how are Polynomial and Multiplicity of Zero connected?

There are 30-megawatt hours (MWh) per year of savings the students had identified for computers at the Penn State Mueller Laboratory Building.

"Information available from the question"

How many megawatt hours (mwh) per year of savings did the students identify for computers at the Penn state Mueller laboratory building?

Now, According to the question:

There are 30-megawatt hours (MWh) per year of savings the students had identified for computers at the Penn State Mueller Laboratory Building.

At Pennsylvania State University, an undergraduate class studied an environmental evaluation in one of their laboratory buildings in biology. They want to answer the question, "How is this building like an ecosystem?" Their evaluation result was a report that contains 52-page noting ways to lessen the Mueller Laboratory Building’s environmental footprint in  of water, energy communications, maintenance, renovation, and food usage. The students establish techniques to save an almost $45,500 yearly in the energy cost alone for a building with 123 scientists and backing staff.

Hence, There are 30-megawatt hours (MWh) per year of savings the students had identified for computers at the Penn State Mueller Laboratory Building.

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The number of rolls of a fair six sided die will be  1/6.

A cube (plural "cubes") is a solid with marks on each face. Since the faces are usually all of the same shape, the dual of the Platonic solids and the Archimedean solids is a natural choice. You can "roll" a die by throwing it in the air and letting it rest on one of its faces. Dice are used in many games to choose random numbers to bet on, and are used in board and role-playing games to determine how many squares to move, the outcome of a competition, etc. Coins are a degenerate two-sided case of dice.

In probability theory, an outcome is the possible outcome of an experiment or trial. Each possible outcome of a given experiment is unique, and different outcomes are mutually exclusive (only one outcome occurs in each trial of the experiment). All possible outcomes of an experiment form an element of sample space.

According to the question,

When a dice is thrown, number of possible outcomes =

1, 2, 3, 4, 5, 6 = 6 = n

Here, 6 occurs one time, i.e. m = 1

Thus, Probability of getting a number 6 = 1/6

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For both part (a), the two nonnegative numbers, x and y must be 0 and 20 for the sum of their squares to be as large as possible, and 10 and 10 for the sum of their squares to be as small as possible. For part (b), x must be 20 and y should be 0 for largest possible result, whereas for smallest possible result x must be 0 and y should be 20.

Nonnegative numbers are numbers which are greater than or equal to zero.

For a much straightforward and easy way of solving such questions we can simply use the trial and error method.

For part (a), we can start off by taking both the numbers as 10. The sum of their squares will now be 100. If we take the numbers as 12 and 8, the sum of their squares will be 208. As we can see by increase one of the numbers we get a larger result. Thus, the largest possible values will be 20 and 0, which will give a result of 400. While carrying out this trial and error method we also found out that the minimum result was obtained when both the numbers were 10.

For part (b), a similar approach can be taken. Through trial and error method we observe that  20 + (0)^1/2 gives the largest possible result, whereas 0 + (20)^1/2 gives the smallest possible result.

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B. 5/3 is the evaluation of [tex]log_{8} 32[/tex] using the base conversion method.

using the base conversion - [tex]log_{a} p= \frac{log_{b} p}{log_{b} a}[/tex]

convert the base 8 into the base 2 algorithm

[tex]\frac{log_{2} 32}{log_{2} 8}[/tex]

since 32=[tex]2^{5}[/tex]

then, [tex]log_{2}(32)=5[/tex]

similarly, since [tex]8=2^{3}[/tex]

then, [tex]log_{2} (8)=3[/tex]

this makes our expression 5/3.

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Answer:

5/3

Step-by-step explanation:

The change of base formula says logb b a = [logc c a] / [logc c b].

To evaluate log8 32, you need to use the following equation: log8 32 = x, where x is the unknown value.

This can be rewritten as 8^x = 32.

Solving for x gives x = 5/3.

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The final coordinates of the vertices of quadrilateral A'B'C'D';

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

The coordinates of the quadrilateral ABCD are;

A(-3, 4)

B(-7, -3)

C(-3, -7)

D(-4, -3)

Now, the first sequence of transformation is reflection across the y-axis. Now, the transformation rule for reflection across the y-axis is;

(x, y) → (−x, y) .

Thus, we now have;

A'(3, 4)

B'(7, -3)

C'(3, -7)

D'(4, -3)

It is now translated 9 units left and as such the transformation rule is;

((x + 9), y)

We now have;

A'(12, 4)

B'(16, -3)

C'(12, -7)

D'(13, -3)

It is now translated 5 units up and as such, the final coordinates are;

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

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Answer:

35

Step-by-step explanation:

Answer:

The answer is C, 1.5

Step-by-step explanation:

In order to find the constant ratio for successive y-values, you must divide a term by the preceding term.

