The graph above is a linear equation that includes the points (-3,-2) and (-1,2). Find the slope of the line. Explain how you arrived at your
answer.

The required linear equation that represents the table is y = -x + 4.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The values of x are 0, 1, 2, 3,

And values of y are 4, 3, 2, 1.

The linear equation that represents the values, can be written as,

y = -x + 4

When the values of x are substitute in the above equation, the values of y are,

At x = 0, the value of y = 4

At x = 1, the value of y = 3

At x = 2, the value of y = 3

And at x = 3 the value of y = 1

Hence, the required linear equation is y = -x + 4.

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Given curves:

See the attached, where both curves and their intersection is shown.

According to this we have:

Answer:

x = 96.05 bushels

p = $2.84

Step-by-step explanation:

Graph the two equations (see attachment).

The market equilibrium is the point of intersection of the graphs for x > 0.

From inspection of the graph, the point of intersection is (96.05, 2.84).

Therefore:

The total distance a baseball player travels is 0 meter from his starting point in the first case when he runs 3 meters forward and then runs 3 meters in the opposite direction.

What is distance ?

A measurement of how far away two things or points are might be quantitative or occasionally qualitative.

If an object covers the same distance in the forward and opposite direction, it will cover 0 meter from his starting point.

It happens because when it covers a distance say 5 Km in forward direction and then, when it goes in the opposite direction with equal distance, it reaches to its starting point from where it was started.

Hence, If the player runs 3 meters forward and then runs 3 meters in the opposite direction, h will be at his starting point or we can say, he will cover 0 meter from his starting point.

However, in all other cases, the distance is not equal in both forward and opposite direction.

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Answer:

f and g share no roots in common

Step-by-step explanation:

The roots of [tex]f(x)=0[/tex] are [tex]x=\pm 3[/tex].

From the graph, the roots of [tex]g(x)=0[/tex] are where the graph of [tex]g(x)[/tex] intersects the [tex]x[/tex] axis, which are at [tex]x=2, 10[/tex].

Answer:

Step-by-step explanation:

You want to identify the equations that are quadratic in form.

A polynomial equation is "quadratic in form" if the powers of the variables are integer multiples of {0, 1, 2}, or some subset of these that includes 2. That is, it will be "quadratic" if some substitution z = f(x) is possible such that the resulting equation in z is a polynomial equation of degree 2.

Term are degrees 0, 2, 4, so this is "quadratic in form". The substitution z=x^2 will give a quadratic in z.

Term degrees are 1 and 4, so this is not quadratic.

The substitution z = (x+5)^2 is suggested by the 4th-power term, but the remaining terms cannot be written as a linear function of z. This is not quadratic.

This is a straight quadratic equation. One could substitute z=2x+4, but that is not necessary. This is "quadratic in form."

Term degrees are 0, 2, 4, so this is "quadratic in form."

Term degrees are 1, 2, 4, so this is not quadratic.

The greatest number of containers is 2⁴ = 16 containers.

Since Mr. Pinello has 80 colored pencils and 64 markers to divide into containers for his class. He wants each container to have the same number of items. To find the number of containers, we need to find the highest common factor (H.C.F) of both numbers.

So, writing both numbers in prime factorization, we have

For the 80 colored pencils,

80 = 2 × 2 × 2 × 2 × 5

= 2⁴ × 5

Also, the prime factorization for the 64 markers, we have

64 = 2 × 2 × 2 × 2 × 2 × 2

= 2⁶

So, the highest common factor is 2⁴

So, the greatest number of containers is 2⁴ = 16 containers.

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Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]

The entire area that is occupied by the flat surfaces of the cylinder's bases and its curving surface is known as the surface area of a cylinder.

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

Diameter is 9 cm, and height is 19 cm,

therefore r = 4.5 cm and height is 19 cm.

A = 2 r² π + 2 r π h

A = 2 * 4.5*4.5 π + 2 ·* 4.5* 19 π

A = 40.5 π + 171 π

A = 211.5 [tex]cm^{2}[/tex]

Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]

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The range of the function y = 1/2 x + 2 is {0, 1, 2}, if the domain of the function is {-4, -2, 0}.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

The given function is,

y = 1/2 x + 2.

