8 An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.
(a) Work out the gradient of the straight line.
(b) What does the gradient of this line represent?

Answer: 6 units

Step-by-step explanation:

There are two ways to do this. You can either choose 2 points on the graph and find the rise/run, or you can plug them in the formula. Let's choose the two points that are dotted. (1,5) and (0,-1)

Let's first do rise/run.

From (0,-1) to (1,5) the rise is 6 units, and the run is 1 unit. So we just divide that. 6/1 which means the slope is 6 units.

We can also use the formula: m = y2 - y1 / x2 - x1

(0,-1) will be our first coordinate and (0,-1) will be our second coordinate. So 0 is x1 and -1 is y1, 1 will be x2 and 5 will be y2. Now we just plug in the numbers

m=5-(-1)/1-0

m=5+1/1-0

m=6/1

m=6 units

So in both ways we get that the slope is 6 units.

The relation is a function in the first graph.

How to check which relation is function in given graph?

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Answer:

x=1

Step-by-step explanation:

To estimate the proportion of U.S adults who have no confidence at all in the media accurately reporting news, you can use the following steps:

Calculate the total number of adults surveyed by the Gallup organization. You can do this by adding the number of adults who said they had a great deal of confidence, a fair amount of confidence, not a lot of confidence, and no confidence at all:

Total number of adults = 81 + 325 + 397 + 214 = 1017

Calculate the proportion of adults who have no confidence at all by dividing the number of adults who said they had no confidence at all by the total number of adults:

Proportion of adults with no confidence = 214 / 1017

                                                                      = 0.2113

Therefore, the estimated proportion of U.S adults who have no confidence at all in the media accurately reporting news is approximately 0.2113, or 21.13%. This represents the proportion of adults who responded "no confidence at all" to the survey question.

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With enough variables, it is possible to get an R2 value close to 1, even if the variables have no particular meaning in the model - True

If the model has a significant number of variables, it is still possible to obtain an R-squared value that is near to 1, even if the variables have no particular significance. R-squared is a metric used to evaluate how well a model fits data; it has a range from 0 to 1, with 1 denoting a perfect fit.

A high R-squared value does not, however, guarantee that the model fits the data well or that the variables it uses are significant. To ensure that the model accurately represents the underlying relationships in the data, it is crucial to carefully analyze the meaning and relevance of the variables included in the model, as well as other evaluation metrics like residual plots and cross-validation.

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The binary form can be represented as AB or AABB. So the write option is b.

One of the four different kinds of number systems is the binary number system. When used in computer programmes, binary numbers are solely represented by the digits 0 (zero) and 1. (one). Here, the base-2 numeric format is used to express the binary numbers.

Because the binary system is directly implemented in electronic circuits using logic gates, nearly all modern computers and computer-based gadgets employ it internally. A bit is used to describe each digit.

The binary form is a set of alphabetical character that is used to describe a musical piece using two sections of equal length. It can be represented as AB or AABB. So the write option is b.

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The expected winnings are $3 for each time that you play the game.

What is expected winnings?

The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

For an event with the outcomes {x₁, x₂, x₃,...} each one with correspondent probabilities {p₁, p₂, ...}

The expected value (here is equivalent to the expected winnings) is given by:

EV = x₁*p₁ + x₂* p₂ + ...

Here the outcomes are:

Winning $20, this happens if you draw a green marble, and there are:

7 green ones

3 yellow ones

10 black ones.

So 7 out of 20, then the probability is p₁ = 7/20

The second outcome is win $30 if you get a yellow one, there are 3 yellow ones, so the probability is p₂ = 3/10

Finally, you lose $15 if you get a black one, the probability now is

p₃ = 10/20

Then the expected winnings (remember that costs $1 to play, so we need to take that in consideration) is:

W = -$1 + $20*(7/20) + $30*(3/20) - $15*(10/20) = $3

Hence, the expected winnings are $3 for each time that you play the game.

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Answer:The relative change is a fraction that describes the size of the absolute change in comparison to the reference value: relative change = absolute change reference value = new value − reference value reference value . 100 100 = 100%. When a quantity triples in value, its relative change is 2 = 200%.

Step-by-step explanation:

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines. |6| = 6 means “the absolute value of 6 is 6.” |–6| = 6 means “the absolute value of –6 is 6.” |–2 – x| means “the absolute value of the expression –2 minus x.”

Answer:

Step-by-step explanation:

For 30: 1,2,3,5,6,10,15,30
For 21: 1,3,7,21
For 56: 1,2,4,7,8,14,28,56
Because you always go times it by the number. Example is: 1 is always in the factors (Doesn't matter if it's the least common factor or whatever) because whatever you times by 1, it's that answer. Or you can look at the answer, (I'm doing the 30) First, find the middle which is 5 and 6. You times 5 and 6 and it will give you 30. People call it a rainbow, 5x6=30, 3x10=30, 2x15=30, and 1x30=30.

