Guess the value of the following limit (if it exists) by evaluating the function at the given numbers.

Answer:

Step-by-step explanation:

To calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method, we need to first find the straight-line rate, and then find the diminishing-balance rate by doubling the straight-line rate.

Step 1: Calculate the straight-line rate

The straight-line rate can be calculated as follows:

SLR = (Cost - Residual Value) / Useful Life

SLR = (32900 - 4700) / 4

SLR = $27,600 / 4

SLR = $6,900 per year

Step 2: Calculate the diminishing-balance rate

The diminishing-balance rate can be calculated as follows:

DBR = 2 * SLR

DBR = 2 * $6,900

DBR = $13,800

Step 3: Calculate the depreciation expense for each year

The depreciation expense for each year can be calculated as follows:

Year 1: Depreciation Expense = Cost * (DBR / 2)

Year 1: Depreciation Expense = $32,900 * ($13,800 / 2)

Year 1: Depreciation Expense = $32,900 * $6,900

Year 1: Depreciation Expense = $227,621

Year 2: Depreciation Expense = (Cost - Year 1 Depreciation) * (DBR / 2)

Year 2: Depreciation Expense = ($32,900 - $22,761) * ($13,800 / 2)

Year 2: Depreciation Expense = $10,139 * $6,900

Year 2: Depreciation Expense = $70,223

Year 3: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation) * (DBR / 2)

Year 3: Depreciation Expense = ($32,900 - $22,761 - $70,223) * ($13,800 / 2)

Year 3: Depreciation Expense = $10,016 * $6,900

Year 3: Depreciation Expense = $68,609

Year 4: Depreciation Expense = (Cost - Year 1 Depreciation - Year 2 Depreciation - Year 3 Depreciation) * (DBR / 2)

Year 4: Depreciation Expense = ($32,900 - $22,761 - $70,223 - $68,609) * ($13,800 / 2)

Year 4: Depreciation Expense = $21,307 * $6,900

Year 4: Depreciation Expense = $146,763

So, the depreciation expenses for each year of the equipment's life are:

Year 1: $22,761

Year 2: $70,223

Year 3: $68,609

Year 4: $146,763

This is how you can calculate the depreciation expense for each year of the equipment's life using the diminishing-balance method.

Answer:

5

Step-by-step explanation:

We can assume ∠KLJ ≅ MLJ. So we put them equal to each other.

[tex]42=9x-3\\45=9x\\5=x[/tex]

The value of x when an angle of the given figure is given as 9x - 3 is x = 5.

Given a figure.

It is required to find the value of x.

Here, consider the two triangles which are split up in the figure.

Consider the triangles JKL and JML.

Comparing the sides and angles:

JK = JM

KL = ML

JL = JL

So, they are similar.

Each corresponding angles are equal.

Here, the angle corresponding to ∠JLK is ∠JLM.

So, they are equal.

∠JLM = ∠JLK

9x - 3 = 42

Add 3 on both sides.

9x = 45

Divide both sides by 9.

x = 5

Hence, the value of x is 5.

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Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.

The second question requires the calculation of 12.5% of $100, which is equal to $12.50.

For the third question, 130 is 20% of 650.

For the fourth question, $5.40 is 120% of $4.50.

For the fifth question, $8.40 is 30% of $28.

For the sixth question, 56% of 39 is $21.84

For the seventh question, $495 is 55% of $900.

For the last question, 144 is 60% of 240.

Step-by-step explanation:

Answer:

Step-by-step explanation:

26

12.5

20%

120%

30%

12.23

900

60%

Answer:

22 feet

Step-by-step explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

Therefore:

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel.  Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

[tex]\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow[/tex]

[tex]\implies \sf h:168=66:42[/tex]

[tex]\implies \sf \dfrac{h}{168}=\dfrac{66}{42}[/tex]

[tex]\implies \sf h=\dfrac{66}{42} \cdot 168[/tex]

[tex]\implies \sf h=\dfrac{11088}{42}[/tex]

[tex]\implies \sf h=264\;inches[/tex]

Convert the height into feet by dividing by 12:

[tex]\implies \sf h=\dfrac{264}{12}=22\;feet[/tex]

Therefore, the height of the flagpole is 22 feet.

