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The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

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a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).

b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.

By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]

As per the given percentage of tax and discount, the final cost of the milk is $3.8186

The term percentage in math is known as a relative value indicating hundredth parts of any quantity.

Here we have given that You buy a gallon of milk that costs $3. 50.

And here we also know that the milk is discounted for 10% off.

Here we have also have to pay tax of 6. 25% on the discounted price.

First we have to calculate the discounted prices, that can be obtained by the following calculation,

=> 3.50 - [3.50 x 10/100]

=> 3.50 - [3.50 x 0.1]

=> 3.50 - 0.35

=> 3.15.

Now, we have to calculated the tax for the price of the milk,

=> 3.50 + [3.50 x 6.25/100]

=> 3.50 + [3.50 x 0.0625]

=> 3.50 + 0.2186

=> 3.8186.

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There is very strong evidence to reject the null hypothesis, and to conclude that the machine gives radiation doses lower than the maximum on the label.

Hypothesis testing is a statistical method used to test a claim or a hypothesis about a population parameter, based on a sample of data. The goal of hypothesis testing is to determine whether there is enough evidence in the sample data to support or reject a claim about a population.

A t-test is a type of statistical hypothesis test that compares the mean of a sample to a known population mean. There are different types of t-tests, depending on the design of the study and the number of samples being compared.

To test the claim that the machine gives a radiation dose lower than the maximum on the label (5.00 milliroentgens), we can use a one-sample t-test. A one-sample t-test compares the mean of a sample to a known population mean (in this case, the maximum on the label). The null hypothesis for this test is that the mean radiation dose given by the machine is equal to or greater than the maximum on the label (5.00 milliroentgens). The alternative hypothesis is that the mean radiation dose given by the machine is less than the maximum on the label.

The test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (4.23 - 5.00) / (1.91 / sqrt(46)) = -4.05

We can use a t-distribution table to find the p-value associated with this test statistic. With 45 degrees of freedom (sample size - 1), the p-value for t = -4.05 is extremely low, much less than 0.001, the significance level commonly used in hypothesis testing.

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A nation cannot have a comparative advantage in the production of every good. Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. The opportunity cost of producing 1 orange for Alpha and Beta, respectively, are: 0.5 apples; 0.25 apples.

A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.

Here,

A country cannot have a competitive advantage in producing every good. Alpha can generate 18 oranges or 9 apples per hour, whilst Beta can produce 16 oranges or 4 apples per hour. The opportunity cost of producing one orange for Alpha and Beta is 0.5 apples and 0.25 apples, respectively.

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In Chapter 3 of "The Strange Case of Dr. Jekyll and Mr. Hyde," we see how Utterson's investigation and how Jekyll's addiction to his dark side starts to unravel.

In this chapter, Dr. Jekyll's friend and lawyer, Mr. Utterson, becomes increasingly concerned about the strange goings-on surrounding his friend and his association with the mysterious Mr. Hyde. Utterson begins to investigate the relationship between the two men, and discovers that Jekyll has made a will leaving all of his property to Mr. Hyde. Utterson also discovers that Jekyll and Hyde have the same handwriting, and becomes convinced that Jekyll is hiding something.

As Utterson continues to dig, he is eventually able to piece together the truth of the situation: Jekyll has been using a potion to transform himself into the violent and evil Mr. Hyde. Jekyll reveals to Utterson that he has been struggling for a long time with his dual nature and that the potion allows him to temporarily indulge his darker impulses without fear of discovery. Utterson urges Jekyll to give up the potion, but Jekyll refuses, saying that he is powerless to stop using it.

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A and E are the vowels that theoretical probability was closet to the experimental probability.

