The minimum number of dots and/or dashes needed so that each letter in the English alphabet can have a unique representation is 4.
We need a code that can handle at least that many characters because there are 26 letters in the alphabet.
One can choose to use one of two symbols in each position, which results in 2^1 = 2 words.
Given two locations and the option to utilize one of two symbols in each, 2^2 = 4 words are produced.
Using one of two symbols in each of the three slots allows for a total of 2^3=8 words.
With 4 positions and the option to use one of two symbols in each, there are 2^4=16 words possible.
The sum of the dots and dashes is
2 + 4 + 8 + 16 = 30
Since there are 26 letters in the English alphabet, 4 dots and/or dashes are required to represent each letter, hence the answer is 4.
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Question 1 of 3
A quadratic function has x-intercepts at (-2,0) and (-1,0). The point (-3, 6) lies on the parabola.
Complete the statements.
The value of a is [Drop Down 1].
The equation of the quadratic function is f(x) = [Drop Down 2] in factored form and f(x) = [Drop Down 3] in standard form.
Drop Down 1:
The value of a is 3
The equation of the quadratic function is
f(x) = 3(x+2) (x+1) in factored form and
f(x) = 3x² + 9x+2 in standard form.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
The x-intercepts of the parabola are (-2,0) and (-1,0).
So the factors are (x- (-2)) and (x- (-1))
That is, (x+2) and (x+1)
Now the equation of the parabola,
y = a(x+2) (x+1)
To find a substitute the values -3 and 6 for x and y as these points are on the parabola.
6 = a(-3+2)(-3+1)
6 = a ( -1)(-2)
a = 3
So the equation of the parabola is y = 3(x+2) (x+1)
Therefore the complete statements regarding the parabola is:
The value of a is 3
The equation of the quadratic function is
f(x) = 3(x+2) (x+1) in factored form and
f(x) = 3x² + 9x+2 in standard form.
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deltamath.com
Plot the points A(3,-2), B(-7, -6), C(-2, 1)
on the coordinate axes below. State the
coordinates of point D such that A, B, C,
and D would form a parallelogram.
(Plotting point D is optional.)
Click on the graph to let a point Click a noi to
Answer:
D (-2, -9)
Step-by-step explanation:
Parallel slopes are equal. From C to A it is down 3 and right 5. To go from B to D go down 3 and right 5.
B go down 3 -6 - 3 = -9
B go right 5 -7 + 5 = -2
How could Liam use red, blue, and yellow cards to describe each of the following motions? Write equations to support your answer. • A green card means move forward 2 spaces. • An orange card means move 8 spaces backward. • A purple card means move forward 10 spaces.
The integer numbers for each card describing the motions are given as follows:
Green card: x = x + 2.Orange card: x = x - 8.Purple card: x = x + 10.What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
Regarding the movements, the integers can be classified as positive or negative, as follows:
Positive integer represents a forward movement.Negative integer represents a backward movement.Considering the movements described for each card in the problem, the equations are built in the answer given at the beginning of the answer.
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!
Answer:
C.
Step-by-step explanation:
The number of guests attending Elise's holiday party increased by approximately
10
%
10%10, percent each year over the past
5
55 years. Which of the following best describes the relationship between time and the number of guests attending Elise's holiday party?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Increasing linear
(Choice B)
B
Decreasing linear
(Choice C)
C
Exponential growth
(Choice D)
D
Exponential decay
Answer:
C. Exponential growth
Step-by-step explanation:
You want to know how to describe the relation that represents a 10% increase per year.
FunctionThe problem statement tells you the number of guests "increased by approximately 10% each year". The nature of the function depends on what "10%" refers to.
If the amount of increase is constant year after year (10% of the original number of guests), then the relationship is linear.
If the amount of increase is 10% of the previous year's number, so the amount increases each year, then the relationship is exponential.
Growth and decayWhen the number increases year on year, the number is said to be growing. If the relationship is exponential, it is described as exponential growth.
If the number were decreasing by 10% per year, it would be an exponential decay relationship.
__
Additional comment
Whenever you're dealing with percentages, you always need to understand what is being used as the base amount. (What does 100% represent?)
