The linear function is V(x) = 800x + 2400.
Given,
The cost of computer when purchased (the initial book value), V = 2400 (x = 0)
Company chooses to depreciate for 3 years using straight line method.
The book value after 3 years = 0 (x = 3)
We have to write a linear function that expresses the book value of the computer as a function of its age V(x).
Here, the value is depreciating over 3 years.
That is 2400 in 3 years = 2400/3 = 800
That is depreciating $800 in a year.
Now we can write the equation as:
V(x) = 800x + 2400
When we consider slope-intercept form, we can check that the above given equation of a line passes through two points: (0, 2400) and (3, 0)
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A bowl contains four candies-red, brown, yellow, and green. Draw two candies at random, one for you to eat, and one for
a friend. (Assume you eat the first candy drawn.)
List the simple events in the sample space. (Enter your answers as a comma-separated list. Enter each simple event in the
format (C₁, C₂) where C, is the color of the ith candy. Use R for red, B for brown, Y for yellow, and G for green.)
By using the given notation and format, we see that the sample space for the experiment is:
( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})
How to get the sample space?The sample space is the set of the total possible events or outcomes in a given experiment.
Here we have 4 candies and you select two, such that the events have the format:
(C₁, C₂)
For example, if the first candy you draw is red and the second is blue, then the event will be:
(R, B)
Which is different to the event when you first draw blue and then red, which is:
(B, R).
So we just need to write all the possible events, it will give use the sample space:
( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})
Where the notation used is the given one:
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Same set up as the problem to the left
Answer:
you need to show the options at the bottom
Step-by-step explanation:
draW AND LABEL A FIGURE THAT HAS ATLEAST 2 LINES , 2 RAYS
The figure with 2 lines and 2 rays is drawn and labeled and can be seen in the attached picture.
In the question, we are asked to draw and label a figure that has at least 2 lines and 2 rays.
First, we need to note three things:
Line: A line is a collection of points that continues endlessly in two opposing directions. Arrows at both ends are used to imply that it goes on indefinitely.Line Segment: An element of a line with a start point and an endpoint is called a line segment. It has two terminals that serve as indicators of its length.Ray: A ray is a segment of a line with an undefined endpoint but a start point. It has a single starting point with an arrow at the other end, indicating that it continues in that direction indefinitely.Now, we are asked to make a figure with 2 lines (that is, two endless collections of points) and 2 rays (that is, a part of the line with a fixed start point, but no end point).
This can be shown in the attached figure.
In the figure, AB and CD are the two lines, and PQ and XY are the two rays.
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x² - 81 and x² - 2x - 63
Find the LCM of the given polynomials.
Factor completely.
The LCM of the given polynomials x² - 81 and x² - 2x - 63 is (x - 9)(x + 7)(x + 9), which on expansion looks like x³ + 7x² - 81x - 567.
In the question, we are given two polynomials x² - 81 and x² - 2x - 63.
We are asked to find the LCM of the given polynomials.
To find the LCM of two polynomials, we multiply all the factors of both polynomials uniquely.
So first, we factor both the given polynomials.
x² - 81
= x² - 9² [∵ 81 = 9²],
= (x + 9)(x - 9) [Using the formula a² - b² = (a + b)(a - b)].
x² - 2x - 63
= x² - 9x + 7x - 63 [Mid-term factorization],
= x(x - 9) + 7(x - 9) [Grouping],
= (x + 7)(x - 9) [Grouping].
After factorizing the polynomials, we can note that the unique factors of x² - 81 and x² - 2x - 63 are (x + 9), (x -9), and (x + 7).
Thus, the LCM can be shown as their products, which is:
LCM = (x - 9)(x + 7)(x + 9), which on expansion looks like x³ + 7x² - 81x - 567.
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x+y = 3
x-3y = -9
What is the solution (x, y) to the system of equations above?
Answer:
(0, 3)
[tex]x=0\\y=3[/tex]
Step-by-step explanation:
You can rewrite the first equation as [tex]y=3-x[/tex]. Then, you can substitute into the second equation as follows:
[tex]x-3(3-x)=-9\\x-9+3x=-9\\4x=0\\x=0\\[/tex]
Now, we can substitute this value into the first equation.
[tex]x+y=3\\0+y=3\\y=3[/tex]
Writing this in the form of [tex](x, y)[/tex] will yield [tex](0, 3)[/tex].
Remember when setting this out, align your equal signs and give good mathematical reasoning as shown above.
Hope this helps you!
a. A square classroom has a perimeter
of 120 yards. What is the length of
each side of the classroom?
