A chopstick model of a catapult launches a marshmallow in a classroom. The path of the marshmallow can be modeled by the quadratic y = −0.07x^2 + x + 2.2, where y represents the height of the marshmallow, in feet, and x represents the horizontal distance from the point it is launched, in feet.

When the marshmallow hits the ground, what is its horizontal distance from the point where it was launched?

16.22 feet

−1.94 feet

7.14 feet

2.2 feet

There are 41 ways to distribute five distinguishable objects into three indistinguishable boxes.

The boxes are indistinguishable, there are 5 different ways to arrange the number of balls in each box: (5,0,0), (4,1,0), (3,2,0), (3,1,1), or (2,2,1).

There is 1 way to put all 5 balls in one box i.e (5,0,0)

(4,1,0): There are 5 choices for the 4 balls in one of the boxes.

(3,2,0): There are 10 choices for the 3 balls in the boxes.

(3,1,1): There are 10 choices for the 3 balls in one of the boxes, and we can simply split the last two among the other indistinguishable boxes.

(2,2,1): There are 10 options for one of the boxes with two balls, then 3 options for the second box with two balls, and one for remaining for the third.

Therefore the boxes with two balls are indistinguishable, we are counting each pair of balls twice so we have to divide by two.

So there are (10×3)/2=15 arrangements of balls as (2,2,1).

Hence the total number of arrangements for 3 indistinguishable boxes and 5 distinguishable balls is 1+5+10+10+15=41.

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The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.

If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000

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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.

To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.

There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
 a) Pennies (P)
 b) Nickels (N)
 c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
 Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.

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Answer:

13.26

Step-by-step explanation:

The formula for arc length is 2πr(\(\frac{angle}{360}\))

Then all you have to do, is sub your values into it

Answer:

Step-by-step explanation:

OK

Answer:

rshjgdlf

FGshjfgsfds

Step-by-step explanation:

GIMME'

The given statement, ' A 5x27 matrix can have six linearly independent columns' is false because  the dimensionality of the column space cannot exceed the number of rows.

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

A 5x27 matrix cannot have six linearly independent columns because the number of linearly independent columns in a matrix is always less than or equal to the number of rows in the matrix. In this case, the number of rows is 5, so the maximum number of linearly independent columns that a 5x27 matrix can have is 5.

This can be seen from the fact that any set of more than 5 columns in a 5x27 matrix must have a nontrivial linear dependence, which means that at least one column can be expressed as a linear combination of the other columns.

Therefore, the maximum number of linearly independent columns in a 5x27 matrix is 5.

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The equation of the plane that passes through the three points (2, −1, 3), (0, 0, 5), and (5, 6, −1) is -15x + 2y + 23z = 80.

To find the equation of the plane that passes through three non-collinear points, we can use the following steps:

Step 1: Find the normal vector of the plane.

Step 2: Use one of the three points and the normal vector to write the equation of the plane in point-normal form.

Let's follow these steps:

Step 1: Find the normal vector of the plane.

To find the normal vector, we can take the cross-product of two vectors that lie on the plane. Let's use the vectors (2, −1, 3) to (0, 0, 5) and (2, −1, 3) to (5, 6, −1):

vector 1 = (0, 0, 5) - (2, -1, 3) = (-2, 1, 2)

vector 2 = (5, 6, -1) - (2, -1, 3) = (3, 7, -4)

normal vector = vector 1 x vector 2 = (-2, 1, 2) x (3, 7, -4) = (-15, 2, 23)

So the normal vector of the plane is (-15, 2, 23).

Step 2: Use one of the three points and the normal vector to write the equation of the plane in point-normal form.

Let's use the point (2, −1, 3) as the reference point. The equation of the plane in point-normal form is:

(-15)(x - 2) + (2)(y + 1) + (23)(z - 3) = 0

Expanding and simplifying, we get:

-15x + 2y + 23z = 80

So the equation of the plane that passes through the three points (2, −1, 3), (0, 0, 5), and (5, 6, −1) is -15x + 2y + 23z = 80.

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The appropriate regression model depends on the stationarity properties of both the dependent and independent variables, as well as the error term. The researcher can use a standard OLS regression model with first-order differencing of both Y and X.

In the first scenario, both Y and X are I(0), which means they are stationary time series. In this case, the researcher can perform a standard linear regression analysis, as the stationary series would lead to a stable long-run relationship. The answer from this model will be reliable and less likely to suffer from spurious regressions. In the second scenario, Y is I(2) and X is I(0). This implies that Y is integrated of order 2 and X is stationary. In this case, the researcher should first difference Y twice to make it stationary before performing a regression analysis. However, this approach might not be ideal as the integration orders differ, which can lead to biased results.

