Answers
Part 1
[tex](f+g)(x)=f(x)+g(x) \\ \\ =4x+9+7x-5 \\ \\ =11x+4[/tex]
Part 2
[tex](f-g)(x)=f(x)-g(x) \\ \\ =(4x+9)-(7x-5) \\ \\ =4x+9-7x+5 \\ \\ =-3x+14[/tex]
Part 3
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =(4x+9)(7x-5) \\ \\ =28x^2-20x+63x-45 \\ \\ =28x^2+43x-45[/tex]
Part 4
[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ =\frac{4x+9}{7x-5}[/tex]
Related Questions
An open-top water tank is in the shape of a cuboid. The tank has a square base of side length s m, and has a volume of 216 m^3. Find expressions, in terms of s, for:
a) the height of the tank.
b) the surface area of the tank
Given that the surface area of the open-top water tank is minimised:
c) find the value of s.
(looking for clear workouts and reasoning / explanation behind every step taken no matter how basic it may be)
Answers:
a) h = 216/s^2
b) A = s^2 + 864
c) s = cube root of 432
Answers
The height of the tank is h = 216/s^2, the surface area is s^2 + 864/s and the value of s is ∛432
How to determine the height of the tank?The given parameters are
Volume = 216
Base length = s
Height = h
The base shape is a square.
So, we have
Volume = s^2h
This gives
216 = s^2h
Divide through by s^2
h = 216/s^2
Hence, the height of the tank is h = 216/s^2
The surface area of the tankThis is calculated as
A = s^2 + 4sh
So, we have
A = s^2 + 4 * s * 216/s^2
Evaluate
A = s^2 + 4 * s * 216/s^2
This gives
A = s^2 + 864/s
How to determine the value of s?Here, we have
A = s^2 + 864/s
Differentiate
A' = 2s - 864/s^2
Set to 0
2s - 864/s^2 = 0
Divide through by s
2 - 864/s^3 = 0
So, we have
864/s^3 = 2
This gives
2s^3 = 864
Divide by 2
s^3 = 432
Take the cube root
s = ∛432
Hence, the value of s is ∛432
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A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
Answers
Step-by-step explanation:
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function =S+16.950.60M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function =I+4.900.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
y=3x2 + 2 translated down three units
Answers
The output of the equation after transformation is y=3x^2 - 1.
According to the statement
We have to find that the mathematical transformation.
So, For this purpose, we know that the
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
From the given information:
The details are:
y=3x^2 + 2 translated down three units
According to this it is clear that the there is decrease of the 3 numbers.
Then the equation become:
y=3x^2 + 2
After transformation of the 3 units then:
y=3x^2 + 2 -3
y=3x^2 - 1
Then the output gets the y=3x^2 - 1.
So, The output of the equation after transformation is y=3x^2 - 1.
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You are driving across America from Knoxville, Tennessee to Nashville, Tennessee. It takes 2 hours and 20 minutes. Nashville is an hour behind Knoxville. If you leave Knoxville 11:13, What time will you arrive in Nashville?
Answers
The time that you will arrive in Nashville is 1:33.
How to compute the time?From the information given, the person leaves Knoxville at 11:13, and the journey takes 2 hours and 20 minutes.
Therefore the time when the person will arrive will be the addition of the time given.
This will be:
= 11:13 + 2:20
= 1:33
Therefore, the person will arrive by 1:33.
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500 g of a radioactive element is decaying exponentially. After 8 days 358 g of the element is left.
a. Write a function in the form y = yo ekt giving the number of grams of the element after t days.
358 f(t)
b. Write the function from part a in the form y=Yo
500
c. Use the answer from part a to find the half-life of the element.
a. The exponential equation in the form y=yoekt is
(Round to three decimal places as needed.)
Answers
The answers are given below:-
a) The exponential function is: [tex]y(t) = 500e^{-0.0117593}[/tex]
b) The rule is: [tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]
c) The half-life of the element is of 16.599 days.
