help me with these 2

Step-by-step explanation:

the ancient Greeks used the system know as the attic numerals

The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.

a. A rational function with a hole at x = 1 and a vertical asymptote at x = -3 can be written as:

(x-1)/(x+3)

b. A rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 3 can be written as:

(x+2)/(x+2) = 3

c. A rational function with an oblique asymptote y = x+1 but no vertical asymptote can be written as:

(x-1)/(x-1) = x+1

d. A rational function with a vertical asymptote at x = 3 and f(x) > 0 can be written as:

(x-3)/(x-3) > 0

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Answer:

Step-by-step explanation:

Let us solve the equation for X-

-1+log 6 (2x+3)-log 6 (2x)=0

adding +1 to both sides-

-1+1+log 6(2x+3)-log 6 (2x)=0+1

log 6(2x+3)-log 6 (2x)=1 . . . (1)

using logarithmic rule,

log a - log b= log(a/b)

equation (1) becomes,

log [6(2x+3)/6(2x)]=1 . . .(2)

equation (2) becomes,

log[(2x+3)/2x]=1....(3)

Again using the logarithmic rule,

log a = b

is equivalent to 10∧b = a

hence equation 3 becomes,

10∧1= (2x+3)/2x

i.e. 10 = (2x+3)/2x. . .(4)

multiplying both sides by 2x, considering x is not 0.

equation( 4) becomes

20x = 2x+3. . .(5)

subtracting 2x from both sides

equation (5) becomes,

18x=3

dividing both sides by 3,

we get,

x=6

Hence value of x is 6.

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deposited some money at 1.7​% annual​ interest, and two equal but larger amounts at 2.2​% and 24​%. The total amount invested was ​$26,000​ and the total annual interest earned was ​$574. How much was invested at each​ rate?

What is an investor?

An investor is an individual or an organization that gives money to A person or entity that invests in another with the hopes of making a profit in the future is known as an investor. According to the rules, anyone can invest: You are an investor if you put money into something.

Answer provided by our tutors

Let

x = the money invested at 1.7%

y = the money invested at 2.2%

y = the money invested at 24%

Since the total money invested was $26,000 we have:

x + 2y = 26000

The total annual interest was $574 means:

0.017x + 0.022y + 0.24y = 574

0.017x + 0.262y = 574

We have the following system of equations:

x + 2y = 26000

0.017x + 0.262y = 574

click here to see the system of equations solved for x and y

x = $24,842

y = $578

$24,842 was invested at 1.7%

$578 was invested at 2.2% and another $578 was invested at 24%.

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The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

Given,

In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°

We know that,

The angles sum in a triangle is 180°.

m∠X+m∠Y+m∠Z=180°

m∠X+71.02°+29.6°=180°

m∠X=180°-100.62°

m∠X=79.38°

Therefore, the measure of exterior angle to ∠X is 79.38°.

So, option 4 is correct.

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Answer:

309 chemistry textbooks and 103 math textbooks.

Step-by-step explanation:

Let c be the number of chemistry textbooks sold and m be the number of math textbooks sold. We know that c + m = 412, because the total number of textbooks sold is 412. We also know that c = 3m, because the number of chemistry textbooks sold is three times the number of math textbooks sold.

We can substitute 3m for c in the first equation to get 3m + m = 412. This simplifies to 4m = 412. Dividing both sides by 4 gives us m = 103.

Since we know that c = 3m, the number of chemistry textbooks sold is 3 * 103 = 309. Therefore, the store sold 309 chemistry textbooks and 103 math textbooks.

Answer: 4/3 of a mile

Step-by-step explanation:

To find the distance that Pepe and Paula ran in 60 minutes, we need to first determine their individual pace in miles per minute. Pepe ran 2/3 of a mile in 5 minutes, so his pace was 2/3 / 5 = 2/15 of a mile per minute. Paula ran 1/4 of a mile in 2 minutes, so her pace was 1/4 / 2 = 1/8 of a mile per minute.

We can now use these values to determine the distance that each of them ran in 60 minutes. Pepe ran at a pace of 2/15 of a mile per minute, so he ran 2/15 * 60 = 8/15 of a mile in 60 minutes. Paula ran at a pace of 1/8 of a mile per minute, so she ran 1/8 * 60 = 3/8 of a mile in 60 minutes.

To find the total distance that Pepe and Paula ran in 60 minutes, we can add their individual distances: 8/15 + 3/8 = 35/60 + 45/60 = 80/60 = 4/3 of a mile. Therefore, Pepe and Paula cumulatively ran a total of 4/3 of a mile on their 60-minute training run.

The cleveland cavaliers and of the golden state warriors in game 7 of the 2016 nba finals the player are 8.

A scatter plot is a hard and fast of factors plotted on a horizontal and vertical axes. Scatter plots are essential in facts due to the fact they could display the quantity of correlation, if any, among the values of determined portions or phenomena (referred to as variables).

Scatter plots are used to plan facts factors on a horizontal and a vertical axis withinside the strive to expose how a great deal one variable is laid low with another. Each row withinside the facts desk is represented through a marker whose role relies upon on its values withinside the columns set at the X and Y axes.

