21n/ 3n

Simplify the algebraic fraction whose numerator is 21n and who’s denominator is 3n

Help me step by step Please thank you.

A prism has two congruent parallel bases and the number of sides on the base determine the number of faces. A base with 13 sides is a 13-gon, so the prism has 2 faces from the 13-gon bases and 13 faces from the rectangular sides. In total the prism has 2+13 = 15 faces.

A prism is a three-dimensional geometric shape that has two congruent and parallel bases, and a set of rectangular faces connecting the bases. The bases are typically polygonal in shape, and the rectangular faces are perpendicular to the bases. The distance between the bases is known as the height of the prism. Prisms are named based on the shape of their bases, for example, a triangular prism has triangular bases, and a rectangular prism has rectangular bases. There are different types of prisms like regular prism, triangular prism, pentagonal prism, hexagonal prism etc.

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Answer:

61.04 degrees

Step-by-step explanation:- To find the angle we must use the sine function which is sin∅ = opp/hyp so sin ∅ = 175/200 = 61.04°

Hope this helps :)

The coordinates of point C is C(x, y) = (- 2, - 10).

In this problem we find a line segment whose endpoints are already known and we are asked to determine the location of a third point such that it is 3 / 7 of the distance from point A to point B. This can be determined by means of the following formula:

C(x, y) = A(x, y) + (3 / 7) · [B(x, y) - A(x, y)]

Where:

If we know that A(x, y) = (4, - 7) and B(x, y) = (- 10, 0), then the location of the thrid point is:

C(x, y) = (4, - 7) + (3 / 7) · [(- 10, 0) - (4, - 7)]

C(x, y) = (4, - 7) + (3 / 7) · (- 14, - 7)

C(x, y) = (- 2, - 10)

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The figure of a square with side length of 7 cm is shown in figure.

A square is a two dimension figure with 4 sides, 4 corners and 4 right angles. The all sides of the square are equal and parallel to each other.

We have to given that;

The side length of square = 7 cm

Now, We know that all sides of a square are equal.

Hence, The figure of a square with side length of 7 cm is shown in diagram.

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The polynomial p with 4 zeros at -4, -2/3, 0 and 9 is,

⇒ p (x) = x⁴ - 13/3x³ - 118/3x² - 24x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The polynomial p is a function of x with 4 zeros are -4, -2/3, 0 and 9.

Now, We can formulate;

The polynomial is,

⇒ p (x) = (x - (-4)) (x - (-2/3)) (x - 0) (x - 9)

⇒ p (x) = (x + 4) (x + 2/3) (x) (x - 9)

⇒ p (x) = x (x + 4) (x - 9) (x + 2/3)

⇒ p (x) = x (x² - 9x + 4x - 36) (x + 2/3)

⇒ p (x) = x (x² - 5x - 36) (x + 2/3)

⇒ p (x) = x (x³ + 2/3x² - 5x² - 10/3x - 36x - 24)

⇒ p (x) = x (x³ - 13/3x² - 118/3x - 24)

⇒ p (x) = x⁴ - 13/3x³ - 118/3x² - 24x

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The points of solution that are obtained for the system of linear equations 3x + 2y = 11 and -8x - 4y = -20 are (-1,7).

2(3x + 2y = 11)

1(-8x - 4y = -20)

3x + 2y - 8x - 4y = 11 - 20 gives -5x - 2y = -9

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The system of linear equations are -

3x + 2y = 11....(1)

-8x - 4y = -20....(2)

When solved initially the value of equation is -

3x + 2y - 8x - 4y = 11 - 20

-5x - 2y = -9

Multiply equation (1) by 2 -

2(3x + 2y) = 2 × 11

6x + 4y = 22.....(3)

Simplify the equation (2) and (3) by adding -

-8x - 4y + 6x + 4y = -20 + 22

-2x = 2

x = -1

Substituting the value of x = -1 in equation (1) -

3x + 2y = 11

3(-1) + 2y = 11

Simplifying the equation -

-3 + 2y = 11

2y = 11 + 3

2y = 14

y = 7

Therefore, the final value is obtained as (-1,7).

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The domain of the quadratic function is represented by all the numbers on the number line, which is the set of values for which the function is defined.

A function is a mathematical rule or procedure that takes an input, performs a specific operation, and produces an output. In programming, functions are blocks of code that are designed to perform specific tasks. They are used to break down complex problems into smaller, manageable parts, and to make code more organized, readable, and reusable. Functions can also be used to share code between multiple programs.

The best way to determine the domain of a quadratic function is to identify the range of values for which the function is defined. The domain of a quadratic function is typically composed of all real numbers, which can be represented by the set of all numbers on a number line. In the graph of the quadratic function, the set of points on the graph represents the range of values for which the function is defined. Therefore, the domain of the quadratic function is represented by all the numbers on the number line, which is the set of values for which the function is defined.

