Equipment was acquired at the beginning of the year at a cost of $36,000. The equipment was depreciated using the double-declining-balance method based on an estimated useful life of ten years and an estimated residual value of $700.

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a. What was the depreciation for the first year?
fill in the blank

b. Assuming the equipment was sold at the end of year 2 for $8,860, determine the gain or loss on the sale of the equipment.
fill in the blank

The geometric sequence in which the 3rd term is of 18 and the 7th term is of 29/8 is defined as follows:

[tex]a_n = 40(0.67)^{n - 1}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms yields always the same result, called common ratio q.

The nth term of a geometric sequence is given by the rule presented as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The rule for the nth term is also called the general rule.

The general takes the first term as the reference term, however, the 7th term can be written as a function of the 3rd term, as follows:

[tex]a_7 = a_3q^{4}[/tex]

The fraction that represents the mixed number 3 and 5/8 is:

(3 x 8 + 5)/8 = 29/8.

Then the common ratio of the sequence is calculated as follows:

[tex]\frac{29}{8} = 18q^{4}[/tex]

[tex]q^4 = \frac{29}{144}[/tex]

[tex]q = \sqrt[4]{\frac{29}{144}}[/tex]

[tex]q = \left(\frac{29}{144}\right)^{\frac{1}{4}}[/tex]

q = 0.67.

Then the first term of the sequence is obtained as follows:

[tex]a_3 = a_1q^2[/tex]

[tex]a_1 = \frac{a_3}{q^2}[/tex]

[tex]a_1 = \frac{18}{(0.67)^2}[/tex]

[tex]a_1 = 40[/tex]

Then the definition of the geometric sequence is:

[tex]a_n = 40(0.67)^{n - 1}[/tex]

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Using the distance formula, the distance between A to point Z to the nearest tenth is 4.1 .

The 2D distance formula gives the shortest distance between two points in a two-dimensional plane.

Using the distance formula,

d = √(y₂ - y₁) + (x₂ - x₁)²

let's use the distance formula, to find the distance between point A and XZ.

Using the coordinates,

A(3, 3) and XZ(4, -1)

Therefore,

x₁ = 3

x₂ = 4

y₁ = 3

y₂ = -1

d = √(4 - 3)² + (-1 - 3)²

d = √1² + (-4)²

d = √1 + 16

d = √17

Therefore,

d = 4.12310562562

d = 4.1

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The sales tax percent when Ava went shopping for a new pair of pants is 3%.

From the information, Ava went shopping for a new pair of pants the listed price of the pair of pants was $21 but the price with tax came out to $21.63.

The sales tax will be:

= $21.63 - $21

= $0.63

The percentage of sales tax will be:

= Sales tax / Original price × 100

= 0.63 / 21 × 100

= 3%

The sales tax is 3%.

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The probability is 0.5881.

From the question, we have

n = 20

P(X[tex]\geq[/tex]10) = 1-P(X<10)

P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)

P(X[tex]\leq[/tex]9) = P(X=0)+P(X=1)+..................+P(X=9)

=0.4119

P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)

=1-0.4119

=0.5881

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:

a)  Line r

b)  Line q

c)  Line s

d)  Line q

e)  Line p

Step-by-step explanation:

A transversal is a line that crosses two other lines in the same plane at two distinct points.

a) The transversal connecting ∠1 and ∠5 is line r.

b) The transversal connecting ∠7 and ∠14 is line q.

c) The transversal connecting ∠8 and ∠11 is line s.

d) The transversal connecting ∠6 and ∠15 is line q.

e) The transversal connecting ∠3 and ∠9 is line p.

The exact interval notation of given equation is  x > - 8.

What is interval notation for compound inequalities?

The numbers that bound a continuous set of real numbers can be used to express the continuous set in interval notation. Intervals have many characteristics in common with ordered pairs when written.

We have,

            3x+1 > 2x-3 > x-11

Apply the rule that if m > v > n, then m > v and v > n to the given compound inequality to find the solution.