Usually, a percentage increase or decrease is referring to the current value. Not always.
Sometimes a change from 10% to 6% is referred to as a 4% decrease, and sometimes it is referred to as a 40% decrease. It depends on who is selling what to whom.
you will work with a matrix whose entries are all prime numbers below 30. i) create this matrix using the function `matrix()` with five rows. save the matrix as `a`. ii) extract the second and third row out of `a`. iii) extract the entry in the 3rd row and first column of `a`. iv) generate the transpose of the matrix using the function `t()`. save this into `t.a`. what is the new dimension of this matrix?
The new dimension of the matrix t. a is 5 columns and 3 rows.
i) To create a matrix whose entries are all prime numbers below 30 using the matrix() function with five rows, you can use the following code:a <- matrix(c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29), nrow = 5)ii) To extract the second and third row out of a, you can use the following code:a_rows_2_3 <- a[2:3, ]iii) To extract the entry in the 3rd row and first column of a, you can use the following code:a_entry <- a[3, 1]iv)To generate the transpose of the matrix a and save it into t.a, you can use the following code:t.a <- t(a)The new dimension of the matrix t.a is 5 columns and 3 rows.
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Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
The translation of 5 units to the left and 3 units down,The new coordinates are therefore (5, 1).
How can coordinates be determined after translation?The coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.
By multiplying the value of the horizontal translation by the original x-coordinate, get the new x-coordinate of the translated point (adding a negative number if translating to the left).
Let (A,B)=(3,5) serve as the new origin and (x,y)=(3,4) serve as the provided point.
new coordinates are therefore (X,Y).
x = X+A and y = Y+B
such as 3=X2 and 4=Y+5.
This results in X=5 and Y=1
The new coordinates are therefore (5, 1).
The translation of 5 units to the left and 3 units down,The new coordinates are therefore (5, 1).
Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down. (3,4) will become
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The number of songs enjoyed from Eminem by all Learn4Life students is normally distributed with a mean of 7.0 songs and a standard deviation of 1.5 songs.
What is the probability an individual student likes between 5.5 and 8.5 songs from Eminen?
The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.
To calculate the desired probabilityWe need to find the z-score corresponding to 5.5 and 8.5 and then use the standard normal distribution table to find the area under the curve between these z-scores.
Z-score for 5.5 is (5.5 - 7.0) / 1.5 = -1
Z-score for 8.5 is (8.5 - 7.0) / 1.5 = 1
The probability of a z-score being between -1 and 1 is equal to the area under the standard normal curve between these two z-scores.
According to the standard normal distribution table, this area is approximately 0.6826.
Therefore, The probability that an individual student likes between 5.5 and 8.5 songs from Eminem is approximately 0.6826 or 68.26%.
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-4x+7y=3
x intercept ( , )
y intercept ( , )
Answer: I think its X intercept is (-0.75,0) and then y is (0,0.429)
Step-by-step explanation:
Tell me if I'm wrong
what is the eigenvalue for the eigenfunction sin4θ of the operator −tanθd/dθ ?\
The eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.
To find the eigenvalue, we need to multiply the operator by the eigenfunction and see what we get:
(-tan(θ)d/dθ)(sin(4θ)) = -tan(θ)(d/dθ)(sin(4θ)) = -tan(θ)(4cos(4θ))
Since sin(4θ) is an eigenfunction, we expect that the result of the operator multiplied by the eigenfunction should be proportional to the eigenfunction. In other words, there should be a scalar factor multiplying the eigenfunction. This scalar factor is the eigenvalue.
So, we can write:
(-tan(θ)d/dθ)(sin(4θ)) = λsin(4θ)
where λ is the eigenvalue. Equating the right-hand sides of the two equations, we find:
-tan(θ)(4cos(4θ)) = λsin(4θ)
Dividing both sides by sin(4θ), we get:
-tan(θ)(4cos(4θ)) / sin(4θ) = λ
So, the eigenvalue λ is equal to -tan(θ)(4cos(4θ)) / sin(4θ). The exact value of the eigenvalue depends on the specific value of θ, as both tan(θ) and cos(4θ) vary with θ.
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11. During a race, you speed up from 3 m/s to 5 m/s in 4 s.