Answer:
the answer is 30 yd
Step-by-step explanation:
substitute the given values into the given formula and solve for the unknown variable. If necessary, round to one decimal place.
The value of the height is 17
what is expression?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
Volume, V = 1/3πr²h
Volume= 1138.8,
π=3.14
r= 8
h= 3V/πr²
h= 3* (1138.8)/3.14* 8*8
h=3416.4/200.96
h=17
Hence, the value of height is 17
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The formula for surface area of sphere is A = 4πr2, Where r is the length of the radius. find the surface area of a sphere with a radius of 14 feet. use 22/7 for π
The surface area of the sphere is 1232² feet.
What is a sphere?A sphere is a three-dimensional analog of a two-dimensional circle. A sphere is a collection of points in three-dimensional space that are all the same distance r from a given point. The given point is the sphere's center, and r is the radius of the sphere.The formula for the surface area of the sphere: 4πr²
Now, substitute the values in the formula as follows:
The formula for the surface area of the sphere = 4πr²The formula for the surface area of the sphere = 4 × 22/7 × 14²The formula for the surface area of the sphere = 4 × 22/7 × 14 × 14The formula for the surface area of the sphere = 4 × 22 × 14The formula for the surface area of the sphere = 1232² feetTherefore, 1232² feet is the surface area of the sphere.
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For the word problems below, you MUST show work to earn full credit
(a.) Hailey's plane took 90 seconds to climb 4,500 feet.
(i)What is the speed of her plane in feet per
second?
(ii) How high was the plane at 35 seconds?
Answer:
(i) 50 ft/s
(ii) 1750 ft
Step-by-step explanation:
(i)
The vertical speed is:
4500 ft / 90 seconds = 50 ft/s
(ii)
50 ft/s × 35 s = 1750 ft
Compare the expressions. Select the correct sign to fill the space.
<
>
=
Answer:
<
Step-by-step explanation:
A figure is shown below. What is the area of the figure?
Answer:
Dimensions: 24, 24, 104
Total: 152 cm²
Step-by-step explanation(Triangles):
Given the triangles are equal to each other, we only need to solve one to get the other.
[tex]A = \frac{h \times b}{2} \\A = \frac{8 \times 6}{2}\\A = 24[/tex]
Therefore, the triangles' area are 24 cm.
Step-by-step explanation(Trapezoid):
Because of the height being unknown, we can define that using the side triangles. These triangles have a height of 8, so that also means the trapezoid has a height of 8. Now we can solve.
[tex]A = \frac{a+b}{2}\times h\\A = \frac{10+16}{2}\times 8\\A = 104[/tex]
Step-by-step explanation(Addition):
Finally, we add the 3 values.
[tex]24 + 24 + 104 = 152\:cm^2[/tex]
Lastly,
Hope this helps!
4^4 x 8^2 = [?]
Will pick brainliest to the most detailed answers, so try your hardest!
Answer:
16,384
Step-by-step explanation:
4^4 = 4×4×4×4=256
8^2 = 8×8=64
256×64=16,384
Answer:
16384 or [tex]2^{14}[/tex]
Step-by-step explanation:
This is easiest done by creating identical bases (the number being raised by the exponent, 4 and 8 here).
How do we do that? Well let’s start with [tex]4^{4}[/tex].
For both 8 and 4 the bases can be rooted to 2
[tex]\sqrt[3]{8} = 2 \\ \sqrt{4} = 2[/tex]
Because the root of 4 is 2, that means [tex]2^{2} =4[/tex].
Therefore, we can substitute [tex]2^{2}[/tex] for 4 in [tex]4^{4}[/tex], which looks like this:
[tex]2^{2^{4} }[/tex]
And, we should know that an exponent raised to an exponent is the same as multiplying those exponents together. This means [tex]2^{2^{4}} =2^{8}[/tex].
We can repeat the process with [tex]8^{2}[/tex]
[tex]8 = 2^{3} \\8^{2} =2^{3^{2} } \\2^{3^{2} } =2^{6}\\8^{2}=2^{6}[/tex]
Now that we have [tex]2^{8}\ and\ 2^{6}[/tex] we can continue. Given that the bases are the same we can simply add the exponents together when we multiply.
[tex]2^{8}[/tex] x [tex]2^{6}[/tex] = [tex]2^{14}[/tex] (or 16384).
19% of 288 estimated + rounding
Answer:
54.7
Step-by-step explanation:
19% of 288
0.19 * 288 = 54.72
54.72 = 54.7
Answer:
Estimated 60 and rounded 55 and normal 54.72.