Also, the domain of the function is {-4, -2, 0}.

Since, the domain of the functions defines the values of x,

And range defines the value of y in function.

The value of y at x = -4

y = 1/2(-4) + 2 = -2 + 2 = 0

At x = -2,

y = 1/2(-2) + 2 = -1 + 2 = 1

At x= 0,

y = 1/2 (0) + 2 = 2

The values of y are 0, 1 and 2.

Hence, the range of the function is {0, 1, 2}.

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The total maximum electrical work the battery could perform during discharge is 11 kj.

When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is actually a function. Simply drawing a vertical line will reveal whether the graph is a function if it touches it once. The graph is not a function if the vertical line is higher. A function is defined technically as a relationship between a set of possible outputs and a set of inputs, where each input is associated to exactly one outcome.

Given

Work is dependent on power.

Power is function on voltage.

Voltage is linear, according to the query, so:

V(t) = at + V

a = Slope

a = 0.70 - 1.45/3600s

P(t) = V*I = V(t) *I (I= 2850 mA)

Then,

W= ∫03600 P(t) dt

=  ∫03600 ( at +1.45 )*I dt

= I × ∫03600 ( at +1.45 )dt

W= 2.850( a*36002 /2  + 1.45*3600)

W = 11

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Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.

What is Random Variable?

A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )

For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.

a) If the random variable Y has a uniform distribution on the interval (0, 1), then the probability density function (PDF) of Y is given by:

[tex]f_Y(y) = 1 for 0 < y < 1[/tex]

= 0

If we let W = Y, then the PDF of W is simply the same as the PDF of Y, since W and Y are equal. Therefore, the PDF of W is given by:

[tex]f_W(w) = 1 for 0 < w < 1[/tex]

= 0

b) If we let W = VY, where V is a constant, then the PDF of W is given by:

[tex]f_W(w) = f_Y(w/V) / |V|[/tex]

Substituting in the expression for the PDF of Y, we get:

[tex]f_W(w) = 1/|V| for 0 < w/V < 1[/tex]

= 0

If V > 0, then this reduces to:

[tex]f_W(w) = 1/V for 0 < w < V[/tex]

= 0

If V < 0, then the range of w is reversed and the PDF becomes:

[tex]f_W(w) = -1/V for V < w < 0[/tex]

= 0

The normalization factor [tex]|V|[/tex] is necessary because the transformation

W = VY stretches or compresses the original uniform distribution on the interval (0, 1) by a factor of [tex]|V|[/tex].

Hence, Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.

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The length of the hypotenuse of the right triangle is 4.1in

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

In trigonometry, if θ is the angle opposite the 4 in line, then sinθ= opp/hyp

cosθ=adj/hyp

tanθ= opp/adj

to find the hypotenuse

sin80= 4/hyp

hyp= 4/sin80

hyp = 4/0.985

therefore the hypotenuse = 4.1 in

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2000/3

Hope it helps

Mark Brainlist

Answer:

equal 3/8 or 0.375 siuuuuu

Answer:

136 in^2

Step-by-step explanation:

The rectangle withOUT the missing part is 20 X 8 = 160 in^2

  now subtract the 4-12 traingle

           160   -   1/2 (4 X 12) = 136 in^2

Answer:

area of triangle = 1/2bh

= 1/2(4)(20-8)

= 1/2(4)(12)

= 24 in²

area of rectangle = lw

= 20(8)

= 160 in²

answer

= area of rectangle - area of triangle

= 160 - 24

= 136 in²

Step-by-step explanation:

Answer:

answer in image blow

Step-by-step explanation:

The standard deviation of the sample of monthly salaries is 2.74

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

>Standard deviation gauges a dataset's dispersion from its mean.

>It is determined as the variance's square root.

Mean  = [tex]\frac{(8+6+12+11+13)}{5} = 10[/tex]

Variance = [tex]\frac{((8-10)^{2}+(6-10)^{2}+(11-10)^{2}+(13-10)^{2} )}{(5-1)} = 6[/tex]

Standard deviation = [tex]\sqrt{7.5} = 2.7386[/tex]

when rounded off to two decimals 2.7386≈2.74.