In the third scenario, Y and X are both I(1) and the error term is I(0). This indicates that both Y and X are non-stationary time series, but their combination might be stationary. The researcher should employ a co-integration analysis, such as the Engle-Granger method or Johansen test, to identify if there is a stable long-run relationship between Y and X. If co-integration is found, then an error correction model can be used for more accurate predictions.

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When workers identified with the interests of capitalists, Marx called it false class consciousness.

False class consciousness is a concept in Marxist theory that describes a situation where members of the working class adopt the beliefs, values, and interests of the capitalist class instead of recognizing and pursuing their own class interests. Marx argued that the capitalist system inherently creates conditions that obscure the true nature of class relations and exploitation.

According to Marx, the capitalist class holds economic and political power and benefits from the labor of the working class. However, the capitalist class uses various means, such as ideology and cultural influences, to shape the consciousness of the working class. This results in the workers aligning themselves with the interests of the capitalists, often believing that their own success is tied to the success of the capitalist system.

Marx believed that false class consciousness hindered the potential for revolutionary class struggle and collective action by the working class. He argued that by accepting the dominant capitalist ideology, workers remained unaware of their own exploitation and continued to support a system that perpetuated their subjugation.

Marx's concept of false class consciousness emphasized the importance of class awareness and the need for workers to develop a true class consciousness, recognizing their common interests and working towards collective action to challenge and transform the capitalist system.

In summary, false class consciousness refers to the situation where workers adopt the beliefs and interests of the capitalist class, failing to recognize their own exploitation and working against their own class interests. It is a concept that highlights the ideological influence of the capitalist class in shaping the consciousness of the working class.

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The time it takes for a wrench to fall 11 floors (33.0m) is approximately 2.59 seconds, disregarding air resistance.

To solve this problem, we can use the equations of motion for objects under constant acceleration due to gravity. The acceleration due to gravity is approximately 9.81 m/s^2, and we can assume that air resistance is negligible. First, we need to determine the time it takes for the wrench to fall from the 15th floor to the 4th floor, a distance of 11 floors or 33.0 m (11 floors x 3.0 m/floor). We can use the following equation to solve for the time: d = 1/2 * a * t^2

where d is the distance, a is the acceleration due to gravity, and t is the time.

Rearranging the equation, we get:

t = sqrt(2*d/a)

Substituting the values, we get:

t = sqrt(2 * 33.0 m / 9.81 m/s^2) = sqrt(6.712) s ≈ 2.59 s

Therefore, it takes approximately 2.59 seconds for the wrench to fall from the 15th floor to the 4th floor.

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Answer: 4/7

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We cannot repeat an x value for the relation to be a function

Since x=3 ,4, 7 are already used

We must let x=5

Answer:

The correct answer is the second alternative!

The expression of the given polynomial 4x³ − 3x² + 16x − 12 in the form of

products of binomial terms is given by option c. (x² + 4)(4x − 3).

Polynomial is equal to ,

4x³ − 3x² + 16x − 12

Now to rewrite the polynomial in the form of a products of binomial terms.

Take out the common factors we get,

Common factors between first two terms 4x³ − 3x² is equal to x² .

Common factors between last two terms 16x − 12 is equal to 4

4x³ − 3x² + 16x − 12

⇒ x² ( 4x - 3 ) + 4 ( 4x - 3 )

⇒ ( x² + 4 )( 4x - 3 )

Therefore, the polynomial in the form of products of binomial  is written as option c. (x² + 4)(4x − 3).

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The above question is incomplete, the complete question is:

Given the polynomial 4x³ − 3x² + 16x − 12, rewrite the polynomial as a product of binomials.

a. (x² − 4)(4x + 3)

b. (x² − 4)(4x − 3)

c. (x² + 4)(4x − 3)

d. (x² + 4)(4x + 3)

Answer:

(x2 + 4)(4x − 3)

Step-by-step explanation:

bc i got it right on my quiz

Answer:

N-2

Step-by-step explanation:

The pattern is top-2=bottom so it is n-2

Answer:

n - 2

Step-by-step explanation:

The algebraic expression for the nth term is n - 2

Answer:

b

Step-by-step explanation:

Answer:

Image attached

Step-by-step explanation:

Origin looks to be (0, -1), so move each point out by 2

If the variables "r" and "s" are inversely proportional and r=7 when s=6 , then when r = 10 , value of "s" will be 4.2 .