Step-by-step explanation:
To get the estimated answer, first convert the percentage to a decimal: 19% = 0.19. Second, you have to round the 2 numbers so they are easier to multiply: 0.19 = 0.20 and 288 = 300. Now that you have the 2 rounded numbers, you can multiply them to get the estimated answer: 0.20 x 300 = 60 so 60 is your estimated answer.
To get the rounded answer, you first have to multiply the 2 given numbers, the whole number and the percentage (as a decimal), together: 0.19 = 54.72. Now that you have the answer to the multiplication problem, you can round the answer to the nearest whole number: 54.72 = 55 so the rounded answer is 55.
To get the exact answer, all you have to do is multiply the percentage (as a decimal), by the whole number to get the answer: 0.19 x 288 is 54.72 so the exact answer is 54.72.
I hope I helped and please mark this answer as brainliest if so!
What greater 480 m or 48 hm
Answer: 48hm
Step-by-step explanation:
48hm = 4800m
480m < 4800m
Each function in parts (a)-(c) is a translation (horizontal/vertical/or both) of f(x). In each case the function can be written in the form y=f(x+h)+k, where h and k denote the corresponding horizontal and vertical shifts. For each of the tables below find a possible formula by applying transformations to f(x).
For the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.
Given a table which contain values of the function h(x) and the respective values of x.
We are required to form the function.
Function is basically the relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain and the values that we get from the function is known as part of range of the function.
We have to just take two points like (0.-4) and (1,3.5).
We have to just form the equation.
y-(-4)={5-(-4)}/{1-0}(x-0)
y+4=9x
y=9x-4
h(x)=9x-4
Hence for the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.
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Question is incomplete as it should include the attached figure.
Convert 41°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=-=-(F-32)
F=C+32
F
The required measure of 41°C in Fahrenheit is given as 105.8°F.
What is temperature?Temperature is defined as the degree of measure of heat in an object.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Conversion from Celsius to Fahrenheit is given as,
F = (41°C × 9/5) + 32
F = 105.8°F
Thus, the required measure of 41°C in Fahrenheit is given as 105.8°F.
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At 4 o clock, devon called 6 friends to let them know that the weather forecast called for snow. At 6 o clock, each of his friends called 6 other friends. At 8'o clock, each of those friends called 6 of their friends.
Write an expression to represent the number of people called at 6 o clock using a base and exponent.
Write an expression to represent the number of people called at 8 o clock using a base and exponent.
how many people were called in all? explain.
THANK YOU BEFOREHAND IM STRUGGLING SO HARD RN
Number of people called at 6 o clock using a base and exponent is 6^2
Number of people called at 8 o clock using a base and exponent is 6^3
Given data
At 4 o clock, Devon called 6 friends
At 6 o clock, each of his friends called 6 other friends
At 8'o clock, each of those friends called 6 of their friends
How to write expression to represent the number of people called at 6 o clock using a base and exponent.Let the friends Devin called at 4 o clock be represented by x
such that 6 friends will be = x + x + x + x + x + x = 6x
At 6 o clock, each of his friends called 6 other friends this means that each x called 6 friends assuming y this time, such that: y represents the number of friends called at 6 o clock by each x
each x called 6y this will lead to a total of
6y + 6y + 6y + 6y + 6y + 6y = 36y
Therefore 36 friends were called at 6 o clock which is equal to 6 * 6 = 6^2
using base and exponent we have
base = 6 and exponents = 2
How to write expression to represent the number of people called at 8 o clock using a base and exponent.Each of the 36 friends called their 6 friends again hence the total calls made is 36 * 6 = 216
using base and exponent
36 * 6 = 216
6^2 * 6^1 = 216
6^(2 + 1 ) = 216
6^3 = 216
base = 6
exponents = 3
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someone please help me with this problem please!
The maximum and minimum set of dimension for the rectangular field are-
Maximum (x, y) = (8.50, 22)Minimum (x, y) = (16.50, 11.33)What is defined as the term rectangle?A rectangle is a four-sided configuration with 90-degree angles at all four corners. A rectangle's sides are same length than the one opposite it.
The perimeter of the rectangular field is given in the form of equation;
4x + 3y = 100
Where the total area is given as;
y(x+x) = 374
2xy = 374
Solving the equation;
(4 x+3 y)² = 16x² + 12×2 x y + 9 y² = 10000
2 x y = 374,12.
