An end behavior model for f(x) = [tex](8x^6-16x^3+8)/4x^2-4x-24)[/tex]

2x^2.
2x^3.
2x^4.
2x^6.

The total amount of the emergency fund is A) $6,516.91

First, we need to calculate the net income after deductions:

Next, we need to calculate the amount of constant expenses:

Fixed prices = 30% of $3,425.88 = $1,027.76

The entire amount saved inside the emergency fund is 5 months' worth of fixed costs:

Emergency fund = $1,027.76 x 5 = $5,138.80

To calculate the quantity inside the 60-day CD

We need to multiply 75% of the emergency fund by means of the interest rate and divide with the aid of 12 to get the monthly interest:

Therefore, the total amount of the emergency fund is:

$5,138.80 + $160.57 + $1,284.70 = $$6,516.91

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The relative frequency of 140-149 pound weight class is [tex]5.6[/tex]%.

The relative frequency refers to number of times an event occurs divided by total number of events occurring, so, its means ratio of frequency of an event to the total frequency.

The relative frequency of a class:

= (Frequency of class) / (Total frequency)

The frequency of 140-149 is 2.

The total frequency = sum of all frequencies which is:

= 2+3+4+7+5+6+5+4

= 36

The relative frequency of 140 - 149 pound weight class is:

= 2 / 36

= 1/18

= 0.056.

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Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

The illustration of p - q and p + (-q) using a number line is added as an attachment

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

p - q

Also, we have

p + (-q)

The above expressions mean that

To add two numbers (positive and negative), we can start from a point p, and then count backwards on the number line in q terms

Using the above as a guide, we have the following:

The illustration using a number line is added as an attachment

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Using the formula of compound interest, the number of years is 7.6 years

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

The formula of compound interest is given as;

[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]

But in this case, the interest was compounded continuously

[tex]A = Pe^r^t[/tex]

Substituting the values into the formula;

[tex]7450 = 5500e^(^0^.^0^5^2^5 ^* ^t^)[/tex]

Solving for t;

t = 7.6 years

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Answer:

-14 = k

Step-by-step explanation:

44 = k+58

Subtract 58 from each side.

44-58 = k+58-58

-14 = k

It will take the train 53.33 seconds to pass completely through the tunnel.

We have,

First, let's convert the speed from km/h to m/s:

54 km/h = 54000 m/3600 s = 15 m/s

We need to find the total distance the train travels, which is the sum of its length and the tunnel's length:

So,

distance = 180 m + 620 m = 800 m

Now we can use the formula:

time = distance/speed

time = 800 m / 15 m/s

time = 53.33 seconds

Therefore,

It will take the train 53.33 seconds to pass completely through the tunnel.

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A graph that represents the compound inequality include the following: D. graph D.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the inequality symbol represents less than, we can logically deduce that the first point would be located at negative 3, followed by positive 1, with an open circle on both sides.

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The expression for the calculation is:

[tex]\sf 3+12\times(14+19)[/tex]

Let us focus on "product of... and the sum of..." first. Whenever you have procedures arranged in an order similar to this, always remember that the second keyword tells you to put a mathematical operation inside grouping symbols, while the first keyword tells you to keep an operation isolated on the outside. In this exercise, the product of 12 tells you that you will be distributing it amongst another individual or set inside grouping symbols, which in this case is a "set inside grouping symbols" because the sum of 14 and 19 tells you that in order to complete the produced expression, the additive expression must be placed inside grouping symbols. Now, all we have left is 3, which can be added on either side of the entire expression because according to the order of operations, in this case, multiplication is performed before addition.

Hence the expression for the calculation is

[tex]\sf 3+12\times(14+19)[/tex]

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Answer:

6.6 x 10^6

Step-by-step explanation:

Question 20:

the complex number in trigonometric form r(cos + i sin 8), with 8 in the interval [0". 360") is  3[cos 90+ i sin 90°).

Option B is correct.

Question 21.

The expression in the standard form a + bi.

[2(cos 15" + i sin 15°)] is [tex]3\sqrt{} 2 + 3\sqrt{2} i[/tex]

Option C is correct.

Question 22

The  complex roots of-21  is :

5√2 (cos 54° + i sin 54°), %√2 (cos 126° + i sin 126°),% √2 (cos 198° + i sin 198°), 5√2 (cos 270° + i sin 270°), 5√2 (cos 342° + i sin 342°).

Option B is correct.

Complex roots are described as  the imaginary roots of equations, which are represented as complex numbers.

The expression : 2(cos 15° + i sin 15°) = 2e^(i15°) can be written in standard from as

2e^(i15°) = 2(cos 15° + i sin 15°)

= 2cos 15° + 2i sin 15°

=2cos 15° + 2i sin 15°

=  [tex]3\sqrt{} 2 + 3\sqrt{2} i[/tex]

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The expression [tex]3log_b(8) - log_b(7)[/tex] written as a single logarithm is [tex]log_b(\frac{512}{7})[/tex].

Given the logarithmetic expression in the question:

[tex]3log_b(8) - log_b(7)[/tex]

To rewrite the expression [tex]3log_b(8) - log_b(7)[/tex] as a single logarithm, we can use the properties of logarithms.