(a) What is your change in speed?
4750
(b) What is the magnitude of your acceleration?
The change in speed equals 2m/s and Magnitude of acceleration = 2.
What does a vehicle moving at a constant speed accelerate to?What is meant by zero acceleration is the rate of change in speed. Thus, the rate of change in speed is zero while the car is moving at a constant pace. As a result, there is no acceleration. Magnitude is the length of any vector that points in the direction of the vector and is denoted by its unit. As a result, the acceleration's magnitude is equal to the acceleration vector's length and is directed in the same direction. For any vector quantity, this is true.
the sense, or the direction the vector is moving (left/right, up/down); the orientation, or the angle(s) governing the vector's alignment (transversal, longitudinal); and
The "strength" of the function is represented by the magnitude, or the value derived from the scalar quantities.
Change in speed = 5 m/s - 3m/s = 2m/s
As acceleration = rate of change in speed
Magnitude of acceleration = 2
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4) The school that Kayla goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 8 adult tickets and 6 child tickets for a total of $192. The school took
in $279 on the second day by selling 9 adult tickets and 12 child tickets. What is the price each
of one adult ticket and one child ticket?
Answer:
Senior ticket = $10
Child's ticket = $8
Step-by-step explanation:
s = senior ticket
c = child's ticket
We need to write 2 equations, and we have 2 unknowns, s and c.
3s + 5c = $7012s + 12c = $216First solve for s using the first equation.3s + 5c = 70 Subtract 5c from each side3s + 5c - 5c = 70 - 5c3s = 70 - 5c Divide each side by 33s/3 = (70 - 5c)/3s = 70-5c/312s + 12c = 216
12() + 12c = 216
(70 - 5c) + 12c = 216
4 (70 - 5c) + 12c = 216
280 - 20c + 12c = 216
280 - 8c = 216 Add 8c to each side
280 - 8c + 8c = 216 + 8c
280 = 216 + 8c Subtract 216 from each side.
280 - 216 = 216 - 216 + 8c
280 - 216 = 8c
64 = 8c Divide each side by 8
64/8 = 8c/8
64/8 = c
8 = c
Now plug c into the first equation and solve for s.
3s + 5c = 70
3s + 5(8) = 70
3s + 40 = 70 Subtract 40 from each side.
3s + 40 - 40 = 70 - 40
3s = 70 - 40
3s = 30 Divide each side by 3
3s/3 = 30/3
s = 30/3
s = 10
So a senior ticket costs $10 and a child's ticket costs $8.
if two times a positive number is added to one third of its square, the result is 9,find the number
Answer:
Step-by-step explanation:
[tex]2x+\frac{1}{3} x^{2} =9[/tex]
Move all terms to l.h.s.
[tex]\frac{1}{3} x^{2} +2x-9=0[/tex]
Multiply everything by 3
[tex]x^{2} +6x-27=0[/tex]
Factorize
[tex](x+ 9)(x-3 )=0[/tex]
therefore
[tex]x+9=0[/tex] or [tex]x-3 =0[/tex]
x= -9 or x =3
Since x is a positive answer the answer must be
x=3
if we flip a coin, we would expect the probability of it landing heads is the same as it landing tails (e.g., 0.50). however, we are more likely to achieve this outcome the more often we flip the coin. that is, over a large number of trials we are more likely to approximate our expected probability. this is referred to as:
if we flip a coin, we would expect the probability of its landing heads to be the same as its landing tails is referred to as the law of large numbers.
The law of large numbers is a probability and statistics, which defines that as a sample size grows, its mean gets closer to the average of the whole population.
This is due to the sample being more representative of the population as the sample becomes larger.
This is the theorem that describes the result of performing the same experiment a large number of times because the average of the results obtained from a large number of trials is close enough to the expected value.
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Olivia needs 2.5 yards of fabric to make a table cloth. A fabric with fall leaves costs $6.64 per yard, and a pumpkin fabric costs $7.98 per yard. How much more would the pumpkin fabric cost?
Answer: It would cost $3.35 ?more than the leave cloth.