2 x y = 12 × 374
2 x y = 4488
16x² + 9 y² = 10000 - 4488
16x² + 9 y² = 5512
Now, solve for the other set of value;
(4 x-3 y)² = 16x² - 12×2 x y + 9 y²
Put the value of 16x² + 9 y² = 5512.
(4 x-3 y)² = 5512 - 12×2 x y
Put 2xy = 374
(4 x-3 y)² = 5512 - 4488
(4 x-3 y)² = 1024
Case1: 4 x-3 y = √{1024}
4 x-3 y = 32
And, 4 x + 3 y = 100
Solving both;
8x = 132
x = 16.5
and y = (100 - 32)/6
y = 11.33
Case 2: 4 x - 3 y = -32
4 x + 3 y = 100
Solving both by elimination method.
x = 8.5 and y = 22
Thus, the minimum and maximum dimension for the rectangular garden are-
Maximum (x, y) = (8.50, 22)
Minimum (x, y) = (16.50, 11.33)
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show how to rewrite multiplication problem 24 x 6
Answer:
144
Step-by-step explanation:
24x6
24 6 times
24 + 24 + 24 + 24 + 24 + 24 = 144
i hopw this helped
if it did pls mark brainliest!
2) Solve for f
3d+2f=21
Answer:
[tex]2f = 21 - 3d \\ f = \frac{21}{2} - \frac{3}{2} d \\ f = - \frac{3}{2} d + \frac{21}{2} [/tex]
Find square root of 456 and 5678 up to 2 d.p by using division method.
Answer:
*HOPE THIS HELPS*
Step-by-step explanation:
Full explanation given in the picture
-4w-2= |6w+20|
W ends up equaling-9 and -11/5 I just need the show the work steps
[tex] - 4w - 2 = |6w + 20| [/tex]
Answer:- Steps:- Part 1:-[tex] - 4w - 2 = |6w + 20| \\ - 4w - 2 = 6w + 20 \\ - 2 - 20 = 6w + 4w \\ - 22 = 10w \\ \frac{ - 22}{10} = w \\ \frac{ - { \cancel{22}}^{ \: \: 11} }{ \cancel{10}^{ \: \: \: 5} } = w \\ \frac{ - 11}{5} = w[/tex]
Part2:-[tex] - 4w - 2 = |6w + 20| \\ - 4w - 2 = | - (6w + 20)| \\ - 4w - 2 = - 6w - 20 \\ 6w - 4w = - 20 + 2 \\ 2w = - 18 \\ w = \frac{ - 18}{2} \\ w = \frac{ - \cancel{18}^{ \: \: 9} }{ \cancel2} \\ w = - 9[/tex]
Consider the following conditional statement and scenario. Is the conditional statement true or false?
Conditional Statement: If you go to school, then you are a student.
Scenario: You go to school to volunteer with a afterschool reading program for 3rd graders.
Group of answer choices
True
False
Answer:
The conditional statement is false and with the scenario it would still be false
Step-by-step explanation:
In the scenario it implies that you aren't a student and are most likely a teacher or tutor of some sort so the statement "If you go to school, then you are a student is false" because not all students go to school and in your scenario not only students go to school.
List all the factors of 39 from least to greatest. Enter your answer below,
using a comma to separate each factor.
Answer:
1, 3, 13, 39
Step-by-step explanation:
because it is
Using each of the digits 3, 5, 7, 9 in two fractions exactly once in an expression of a sum, what is the larger of the two common fractions that would give a sum between 0.75 and 1?
The two fractions that will give a sum between 0.75 and 1 are 3/7 + 5/9 and the larger fraction is 5/9
How to add fractions?We want to find two fractions using the digits 3, 5, 7 and 9 to find the one that gives a sum between 0.75 and 1.
Since it has to be a sum between 0.75 and 1, it means that the denominator must be greater than the numerator. Thus, let us try as follows;
3/5 + 7/9
Factorize out 45 to get;
¹/₄₅((3 * 9) + (7 *5))
= ¹/₄₅(27 + 35)
= ¹/₄₅(52)
This will not work because it will lead to a sum greater than 1
Let us try another one;
3/7 + 5/9
Factorize out 63 to get;
¹/₆₃((3 * 9) + (5 *7))
= ¹/₆₃(27 + 35)
= 52/63
= 0.8254
Thus, the two fractions that will give a sum between 0.75 and 1 are 3/7 + 5/9 and the larger fraction is 5/9
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The following table shows the world record times for the 200m race for flying start machines (a kind of bicycle). Find the line of best fit model, R(t) , that represents the world record times , t, since 1970. Before determining the equation , we need to convert all years to years since 1970. The first two rows are completed for you . Complete the rest of the table with the correct years since 1970 . After completing the table , use Excel to create a linear regression equation using only the second two columns . Do not use any spaces in your submission .