The probability is 0.1685%

Probability:

Probability defines the probability of an event occurring. There are many real world situations where we need to predict the outcome of an event. We may or may not be certain about the outcome of an event. In such cases, I say that this event may or may not occur. Probability in general has excellent applications for making probability-based predictions in games and economics, and it also has widespread applications in this emerging field of artificial intelligence. The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative. The formula for calculating the probability of a

event is:

probability (event) = favorable outcome/total outcome

Now,

According to the Question:

N vowels = N(A) + N(E) + N(I) + N(O) + N(U)

                =9 + 12 + 9 + 8 + 4

                =42

The total number of letters is:

1×5+2×10+3×1+4×4+6×3+8×1+9×2+12×1=100

This is because dragging the tile reduces the number of vowels and the total number of letters.

p =42×41×...×36100×99×...×94

= 5916335104300

≈ 0.1685%

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Answer:B or A depending on if it went per year or overall

Step-by-step explanation:100 137, 137-100=37

37/5=7.4

Answer:

48

Step-by-step explanation:

if 3;12

12;X

so 3x=12 X 12

so x =48

Answer:

48 yd^2

Step-by-step explanation:

We can cut this shape into 4 squares which areas are all 4x3 or 12. Therefore, we add 12 four times to get 48.

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Answer:

Step-by-step explanation:

x=11

y=14

Answer: 3987.8cm³

Step-by-step explanation:

Volume of a cylinder = πr²h

where

π = 3.14

r = diameter / 2 = 10in/2 = 5inches

h = height = 20in

Volume = πr²h

= 3.14 × 5² × 20

= 3.14 × 25 × 20

= 1570inches³

Since 1 inch = 2.54cm

1570 inch = (1570 × 2.54) = 3987.8cm³

Therefore, the volume of the cylinder is

3987.8cm³ cubic centimeters.

An imaginary number is produced when we square a negative number.

The value of I is -1.

This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.

Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.

The value of I is -1.

The concept of complex numbers is understood using this value of i.

x2 plus 1 equals zero in a quadratic equation.

x2 = -1

x = √-1

The imaginary portion is shown as -1.

I = √-1

i2 = -1

An imaginary number can be squared to get a negative value, as was previously discussed.

I = √-1

both sides being square

i2 = -1

An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.

Real numbers include 10, -20, 3, and other like values.

The integers 2i, -5, -i, etc. are examples of imaginary numbers.

Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.

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Answer:

12x-3

Step-by-step explanation:

Perimeter is : 3*(4x-1)

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.

To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:

Write the number in base 2, 8, or 16 and the corresponding base 10 place values.

Multiply each digit by its corresponding place value and add the results.

For example, to convert the base 10 number 11.011 to a base 10 number:

Write the number and the corresponding base 10 place values: 11.011

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

As the number is already in base 10, it does not need to be converted. The value is 11.011

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Explanation:

Her original balance starts off at $32. After making the $60 purchase, her balance becomes 32-60 = -28 dollars. We wouldn't say 60-32 = 28 because the expense is larger than her balance.

Being in the negative territory means Emily is in debt to the bank, until she can get her balance back to $0 or higher. Since they charge her $3 a day for being in the negative area, and her balance is like this for 7 days, then they charge a total of 7*3 = 21 dollars.

So the -28 will drop to -28-21 = -49 dollars

If she doesn't want any more charges done, she needs to deposit $49 or more into the account on the 8th day.

The required scale factor that Amir will use to go from Polygon F to G is 1/9.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
Area of polygon F = 36 square units
Area of polygon G = 4 square units

Now,
The scale factor to go from polygon F to polygon G is given as,
SF = Area of polygon G / Area of polygon F
SF= 4/36
SF = 1/9

Thus, the required scale factor that Amir will use to go from F to G is 1/9.

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Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.

Absolute Value Function:

An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values ​​of x and find some ordered pairs.

In mathematics, the absolute value or modulus of the real number x, represented as.

|x| is the non-negative value of x, regardless of sign.

x is positive and |xI =-x}.  For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.

Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.

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Using the information in the table the domain is 4 and the range  [-1,1]

The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis. The y-axis displays the range, which is a collection of possible output values.

The domain is typically listed in the left column and the range is typically listed in the right column in a table like the one below. The domain and range of a relation or function, respectively, can be thought of as the input values (x) and the output values (y), respectively.

