Leo has 38 toy troops as there aren't enough for him to line them up four by four.
what is equation ?The equal symbol (=) is frequently used to separate the expressions in equations. The left-hand side (LHS) and right-hand side (RHS) of the equation, respectively, are the formulas on either side of the equal sign. If you replace the variable(s) in both expressions with the same value, they will have the same value, as indicated by the equal symbol, which denotes that the two sides are equivalent.
given
We'll name Leo's collection of toy soldiers "x" the amount.
Finally, we know that the remainder is 3 when x is split by 5. Thus, x Plus 2 must be a multiple of 5.
Using this knowledge, we can construct the following system of equations:
x = 4n (where n is a positive number) (where n is a positive integer)
x + 1 = 7m (where m is a positive number) (where m is a positive integer)
x + 2 = 5p (where p is a positive number) (where p is a positive integer)
Testing different values of x that meet these two requirements reveals that x = 38 is the only answer that also resolves the second problem.
Leo has 38 toy troops as there aren't enough for him to line them up four by four.
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*NEED HELP PLEASE*
Solve each radical equation for x
and check your solution. (Isolate,
solve, check)
Step-by-step explanation:
1. sqrt(x + 6)/5 = 2
sqrt(x + 6) = 10
x + 6 = 100
x = 94
sqrt(94 + 6)/5 = 2
sqrt(100)/5 = 2
10/5 = 2
2 = 2
confirmed.
2.
sqrt(9x + 2) = sqrt(11x - 12)
9x + 2 = 11x - 12
14 = 2x
x = 7
sqrt(9×7 + 2) = sqrt(11×7 - 12)
sqrt(63 + 2) = sqrt(77 - 12)
sqrt(65) = sqrt(65)
confirmed.
3.
cubic root(6x + 3) + 10 = 13
cubic root(6x + 3) = 3
6x + 3 = 27
6x = 24
x = 4
cubic root(6×4 + 3) + 10 = 13
cubic root(24 + 3) + 10 = 13
cubic root(27) + 10 = 13
3 + 10 = 13
13 = 13
confirmed.
4.
2×sqrt(5x - 4) - 24 = -6
sqrt(5x - 4) - 12 = -3
sqrt(5x - 4) = 9
5x - 4 = 81
5x = 85
x = 17
2×sqrt(5×17 - 4) - 24 = -6
2×sqrt(85 - 4) - 24 = -6
2×sqrt(81) - 24 = -6
2×9 - 24 = -6
18 - 24 = -6
-6 = -6
confirmed.
P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
Which equation represents the situation below?
After a 20% discount, the cost of a pair of headphones was $260. How much did the headphones cost before the discount?
Let h = original cost of headphones
Answer:
Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:
Precio original = Precio después del descuento / (1 - Porcentaje de descuento)
Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.
Sustituyendo los valores conocidos, obtenemos:
Precio original = 260 / (1 - 0.2)
Precio original = 260 / 0.8
Precio original = 325
Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:
Answer:
The answer is D. (1-0.2)h=260
Step-by-step explanation:
If n(Ax B) = 72 and n(A) = 24, find n(B).
Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.
What is Cartesian product?The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.
In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.
For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.
By the question.
We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.
Using the formula for the size of the Cartesian product, we have:
n (Ax B) = n(A) x n(B)
Substituting the given values, we get: 72 = 24 x n(B)
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A-1 chemical supply pays sam sanchez a $1950 monthly salary plus a 3% commission on merchandise he sells each month. assume Sam's sales were $46,400 for last month
Answer:
Sam's commission for last month can be calculated as follows:
Commission = 3% of sales
Commission = 3/100 * $46,400
Commission = $1,392
Therefore, Sam's total income for last month would be his salary plus commission:
Total income = Salary + Commission
Total income = $1,950 + $1,392
Total income = $3,342
So Sam earned $3,342 in total for last month.
Step-by-step explanation:
A forest ranger sights a fire directly to the south. A second ranger, 9 miles east of the first ranger, also sights the fire
The bearing from the second ranger to the fire is S 28° W. How far is the first ranger from the fire?
#HELP! I WILL MAKE U BRAINLIST!
