Team B will need to sell at least 192 candies to avoid losing money.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given total amount to be raised by each team is $100,
Team B wants to sell cotton candy,
rent of candy machine = $25
total cost to be earned for team B = $100 + $25 = $125
let the number of candies sold be x
cost used in candy sticks = $0.10 per stick
cost used in x candy sticks = $0.10x
the selling price of each candy = $0.75
the selling price of x each candy = $0.75x
total gain = $0.75x - $0.10x
total gain = $0.65x
minimum candies to be sold for no loss
$0.65x = $125
x = 125/0.65
x = 192.30
x = 192
Hence for no loss, at least 192 candies are to be sold.
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What is the answer to 1+5s≤ – 4?
Answer:
This is what I found, but not sure if it's right.
find a basis for the nullspace of the matrix. (if there is no basis, enter none in any single cell.) a = 1 2 −4 5 0 1 −1 3 −2 −4 8 −10
The basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.
The basis for the nullspace of the matrix can be found by reducing the augmented matrix to row echelon form and finding the free variables. The free variables correspond to the columns that have a leading entry of 0 and non-zero entries below it, which are the basis vectors for the nullspace.
Using row operations, the augmented matrix can be reduced to:
1 2 -4 5 | 0
0 1 -3 2 | 0
0 0 0 0 | 0
From this, we can see that the free variables are x2 and x4, so the basis for the nullspace is:
-3 x2 + x4
x2
So the basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.
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Find the missing number.
Increased
by 25
Decreased
by. %
The percentage by which the number has to be decreased is 20%.
What do you mean by algebraic expression?It represents a mathematical relationship or calculation. For example, the expression "2x + 3" is an algebraic expression that represents a linear equation with a variable x and constants 2 and 3. Algebraic expressions can be simplified, evaluated for specific values of the variables, and used to solve equations.
Given:
A number is increased by 25%
To find:
The percentage by which it has decreased
Solution:
The percentage by which the number has to be decreased is 20%.
We can find the percentage by following the given steps-
We know that a number increased by a percentage decreases by a different percentage.
Let us assume that the number is 100.
We know that this number has been increased by 25%.
So, the new number=100+25% of 100
=100+25/100×100
=100+25
=125
Now, the new number is 125.
Let us assume that this number has to be decreased by X% to obtain 100.
So, 125-X% of 125=100
125-X/100×125=100
125-1.25X=100
125-100=1.25X
25=1.25X
25×100/125=X
2500/125=X
X=20%
Therefore, the percentage by which the number has to be decreased is 20%.
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5 times the sum of two numbers is 250 and the difference of the numbers is 18
how many cards in the deck are either a jack or a heart?
The number of cards in the deck that are either a jack or a heart = 16
We know that a standard deck of cards has four suites.
These four suits are:
a) Hearts,
b) Clubs,
c) Spades,
d) Diamonds.
Each suite has thirteen cards.
These thirteen cards are:
Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and king.
This means, the entire deck of cards has 52 cards total.
The number of Jack cards in a standard deck of cards = 4
The number of Hearts in a standard deck of cards = 13
This means, there are 13 + 3 = 16 cards in the deck are either a jack or a heart.
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use calculus to find the volume of a frustrum of a pyramid with square base of side , square top of side , and height ℎ.
The volume of the frustum of a pyramid with square base of side "b", square top of side "a", and height "h" is (b² - a²) × h / 3 cubic units.
Describe calculus.The two primary divisions of calculus, differential calculus and integral calculus, are concerned with rates of change and slopes of curves.
A pyramid's frustum can be thought of as two pyramids with the same height "h" and square bases on sides "a" and "b," as well as a square top on side "a" and that height.
The formulas below give the volume of a pyramid with a square base and sides "s" and height "h":
The volume of a pyramid with square base of side "s" and height "h" is given by:
V = (s² × h) / 3
The volume of the frustum can be found by subtracting the volume of the smaller pyramid from the volume of the larger pyramid:
V = [(b² × h) / 3] - [(a² × h) / 3] = (b² - a²) × h / 3
Hence, the volume of the frustum of a pyramid with square base of side "b", square top of side "a", and height "h" is (b² - a²) × h / 3 cubic units.
