EXPLANATION
Distribution ---> 5 skittles per student
Ate ---> 8 remained
Originally ---> 143 skittles
Let's call x to the number of students.
So, if the total number of skittles is 143, the relationship should be:
143 = 5*x +8 [EQUATION]
Now, adding +8 to both sides:
143 - 8 = 5x
Adding terms:
135 = 5x
Dividing both sides by 5:
135/5 = x
Simplifying:
27 = x
Switching sides:
x=27
There are 27 students.
Determine the value of a if f(x) =(ax²-1 if x < 1 a(x² - 2x + 1) ifx>1 is continuous atx = 1.
-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.
To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.
First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:
lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.
Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:
lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.
For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:
a - 1 = a.
To solve this equation for "a," we subtract "a" from both sides:
-1 = 0.
Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.
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What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.
The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:
Define the formula p(x, y) as x = yo(x).
This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.
Define the set F as {(x, x) (x)}.
This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.
Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.
This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.
The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.
Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.
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Identify whether each function is linear or exponential.
Function A:
Function C
Function D:
You have $200 in
a savings
account that
earns 1% annual
interest
b. Which function has the greatest growth factor? Justify your response.
Answer:
A)
Function A: Exponential
Function B: Linear
Function C: Exponential
Function D: Exponential
B) Function A
Step-by-step explanation:
Function A: This is exponential because- (1, 3)(2,9)(3,27)
It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.
Function B: This is linear because- (1, 64)(1, 80)(1, 96)
It is going up by 16 each time, (a constant number) which means it is linear.
Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.
Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.
The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.
What’s the correct answer answer asap for brainlist
Answer: serbia
Step-by-step explanation:
Help Me PLEASE!!!
A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?
Answer:
P = 0.5207
Step-by-step explanation:
First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.
Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).
So, the probability that just the first card is a diamond or an ace is calculated as:
\(P_1=\frac{16}{52}*\frac{36}{52}=0.2130\)
At the same way, the probability that just the second card is a diamond or an ace is:
\(P_2=\frac{36}{52}*\frac{16}{52}=0.2130\)
Finally, the probability that both cards are diamonds or aces is:
\(P_3=\frac{16}{52}*\frac{16}{52}=0.0947\)
Therefore, the probability that at least one of the cards is a diamond or an ace is:
\(P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207\)
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
This is Section 3.8 Problem 32:
A concert organizer learned from a market survey that when the admission price is\$30, there is an average attendance of 800 people. For every $1 drop in price, there is a gain of 20 customers. Each customer spends an average of $5 on concessions. The concert hall has 1,000 seats.
(a) The demand function, expressed by p, the price in dollars charged for each ticket, as a function of x, the number of average attendance, is p=D(x)= 70−(1/20)x, where x is defined between 0 and 1,000
(b) The revenue function is R(x)= 70x−(1/20)x2+5x , where x is defined between 0 and 1,000
(c) To maximize its revenue, the price the concert organizer charges should be 32.5 dollars for each ticket. (Keep 2 decimal places (rounded), unless the exact answer has fewer decimal places.)
(This is the correct answer I just don't know how to get to it)
To maximize revenue, the concert organizer should charge $32.50 for each ticket. This price corresponds to an attendance of 325 people.
To find the price that maximizes revenue, we need to differentiate the revenue function with respect to x and set it equal to zero:
R'(x) = 70 - (1/10)x + 5
Setting R'(x) equal to zero, we get:
70 - (1/10)x + 5 = 0
Simplifying, we get:
x = 325
So the optimal attendance is 325. To find the corresponding price, we can use the demand function:
p = 70 - (1/20)x
Substituting x = 325, we get:
p = 70 - (1/20)(325) = 32.5
So the price that maximizes revenue is $32.50.
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determine the quotient between 9/10 and 3/5
Answer:
Step-by-step explanation:
Short answer 2/3 if you need more just text bcak I will be happy to explain
What is a product of 10 and the counting numbers 1 2 3 and so on? Answer for 25 points!
Is -9/37 rational or irrational
Answer:
It is rational
Step-by-step explanation:
Any fraction is a rational number
A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length L (in miles) that is left to lay after d days is given by the following L (d)=189-7d
The number of days it will take the crew to lay all the track is; 27 days
The number of miles of track the crew has left to lay after 18 days is; 65 miles
How to solve Algebraic Equations?
We are given the equation that represents the length L (in miles) that is left to lay after d days as;
L(d) = 189 - 7d
where;
L is length in miles
d is number of days
Thus, the number of days it will take to lay all the tracks is;
Number of days = 189/7
Number of days = 27 days
The length L (in miles) that is left to lay after 18 days is;
L= 189 - 7(18)
L= 189 - 126
L= 65 miles
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Complete question is;
A railroad crew can lay 7 miles of track each day. They need to lay 189 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function. L(d) = 189 - 7d
(How many days will it take the crew to lay all the track?)
(How many miles of track does the crew have left to lay after 18 days?)
Please help it’s URGENT!
The least common denominator needed to solve the equation is given as follows:
D. x(x - 3).
How to obtain the least common denominator?The equation in this problem is given as follows:
1/x + 2/(x - 3) = 5.
The denominators of each expression are given as follows:
x.x - 3.x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:
D. x(x - 3).
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Music students and art students at a middle school were surveyed to choose a cardiovascular activity: playing sports or dancing.
