Total Monthly Cost ($)
Kyle's Monthly Website Costs
y
160
140
120
100
80
60
40
20
0
2 4 6 8 10 12 14 16
Number of Hours of Video Stored
Which equation shows the relationship between the
number of hours of video Kyle has stored on the
website and his total monthly cost in dollars?
y=10x +4
y = 4x+10
y-10x+0.25
Y=0.25x+10

From the question, the first table is not a function while the other two tables are functions.

A function is a correspondence or mapping from a first set of numbers, called the domain of the function, to a second set of numbers, called the range of the function, such that for each member of the domain there is exactly one member of the range.

A function is said to be one-to-one if every y value has exactly one x value mapped onto it, and many-to-one if there are y values that have more than one x value mapped onto them. This graph shows a many-to-one function.

4) We see that all the y-values are the same or equal. Thus, we can say that it is not a function because it doesn't match the definition above.

5) Yes the table describes a function because all input values produces a unique output y-value.

6) Yes, the table represents a function because all input values produces a unique output y-value.

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Predictive analytics may be applied to "Prescriptive analytics," which is a set of techniques that use descriptive data and forecasts to identify the decisions most likely to result in the best performance.

Descriptive analytics focuses on analyzing historical data to understand what has happened in the past and gain insights into patterns and trends. It helps in summarizing and presenting data in a meaningful way.

Prescriptive analytics, on the other hand, goes beyond descriptive analytics by providing recommendations and suggestions for optimal decision-making. It leverages predictive analytics techniques to forecast future outcomes and combines them with business rules, constraints, and optimization algorithms to identify the best course of action.

In the context of predictive analytics, prescriptive analytics helps organizations make informed decisions by considering various potential outcomes and recommending the actions that are most likely to lead to the desired performance.

Therefore, predictive analytics can be applied to prescriptive analytics to leverage descriptive data and forecasts to identify the decisions that are expected to yield the best performance.

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Answer:

Distance between home plate and second base = 127.3 ft (Approx)

Step-by-step explanation:

Given:

Base distance = 90 ft

Find:

Distance between home plate and second base

Computation:

Distance between home plate and second base = √90²+90²

Distance between home plate and second base = √8100 + 8100

Distance between home plate and second base = √16200

Distance between home plate and second base = 127.3 ft (Approx)

Answer:

-16s+40

Step-by-step explanation:

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

Step-by-step explanation:

The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.

To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:

[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]

R2 - 3R1 -> R2
R3 -> R3 + 2R1

[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]

-1/2R2 -> R2

[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]

R3 - R2 -> R3

[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]

We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:

[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]

Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.

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Answer:

Option 3

Step-by-step explanation:

The slope is \(\frac{-2-6}{5-1}=-2\).

The equation of the line through \((x_1, y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

y-6=-2(x-1) is the equation is a point slope form equation for line AB

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

point A, with coordinates (1, 6), and point B, with coordinates (5, -2)

m=-2-6/5-1

m=-8/4

=-2

So slope is -2.

The point slope intercept of line is

y-y₁=m(x-x₁)

y-6=-2(x-1)

Hence y-6=-2(x-1) is the equation is a point slope form equation for line AB

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The equation y = (14 / 3) · x³ - 3 · x² + (4 / 3) · x represent the standard form of the cubic polynomial.

Let suppose that figure given represents a polynomial equation. The function represents an odd function, since y < 0 for x → - ∞ and y > 0 for x → + ∞. The function is perhaps a cubic polynomial, whose standard form is:

y = a · x³ + b · x² + c · x + d

Where:

According to the figure, the polynomial includes the points (x₁, y₁) = (0, 0), (x₂, y₂) = (1, 3), (x₃, y₃) = (- 0.5, - 2) and (x₄, y₄) = (0.5, 0.5). All coefficients are determined by solving the following system of linear equations:

d = 0

a + b + c + d = 3

- (1 / 8) · a + (1 / 4) · b - (1 / 2) · c + d = - 2

(1 / 8) · a + (1 / 4) · b + (1 / 2) · c + d = 0.5

The solution to the system is: (a, b, c, d) = (14 / 3, - 3, 4 / 3, 0)

The standard form of the cubic polynomial is the equation y = (14 / 3) · x³ - 3 · x² - (4 / 3) · x.