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Answer:

3(2x - 5)(x - 2)

Step-by-step explanation:

-27x + 6x^2 + 30 =

= 6x² - 27x + 30

= 3(2x² - 9x + 10)

= 3(2x - 5)(x - 2)

Answer:75

Step-by-step explanation:The complementary angle of 15° is 75°. To find the complement of an angle, say ' x ', use the formula below: So, the complementary angle of 15° = 90 - 15 = 75°. Important: the angle unit is set to degrees. You browser does not support "Canvas"

The U.S centers for disease control (CDC) uses Secondary Data if it is buying data from hospitals for its own analysis.

Data can be divided into 2 categories based on the source of collection.

When the data is collected firsthand by the research person or organization through sampling or other means for their own research purpose, it is known as Primary data. This is because it directly pertains to the purpose of the said event.

When the organization, however, does not collect data on its own but rather it uses data/ research of other organizations, it is known as secondary data.

Here, in this case, we find CDC saves time and effort by directly buying and utilizing the data collected by the hospitals for their own purpose, they use secondary data.

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The equation of the quadratic function whose zeros are 3 and 5 is x² - 8x + 15 = 0

The term equation in math is known as a mathematical statement that is made up of two expressions connected by an equal sign

Here we have the zeros are 3 and 5.

As we all know that the quadratic polynomial can be expressed using its zeros as follows,

=> x² - (α + β)x + (αβ) = 0

Here we know the values of α = 3 and the value of β = 5.

Now, we have to apply the value on the equation, then we get,

=> x² - (3 + 5)x + (3 x 5) = 0

When we simplify this then we get the expression,

=> x² - 8x + 15 = 0

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The rate of points scored is 1.25 points per quarter.

A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.

For example, a distance runner completed 50 kilometers in five hours.

To determine the rate of points scored, we need to determine how many points are scored per unit of time. In this case, the unit of time is a quarter, and the number of points scored is 5.

Therefore, the rate of points scored is 5 points / 4 quarters = 1.25 points per quarter.

It is also the average of points scored in a quarter.

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Answer:

48

Step-by-step explanation:

72/6 =12

12(4)=48

Answer:

30.4 units

Step-by-step explanation:

This Question asks on the concept of Similar Triangles.

Given information from the question, we know that:

DM = MA

CN = NB

DC and AB are parallel.

We can use the ratio formula to find the length of AB based on the length ratio between MN and DC.

[tex]\frac{AB}{MN} =\frac{MN}{DC} \\\frac{AB}{18.7} =\frac{18.7}{11.5} \\AB = \frac{18.7}{11.5} * 18.7\\AB = 30.4\ units[/tex]

Therefore the length of AB is 30.4 units.

LOOK DOWN

Step-by-step explanation:

Locate two points on the line whose coordinates are integers.

Starting with the point on the left, sketch a right triangle, going from the first point to the second point.

Count the rise and the run on the legs of the triangle.

Take the ratio of rise to run to find the slope. m=riserun.

We can start by using the following formula to find the original price:

Original price = Sale price / (1 - (Discount percentage / 100))

To use this formula, we need to convert the discount percentage from 18% to a decimal. We can do that by dividing 18 by 100.

Discount percentage as decimal = 18 / 100 = 0.18

Now we can use this value in the formula:

Original price = $522.75 / (1 - 0.18) = $522.75 / 0.82 = $638.57

So the original price of the television set was $638.57.

Rounding to the nearest cent, the original price of the television set is $638.57

Answer: The smallest number that can be divided by 90, 80 and 72 without a remainder is 720.

Step-by-step explanation:

To find the smallest number that can be divided by 90, 80, and 72 without a remainder, you can find the least common multiple (LCM) of 90, 80, and 72. The LCM is the smallest positive number that is a multiple of all the given numbers.

One way to find the LCM is to list out the multiples of each number and then find the smallest one that is common to all.

Multiples of 90: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170...

Multiples of 80: 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960, 1040, 1120...

Multiples of 72: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008...

As you can see 720 is the smallest common multiple for all the numbers 90,80 and 72. Therefore, the smallest number that can be divided by 90, 80, and 72 without a remainder is 720.