Using the quotient rule property, which states that:

logₙ(a) - logₙ(b) = logₙ(a/b)

Applying the quotient rule:

First, rewrite [tex]3log_b(8) - log_b(7)[/tex] as:

[tex]log_b(8^3) - log_b(7)[/tex]

Now, since the base of the logarithm is the same (b), we can combine the two logarithms using the power rule, which states that logₙ(aᵇ) = b × logₙ(a).

[tex]log_b(\frac{8^3}{7})[/tex]

Simplify

[tex]log_b(\frac{512}{7})[/tex]

Therefore, the single logarithm is [tex]log_b(\frac{512}{7})[/tex].

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A hot dog costs 2.25 we get it by solving the equation

Let's denote the cost of one hot dog by x.

Then we can set up two equations:

5x + 6y = 18.39

x + 2y = 4.63

where y is the cost of one bag of chips.

We want to solve for x.

Let us isolate variable y in the second equation

y = 4.63 - x/2

Substitute the y equation in the equation (1)

[tex]$5x + 6\left(\frac{4.63 - x}{2}\right) = 18.39$[/tex]

Simplifying this equation gives:

5x + 13.89 - 3x = 18.39

2x = 4.5

x = 2.25

Hence, a hot dog costs 2.25.

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Answer:

231002 = (2340)25 · 232 ≡ 125 · 529 = 529 ≡ 37 mod 41.

From matrix property it can be showed that A=B.

Given,

If A,B and x are matrices with x≠0 and AX=BX

Now,

X must be non-singular matrix because

A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]

AI = BI

= I( identity matrix )

⇒A = B

Hence Proved, A = B .

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After 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.

To calculate the final amount in your savings account after 7 years with continuous compounding, we can use the formula for compound interest with continuous compounding:

[tex]\[ A = P \times e^{rt} \][/tex]

Where:

- A is the final amount in the account

- P is the initial principal (the amount you deposit)

- e is Euler's number (approximately 2.71828)

- r is the interest rate (expressed as a decimal)

- t is the time period in years

In this case, you have won $12,000 in the lottery, so P = $12,000. The interest rate is [tex]7.5\%[/tex], which is equivalent to [tex]0.0.75[/tex] in decimal form. The time period is [tex]7[/tex] years.

Plugging these values into the formula, we get:

[tex]\[ A = 12000 \times e^{0.075 \times 7} \][/tex]

Calculating the exponential term:

[tex]\[ e^{0.075 \times 7} \approx 2.013 \][/tex]

Substituting this back into the equation:

[tex]\[ A = 12000 \times 2.013 \]\[ A \approx 24156.36 \][/tex]

So, after 7 years, you will have approximately $[tex]24,156.36[/tex] in your savings account.

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Answer: 21

Given:

  |7 + (-12)| + |-16|

Absolute value of -16:

  |7 + (-12)| + 16

Addition times subtraction is subtraction:

  |7 - 12| + 16

Subtract:

  |-5| + 16

Absolute value of -5:

  5 + 16

Add:

  21

The equation of the data table of values is y = 2ˣ

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

The data table with the values

x values 1, 2, 3, 4, 5

y values 2, 4, 8, 16, 32

From the above, we can see that the relationship between x and y is that

The number 2 takes the variable x as its exponent to get the variable y

Mathematically, this can be expressed as

y = 2ˣ

This represents an exponential function with a base of 2

Hence, the equation of the data table is y = 2ˣ

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The length of the other diagonal of the kite is: 50 cm

We want to find the area of the given kite but It should be noted that:

The hypotenuse is usually the slanted line part in a triangle.

Area of a kite = pq/2

where:

p and q are diagonals

We are given:

Area of Kite = 180 cm²

Length of diagonal = 16 cm

Thus:

16q = 180

q = 180/16

q = 50 cm

This gives us the length of the other diagonal of the kite

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The function of C(d) in the given inverse function is determined as C(d) = (d - 3)/10

option A.

The inverse of the given function is calculated by applying the principle of inverse of functions as follows;

let C(d) = 10d + 3

The inverse of the function is calculated as follows;

C = 10d + 3

make d the subject of the formula;

10d = C - 3

d = (C - 3)/10

Now replace, C with d;

C = (d - 3)/10

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Answer: 27.3 inches

Step-by-step explanation:

The value of the expression 20 − 9 ÷ m × 2 × n  for m = 3 and n = 2 is 8

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

20 − 9 ÷ m × 2 × n

The values of m and n are given as

m = 3 and n = 2

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

20 − 9 ÷ 3 × 2 × 2

Evaluate the quotient

So, we have

20 − 3 × 2 × 2

Evaluate the products

So, we have

20 − 12

Evaluate the difference

So, we have

8

Hence, the value of the expression is 8

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The mass of 405 cm³ of milk is 417.15 g.

To solve this problem need to use the formula:

mass = volume x density

The volume of milk given in the problem is 405 cm³ and the density of milk is 1.03 g/cm³.

Substitute these values in the formula to calculate the mass of the milk.

mass = 405 cm³ x 1.03 g/cm³

mass = 417.15 g

The mass of 405 cm³ of milk is 417.15 g.