What is the exponential function?The mathematical expression [tex]f(x) = e^x[/tex] denotes the exponential function. The phrase typically refers to the positive-valued function of a real variable, unless otherwise specified.
Following t days, the substance's amount's exponential function is given by:
[tex]y(t) = y(0)e^{-kt}[/tex]
For this problem, we have that:
y(0) = 500, y(8) = 358.
Hence we can solve for k as follows:
[tex]y(t) = y(0)e^{-kt}[/tex]
[tex]358=500e^{-8k}[/tex]
[tex]e^{-8k}=\dfrac{358}{500}[/tex]
[tex]lne^-8k}=ln0.716[/tex]
-8k = ln(0.716)
k = -ln(0.716)/8
k = 0.041759389.
Hence:
[tex]y(t) = 500e^{-0.0117593}[/tex]
For item b, 358/500 of the material is what is left over after each 8-day period, therefore f(t) = t/8, and the rule is as follows:
[tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]
For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:
[tex]y(t) = y(0)e^{-0.0117593}[/tex]
[tex]0.5y(0)=y(0)e^{-0.0117593[/tex]
[tex]e^{-0.0117593}=0.5[/tex]
[tex]lne^{-0.0117593}=ln0.5[/tex]
-0.041759389t = ln(0.5)
t = -ln(0.5)/0.041759389
t = 16.599.
The half-life of the element is of 16.599 days.
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Shep Company’s records show the following information for the current year:
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Determine net income (loss) for each of the following separate situations. (For all requirements, losses should be entered with a minus sign.)
a. Additional common stock of $4,600 was issued, and dividends of $8,600 were paid during the current year.
b. Additional common stock of $15,400 was issued, and no dividends were paid during the current year.
c. No additional common stock was issued, and dividends of $13,600 were paid during the current year.
.
Answers
The determination of the net income for each of the following separate situations is as follows:
Situation A Situation B Situation C
Net income $21,800 $2,400 $31,400
How is the net income determined?The formula for determining the net income (loss) for the year is:
Net Income (loss) = Ending Equity - Beginning Equity - Additional stock + Dividend Paid).
Data and Calculations:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Situation A:
Common Stock issued = $4,600
Dividend paid = $8,600
Situation A:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 4,600
Dividend paid (8,600)
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$21,800 ($47,400 - $29,600 - 4,600 + 8,600)
Situation B:Common Stock issued = $15,400
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 15,400
Dividend paid
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$2,400 ($47,400 - $29,600 - 15,400)
Situation C:Dividends paid = $13,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued
Dividend paid $13,600
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$31,400 ($47,400 - $29,600 + 13,600)
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Point J is on line segment I K ‾ IK . Given J K = 10 JK=10 and I K = 19 , IK=19, determine the length I J ‾ . IJ
Answers
The length of the line segment IJ is 9.
What is the length of a line segment?
In this question we find that the line segments IJ and JK are collinear, that is, part of one same line. By Euclidean geometry and algebra, we construct the following formula:
IK = IJ + JK
IJ = IK - JK
If we know that IK = 19 and JK = 10, then the length of the missing line segment is:
IJ = 19 - 10
IJ = 9
The length of the line segment IJ is 9.
RemarkThe statement is poorly formatted, correct form is shown:
The point J is on line segment IK. Given that JK = 10 and IK = 19, determine the length IJ.
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A couple buys furniture for R50 000. They put down a cash deposit of 20% and pay off the balance using a higher purchase agreement, over 4years. The institution charges interest of 10% p.a and monthly Insurance fee of R75.00. Calculate the couple's monthly repayments
Answers
The amount of the 1167 rupees he have to pay every month according to the interest rate.
According to the statement
We have to find that the monthly repayments.
So, For this purpose, we know that the
Interest rate is the annual rate that is charged for borrowing , expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan.
