Answer:
Step-by-step explanation:
5. A n B = ∅ (the empty set)
6. A u B = {x|x is an integer, x ≠ 0}
7. B n C = {x|x<0}
8. B u C = {x|x<0 or a positive odd integer}
Leah has a home-based business making and selling scented soaps. She initially spent $100 to purchase soap-making equipment, and the materials for each pound of soap cost $5. Leah sells the soap for $15 per pound. Eventually, she will sell enough soap to cover the cost of the equipment. What will be Leah's total sales and costs be? Write a system of equations, graph them, and type the solution.
Answer:
Equations:
Cost equation C(x) = 100 + 5x
Sales equation S(x) = 15x
Graph provided
Solution at breakeven point i.e. where sales = costs is at x = 10 lbs
Step-by-step explanation:
Total cost = $100 capital cost of equipment + production cost of $5 per pound of soap
Cost equation C(x) = 100 + 5x where x is the number of pounds of soaps produced
Sales Equation S(x) = 15x where x is the number of pounds of soap sold
The break-even quantity (in lbs) of soap to be sold to pay for equipment is when both equations are equal to each other
100 + 5x = 15x
==> 15x = 100 + 5x
==> 15x - 5x = 100 (subtract 5x on both sides)
==> 10x = 100
==> x = 10 lbs of soap
At this quantity, Sales and Costs are evened out
Sarah leaves her house at 6:25 a.m. to walk to school, which is 4.5 miles away. she meets ur friend at 6:45 a.m. a mile away from her home. if she continues to walk with her friend without increasin speed, what time will she make it to school?
Sarah will take 90 minutes to reach her school from her house if she continues to walk with her friend without increasing speed.
According to the question,
We have the following details:
Sarah leaves her house at 6:25 a.m.
She meets her friend at 6:45 a.m.
So, we have:
The time taken by Sarah to meet her friend after 1 mile = (6:45 - 6:25) minutes
The time take by Sarah to meet her friend after 1 mile = 20 minutes
Now, we can find Sarah's speed.
We know that the formula of speed is as follows:
Speed = distance/time
Speed = 1/20 mile/min
Now, the distance of her school from her house is 4.5 mile.
So, we have:
Time taken = distance/speed
Time taken = 4.5/(1/20) min
Time taken = 4.5*20 min
Time taken = 90 minutes
Hence, the time taken by Sarah to reach her school from her house is 90 minutes.
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PLEASE ANSWER AS QUICKLY AS POSSIBLE PLEASE. WILL GIVE BRAINlESt
A linear function with the same y-intercept as the one that is represented by the graph is: table 1.
How to calculate the slope of a linear function?In Mathematics, the slope of any linear function can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
At points (-3, -4) and (-1, 2) from table 1, the slope of the line would be calculated as follows:
Slope, m = (2 + 4)/(-1 + 3)
Slope, m = 6/2
Slope, m = 3.
Note: The y-intercept of the line shown on the graph is equal to 5 because the x-value is zero (0) at this point.
By using point (-3, -4), the y-intercept of this line would be calculated by using the slope-intercept form:
y = mx + b
Where:
x and y are the points.b is the y-intercept.m represents the slope.Making y-intercept (b) the subject of formula, we have:
y-intercept, b = y - mx
y-intercept, b = -4 - 3(-3)
y-intercept, b = -4 - (-9)
y-intercept, b = -4 + 9
y-intercept, b = 5.
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Complete Question:
Which linear function has the same y-intercept as the one that is represented by the graph?
Is this sentence a fact or an opinion
Many Hindus celebrate a holiday called Diwali by lighting candles and exchanging gifts
Answer:fact
Step-by-step explanation:Opiians have a persianal veiw sush as "the cows should sleep in the shed" while facts are absolute "the cows sleep in the shed"
Given f(x) = 3x³ + x + k, and x + 1 is a factor of f(x), then what is the value of
k?