The standard deviation of the sample of monthly salaries is 2.74

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Answer:

appt

Step-by-step explanation:

Answer: y = -x + 5

(0, 5), (1, 4), (2, 3), (3 2) ...

a. The response variable in this study is the draft.

The response variable is the variable that is being measured or predicted in a study. It is also known as the dependent variable. The treatments are the standard hitch and the new hitch. The experimental units are the 25 randomly selected points in each plot.

b. Yes, randomization was used properly in this study.

By randomly assigning one plot to use the standard hitch and the other plot to use the new hitch, the researcher is ensuring that any difference in draft observed between the two plots is not due to any other factors besides the hitch.

c. No, replication was not used properly in this study. Replication involves taking multiple measurements of the same treatment to ensure that any observed differences between treatments are not due to random variation.

By only taking 25 measurements of each treatment, it is impossible to determine whether any observed differences are due to the treatment or just random variation.

d. Plot of land is a confounding variable in this experiment.

This is because the two plots may differ in soil type, terrain, and moisture, which can all affect the draft. This means that any observed difference in draft between the two plots may be due to the hitch, but it may also be due to the difference in environment between the two plots.

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The Maid of the Mist is a boat tour at the bottom of Niagara Falls. the fare that will maximize the revenue of the Maid of the Mist boat tours is $30.

Generally, To maximize the revenue of the Maid of the Mist boat tours, we need to find the fare that results in the highest total revenue.

The total revenue is equal to the price of the ticket multiplied by the number of tickets sold. We are given that the boat tour currently charges a fare of $20/each and that for each $1 increase in fare, 20 fewer people will take the trip.

Let's call the number of tickets sold at a given fare "x". We can express the total revenue as a function of the fare as follows:

Total revenue = Fare * x

We are also given that for each $1 increase in fare, the number of tickets sold decreases by 20. We can express this relationship as follows:

x = 500 - (Fare - 20) * 20

Substituting this expression for x into our equation for total revenue, we get:

Total revenue = Fare * (500 - (Fare - 20) * 20)

To find the fare that maximizes the total revenue, we can take the derivative of this function with respect to Fare and set it equal to zero:

d(Total revenue)/d(Fare) = 0 = 1 - (Fare - 20) * 40

Solving for Fare, we find that the fare that maximizes the total revenue is $30.

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The student has completed in Rhythm will be 57.7%

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.

To find,

a) The student has competed in none of the categories is 10.3%

b) The student has competed in all three of these categories is 14.1%

c) The student has competed in Smooth or Standard, but not Rhythm

d)  The student has competed in Rhythm and Standard, but not Smooth is 17.9%

The student has completed in Rhythm will be 57.7%

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Answer:

Below

Step-by-step explanation:

h = height = 0 when it hits the ground

sooooo...

  0 = -16t^2 + 20t + 1200   <==== you equation ommited the t' s  and 20t

           Use Quadratic Formula   a = -16    b = 20   c = 1200

                           to find t = 9.3 s

The best description of a simple random sample of size n from the population of size N is that any method of sampling in which every individual is equally likely to be selected. The correct answer is option C.

Simple random sampling is a kind of probability sampling in which the researcher randomly chooses a subset of participants from a population. Every member of the population has an equal chance of being chosen. Then, the data is collected from as large a percentage as possible of this random subset.

A simple random sample is identical to a random sample. The difference is that in a simple random sample, each member in the population has an equal chance of being selected. With random sampling, each member does not automatically have an equal chance of being selected.