From the given information:
A couple buys furniture for R50 000. They put down a cash deposit of 20% and pay off the balance using a higher purchase agreement, over 4years. The institution charges interest of 10% p.a and monthly Insurance fee of R75.00.
Then
A couple buys furniture = 50,000
cash deposit of 20% = 20% of 50,000
cash deposit = 20/100*50,000
cash deposit = 0.2*50,000
cash deposit = 10000
Left money on which company put interest of 10% =50000 - 10,000
Left money on which company put interest of 10% = 40,000
Then
interest amount per year = 10% of 40,000
interest amount per year = 10/100*40,000
interest amount per year = 0.1*40,000
interest amount per year = 4000
It means interest paid by the customer in 4 years = 4000*4
It means interest paid by the customer in 4 years = 16000
Then
Total money he pays with interest rate in 4 years = 16000 +40,000
Total money he pays with interest rate = 56000
Then
The money he have to pay every month in 4 years = 56000/48
The money he have to pay every month in 4 years = 1167.
So, The amount of the 1167 rupees he have to pay every month according to the interest rate.
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Una empresa tiene costos fijos de $300 y vende cada artículo en $15. Si se sabe que el punto de equilibrio es q=100. Plantear la función de Costos Totales
CT=__________________________
Answers
Based on the fixed costs and the equilibrium point, the function for total costs would be TC = 300 + 100VC
What s the function for total cost?The total cost that a company incurs for making a good or service is a combination of both the fixed cost and the variable cost.
The total variable cost is found as:
= Number of units produced x variable cost per unit
= 100 units x vc
= 100vc
The total cost would therefore be:
= Fixed cost + Total variable cost
= 300 + 100vc
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Triangle xyz x’y’z’ What scale factor was used in dialation xz=4 x’z’=5
Answers
The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Triangle X'Y'Z' is the image of triangle XYZ after a dilation by a scale factor.
Given that XZ = 4; X'Z' = 5
Hence:
Scale factor = X'Z'/XZ = 5/4
The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.
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Can someone please help me of solving this and show answer
Answers
By solving inequality [tex]x[/tex] ∈ [tex][-2,3)[/tex]
What is inequality?
A declaration of the relation in terms of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions is known as inequality.
[tex]4\leq 3x+10 < 19[/tex]
Rearranging the above equation
[tex]\left \{ {{4\leq 3x+10} \atop {3x+10} < 19} \right.[/tex]
Subtracting 10 from the above equation
[tex]\left \{ {{4-10\leq 3x+10-10} \atop {3x+10-10 < 19-10}} \right[/tex]
[tex]\left \{ {{-6\leq 3x} \atop {3x < 9}} \right.[/tex]
Dividing the above equation by 3
[tex]\left \{ {{\frac{-6}{3}\leq \frac{3x}{3} } \atop {\frac{3x}{3} < \frac{3}{3} }} \right.[/tex]
[tex]\left \{ {{-2\leq x} \atop {x < 3}} \right[/tex]
[tex]-2\leq x < 3[/tex]
Therefore, by solving inequality we get [tex]x[/tex] ∈ [tex][-2,3)[/tex]
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The sum of the squares of three consecutive positive integers is 2030. What is the middle integers?
Answers
The value of the middle integer is 26
Solving Linear equationsFrom the question, we are to determine the middle integer
From the given information,
"The sum of the squares of three consecutive positive integers is 2030"
Let the first integer be x,
Then the middle integer will be x + 1
and the third integer will be x + 2
Thus,
x² + (x +1)² + (x +2)² = 2030
x² + x² + 2x + 1 + x² + 4x + 4 = 2030
3x² + 6x + 5 = 2030
3x² + 6x + 5 - 2030 = 0
3x² + 6x - 2025 = 0
x² + 2x - 675= 0
Solve quadratically
x² + 27x - 25x - 675 = 0
x(x + 27) -25(x + 27) = 0
(x - 25)(x + 27) = 0
x - 25 = 0 and x + 27 = 0
x = 25 and x = -27
Since x is a positive integer,
x = 25
Thus,
The middle integer,
x + 1
= 25 + 1
= 26
Hence, the value of the middle integer is 26
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What question is correct? A-B-C-D?