I hope this  helps

Answer: k=4

Step-by-step explanation:

4x²-17x+k=0

Divide both parts of the equation by 4:

[tex]\displaystyle\\\frac{4x^2}{4}-\frac{17x}{4}+\frac{k}{4}=0\\\\x^2-\frac{17}{4} x +\frac{k}{4} =0\\[/tex]

Let one of the roots of this equation be α

Then the other root of this equation is 1/α

Hence,

[tex]\displaystyle\\\alpha (\frac{1}{\alpha })=\frac{k}{4} \\\\\frac{\alpha }{\alpha }= \frac{k}{4} \\\\1=\frac{k}{4}[/tex]

Multiply both parts of the equation by 4:

4=k

Thus, k=4

The required probability is 0.8437 that a dart hitting the board will land in the unshaded area.

The total area of the board = 8 x 8 = 64 square inches

The area of the shaded region = 15 square inches

The probability of landing in the shaded region is the ratio of the unshaded area to the total area.

The unshaded area = 64 - 15 = 54 square inches

So, the required probability is:

P(unshaded) = 54/64 = 0.8437

Thus, the required probability is 0.8437 that a dart hitting the board will land in the unshaded area.

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Answer:

ANS:- 2

Step-by-step explanation:

= (2^2)(2^3/2^4)

= (4)(8/16)

=(4)(1/2)

=4/2

= 2

Answer:

[tex]f(x) > \sqrt{1 -x}[/tex]

which is the third choice

Step-by-step explanation:

We could just plot each and see which plot corresponds to the given graph

However, that is not necessary.

First note that the plot is a dotted line. This means the inequality is either a < inequality or a > inequality. If it were a ≤ or  ≥ inequality, the plot of the line would be a solid line

That eliminates first and last choices

To see which of the remaining two options fits the graph, take a point in the shaded region and see which one satisfies which inequality .

Checking second choice....

Point (0, 2) is in the shaded region
Does (0, 2) satisfy the second choice:  [tex]f(x) < \sqrt{1-x}\;\; ?[/tex]
Let's check by substituting 0 for the value of x
[tex]1-x = 0\; so \; \sqrt{1-x} = \sqrt{0} = 0[/tex]

But the corresponding value of y should be 2, not 0 so this inequality is not satisfied for a point in the shaded region. Eliminate second choice

Third choice is the correct answer

The depreciation schedule for the new machines of University Car Wash, using the activity-based method, is as follows:

Year   Initial Cost   Depreciation    Accumulated    Net Book Value

                                  Expense        Depreciation

1         $267,000        $60,750            $60,750            $206,250

2        $267,000        $24,300            $85,050             $181,950

3        $267,000        $26,325             $111,375            $155,625

4        $267,000        $54,675           $166,050           $100,950

5        $267,000        $50,625          $216,675             $50,325

6        $267,000        $26,325         $243,000             $24,000

A depreciation schedule is a table that shows the annual depreciation expense, the accumulated depreciation over the years, and the net book value of each asset, including the initial cost.

An activity-based method of depreciation uses the machine hours or other activity bases used to determine each year's depreciation expenses.

Cost of machines = $267,000

Residual value = $24,000

Depreciable amount = $243,000 ($267,000 - $24,000)

Estimated useful life = 6 years or 12,000 total hours

Hourly depreciation rate = $20.25 ($243,000/12,000)

Year   Annual Depreciation Expense

1           $60,750 (3,000 x $20.25)

2          $24,300 (1,200 x $20.25)

3          $26,325 (1,300 x $20.25)

4          $54,675 (2,700 x $20.25)

5         $50,625 (2,500 x $20.25)

6         $26,325 (1,300 x $20.25)

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The length of segment IJ is 6 units.

What is a line segment?

A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.

Given that IJ is a midsegment of △LMN.

The line segment IJ is parallel to NL.

Thus the length of IJ is half of NL.

Therefore,

2 × IJ = LN

2 (x + 3) = 3x

2x + 6 = 3x

Subtract 3x from both sides:

-x + 6 = 0

x = 6.

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The percentage for blue balls will be 56% and the percentage for red balls will be 44%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred.

In this situation, there are 4000 balls and 2240 of then are blue while 1760 are red.

The percentage for blue balls will be:

= Number of blue balls / Total balls × 100

= 2240 / 4000 × 100

= 56%

The percentage for red balls will be:

= Number of red balls / Total balls × 100

= 1760 / 4000 × 100

= 44%

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Answer:

  B)  31

Step-by-step explanation:

Given a stem and leaf plot, you want to identify the minimum value.

The values in a stem and leaf plot are ordered with the smallest stems at the top, and the smallest leaves to the left. The smallest value on the plot will be the one at upper left.

The minimum value on this chart has a "stem" of 3 and a "leaf" value of 1. That is the representation of the data value 31.

The minimum temperature shown on the chart is 31.