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Answer:

93.3% i hope this is right

Step-by-step explanation:

percentage increase= final-original/originalx100

58-30/30x100=93.3333%

Answer:

meter per second(m/s)

Answer:

Hey there! The metric system has a unit called meters per second for measuring speed. It's abbreviated as m/s and it's used to measure how far something travels in a certain amount of time. For example, if something goes 50 meters in 10 seconds, its speed would be 50 m/s / 10 s = 5 m/s. There are other units for measuring speed too, like kilometers per hour (km/h) and centimeters per second (cm/s). It just depends on what you're measuring and how precise you need to be.

________________________________________________________

Well, speed is all about how far something goes in a certain amount of time. So if you increase the distance traveled or decrease the time it takes to travel that distance, the speed will increase. On the other hand, if you decrease the distance traveled or increase the time it takes to travel that distance, the speed will decrease.

There are all sorts of situations where knowing the speed of something is important. For example, if you're driving a car, it's important to know how fast you're going so you can stay safe and follow the speed limits. In sports, measuring speed can help coaches and players improve their performance. And in science, measuring the speed of light or other phenomena can help us better understand the world around us. So as you can see, speed is a pretty important concept!

Answer:

10

Step-by-step explanation:

10/10 For sure. I see that musical ly logo. Good times

Given:

Total number of food cans = 12

Cans of Beets = 8

Cans of corn = 3

Can of beans = 1

To find:

How many distinct orders can the cans be arranged if two cans of the same food are considered identical.

Solution:

To find the distinct ways arrangement, we have a formula:

[tex]\text{Number of distinct ways}=\dfrac{n!}{r_1!r_2!...r_k!}[/tex]        ...(i)

Where, n is the number of objects and [tex]r_1,r_2,...,r_k[/tex] are repeated objects.

Total number of food cans is 12. So, [tex]n=12[/tex].

She has 8 cans of beets. So, [tex]r_1=8[/tex]

She has 3 cans of corns. So, [tex]r_2=3[/tex]

She has 1 can of beans. So, [tex]r_3=1[/tex]

Substituting these values in (i), we get

[tex]\text{Number of distinct ways}=\dfrac{12!}{8!3!1!}[/tex]

[tex]\text{Number of distinct ways}=\dfrac{12\times 11\times 10\times 9\times 8!}{8!\times 3\times 2\times 1\times 1}[/tex]

[tex]\text{Number of distinct ways}=\dfrac{11880}{6}[/tex]

[tex]\text{Number of distinct ways}=1980[/tex]

Therefore, the number of distinct orders to arrange the cans is 1980.

Answer:

Surface area: 18,144m

Volume: 139,968m³

Step-by-step explanation:

Surface area:

72x72 =  5184m on bottom, as well as top

5184+5184= 10368

27x72 for side length =  1944

1944 x 4 sides = 7776

7776+10368 = 18,144m surface area

Volume:

72x72x27 = 139,968m³

Answer: 3 hours and 45 minutes

Step-by-step explanation:

We can see that the first clock is at 10:30 am (the short hand is the hour, and it's pointing at 10, and the long hand is the minutes, and it's pointing at 6, which would mean 30 minutes since you multiply 6 by 5)

The second clock is at 2:15 pm using the same logic.

12:00 is when the time changes from am to pm. So, find the time difference from 10:30 am to 12:00

Subtract 30 from 60, and we get thirty, so after 30 minutes, the time will change from 10:30 to 11:00. Then we have 1 hour from 11:00 to 12:00. This means that from 10:30 to 12:00, the time spent is 1 hour and 30 minutes.

Finally, we add 2 hours and 15 minutes, since that's the second time.

Add both those times together:

1 hour and 30 minutes plus 2 hours and 15 minutes = 3 hours and 45 minutes.

Answer:

4 hours and 45 minutes

Step-by-step explanation:

the first clock shows 10:30am and the second clocks shows to be at 2:15pm

which you count by hours is 10,11,12,1,2 so you went but 4 hours and 45 minutes

Answer for no.2: 800

Step-by-step explanation:

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.

A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.

Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.

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Answer:

1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.

2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.

3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.

4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.

5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.

6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.

7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.

8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.

Answer:

107

Step-by-step explanation:

Sum of all angles is 180

12+BC+61 = 180

73+ BC = 180

73 - 73 + BC = 180 - 73

BC = 107