Which statement is true about the diagram?
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The long term behavior of the rational function f(x) = (x² - 3) / (x³ + 2) is 0, for the rational function g(x) = (x³ - 3) / (x³ + 2) is 1 and for the rational function h(x) = (x⁴ - 3) / (x³ + 2) does not exist.

In this case we find three rational functions, that is, functions of the form:

m(x) = p(x) / q(x)

Where:

Please notice that both numerator and denominator are polynomic functions, the long run behavior of the function depends on the grades of numerator and denominator according to these rules:

Now we proceed to analyze the long run behavior of each rational function:

Case 1: f(x) = (x² - 3) / (x³ + 2)

Grade of numerator: 2, grade of denominator: 3

Result: 0

Case 2: g(x) = (x³ - 3) / (x³ + 2)

Grade of numerator: 3, grade of denominator: 3

Result: 1

Case 3: h(x) = (x⁴ - 3) / (x³ + 2)

Grade of numerator: 4, grade of denominator: 3

Result: N / A

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5150\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years \end{cases}[/tex]

[tex]5150=4500e^{0.075\cdot t} \implies \cfrac{5150}{4500}=e^{0.075t}\implies \cfrac{103}{90}=e^{0.075t} \\\\\\ \log_e\left( \cfrac{103}{90} \right)=\log_e(e^{0.075t})\implies \log_e\left( \cfrac{103}{90} \right)=0.075t \\\\\\ \ln\left( \cfrac{103}{90} \right)=0.075t\implies \cfrac{\ln\left( \frac{103}{90} \right)}{0.075}=t\implies\stackrel{\textit{about 1 year and 291 days}}{ 1.8\approx t}[/tex]

Answer:

10z + 2

Step-by-step explanation:

combine the like terms

3z + 7z = 10z

1 + 1 = 2

10z + 2

(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

At a specific zoo, the typical mass of one blue whale is estimated to be 190000 kilograms. Utilize logical documentation to communicate the mass of 125 blue whales.

⇒ 190,000 × 125

Simplify the expression in the scientific notation, then we have

⇒ 190,000 × 125

⇒ 23,750,000

⇒ 23.75 × 10⁶ kilograms

The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.

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Answer:

[tex]y=x^2-8x+16[/tex]

Step-by-step explanation:

[tex]x=t+4 \implies t=x-4 \\ \\ y=(x-4)^2=x^2-8x+16[/tex]

Answer:

y=-1/2x+6

Step-by-step explanation:

slope: -5/10 = -1/2

y=mx+b

y=-1/2x+b

substitute points to find b: 8=-1/2(-4)+b

8=2+b

6=b

The first two columns of the table, considering logarithms, are completed as follows:

The table is completed in this problem applying the logarithms.

This is because on the first column we had that:

10^(0.3) = 2, which means that log10(2) = 0.3.

(log10(x) represents the logarithm of base 10 of x).

For the second row, the decimal approximation is found applying the power of 10^0.7, hence:

10^0.7 = 5.

For the third and fourth rows, to obtain the power of 10 expression, we need to calculate the logarithms of these numbers, as follows:

Hence the power of 10 expressions are given as follows:

For the fifth row, we just need to calculate the exponential expression, hence:

10^(0.4) = 2.51.

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Answer:

:)

Step-by-step explanation:

-5a + 6 + 3a + 2

Combine like terms:
-5a + 3a + 6 + 2

2a + 8 is your answer, you can't simplify it further

----------------------------------------------------------------------------------------------------------

If you want to solve for the a value:

-5a + 6 = 3a + 2

Subtract 2 from both sides

-5a + 6 = 3a + 2

      - 2          - 2

-5a + 4 = 3a

(The +2 and -2 cancel each other out, it makes 0)

Add +5a to both sides

-5a + 4 = 3a

+5a        +5a

(The -5a and +5a cancel each other out, it makes 0)

4 = 8a

Divide by 8 on both sides

4/8 (OR 1/2 OR 0.5) = a

Thanks for reading my ted talk lol pls mark as brainliest and give lots of points i need them lol help a girl out!!

The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth

What are exponential growth and exponential decay?

Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.

From question,

1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500

This means it is decaying. The difference between the initial price and after 2 years price is $7500.

To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.

Thus exponential decay.

2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.

After 4 hours, the loss is (60 -20) = 40%

As the loss is the same in equal intervals of time, the decay is linear.

3) In the third one, A tiger reserve had an initial population of 20 tigers.

After 5 years the population was 30 tigers, thus the growth is (30-20) =10.

After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.

Thus the increase is non-linear, and so is exponential growth.

