Option b. The number of girls is neither significantly low nor significantly high.
How is the subjective judgement given?
Total number of births selected= 600
Half of the total number = 300
Number of girls = 309
As we can see, the number of girls is slightly higher than the half and not significantly higher . Therefore I can subjectively describe and conclude that the number 309 is neither significantly low nor significantly high. The total population of boys and girls are almost similar.What is subjective judgement ?
Subjective judgement is something that is based more on the individual's thoughts and feelings than on actual facts. The dominating eigenvector of a matrix of paired comparisons is a widely used technique for quantifying subjective judgement .To learn more about population, refer:
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To measure the height of a building, a person stands away from the base and measures the angle of elevation to the top of the building to be 48∘. Moving 170 feet closer, the angle of elevation to the top of the building is 73∘. How tall is the building?
The height of the building is 118. 89 feet
What are trigonometric identities?Trigonometric identities are simplify defined as arithmetic expressions or equations relating to many trigonometric functions, and is also known for holding true for all the values in the domain of the functions.
The different types of trigonometric identities includes;
sinecosinetangentcotangentsecantcosecantThe trigonometric ratios for major identities are;
sine = opposite/hypotenuse
tangent = opposite/adjacent
cosine = adjacent/hypotenuse
From the information given;
cos 43 = x/170
cross multiply
x = cos 43(170)
expand the bracket
x = 124.33 feet
To determine the height of the building is the opposite side
sin 73 = x/ 124.33
cross multiply
x = sin 73(124.33)
expand the bracket
x = 118. 89 feet
Hence, the value is 118. 89 feet
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HELP PLEASEE
MATHHHHHHH
Answer:
24
Step-by-step explanation:
divide the sides added together by the middle
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
The value of x such that f(x) and g(x) have equal values is 3
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?From the question, we have
f(x) = -2x + 4
g(x) = 2x - 8
The question implies that the functions have equal values
This means that
f(x) = g(x)
Substitute f(x) = -2x + 4 and g(x) = 2x - 8 in f(x) = g(x)
So, we have the following equation
-2x + 4 = 2x - 8
Collect the like terms
2x + 2x = 8 + 4
Evaluate the like terms
4x = 12
Divide both sides of the equation by 4
x = 3
Hence, the value of x such that the equations are equal is 3
The graph of the functionsSee attachment for the graph of the functions
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solve similar triangles (advanced) khan academy. solve for x
Answer: 10/3
Step-by-step explanation:
[tex]\frac{2}{6}=\frac{x}{10}\\\\x=\frac{10}{3}[/tex]
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To
make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts
that cost $3.00 per pound. He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does Sergio use? How many pounds of Spanish peanuts does Sergio use?
How many pounds of Virginia peanuts does Sergio use?
Assume he is making 10 lb of the $3.40 mixture
Let x = no. of pounds of the Virginia ($3.50) peanuts
Then (10-x) = no. of pounds of the Spanish ($3) peanuts
The Equation:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
.5x = 34 - 30
x = 4/.5
x = 8 pounds of Virginia peanuts
:
(b)How many pounds Spanish peanuts does Sergio use?
Spanish peanuts must be 2 pounds since the total is 10 pounds
:
Check:
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
How to get the equation of a parabola with 3 pointsy- intercept : (0, -1.4)x-intercept : (0.905,0)3rd point: (2,0.6)
he standard form of a quadratic efunctionis:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Where } \\ a,b,\text{ and }c\text{ are real constants such that }a\ne0. \end{gathered}[/tex]Since the y-intercept is (0, -1.4), it follows that:
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ \text{ Therefore,} \\ c=-1.4 \end{gathered}[/tex]Substitute c = -1.4 into the equation:
[tex]y=ax^2+bx-1.4[/tex]Since the x-intercept is (0.905, 0), it follows that:
[tex]\begin{gathered} a(0.905)^2+b(0.905)-1.4=0 \\ \text{Therefore,} \\ 0.819025a+0.905b=1.4-------(1) \end{gathered}[/tex]Since the graph passes through the third point (2, 0.6), it follows that:
[tex]\begin{gathered} 0.6=a(2)^2+b(2)-1.4 \\ \text{Therefore} \\ 4a+2b-1.4=0.6 \\ 4a+2b=0.6+1.4_{} \\ 4a+2b=2 \\ \text{Divide both sides by }2 \\ 2a+b=1 \\ \text{Hence} \\ b=1-2a---------(2) \end{gathered}[/tex]Substitute equation (2) into equation (1):
[tex]\begin{gathered} 0.819025a+0.905(1-2a)=1.4 \\ 0.819025a+0.905-1.81a=1.4 \\ \text{ Collect like terms:} \\ 0.819025a-1.81a=1.4-0.905 \\ -0.990975a=0.495 \\ \text{ Therefore,} \\ a=\frac{0.495}{-0.990975} \\ a\approx-0.5 \end{gathered}[/tex]Substitute a = -0.5 into equation (2), therefore,
[tex]b=1-2(-0.5)=1+1=2[/tex]Therfore the function is given by:
[tex]y=-0.5x^2+2x-1.4[/tex]The equation of the parabola is y = -0.5x² + 2x - 1.4
.