Answers
Answer:
b is the answer
Step-by-step explanation:
b is the answer
The beginning balance of the check register was $492.88. During the month, deposits were made for $210 and $499.88. Checks were
written for $18.25, $19.82, and $309.82. What is the ending balance of the check register?
Note: Round your answer to 2 decimal places.
Answers
Answer:
$840.77
Step-by-step explanation:
What are the common factors of 70 and 110
Answers
Answer:
Do you mean GCF? If so, it is 10.
If you mean factors that they have in common it is: 1,2,5 and 10.
Step-by-step explanation:
Factors of 70: 1,2,5,7,10,14,35,70
Factors of 110: 1,2,5,10,11,22,55,110
GCF is 10
Answer:
10
Step-by-step explanation:
7+1/X (1/x) multiply
Answers
The value of the linear equation after multiplying is 8/xX.
According to the statement
We have to find that the value of the statement.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is a:
7+1/X (1/x)
Here we know that the X and x are the different variables.
Then
7+1/X (1/x)
Now add the terms which are possible then
8/X (1/x)
Now, multiply the terms which are possible to multiply
Then the equation become
8/xX.
So, The value of the linear equation after multiplying is 8/xX.
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Cheryl's softball batting average is 0.340 and Karen's is 0.304. Karen says they have the same average. What error did she make
Answers
The mistake is that in both numbers 0.304 and 0.340, 4 is in the tenth position following the point.
What is place value system?The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression. A place-value system gives a number's specific location within a series a value.
Karin's softball batting average is 0.304, whereas Cheryl's is 0.340. They have the same average, according to Karin.
Because the numbers 0.340 and 4 are in the tenth position, as opposed to 0.304 and 4, the values are different from one another.
He made a mistake in his estimation because both averages are equal.
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Write an equation for line L in point-slope form and
slope-intercept form.
L is perpendicular to y = 2x.
6
-2
6
15
y = 2x
(12)
2
50
Write an equation for line L in point-slope form.
(Simplify your answer. Use integers or fractions
for any numbers in the equation.)
Answers
Step-by-step explanation:
the line is perpendicular to
y = 2x.
and it goes through the point (1, 2).
the point-slope form looks like
y - y1 = a(x - x1)
"a"being the slope, and (x1, y1) being a point on the line.
the slope-intercept form is
y = ax + b
"a" is again the slope, "b" is the y-intercept (the y value when x = 0).
as you can see, we need the slope of the new line in both cases.
then we will start with the point-slope form, and transform it into the slope-intercept form.
the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
it is always the factor of x.
we can see it is 2 for the original line. that means 2/1.
a perpendicular slope is turning the x and y values upside down, and is flipping the sign.
so, in our case it is
-1/2
so, starting with the new slope and the point to create the point-slope form :
y - 2 = -1/2 × (x - 1)
and from there we transform into the slope-intercept form :
2y - 4 = -x + 1
2y = -x + 5
y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)
all of the expressions in the last line are valid forms to write it.
The length of a rectangular pool is three times its width. If the perimeter of the pool is one hundred and sixty meters, find the length and width of the pool.
Answers
Answer:
w = 20m
l = 60m
Step-by-step explanation:
P = 2l + 2w
We know the perimeter = 160 and we know that l = 3w, so write what we know and solve for w.
P = 2l x 2w
160 = 2(3w) + 2w
160 = 6w + 2w
160 = 8w
Divide both sides by 8
20 = w
Now we can figure out the length, which is 3(w) or 3 x 20 = 60
Answer:
w = 20m, l = 60m
Step-by-step explanation:
which is an algebraic expresson for 5 more than z
Answers
Answer:
z+5
Step-by-step explanation:
the word more indicates addition
puzzle one find the values of the unknown variables a b c d e and f substitude the values of the unknown numbers
Answers
The values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.