Using a calculator, the linear regression equation is given by:
R(t) = -0.22552t + 10.89293.
What is the missing information?The table of values is missing, and the values are as follows:
Years since 1970: 4, 5, 6, 7, 9, 15, 16, 22.Record time: 10.4, 10, 9.4, 9.1, 8.8, 7.2, 6.8, 6.5.How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, inserting the points (Years since 1970, Record Time), the regression line is given as follows:
R(t) = -0.22552t + 10.89293.
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Estimate: 11.72 • 3.01
36
33
48
44
The value of the product of the two decimal numbers is 35.2772 which is closest to 36 of all the given numbers.
The outcome of multiplication or an expression that specifies factors to be multiplied is a product.
The commutative law of multiplication states that the result is independent of the order in which real or complex numbers are multiplied. The result of a multiplication of matrices or the elements of other associative algebras typically depends on the order of the factors. For instance, matrix multiplication and multiplication in general in other algebras are non-commutative operations.The two numbers are 11.72 and 3.01
To multiply this two decimal numbers we will use the fraction property.
11.72 can be written as [tex]\frac{1172}{100}[/tex] and 3.01 can be written as [tex]\frac{301}{100}[/tex]
So the product of 11.72 and 3.01 is written as
[tex]=\frac{1172}{100}\times\frac{301}{100}\\\\\\=\frac{352772}{10000}[/tex]
= 35.2772
This number in decimal can be estimated to 36 because it is closest to the given options.
Hence the product is approximately 36.
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help pleaseeeeeeeeeeeee
The value of the function g(-2) is -46
What is a function?A function can be defined as an expression, law , rule of hypothesis that explains or compares the relationship between two variables - the dependent and the independent variable.
Given the function;
g(x) = -4x³ - x² + 2x - 2
To determine the function, g(-2)
We substitute the value of x as -2 into the function, we have;
g(-2) = -4(-2)³ - (-2)² + 2(-2) - 2
expand the bracket
g(-2) = -4(8) - 2(4) + 2(-2) - 2
expand further
g(-2) = -32 - 8 - 4 - 2
g(-2) = -46
Thus, the value of the function g(-2) is -46
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Four players are to be selected from a 25-player baseball team to visit schools to support a summer reading program. In how many ways can this selection be made?
The total number of possible ways in which the selection can be made is 12650.
We have a baseball team.
We have to determine in how many ways can the selection be made from 25 students to form a group of 4 students.
What is Combination ?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
According to the question -
Total number of players in team = 25
Number of players to be selected = 4
The total number of possible ways in which this selection can be made is-
[tex][25]C_{4}[/tex] = [tex]$\frac{25!}{(25-5)!5!}[/tex] = 12650
Hence, the total number of possible ways in which the selection can be made is 12650.
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HURRY ITS DUE IN 2 MINUTES!!!!!!
At what value of x does the second function's output exceed (get bigger than) the first function's output? Explain your solution steps.
f(x)= x+7 and f(x)= x²
The value of x, at which the second function's output exceeds the first function's output is
[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right)$[/tex]
This is further explained below.
At what value of x does the second function's output exceed (get bigger than) the first function's output?Generally, The second function's output exceeds (get bigger than) the first function's output for
[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{20}}{2}, \infty\right)$[/tex]
Given the functions f(x)=x+7 and f(x)=x^2
To know when to exceed, need to equate both functions.
[tex]$$\begin{aligned}&\Rightarrow x^2=x+7 \\&\Rightarrow x^2-x-7=0 \\&\mathrm{x}=\frac{-b+\sqrt{D}}{2 a} \text { and } \frac{-b-\sqrt{D}}{2 a} \\&\Rightarrow \mathrm{x}=\frac{1-\sqrt{29}}{2}, \frac{1+\sqrt{29}}{2}\end{aligned}$$[/tex]
f(x)=x^2 drops from infinity to zero and grows from zero to infinity; it cuts the graph of x+7 twice, and for each of those instances, it results in the same shape.
[tex]x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right) f(x)=x^2$[/tex] is greater than f(x)=x+7
As a result, the output of the second function surpasses (acquires a greater size than) the output of the first function for
[tex]$x \in\left(-\infty, \frac{1-\sqrt{29}}{2}\right) \cup\left(\frac{1+\sqrt{29}}{2}, \infty\right)$[/tex]
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