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find the following limit or state that it does not exist. x-3 x-9
The limit of (x-3) / (x-9) as x approaches 9 does not exist due to the undefined value in the denominator.
The limit is an important concept in calculus that describes the behavior of a function as the independent variable approaches a specific value.
In this problem, we want to find the limit of the expression (x-3) / (x-9) as x approaches a specific value.
To find the limit, we must substitute values of x that are very close to the specific value and see what the expression approaches.
However, it is important to note that if the limit does not exist, then the function is undefined or has a vertical asymptote at the specific value.
In this case, it is easy to see that the limit does not exist as x approaches 9 because the denominator of the fraction is equal to 0, which is undefined.
The fraction becomes undefined at x = 9 and the limit does not exist.
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Find the ratio of the volume of the triangular prism to the volume of the cuboid.
The ratio of the volume of the triangular prism to the volume of the cuboid is 1:2.
The volume of a triangular prism is calculated by multiplying the area of the base by the height of the prism. The volume of a cuboid is calculated by multiplying the length, width, and height of the cuboid.
For a triangular prism with base area A and height h, the volume is A x h.
For a cuboid with length l, width w, and height h, the volume is l x w x h.
Therefore, the ratio of the volume of the triangular prism to the volume of the cuboid is A x h : l x w x h, which simplifies to 1:2.
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Bob wants to catch an elevator before the door closes. He is 42ft away when the door starts to close. The door has to travel 4.1ft to fully close, and is closing at a rate of 1.1ft/s. Bob needs to get to the door while it is at least 0.7ft open. How fast does he have to run in order to catch the elevator? Give your answer in feet per second, and round to the nearest hundredth.
If Bob wants to catch an elevator before the door closes. He is 42ft away when the door starts to close. How fast does he have to run in order to catch the elevator is: 12.50 ft/s.
How to find the speed?Let's v represent Bob's speed in ft/s.
First, let's find the time it takes for the door to close from 4.1 ft to 0.7 ft:
t = (4.1 - 0.7) / 1.1 = 3.4 / 1.1
t = 3.09 s
Next, let's find the distance Bob has to cover in that time:
d = 42 - 3.4
d = 38.6 ft
Now we can find Bob's speed using the formula:
d = v * t
Solving for v:
v = d / t = 38.6 / 3.09
v= 12.50 ft/s (rounded to the nearest hundredth)
Therefore Bob needs to run at a speed of 12.50 ft/s in order to catch the elevator.
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Given the relation, find its inverse and determine whether or not the function and its inverse are functions.
((-5,0), (-1, -2). (-2, 1), (0,4), (1, 2), (2, -1)}
A. The relation is a function, but the inverse is not.
B. The relation is not a function, but the inverse is.
C. Both the relation and inverse are functions.
D. Neither the relation nor the inverse are functions.
Answer:
C; both the relation and inverse are functions
Step-by-step explanation:
A function has no more than one output for a specific input, therefore, the original set of points is a function.
To find the inverse, you swap the x and y, so you would get:
(0, -5), (-2, -1), (1, -2), (4, 0), (2, 1), (-1, 2)
The inverse is also a function, because each input has only one output.
1
• En una plaza comercial se desea construir un
domo que permita dar sombra a un espacio de
forma triangular. ¿En qué punto se recomienda
poner el pilar de apoyo que sostenga el domo?
¿A qué se debe esto?
You have a biased coin, where each toss has a 3 / 5 3/5 chance of landing heads. But each toss is independent of the others. Suppose you’re going to flip the coin 1 , 000 1,000 times. The first 998 tosses all land tails. What is the probability at least one of the last two flips will be tails?
The probability of getting at least one tails on the last two flips is 8/25.