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x = 7.26

1. Add 11.24 to both sides

-3.98 = x - 11.24

-3.98 + 11.24 = x - 11.24 + 11.24

2. Simplify

Add the numbers:

-3.98 + 11.24 = x - 11.24 + 11.24

7.26 = x - 11.24 + 11.24

Add the numbers:

7.26 = x - 11.24 + 11.24

7.26 = x

Move the variable to the left:

7.26 = x

x = 7.26

x = 7.26

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

x = 7.26

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

First, add 11.24 to both sides of the equation:

-3.98 = x - 11.24

-3.98 (+11.24) = x - 11.24 (+11.24)

Next, simplify.

11.24 - 3.98 = x

x = 7.26

x = 7.26 is your answer.

~

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The expression for the discount will be written as d = 0.5L.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the discount d is 50% of the list price L. The expression for the discount will be written as below,

Discount = 50% of the list price

d = ( 50 / 100) x L

d = 0.5L

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The percent of the original price was the price after markup will be 6.29%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

During a deal, a store offered a 25% rebate on a bed that initially sold for $890. After the deal, the limited cost of the bed was increased by 25%.

The marked-up price is given as,

⇒ $890 x (1 - 0.25) x (1 + 1.25)

⇒ $890 x 0.75 x 1.25

⇒ $834

The percentage is given as,

P = [(890 - 834) / 890] x 100

P = (56 / 890) x 100

P = 0.0629 x 100

P = 6.29%

The percent of the original price was the price after markup will be 6.29%.

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Answer: 94%

Step-by-step explanation:

Find what percent of the original price this represents:

$834.375 / $890 = 0.9375

0.9375 × 100 = 93.75%

93.75% ≈ 94%

Round to the nearest whole number

The price after markup was 94% of the original price.

Step-by-step explanation:

[tex]x + \frac{75}{4} (x) = 0[/tex]

[tex] \frac{79x}{4} = 0[/tex]

[tex]x = 0[/tex]

The monomial that completes the expression 0.01 b²+.....+100 c² is 2bc

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

0.01 b²+.....+100 c²

Complete the expression with a variable

So, we have

0.01 b² + x + 100 c²

The given terms of the expression are factors/multiples of 10

By trial and error, we make use the following representation

0.01 b² + x + 100 c² = (0.1b + 10c)²

Expand the expression

0.01 b² + x + 100 c² = 0.01 b² + 2bc + 100 c²

Evaluate the like terms

x = 2bc

Hence, the monomial is 2bc

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It will take 12.91 years to earn $ 500 in interest  

Compound interest refers to the interest added to a loan or deposit. It is the concept that we employ every day on a regular basis. Amounts are based on both the principal amount and Rate of interest when calculating compound interest. 

The formula used for

P = Principal amount

r = Rate of interest  

n = Number of compounds in a year  

t = Time period in years

And the formula for

Here we have

Principal amount = 1700,

Rate of interest = 2% = 2/100  = 0.02 on decimals  

Given that compound interest gained = $ 500

Number of compounds = 4 times

Let a be the time period

By the given formula,

Amount, A = 1700(1+0.02/4)^4t  

= 1700(1+0.005)^4t    

= 1700 (1.005)^4t  

Compound interest = 1700 (1.005)^4t - 1700

From the given data,

Compound interest = $ 500

=> 1700 (1.005)^4t - 1700 = 500

=> 1700 (1.005)^4t = 2200

=> (1.005)^4t = 1.294

Take logs on both sides

=> log (1.005)^4t = log 1.294

=> 4t log (1.005) = log (1.294)

=> 4t = log(1.294)/log(1.005)

=> 4t = 0.111934276/ 0.00216606176      

[ Use calculator for log(1.294) and log(1.005) ]

=> 4t = 51.6764012

=>  t = 12.9191003  

=>  t = 12.91  

Therefore,

It will take 12.91 years to earn $ 500 in interest

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Answer:

1 divided by 7 raised to the third power

Step-by-step explanation:

To find the equivalent expression, we can start by applying the rule for multiplying powers with the same base:

(7^(-2)) * (7^3) = 7^(-2+3) = 7^1 = 7

Then, we can apply the rule for raising a power to a power:

7^1 = (7^1)^(-3) = 7^(-3)

Finally, we can apply the rule for raising a number to a negative power:

7^(-3) = 1 / (7^3) = 1 / 343 = 1/7^3

Therefore, the equivalent expression is 1 divided by 7 raised to the third power.

If the expression  (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2

The expression is (4k + 8) / 4

The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.