Answer: Scroll down

Step-by-step explanation:

Image one:

1. Using SAS similarity, we can find 48/60 = 20/ML

1200 = 48 ML

ML = 1200/48 = 25 = Circle one

2. 24/x+5 = 54/36

   x = 11

3. 20/36 is not equal to 24/42, so the triangles are not similar, = D

Image two:

1. 21/17.5 = 18/15 = 1.2

PQR is similar to D

2. D because then the ratios of the sides are all 3:1, and thats SSS similarity.

Image three:

1. Given

2. Property of cross multiplication

3. Given

4. SAS

Finished :>

A vertical number line ranging from a negative 2.00 to a positive 2.00 is displayed. Therefore, on the provided number line, point A corresponds to 0.25.

On the given number line, point A denotes a decimal number.

Given: A vertical number line ranging from a negative 2.00 to a positive 2.00 is displayed.

The horizontal straight lines known as "number lines" are where integers are spaced equally apart.

A number line can be used to visualize all the numbers in a succession.

Both endpoints of this line continue indefinitely.

Tick marks are used to indicate 1 over 4 increments.

At the third tick, Point A is plotted.

The result is that Point A is indicated as 1 over 4.

Divide 1 by 4 to get 1 over 4.

Therefore, on the provided number line, point A corresponds to 0.25.

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Describe to a child the analogy between owing money when you have none at all and a negative number. It is not zero, though. As a result, when the numeral is larger, the value is lower or less.

A negative number is one that always has a value lower than zero and is denoted by the minus (-) symbol.

Negative numbers are shown to the left of zero on a number line.

Negative numbers include -6 and -15 as examples.

A negative number in mathematics represents the reverse.

A negative number is one that is less than zero in the real number system.

Negative numbers are frequently used to indicate how great a loss or a shortage is.

One could consider an unpaid debt to be a negative asset.

To a child describe how a negative number is equivalent to owing money when you have none at all.

It is not equal to zero.

Therefore, the value is smaller or less when the numeral is larger.

Therefore, describe to a child the analogy between owing money when you have none at all and a negative number. It is not zero, though. As a result, when the numeral is larger, the value is lower or less.

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If there is a 20% chance that the company will lose $250000,  a 50% chance of a break even, a 30% chance of a $150000 profit, then (d) The expected value is -$5000 , so man should not make the investment​ .

the percent chance for the loss is : 20% chance that the company will lose $250000 ;

the percent chance that there is break even : 50% chance  ;

the percent chance for profit is : 30% chance of a $150000 profit ;

So , the expected value can be calculated as :

⇒ -(20% of 250000) + (30% of 150000) ;

⇒ -(0.2 × 250000) + (0.3×150000)  ;

⇒ -50000 + 45000 ;

⇒ -5000 .

The Expected value is in negative ,

Therefore , the Man should not make an investment .

The given question is incomplete , the complete question is

A man plans on making a large speculative investment in a new company. There is a 20% chance that the company will lose $250,000, a 50% chance of a break even, and a 30% chance of a $150,000 profit. Based ONLY on this information, what should the man do?

(a) The expected value is $5000, so the man should make the investment.

(b) The expected value is $45000, so the man should make the investment.

(c) The expected value is -$50000 , so the man should make the investment

(d) The expected value is -$5000  , so the man should not make the investment​

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Answer:

There is still no attachment.

Step-by-step explanation:

The required value of k the following pair of equations has no solution is k = 2.

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

3x + y -1 = 0

(2k -1)x + (k-1)y - 2k -1 = 0

A1/A2 = 3(2k -1); B1/B2 = 1/(k-1); and C1/C2 = -1/(-2k -1) = 1/(2k +1).

as there are none

A1 = B1 + B2 = C1 + C2

3/(2k-1) = 1/(k -1) ≠ 1/(2k +1)

3/(2k –1) = 1/(k -1) (k -1)

3k -3 = 2k -1

k =2

The above pair of linear equations will therefore not have a solution for k = 2.

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Complete question:

For which value of k will the following pair of linear equations have no solution?

3x + y = 1

(2k – 1) x + (k – 1) y = 2k + 1

Answer: a) 040°    b) 125°     c) 218°

The number 7 can be written as number name, ordinal form, roman numerals and square root form.

The natural number 7, which is a number, numeral, and digit, is the one that follows after 6 and before 8. The cube of a number, 2, is preceded by only one other prime odd number. Its only divisors, as it is a prime number, are 1 and 7. In a lot of western nations, this number is seen as lucky.

The number 7 can be written in a variety of ways, including:

(1) In number names: The number seven is written as 7.

(2) In ordinal form: The number 7 is written as seventh or seventh in ordinal form.

(3) Roman numerals: The sign Vll is used to represent the number 7 in roman numerals.

(4) In square root form: The number 7 is written as the square root of 49, i.e. √49, when expressed in terms of a number.

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The theoretical probability and experimental probability of the spinner landing on the purple will be 0.3333 and 0.40, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The spinner below is spun 75 times and the results are shown in the table.