∴ m = 3x + 1,

   v = 2x - 3,

   n = x - 11.

Hence, by applying the rule of compound inequality we get,

          3x + 1 > 2x - 3 and 2x - 3 > x - 11

3x + 1 > 2x - 3

3x + 1 - 1 > 2x - 3 -1

3x > 2x - 4

3x - 2x > 2x - 4 - 2x

x > - 4

2x - 3 > x - 11

2x - 3 + 3 > x - 11 + 3

2x  > x - 8

2x  - x > x - 8 - x

x > - 8

The two computations above indicate that the acquired intervals, x > - 4 and x > - 8, will be combined to yield the answer to the given inequality.

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The probabilities are given as follows:

a) P(both marbles are red) = 0.167 = 16.7%.

b) P(red then green) = 0.111 = 11.1%.

c) P(green then blue) =  0.083 = 8.3%.

d) P(blue and red, any order) = 0.333 = 33.3%.

The probability of an event in an experiment is calculated as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, the are nine marbles, of which four are red, hence the probability of both red is:

p = 4/9 x 3/8 = 0.167 = 16.7%.

(the marble is not replaced, hence for the second marble there will be eight possible marbles, of which 3 are red).

For red then green, the probability is:

p = 4/9 x 2/8 = 0.111 = 11.1%.

For green then blue, the probability is:

p = 2/9 x 3/8 = 0.083 = 8.3%.

For blue or red, there are two possible outcomes, blue then red or red then blue, hence:

p = 3/9 x 4/8 + 4/9 x 3/8 = 0.333 = 33.3%.

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The area of triangle XYZ in the given graph with points X(-6,-5), Z(-4,-2) and Y(-2,-6) is 4 units square.

If the triangle's three vertices are specified on the coordinate plane, the area of a triangle in coordinate geometry may be determined. In coordinate geometry, a triangle's area is the area or space it occupies in the 2-D coordinate plane. The formula for finding the area of a triangle with three coordinates [tex](x_1,y_1), (x_2,y_2),[/tex] and [tex](x_3,y_3)[/tex]  is as follows:

Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Now, finding the area of trianlge with points X(-6,-5), Z(-4,-2) and Y(-2,-6).

Area of triangle [tex]=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

[tex]=\frac{1}{2}|-6(-2+5)-4(-6+5)+-2(-5+2)|\\=\frac{1}{2}\times|-18+4+6|\\ =4[/tex]

Therefore, the area of triangle XYZ in the given graph is 4 units square.

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Answer:

36.147580645161

Step-by-step explanation:

Hope it helps you

The equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.

According to the question,

We have the following information:

Points = (3,1)

Equation of the line: 2x+4y = 5

Now, converting this line into y = mx+b form:

4y = -2x+5

y = -2y/4+5/4

y = -y/2+5/4

Now, the slope of this line is -1/2.

Slope of the line perpendicular to this line will be 2 (-1/m).

Now, the equation of the line will be:

(y-y') = m(x-x')

x' = 3 and y' = 1

y-1 = 2(x-3)

y-1 = 2x-6

y = 2x-6+1

y = 2x-5

The value of m is 2 and b is -5.

Hence, the equation of the line that goes through the point (3, 1) and is perpendicular to the line 2x + 4y = 5 can be written in the form y = mx + b where m= 2 and b= -5.

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The previous population for the city is 23460.

Given that the population of a city has increased by 15% since it was last measured, the previous population will be:

= 1 - 15%

= 85%

Therefore, the previous population will be:

= Percentage × New population

= 85% × 27600

= 0.85 × 27600

= 23460

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By applying the distributive property of multiplication, this mathematical expression can be rewritten as -3(-4x + 5) = 12x - 15.

The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Mathematically, the distributive property of multiplication can be represented by this mathematical expression:

a(b + c) = ab + ac.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

-3(-4x + 5) = -3(-4x) + [-3(5)]

-3(-4x + 5) = 12x - 15.