Answer:
x = 1.5
y = 12.99
Step-by-step explanation:
let's call cost of 1 song is x and cost of 1 album is 6
6x + y = 21.99
4x + 3y = 44.97
6x + y = 21.99 => y = -6x + 21.99
Substitute into 4x + 3y = 44.97
4x + 3(-6x + 21.99) = 44.97
4x - 18x + 65.97 = 44.97
-14x = -21
x = -21/-14 = 1.5
y = -6x + 21.99 = -6(1.5) + 21.99 = 12.99
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Answer:
The perimeter of the shape is 53km.
Answer : 53km
Step-by-step explanation: To find the perimeter you need to add all the sides so 8+18+18+9=53 and dont forget the unit km! Have a great day! And good luck!
The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
The zero product property states that if the product of two real numbers is 0, then one of the numbers must be 0.
The contrapositive of the above answer is "If neither of the numbers is 0, then the product is not 0."
In other words, if two non-zero numbers are multiplied, then the result is non-zero.
a) We can use the zero-product property to factorize the expression as an example of[tex](x - 2) (x - 3) = 0[/tex], and obtain the two roots of the equation, [tex]x = 2[/tex]and [tex]x = 3[/tex]. Therefore, the zero-product property is a powerful tool that allows us to solve complex problems and equations involving algebraic expressions and real numbers.
b) A non-zero product can only be obtained by multiplying two non-zero numbers. So, if the product is zero, then at least one of the factors must be zero as well. This is the informal version of the contrapositive of the zero product property.
c)The zero product property is an essential concept in algebra that involves the understanding of real numbers and their product. It is widely used in algebra and calculus to solve equations and expressions that involve polynomial functions, quadratic equations, and exponential functions.
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How to find the missing side of a triangle using the Law of Sines?
Step-by-step explanation:
the law of sine is
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides. A, B, C are the corresponding opposing angles.
you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.
Find the magnitude of the projection
The magnitude of the projection of the two vectors is:
M = 8.73
How to find the magnitude of the projection?
If we have two vectors A and B, and we want the projection of A onto B, we need to solve:
projection = A·B/|B|
Here the vectors are <7, -6> and <5, -2>
First, the dot product between the two vectors gives:
7*5 - 6*-2 = 35 + 12 = 47
The dot product is 47.
And the module of the second vector is:
√(5² + (-2)²) = √(25 + 4) = √29
Then the magnitude of the projection is:
M = 47/√29 = 8.73
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How is pi and apple pie related to each other?
Answer: Pie is the unofficial food of Pi Day; its symbol, π, is often carved into pie crusts.
Step-by-step explanation:
Answer:
You can divide and divide, but with pi, you never reach the end of the digits after a decimal point.
Step-by-step explanation:
This is why most people know pie as 3.14. It also means that the circumference is a bit more than 3 times the size of the diameter. It doesn't matter what circle you measure—the relationship will always be the same.
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Question 4(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Order √50,-7.1.3-7 from least to greatest.
0 -7.1.-7. √50,23
O
0-71.-7.7.23,√50
O
0 -7.1.-723√50
0-7-7.1,√50,23
Answer:
D
Step-by-step explanation:
The square root of 50 is approximately equal to 7.07
-7.1111… can be rounded to -7.11
23/3 is equal to approximately 7.67
-7 1/5 is equal to -7.2
Classify each as Polynomial or Not a Polynomial.
1.) 9x-^3 - 2y
2.) 2x^2 - 4√x
3.) 2x 2/3 - 4y
4.) 20x^2
5.) w/2 + 7
6.) 4y/2x
7.) -20x^2 + y
in the vector space model, the dimensions in the multi-dimensional space are the terms the documents
In the vector space model, the terms in the documents represent the dimensions in the multi-dimensional space.
What is the vector space model?A vector space model is a mathematical model that is utilized in information retrieval to represent a document as a multidimensional array of numbers (terms or concepts), in which each dimension corresponds to a specific term, and each value in the array represents the weight or importance of the corresponding term in the document. This representation is used to evaluate the relevance of documents to a given search query.
The dimensions in the multi-dimensional space of a vector space model correspond to the terms that the documents contain. In other words, each dimension represents a term, and each document is represented as a vector of weights or scores associated with each term.
The more frequently a term appears in a document, the higher the weight assigned to it. The goal of the vector space model is to represent documents in a way that facilitates comparison and ranking based on the similarity between the document and the query.
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Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point. (Order your answers from smallest to largest xx, then from smallest to largest yy.)f(x,y)=(x−y)(xy−9)
The critical points of function f(x,y) are (0,0) and (2,1), and (2,1) is a local maximum.