Answer: k=-2
Step-by-step explanation:
[tex]\displaystyle\\3 x^2+x+k=\\\\3x^2+3x-2x+k=\\\\3x(x+1)-2(x-\frac{k}{2}) \\\\Hence,\\\\x-\frac{k}{2} =x+1\\\\-\frac{k}{2} =1\\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\-\frac{k}{2}(-2) =1(-2)\\\\k=-2[/tex]
Dolores runs 2.2km north and 1.5km west. What is the shortest distance she must run back to the starting point, to the nearest tenth of a metre
Please show your work
I think this has something to do with the Pythagorean Theorem but I don't know what
The shortest distance to reach the starting point by Dolores is 2.7 kilometres.
The shortest distance will be the line directly connecting the two points. This will form the right angled triangle and hence can directly be calculated. We will be calculating hypotenuse from Pythagoras theorem.
Distance² = 2.2² + 1.5²
Taking square on Right Hand Side
Distance² = 4.84 + 2.25
Performing addition on Right Hand Side of the equation
Distance² = 7.09
Taking square root on Right Hand Side
Distance = ✓7.09
Distance = 2.7 kilometres
Thus, the shortest distance back to the starting point is 2.7 kilometres.
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Ed earned $112 for 8 hours ofwork. At this rate, how much will heearn for 40 hours of work?
Ed earned $112 for 8 hours of
work.
At this rate, how much will he
earn for 40 hours of work?
For 40 hours of work = (112 x 40) /8 = $ 560
John runs each lap in 7 minutes. He will run at most 35 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.
Answer: At most 5 laps.
Step-by-step explanation:
N= # of laps
7mins times the number of laps= 7N
35 mins= at most
[tex]7n\leq 35\\\\\frac{7n}{7} \leq \frac{35}{7} \\\ \ \ \ n\ \leq \ 5[/tex]
whats the co-ordinates of the midpoint of (8,10) and (7,2)
Answer:
[tex](\frac{15}{2},6)[/tex]
Step-by-step explanation:
Hey, Grace! Pleasure to meet you.
To solve this problem, I would strongly suggest for you to use the midpoint formula.
I have attached an image below of the formula used for plugging in values.
Confused? Let me show you! :)
M means midpoint by the way...
M = [tex](\frac{8+7}{2},\frac{10+2}{2}) = (\frac{15}{2} ,6)[/tex]
There you go! Let me know if you have any questions, and best of luck with the rest of your assignment.
Determine another point on the line given two points on the line.
(0, 4), (2, 5)
The coordinates of another point are (4, 6).
We are given the coordinates of two points. The two points are (0, 4) and (2, 5). A straight line passes through the two given points.
We will find the equation of the straight line using the formula given below :
(y - y1) = [(y2 - y1)/(x2 - x1)](x - x1)
(y - 4) = [(5 - 4)/(2 - 0)](x - 0)
(y - 4) = (1/2)x
y = (1/2)x + 4
We have to find another point on the line. Let us choose a value for the x-coordinate equal to 4. The y-coordinate can be calculated as given below :
y = (1/2)4 + 4
y = 2 + 4
y = 6
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3x-2y=109x+4y=-50Solve each system of equations by graphing. Clearly identify your solution.
Plot two points of each equation
Equation 1 Equation 2
3x - 2y = 10 9x + 4y = - 50
x y x y
0 -5 0 12.5
10/3 0 -50/9 0
Graph
Solve for x . Show work and round to the nearest tenth if necessary
Step-by-step explanation:
(b) what are the quotient and remainder when −34 is divided by 6? remember that the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.
The quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.
What is termed as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 divided into three equal groups adds up to 4 in each cluster in division.Each component of a division equation is given its own name.Dividend: The dividend is just the number divided during the division process.Divisor: The divisor is the number whereby the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.Dividend = Divisor x Quotient + Remainder
For the given question,
The number -34 is to be divided by 6.
In this, dividend is -34 and divisor is 6.
Now while dividing the number comes should be less than -34.
Thus, -34 divided by 6 gives quotient as -36 and remainder as 2.
Where, the remainder r has to satisfy 0≤r<6, and in particular cannot be negative.
Therefore, the quotient and remainder when −34 is divided by 6 is -6 and 2 respectively.
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Read the following description of a data set.
Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any.
Rod noted the age of each person he spoke with, x, and the number of songs each could name, y.
