⅕(x + 2 ) -¼(2-x) ≥ ⅓ (x + 4) - ¼ ( 5-x)​

Nothing that we can say regarding an we are unsure of whether the terms of an are rising or falling, a passes the Comparison Test and sequence, Since bn, an also converges.

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.

We are unable to comment on an.

This is due to the fact that bn converges, causing a to exceed bn, and as a result, we are unable to determine whether the terms of an are increasing or decreasing.

What can you say about an if a bn for all n? a passes the Comparison Test and converges.

This is due to the fact that since bn converges and a converges since bn, we may infer that the terms of an are likewise decreasing and that an also sequence since bn based on the comparison test.

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The fill ups are as follow.

1. vertical Opposite Angle.

2. alternate Interior Angle.

3. b || c, Co- interior angle.

4.  a || c, corresponding Angle.

5. Linear pair.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

First, <3 = <9 because they vertical Opposite Angle.

Second, <2 = <10 are equal because of alternate Interior Angle.

Third, If <9 and <8 are supplementary then line b || line c because they are Co- interior angle.

Fourth, if <11 = <7 then a || c because they corresponding Angle.

Fifth, < and <6 are supplementary because they are Linear pair of Angle.

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Answer: \:y=-3\frac{1}{2}x

Step-by-step explanation:

pls tell me if its wrong so i can fix it

The required difference in time taken by bob and sam is 0.8 hour.

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Bob can drive 50 miles in 40 minutes.

So, Speed of bob = 50×60/40 = 75 miles/hour

And Sam can drive 90 miles in 105 minutes.

Speed of Sam = 90×60/105 = 51.4 miles/hour

Now/

Time taken by bob(d) = 120/75 = 1.6

Similarly,

Time taken by Sam(e) = 120/51.4 = 2.4

So,

d - e

|1.6 - 2.4|

0.8

Thus,required difference in time is 0.8.

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Answer: The graph of g(x) = 4cosx is a horizontal dilation of the graph of y = cosx by a factor of 4.

To graph the function, we can use the following two points:

(0, 4) which is the point on the midline closest to the origin

(3.14/2, 0) which is the maximum point closest to the first point

We can then use these points to plot the graph of g(x) = 4cosx using the sine tool. It will be horizontal shifted of the graph of y = cos(x) by a factor of 4.

Step-by-step explanation:

Given that each pie requires 6-8 apples, and each batch of applesauce requires 8 apples, it is possible to make approximately 22 apple pies and 24 batches of applesauce from the 264 apples that were picked.

Number in math is a symbol or group of symbols used to represent a numerical quantity. Numbers include both rational numbers, such as integers, fractions, and decimals, and irrational numbers, such as pi and e. The use of numbers in mathematics allows us to represent many different types of mathematical objects, such as sets, functions, and equations. Numbers also have numerous applications in everyday life, such as in finance, engineering, and science.

This would leave 4 apples leftover. It is important to note that the exact number of pies and batches of applesauce that can be made will depend on the size of the apples. If smaller apples are used, more pies and batches of applesauce could be made.

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Answer: It is greater than 4.

Step-by-step explanation: It is equal to 2 root 5. But if you convert to a decimal you get 4.4721 which is greater than 4.

The formula to find the square root is: y=√a

Answer:

Step-by-step explanation:

Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample  selected group of individuals from the neighborhood at random times throughout the day.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

Both the wristband and a conventional blood test were used to measure the blood sugar of a random sample  selected group of individuals from the neighborhood at random times throughout the day.

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Answer: The domain and range is equal to all positive real numbers.

Explanation: The domain and range of the function shown is equal to all positive real numbers because there is no such a value that the function can have an indeterminate situation and also there is no such another positive value that the function cannot have as a result.

The probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.

The probability that their total completion time in the maze for all rats is between 6 and 8 minutes can be calculated using the Binomial Distribution formula. The formula is P = (nCr) * (p^r) * (1-p)^(n-r), where n is the number of trials, r is the number of successes, and p is the probability of success.

In this case, n = 4 (4 rats), r = 2 (completion time between 6 and 8 minutes), and p = 0.5 (50% chance of success). Therefore, P = (4C2) * (0.5^2) * (1-0.5)^(4-2) = 0.375.

This means that the probability that their total completion time in the maze for all rats is between 6 and 8 minutes is 0.375, or 37.5%.

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The system of equations can have an infinite number of solutions when the equations are equivalent.

A system of equations can have infinitely many solutions when the equations are equivalent, meaning that the equations are identical when one is subtracted from the other. When this happens, the system of equations is said to have an infinite number of solutions. To solve a system of equations by elimination with infinitely many solutions, the equations must first be rearranged so that the same variable terms are on one side and the constant terms are on the other. Then, the coefficients of one variable must be made equal by multiplying one or both equations by a constant. After this, the equations can be added together or subtracted from one another and the variable terms will cancel out. This will result in an equation with only the constant terms, which is equivalent to 0=0. This equation is true for all values of the variables, so the system of equations has an infinite number of solutions.