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The fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).

Given are three length parameters as [a], [b] and [c].

For the fourth proportional {x}, the relationship can be written as -

a/x = b/c = k  {constant}

x = (ac/b) = k  {constant}

Therefore, the fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).

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Arun sold 41 pound of raspberries and 25 pound of grapes.

What is a linear equation?

The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).

Given that the cost of 1 pound of raspberries is $1.50 and 1 pound of grapes is $2.75.

Arun sells 66 pounds with cost $130.25.

Assume that Arun sells x pound of raspberries and y pound of grapes.

Therefore,

x + y = 66   ......(i)

The cost of x pound of raspberries and y pound of grapes is 1.50x + 2.75y.

1.50x + 2.75y = 130.25  .....(ii)

Solving equation (i) and (ii) by using elimination method.

Multiply equation (i) by 1.5

1.50x + 1.50y = 99 ....(iii)

Subtract equation (iii) from (ii)

1.50x + 2.75y = 130.25

1.50x + 1.50y  = 99

(-)      (-)             (-)

________________

              1.25 y = 31.25

                     y  = 25

Putting y = 25 in equation (i)

x + 25 = 66

x = 41

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The probability of getting heads on the a coin and a number less than 3 on cube is given as 1/6.

In order to find the probability take the ratio of the favorable outcome to the total possible outcome.

The set of total possible outcomes is known as sample space.

The number of elements in the sample space is given as,

Possible outcomes for coin × Possible outcomes for cube

= 2 × 6 = 12

The given two events flipping of coin and rolling of cube are mutually independent.

Which implies it is not the case of conditional probability.

The favorable number of outcomes are as below,

Number of head × Number of numbers less than 3

= 1 × 2 = 2

Now, the probability is given as,

P(getting head on coin and less than 3 on cube) = 2/12 = 1/6

Hence, the probability of getting the required outcome is given as 1/6.

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The interval containing the rational zero of f(x) = 3x³ - 5x² + 5x + 7 is given as follows:

-1 < x < 0.

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible zeros are given as follows:

±1/3, ±1, ±7/3, ±7.

The numeric values for the function are these points are of:

This means that there is a zero between -7/3 and -1/3, as the function changes from negative to positive, hence the interval is given as follows:

-1 < x < 0.

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Answer:

1.6

Step-by-step explanation:

Firstly, we know the rate of change of volume [tex]v'=8[/tex].

The equation for surface area is: [tex]A = 4\pi r^2[/tex].

The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]

The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].

The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].

This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].

We can then plug that into our equation for [tex]A'[/tex] and get:

[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]

After that, we can just plug in:

[tex]2*\frac{8}{10}=1.6[/tex]

Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and  the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

To find the fifth power of the matrix A, we can simply multiply A by itself five times:

A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

To find the probability that state 2 changes to state 4 after five repetitions of the experiment, we need to look at the element in the fifth power matrix A^5 that corresponds to state 2 and state 4. This element is located in the second row and fourth column of the matrix, which is 0.14.

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

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A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

The perimeter of the shape is 12.82 units

From the question, we have the following parameters that can be used in our computation:

A = (0, 2.76)

B = (3.65, 2.76)

C = (3.65, 0)

D = (0, 0)

Because the point D is at the origin, and the shape is a rectangle.

The perimeter of the shape can be represented as

P = 2 * (Bx + By)

Substitute the known values in the above equation, so, we have the following representation

P = 2* (3.65 + 2.76)

Evaluate

P = 12.82

Hence, the perimeter is 12.82 units

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Option of the matrices a, b, and d are non symmetric.

Symmetric matrices are those matrices that have equal dimensions, i.e. the number of rows is same as the number of columns. They are also known as square matrices.

It is provided that A and B are symmetric n × n matrices.

To multiply two matrices of different order, the number of rows of the first matrix must be same as the number of columns of the second matrix.

Suppose X is a 2 × 3 matrix and Y is a 3 × 2.

Then the product AB will be a n × n matrix.

(a) A= C+CT

Thus the sum of matrix A and B will be a n × n matrix.

Thus, the matrix A is non symmetric.

(b) B = C-CT

So, matrix D will also be a n × n matrix.

Thus, the matrix D is non symmetric.

(c) D = CTC = (CT) × C

Then the product CT will be a n × n matrix.

The next step would be to multiply CT and C.

Both are n × n matrices.

Thus, the matrix D is symmetric.

(d) E = CTC - CCT

Then he product CT will be a n × n matrix.

Similarly, the product CT will be a n × n matrix.

Thus, the matrix E is non symmetric.

Similalry,

(e) F = (I +C)(I + CT

Thus, the matrix F is symmetric.

(f) G = (I +C)(I -CT)

Thus, the matrix G is symmetric.

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Answer:

Below in bold.

Step-by-step explanation:

Let the height be h in.

Area of a triangle = 1/2 * base * height

= 1/2 * (h + 6) * h = 600

Multiply both sides by 2:

h(h + 6) = 1200

h^2 + 6h = 1200

(h + 3)^2 - 9 = 1200

(h + 3)^2 = 1209

h + 3 = +/- sqrt(1209

h = -3 +/-sqrt(1209)

  = 31.77 in  (we ignore the negative root).