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Answer:

y = -2/3 x + 8

Step-by-step explanation:

here is the answer in the image above

Step-by-step explanation:

your intercepts are:

y-intercept:

y = - 7/2x + 2

y = - 7/20 + 2

y = 2

( 0 , 2 )

x-intercept:

y = - 7/2x + 2

0 = - 7/2x + 2

-2 = - 7/2x

-7/2x = -2

2x = 2/7

x = 4/7

( 4/7 , 0 )

We have an odd degree polynomial wit a positive leading coefficient, then the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

Here we have the function:

f(x) = -10 + 6x^5 + 4x^3

Notice that this is a polynomial of degree 5 (odd degree).

When we have a odd degree polynomial, we know that:

If the leading coefficient is positive, then the end behavior is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

If instead, the leading coefficient is negative, then:

as x → -∞, f(x) → ∞

as x → ∞, f(x) → -∞

For the case of:

f(x) = −10+6x^5+4x^3

The leading coefficient is 6, so it is positive, then the end behavior of our function is:

as x → ∞, f(x) → ∞

as x → -∞, f(x) → -∞

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Answer: f(x) = x³ + 7x² -8x

Step-by-step explanation:

Zeros means that at that x-value, the graph crosses the x-axis and y = 0. Hence, to meet those criteria, the function would be:

[tex]f(x)=x(x+8)(x-1)[/tex]

At those three x-values, the corresponding y-values would equal 0.

Multiply them out to find the polynomial function:

[tex]f(x)=x(x+8)(x-1)=x(x^{2} -x+8x-8)=x^{3} +7x^{2} -8x[/tex]

Answer: not a function

Step-by-step explanation: one input has more than one output and to be a function it must have one output for every input.

I hope it’s right, best of luck :)

The number of calories in each serving is 125.14 calories.

The bad of popcorn has 438 calories. Also, it was stated that it can serve 3.5 people.

The number of calories for each serving will be the division of the calories given.

This will be:

Number of calories = Total calories / Number of people

= 438 / 3.5

= 125.14 calories

Each serving has 125.14 calories.

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Answer:

3

Step-by-step explanation:

[tex]27^{\frac{1}{3}}[/tex]

1 ) Factor the number [tex]27=3^{3}[/tex]

[tex]=\left(3^3\right)^{\frac{1}{3}}[/tex]

2 ) Simplify...

3

Hope this helps! :)

Area of the given figure is 27.852 in².

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

In the given figure there is a square.

First let us find the area of square, which has length of side 3 in

Area of square=3²=9

Now there are two semicircles with diameter 3 in.

Radius of semicircle = 3/2=1.5 in

Area of semicircle=2πr

=2×3.142×1.5

=9.426

As there are two semicircles

2×9.426

18.852

Area of figure is 9+18.852

27.852 in²

Hence, area of the given figure is 27.852 in².

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The number of cars that Tim has in all is 215.

The boxcars that Tim has is written in standard form. While the boxcars that Tim's grandfather gave him is written in scientific form. The first step is to convert the scientific form to standard form.

Number of boxcars that Tim's grandfather gave him: 1.62 x 10²

= 1.62 x 100

= 162

The next step is to add the boxcars that Tim's grandfather gave him to the number of boxcars that Tim has.

Total boxcars that Tim has = 162 + 53 = 215 box cars

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Answer:

1

Step-by-step explanation:

Answer:17

Step-by-step explanation:

its just the order of operations aka PEMDAS If you want to know more about the order of operations just look it up. :)

Answer: 190

Step-by-step explanation:

first you add 29 + 29 and you get 58.  Next, you add 66 + 66 which is 132 then you add the 2 sums together and get 190.  :)

The probability of more than 5 people is 0.4729

Since 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. To find the probability of more than 5 people use the emergency room, we use binomial probability.

The binomial probability of x is given by  P(X = x) = ⁿCₓpˣ(1 - p)ⁿ⁻ˣ

where

Since

We determine the probability of x ≤ 5.