The code is 2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).
How to find the values of a,b,c,d,e and f?1.given that
[tex] x^4 . x^a = {x}^{12}[/tex]
we know the formula
[tex] a^m . a^n = {a}^{m+n}[/tex]
so, [tex] {x}^{(4+a)} = {x}^{12}[/tex]
if bases are equal then Powers will be equals.
then 4 + a = 12
a = 12 - 4
a = 8.
2. given that.
[tex] (y^b)/(y^5)= y^2[/tex]
we know the formula
[tex] a^m/a^n = {a}^{(m-n)}[/tex]
so, [tex] {y}^{(b-5)} = y^2[/tex]
when bases are equal then Powers will be equal.
b - 5 = 2
b = 2 + 5
b = 7
3.given that
[tex] 3^c = (1)/(27)[/tex]
so, [tex] 3^c = ( 1/3)^3 [/tex]
[tex] 3^c = {( 3/1)}^{-3} [/tex]
if bases are equal then Powers will be equals.
then c = -3.
4.given that
[tex] (m^3)^2 = m^d[/tex]
we know the formula
[tex] (a^m)^n = {a}^{m.n}[/tex]
[tex] m^6 = m^d[/tex]
if bases are equal then Powers will be equals.
then d = 6
5. given that
[tex] 7^0 = e[/tex]
e = 1
6. given that
[tex] {4}^{(-2) }. {4}^{9}. {4}^{(-5)} = 4^f[/tex]
we know the formula
[tex] a^m . a^n = {a}^{(m+n)}[/tex]
so, [tex] {4}^{(-2+9-5)} = 4^f[/tex]
if bases are equal then Powers will be equals.
then -7+9 = f
f = 2.
Hence, the values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.
The code is
f ( b + d ) + a ( e - c )
2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).
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How many different 4 card hands can be dealt from a deck of 52 cards
Answers
Answer:
There are thirteen 4 card hands are possible with a 52 card deck.
Answer:
Thirteen 4 card hands are possible with a 52 card deck
Graph this function.
f (x) = ¾x -2
Answers
The points of the graph are (0,-2), (4,1) and they are drawn on the graph below. The graph of the equation y= (3/4)x – 2 is a straight line.
What do you mean by a function's graph?The totality of the points in the plane with the form (x, f(x)) that make up the graph of a function f. The graph of y = f is another name for the graph of f. (x). Thus, the graph of an equation serves as a particular illustration of the graph of a function.
The given equation is
f(x)= ¾ x-2
Put x=0 in the equation
y = (¾)(0)-2
y = -2
Put x=4 in the equation
y = (3/4) (4)-2
y = 3-2
y = 1
Graph the points of the function on a graph as given below
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Evaluate.
18-2³ 0
I don’t understand it and I need help
Answers
18-8 = 10
answer is 10
Which functions represent a piece of the function? Select three options.
Answers
option B. g(x)=-2, x<-2, option D. g(x)=-2x+6, x>1 and option E. g(x)=x/2+1 represent a piece of the function in given graph.
The graph of a function is a collection of all ordered pairs of the relation. These are usually represented as points in a Cartesian coordinate system. It is a relationship between an independent variable and a dependent variable. The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).
Reasons are given below:
In first option that is g(x)=-2x, -2<x<0, we can see a negative sign which indicates that the graph should be downward (negative slope). Also, g(x)=-2x has no y-intercept therefore g(x)=-2x, -2<x<0 does not represent a piece of the function in given graph.
In second option that is g(x)=-2, x<-2, we can see a negative sign and no y-intercept which indicates that it is a horizontal line parallel to x-axis. Also given that x is less than -2, therefore the line should move away from y-axis to the left where lies more negative values. The given data matches the slope given in third quadrant. Hence, it represents a piece of function in given graph.