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The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer:

b=4

Step-by-step explanation:

[tex]a^{2}+b^{2}=c^{2}[/tex]

[tex]3^{2}+b^{2}=5^{2}[/tex]

[tex]9+b^{2}=25[/tex]

[tex]b^{2}=16[/tex]

[tex]\sqrt{b^{2}} = \sqrt{16}[/tex]

b=4

Answer:

14

Step-by-step explanation:

[tex]\frac{90n+90n}{n+1}=168 \\ \\ 180n=168n+168 \\ \\ 12n=168 \\ \\ n=14[/tex]

Answer:

Step-by-step explanation:

Let the sum of the original list of n numbers be S. The average of the list is given by:

average = S/n

Since the average is 90, we can write:

90 = S/n

Multiplying both sides by n, we get:

90n = S

After the number 90n is added to the list, the average of the list becomes 168. The sum of the list is now S + 90n. The number of elements in the list is now n+1. The average of the list is given by:

average = (S + 90n) / (n+1)

Since the average is 168, we can write:

168 = (S + 90n) / (n+1)

Multiplying both sides by n+1, we get:

168(n+1) = S + 90n

Substituting for S using the equation S = 90n, we get:

168(n+1) = 90n + 90n

Simplifying, we get:

168n + 168 = 180n

Subtracting 168n from both sides, we get:

168 = 12n

Dividing both sides by 12, we get:

14 = n

Therefore, n = 14.

Answer:

y=2x-2

Step-by-step explanation:

formula for the equation of a line is y=mx+b

formula for slope is (y2 - y1)/(x2-x1)

which makes the slope 2 (m=2)

then calculate for b which is -2

finally the formula is y = 2x - 2

The ratio of the length of the piece of wire to the length of the rope to the length of the piece of string is 6:5:1.5

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Let the length of the rope = x

Length of a piece of wire = (5/6)x

Length of a piece of string = (1/4)x

Length of the piece of string = 4.5cm

This can be written as,

4.5cm = (1/4)x

45/10 x 4 = x

x = 9 x 2

x = 18 cm

Now,

Length of the rope = 18 cm

Length of a piece of wire = 5/6 x 18 = 15 cm

Now,

Length of the rope : Length of a piece of wire : Length of a piece of string

18:15:4.5

We can simplify the ratio as,

Taking out the common factor 3.

6:5:1.5

Thus,

The required ratio is 6:5:1.5

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Answer: The wording may be confusing, but the problem is simple.

All they are asking you to do is to plot those x-y value pairs as data points on a graph. Doing that is very basic to science. In science, you put your data on a chart and look at how it shapes up to draw conclusions.

So your first point has x=325.0 and y=1.10,

your second point has x=348.9 and y=1.40, and so on.

If using pencil and paper, your best bet is to use graphing paper, or at least grid paper. Then your first step would be setting up the scale on the axes. You need to fit points with y values between 0.25 and 1.40, so you may want to set the scale on the y-axis so it covers the range from 0 to 1.6 at least (maybe even 0 to 2). Your x values are between 230.0 and 348.9, so you could set up your x-axis so that it includes 0 to 360 (or 0 to 400). Alternatively, you may not include x values all the way down to zero and set your x scale from 200 to 360 only,

The conclusion that you would draw from your plot is that the power seems to vary linearly with speed. The data points are almost in a straight line. They are not perfectly aligned, of course. There is always some variability in accurate data, but you can see a trend. You could draw a line that seems to fit the points best and use it to predict that the power at 250 rpm would be 0.44 hp for example.

Step-by-step explanation:

The domain is R(-∞,∞) and the range is R(-∞,∞) for this graph.

What do you mean by the domain and range of the graph?

Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.

According to the given question,

We have a given graph in the question.

Now, we can see that line on the graph is covering both sides of the x-axis and y-axis on the graph,

Domain of the graph is  R(-∞,∞).

Range of the graph is  R(-∞,∞).

Therefore, the domain is R(-∞,∞) and the range is R(-∞,∞) for this graph.

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According to the given information the domain of this graph is (− ∞, + ∞)  and the range of this graph 2.

Graphs may be used as another tool for determining the domain as well as range of functions. The domain of something like a graph is made up of each of the input values displayed on the x-axis since the term "domain" refers towards the set of potential input values. The y-axis of a graph represents the potential output values, or range.

In order to identify the numbers of something like the autonomous variable x and acquire the domain, we simply solve the formula y = f(x). Simply put, x=g(y) will determine the function's range once we identify g's domain (y).

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