The least squares regression line of this data set is:
y = 0.441x- 12.918
Complete the following sentence:
The least squares regression line predicts that if a person is one year older, they will able to name how many more songs.
the person is able to name .441 more songs
. (10 points) place these functions in order from slowest asymptotic growth to fastest asymptotic growth. justify the claimed order for each pair of consecutive functions that appear in your ordered list. for instance, if you claim that ????????(????)<????????(????) in growth rate for some choice of the functions ????????(????) and ????????(????), show that the limit test yields lim????→[infinity]????????(????)/????????(????)
Placing these functions from slowest asymptotic growth to fastest asymptotic growth. f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).The exponents we got.
Given that,
Placing these functions from slowest asymptotic growth to fastest asymptotic growth,
Come to question,
f₇(n) < f₄(n) < f₀(n) < f₃(n) < f₅(n) < f₉(n) < f₂(n) < f₆(n) < f₁(n) < f₈(n).
(ln ln ln n) < (ln n + 2021) < ([tex]n^{lg n}[/tex] ) < ((n/lg n)⁸) < (n⁸ - n⁶ + n⁴ - n² + 1) < (n²⁰²¹) < ([tex]32^{n/5}[/tex]) < (3³ⁿ) < ([tex]16^{lgn}[/tex]) < ( 2021 ∛n)
Let's understand, lg n < n < exponential. on the basis of it,
f₇(n) comes first, it will be smaller than f₄(n), because ln n is > ln ln ln n.
f₄(n) comes second, it will be smaller than f₀(n), because O(n) functions are larger than O(log n).
f₀(n) comes third, it will be smaller than f₃(n), because O(n⁸) functions are larger than O([tex]n^{log n}[/tex]).
f₃(n) comes fourth, it will be smaller than f₅(n), because (n⁸ - n⁶ + n⁴ - n² + 1) will give more larger value than ((n/lg n)⁸), these both functions are O(n⁸).
f₅(n) comes fifth, it will be smaller than f₉(n), because n⁸< n²⁰²¹.
f₉(n) comes sixth, it will be smaller than f₂(n), because n²⁰²¹ is O(n), whereas [tex]32^{n/5}[/tex] = 2n is exponential, and exponential are larger than O(n).
f₂(n) comes seventh, it will be smaller than f₆(n), because 2n < 3³ⁿ, both are exponential (2 < 3).
f₆(n) comes eight, it will be smaller than f₁(n), because 3³ⁿ < [tex]16^{logn}[/tex], both are exponential (3 < 16).
f₁(n) comes ninth, it will be smaller than f₈(n), because [tex]16^{logn}[/tex] < 2021 ∛n, both are exponential (16 < 2021).
Complete question: Place these functions in order from slowest asymptotic growth to fastest asymptotic
growth. Justify the claimed order for each pair of consecutive functions that appear in your ordered
list. For instance, if you claim that
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kurt bought 10 packs of sunflower seeds and 4 pots. each pack of seeds cost $4, and each post for $12. how.much did kurt spend in all
Answer:
$88
Step-by-step explanation:
The length of a rectangle is three times its width.
If the perimeter of the rectangle is 48 in, find its length and width.
length: in
width: in
Length: 18 in.
Width: 6 in.
We can use “x” as the width in this scenario. If the width is x, then the length is 3x, since length is three times the width. The perimeter would be length + length + width + width. Since the perimeter is 48, we could say that:
x + x + 3x + 3x = 48
Which simplifies to 8x=48
If you divide by 8 on both sides, you get
X=6. Then you Can plug 6 back into your x width and 3x length.
(See attached image) hope this helped!
Hello!
Let's set up some variables:
L: length of the rectangleW: width of the rectangleLet's consider the relationship between the length and the width:
The length of a rectangle is three times its width[tex]\hookrightarrow L=3W[/tex]
The perimeter of the rectangle is equal to 48 and 2W + 2L
[tex]\hookrightarrow 2L + 2W = 48[/tex]
Let's replace the 'L' in terms of 'W' and solve:
[tex]2(3W) + 2W = 48\\6W + 2W=48\\8W = 48\\W = 6[/tex]
Since L = 3W
[tex]\hookrightarrow L = 3W = 3*6 = 18[/tex]
Answer:
Length = 18Width = 6Hope that helps!
