166 students went on a field trip. Three buses were filled and 22 students traveled in cars. How many students were in each bus?

Answer: 3^4x5^2

Step-by-step explanation:

Answer:

8,377.58 \(mi^{3}\)

Step-by-step explanation:

To solve for the volume of a right circular cone like the one in the picture, you use \(\pi\)\(r^{2}\)\(\frac{h}{3}\).

Plug in the radius and height to get \(\pi\)\(20^{2}\)\(\frac{20}{3}\).

Then solve (and round to the nearest hundredth) and you should get 8,377.58.

Answer:

D

Step-by-step explanation:

It matches all specified equations.

The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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i. Arrow Diagram to represent the relation R:In an arrow diagram of relation R, each arrow represents the ordered pair of elements in the relation R. So, for the given relation R, the arrow diagram can be constructed as follows:ii. Proving R as an Equivalence RelationFor a relation R to be an equivalence relation, it needs to be reflexive, symmetric, and transitive.Reflextive: An ordered pair (a, a) should be a part of the relation R, for every element a ∈ A. In other words, every element of A should have a self-loop in the arrow diagram. Here, (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6) are all a part of the relation R. Therefore, the relation is reflexive.Symmetric: If (a, b) ∈ R, then (b, a) ∈ R should also be true, for every pair of elements (a, b) ∈ R. Here, (4, 5) and (5, 4), (5, 6) and (6, 5), and (4, 6) and (6, 4) are all part of the relation R. Therefore, the relation is symmetric.Transitive: If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R should also be true, for every three pairs of elements (a, b), (b, c) and (a, c) ∈ R. Here, (4, 5), (5, 6), and (4, 6) are all part of the relation R. But (4, 6) is not related to (5, 6). So, the relation is not transitive.Thus, the relation R is not an equivalence relation.iii. Equivalence Classes of R:The equivalence class of an element a is defined as the set of all elements that are related to a by the relation R. Therefore, the equivalence classes of R can be defined as follows:[1] = {1}[2] = {2}[3] = {3}[4] = {4, 5, 6}[5] = {4, 5, 6}[6] = {4, 5, 6}

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Answer:

20 cakes

Step-by-step explanation:

28/7=4 cakes per day

4x5= 20

20 cakes in 5 days

Hope it helps :)

Answer:

20 cakes in 5 days

Step-by-step explanation:

To find this, we need to find out how much he can make in 1 day.

So divide 7 by 7 and 28 by 7 and get 4 cakes in 1 day.

After we got 4 cakes each day, we multiply it by 5 to see how much we get in 5 days and get 20 cakes in 5 days.

Hope this helps! PLEASE mark brainliest!

Answer:

20 cups are in 5 quarts

Step-by-step explanation:

Answer:20 cups

Step-by-step explanation:because each cup is 0.25 quarts

plz leave a like

Answer:

  See below

Step-by-step explanation:

Each point on the triangle moves to half its previous distance from P.

a) The set {1, 2, 3} does not represent vectors, but rather a collection of scalars. Therefore, there are no vectors in {1, 2, 3}.

b) The number of vectors in "col a" cannot be determined without additional context or information. "Col a" could refer to a column vector or a collection of vectors associated with a variable "a," but without further details, the exact number of vectors in "col a" cannot be determined.

c) Without knowing the specific context of "p" and "col a," it is impossible to determine if "p" is in "col a." The inclusion of "p" in "col a" would depend on the definition and properties of "col a" and the specific value of "p."

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Answer: 10

Step-by-step explanation:

Because Lauren gave 1/6 of the stamps to Brianna, we divide 12 by 6 to get 1/6 of 12.

12/6=2

The question asks how many stamps Lauren kept for herself, so subtract 2 from 12.

12-2=10

Lauren kept 10 stamps for herself.

Answer:

it's already simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(x + 4) - 5 = 2x + 4

solve for x

x = -3

1. The slope of each object are: a) 0.6. b) 1.375.

2. The slope of the road section is 0.02.

3. No, a wheelchair ramp with a vertical rise of 1.4 m along a horizontal run of 8 m does not satisfy the regulation.

4. The slope of each line segment are: a) 0.6. b) -0.6.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

By substituting the given data points into the formula for the slope of a line, we have the following;

Part 1

Slope of a = 3/5

Slope of a = 0.6

Slope of b = 4.4/3.2

Slope of b = 1.375

Part 2.

Slope of road section = 2.5/152

Slope of road section = 0.0165 ≈ 0.02.

Part 3.