The probability of getting a tails on a single toss of the coin is 3/5. Therefore the probability of getting tails on the last two flips is (3/5)^2. This is because the coin tosses are independent of one another.
Therefore the probability of getting at least one tails on the last two flips is 1 - (3/5)^2 = 8/25.
This is because the probability of getting two tails is (3/5)^2, and the probability of getting at least one tails is the complement of that. Therefore the probability of getting at least one tails on the last two flips is 8/25.
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How ti calculate loan interest?
Divide your interest rate by the number of payments you’ll make that year
How to calculate simple interest
By utilizing the following calculation, you may get your total interest:
Interest is calculated as follows: principal loan amount x interest rate x duration
The simple interest formula is $20,000 x.05 x 5 = $5,000 in interest, for instance, if you take out a $20,000 loan with a five-year term and a 5% interest rate.
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"Simple Interest is Principal x Interest Rate x Time" is the written formula.The simplest method for computing interest is using this equation.
What is the simplest interest formula?The easy interest calculation is as follows:Interest is equal to P x R x T.principal amount (the beginning balance). The interest rate, R (usually per year, expressed as a decimal).T is the quantity of time periods (generally one-year time periods).If, for instance, your current APR is 17.99% and you currently owe $500 on your credit card over the course of the month, you can get your monthly interest rate by dividing 17.99% by 12, which is roughly 1.49%.To get a monthly payment of $7.45 from $500, multiply the sum by 0.0149.Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.To learn more about Interest refer
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Solve the initial value problem. dt/ds = 8 sin2 +[t=π/12] s(0)=2 (Type an exact answer, using à as needed
After integration, the expression will be[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]
Indicate integrationIntegration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).
Fundamental IntegralAn integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.
∫f(x)dx from a to b.
Indefinite integralThe definition of integrals without upper and lower bounds. It appears as follows:
A definite Integral is represented as:
∫f(x)dx = F(x) + C
Where C is any constant and the function f(x) is called the integrand.
Now,
Right expression is
[tex]\frac{dS}{dt} = 8sin^{2}(t+\frac{\pi}{12} )[/tex]
After integration
[tex]S = 8sin^{2} (t+\frac{\pi}{12} ).dt[/tex]
[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]
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one point is in quadrant lll. The points are reflections of each other across the y-axis
The points are reflections of each other across the y-axis is,
⇒ ( x, - y)
What is Refection?Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
We have to given that;
One point is in quadrant lll.
And, The points are reflections of each other across the y-axis.
Now, Let a point is in quadrant III = (-x, - y)
Where, x > 0, y > 0
We know that;
The rule of the reflection across the y - axis is,
⇒ (x, y) → (- x, y)
Thus, We get;
The points are reflections of each other across the y-axis is,
⇒ (- x, - y) → (- (-x), - y)
→ (x, - y)
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Find the length of AE if BD is a midsegment. PLEASE HELP
The length of AE is given as follows:
AE = 7 units.
What is the midsegment theorem?The midsegment of a triangle states that the segment connecting the midpoints of two sides of a triangle is parallel to and half the length of the third side.
The midsegment of the triangle in this problem is given by the following segment:
BD.
The length of BD is given as follows:
BD = 2 - (-1.5)
BD = 3.5 units.
Hence the length of AE is obtained as follows:
AE = 2BD
AE = 2 x 3.5
AE = 7 units.
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Given EFG = XYZ, find m
A. 45 degrees
B. 60 degrees
C. 90 degrees
D. 30 degrees
Based on the definition of congruent triangles, m<X = 45 degrees.
What are Congruent Triangles?Congruent triangles are two triangles that have exactly the same size and shape, which connotes that every corresponding parts of the triangles are equal.
Given EFG = XYZ, therefore, the measure of angle E will be congruent to the measure of angle X.
m<E = m<X
m<E = 180 - 90 - 60
m<E = 30°
Therefore, m<X = 30°.
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What are Corresponding Angles in Geometry?
The corresponding angles must be equal for the transversal to join two parallel lines.