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
coordinate plane with points at negative 14 comma 1 labeled Woozy Wheel, negative 6 comma 2 labeled Bumper Boats, negative 2 comma negative 4 labeled Roller Rail, negative 2 comma negative 6 labeled Trolley Train, 2 comma negative 3 labeled Silly Slide, and 6 comma 11 labeled Parachute Plunge
Determine the distance between the Bumper Boats and the Parachute Plunge.
15 units
225 units
8 units
63 units
help pls i dont have lot of time!
The distance between the Bumper Boats and the Parachute Plunge is given by:
15 units.
What is the distance between two points?Suppose that we have two points with coordinates given yb [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following rule:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse representing the distance between them.
In the context of this problem, the coordinates of the Bumper Boats and of the Parachute Plunge are given as follows:
Bumber Boats: (-6, 2).Parachute Plunge: (6, 11).Hence the distance between these two points is given as follows:
[tex]D = \sqrt{(6 - (-6))^2+(11 - 2)^2}[/tex]
D = sqrt(12² + 9²)
D = 15 units.
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Answer: its 225
Step-by-step explanation: you should try it and find out. / I did
the table shows information about the population of a city, what is the population in 2021
A meteorologist was monitoring the temperature outside in degrees Fahrenheit (°F) and wrote the expression 78+(-6) -5. Which statement best describes this expression?
A
The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.
B
The temperature started at 78°F and increased by 6°F. Then the temperature decreased by 5°F.
C
The temperature started at 78°F and increased by 6°F. Then the temperature increased by 5°F.
D
The temperature started at 78°F and decreased by 6°F. Then the temperature increased by 5°F.
Correct option is A, The temperature started at 78°F and decreased by 6°F. Then the temperature decreased by 5°F.
What is an expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.
An expression is, for instance, 3x - 2. While an equation, on the other hand, denotes the connection between two separate expressions via an equal to sign, One such equation is 3x - 2 = 5 + x.
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the radius of a circular disk is given as 30 cm with a maximum error in measurement of cm. use differentials to estimate the maximum possible error in the calculated area of the disk.
The calculated area's maximum percentage relative error is approximately 1.33%.
we know that:
Area of the circular disc is given by A = πr²
consider A = πr²
Differentiate both sides with respect to r, we get
dA/dr = 2πr
⇒ dA = 2πr dr
calculate area:
A = πr²
A = π(30)²
A = 900π
A = 2826 cm²
Because of an error in measurement, the radius might actually be as big as 30+0.2 cm
= 30.2 cm
If r is increased from 30 by an amount Δr = dr = 0.2
Then the actual change in the calculated area would be :
ΔA = A(30+Δr)-A(30)
ΔA = A(30.2)-A(30)
ΔA = (30.2)²π - 900π
ΔA = 912.04π - 900π
= 12.04π cm²
So we estimated the maximum error in calculated area as 12.04π cm²
≅ 37.8 cm²
The maximum relative error in calculated area is:
ΔA/A= dA/A = 12.04π/900π
= 0.013
= 1.33 %
The maximum % relative error in calculated area is about 1.33%.
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Use the following equation to answer the questions:
−3x+y=9
Rewrite the equation in function notation:
Response area
What is the slope of the line? Response area
What is the y-intercept? (Response area, Response area)
What is the x-intercept?
The equation in function notation is: f(x) = 3x + 9.
Slope of the line = 3
Y-intercept = 9
X-intercept is: -3.
How to Write the Equation of a Line in Function Notation?In function notation, the equation can be written as .f(x) = mx + b, where:
m = slopeb = y-intercept of the line.Given the equation, -3x + y = 9, rewrite in function notation as:
-3x + y + 3x = 3x + 9
y = 3x + 9
f(x) = 3x + 9
Slope of the line is, m = 3.
The y-intercept of the equation is, b = 9.
To find the x-intercept, substitute y = 0 into y = 3x + 9:
0 = 3x + 9
-3x = 9 [subtraction property of equality]
-3x/-3 = 9/-3 [division property of equality]
x = -3
The x-intercept is: -3.
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HELP ME
solve x^4-17x^2+16=0
select all of the solutions to the original equation
x=4
x=-16
x=-4
x=16
x=-8
x=-1
x=1
x=8
Zara and Chester are building fences.
Zara uses fence panels that are each 6 feet long and Chester uses fence panels that are each 4 feet long.
