Need help with number 33

The statement that describes the end behavior of the function\(f(x) = x^2 - 100 / x^2 - 3x - 4\)  is B. The function approaches 1 as x approaches -∞ and ∞

To determine the end behavior of the function, we can look at the highest degree terms in the numerator and denominator, which are \(x^2\) and \(x^2\), respectively. Therefore, we can simplify the function as:

\(f(x) = x^2 - 100 / x^2 - 3x - 4\) ≈ \(x^2/x^2 = 1\)

As x approaches ±∞, the denominator \(x^2\) becomes much larger than the numerator \(x^2 - 100\), and thus f(x) approaches 1. Therefore, the correct answer is "The function approaches 1 as x approaches -∞ and ∞" (option B)

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It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

122/1×1/100=1,22meters

The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Answer:

Step-by-step explanation:

\(x_{1}=7 \ ; y_{1} = -4\\\\x_{2} = -8 \ ; y_{2}=5\\\\CD = \sqrt{(-8-7)^{2}+(5-[-4])^{2}}\\\\=\sqrt{(-15)^{2}+(5+4)^{2}}\\\\=\sqrt{225+(9)^{2}}\\\\=\sqrt{225+81}\\\\=\sqrt{306}\\\\=\sqrt{3*3*2*17}\\\\=3\sqrt{34}\)

Distance = \(\sqrt{(x_{2}-x_{1})^{2}-(y_{2}-y_{1})^{2}}\)

Answer:

Simplifying radicals is the process of manipulating a radical expression into a simpler or alternate form. Generally speaking, it is the process of simplifying expressions applied to radicals.

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available.

Step-by-step explanation:

The radical symbol represents the root of a number and is read as x radical n or the nth root of x.

The symbol " that expresses a number's root is known as radical, and it is read as x radical n or the nth root of x. The horizontal line that surrounds the number is known as the vinculum, and the number beneath it is known as the radicand. The index or degree is the number n written before the radical.

The process of transforming a radical expression into a simpler or alternate form is known as simplifying radicals. In general, it is the process of simplifying expressions that are applied to radicals.

Estimation (or estimating) is the process of determining an estimate, or approximation, which is a value that can be used for a specific purpose despite the fact that the input data may be incomplete, uncertain, or unstable. The value is still useful because it is based on the best available information.

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We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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Answer:

The answer is B.

hope this helps

have a good day :)

Step-by-step explanation:

v=pi*r^2h

Answer:

5626.9m³

Step-by-step explanation:

V = πr²h

radius = 8

height = 28

to make it easier first step is to get the multiply the radius and the height but first multiple the radius by itself

=> 8 x 8 = 64

=> 64 x 28 = 1792

then multiply 1792 by π (3.14)

=> 1792 x 3.14 = 5626.88

when you round the answer it will be 5626.9

hope this helps and is right :)

Answer:

Hey mate.......

Step-by-step explanation:

This is ur answer......

Hope it helps!

Brainliest pls!

Follow me! :)

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Answer:

432000/135×100

Step-by-step explanation:

current house value is an increase of 35% oner the original value,

so if current value is 100% plus 35% or 135% of original value,

then original value is $432,000 / 135 x 100

The quotient of 258 divided by 4 is calculated to be 64.5

Division is considered to be one of the four basic operations of arithmetic. The other three are multiplication, addition, and subtraction, and they can be defined as how numbers are combined to make new numbers.

Out of the four basic operations, division is the process of splitting an amount or a number into equal parts.

In division, the numerator is the top number of a fraction, and on the other hand, the denominator is the bottom number of a fraction and the result of division is called the quotient

In this case, 258 is the numerator and 4 is the denominator;

258 / 4 = 64.5

Therefore the quotient of this division is calculated to be 64.5

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Answer:

14.4494397919

Step-by-step explanation:

Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.

A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.

Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.

According to the given information:

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Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)

\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)

Answer:

adef

Step-by-step explanation:

The mean of the test is 20.

To determine the mean of the test, we need to use the information provided about the scores falling above the mean in terms of standard deviations.

Let's denote the mean of the test as μ, and the standard deviation as σ.

We are given that a score of 29 falls three standard deviations above the mean, so we can write this as:

29 = μ + 3σ

Similarly, we are told that a score of 23 falls one standard deviation above the mean, which can be expressed as:

23 = μ + σ

Now we have a system of two equations with two variables (μ and σ). We can solve this system of equations to find the values of μ and σ.

From the second equation, we can isolate μ:

μ = 23 - σ

Substituting this value into the first equation, we have:

29 = (23 - σ) + 3σ

Simplifying the equation, we get:

29 = 23 + 2σ

2σ = 29 - 23

2σ = 6

σ = 3

Substituting the value of σ back into the second equation, we find:

μ = 23 - 3

μ = 20

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Answer: x = { 2 ; 3 }

+) x² - 3 = x² - 1 - 2 = (x - 1)(x + 1) - 2

+) x² - 3 is divisible by x-1 but (x -1)(x + 1) is divisible by x-1

=> 2 must be divisible by x-1

=> x - 1 is divisor of 2

=> (x - 1) ∈ {-1; 1; 2; - 2;}

but x > 1 => x - 1 > 0

⇒ x - 1 = {1; 2; }

+) with x - 1 = 1 => x = 2

           x - 1 = 2 => x = 3

Step-by-step explanation:

Check the picture below.

Answer:

english yes

Step-by-step explanation:

When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The two triangles are congruent if we can demonstrate that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.

Triangles are considered congruent by SAS if their two sides match those of the other triangle's corresponding two sides, and if their included angles are parallel in both triangles.

Hence we get the required answer.

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Answer:

approximately 4.75 units

Step-by-step explanation:

Using the law of sines, we have:

sin(A)/a = sin(B)/b

Substituting the given values, we get:

sin(45°)/a = sin(77°)/8

Solving for 'a', we have:

a = sin(45°) * 8 / sin(77°)

a ≈ 4.75 (rounded to two decimal places)

Therefore, the length of CB is approximately 4.75 units

Answer:5.81

Step-by-step explanation: I'm doing the assignment rn and got it right.

Answer:

A'(2,-5), B'(2,-1), C'(17,-5)

Answer:

Hi There

Your answers are:

4) 12/3

-10) YES!

0/10) 0 (zero)

2 & 3/4 ) 11/4

10 & 1/2 ) 21/2

.3) 3/10

-.16) -4/ 25

3.17) 3 & 17 /100

.3 repeating ) YES

.16 repeating) 1/ 6

-1.2 repeating ) YES!

If a decimal does not terminate or repeat is is not a rational number

Step-by-step explanation:

For 4)

4/1 = 12/x

Ask yourself, how do i get from 4 to 12?

Multiply by 3! HOWEVER, whats done to the numerator MUST be done to the denominator!

4/1 * 3/3 = 12/3

For -10 )

-10/1 = -20/2

Simplify -20/2!

Divide -20 by 2 = -10

-10/1 = -10/1 YES!

For 0/10 )

When you have ZERO tenths, what does that equal? Zero!

For 2 & 3/4ths )

To change to an improper fraction, multiply the 2 by the denominator and add that to the numerator. Put that over the original denominator

(2*4 +3) / 4

8+3 / 4 = 11/4

For 10 & 1/2 )

Repeat what you did for 2& 3/4ths!

(10*2+1)/2

20+1/2

21/2