The system of equations can have an infinite number of solutions when the equations are equivalent. To solve the system of equations by elimination with infinitely many solutions, the equations must first be rearranged, the coefficients of one variable must be made equal, and the equations can be added or subtracted so that the variable terms cancel out. This will result in an equation equivalent to 0=0, meaning that the system of equations has an infinite number of solutions.

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Answer: 45°

Step-by-step explanation:

Let the angle be x and its complement be y

Also,

Complement = 1/3 × Supplement

So,

Supplement = 3 × Complement

                     = 3y

According to Question:

I.              x + y = 90°                          -----(1)

II.             x + 3y = 180°                       -----(2)

On subtracting eq (1) from (2) we get

               2y=90°

                 y=45°

Now, From eq (1)

                x + y = 90°  

                 x = 90° - 45°

                 x = 45°

∴ The angle is 45°

The measure of angle ∠WDY is 89° in problem 20.

Two rays (half-lines) that share an endpoint make up an angle. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

Two angles are said to be congruent by this definition if either of their vertex and side coordinates can be rigidly moved to coincide with the other. The angle may be written as AOB or BOA if O is the vertex and A and B are the points on the two sides (and this for any selection of the two points A and B.)

Given that D is the common point of line segments DW, DX and DY

m∠WDX = 2x - 5

m∠XDY = 52

m∠WDY = 5x - 16

to find m∠WDY

m∠WDY = m∠XDY + m∠WDX

5x - 16 = 52 + 2x - 5

5x - 2x = 52 - 5  + 16

3x = 63

x = 63/3

x = 21

m∠WDY = 5(21) - 16

m∠WDY = 89

Thus, the measure of angle ∠WDY is 89° in problem 20.

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They describe a model of an atom with two protons, two neutrons, electron density (orbitals), and two electrons. Now suppose we want to know what the labels A and B stand for.

The nucleus is at the center where the protons and neutrons are arranged. This is supported by his three models: the Rutherford model, the Bohr model and the (now accepted) quantum model.

So the red sphere and the two overlapping spheres in the middle represent protons and neutrons.

The line labeled A with the sphere in brackets represents the nucleus, as it signals both protons and neutrons within the nucleus.

The green blurry circular clouds represent the regions where electrons reside. This is blurry according to the quantum model, which states that the electrons are not in a fixed position, but in the region around the atom. This area is called the trajectory. According to the model, the electron's exact position cannot be determined, which means a blurry cloud.

This white line, which in Bohr's model should be circular where the electrons are, represents the electron orbits and shells identified by the letters L, M, N, and K. The first shell was the L shell.

In the quantum model, this line corresponds to the principal quantum number n (principal energy level). Therefore, the lines leading to brackets overlapping the white lines indicate the main energy levels.

Atoms are neutral because they contain as many electrons as protons around the nucleus.

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Answer:

A: nucleus

B:  electron cloud

Step-by-step explanation:

The probability of a randomly chosen divisor of [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$[/tex].

The prime factorization of [tex]$11!$[/tex] is 11!=[tex]11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$[/tex], so there are [tex]$(2+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1) = (3^{2})(2^{10})$[/tex] divisors of  [tex]$11!$[/tex]

The prime divisors of  [tex]$11!$[/tex] are [tex]$2,3,5,7,11$[/tex], and there are [tex]$(1+1)(1+1)(1+1)(1+1)(1+1) = 2^{5} = 32$[/tex] divisors that are prime.

So the probability of a randomly chosen divisor of  [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$$[/tex]

A common fraction is a way of representing a ratio of two integers, where the numerator (the top part) represents the number of "favorable outcomes" and the denominator (the bottom part) represents the total number of possible outcomes.

In this case, the favorable outcome is a randomly chosen divisor of 11! being prime, and the total number of possible outcomes is the total number of divisors of 11! which is[tex]$(3^{2} )(2^{10})$[/tex]. So the probability of a randomly chosen divisor of 11! being prime can be represented as a common fraction by writing [tex]$\frac{32}{3^{2} \cdot2^{10}}$[/tex], with 32 as the numerator and [tex]$(3^{2})(2^{10})$[/tex] as the denominator.

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When Marcus tests a hair sample from the telogen stage. The result likely to be true about this sample is there will be a nuclear DNA present.

DNA (Deoxyribonucleic acid) is a polymer comprised of two polynucleotide chains that loop around each other to form a double helix having genetic instructions for the development, functioning, growth and reproduction of all known organisms and many viruses. DNA and ribonucleic acid both are nucleic acids.