In triangle ABC, angle B is one-quarter of angle A and angle C is two fifth of angle A. If the size of angle A is (x- 10)°. Form an equation in x and hence calculate the angle of triangle ABC to the nearest degree.
When in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
The ∠A = (x-10) degrees
Angle B is one-quarter of angle A
∠B = (1/4)×(x-10)
= (1/4)x - (5/2)
= 0.25x-2.5
The angle C is two fifth of angle A
∠C = (2/5)(x-10)
= (2/5)x - 4
= 0.4x-4
We know sum of the angles in a triangle is 180 degrees
Then,
∠A + ∠B + ∠C = 180
Substitute the values in the equation
(x-10) + 0.25x-2.5 +0.4x-4 = 180
1.65x-16.5 = 180
1.65x = 196.5
x ≈ 119
∠A = (x-10)
= 119-10
= 109 degrees
∠B = 0.25x-2.5
= 0.25×119-2.5
≈ 27 degrees
∠C = 0.4x-4
= 0.4×119-4
≈ 44 degrees
Hence, when in triangle ABC, angle B is one quarter off angle B and angle C is two fifth of angle A and the angle A is (x-10) degrees, then the ∠A, ∠B and ∠C are 109 degrees, 27 degrees and 44 degrees respectively
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Choose all the expressions that are equal to 5/9 × 8
A.
[tex]\frac{9}{5\cdot8}=\frac{9}{40}\ne\frac{40}{9}[/tex]This is not a correct choice
--------------------------
B.
[tex]\frac{8}{9}\times5=\frac{40}{9}[/tex]This is a correct choice
---------------------------
C.
[tex]\frac{5}{8\times9}=\frac{5}{72}\ne\frac{40}{9}[/tex]This is not a correct choice
------------------------------------------------
D.
[tex]5\times\frac{1}{9}\times8=\frac{40}{9}[/tex]This is a correct choice
-------------------------------------------
E.
[tex]\frac{5\times8}{9}=\frac{40}{9}[/tex]This is a correct choice
In a certain instant lottery game, the chances of a win are stated as "4 in 25." Express the indicated degree of likelihood
as a probability value between 0 and 1 inclusive
The probability is
the probability of winning a lottery game out of all the games played is 0.16.
We are given that:
In a lottery game, the chances of win are = 4 in 25
So, this means that:
if a person plays 25 games of lottery, then he will probably win 4 games out of them.
So, we get that:
Total games = 25
Win games = 4
Probability = win games / total games
Substituting the values, we get that:
Probability = 4 / 25
P = 0.16
Therefore, we get that, the probability of winning a lottery game out of all the games played is 0.16.
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what is the y-intercept for the exponential function graphed below
Based on the attached graph, the y-intercept is 3
What is the y-intercept of the function?The y-intercept of the function is the point or points where the graph of the function crosses the y-axis i.e. the point where the value of x equals 0
How to determine the y-intercept for the graph of the exponential function?The graph that completes the question is added as an attachment
Using the definition above, we understand that
The y-intercept for the graph of the exponential function is the point where x = 0
On the attached graph, we have
y = 3, when x = 0
This means that the y-intercept for the graph of the exponential function is 3
This is so because the graph of the function crosses the y-axis at y = 3 when x = 0
Hence, the y-intercept of the exponential function is 3
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What amount of sales will produce a commission of $102.00 if the commission rate is 8.5%?
You would need sales of $[
Find the standard form of the equation
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y = x² +6x -16[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x for which the curve cuts/touches the x - axis are roots of that particular polynomial.
