13. Which equation represents y = x2 - 10x + 30 in vertex form?
y = (x - 5)2 + 5
y = (x – 5)2 + 55
y = (x – 5)2 - 5
y = (x - 5)2 + 30

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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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 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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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 value of y is less than or equal to 0 (y ≤ 0).

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

4y + 1/5 ≤ 4/5

We have to find the value of y.

Subtract 1/5 from both sides,

4y + 1/5 - 1/5 ≤ 4/5 - 1/5

               4y ≤ 3/5

Multiply both sides by 1/4

4y x 1/4 ≤ 3/5 x 1/4

y ≤ 3/20

y ≤ 0.15

Hence, the value of y is less than or equal to 0 (y ≤ 0).

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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 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 function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t

A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.

The area Julian's carpet covers = 160 square feet

The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.

A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;

Time, t (minute)    [tex]{}[/tex]    Area remaining to be cleaned (square feet), A(t)

0          [tex]{}[/tex]                              160

1          [tex]{}[/tex]                               151

2          [tex]{}[/tex]                              142

3          [tex]{}[/tex]                              133

4          [tex]{}[/tex]                              124

5          [tex]{}[/tex]                              115

The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c

Where;

m = The slope = (151 - 160)/(1 - 0) = -9

c = The y-intercept  The value of the function when the input (time) is zero, which is 160

c = 160

x = The number of minutes that elapse, t

y = The number of square feet remaining after t minutes, A(t)

Plugging in the above value, we get;

A(t) = -9·yt + 160

The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t

The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;

A(t) = 160 - 9·t

A(t) = 160 - 0.1^t

A(t) = 160·(0.1)^t

A(t) = 160·(0.9·t)

A(t) = 160 - 0.9·t

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c. √49  and  d. _³√125  are irrational numbers .

RATIONAL NUMBERS

A rational number is a number that can be written in the form p/q , where p and q are integers and  q ≠ o.

IRRATIONAL NUMBER

An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.

a.  √27 = 5.196152.

Do you think the decimal part stops after 5.196152? No, it is never-ending. Therefore, it is a non-terminating decimal with non-repeating numbers.

The number 5.1961524227... can't be written in p/q form. So √27 is an irrational number.

b . The number 5.1961524227... can't be written in p/q form. So it is an irrational number.

c. The number √49 can be written in p/q form as 7/1 . So √49 is an irrational number.

d. The number 3√125 can be written in p/q form as 5/1 . So it is an irrational number.

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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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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:

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.

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:

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 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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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

Answer:

140.69

Step-by-step explanation:

I hope this helps

Answer:

equal 3/8 or 0.375 siuuuuu

Based on the definition of isosceles triangle, the value of x is: 25.

An isosceles triangle has two base angles that are equal and are opposite two equal sides.

The image shows an isosceles triangle that is inscribed in the circle. Therefore, the two base angles will each equal (2x - 5).

To find the value of x, create the equation below:

2(2x - 5) + 90 = 180

4x - 10 + 90 = 180

4x + 80 = 180

Subtract 80 from both sides:

4x + 80 - 80 = 180 - 80

4x = 100

Divide both sides by 4:

4x/4 = 100/4

x = 25

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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 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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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:

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].

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

-15

Step-by-step explanation: your welcome

Answer: y = -x + 5

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

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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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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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 probability that the child will choose a number that is not a multiple of 9 is 90%.

Probability refers to the chance or likelihood that an expected outcome occurs when multiple developments or events could have happened.

Probability describes the ratio between expected favorable outcomes and possible outcomes.

Probability as a ratio is described as a fractional value when it is not 100% certain or uncertain.

In such cases, probability hovers between zero and 1.

The multiples of 9 from 1 through 50 are five (9, 18, 27, 36, and 45).

The other numbers from 1 to 50 are 45 (50 - 5).

The probability of choosing a multiple of 9 is 10% (5/50 x 100).

The probability of choosing a number that is not a multiple of 9 is 90% (45/50 x 100) or (1 - 0.05).

Thus, the probability that the child chooses a non-multiple of 9 between 1 and 50 is 90%.

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