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Answer:

x ≈ 14.6

Step-by-step explanation:

Using the sine ratio in the right triangle

sin59° = \(\frac{opposite}{hypotenuse}\) = \(\frac{x}{17}\) ( multiply both sides by 17 )

17 × sin59° = x , then

x ≈ 14.6 ( to 1 dec. place )

Answer:

Step-by-step explanation:

To calculate the length of the training track running around the field, we need to add the lengths of the two semicircles and the rectangle. The rectangle has a length of 84m and a width of 50m, so its perimeter is 2(84m + 50m) = 268m. The semicircles have a diameter of 50m, so their radius is 25m. The perimeter of each semicircle is half of the circumference of a full circle with a radius of 25m, which is 2 x 3.14 x 25m = 157m. The total length of the training track is therefore 268m + 2 x 157m = 582m.

The rule of inference used to arrive at the statements s(y) and c(y) from the statement s(y) ∧ c(y) is called Simplification. Simplification allows us to extract individual components of a conjunction by asserting each component separately.

The rule of inference used in this scenario is Simplification. Simplification states that if we have a conjunction (an "and" statement), we can extract each individual component by asserting them separately. In this case, the conjunction s(y) ∧ c(y) represents the statement "y is a movie produced by Sayles and y is a movie about coal miners."

By applying Simplification, we can separate the conjunction into its individual components: s(y) (y is a movie produced by Sayles) and c(y) (y is a movie about coal miners). This allows us to conclude that there is a movie produced by Sayles (s(y)) and there is a movie about coal miners (c(y)).

Using the Simplification rule of inference enables us to break down complex statements and work with their individual components. It allows us to extract information from conjunctions, making it a useful tool in logical reasoning and deduction.

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Answer:

4 cm

Step-by-step explanation:

Base 6 cm

Area 12 cm²

Formula:

h_b = 2 A/b

Answer:

If he mows 3/20 in 1/6 of an hour he'll mow 18/20 or 9/10 in one hour

which means the ratios are equal

1/6:3/20 = 1:18/20 = 1:9/10

Therefore, Jerry will mow 90% of the lawn in one hour

Step-by-step explanation:

Hope this helps:)...if not then sorry for wasting your time and may GOd bless you

y=4x+64

Explanation:

Two lines are perpendicular if the product of their slopes is -1.

Step 1: Find the slope of the line a

Line a passes through the points (1,-3) and (9,-5)

The slope of line a = -1/4

Step 2: Determine the slope of line b.

Let the slope of line b = k

Since the product of the two slopes is -1:

The slope of line b = 4

Step 3: Find the equation of line b.

Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.

Using the slope-point form of the equation of a line:

Substitute the given values

The equation of line b is y=4x+64.

Virinia used 11.75 cups of flour, which is equivalent to 47/4 cups of flour. This represents a fraction of 47/60 of the total flour she had.

Virinia uses 16/1 (or 16) teaspoons of baking powder per loaf of bread. Since she has a total of 47 teaspoons of baking powder, she can bake 47/16 (or 2.9375) loaves of bread. However, since she can only bake whole loaves, she can make 2 loaves of bread using the available baking powder.

For each loaf of bread, Virinia uses 4 cups of flour. Since she has 15 cups of flour in total, she can bake 15/4 (or 3.75) loaves of bread. However, she can only bake 2 whole loaves, as mentioned earlier.

Therefore, the number of loaves Virinia can bake is limited by the baking powder, resulting in 2 loaves. For these 2 loaves, she uses a total of 2 * 4 = 8 cups of flour.

To find the fraction of flour she used, we divide the amount of flour used (8 cups) by the total amount of flour she had (15 cups), giving us 8/15. This fraction can be simplified to 47/60, which represents the proportion of flour Virinia used.

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P(overall) = 0.2109. The correct option is A) 0.1318.  There might be a calculation error on the answer sheet or in the problem statement itself, as the solution does not match the options provided.

To solve this problem, we need to calculate the probability of selecting 3 red marbles out of 4 marbles drawn with replacement.

Step 1: Find the probability of selecting a red marble.