So, the values of x, when y = 0 are the roots of the given quadratic function.
that is : x = -8 and x = 2
And it can be represented as :
[tex]\qquad \tt \rightarrow \: (x - h1)(x - h2)= 0[/tex]
[ h1 and h2 represents roots of the quadratic function ]
[tex]\qquad \tt \rightarrow \: (x -2)(x + 8) = 0[/tex]
It can be further simplified as :
[tex]\qquad \tt \rightarrow \: {x}^{2} -2x +8x -16 = 0[/tex]
[tex]\qquad \tt \rightarrow \: x {}^{2} +6x -16 = 0[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Can someone help me with this please and thank youuu
The correct answer is:
[A]: " ∡2 is supplementary to ∡3 " .
___________________
The other answer choices given—which are correct statements—only prove that " a || b " {that is: "Line A" is parallel to "Line B".}
___________________
Find the difference.
(-3x²-xy-3y²) - (6x²-4xy+y²)
Enter the correct answer.
The difference between expression (-3x²-xy-3y²) - (6x²-4xy+y²) is
(-9x²+3xy-4y²).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Numerical ExpressionNumbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.
Algebraic ExpressionUnknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
= (-3x²-xy-3y²) - (6x²-4xy+y²)
= -3x²-xy-3y² - 6x²+4xy-y²
= (-9x²+3xy-4y²)
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Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T= {x|x is an integer and -5
The set T can be rewritten by listing its elements as T = {-4}.
What are sets?A set is a grouping of unique components that are denoted by curly brackets and commas.The term "elements of a set" refer to the collection of items in a set. A collection of fruits or a collection of images are two examples. Sets are additionally shown as follows.Set A = {a, b, c, d}. These are the elements of set A: a, b, c, and d.
Given:
Set T is equal to {x | x is an integer and -5 < x < -3}.
By examining the interval in the set, the set can also be written as something else.
It should be noted that the interval consists of two inequalities combined so that x > -5 and x < -3.
As -4 > -5 and -4 < -3 via the number line so it is the only element listed in the required set notation.
Hence, the set can be rewritten as
T = {-4}
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The complete question is: "Rewrite the set T by listing its elements. Make sure to use the appropriate set notation.
T = {x | x is an integer and -5 < x < -3}."
LET f(x)=4x+1 and g(x)=x²-5 (find (f+g) (x)
The function operation ( f + g )(x) of the functions f( x ) = 4x + 1 and g( x ) = x² - 5 is x² + 4x - 4.
What is the function operation ( f + g )(x) in the function?A function is simply a relationship that maps one input to one output.
Each x-values must have one y-value to qualify as a function.
Given the data in the question;
f( x ) = 4x + 1g( x ) = x² - 5( f + g )(x) = ?First, set up the function operation
( f + g )(x) = f(x) + g(x)
Replace the function designators f(x) and g(x) with the actual functions.
( f + g )(x) = f(x) + g(x)
( f + g )(x) = ( 4x + 1 ) + ( x² - 5 )
Collect and add like terms
( f + g )(x) = 4x + 1 + x² - 5
( f + g )(x) = 4x + x² - 5 + 1
( f + g )(x) = 4x + x² - 4
Reorder the function
( f + g )(x) = x² + 4x - 4
Therefore, the function operation ( f + g )(x) is x² + 4x - 4.
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oris is playing a game. She rolls three six-sided number cubes to tell her how many squares to move. If two number cubes show 4 and 3, how many different possible numbers of squares may she move on her turn?
6 possible values of squares that she can move.
What is possibility or probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
it is already known that Oris has to move 7 squares (because 3 + 4 = 7), yet she has another 6 sets of possibilities because a dice has 6 facets.
Hence she has 6 different possible numbers of squares she can move.
The possibilities are:
-8 squares (if she rolls a 1)
-9 squares (if she rolls a 2)
-10 squares (if she rolls a 3)
-11 squares (if she rolls a 4)
-12 squares (if she rolls a 5)
-13 squares (if she rolls a 6)
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If TR = 11 ft, find the length of PS. Round to the nearest hundredth.PTR16°Sarc PS =ft
Given:
TR = 11 Ft
∠RTS = 16°
Let's determine the length of Arc PS,
Step 1: Let's first determine the angle of Arc PS.
∠RTS = 16°
∠PTQ = 16° ; Vertical angle pair of ∠RTS
Since ∠QTR = ∠PTS under the rule of vertical angles, we can now determine the measure of ∠PTS or Arc PS.