To find the critical points of f(x,y), we need to find all values of (x,y) where the gradient of f(x,y) equals zero. The gradient of f(x,y) is given by:
∇f(x,y) = <(y-2xy), (x-2y^2)>
Setting each component of the gradient equal to zero yields two equations:
y - 2xy = 0
x - 2y^2 = 0
Solving these equations simultaneously, we obtain two critical points: (0,0) and (2,1).
To determine the nature of each critical point, we compute the Hessian matrix of f(x,y):
H(f) = [ 2y -2x ]
[-2y 4y ]
At (0,0), H(f) = [0 0; 0 0], which is a degenerate matrix. Therefore, we cannot use the second derivative test to determine the nature of this critical point.
At (2,1), H(f) = [2 -4; -2 4], which has a negative determinant and a positive trace. Therefore, by the second derivative test, we conclude that (2,1) is a local maximum.
In summary, the critical points of f(x,y) are (0,0) and (2,1), and (2,1) is a local maximum.
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D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre
Answer:
Step-by-step explanation:
Perimeter
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Does anyone know how to solve this question with a method pls.
Answer:
(a) AC = 4√2 cm
(b) AM = 2√2 cm
(c) EM = √41 cm
(d) EF = 3√5 cm
Step-by-step explanation:
You want to solve for various lengths in the right square pyramid shown with base edge 4 cm and lateral edge 7 cm.
Right trianglesEach right triangle can be solved for unknown lengths using the Pythagorean theorem: the square of the hypotenuse is the sum of the squares of the other two sides.
Right triangles of interest here are ...
ADC . . . . for finding AC and AM (isosceles right triangle)
CME . . . . for finding EM
FME . . . . for finding EF
(a) ACAC is the hypotenuse of ∆ADC, so ...
AC² = AD² +DC²
AC = √(4² +4²)
AC = 4√2 . . . . cm
(b) AMM is the midpoint of AC, so ...
AM = AC/2 = (4√2)/2
AM = 2√2 . . . . cm
(c) EMFM is half the length of one side of the base, so is 2 cm. CM = AM = 2√2.
CE² = CM² +EM²
EM = √(CE² -CM²) = √(7² -(2√2)²)
EM = √41 . . . . cm
(d) EFEF is the hypotenuse of ∆EMF.
EF² = EM² +FM²
EF = √(EM² +FM²) = √(41 +2²) = √45
EF = 3√5 . . . . cm
The table shows the number of hours spent studying for a history final exam and the score on that exam. Each row represents a single student. Which value is an outlier in the table below?
Exam Scores
Number of hours spent studying, x
Exam score
(out of 100), y
1.5
65
2
68
3.5
71
4.5
98
4.5
82
6
84
6.5
88
7
85
7
80
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Answer:Given : number of hours spent studying for a history final exam and the score on that exam.
To Find : Which value is an outlier
(1.5, 65)
(3.5, 71)
(4.5, 98)
(6.5, 88)
Solution:
Number of hours spent studying =x
Exam score = y
x y
1.5 65
2 68
3.5 71
4.5 98
6 82
1.5 - 2 difference = 0.5
2 - 3.5 difference = 1.5
3.5 - 4.5 difference = 1
4.5 - 6 difference = 1.5
No outlier
65 - 68 Difference 3
68 - 71 Difference 3
71 - 98 Difference 27
71 - 82 Difference 11
Hence 98 is outlier
(4.5 , 98 ) is outlier
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Mrs. Juarez graded ten English papers and recorded the scores. 92 ...
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If the first quartile is 142 and the semi-interquartile range is 18, find ...
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first quartile is 20 then semi-inter quartile range is
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Step-by-step explanation:
Match the description with its mathematical expression. Residual from an estimated regression equation Choose the correct answer below. obo Oba o O y o bo +61 oy
We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".
What is the correct expression?Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".
Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".
Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.
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Pablo needs to memorize words on a vocabulary list for Latin class he has 12 words to memorize and he is 3/4 done how many words has Pablo memorized so far
Answer:
9 words
Step-by-step explanation:
We know
He has 12 words to memorize, and he is 3/4 done.
How many words has Pablo memorized so far?
We Take
12 x 3/4 = 9 words
So, Pable has memorized 9 words.