In third option that g(x)=x-2, -2<x<1, we can see that the function indicates that it has y-intercept at y=-2 and a slope of value 1(positive) which means it should move in upward direction and must cut y-axis at y=-2. The given data does not match with the graph given. Hence, it does not represent a piece of function in the given graph.
In fourth option that is g(x)=-2x+6, x>1, we can see negative sign therefore it should be downward and +6 indicates that it is with y-intercept too. Hence the given data matches with the graph given and therefore it represents a piece of the function in the given graph.
In fifth option that is g(x)=x/2+1, -2<x<1. As we can see, x lies between -2 and 1, to understand let us assume x=2 then x/2=2/2=1. Therefore, the slope can start at x=1 and extend till -2. Hence, it represents a piece of the function in the given graph.
Therefore, Functions g(x)=-2, x<-2, g(x)=-2x+6, x>1 and g(x)=x/2+1 represent a piece of the function in the given graph.
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[tex] \frac{6}{7} + \frac{1}{2} =[/tex]
Add. Write the answer in simplest form?
Answers
Duration (amount of time) is what type of data in the scenario? A study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local gym in San Antonio, Texas. The first car in the parking lot was selected randomly, and then the resident of every eighth car in the lot around the gym was interviewed.
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The sampling method used to get the sample is Systematic sampling.
The variable type of color of cars around the gym is qualitative.
Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population. It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.
The different sampling methods used are:
Simple random sampling: Every member of the population has an equal probability of getting chosen.Systematic sampling : Members are chosen after a fixed interval every time.Stratified sampling: The entire population is divided into sub populations and then the sample is chosen from each sub population. Cluster sampling: The population is also divided into smaller groups for cluster sampling, although each smaller group should share traits with the larger sample. You choose complete subgroups at random rather than picking a representative sample of each subgroup.Now the given sample of the residents that were selected was every eighth car . Hence Systematic sampling is used.
Disclaimer: Missing question stem: Identify the sampling method(simple , stratified, cluster, systemic).
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Ryan downloaded a video game to his computer. The size of the file was 3.1 times 10E4 kilobytes. After the game, Ryan installed a patch that is 40000 kilobytes. What is the size of the game file written in standard form?
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The size of the game file written in standard form is 350000 kilobytes
What is the size of the game file written in standard form?The given parameters are:
Size of the file = 3.1 x 10E4 kilobytes
Patch = 40000 kilobytes
The size of the game file written in standard form is then calculated as
Size = Size of the file + Patch
This gives
Size = 3.1 x 10E4 kilobytes + 40000 kilobytes
Rewrite as
Size = 310000 kilobytes + 40000 kilobytes
Evaluate the sum
Size = 350000 kilobytes
Hence, the size of the game file written in standard form is 350000 kilobytes
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Lisa wants to buy some new shirts at her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to spend.
Let S represent the number of shirts that Lisa buys.
Which inequality describes this scenario?
(A) 137> 15s +35
(B) 137< 15s +35
(C) 137≥ 15s +35
(D) 137≤ 15s +35
Answers
Considering the definition of an inequality, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that
Each shirt costs $15.Lisa wants to buy a pair of shoes that are $35.Lisa only has $137 to spend.Being "S" the number of shirts that Lisa buys, the inequality that expresses the previous relationship is
15×S + 35≤ 137
Finally, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.
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A Ferris wheel has 15 cars that are equally spaced around the circumference of the wheel.
The wheel rotates so that the car at the bottom of the ride is replaced by the next car. By
how many degrees does the wheel rotate?
The Ferris wheel rotates____
between successive cars being at the bottom.
Answers
The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.
What is the angle measure over which the Ferris wheel rotates between successive cars?It follows from the task content that the Ferris wheel in discuss has 15 cars spaced around it.
Since the Ferris wheel in discuss is circular and has a total angle measure of 360.
Hence, the total angle rotated between successive cars can therefore be evaluated as;
Angle rotated = 360°/15
= 24°.
Ultimately, The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.
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