We get,
[tex]\angle RTS\text{ + }\angle PTQ\text{ + }\angle QTR\text{ + }\angle PTS=360[/tex][tex]16\text{ + }16\text{ + }\angle PTS\text{ + }\angle PTS=360[/tex][tex]32\text{ + }2\angle PTS=360^{}[/tex][tex]\angle PTS=\frac{360^{}\text{ - 32}}{2}[/tex][tex]\angle PTS=\frac{328}{2}[/tex][tex]\angle PTS=164^{\circ}[/tex]Step 2: Let's determine the perimeter of the circle.
[tex]\text{ Perimeter = }2\pi r[/tex][tex]\text{ = 2}\pi(11)[/tex][tex]\text{ Perimeter = 22}\pi[/tex]Step 3: Let's determine the length of Arc PS.
[tex]\text{ Arc Length = (}\frac{\theta}{360})(\text{Perimeter of the Circle)}[/tex][tex]\text{ = (}\frac{164}{360})(22)(3.14)[/tex][tex]\text{ Arc Length = }31.469777\ldots\text{ }\approx\text{ 31.47 ft.}[/tex]Therefore, the length of Arc PS is 31.47 ft.
A unicycle wheel has a diameter of 24 inches.
Image_3150
If the wheel revolves 3 times clockwise, approximately how far does the unicycle travel? (Use 3.14 for π.)
The distance travelled by the unicycle is 226.08 inches.
What is the distance travelled?The first step is to determine the circumference of the wheel of the unicycle. A circle is a bounded figure which points from its center to its circumference is equidistant. The circumference of a circle is the distance round the circle.
Circumference of a circle = 2πr
Where:
π = pi = 3.14 r = radius = diameter / 2 = 24 / 2 = 12 inches3.14 x 2 x 12 = 75.36 inches
The next step is to multiply the circumference of the unicycle by the number of revolutions the tire made.
Distance travelled = 3 x 75.36 inches = 226.08 inches
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i..i
哈!
Natalie used 2 1/2 tubes of blue paint to
paint the sky in her picture. Each tube
holds 4/5 ounces of paint. How many
ounces of blue paint did Natalie use?
Estimate the intercepts of the graph of the function.
The graph of y equals two-thirds x minus 1 is shown. The graph appears to pass through the points ordered pair 0 comma negative 1 and ordered pair three-halves comma 0.
The x-intercept is about
, and the y-intercept is about
.
The x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .
X intercept of a function is defined as the point where the graph crosses the x axis ,
and the y intercept of the function is defined as the point where the graph crosses the y axis .
In the question ,
it is given that
the function is y= (2/3)x-1
to find the x intercept we substitute y as 0 in the equation
On substituting y as 0 , in the equation , we get
0 = (2/3)x-1
1=(2/3)x
x=1*(3/2)
x=3/2
the x intercept is 3/2.
to find the y intercept we substitute x as 0 in the equation
On substituting x as 0 , in the equation , we get
y=(2/3)*0-1
y=0-1
y= -1
so, the y intercept is -1 .
Therefore , the x intercept of the function y=(2/3)x-1 is 3/2 , and y intercept is -1 .
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Only #29,33,37,41,49 please show work THANK YOU
29) 3[tex]e^{2i}[/tex] = – 1.248 + 2.728 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{2i}[/tex] = 3 (cos[tex]2^{c}[/tex] + i sin[tex]2^{c}[/tex]) = 3 ( – 0.416 + i 0.909) = – 1.248 + 2.728 i
33) 3[tex]e^{\frac{5\pi i}{4} }[/tex] = – 2.12 + 2.12 i (conversion from polar form to rectangular a+bi form of complex number)
3[tex]e^{\frac{5\pi i}{4} }[/tex] = 3 (cos[tex](\frac{5\pi }{4})^{c}[/tex][tex]\frac{5\pi }{4}^{c}[/tex] + i sin[tex](\frac{5\pi }{4})^{c}[/tex] ) = 3 ( – 0.707 + i 0.707) = – 2.12 + 2.12 i
37) – 4 i = 4[tex]e^{\frac{3\pi}{2}i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 4 i = 0 – 4 i = [tex]\sqrt{0^{2}+(-4)^{2}}[/tex][tex]e^{i tan^{-1}\frac{-4}{0} }[/tex] = 4[tex]e^{\frac{3\pi}{2}i}[/tex]
41) – 3 + 4 i = 5 [tex]e^{2.214i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
– 3 + 4 i = [tex]\sqrt{(-3)^{2}+(4)^{2}}[/tex][tex]e^{tan^{-1}\frac{4}{-3}i}[/tex] = 5 [tex]e^{(\pi - 0.927)i}[/tex] = 5 [tex]e^{2.214i}[/tex]
49) 5 – i = [tex]\sqrt{26}e^{-0.197i}[/tex] (conversion from rectangular a+bi form to polar form of complex number)
5 - i = [tex]\sqrt{5^{2}+1^{2}}e^{tan^{-1}(\frac{-1}{5})i}[/tex] = [tex]\sqrt{26}e^{-0.197i}[/tex]
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On a horizontal number line, -43 is located to the left of -35.