To understand the concept behind this formula we need to understand what density is.

Density is defined as the amount of mass per unit volume of a substance.

It is expressed in units of grams per cubic centimeter (g/cm³) for solids and liquids.

The formula for calculating the mass of a substance is the product of its volume and density.

In this problem we have been given the volume and density of milk so we can easily calculate its mass using this formula.

The density of a substance can vary with changes in temperature and pressure.

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the paint set, sketchbook, brush price in turn are : 26 ; 19,5 ; 3,25$

Step-by-step explanation:

assume the price of the paint set is x($)

we have an equation

52,75-4= X + 3/4X +1/6×3/4X (4$ is the remaining amount after shiva bought these things above)

<=> X=26($)

Answer:

62.25

Step-by-step explanation:

this quadrilateral is a trapizoid

A = (a+b)/2 * h

a = x

b = 2.4+4.2+x

h = 7.5

we know x is 5 so we just plug it in

after doing that we get 62.25

An information that is needed to conclude that line segment EF is the bisector of ∠DEG include the following: m∠FEG ≅ ∠DEF.

In Mathematics and Geometry, an angle bisector simply refers to a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

By applying the angle bisector theorem, we can reasonably infer and logically deduce the following congruent angles;

m∠FEG ≅ ∠DEF (definition of angle bisector).

In conclusion, m∠FEG ≅ ∠DEF is the required information that proofs that line segment EF is the angle bisector of ∠DEG

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I'm also getting 22.9875, but the instructions say to round to 2 decimal places.

22.9875 rounds to 22.99 because 0.9875 is closer to 0.99 than it is to 0.98

In other words, 9875 is closer to 9900 than it is to 9800.

The value of angle marked 2xand x in the figure is

2x = 60

x = 30

The value of the angle is solved using complementary angles. These helps us arrive at the equation 2x + x = 90

solving for x

2x + x = 90

(2 + 1)x = 90

3x = 90

3x/3 = 90/3

x = 30

There fore

x = 30

2x = 2 * 30 = 60

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a) there are 8,535,316 ways to choose a dance committee of 8 students. b) there are 497,070 ways to choose a dance committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors. c) there are 4,410 ways to choose a dance committee consisting of 4 juniors and 4 seniors.

a) To determine the number of ways a dance committee of 8 students can be chosen, we need to consider the total number of eligible students and choose a group of 8 from them.

Total number of eligible students = 7 freshmen + 10 sophomores + 9 juniors + 7 seniors = 33 students

The number of ways to choose a committee of 8 students from a pool of 33 is given by the combination formula:

C(33, 8) = 33! / (8!(33-8)!) = 8,535,316

Therefore, there are 8,535,316 ways to choose a dance committee of 8 students.

b) To choose a dance committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors,

Number of ways to choose 2 freshmen from 7 freshmen = C(7, 2) = 21

Number of ways to choose 2 sophomores from 10 sophomores = C(10, 2) = 45

Number of ways to choose 2 juniors from 9 juniors = C(9, 2) = 36

Number of ways to choose 2 seniors from 7 seniors = C(7, 2) = 21

Total number of ways to choose the dance committee = 21 * 45 * 36 * 21 = 497,070

Therefore, there are 497,070 ways to choose a dance committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors.

c) To choose a dance committee consisting of 4 juniors and 4 seniors,

Number of ways to choose 4 juniors from 9 juniors = C(9, 4) = 126

Number of ways to choose 4 seniors from 7 seniors = C(7, 4) = 35

Total number of ways to choose the dance committee = 126 * 35 = 4,410

Therefore, there are 4,410 ways to choose a dance committee consisting of 4 juniors and 4 seniors.

d) The probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors

Favorable outcomes = 497,070 (from part b)

Total possible outcomes = 8,535,316 (from part a)

Probability = Favorable outcomes / Total possible outcomes

= 497,070 / 8,535,316

≈ 0.058 (rounded to the nearest thousandth)

Therefore, the probability of selecting a committee consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors is approximately 0.058.

e) The probability of selecting a committee consisting of 4 juniors and 4 seniors

Favorable outcomes = 4,410 (from part c)

Total possible outcomes = 8,535,316

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The theoretical probability of Constance getting an orange ring from the coin-operated machine is 0.182. This means that out of all the possible outcomes, there is an 18.2% chance that Constance will get an orange ring.

To find the theoretical probability of Constance getting an orange ring from the coin-operated machine, we need to first understand what theoretical probability means. Theoretical probability is the likelihood or chance of an event happening based on the number of possible outcomes. In this case, the possible outcomes are the different colored rings that the machine contains.

We are given that the machine contains 5 white rings, 6 orange rings, 7 purple rings, and 15 pink rings.

Therefore, the total number of rings in the machine is 5 + 6 + 7 + 15 = 33.

The probability of Constance getting an orange ring can be calculated by dividing the number of orange rings by the total number of rings in the machine.

Therefore, the theoretical probability of Constance getting an orange ring is:

6 / 33 = 0.181818...

To express this as a decimal, we can round it to the nearest thousandth, which is 0.182.

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