Answer: The profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), so:

P(x) = R(x) - C(x) = (-0.5(x-80)^2 + 3,200) - (30x + 200)

The domain of P(x) is the set of all possible values of x for which the profit calculation makes sense. In this case, the company has a maximum capacity of 130 items, so the domain of P(x) is 0 <= x <= 130.

To calculate the profit when producing 50 items and 60 items, we simply plug in these values for x in the profit function:

Profit when producing 50 items = P(50) = (-0.5(50-80)^2 + 3,200) - (30 * 50 + 200) = $2350

Profit when producing 60 items = P(60) = (-0.5(60-80)^2 + 3,200) - (30 * 60 + 200) = $2280

Since the profit is higher for producing 50 items, the company should choose to produce 50 items.

From our model, we can see that as the production increases, the cost also increases linearly with a slope of 30, while the revenue increases parabolically but with a negative slope, meaning that after reaching a certain point, the increase in revenue becomes slower compared to the increase in cost. This is why the profit decreases as the production increases, and therefore the company makes less profit when producing 10 more units.

Step-by-step explanation:

The equation in slope-intercept form is y = 10x + 41.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-3, -4).

Points on y-axis = (11, 1).

At point (-3, 11), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 11 = (1 - 11)/(-4 + 3)(x + 3)

Y - 11 = 10(x + 3)

y = 10x + 30 + 11

y = 10x + 41.

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Answer

D. 4.2794....

Step-by-step explanation:

A, B, and C all have repeating decimal numbers, meaning they are rational. D's decimals are not repeating but infinite, meaning it is an irrational number.

The input is 8, the output of the function f(x) would be -5.

What is the function?

Function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet

To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:

f(x) = 8/x - 6

f(8) = 8/8 - 6

f(8) = 1 - 6

f(8) = -5

Hence, if the input is 8, the output of the function f(x) would be -5.

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Answer:

The 3rd and 6th equations

Step-by-step explanation:

Any equation that has a variable with an exponent is nonlinear and the 3rd and 6th equations follow this requirement.

Amelia and Lucas' son's weight is 17.41 kilograms.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 km = 1000 m

We have,

Amelia and Lucas' son's Weight = 38.3 pounds.

1 kilogram = 2.2 pounds

Multiply 38.3/2.2 on both sides.

17.41 kilograms = 38.3 pounds

Thus,

Amelia and Lucas' son's weight is 17.41 kilograms.

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Using a TI-83, TI-83 Plus, or TI-84 Population standard deviation is 56.4 and Population variance is 3178.5 .

To calculate the population standard deviation and variance using a TI-83, TI-83 Plus, or TI-84 calculator, we can use the following steps:

Enter the data into a list on the calculator. To do this, press the STAT key, then select Edit. Enter the data into L1.

Calculate the sample mean by pressing STAT, then CALC, then 1-Var Stats. Make sure L1 is selected as the list, then press ENTER.

Find the population variance by pressing STAT, then CALC, then 2-Var Stats. Make sure L1 is selected as the list, then press ENTER. The variance will be displayed as sX².

Take the square root of the population variance to find the population standard deviation. To do this, press the MATH key, then select PRB, then select 5:√(. Enter the population variance, then press ENTER.

Using this method, we find that the population standard deviation is approximately 56.4 and the population variance is approximately 3178.5.

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Complete question is:

A statistics professor gives a survey to each of the 10 students in an introductory statistics course. The survey asks the students how many text messages they think they sent yesterday. The data are included below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the population standard deviation and the population variance. Round your answers to one decimal place .

Texts sent yesterday: 29 211 130 21 5 21 19 67 60 95

Answer:

6.28375

Step-by-step explanation:

times the radius will fit = x

8 * x = 50.27

x= 50.27÷8

x=6.28375

The probability that the hacker guesses the password on his first try is, 0.001600.

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.