7.5/5=1.5

The linear function that relates your distance to the number of seconds is y = Sx, and the graph is attached below.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

The formula for distance covered is given by,

[tex]Distance = Speed \times time[/tex]

Assume the speed is constant,

D = S × t

Assume distance is in y direction and time is in x direction, the equation can be written as,

y = Sx

Suppose my speed of mine is 5 m / s and the speed of my friend's is 10 m/s then the function of distance for my friend,

Y = 10X

And for me

y = 5x

The graph of this is attached below, the red line in the graph is my distance equation and the green line is of my friend.

Therefore, the linear function that relates your distance to the number of seconds is y = Sx.

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Answer:

angle B = 55°

.............

 Third or upper quartile, or 75th percentile, is another name for this group. The figure at which 25% of the responses are higher and 75% of the answers are lower is known as the 75th percentile.

A suitable compromise between representing the great majority of measures and being unaffected by outliers is the 75th percentile. The 75th percentile is a suitable choice for identifying medium- to long-term trends even if it is less steady than the median. Additionally, we believe that when establishing performance budgets, the 75th percentile is the ideal figure to employ.  Although the term "percentile" is frequently used, it lacks a common definition. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall. You may already be aware of your test score of 67 out of 90. But without you know the percentile you fall into, that number has no actual relevance. If you know that you scored in the 90th percentile, it signifies that you outperformed 90% of test-takers.

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Answer: 25 dogs

Step-by-step explanation:

We know that every 4 cats will be with 5 dogs

So

First, take 20 divided by 4 = 5

Then take 5 times 5 = 25 dogs

Answer: Answer is NONE

Step-by-step explanation:

I took the test

The inequality - 2 · x + y > - 4 represents the figure on Cartesian plane.

In this problem we have a picture with a representation of a linear inequality of the form:

y > m · x + b

Where:

By analytic geometry, a line can be generated from the knowledge of the location of two points on Cartesian plane. First, determine the equation of the line:

m · 0 + b = - 4

2 · m + b = 0

b = - 4

2 · m = - b

m = - b / 2

m = 2

Second, write the inequality:

y > 2 · x - 4

- 2 · x + y > - 4

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Answer:

C, D, E, and F

Step-by-step explanation:

C is correct because if you have a negative exponent in the denominator, you can make it positive by flipping the fraction over. Therefore, you end up with the simplified given expression.

D is correct because according to exponent rules, you subtract the exponents when you divide.

E is correct because they both equal 729 when calculated.

F is correct because the given expression equals 729 when calculated.

According to the equation model V=P(1-r)^t, the approximate value of Doug's car after 4¹/₂ years is $9,200.

The equation is a mathematical statement or model that shows that two mathematical expressions are equal.

In this situation, the mathematical expressions equal to each other are V, the car's depreciated value, and P(1-r)^t, which combines variables.

Cost of the new car = $25,000

Depreciation rate per annum = 20%

Value of the car = V

The price paid initially = P = $25,000

The annual rate of depreciation = r

Depreciation period = 4¹/₂ years

Equation model: V=P(1-r)^t

Depreciated value after 4 1/2 years, V = $25,000 (1 - 0.2)^4¹/₂

= $9,158.93

= $9,200

Thus, using the equation model, after 4¹/₂ years, the value of Doug's car has depreciated to $9,200.

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Answer:

post cards cost .06 each and envelopes cost .08 each.

Step-by-step explanation:

Let p = the cost of the post cards

Let e = the cost of the envelopes

15p + 10e = 1.70

e = p + .02  Substitute  p + .02 for e in the first equation

15p + 10(p + .02) = 1.70   Distribute the 10

15p + 10p + .2 = 1.70     Combine like terms

25p + .2 = 1.70  Subtract .2 from both sides

25p = 1.50  Divide both sides by 25

p = .06

Post cards cost .06 each.

Envelopes cost .08 each

Answer:

20%

Step-by-step explanation:

The width of the bumper sticker is 6 1/4 inches .

In order to determine the width of the bumper sticker, the first step is to determine the relationship between the height of the design and that of the bumper sticker.

The relationship can be determined by dividing the height of the bumper sticker by the height of the design.