If both of their fences are the same length, what is the shortest possible length that Zara's fence could be ? Give your answer in feet
The shortest possible length that Zara's fence could be is 12 feet long.
The fence panels Zara uses are 6 feet long each and the fence panels that Chester uses is each 4 feet long.
The multiple of the number 6: 6, 12, 18, 24
The multiple of the number 4: 4, 8, 12, 16, 20, 24
The numbers 6 and 4 have the same multiple 12, 24. The least common multiple of them is 12.
So Zara's fence has the shortest length is 12 feet, because Zara and Chester have the same length fence as Zara uses fence panels that are each 6 feet long. Chester uses are 4 feet long.
The shortest length of Zara's fence is 12 feet.
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In a class, 2/5 of the students are less than 115 cm in height and 7/10 are less than 130 cm in height. what fraction are more than 115 cm but less than 130 cm?
Find the equation for a polynomial f(x) that satisfies the following:
Degree 4
Root of multiplicity 2 at x=2
Root of multiplicity 1 at x=1
Root of multiplicity 1 at x=−1
y-intercept of (0,−8)
Hello, you just missed one multiplicity which has a root at
[tex]x = 2[/tex]
The detailed solution is given below. Good luck!
Answer:
f(x) = 2(x - 2)²(x + 1)(x - 1)
Step-by-step explanation:
a polynomial of the 4th degree has as highest exponent for terms in x : 4
your previous attempt only gets you to x³ terms, so to a polynomial of 3rd degree.
you made the following mistakes :
you used the factor for the root (zero) at x = 2 only once, although it has a multiplicity 2 (that means it has to be used twice : the same zero solution appears twice) :
e.g. (x - 2)²
you used the same factor for the root at -1 and at +1.
no, they are different, of course, as -1 and +1 are different.
e.g.
(x + 1)(x - 1)
you miscalculated the factor to fulfill also the last criteria to have a y- intercept at (0, -8), y = f(0) = -8.
so, the equation is
f(x) = 2(x - 2)²(x + 1)(x - 1)
why ?
when x = 0, all terms are eliminated except for the last one that is the multiplication of all constant integers of the factors. and to get -8 in such a multiplication, we have already 3 negative factors (that will create a negative result), and any other factor needs to be positive to keep that negative result.
as -2, -2 (due to the ² factor we have it twice in the calculation), +1 and -1 are necessary for the roots (giving us -4 as result), we need an initial integer factor to now create the needed -8 result (2 × -4 = -8) :
2 × -2 × -2 × +1 × -1
Complete the missing terms in the arithmetic sequence shown here: 2, ____, 7, ____, 12?
Complete the missing terms in the arithmetic sequence shown here: 2, ,4.5, 7, 9.5, 12?
How to calculate the values?It should be noted that an arithmetic sequence has a first term and common difference.
In this case, a = first term = 2
a + 2d = 3rd term = 7
Since a + 2d = 7
2 + 2d = 7
2d = 7 - 2
2d = 5
Divide
d = 5/2 = 2.5
The common difference is 5
The second term will be:
= a + d
= 2 + 2.5
= 4.5
The 4th term will be:
= a + 3d
= 2 + 3(2.5)
= 2 + 7.5
= 9.5
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the 175 workers at a factory together produce 21,175 items per day what is the unit rate of items per worker
Answer: 121 im pretty sure
Step-by-step explanation: 21175 divided by 175
Can you help me with 8
Answer:
3= 95
a= 85
b=85
4=85
Step-by-step explanation:
Angles on a line add up to 180°
Corresponding angles are equal.
Arno buys a student ticket for $43.68 .
This is a saving of 16% on the full price of a ticket.
Calculate the full price of a ticket.
Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, the full price of the ticket is 293.75.
What is Percentage?Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.
The cost of the ticket Arno buys is $43.68.
The discount she got for the original cost of ticket is 16%.
We need to find the original cost of the ticket.
We need to convert the percentage to a decimal number.
by dividing 16 with 100 we get the decimal value.
16%=16/100=0.16
Now, to find the original or full price of ticket, we need to multiply zero point one six with x equal to forty three point six eight.
0.16×x=43.68
Divide both sides by 0.16
x=293.75
Hence the full price of the ticket is 293.75.
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