The box contains a total of 6 red marbles, 8 blue marbles, and 2 yellow marbles. Therefore, the probability of selecting a red marble is:

P(red) = Number of red marbles / Total number of marbles

P(red) = 6 / (6 + 8 + 2)

P(red) = 6 / 16

P(red) = 3 / 8

Step 2: Calculate the probability of selecting 3 red marbles.

To find the probability of selecting 3 red marbles, we need to multiply the probability of selecting a red marble by itself three times since the marbles are drawn with replacement. Therefore, the probability of selecting 3 red marbles is:

P(3 red) = P(red) × P(red) ×P(red)

P(3 red) = (3/8) × (3/8) × (3/8)

P(3 red) = (27/512)

Step 3: Calculate the probability of selecting 1 non-red marble.

Since we are selecting 4 marbles with replacement, the fourth marble must be a non-red marble. The probability of selecting a non-red marble is the complement of selecting a red marble. Therefore, the probability of selecting 1 non-red marble is:

P(non-red) = 1 - P(red)

P(non-red) = 1 - (3/8)

P(non-red) = (8/8) - (3/8)

P(non-red) = (5/8)

Step 4: Calculate the overall probability.

The probability of selecting 3 red marbles and 1 non-red marble can happen in any of the four orders (RRRN, RRRR, RNRR, RRRN). Since the marbles are drawn with replacement, the order doesn't matter. Therefore, we need to consider all possible orders.

P(3 red) and P(non-red) can be arranged in 4 different orders:

P(3 red) ×P(non-red) ×P(3 red) ×P(3 red)

P(non-red) × P(3 red) × P(3 red) × P(3 red)

P(3 red) × P(3 red)× P(non-red) × P(3 red)

P(3 red) ×P(3 red) × P(3 red)× P(non-red)

The overall probability is the sum of these four possibilities:

P(overall) = (27/512) + (27/512) + (27/512) + (27/512)

P(overall) = (108/512)

P(overall) = 0.2109

According to the answer sheet, the correct option is A) 0.1318. There might be a calculation error on the answer sheet or in the problem statement itself, as the solution does not match the options provided.

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Answer:

12.

Step-by-step explanation:

y /x = 6/8 = 3/4

y/x = 18/24 = 3/4

The relation is y = 3/4 x.

So, the missing value is 16 * 3/4

= 12.

Answer:

Alternate interior angles theorem

Step-by-step explanation:

Alternate interior angles theorem

Answer:

I don't know if there is one that says reflexive property, but that is the answer

Step-by-step explanation:

Answer:

f(5) = 22; f(9) = 34

Step-by-step explanation:

f(5) = 3(5) +7

f(5) = 22

f(9) = 3(9) +7

f(9) = 34

Answer:

3 ( 9e + 8)

Step-by-step explanation:

Answer:

3 (9e+8)

Step-by-step explanation:

3 times 9e is 27e

3 times 8 is 24

So 3 (9e+8) is equal to 27e + 24

Answer:

6x square +14x+4

Step-by-step explanation:

hope this helps................

Answer:

6x^2+14x+4

Step-by-step explanation:

6x^2+12x+2x+4

6x^2+14x+4

The vectors x in the null space of A are all those for which Ax = 0. (A). As a result, all that is required to determine whether a vector x is in the null space is to compute Ax and determine whether it is the zero vector, because the null space of an m x n matrix A is a subspace of \(R^{n}\).

Any matrix A's null space is made up of all vectors B such that AB = 0 and B is not zero. A known matrix of size m x n and a matrix that needs to be found of size n x k make up the equation for this equation, which can also be thought of as the solution.

The null space encompasses the whole domain since it is obvious that for Z, a zero matrix, and any vector v in the domain, Zv = 0 results in the zero vector. As a result, the nullity of any matrix with just zeroes would be equal to the number of columns in the matrix, or the domain's dimension.

A null space is also  the vector space.

We know that a null set satisfies the following properties of a vector space.