Slope of wheelchair ramp = 1.4/8

Slope of wheelchair ramp = 0.0175 ≈ 0.02.

Part 4.

a) The rise for graph a is 3 units.

The run for graph a is 5 units.

Slope of graph a = 3/5

Slope of graph a = 0.6

b) The rise for graph b is -3 units.

The run for graph b is 5 units.

Slope of graph b = -3/5

Slope of graph b = -0.6

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Answer:

4 = 12

Here is your answer.

Answer:

1x4=4

2x4=8

3x4=12

4x4=16

5x4=20

The relevant details from the poem and the description of how they develop the subject are:

The fact that the narrator mentions how there are a pair of them means that they are not alone. It means that just because they are a nobody does not mean that they consider themselves to be alone.

The fact that they could be banished means that being a nobody is a bad thing that warrants the punishment of being banished from the society in question.

When a person is deary, it means that they are doing something that can either bring them praise or punishment which means that being somebody can either be positive or negative so it can be a positive to be a nobody.

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Answer:

0.875

Step-by-step explanation:

7 divide by 8

<3

Red

Answer:

0.875

Step-by-step explanation:

The answer of the function found to be x = −4 and x = 2,  with M = 38.

We must consider the function,

f (x) = x³ + 6x² + 6

Over the interval  

-5 \(\leq\) x \(\leq\) 2

To obtain the extrema we start from the function's derivative.

f' (x) = 3x² + 12x

Equating it to 0,

f' (x) = 0 = 3x(x +4) = 0

We arrive at two solutions,

x1 = 0,     x2 = -4   both inside the interval.

Evaluating the function at the stationary points,

f (x1) = 6

f (x2) = (-4)³ + 6 . (-4)² + 6 = -64 + 96 + 6 = 38

These values must be compared to that of the function at the interval frontiers,

f (-5) = (-5)³ + 6 . (-5)² + 6 = -125 + 150 + 6 = 31

f (2) = 2³ + 6 . 2² + 6 = 38

Comparing the results we can conclude that the function attains its absolute minimum at,

x = 0,      m = 6

Meanwhile, the absolute maximum is attained at the points,

x = −4 and x = 2,  with M = 38.

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The matrix A must have 8 rows and 9 columns to ensure the mapping from ℝ⁸ into ℝ⁹ can be properly represented and computed using the rule t(x) = Ax.

In order to define a mapping from ℝ⁸ (8-dimensional real space) into ℝ⁹ (9-dimensional real space) using the rule t(x) = Ax, where A is a matrix, the matrix A must have dimensions such that the number of columns matches the dimension of the input space (ℝ⁸) and the number of rows matches the dimension of the output space (ℝ⁹).

Therefore, the matrix A must have 8 rows and 9 columns.

The dimensionality of a matrix is determined by the number of rows and columns it has.

In this case, we want the matrix A to represent a mapping from ℝ⁸ to ℝ⁹, which means the matrix needs to transform an 8-dimensional input vector into a 9-dimensional output vector.

To achieve this, the matrix must have 8 rows to match the dimension of the input space and 9 columns to match the dimension of the output space.

Each column of the matrix A represents the coefficients of the linear combination of the input vector's components that produces the corresponding component of the output vector.

Since we have 9 components in the output vector, we need 9 columns in the matrix to account for the transformation of each component.

Similarly, since the input vector has 8 components, we need 8 rows in the matrix to represent the coefficients of the linear combination for each component.

By defining the matrix A with 8 rows and 9 columns, we ensure that the mapping from ℝ⁸ into ℝ⁹ can be properly represented and computed using the rule t(x) = Ax.

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The sequence {an} = (6+13n^2) / (n^2 + 15n^2) diverges. Using the limit comparison test with bn = n^2, the ratio of an and bn approaches a finite positive number, so the divergence of ∑n^2 implies that ∑an also diverges.

To determine whether the sequence {an} converges or diverges, we can use the limit comparison test. Specifically, we can compare the given sequence to a known sequence whose convergence behavior is known.

Let bn = n^2. Then:

lim n→∞ (an / bn)

= lim n→∞ [(6+13n^2) / (n^2 + 15n^2)]

= lim n→∞ [(6/n^2 + 13) / (1 + 15)]

= 13/16

Since the limit of the ratio of an and bn is a finite positive number (13/16), and the series ∑n^2 diverges, by the limit comparison test, we conclude that the series ∑an also diverges.

Therefore, the sequence {an} also diverges.