What is meant by Corresponding Angles?In the intersection of two parallel lines and a transversal, corresponding angles are created. The opening and closing of a lunchbox, completing a Rubik's cube, and endless parallel railroad tracks are a few examples of matching angles in daily life.
The angles in the same corners of two lines, which are typically parallel, are referred to as corresponding angles when they cross each other across a plane (a transversal). In two separate shapes, corresponding sides and angles refer to a pair of matching sides or angles that are in the same location.
Every matching angle is not created equally. The transversal must connect two parallel lines in order for the corresponding angles to be equal. The equivalent angles that are created when a transversal encounters a line that is not parallel are not congruent and have no connection to one another.
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Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) a_n = sin (4n)/2n + squareroot n lim n rightarrow a_n = DNE
The sequence aₙ = sin (4n)/2n + √n diverges because it does not have a limit that can be expressed in a finite manner.
A sequence is a set of numbers that follow a certain pattern. The behavior of the sequence as n approaches infinity determines whether the sequence converges or diverges.
In this case, the sequence
=> aₙ = sin (4n)/2n + √n.
To determine whether the sequence converges or diverges, we need to find the limit as n approaches infinity.
However, in this case, the limit as n approaches infinity is DNE, meaning it does not exist. This means that the sequence diverges, as it does not approach a limit as n approaches infinity.
In this case, the sequence
=> aₙ = sin (4n)/2n + √n
converges to DNE, meaning that it does not have a limit that can be expressed in a finite manner.
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ABCD is a trapezoid with shorter base DC = 3 cm and altitude PQ going through the point of intersection of the diagonals O, such that PO = 1 cm and 0Q = 3 cm. Find AB, the ratio CO: AO, and the ratio between the areas of ADOC and ABOA.
The ratio of Areas is 1:1.
What is Trapezium?A quadrilateral with one set of parallel opposite sides is a trapezium. The bases and legs of a trapezium are referred to as parallel and non-parallel, respectively. It also goes by the name trapezoid.
As, The diagonals of a trapezium divide each other proportionally.
AO / OC = OB/ OD
Also, OA= OB and OC= OD
So, OA/ OC = 1: 1
In Triangle DOC and BOA
<AOB = <COD (Vertical Opposite angle)
<BAO = <OCD ( Alternate Interior angle)
By AA similarity Criteria Triangle DOC and BOA are similar.
So, ar (Δ DOC)/ ar (ΔBOA)
= DO / OB = OC / OA = DC / BA
As, the ratio of corresponding length is equal.
So, the ratio of Triangle is 1:1
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Jack Pott is paid a straight commission of 6% on his sales. During
February, his sales were $38,000. What was his commission?
Answer:
$2280
Step-by-step explanation:
38000*6% =2280
When we say ‘the limit does not exist’, do we mean it is actually in a determinate form or it is defined (like it's not something divided by zero)? If not, what is the basic meaning of ‘the limit does not exist’?
The limit does not exist if the graph features a vertical asymptote with one side going toward infinity and the other toward negative infinity.
What is meant by negative infinity?Since the graph is infinitely negative as one approaches zero from either side, the limit as x approaches zero would be negative infinity: In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function). The set of real numbers does not include infinity. The real number set is closed under addition and multiplication, which is one of its axioms. That is, you will always obtain a real number if you add two real numbers together. However, the closure rule is broken by the expressions ∞+(−∞) And ∞×0 for which there is no valid definition.To learn more about negative infinity, refer to:
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let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and f '(4) = 7. find r'(1). r'(1)
The value of r'(1) is 112.
To find the derivative of r(x) at x = 1, we'll use the chain rule. The chain rule states that if r(x) = f(g(h(x))), then the derivative of r(x) with respect to x is given by r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x).