The theoretical probability of the spinner landing on the purple will be given as,

P = 1 / 3

P = 0.3333

The experimental probability of the spinner landing on purple will be given as,

P = 30 / 75

P = 2/5

P = 0.40

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The missing table is given below.

Color         Frequency

Purple            30

Red                30

Green            15

The probability of getting either 1 or 6 more than two times is P(T)=121/1296

To find the probability we use the binomial distribution.

Here we have 4 independent experiments. Each time, the sample space is (1,2,3,4,5,6) so the prob of getting a 6 is 1/6.

so p=1/6

prob of coming 6 and q= 1-p = 1-(1/6)=5/6

prob of not coming 6 is 5/6

p= prob of success. here our success event is getting 6

q= prob of failure. here our failure event is not getting 6

no of trials n=4

now using the binomial distribution formula:

ncr(p)^n(1-p)^r

here we want at least two 6, desirable outcomes are two 6 or three 6, or four 6 because at least two 6 doesn't mean that we can't get more than two 6 .

so r in these cases take the value of 2,3,4 respectively.

so for r=2

c(4,2)*(1/6)^2*(5/6)^2

P(A)=  150/1296

for r=3

c(4,3)*(1/6)^3*(5/6)^1

P(B)= 20/1296

for r = 4

c(4,4)*(1/6)^4*(5/6)^0

P(C)= 1/1296

here we will add these prob ..Getting two 6 fulfills our condition so we will stop and calculate the prob and keep it aside

now adding these we get P(T)=P(A)+P(B)+P(C).

(150/216) +(20/216) + (1/216)

P(T)= 171/1296

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Answer:

f(0)=-5

f(2)=3

f(-2)=-15

f(4)=11

f(-1)=-9

Step-by-step explanation:

Pretty simple once it clicks.You just need to substitute the x in f(x). So f(2) is just replacing the x in the equation. We would get 4*2-5. This would get us 8-5 which is 3. So rule of thumb, just substitute the x.

The wavelength of the electromagnetic radiation exists utilized 2.42 pm.

Waves-based radiation that has an electric and magnetic field. It derives from both natural and artificial sources. From low energy to high energy, electromagnetic radiation can have different intensities. It consists of x-rays, gamma rays, microwaves, infrared light, visible light, ultraviolet light, and radio waves.

The wavelength of radiation used to annihilate a positron and an electron is required.

The wavelength of the electromagnetic radiation exists utilized [tex]$\mathbf{2 . 4 2} \mathbf{~ p m}$[/tex].

The mass of positron and electron are equal

[tex]$$\begin{aligned}& \mathrm{m}=\text { Mass }=\frac{0.000549}{6.022 \times 10^{26}}=9.11 \times 10^{-31} \mathrm{~kg} \\& \mathrm{c}=\text { Speed of light }=3 \times 10^8 \mathrm{~m} / \mathrm{s} \\& \mathrm{h}=\text { Planck's constant }=6.626 \times 10^{-34} \mathrm{Js}\end{aligned}$$[/tex]

Total energy in the collision is

[tex]$$\begin{aligned}& E_T=m c^2+m c_2 \\& \Rightarrow E_T=2 m c^2 \\& \Rightarrow E_T=2 \times 9.11 \times 10^{-31} \times\left(3 \times 10^8\right)^2 \mathrm{~J}\end{aligned}$$[/tex]

Energy released per photon is

[tex]$$\begin{aligned}& E=\frac{E_T}{2} \\& \Rightarrow E=\frac{2 \times 9.11 \times 10^{-31} \times\left(3 \times 10^8\right)^2}{2} \\& \Rightarrow E=9.11 \times 10^{-31} \times\left(3 \times 10^8\right)^2 \mathrm{~J}\end{aligned}$$[/tex]

Energy is given by

[tex]$$\begin{aligned}& E=\frac{h c}{\lambda} \\& \Rightarrow \lambda=\frac{h c}{E} \\& \Rightarrow \lambda=\frac{6.626 \times 10^{-34} \times 3 \times 10^8}{9.11 \times 10^{-31} \times\left(3 \times 10^8\right)^2} \\& \Rightarrow \lambda=2.42 \times 10^{-12} \mathrm{~m}=2.42 \mathrm{pm}\end{aligned}$$[/tex]

The wavelength of the electromagnetic radiation exists utilized 2.42 pm.

The complete question is:

A positron and an electron annihilate each other upon colliding, thereby producing energy in the form of two gamma rays. Assuming that both gamma rays have the same energy (since both particles have the same mass), calculate the wavelength of the electromagnetic radiation used in pm. (1 pm = 10⁻¹² m; mass of electron (amu) = 0.000549)

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