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The validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

The validity of the Universal Modus Tollens can be derived from the validity of Universal Instantiation and Modus Tollens. Let's examine the logic behind each of these rules and how they lead to the validity of Universal Modus Tollens.

Universal Instantiation (UI): This rule allows us to infer a specific instance of a universally quantified statement. For example, if we have the universal statement "For all x, if P(x) then Q(x)," we can instantiate it to a particular instance by replacing the variable x with a specific element, resulting in "If P(a) then Q(a)." This rule is valid and widely accepted in formal logic.

Modus Tollens (MT): Modus Tollens is a deductive rule of inference used to infer the negation of the consequent of a conditional statement. It states that if we have a conditional statement "If P, then Q," and we know the negation of Q (¬Q), we can conclude the negation of P (¬P). This rule is also valid and widely accepted.

Now, let's demonstrate how the validity of Universal Instantiation and Modus Tollens leads to the validity of Universal Modus Tollens:

Universal Modus Tollens (UMT): If we have the universally quantified statement "For all x, if P(x) then Q(x)," and we know the negation of Q for a specific instance, ¬Q(a), then we can conclude the negation of P for that same instance, ¬P(a).

To derive UMT, we can apply the following steps:

Apply Universal Instantiation (UI) to the universally quantified statement, replacing x with a specific element, let's say a. This gives us "If P(a) then Q(a)."

Assume the negation of Q for that specific instance, ¬Q(a).

Apply Modus Tollens (MT) to the conditional statement "If P(a) then Q(a)" and the negation of Q, which allows us to conclude the negation of P, ¬P(a).

Thus, by using Universal Instantiation to instantiate a universally quantified statement, and then applying Modus Tollens to the instantiated conditional statement and the negation of the consequent, we can derive Universal Modus Tollens.

It's important to note that the validity of Universal Modus Tollens relies on the validity of Universal Instantiation and Modus Tollens, which are well-established logical rules.

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Answer: 42 I think

Step-by-step explanation:

I did 6 times 7

The standard deviation of the sampled containers' contents is 0.36

Mean = summation of data / number

μ = 204.72 / 10

μ = 20.472

σ = √[[(x₁ - μ)² + (x₂ - μ)² + (x₃ - μ)² + (x₄ - μ)² + (x₅ - μ)² + (x₆ - μ)² + (x₇ - μ)² + (x₈ - μ)² + (x₉ - μ)² + (x₁₀ - μ)²] / n]

σ = √[[(20.72 - 20.472)² + (20.6 - 20.472)² + (20.71 - 20.472)² + (20.92 - 20.472)² + (19.79 - 20.472)² + (20.93 - 20.472)² + (20.09 - 20.472)² + (20.27 - 20.472)² + (20.49 - 20.472)² + (20.2 - 20.472)²] / 10]

σ = 0.36

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Answer:

To find the number of nickels and dimes, we can use this equation: 0.10d + 0.05n = 5.25

We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.

0.10d + 0.05n = 5.25

0.10(21) + 0.05n = 5.25

2.10 + 0.05n = 5.25

0.05n = 3.15

n = 3.15 / 0.05

n = 315 / 5

n = 63

Sonji has 63 nickels.

Let's check our answer.

21(0.10) + 63(0.05) = 2.10 + 3.15 = 5.25

It seems that our answer is correct.

Step-by-step explanation:

Answer:

she has 63 nickels

Step-by-step explanation:

21 dimes = 2.10$

5.25 - 2.10 = 3.15

3.15 ÷ 0.05 = 63

63 = 63 nickles

Hope this helped :3

Answer:

A im pretty sure :)

Step-by-step explanation:

A and B do not necessarily have to be equal.

(a) If Ax = Bx holds for all n-vectors x, then we can choose x to be the standard basis vectors e_1, e_2, ..., e_n. Then we have:

Ae_1 = Be_1

Ae_2 = Be_2

...

Ae_n = Be_n

This shows that A and B have the same columns. Therefore, if A and B have the same dimensions, then it must be the case that A = B. So, under this assumption, we have A = B always.

(b) If Ax = Bx holds for some nonzero n-vector x, then we can write:

(A - B)x = 0

This means that the matrix C = A - B has a nontrivial nullspace, since there exists a nonzero vector x such that Cx = 0. Therefore, the rank of C is less than n, which implies that A and B do not necessarily have the same columns. For example, we could have:

A = [1 0]

[0 0]

B = [0 0]

[0 1]

Then Ax = Bx holds for x = [0 1]^T, but A and B are not equal.

Therefore, under this assumption, A and B do not necessarily have to be equal.

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