Step-by-step explanation:so for 2.5 yards the leaves of fabric would cost $16.6 because 6.64×2=$13.28+6.64/2=16.6
Then for the pumpkin which costs $19.95 because you would multiply 7.98 by 2 then add 7.98 divided by 2. So it would cost 19.95-16.6=$3.35
PLEASE I NEED THE ANSWERS FAST MATHEMATICS HIGHSCHOOL HOMEWORK!!!!! (I will choose the best answer)
let me know if answers are correct coz it has been a year that I learnt it and now I'm not doing those exercises so...
Step-by-step explanation:
c) 24 degree
d) 80 degree
e) 93 degree
f) 26 degree
g) ist es gegeben, dass Alpha das Zentrum ist? Wenn ja, ist der Winkel 150
h) Hier gilt das gleiche
suppose you have just poured a cup of freshly brewed coffee with temperature in a room where the temperature is . newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. therefore, the temperature of the coffee, , satisfies the differential equation where is the room temperature, and is some constant. suppose it is known that the coffee cools at a rate of per minute when its temperature is . a. what is the limiting value of the temperature of the coffee? b. what is the limiting value of the rate of cooling? c. find the constant in the differential equation. . d. use euler's method with step size minutes to estimate the temperature of the coffee after minutes. .
a) The limiting value of the temperature of the coffee is 25°C.
b) The limiting value of the rate of cooling is equals to 0.
c) The value of constant k in the
differential equation is -0.05.
d) The temperature of the coffee at time t = 10 is 66.33°C.
Newton's Law of Cooling: The rate at which an object's temperature changes is proportional to the difference in temperature between the object and its surroundings. For an object that has a temperature very close to that of its surroundings, the rate of heating or cooling becomes very small. We have the temperature of the coffee, T(t), satisfies the differential equation,
dT/dt= k(T − T (room)),
where T(room) = 25 is the room temperature, and k is some constant.
A) Limiting value of the temperature
= 25°C
B)limiting value of dT/dt = k[(limit temp) - (room temp)] = k(25 - 25)= 0
C) dT/dt = k(T - 25)
=> -2 = k (65 - 25)
=> -2 = 40k
=> k = -0.05
D) T' = -0.05 x (95-25) = - 3.5
h = 2, ∆T = -3.5x 2 = -7
T = 95- 7 = 88
Then T' = -0.05 x (88-25) = - 3.15
=> T = 88 - 2 x 3.15 = 81.7
=> 81.7 after 4 minutes
Then T' = -0.05x (81.7-25) = -2.835
T = 81.7 - 2x 2.835 = 76.03 after 6 mins
Then T' = -0.05 x (76.03-25) = -2.5515
T = 76.03 - 2 x 2.5515 = 70.92700 after 8 mins
Then T' = -0.05 x (70.927-25) = -2.29635
T = 70.927 - 2 x 2.29635
= 66.3343 after 10 minutes
so temperature = 66.33 after 10 mins by Euler's method.
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Complete question:
Suppose you have just poured a cup of freshly brewed coffee with a temperature of 90∘C in a room where the temperature is 25∘C. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation
dT/dt= k(T−Troom), where T(room) = 25 is the room temperature, and k is some constant.
Suppose it is known that the coffee cools at a rate of 2∘C per minute when its temperature is 65∘C.
A. What is the limiting value of the temperature of the coffee?
B.What is the limiting value of the rate of cooling?
C. Find the constant k in the differential equation.
D. Use Euler's method with step size h = 2 minutes to estimate the temperature of the coffee after 10 minutes_ Answer (in Celsius): T(10)
I DON'T GET THIS WHAT DID I DO WRONG FOR (4,1) (8,2)???!??!?!?!?!?!? PLS HELP!!P!P!P!P!!!?!?!?!?!
Answer:
Look at the y axis
Step-by-step explanation:
Each division is 2 units, so look and mark 8,2 carefully
If it confuses you, take 16, 4 as well because I dunno how flexible are your drawing tools
Hope this helps :)
Edit: Sorry but I have just realized what had happened, I took the time variable for the y axis. (Sorry, I am used to using the time variable on the y axis
* Please answer fast *
The required fill-in-the-blank below as:
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given in question as:
RS ⊥ ST
RS ⊥ SQ
∠STR = ∠SQR
To prove:
△RST ≅ △RSQ
1.) RS ⊥ ST, RS ⊥ SQ, ∠STR ≅ ∠SQR | Given
2.) RS≅RS | Reflexive Property
According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
3.) △RST ≅ △RSQ | AAS Triangle Congruence Property
Hence, △RST ≅ △RSQ
Thus, the required fill-in-the-blank above is in the solution.