Moreover, DNA is the information molecule. It holds the instructions for creating other large molecules, called proteins. These instructions are kept inside each of our cells, distributed among 46 long structures called chromosomes.

Hence, DNA is made of chemical structures called nucleotides. These structures are made of three parts: a sugar group, a phosphate group, and one of four types of nitrogen bases.

Hence the correct option is c.

--The given question is incomplete, the complete question is

''Marcus is testing a hair sample from the telogen stage. What is likely to be TRUE about this sample?

A. There will be several medullas present.

B. There will be mitochondrial DNA present.

C. There will be nuclear DNA present.

D. There will be very little DNA present."--

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Roxy can make her goal SMART by deciding an attainable amount of money, diving the total of money in paymets and using the money for emergencies only.

This is a technique to plan and achieve goals based on 5 characteristics:

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Answer:

The slope is 17

Step-by-step explanation:

The slope in a point-slope form equation is always the coefficient of x, which in this case is 17.

Answer: To find out how many days it will take for the family to pay off their credit card balance, we can use the following equation:

Days = (-300) / 33

Solving for Days gives us:

Days = (-300) / 33 = -9

So it will take the family 9 days to pay off their credit card balance, assuming they only spend money on essential items and don't add any more to their debt.

Step-by-step explanation:

The greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}

The property of the set s states that for every element x in s, the arithmetic mean of the set obtained by deleting x from s is an integer.

To understand this property, we can start by considering the case when the set s has only two elements, say x and y. In this case, the arithmetic mean of the set obtained by deleting x from s is y, and the arithmetic mean of the set obtained by deleting y from s is x. As both x and y are integers, this property holds true.

When the set s has three elements, say x, y, and z. The arithmetic mean of the set obtained by deleting x from s is (y+z)/2. as y and z are integers, (y+z) is always even, thus (y+z)/2 is always an integer. The same applies to the arithmetic mean of the set obtained by deleting y and z.

As we can see, this property holds true for any set of distinct positive integers, no matter the number of elements.

Given that 1 belongs to s and that 2002 is the largest element of s, we can use the property of the set to find the greatest number of elements that s can have.

The arithmetic mean of the set obtained by deleting 1 from s is (x+y+z+...+2002)/(n-1) = (x+y+z+...+2002)/n + 1/n. as x, y, z... 2002 are integers, (x+y+z+...+2002) is always an integer, thus (x+y+z+...+2002)/n is always an integer. Then, as 1/n is always an integer, (x+y+z+...+2002)/n + 1/n is always an integer.

Therefore, the greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}

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Answer: 36.5 miles

Step-by-step explanation:

It looks like you have the right idea! You simply need to divide the 438 miles by the 12 days to find the miles traveled per day. This results in 438 / 12 = 36.5

Answer:

the answer would be

0.0256

The imaginary line which divides any shape into two equal halves is known as line of symmetry.

As given in the question,

To divides the given shape into two equal parts :

Therefore, the imaginary line used to divide the given shape into two equal halves is called line of symmetry.

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Solving the provided question, can say can't calculate square root. The solution to this equation could not be determined, quadratic equation can be factorized.

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation we have is ,

[tex]6x^2 = 17x - 42[/tex]

[tex]6x^2 - 17x + 42 = 0\\[/tex]

can't calculate square root. The solution to this equation could not be determined.

so this quadratic equation can be factorized.

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Answer:

50%

1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%.

please mark me as a brainalist

Answer:

Step-by-step explanation:

120 degrees per angle - It says that it's a *regular* hexagon

To steps to construct a line segment that is 1/3 the length of the given segment is:

Draw a line segment CD of any length.

Fix the compass's end on C and pencil on D. This gives the length of CD.

Now divide the length of CD by 3. That is the 1/3 the length of CD.

Draw a line 1. Mark a point A on line 1. Change compass's setting into 1/3 the length of CD, place the compass at A.

Make an arc on the line l which cuts l at B. Now, AB is a copy of CD which is 1/3 the length of CD.

What is line segment?

A line segment is bounded by two definite points on a line. We also can say a line segment is part of the line which connects two points. A line has no endpoints and extends immensely in both the direction but a line segment has two fixed or distinct endpoints.

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Answer:

- 8i

Step-by-step explanation:

the Fundamental theorem of algebra states that

A polynomial of degree n has n roots, some may be complex

• Complex roots occur as conjugate pairs

For this polynomial of degree 4, there are 4 zeros

given 8i , 6 , - 6 , then the fourth root is the conjugate of 8i , that is - 8i

Answer:

x(x+1)

Step-by-step explanation:

x^2+x=x(x+1)

Answer: x (x + 1)

Step-by-step explanation: Factor out the X

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