to take away the 5 and set it to the side then take the (6-3) and subtract the 3 from the 6 which gives you 3.

Next you need to subtract 3 from 5 giving you the answer of 2.

Answer:

56

Step-by-step explanation:

The sum of the exterior angles is 360 degrees, so:

50+75+x+x+x+67=360

192+3x=360

3x=168

x=56

The factored form of the trinomial 3x² + 11x - 4 is (3x - 1)(x + 4). The correct option is A).

To factor the trinomial 3x² + 11x - 4, we need to find two binomials that multiply to give the trinomial. We can use a method called the AC method to do this.

First, we need to find two numbers that multiply to give the product of the first and last coefficients of the trinomial, which are 3 and -4, respectively. These numbers are 12 and -1.

Next, we need to rewrite the middle term of the trinomial as the sum of two terms whose product is equal to the product of the two numbers we just found. So, we rewrite 11x as 12x - x.

Now, we can rewrite the trinomial as 3x² + 12x - x - 4, and factor it by grouping the first two terms and the last two terms

(3x² + 12x) - (x + 4)

= 3x(x + 4) - 1(x + 4)

= (3x - 1)(x + 4)

So, the two factors are (3x - 1) and (x + 4). The correct answer is A).

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--The given question is incomplete, the complete question is given

" Please help!

Factor the trinomial 3x^2+11x-4. Which of the following is a factor?

(3x - 1)(x + 4)

(3x + 1)(x - 4)

(x - 1)(3x + 4)"--

Hence option (B) is a correct choice and rest all other options are incorrect

1/b^2 ∑ (-1)^k(t^2/b^2)^k                                        
                             

Step-by-step explanation:

 Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r

S=a/1 - r                                          

Wherever the common ratio r falls within the interval (-1,1)

When the given series is compared to the infinite sum:

First term=a
Common ratio=r
S=  a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:

Hence option (B) is a correct choice.

What are real numbers simple definition?

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.

INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k

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On solving the provided question, we can say that - Area enclosed by the square and the circle= 400 - 314 = 86 ft sq

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Side of the square =20feet

Therefore,

Radius of the inscribed circle= 20/2 = 10 feet

Area of square=20 X 20 = 400 feet sq.

Area of circle=\(\pi * r^{2} \\\pi * 10*10\\3.14*100\\314 ft sq\)

Area enclosed by the square and the circle= 400 - 314

                                                                           = 86 ft sq

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Answer:

If 3x + 8x + 4x = 6x + 63, then what is 5x + 23?

Step-by-step explanation:

Answer:

\(3y+5x=11\)

Answer:

  y +3 = 5(x +2)

Step-by-step explanation:

You want the equation of a line with slope 5 through the point (-2, -3).

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y +3 = 5(x +2) . . . . . . line with slope 5 through point (-2, -3)

__

Additional comment

This can also be written as ...

  y = 5x +7 . . . . . . . . . subtract 3 and simplify

<95141404393>

The amount that each charity gets is $25.

The charity raise simply define as we raise funds in the form of small amounts of money from a huge crowd of people within a specific period of time.

For example, if 100 people donate $50 each to your crowdfunding campaign in two weeks, you will be able to raise $5000.

To find the amount that each charity got, we have to divide the total charity amount raised in the proportion given, i.e., 1/6.

Each charity gets 1/6 of the total amount raised, which is $150.

So, we need to divide $150 by 6:

$150 ÷ 6 = $25

Therefore, each charity received $25.

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Answer:The error in #1 is that it should read "3x²•(-2x⁴)=3•(-2)•x²⁴=6x⁸". The error in #2 is that it should read "4a²•3a⁵=4•a²•3•a⁵=12a⁷". The error in #3 is that it should read "x⁶•x³=x⁶•x³=x⁹". The error in #4 is that it should read "3⁴•2³=3⁴•2³=24".

Step-by-step explanation:

easy

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

(3, \(\frac{1}{8}\) )

Step-by-step explanation:

Hi there,

To find the answer to this question, you can simply use a graphing calculator to graph this function. When looking at the values of points along the function, we find that (3, \(\frac{1}{8}\) ) is one of the answer choices.

Hope this answer helps.

Cheers.

To solve equations with fractions and variables in the denominator, we need to eliminate it by moving it to the other side. To do this, we multiply both sides of the equation by the term in the denominator. This will cancel out the fraction and leave us with a simpler equation to solve.

For example, suppose we have the equation (3 + x) / x = 2. To get rid of the fraction, we multiply both sides by x. This gives us: x * (3 + x) / x = x * 2. The x in the numerator and denominator cancel out, leaving us with:

3 + x = 2x. Now we can solve for x by subtracting x from both sides: 3 = x

This is the solution of the equation.

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(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

It would take Ruth 45 hours to do the job alone.

We have,

Let's assume that Ruth takes x hours to do the job alone.

If Jim and Ruth can roof a house together in 20 hours, their combined work rate is 1 house per 20 hours.

We can express this as:

1/20 = (1/x) + (1/36)

To solve for x, we can multiply both sides of the equation by the least common denominator (LCD) which is 36x:

36x/20 = 36x/x + 36x/36

Simplifying further:

1.8x = 36 + x

Rearranging the equation:

0.8x = 36

Dividing both sides by 0.8:

x = 45

Therefore,

It would take Ruth 45 hours to do the job alone.

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Answer:

28 m

Step-by-step explanation:

r = l/a

 = 16/4/7

 = 16*7/4

  = 28

The formula r = (arc length / central angle) is used to calculate the radius of a circle. Consequently, r = (16/4/7) = 4.57 m

1. Multiply the central angle (4/7 rad) by the arc length (16 m).

2. Determine the outcome to determine the circle's radius (r): 16 / 4/7 = 4.57 m

The equation r = (arc length / central angle) can be used to calculate the radius of a circle. With the help of this formula, we can determine the radius of a circle given the length of an arc and its central angle. In this instance, the centre angle is 4/7 rad, and the arc length is 16 m. Divide the arc length by the central angle to get the radius: 16 / 4/7 = 4.57 m. The circle's radius is 4.57 m as a result.

Finding other circle measures is made easier by knowing the radius of the circle. For instance, using the formula circumference = 2r, we can determine the circumference of a circle if we know its radius. Any circle's circumference can be determined using this formula given its radius. The circumference in this instance would be 2 x 4.57 m, or 28.7 m. Furthermore, we may utilise the radius to get the circle's area by applying the formula area = r2. Any circle's area can be determined using this formula given its radius. The area in this instance would be x 4.572 = 66.3 m2.

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

To create function h, function f was translated 2 units to the right, translated 4 units down and reflected across the y-axis.

Step-by-step explanation:

Since f(x) = x^3 is transformed to h(x) = -(x+2)^3-4, by

1. Adding 2 to x in x³ to give f'(x) = f(x + 2) = (x + 2)³.

2. We now translate f(x + 2) down by subtracting 4 from f(x + 2) to give

f''(x) = f'(x) - 4 = f(x +2) - 4 = (x + 2)³ - 4.

3. We now reflect f'(x) across the y-axis by multiplying (x + 2)³ by -1 to get

h(x) = -(x + 2)³ - 4.

Answer:

its 2 to the left, 4 units down, and over the x axis.

Step-by-step explanation:

not my answer just the one from the comments