Which of the following can be used to evaluate the series 8∑k=1 5(2/3)^k-1?

Answer:

12 ounces

Step-by-step explanation:

168 divided by 14 = 12

Answer:33

Step-by-step explanation: The expressions have equivalent values when x + 6

The expressions have equivalent values for any value of x.

When x=10 , both expressions have a value of 33.

Answer:

slope = 11/2

Step-by-step explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7)                Point 2: (-6, -4)

x₁ = -4                              x₂ = -6

y₁ = 7                               y₂ = -4

y₁ - y₂ = m(x₁ - x₂)                               <----- Point-slope form

7 - (-4) = m(-4 - (-6))                            <----- Insert values

11 = m(2)                                             <----- Simplify

11/2 = m                                             <----- Divide both sides by 2

[tex]\huge\boxed{\frac{11}{2}}[/tex]

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are your points:

[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values and simplify to find the answer.

[tex]\dfrac{(-4)-7}{(-6)-(-4)}[/tex]

[tex]\dfrac{-4-7}{-6+4}[/tex]

[tex]\dfrac{-11}{-2}[/tex]

[tex]\boxed{\frac{11}{2}}[/tex]

Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The standard deviation is:

[tex]S = \sqrt{\frac{(b - a)^2}{12}}[/tex].

For this problem, the bounds are:

a = 0, b = 120.

Hence the standard deviation is found as follows:

[tex]S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64[/tex].

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The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

The equation rule for the reflection of the triangle over the line y = -x is given as (x, y) ⇒ (-y, -x)

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The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

In this question we have an algebraic expression to be expanded by means of algebraic properties, the purpose of this handling is to modify the polynomial until its standard form is finally obtained and later we find its factor form by Cardano's method. Now we proceed to show the procedure in detail:

2 · x · (2 · x + 1)² + (2 · x + 1) · (4 · x² - 3)     Given

2 · x · (4 · x² + 4 · x + 1) + (2 · x + 1) · (4 · x²) + (2 · x + 1) · (- 3)      Perfect square trinomial/Distributive property

8 · x³ + 4 · x² + 2 · x + 8 · x³ + 4 · x² - 6 · x - 3     Distributive property/(- 1) · a = - a

16 · x³ + 8 · x² - 4 · x - 3     Distributive property/Definitions of addition and subtraction

(x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242)      Cardano's method/Result

The factored form of the polynomial is (x - 0.556) · (x + 0.528 - i 0.242) · (x + 0.528 + i 0.242).

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The polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0

From the question, we are to divide the given polynomial P(x) by the divisor d(x)

From the given information,

P(x) = x³ + 8

d(x) = x + 2

The division operation is shown in the attachment below.

The quotient, Q(x) = x² -2x + 4

and the remainder, R(x) = 0

We area to express P(x) in the form

P(x) = d(x).Q(x) + R(x)

Thus, we get

x³ + 8 = (x+2)(x² -2x + 4) + 0

Hence, the polynomial P(x) expressed in the form P(x) = d(x).Q(x) + R(x) is x³ + 8 = (x+2)(x² -2x + 4) + 0

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According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.

By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.

Next, we would approximate two points on the line of best fit and then find the slope as follows:

Slope, m = ΔC/Δx

Slope, m = (C₂ - C₁)/(x₂ - x₁)

Slope, m = (400 - 200)/(4000 - 1500)

Slope, m = 0.08.

Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.

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Answer:

Step-by-step explanation:

The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.

Let w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.

  A = LW

  54 = (2w +3)(w)

Rewriting this equation to standard form gives ...

  2w² +3w -54 = 0

  (2w -9)(w +6) = 0 . . . . factored

  w = 9/2, -6 . . . . . . . . . values that make the equation true

Only the positive width makes sense in a geometry problem, so we have ...

  w = 9/2

  length = 2w +3 = 12

The length of the rectangle is 12 meters; its width is 4.5 meters.

Answer:  True

Explanation:  Parallel lines are two lines that lie on the same plane and they never intersect.  

Step-by-step explanation:

x is the number

x = 3y + 2

the square

x² = (3y + 2)² = 9y² + 12y + 4

9y² is a multiple of 3 (because of the factor 9)

12y is a multiple of 3 (because of the factor 12)

4 is 1 more than a multiple of 3 (1×3).

so, the sum of all 3 terms is 1 more than a multiple of 3.

Based on the change in the company stock over the three weeks, the total increase in those three weeks is 1.38%.

assuming the stock has a value of $1, the value in the third week would be:
= 1 x (1 + 5/8%) x (1 + 1/2%) x (1 + 1/4%)

= $1.013809453125

the total increase is:
= (1.013809453125 - 1) / 1

= 1.38%

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Answer:

f¯¹(x)=x²+12x+36

Step-by-step explanation:

[tex]f(x) = \sqrt{x} - 6 \\ substitute \: y \: for \: f {}^{ - 1} (x) \\ y = \sqrt{x} - 6 \\ interchange \: x \: and \: y \\ x = \sqrt{y} - 6 \\ swap \: the \: side \: of \: the \: equation \\ \sqrt{y } - 6 = x \\ move \: the \: constant \: to \: the \: right \: hand \: side \\ \sqrt{y} = x + 6 \\ square \: both \: sides \: of \: the \: equation \\ y = x {}^{2} + 12x + 36 \\ substitute \: f \frac{}{ -1} (x) \: for \: y \\ f {}^{ - 1} (x) = x {}^{2} + 12x + 36 \\ domain \: x∈R[/tex]

Answer:

Step-by-step explanation:

Let the age of Abel is x and age of Asare is y.