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Music students 32 15 47
Art students 31 22 53
Column totals 63 37 100
What is the marginal frequency of students who chose dancing?
15
22
37
53
The marginal frequency of students who chose dancing is 37.
The correct answer to the given question is option 3.
The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.
Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.
It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.
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Trapezoid JKLM with the vertices J(2,1), K(5,1)L(8,-4)and M (1.-4) 90 clockwise rotation about y(-1,3)
The coordinates of the vertices of trapezoid J'K'L'M' with its graph include the following:
J' (-3, 0).
K' (-3, -3).
L' (-8, 6).
M' (-8, 1).
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise to the vertices of trapezoid JKLM, the coordinates of the vertices of the image are as follows:
(x, y) → ((y - b) + a, -(x - a) + b)
J (2, 1) → ((1 - 3) - 1, -(2 + 1) + 3) = (-2 - 1, -3 + 3) = J' (-3, 0).
K (5, 1) → ((1 - 3) - 1, -(5 + 1) + 3) = (-2 - 1, -6 + 3) = K' (-3, -3).
L (8, -4) → ((-4 - 3) - 1, -(8 + 1) + 3) = (-7 - 1, -9 + 3) = L' (-8, 6).
M (1, -4) → ((-4 - 3) - 1, -(1 + 1) + 3) = (-7 - 1, -2 + 3) = M' (-8, 1).
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Solve for w: 2w/5 - 9 = 11
Answer:
w= 50
Step-by-step explanation:
Answer: x = 50
Step-by-step explanation: 2w/5 - 9 = 11
+9 +9
20
2w/5 = 20
*5 *5
100
2w = 100
2 2 = 50 so x = 50
The table shows the cost of long distance calls
Answer:
nnnvvg
Step-by-step explanation: mm
put equation in conic form
Answer:
I'm happy to help you put an equation in conic form, but you haven't provided an equation to work with. Please provide the equation and I'll do my best to assist you.
Which equation written below in vertex form is
equivalent to the equation y=x²-6x+12?
y=(x-3)²
y=(x-6)² + 12
y= (x+3)² +3
y=(x-3)² +3
y=x²-6x+12
y=x²-6x-9+12
what is 1*5+89 20 points
Answer:
your answer is going to be 94
Step-by-step explanation:
1×5=5
5+89=94
Answer: 1*5+89 = 94
The answer is 94
After 4 pm, the rides are 50% off. If the price is $7, how much will it cost after 4 pm?
Answer:
answer is 3.5 dollar
dividing 7 ÷ 2 = 3.5 dollar
as we have to take 50 percent
The following angles are supplementary to each other.
m∠C = (x + 19)° and m∠D = (3x − 19)°
Determine x.
60
45
38
19
Answer:
45
Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180
Answer: 45
Step-by-step explanation:
Did the test.
Which number set below in
ordered from least to greatest?
A. -3.0,-3.01, -3.1, -3.15
B. -3.15,-3.1, -3.01,-3.0
C. -3.15,-3.1, -3.0,-3.01
X
Calculate 75% of 1200
Answer:
it is 900
Step-by-step explanation:
you multiply 1200 by 0.75
Answer:
Answer:75% of 1200
Answer:75% of 1200(100-75%)=25%
Answer:75% of 1200(100-75%)=25%25*1200/100
Answer:75% of 1200(100-75%)=25%25*1200/10030,000/100
Answer:75% of 1200(100-75%)=25%25*1200/10030,000/100300
A boat's value over time is given as the function f(x) and graphed below. Use A(x) = 400(b)x + 0 as the parent function. Which graph shows the boat's value decreasing at a rate of 40% per year?
Answer: I can't really tell you the answer because you didn't show the graphs...
Step-by-step explanation:
A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ
What is an exponential function?An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Given that the boat's value decreasing at a rate of 40% per year, hence:
b = 100% - 40% = 60% = 0.6
A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ
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help me please asap I'll give brainleist
B!!!!!!!!!!!!!!!!!!!!!!
hope this helps
=
Given f(x) = 3x2 + 5x + k, and the remainder when f(x) is divided by
x + 3 is 29, then what is the value of k?
Answer:
the answer is k=2
Step-by-step explanation:
S={(3,p),(3,0),(4,q),(1,4)}
Answer:
S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:
(3,p): The first element is 3 and the second element is p.
(3,0): The first element is 3 and the second element is 0.
(4,q): The first element is 4 and the second element is q.
(1,4): The first element is 1 and the second element is 4.
What is the solution to the system of equations?
3x+2y = 39
5x-y= 13
A. (4, 7)
B. (7, 4)
C. (12, 5)
D. (5, 12)
Answer: (5,12)
Step-by-step explanation:
Did it on Desmos graphing calculator
What is 0.08 is 10 times as much as
Answer:
Answer. Step-by-step explanation: The answer is 0.8 because if something is 10 x of something in decimal terms it would be the number after the decimal getting smaller.
Which numbers are equal to 24
8 divided by 1/3
6 divided by 1/8
9 divided by 1/4
4 divided by 1/6
12 divided by 1/2
Answer:
The first one
Step-by-step explanation:
I did this and got it right and I solved it
8×3 equal 24/1 so make it to a whole number 24