1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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Hanna has a bag of 20 sweets and eats 7 of them what fraction of the sweets does she eat?
The fraction of sweets that does she eat is 7/20
In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.
Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.
So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:
=> 7/20
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[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio
The point that partitions segment AB in a 1:4 ratio would be (-3/5, -1/5).
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
We can use the formula for finding the coordinates of a point that partitions a line segment in a given ratio. The formula is:
C = ((1 - r) * A + r * B) / 4
where, r is the ratio (in this case, 1:4, so r = 1/5).
Substituting the values for A, B, and r, we get,
C = ((1 - 1/5) * (-3, 2) + (1/5) * (7, -10)) / 4
Simplifying,
C = (4/5 * (-3, 2) + 1/5 * (7, -10)) / 4
C = (-12/5, 8/5 - 2) / 4
C = (-12/20, 8/20 - 10/20)
C = (-3/5, -1/5)
Therefore, the point that partitions segment AB in a 1:4 ratio is (-3/5, -1/5).
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If a certain apple tree grew 2 feet and then tripled its height, it would become 4 feet
shorter than the pine tree that grows on the other end of the street. Which
of the formulas below describes the relation between the height of the apple tree a
and the height of the pine tree p?
A) P-4=3a+2
B) P=2(a+3)+4
C) P=3(a+2)-4
D) P=3a+10
Answer:
Step-by-step explanation:
C.) P = 3(a+2)-4
The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
We are given that;
Growth of apple tree= 2feet
Now,
Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:
3(h+2) - 4 = p
Simplifying, we get:
3h + 2 = p
Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.
Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:
P = 3a + 6
This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:
P = 2a + 10
This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.
Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:
P = 3a + 2
Therefore, by equation the answer will be P=3(a+2)-4.
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Sandesh sold 15kgs of apples for 2100rs and gained 12%. At what price per kg should he sell to gain 20% ?
As per the given percentage, Sandesh should aim to sell his apples at 250rs per kg in order to gain 20% profit.
Let C be the cost of the 15kgs of apples. Sandesh gained 12%, so his profit is 0.12C. We know that Sandesh sold the apples for 2100rs, so we can write an equation:
C + 0.12C = 2100
Simplifying this equation gives:
1.12C = 2100
Dividing both sides by 1.12 gives:
C = 1875
So Sandesh's cost for 15kgs of apples was 1875rs.
Now, we need to find the selling price per kg of apples that Sandesh should aim for in order to gain 20% profit. Let P be the selling price per kg of apples.
Since Sandesh wants to gain 20% profit, his selling price per kg of apples needs to be his cost plus 20% of his cost, or 1.2 times his cost.
So we can write another equation:
1.2C = 15P
Substituting the value of C we found earlier, we get:
1.2(1875) = 15P
Simplifying gives:
P = 250
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Smart mugs are the next generations of hot drinks dispensers tha om with built in technology to keep drinks at the perfect temperature for hours on end initial cost of a smart mug was aed 896, because of high demand in market the cost increased by 12% find the new price of the mug
Pls quick its due 30 mins! And also explain with steps pls! it will help alot, also will make brainliest!
JAR
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Answer:
N
Q
Cost (dollars)
0
cost of the tickets in dollars.
32 Each ticket to ride a carousel costs $2 50. The table st
relationship between x, the number of tickets bought, -
Y
8 10
Number of Tickets
LA COORDINATE PLANE
Carousel Rides
Number of Tickets, x
1
5
2
3
Carousel Rides
which graph best represents the data shown in the table?
Carousel Rides
Carousel Rides
Cost (dollars)
DO
6
6
Cost (dollars)
12
0
Cost, y (dollars)
2.50
5.00
7.50
12.50
4
2
6
Number of Tickets
Carousel Rides
12
Step-by-step explanation:
Based on the data given in the table, the graph that best represents the relationship between the number of tickets bought and the cost of riding the carousel is the one that shows a linear relationship between the two variables.
The table shows that for each ticket bought, the cost of riding the carousel increases by $2.50. This means that the relationship between the number of tickets bought and the cost of riding the carousel is linear, with a slope of $2.50.
Therefore, the graph that best represents this relationship is the one that shows a straight line with a slope of $2.50 passing through the points (1, $2.50) and (5, $12.50). This graph is represented by the option labeled "Carousel Rides" with the x-axis showing the number of tickets bought and the y-axis showing the cost in dollars.