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Can someone please please help mke i was suppose to finnish this at least 4 weeks ago please can someone answer these 3 question for at leat 150 or 200 points.
a box contains 3 marbles: 1 red, 1 green, and 1 blue. consider an experiment that consists of taking 1 marble from the box and then replacing it in the box and drawing a second marble from the box. describe the sample space
The sample space for this experiment is the set of all possible outcomes of drawing 2 marbles from the box, where order matters. There are 3 choices for the first marble, and 3 choices for the second marble, so the sample space is {RR, RG, RB, GR, GG, GB, BR, BG, BB}. There are 9 possible outcomes in this sample space.
Marble Draw Experiment Sample SpaceTo determine the sample space for this experiment, we first list all the possible outcomes for the first marble that we could draw. There are 3 marbles in the box (red, green, and blue), so there are 3 choices for the first marble. We can represent these choices as R, G, and B.
Next, we list all the possible outcomes for the second marble that we could draw. Since the box is being replaced with the first marble before the second draw, there are still 3 marbles in the box (red, green, and blue), so there are still 3 choices for the second marble. We can represent these choices as R, G, and B.
Finally, we list all possible combinations of the first and second marble, which forms the sample space. Since order matters, we list all the possible combinations of R, G, and B as pairs. In this case, there are 3 choices for the first marble and 3 choices for the second marble, which gives us 3 * 3 = 9 possible outcomes in the sample space: {RR, RG, RB, GR, GG, GB, BR, BG, BB}.
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Adrian invested $790 in an account paying an interest rate of 6.9% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $2,550?
It would take 17 years for the value of the account to reach $2,550. The solution has been obtained by using the concept of compound interest.
What is compound interest?
The principal as well as the interest that has accrued over the previous period are both used to compute interest. Compound interest factors the principal into the calculation for determining the interest for the subsequent month, in contrast to simple interest, which does not. In mathematics, the symbol for compound interest is typically the letter C.I.
We are given the principal amount as $790 paying an interest rate of 6.9% compounded continuously.
The final balance is $2,550.
We know that formula for continuous compounding interest is
[tex]P(t) = P_{0} e^{rt}[/tex]
So, using this, we get
⇒[tex]2550 = 790 e^{0.069*t}[/tex]
Solving this, we get
t = 17
Hence, it would take 17 years for the value of the account to reach $2,550.
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Evaluate: a 6.24 x 10
A polygon will be dilated on the coordinate grid to create a large polygon. The polygon i dilated uing the origin a the center of dilation
The rule for dilation around the origin with a scale factor of k is (x,y) -> (kx,ky).
Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. A dilation centered at the origin involves scaling the figure down by a factor, causing it to become smaller.
In this case, the origin acts as the center of dilation, with the original figure being mapped to a smaller, similar figure.
To perform a dilation, each point of the original figure is multiplied by the same scale factor, resulting in a smaller, proportional figure.
The scale factor determines how much the figure will be reduced. It is important to note that dilations centered at the origin preserve the orientation of the figure, meaning it will look the same as the original, but just smaller.
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A random experiment has three possible outcomes a, b, and c, with P(a) = p, P(b) = p^2, and P(c) = p. What choice(s) of p makes this a valid probability model?
The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.
For this to be a valid probability model, p must be a positive integer between 0 and 1, and p + p2 + p must equal 1. This random experiment must have a probability rea, circumference, and other parameters because it is symmetrical. of each of the three outcomes adding up to 1 in order to be a reliable probability model. This implies that the probabilities p, p2, and p associated with outcomes a, b, and c must all add up to 1. In other words, p + p2 + p = 1 would be the equal. Since p must be a real value between 0 and 1 and satisfy the equation p + p2 + p = 1, this random experiment must be a legitimate probability model.