The probability can be calculated as:

= 1 / 5⁴

= 1 / 625

= 0.0016

Rounded to six decimal places, the probability is: 0.0016 = 0.001600.

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Answer:

The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.

Step-by-step explanation:

(a) A' = {b, d}

(b) B' = {a, c, d}

(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)

(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)

(e) A' n B = {} (the intersection of A' and B is an empty set)

(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)

(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)

(h) B' n B = {} (the intersection of B' and B is an empty set)

(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)

(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)

(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)

(l) A' n B' = {} (the intersection of A' and B' is an empty set).

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

The number is 29.

Step-by-step explanation:

"five times the sum of a number and two" can be represented as 5(x + 2), where x is the number. "nineteen less than six times the number" is the same as 6x - 19. The word "is" determines that these two parts are equal. So, 5(x + 2) = 6x - 19.

Solve:

5x + 10 = 6x - 19

10 = x - 19

x = 29

Check:

5 * (29 + 2) = 5 * 31 = 155

(6 * 29) - 19 = 155

155 = 155

The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21

What is a plane?

Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.

Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3

Any  plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k

Now, this plane should contain the line mentioned above

On substituting the terms,

5(2 + t) + 2(4 - t) + (3 - 3t) = k

10 + 5t + 8 - 2t + 3 -3t = k

21 = k

Therefore, The equation of the required plane is 5x + 2y + z = 21

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Answer:

A = 0.50x+20

B= 0.75x+22

4 games

$19

Step-by-step explanation:

For abbey, the 20 dollars she starts with is the initial value. the 50 cents per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be A = 0.50x + 20. For Bianca, the 22 dollars she starts with is her initial value. the 75 centers per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be B = 0.75x + 22.

We can find out when they will have the same amount of money left by making two small tables -> one for abbey and one for Bianca.

Abbey: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

Bianca: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

For both girls after four games, they have the same amount of money- $19.

There are a total of 13 different ornaments to choose from, with 3 types of ornaments.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

When Cherry chooses at least 1 of each type, she will have to select a total of 5 ornaments. This means that Cherry can make a total of 13C5 (13 choose 5) different selections. This is equal to 715 different selections.

This can also be calculated by first selecting 1 ornament from each of the 3 types, which gives 3 different selections. Then, for the 2 remaining ornaments, Cherry can select any of the 13 ornaments, giving a total of 3 x 13 = 39 different selections. In total, this gives 3 + 39 = 42 different selections.

To conclude, Cherry can make a total of 715 different selections when she chooses at least 1 of each type of ornament.

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The number of gallons of paint that the painter should buy is; 4 gallons

The parameters given are;

Side length of cube = 20 ft

Area that a gallon of paint can cover = 400 square feet

Since the room is shaped like a cube, then it will have 4 equal wall areas.

Area of one wall = 20 * 20 = 400 square feet

Area of 4 walls = 4 * 400 = 1600 square feet

Since 400 sq.ft  is covered by 1 gallon, then;

1600 sq.ft = (1600 * 1)/400

= 4 gallons

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Reciprocal of 0.0002 is:

Reciprocal of c/d:

Reciprocal of 1 2/3 is:

Use identity x² - y² = (x - y)(x + y) to solve the following questions.

Evaluate  173² - 127²:

Evaluate (8.70)²- (8.60)²:

Evaluate 1003²- 9​:

Organizar la riqueza a través de la pro- ducción de bienes y servicios es una característica de la empresa que se relaciona con su A) fin lucrativo.

Las empresas tienen como objetivo principal la maximización de sus ganancias y el crecimiento económico a través de la producción y venta de bienes y servicios. La obtención de ganancias es el fin lucrativo de la empresa y es a través de él que se organiza la riqueza generada por la empresa.

Sin embargo, las empresas también tienen una serie de responsabilidades sociales y éticas, por lo que pueden combinar su fin lucrativo con una cierta responsabilidad social o económica.

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In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.

In right triangle ABC,

BC is the base.

Midpoint of AB is D.

CD bisects ACB.

Measure of ∠ACD = Measure of ∠BCD

AC = 4

BC = 7.5

AD = 3

BD = x

CD bisects angle ACB and intersect at midpoint of AB at point D.