Step-by-step explanation:
On a horizontal number line, -43 is located to the left of -35. TRUE because -43 is farther away (to the left) from 0 than -35.
At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply
Solution
Step 1:
Write the rational expression:
[tex]\begin{gathered} f(x)\text{ = }\frac{x+4}{x^2+5x-24} \\ \end{gathered}[/tex]Step 2:
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).
Step 3
[tex]\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}[/tex]Step 4:
\ertical} Asymptote is =-8,\ =3,
7.5.PS-13 Identify the solid from its net. Choose the correct answer below. o triangular prism o rectangular prism o square pyramid O triangular pyramid Click to select your answer and then click Check Answer.
The net image of a figure is a visual representation of the original figure.
From the given net image, the solid that has the net image can be said to be a traingular
g(x)=3x evaluate the function when x=-2, 0, 5
The function g(x) when x= - 2, 0 , 5 is -6 , 0 and 15 respectively.
What are functions?
The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given: g(x) = 3x
To evaluate : The function x= - 2, 0, 5.
g(-2) = 3× -2 = -6
g(0) = 3×0 = 0
g(5)= 3×5 = 15
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the total consumption of fruit juice in a particular country in 2006 was about 2.28 times 10 squared 9 gallons. The population of that country that year was 3 times 10 squares 8 what was the average number of gallons consumed per person in the country 2006
The average consumption of the fruit juice would be 7.6 gallons for the year 2006.
What do you understand by average consumption?Average consumption is derived by dividing the total measured consumption of that municipal service by that consumer during the three months before by three. It refers to the average consumption of a consumer of a municipal service during a certain time.
How is the average consumption determined?Utilizing the total of quantities consumed or dispersed over a period of time, typically 12 months, the average monthly consumption can be computed. The average number of units used each month is known as average monthly consumption, stock-outs corrected (CA).
Total consumption of the fruit juice in 2006=2.28x109 gallons.
Total population of the country in year 2006=3x108
Average Consumption=(2.28x109)/(3x108)
= 7.6 gallons
Hence the average consumption would be 7.6 gallons per person.
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In 2003, the price of a certain automobile was approximately $30,600 with a depreciation of $1,440 per year. After how many years will the car's value be $19,080?
a) Write an equation to model the problem. Let t represent the number of years after 2003. For example, the year 2005 would be represented by t = 2.
Answer: ?
b) Solve the equation to find the answer to the question above. (Note: Include the units, in this case years.)
Answer: ?
1) An equation that models the problem is x = 30,600 - 1,440t, where x is the value after t years.
2) After 8 years of straight-line depreciation, the car's value will be $19,080.
What is depreciation?Depreciation is an accounting term that refers to the periodic expensing of the cost of a long-term asset.
Using depreciation, a reporting entity annually recognizes the cost of an asset used for many years.
Intangible long-term assets use amortization or depletion instead of depreciation to describe the same meaning.
Price of an automobile in 2003 = $30,600
Annual depreciation = $1,440
The car's value after t years = $19,080.
Equation Solution:Value after t years = 30,600 - 1,440t
If 19,080 = 30,600 - 1,440t
1,440t = 30,600 - 19,080
1,440t = 11,520
t = 8 (11,520/1,440)
t = 8
= 8 years
Check:
x = 30,600 - 1,440t
x = 30,600 - 1,440(8)
x = 30,600 - 11,520
x = 19,080
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Hello I need help please
olution
e have the following statement:
If < ABC and < CBD are supplementary angles then m < ABC and m< CBD = 180º represents the definition of:
A) supplementary angles
help me answer this.
Solution:
The cube is numbered from 1 to 6
[tex](S)=6[/tex]The probability that any of the numbers from 1 to 6 will show will be
[tex]Pr(R)=\frac{1}{6}[/tex]The expected value will be calculated below as
[tex]E.V=xP(x)[/tex][tex]undefined[/tex]