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(5) The denominator of a fraction is 4 more than its numerator (y). the value of the fraction was 3/4 or more. Find the least value of Y
What is the positive and negative of the function k(x)=20-x^2
Answer:
a function is said to be positive if all the values of y are above the x-axis and it is said to be negative if all the values of y are below the x-axis.
What is the total volume of concrete that Jimmy will need to create the 4 spheres?
Answer: The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.
Step-by-step explanation:
To find the total volume of concrete needed for the 4 spheres, we need to find the volume of each sphere individually and then add them up. The formula for the volume of a sphere is (4/3)πr^3, where r is the radius of the sphere.
First, we need to find the radius of the largest sphere, which is 4 feet in diameter. The radius is half the diameter, so it is 2 feet.
The radius of the next sphere is half of the radius of the first sphere, which is 1 foot.
The radius of the next sphere is half of the radius of the second sphere, which is 0.5 feet.
The radius of the last sphere is half of the radius of the third sphere, which is 0.25 feet.
We can now use the formula to find the volume of each sphere and then add them up.
The volume of the first sphere = (4/3)π(2^3) = (4/3)π(8) = 33.49 cubic feet
The volume of the second sphere = (4/3)π(1^3) = (4/3)π(1) = 4.19 cubic feet
The volume of the third sphere = (4/3)π(0.5^3) = (4/3)π(0.125) = 0.52 cubic feet
The volume of the last sphere = (4/3)π(0.25^3) = (4/3)π(0.015625) = 0.05 cubic feet
Total volume of all spheres = 33.49 + 4.19 + 0.52 + 0.05 = 38.25 cubic feet
The total volume of concrete that Jimmy will need to create the 4 spheres is 38.25 cubic feet, rounded to the nearest whole number.
consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2−9x−18. find the area, in square units, between the two functions over the interval [−3,3].
The area, in square units, between the two functions over the interval [−3,3]. is 36 square units
integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the
x-axis.
Also note that the notation for the definite integral is very similar to the notation for an indefinite integral.
the fact that a and b were given as an interval the lower limit does not necessarily need to be smaller than the upper limit. Collectively we’ll often call a and b the interval of integration.
[tex]\int\limits^3_3 {f(x)} \, dx -\int\limits^3_3 {g(x)} \, dx\\=\int\limits^3_3 {f(x) - g(x) } \, dx \\= \int\limits^3_3 {(x^{2} -9x-18) - (-9x-9)} \, dx \\=\int\limits^3_3 {x^{2} -9x-18 + 9x+9} \, dx \\\\=\int\limits^3_3 {x^{2} -9} \, dx[/tex]
=[tex]\left \{ {{y=3} \atop {x=-3}} \right. (\frac{x^{3} }{3} -9x)\\= \frac{3^{3} }{3} -9*3 -( \frac{3^{-3} }{3} -9*-3)\\=9-27 +9-27\\= -36[/tex]
The area, in square units, between the two functions over the interval [−3,3]. is 36 square units
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Finley has 8 game pieces that differ only in colour. Each game piece is either all red or all black. When Finley lines up the 8 game pieces in a single row, there are 28 distinguishable arrangements. Based on the information above, Finley could have i red game pieces and ii black game pieces The statement above can be completed by the information in row i, ii (1 point) 4,4 5,3 6,2 7,1
This means that when all 8 parts are arranged in a single row, probability there are 28 different conceivable configurations. Finley can have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces.
Finley features eight game pieces, each of which is entirely either all red or all black and simply differs in colour. This indicates that there are 28 distinct configurations that may be made using the 8 pieces arranged in a single row. Finley could have 4 red and 4 black, 5 red and 3 black, 6 red and 2 black, or 7 red and 1 black, depending on the quantity of red and black pieces. This is due to the fact that the 8 pieces can be arranged in a variety of ways, and each arrangement will be deemed distinct as long as it contains at least one red and one black piece. For instance, the configuration could be as follows if there are 4 red and 4 black pieces: If there are four red pieces and four black pieces, for instance, the arrangement might be either black-red-black-red-black-red-red or red-black-red-black-red-black. No matter the configuration, there are a total of 28 arrangements.
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