The value of the expression 2/125x1013 + 2/27x1013 is 91.248.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The expression will be Illustrated as:

2/125x1013 + 2/27x1013

= (0.016 × 1013) + (0.0740741 × 1013)

= 16.208 + 75.04

= 91.248

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Complete question

2/125x1013 + 2/27x1013

Answer:v=2.5

Step-by-step explanation:

isolate the variable by dividing both sides by 5

v=2.5

The option that is not one of the application described is C. Building a bridge.

Origami created through mathematical interpretation and computation is known as mathematical origami, and it has resulted in the modeling of numerous novel origami-based structures outside of the realm of the arts. Furthermore, mathematical origami inspires the creation of new structures and mechanisms in engineering.

Origami-inspired engineering has been used in NASA space equipment, the development of better heart stents, and even DNA folding in microbiology.

Origami-based designs are the use of the ancient art of origami to solve various engineering problems. Regardless of the scale at which they are implemented, origami-based designs are always defined by the laws that govern their geometrical properties at any scale.

Furthermore, for large flat structures, origami allows for the reduction of dimensions while ensuring simple deployment this is especially useful for solar arrays in space applications.

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The Video "The Math and Magic of Origami" describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?  

A.A heart stent

B. A space telescope

C. Building a bridge

D. Air bags in cars

The function is f(x) = 25100(1 + 0.06)ˣ and the estimate fox population in the year 2008 is 40,0005.

It is defined as a function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x

where a is a constant and a>1

It is given that:

The fox population in a certain region has a continuous growth rate of 6 percent per year

f(x) = a(1 + r)ˣ

f(x) = 25100(1 + 0.06)ˣ

Plug x = 8 years

f(8) = 25100(1 + 0.06)⁸

f(8) = 40,0005

Thus, the function is f(x) = 25100(1 + 0.06)ˣ and the estimate the fox population in the year 2008 is 40,0005.

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The required hourly wage of Mr. Freeze is given as $217.8.

Wage is defined as the defined earnings of the worker for their respective work. It can be evaluated in parameters based on degrees of time and difficulty.

Here,
As mentioned in the question,
Mr. Freeze is paid $30 per pound of ice,
it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds.
Total ice he used = 530 pounds,
For 530 pounds of ice Mr. Freeze gets paid,
= 530 × 30
= $15900

Now, Divide the whole amount for a pound of ice by the total hours Mr. Freeze works so we get the hourly wage.
hourly wage,
= 15900 / 73
= $217.8

So, Mr. Freeze gets paid of $217.8 hourly.

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Answer:

s = 1000 + 15m

Save $10,000 equation: 10,000 + 15 m

Months it takes to save = 600 months

Step-by-step explanation:

You first deposit the $1000 your uncle gave you and then, each month, you add $15. So the first month the account will have,

1000 + 15

After the second month, it will have,

1000 + 15 + 15

And so on. Therefore, the equation that models your savings s after m months is,

s = 1000 + 15m

If we want to find how many months it will take to save $10,000 we have to solve the equation for s = 10,000:

10,000 = 1000 + 15m

To solve it, subtract 1000 from both sides of the equation,

10,000 - 1000 = 1000 - 1000 + 15m

9000 = 15m

And divide both sides by 15,

9000/55 = 55m/55

600 = m

It will take 600 months to save $10,000.

Answer:

  (300 ÷ 5) + (35 ÷ 5)

Step-by-step explanation:

You want an expression that has the same value as 335÷5.

The given division expression can be rewritten as ...

  [tex]335\div5=\dfrac{335}{5}\\\\=\dfrac{300+35}{5}=\dfrac{300}{5}+\dfrac{35}{5}\\\\=\boxed{(300\div5)+(35\div5)}[/tex]

Answer:

  (7)  (2, 4)

Step-by-step explanation:

You want to know which of the offered points is closest to the point of intersection of the two graphed lines.

The point of intersection can be read from the graph as approximately (2 1/3, 3 3/4). The nearest grid intersection to that point is (2, 4), which is the last point on the list of choices.

  (2, 4) is closest to the actual solution

__

Additional comment

You can see this, too, by graphing the offered choices. There are none closer than (2, 4).

The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given trinomial,

a² + 2a - 3 = 0

a² + 2a = 3

Add 1 on both sides,

a² + 2a + 1 = 3 + 1

(a + 1)² = 4

(a + 1)² - 4 = 0

As per the given trinomial,

a² - 2a - 8 = 0

a² - 2a = 8

Add 1 on both sides,

a² - 2a + 1 = 8 + 1

(a - 1)² = 9

(a - 1)² - 9 = 0

As per the given trinomial,

p² + 16p - 22 = 0

p² + 16p = 22

Add 64 on both sides,

p² + 16p + 64 = 22 + 64

(p + 8)² = 86

(p + 8)² - 86 = 0

Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".

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Answer:

10

Step-by-step explanation:

100 = 10 x 10 = 10^2

n^2  = 10^2

n = 10