This implies

BD / AD = BC / AC

⇒x / 3 = 7.5 / 4

⇒ x = ( 7.5 × 3 ) / 4

⇒ x = 22.5 / 4

⇒ x = 5.625

Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.

The above question is incomplete , the complete question is :

What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.

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Answer:

A=25t.

Step-by-step explanation:

..........................

y-intercept(s): (0,−2)

Answer:

2

Step-by-step explanation:

The [tex]x^{2}[/tex] and x terms are made to follow the sequence:

[tex][a-b]^{2} =a^{2} -2ab + b^{2}[/tex]

Therefore the [tex]b^{2}[/tex] term has to be added to complete the [tex][a -b]^{2}[/tex] sequence, but at the same time the [tex]b^{2}[/tex] term has to be balanced as it is not originally present in the equation:

[tex]y = x^{2} - 3x + 2 = [(x)^{2} - 2(x)(\frac{3}{2}) + (\frac{3}{2})^{2}] + 2 - (\frac{3}{2})^{2}[/tex]

  [tex]= [x - \frac{3}{2}]^{2} + 2 - \frac{9}{4}[/tex]

  = [tex][x - \frac{3}{2}]^{2} + \frac{8}{4} - \frac{9}{4}[/tex]

  = [tex][x- \frac{3}{2}]^{2} \frac{+ 8-9}{4}[/tex]

  = [tex][x-\frac{3}{2}]^{2} -\frac{1}{4}[/tex]

y-intercept is the y-value obtained when x = 0 in the equation:

[tex]= [0 - \frac{3}{2}]^{2} -\frac{1}{4}[/tex]

= [tex](-\frac{3}{2})^{2} -\frac{1}{4}[/tex]

= [tex]\frac{9}{4} - \frac{1}{4}[/tex]

= [tex]\frac{8}{4}[/tex]

= 2

The number of bags of sand that has to be used would be 92

diameter = 30 yards

width of path = 5 yards

diameter with path

30 + 2 * 5

= 40 Yd

area of path = area of garden with path - ara of garden

= 3.14 * 40² / 4 - 3.14 * 30² / 4

= 1256 - 706.5

= 549.5

area covered by bag = 549.5 / 6

= 91.58

= 92 bags

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Answer:

Below

Step-by-step explanation:

See image

L side goes from    3 units   to   6 units    so scale factor is 2

Step-by-step explanation:

(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:

36,078 feet / 6 feet/fathom = 6,013 fathoms

So the depth of the seabed is 6,013 fathoms.

(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):

36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)

So the depth of the seabed is approximately 6.52 leagues (marine).

The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years

To solve this problem, we can use the formula for exponential growth:

V(t) = V₀ * (1 + r)^t

Given that the parameters are;

To determine time t when the value of the equipment will be less than $7500.

Let's set up an inequality;

V(t) < 7500

Substituting the formula for V(t), we get:

V₀ * (1 + r)^t < 7500

Substitute the values

(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

Hence, the value is 2.64 years.

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Answer:10 1/2

Step-by-step explanation:

Jasper is approximately 18.67 years old as per the given ratio.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, the ratio of your age and the age of Jasper is 3:4.

Let's use this ratio to find out how old Jasper is if you are 14.

First, we can set up a proportion:

3/4 = 14/x

where x is Jasper's age.

To solve for x, we can cross-multiply:

3x = 4 * 14

3x = 56

x = 56/3

x ≈ 18.67

So if you are 14 and the ratio of your age to Jasper's age is 3:4, then Jasper is approximately 18.67 years old.

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On solving the provided question, we can say that the function is

[tex]f(z) = 3 - 4z^2[/tex]  and f(-2) = -13 and f(0) = 3.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is

[tex]f(z) = 3 - 4z^2[/tex]

[tex]f(-2) = 3 - 4(-2)^2[/tex]

= 3 -  4(4)

= 3 - 16

=-13

[tex]f(0) = 3 - 4(0)^2[/tex]

= 3 - 4(0)

= 3 - 0

= 3

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