Proportion of the heights = 3 1/2 ÷ 2

5/2 ÷ 2

= 5/2 x 1/2 = 5/4 = 1 1/4

Now, multiply the proportion of the heights by the width of the design :

Width of the design = 1 1/4 x 5

5/4 x 5/1 = 25/4 = 6 1/4 inches

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Answer: 6 1/4

Step-by-step explanation: stickers that can be custom screen printed. The most common or average size is probably the 3″ X 11.5″

Test c had 60 items

It is the most accurate statement that can be made about the reliability of these tests.

The reason that objective tests include so many items is to increase the reliability of the test.

Reliability Test

It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.

Probability

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

A measure of reliability between two variants of the same test is known as alternate forms reliability. The results of two identical (but distinct) tests are correlated, and a reliability coefficient is computed. If variations in one test's observed results correspond to variations in the scores of an equivalent test, the test is said to be dependable. A psychological test's practise effect which is typical of test-retest reliability, can be mitigated by a survey instrument's alternate-form reliability. The goal is to reword the survey questions in a way that makes them functionally identical, or just rearrange the questions in the first and second surveys of the same respondents.

Test c had 60 items

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The value of f(2) is 4.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), alternative shorthand symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or uncertain.

Given function is

f(x) = x²

Putting x = 2 in the given function:

f(2) = 2²

Putting 2² = 4 in the above function:

f(2) = 4

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The mean number of number of people in passengers cars on the highway is given as follows:

E. 6.28.

The expected value of a discrete distribution is calculated as the sum of each value multiplied by it's respective probability.

The distribution in this problem is given as follows:

Then the expected value before the transformation is given as follows:

E(X) = 0.56 x 1 + 0.28 x 2 + 0.08 x 3 + 0.06 x 4 + 0.02 x 5 = 1.7.

The transformation is given as follows:

Y = 0.75x + 5.

Thus the expected value after the transformation is of:

E(X) = 0.75(1.7) + 5 = 6.28.

Meaning that option E is correct.

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Answer:

no solution

Step-by-step explanation:

The answer is to the 7 1/3 th mark.

Consider the provided question,

Since, in wide cylinder, water rises to 4th mark while in narrow cylinder same amount of water rises to 6th mark.

So, 6th mark on narrow cylinder = 4th mark on the wide cylinder which implies that 3rd on narrow cylinder = 2th mark on the wide cylinder

From the above,

Since, 3rd on narrow cylinder = 2th mark on the wide cylinder that means 1 mark on narrow cylinder is equal to 2/3 the of the 1st mark of the wider cylinder.

Hence the 11th mark of the narrow cylinder is equal to the

11 * 2/3 = 22/3  = 7 1/3 mark of the wider cylinder.

Hence, the correct answer is option to the 7 1/3th mark.

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The greatest amount of sap collected from any one tree is two times.

The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.

Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.

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Correct Question:

The greatest amount of sap collected from any one tree is _____________

9 minutes long will it take for the fire engine to reach the fire .

Given :

if a fire engine is traveling at 40 miles per hour to a fire that is 6 miles away .

we know that ,

speed = distance / time

where

distance = 6 miles

speed = 40 miles / hour

substitute

40 = 6 / times

cross multiplication

40 *  time = 6

time = 6 / 40 hours

converting hours to minutes

= 6 / 40 * 60 minutes

= 6 * 6 / 4

= 36 / 4

= 9 minutes

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Time ∝ 1/Speed

Time = k/Speed

k = Time x Speed

The time taken for the trip for the car moving at 30 mph is 12 hours.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Time ∝ 1/Speed

This can be written as,

Time = k/Speed

k = Time x Speed

Now,

The trip takes 8 hours for a car moving at 45 mph.

This means,

k = 8 x 45

k = 360

Now,

The time taken at the speed of 30 mph.

Time = k / Speed

Time = 360/30

Time = 12 hours

Thus,

The time taken for the trip for the car moving at 30 mph is 12 hours.

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The correct answer is the quotient of six and Nineteen times a number. Option C

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures

Given 6/19n

6/9  can be written as the quotient of six and nineteen multiply by a number

Quotient means that you divide something by another

A quotient means a ratio or one quantity being divided by another, or in algebraic terms (a/b).

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The log notation for 3ˣ = 64 is ㏒₃64 = x as the logarithm is the inverse of exponentiation.

The mathematical expression that is used to represent any exponential relationship in the inverse form is termed as log notation.

We use log notation to determine any unknown values from an exponential equation.

the log notation for above equation is written as

3ˣ = 64

㏒₃64 = x

now we can determine the value of x

hence, the log notation is x= ㏒₃64

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