Now let \(x,y\) ∈ Null (A), ∝ ∈ IR, then

A[ax + y] =  ∝ A(x) + A(y)

A[ax + y] = ∝.0 + 0

A[ax + y] = 0

Thus,

∝x + y ∈ Null (A)

Therefore,

The vectors x in the null space of A are all those for which Ax = 0. (A). As a result, all that is required to determine whether a vector x is in the null space is to compute Ax and determine whether it is the zero vector, because the null space of an m x n matrix A is a subspace of \(R^{n}\).

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We need to find the angle measure of the minor arc which is \(\sf\widehat{AC}\) . We note that the measure of a complete angle is 360 degree. So that ,

Using this :-

\(\sf : \implies \angle ABC + m\angle ABC = 360^o \\\\\sf: \implies 106^o + m\angle ABC = 360^o \\\\\sf: \implies m\angle ABC = 360^o - 106^o \\\\\sf: \implies \red{ m \angle ABC = 254^o }\)

Hence the required answer is 254° .

The price of the widgets for which it should be sold to make the maximum profit is $25.4   .

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We know that the quadratic equation ax² + bx + c ,

If a < 0; then the maximum value of the quadratic equation will be at x = -b/2a .

Given;

a company is selling a widget;

the selling price of each widget is = x

the profit made by the company = y

the equation of profit is given as y = −3x² + 152x − 1150 ,

here a = -3 , b = 152 and c = -1150

In the given quadratic equation we can see that;

a < 0 , so , the maximum will be at;

x = -b/2a

x = -152/2(-3)

x = 152/6

x = 25.333

x ≈ 25.4

Hence, the price of the widget will be $25.4  

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3/5 part of an hour passes in between two times given.

What is fraction?

A fraction represents a vicinity of a full or, a lot of typically, any variety of equal elements. once spoken in everyday English, a fraction describes what number elements of a precise size there ar,

Main body:

The time given are = 4:56 and 5:32

Total time spent between = 4+ 32

                                           = 36 minutes

Total minutes in 1 hour = 60

So parts spent = 36/60

now simplifying we get.

= 3/5

Hence the answer is 3/5 .

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Answer:

10

Step-by-step explanation:

For every lawn mowed, the amount earned increases by 10 dollars

Answer:

Step-by-step explanation:

From the question we are told that:

Initial bearing \(\angle _1=21 \textdegree\)

Initial distance \(d_1=99miles\)

Final bearing \(\angle _2=227 \textdegree\)

Let \(\triangle OAB\) be the perimeter travailed

\(\angle OAB=90+21=111 \textdegree\\\angle ABO=270-227=43 \textdegree\)

Generally the equation for OB using sine rule is mathematically given by

\(OB=99*\frac{sin111}{sin43}\)

\(OB=135.52miles\)

Therefore the helicopter flight on the final leg of its​ journey is

\(OB=135.52miles\)

After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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The correct option is C, Prices have increased about 16-fold over the last 80 years, assuming an average annual U.S. inflation rate of 4 percent.

The inflation rate is a measure of the rate at which the general level of prices for goods and services is rising over a period of time, usually a year. It is typically expressed as a percentage increase or decrease in the average price level of a basket of goods and services over a certain period of time.

Here, the price index is a weighted average of the prices of a specific set of goods and services. The inflation rate is a key indicator of the overall health of an economy, as high inflation can erode purchasing power and reduce the standard of living for individuals, while low or negative inflation can lead to economic stagnation or deflation. Governments and central banks closely monitor inflation rates to ensure that they remain within a targeted range, typically around 2-3% per year, through the use of monetary and fiscal policies.

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In the year 2009, the factory produced 5,249,789 bulbs, while in the year 2010, it produced 624,986 bulbs. The factory produced more bulbs in 2009, with a difference of 4,624,803 bulbs.

To determine in which year the factory produced more bulbs and by how much, we compare the number of bulbs produced in 2009 and 2010. In 2009, the factory produced 5,249,789 bulbs, whereas in 2010, it produced 624,986 bulbs.

To calculate the difference, we subtract the number of bulbs produced in 2010 from the number produced in 2009: 5,249,789 - 624,986 = 4,624,803.

Therefore, the factory produced 4,624,803 more bulbs in 2009 compared to 2010. This signifies that the production output was significantly higher in 2009, indicating a more productive year for the factory in terms of bulb production.

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