Three times the age of Abel is four more than the age of Asare:

And

In three years, the sum of their ages will be 30 years:

We got two equations.

Simplify and solve by substitution:

Find y:

A. (1,4)

EXPALINATION :

IF WE WRITE THE VALUE x = -1 AND y = 4

THEN, y= -8x - 4

4= -8×-1-4

4= 8-4

AND SECOND EQUATION IS : y = x+5

y = -1 +5

y = 4

hence, solved and explained

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Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

Assuming the given relation is:

y + 5x = 0

We can rewrite it to:

y = -5x

Then the inverse will be a function g(x) such that:

y = -5*g(x) = x

Solving for g(x):

g(x) = (-x/5).

Then the inverse of the relation is:

y = -x/5

Remember that an ordered pair is of the form (x, y), then the ordered pairs on the inverse of the relation are (x, -x/5).

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A range of 2 reveals that the smallest and largest data values are 2 units away from each other.

Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.

Range = highest value - lowest value

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The constant of proportionality of our given tables is; 5.

We are given that x and y are proportional, and this means that:

y = r*x

where;

r is the constant of proportionality.

We are given the table;

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair: 35 = r*7

r = 35/7 = 5

For the second pair:

60 = r*12

60/12 = r

r = 5

Thus, we can conclude that the constant of proportionality is 5.

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Answer: 3

Step-by-step explanation:

Hope that helps...........................

The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

In this question we must determine the location of the center and the measure of the radius of a circle. According to Euclidean geometry, diameters are the longest possible chords of a circle. First, we determine the location of the center by definition of midpoint:

(h, k) = (1/2) · (4, 5.5) + (1/2) · (4, 10.5)

(h, k) = (4, 8)

And the radius is found by Pythagorean theorem:

[tex]d = \sqrt{(4 - 4)^{2}+(10.5-5.5)^{2}}[/tex]

d = 5

r = 0.5 · 5

r = 2.5

The location of the center of the circle is (h, k) = (4, 8) and the radius of the circle is equal to 2.5.

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Answer:

14

Step-by-step explanation:

If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.

The list price of the house is $260,869.57

What is a list price?

This is the price the property is valued to sell at in an arm's length transaction in a transaction that occurs between independent parties.

In this case, the property was sold for 92% of its list price, which means the sales price is 92% multiplied by the list price.

sales price=92%* list price

sales price=$240,000

list price=unknown(assume it is X)

$240,000=92%*X

X=$240,000/92%

X=$260,869.57

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Children learning to duplicate patterns when they can identify the rule, that is, when the unit repeats and the pattern becomes predictable is a true statement.

This involves the regularity or repeated way in which something is done or arranged.

Children are very inquisitive and tend to make logical connections when dealing with patterns due to their reasoning skills thereby aiding their learning process.

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Answer:

[tex]2\sqrt{6} +4[/tex]

Step-by-step explanation:

Let x be that unknown number.

From the information given from the question, we can deduce:

[tex]x^{2} -8=8x[/tex]

From here, we can solve for x to find what is the number.

[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)

From here we can use the Quadratic Formula to solve for x.

[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]

In this case,

a = 1, b = -8 , c = -8

We substitute a, b and c to find x.

[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]

(Reject the negative solution)

The correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

In the question, we are given that a researcher uses a random number generator to simulate the results of an experiment and are asked for the appropriate assignment of random digits for its experimental design.

For the assignment to be correct, the probability of the random numbers must be equal to the probability of the experiment.

We analyze each option:

Thus, the correct assignment of digits is D. let 1,3,5,7, and 9 represent flipping heads with a fair coin, and 0,2,4,6, and 8 represent flipping tails with a fair coin, as the probability of heads and tails is 1/2, and that of the assigned digits is 1/2.

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Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .

This can be found by using the Economic Order Quantity.

= √ ( (2 x Setup costs x annual demand) / holding costs for the year)

Solving gives:

= √ ( ( 2 x 33 x 38,016) / 9)

= √278,784

= 528 units

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The quantity reported an equivalent net percentage change of 28 percent.

In this problem we must determine the simple percentage change equivalent to two consecutive percentual changes. The formula that describes the situation is:

1 + r/100 = (1 - 60/100) · (1 + 80/100)

1 + r/100 = 72/100

r/100 = - 28/100

r = - 28

The quantity reported an equivalent net percentage change of 28 percent.

The statement is incomplete. Complete form is presented below:

A quantity is changing. At first it descreased by 60 percent and it increased by 80 percent. What is net change of the quantity in percentage?

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Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given the data in the question;

We substitute the given values into the above equation.

Percentage = ( Part / Whole ) × 100%

Percentage = ( 4554 / 9900 ) × 100%

Percentage = ( 0.46 ) × 100%

Percentage = 46%

Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

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A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.

Correlation is a statistical measure used to measure the linear relationship that exists between two variables.

If the sign of the  correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the  correlation coefficient is, the stronger the linear relationship.

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