When r(x) = f(g(h(x))) by chain rule
r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)
So r'(1) = f'(g(h(1))) * g'(h(1)) * h'(x)
As h(1) = 2 and h'(1) = 4
r'(1) = f'(g(2)) * g'(2) * 4
As g(2) = 4 and g'(2) = 4
r'(1) = f'(4) * 4 * 4
As f'(4) = 7
r'(1) = 7 * 4 * 4
r'(1) = 112
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write negations for each of the following statements: a) john is 200 pounds, and he is at least 6 feet. b) tom’s watch was slow or the bus was late
The neg-ations of the given statements are: a) John is not 200 pounds or he is less than 6 feet and b) Neither Tom's watch was slow nor was the bus late.
To answer this question first let's understand what negation is.
Neg-ation is a concept in mathematical reasoning which is represented by the symbol "∼" and represents the opposite of the given mathematical statement. For example negation of “A and B” is “not(A) or not(B).
a) The neg-ation of the statement "john is 200 pounds, and he is at least 6 feet" is "John is not 200 pounds or he is less than 6 feet"
b) The neg-ation of the statement "tom’s watch was slow or the bus was late" is "Neither Tom's watch was slow nor was the bus late."
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54 kilometers in 4 hours = 81 kilometers in __ hours
Answer:
6 hours
Step-by-step explanation:
create a proportion:
54 km/4 hrs equals 81km/? hours
[tex]\frac{54}{4}[/tex] = [tex]\frac{81}{?}[/tex]
solve a proportion by cross-multiplying:
54? = 324
? = 324/54
? = 6
Answer:
6 hr
Step-by-step explanation:
If 54 km --> 4 hr then,
81 km --> ? hr
You can make a rule of three:
? hr = (81*4)/54
? hr = 6
So 81 km in 6 hours
PLEASE HELP ME. THE ASSIGNMENT IS ON THE SCREEN
Answer:
D.) the ovens temperature after 1 minute.
Step-by-step explanation:
if "x" is the number of minutes that have passed then the output is the temp after the oven was preheating for 'x" amount of minutes
I need help my homework is due in 15 mins
Answer:
1st box = 200
2nd box = 7
3rd box = 237
4th box = 270
5th box = 333
Step-by-step explanation:
1st box:
27. write the following mask in slash notation (/n): a. 255.255.255.0
255.255.255.0 is written as /24 in slash notation (/n).
Slash notation is a compact way to show or write an IPv4 subnet mask. When you use slash notation, you write the IP address, a forward slash (/), and the subnet mask number.
1- To find the subnet mask number:
2- Convert the decimal representation of the subnet mask to a binary representation.
Count each “1” in the subnet mask. The total is the subnet mask number.
In IPv6, slash notation is used to represent the network identifier prefix for an IPv6 network. The prefix is expressed as a slash (/) followed by the prefix size, which is a decimal number between 1 and 128.
Thus, 255.255.255.0 is written as /24 in slash notation (/n).
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A scatter plot is shown on the coordinate plane.
Which two points would a line of fit go through to best fit the data?
(1, 10) and (10, 1)
(1, 7) and (2, 6)
(3, 7) and (7, 4)
(3, 8) and (6, 6)
Line of fit go through (1, 10) and (10, 1) to best fit the data.
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Line of best fit of the scatterplot should go through as many points as possible of the graph.
If we draw a line passing through the pair of points given in the options, the line passing through (1, 10) and (10, 1) passes through (9, 2), (7, 4) and (3, 8).
No other line drawn through points in the options passes through 5 points.
Hence the line of best fit is the line passing through (1, 10) and (10, 1).
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4. You are painting the roof of a
boathouse. You are going to
place the base of a ladder
3.2 feet from the boathouse.
How long does the ladder
need to be to reach the
roof of the boathouse?
K
3.2 ft
12.6 ft
The length of the ladder is 12.9 feet
How to find the length of the ladderAssuming the height of the boat house is 12.6 feet
The problem is solved using the Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
The length of the ladder is the hypotenuse
plugging the values as in the problem
let x be the required distance
x² = 3.2² +12.6²
x² = 166.49
x = √166.49
x = 12.9 feet
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