The given expression is (4k + 8)/ 4

Solve the expression

(4k + 8) / 4 = 4k/4 + 8/4

Divide the terms

=k + 2

The result is in the form of ak + b

The value of a = 1

The value of b = 2

The value of a/b = 1/2

Therefore, the value of the expression a/b is 1/2

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total = 15x + 30

EDIT: She has to mow 8 lawns. I didn't read the question

there you go its that simple

The difference between book value and the amount received is $2000

What was the difference between the book value and the amount received ?

van cost = $16000

Estimated life= 4 years

Residual value= $4000

using straight line method of depreciation

Depreciation per year= 16000-4000/4= 3000

Therefore book value after two years = $16000- 2*3000= $10000

Selling price of book after 2 years= $8000

hence the difference between book value and the amount received

10000-8000= $2000

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Answer:

Step-by-step explanation:

The grams of coffee beans Diana uses when the company comes is:

                                              62.5 grams

Answer:

Step-by-step explanation:

Triangle Area = 1/2bxh

Base (b) = 12 units

Height (h) = 5 units

1/2 × 12 × 5 =

6 × 5 =

30 units²

By using the concept of probability, it can be calculated that-

1)   P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]

2)  P(Ace [tex]\cap[/tex] 5) = 0

3)  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4)   P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]

5)   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

1) Number of ace card = 4

  Number of '5' card = 4

  P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]

                    = [tex]\frac{8}{52}[/tex]

2) P(Ace [tex]\cap[/tex] 5) = 0

3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)

 Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]

  P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]

4) Number of black coloured even numbered card = 10

   Number of even numbered card = 20

   Number of card of black colour = 26

  P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]

                              = [tex]\frac{36}{52}[/tex]

5) Number of face cards of diamond = 3

   P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]

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Olivia wants to have a 90 average in algebra, where tests count for 55%, quizzes count for 30% and homework counts for 15%. The quiz average is 82%.

It is forming the outcome of multiplying the total of multiple quantities by their sum and then dividing this result by the number of quantities

Given,

She has test count = 55%,

quizzes count = 30%,

homework counts = 15%

If she had

test count = 92%

Homework counts = 100%

quizzes count = ?

Let x be the test count

x = (90 - (0.55(92) + 0.15(100)))/0.30x

  = 82

Olivia must have an 82 average on quizzes in order to have a 90 average in algebra.

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To find the equation of a line that is parallel to y=−7+4x and passes through the point (-2,-1), we can use the point-slope form of the equation of a line. The point-slope form of the equation of a line is:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

Since the given line y=−7+4x is in slope-intercept form, we can find the slope by taking the coefficient of x, which is 4. This means that the slope of the line is 4.

We can then use the point-slope form to find the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1). Plugging in the values for the slope and the point, we get:

y - (-1) = 4(x - (-2))

Simplifying this expression gives us:

y + 1 = 4(x + 2)

Which simplifies to:

y = 4x + 5

So the equation of the line that is parallel to y=−7+4x and passes through the point (-2,-1) is y = 4x + 5.

Answer:

Step-by-step explanation: Q13 Find the perimeter of the shape

42x *2=84x

72x*2=72x

Perimeter=84x+72x=156x

Q14 Find the perimeter of the shape just add up 3x +(4x+8)+3(x-2)

=3x+4x+8+3*x+3 *-2

=3x+4x+8+3x-6

=3x+4x+3x+8-6......add together like terms and number terms

=10x+2

Answer:

13.) 156x

14.) 10x + 2 or 2( 5x + 1)

Step-by-step explanation:

13.)perimeter of a parallelogram is

p = 2(a + b)

P = 2( 36x + 42x)

P = 2( 78x )

P = 156x

14.) perimeter of a scalene triangle

P = a + b + c

P = 3x + 3(x – 2) + 4x + 8

P = 3x + 3x –6 + 4x +8

P = 6x + 4x –6 + 8

P = 10x + 2

in factorise form

P = 2(5x + 1)

I hope this helps pls rate as brainliest

Answer

The first equation is the same (4x+2y=26), so we only need to compare the second equation. Just by looking at the second equation, you can see that x+y=8 and -2x - 2y = -16 are the same equation because -2 is multiplied to both sides of the equation x+y=8.

The mapping diagram above is a function since there are no two values in set B where there is only one mapping from  Set A.

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.

In the example provided, each element in Set A is mapped to one specific element in Set B.

Set A stands for the domain, whereas Set B stands for the range. There would be exactly one value in the range for each value in the domain as a result.

Hence, the mapping diagram above is a function since there are no two values in set B where there is only one mapping from  Set A.

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The risk-free rate of return on Hilo stock is 1.58%

What is the market risk premium?

Expected return on the stock=risk free rate beta x (expected market return-risk free rate)

14.08%=risk free rate+1.26 x (11.5%-risk free rate)

14.08%=risk free rate+14.49%-1.26 x risk free rate

0.41=0.26 x risk-free rate

risk-free rate=[tex]\frac{0.41}{0.26} %=1.58%[/tex]%=1.58%

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