So, the height is 31.77 in and the base is 37.77 in

Answer: 1/4,2/5,3/10

Step-by-step explanation:

Answer:

The cost of producing 200 units can be calculated by plugging in 200 for q in the equation E = 1.43q + 43,123. This gives us E = 1.43*200 + 43,123 = 286 + 43,123 = $43,409.

Step-by-step explanation:

always remember that 100% is the whole.

so, 15% means 15/100 of the whole.

1/5 = 0.2 = 20/100 of the whole.

so, Target is taking 15/100 off the price.

Walmart is taking 20/100 off the price.

20/100 is bigger than 15/100, so Walmart deducts more off the price, and has therefore the lower and therefore better sale price.

Target sale price :

100/100 - 15/100 = 85/100 × 80 = $68

in short

80 × (1 - 0.15) = 80 × 0.85 = $68

Walmart sale price :

100/100 - 20/100 = 80/100 × 80 = $64

in short

80 × (1 - 0.20) = 80 × 0.80 = $64

The x and y values for the given equation are x= -20 and y=8

One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.

Given,

-1/4[ x 12 -32 ] = [ 5  -3  y ]

[(-1/4)x    (-12/4)    (-32/-4)]=[5  -3  y]

-x/4=5

-x=20

x= -20

-32/-4=y

y=8

Therefore, the x and y values for the given equation are x= -20 and y=8

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Answer:  its 18 im pretty sure

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

1: Add up the ratio then divide by the number of students.

3+5=8

40/8=5

2: Each count is equal to 5 students.

3: Multiply the ratio of students who stay after soccer practice by Each count

5*5=25

Answer:

B

Step-by-step explanation:

First, we compute the exponent (3² = 9).

Next, we compute the multiplication and division (from left to right), so we have (40 - 2 × 9) = (40 - 18) = 22.

Thus, the number sentence 40 -2 × 3² = 22 is true.

B is true .22 is the real answer

Based on Simple Interest, 8125 was invested at the rate 1.7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

> The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest.

> Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest.

> Simple interest loans are frequently used for auto loans and short-term personal loans.

Let the amount at 1.7% be x. Then:

[tex]0.017x+0.023(\frac{(25000-x)}{2}) +0.024(\frac{(25000-x)}{2})=535[/tex]

[tex]0.023+0.024 = 0.047 \\\frac{0.047}{2} = 0.0235[/tex]

Now we got rid of the two divisions. Rewrite the equation:

[tex]0.017x+0.0235(25000-x) = 535[/tex]

[tex]0.017x+587.5-0.0235x = 535[/tex]

[tex]-0.006x = -52.5[/tex] Divide both sides by -0.006 and remember -/- = +

x = 8750

This is how much was invested at 1.7% The rest, the problem says, was invested in equal amounts:

[tex]25000-8750 = 16250[/tex]; [tex]\frac{16250}{2}=8125[/tex] So, 8125 was invested each at 2.3% and 2.4%

Based on Simple Interest, 8125 was invested at the rate 1.7%.

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67 books will fit on the shell.

One foot has 12 inches (in) (ft). In the US customary and imperial measurement systems, both feet and inches are units of length. The foot has had many different definitions throughout history, but since 1959, it has been defined as exactly 0.3048 meters, and the inch as 2.52 centimeters. The meter is the International System of Units' base unit of length (SI).

In the given question,

Then the number of books

= 42 / (5/8)

= 42 (8/5)

= 336/5

= 67 1/5

Finally, we round 67.2 to the nearest LESSER integer number and obtain

67.

Hence, 67 books will fit on the shell.

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It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.

To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:

Q(t) = Pe^(rt)

where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the values, we get:

Q(t) = 10 * e^(-432.2t)

This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.

To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.

[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]

t = approximately 7.66 years

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An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.

Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."

Give the null hypotheses a name.

Negative hypothesis:

H. There is no correlation between gender and election participation.

Other possibilities:

H: Gender and participation in the most recent election are linked.

Rule of rejection:

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Answer:

In modular arithmetic, the modulo operation is used to find the remainder when one number is divided by another. For example, the expression "9 % 3" would evaluate to 0 because 9 divided by 3 leaves a remainder of 0.

In the given equation, taking the modulo 9 of both sides gives:

79z % 9 ≡ 92x + 9y % 9

The modulo operation distributes over addition, so we can simplify this to:

(79z % 9) ≡ (92x % 9) + (9y % 9)

Since any number divided by 9 has a remainder of itself, we can simplify this further to:

(z % 9) ≡ (2x % 9) + (y % 9)

This gives us the result:

-2z % 9 ≡ 2x % 9

Multiplying both sides by 5 gives:

(-2z % 9) * 5 ≡ (2x % 9) * 5

Which simplifies to:

-z % 9 ≡ x % 9

Since x is between 0 and 10, we know that x % 9 is between 0 and 9. Therefore, we can conclude that z = 9 - x.

Answer 34

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