So, P(X ≤ 5) = ¹¹C₀p⁰(1 - p)¹¹⁻⁰ + ¹¹C₁p¹(1 - p)¹¹⁻¹ + ¹¹C₂p²(1 - p)¹¹⁻² + ¹¹C₃p³(1 - p)¹¹⁻³

+ + ¹¹C₄p²(1 - p)¹¹⁻⁴ + ¹¹C₅p⁵(1 - p)¹¹⁻⁵

= ¹¹C₀(0.49)⁰(1 - 0.49)¹¹ + ¹¹C₁(0.49)¹(1 - 0.49)¹⁰ + ¹¹C₂(0.49)²(1 - 0.49)⁹ + ¹¹C₃(0.49)³(1 - 0.49)⁸

+ ¹¹C₄(0.49)⁴(1 - p)⁷ + ¹¹C₅(0.49)⁵(1 - 0.49)⁶

= (1)(1)(0.51)¹¹ + (11)(0.49)(0.51)¹⁰ + (55)(0.49)²(0.51)⁹ + (165)(0.49)³(0.51)⁸

+ (330)(0.49)⁴(0.51)⁷ + (462)(0.49)⁵(0.51)⁶

= 0.0006071 + (11)(0.49)(0.0011904) + (55)(0.2401)(0.0023341) + (165)(0.117649)(0.0045768)

+ (330)(0.0576480)(0.0089741) + (462)(0.0282475)(0.0175963)

= 0.0006071 + 0.0064163 + 0.0308230 + 0.0888452

+ 0.1707218 + 0.2296378

= 0.5270512

≅ 0.5271

So, P(X ≤ 5) = 0.5271, the probability of more than 5 people is P(X ≥ 5) = 1 - P(X ≤ 5)

= 1 - 0.5271

= 0.4729

The probability is 0.4729

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Answer: 12,000pd=6 tons

Step-by-step explanation:

Answer: function

Step-by-step explanation: for ever input the is one output, even though -10,5 showed up multiple times it had the same input and output. So it’s a function …if I remember correctly.

If the 5 is negative on just one, it’s not a function.

so sorry if it’s wrong, best of luck :)

Answer:

===================================

Continuous compounding equation:

Now find the time t for the balance to grow to $51806.67:

The time required is about 9 years.

Answer:

9 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for r to find the annual interest rate:

[tex]\implies \sf 39786.15=36000 \cdot e^{2.5r}[/tex]

[tex]\implies \sf \dfrac{39786.15}{36000}= e^{2.5r}[/tex]

[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=\ln e^{2.5r}[/tex]

[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=2.5r[/tex]

[tex]\implies \sf \dfrac{1}{2.5}\ln \left(\dfrac{39786.15}{36000}\right)=r[/tex]

[tex]\implies \sf r=\dfrac{2}{5}\ln \left(\dfrac{39786.15}{36000}\right)[/tex]

[tex]\implies \sf r=0.03999996933...[/tex]

[tex]\implies \sf r=0.04\;(2\;d.p.)[/tex]

Therefore, the annual interest rate is 0.04 = 4%.

To calculate how many years it will take for $36,000 to grow to $51,806.67, substitute the values into the formula and solve for t:

[tex]\implies \sf 51806.67=36000 \cdot e^{0.04t}[/tex]

[tex]\implies \sf \dfrac{51806.67}{36000}= e^{0.04t}[/tex]

[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= \ln e^{0.04t}[/tex]

[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= 0.04t[/tex]

[tex]\implies \sf \dfrac{\ln\left(\dfrac{51806.67}{36000}\right)}{0.04}=t[/tex]

[tex]\implies \sf t=9.10 \; (2\;d.p.)[/tex]

Therefore, it will take about 9 years for $36,000 to grow to $51,806,67.

Answer:

87 [tex]ft^{2}[/tex]

Step-by-step explanation:

11x9=99

99 ft is the area of the rectangle

Now we need the area of the triangle

4x6=24

24/2=12

12 ft is the area of the triangle so we subtract this from the area of the rectangle

99-12=87

Hopes this helps please mark brainliest