When the two variables are inversely proportional, their product is constant. That means, for two variables "r" and "s" , the it is represented in equation as :

⇒ r × s = k, where k is a constant ;

the value of variable "r" = 7 when s = 6,

First , we have to find the value of k:

⇒ k = r × s = 7 × 6 = 42 ;

So, for any value of r and s, the product "rs" will always be equal to 42.

When r = 10, we can use the equation to find s:

⇒ s = k/r = 42/10 = 4.2

Therefore , when r = 10 , the variable "s" is 4.2.

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Answer:

Only odd numbers are existed.

Answer: x=-1, y=5

Step-by-step explanation:

First, 7x+12 is substituted in for y in the second equation

7x+12=-8x-3

Add 8x to both sides

15x+12=-3

Subtract 12 from both sides

15x=-15

Divide both sides by 15

x=-1

To solve for y, substitute x into the first equation

7(-1)+12=y

-7+12=y

5=y

Answer:

Step-by-step explanation:

The formula for the area of a circle is:

A = πr^2

where A is the area, π (pi) is approximately 3.14, and r is the radius.

Substituting the given radius of 17 inches into the formula, we get:

A = 3.14 × 17^2

A = 3.14 × 289

A = 907.06

Therefore, the area of the circle is approximately 907.06 square inches.

Answer:

907.46

Step-by-step explanation:

Area of a circle formula is πr^2

It says the radius is 17

**Simplify**

(3.14)(17)^2=907.46

Answer:

20

Step-by-step explanation:

If you take (2x+5) (2x+5) = 0

then 4x^2 + 20x +25 = 0

Answer:

x= 20

Step-by-step explanation:

The sum of the three angles is 90 degrees

x+2x+x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10

4x+10-10 = 90-10

4x= 80

Divide by 4

4x/4=80/4

x = 20

Hello,

a) photo attached

b) When y = 1, x ≈ 0.5

Verification through calculation :

We have :

y = 4x - 1

⇔ 1 = 4x - 1

⇔ 4x = 2

⇔ x = 2/4 = 0.5

This is just !

:-)

1) The set S is: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.
2) The Cartesian product A x B is: {(a, a), (a, d), (b, a), (b, d), (c, a), (c, d)}.
3) The cardinality of set A is 3, as A contains three elements: {a, b, c}.

1) The members of the set S are: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. To get this set, we start with the set of odd positive integers {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, ...}, and then we restrict it to those that are less than 20.
2) The Cartesian product of A and B is: {(a,a), (a,d), (b,a), (b,d), (c,a), (c,d)}. To get this, we take every possible ordered pair where the first element comes from A and the second element comes from B.
3) The cardinality of a set is the number of elements in the set. So, to find the cardinality of a set, we simply count how many elements are in the set. For example, if we have a set {1, 2, 3}, the cardinality of the set is 3.
1) The members of the set S are determined by the given conditions: x is an odd positive integer and x < 20. To find the members of S, list all odd positive integers less than 20. The set S is: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.
2) The Cartesian product of sets A and B, denoted as A x B, is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B. Given A = {a, b, c} and B = {a, d}, the Cartesian product A x B is: {(a, a), (a, d), (b, a), (b, d), (c, a), (c, d)}.
3) The cardinality of a set is the number of elements in the set. To find the cardinality of set A, count the number of elements in A. The cardinality of set A is 3, as A contains three elements: {a, b, c}.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

Step-by-step explanation: The first one would be -40 X 30. The parentheses around -25 turns it into a positive. And 5 make you round up

For 2, the -18 turns into a positive 18 bc of the parentheses. So round up to 20. Round 38 up to 40. 20 x 40

For 3, the negative 16 turns positive, making the equation -21 x 9 x 16. Round them to -20, 10, and 20. The equation is -20 x 10 x 20. Hope this helps!

Step-by-step explanation:

F = ma

= (24.3 kg)(1.2 m/s^2)

= 29.16 N

1. (6 + 3)² - 17 × 3 + 70 = 100.

2. $20,000 1+0.07×12 = 36,800$

3. Michael Jordan made approximately 7,320 completed free throws during his NBA career.

1. Solving the expression using BODMAS

a). Start with the bracket:

(6 + 3)² - 17 × 3 + 70

= 9² - 17 × 3 + 70

b. Square 9:

81 - 17 × 3 + 70

c. Perform multiplication:

81 - 51 + 70

d. Perform addition and subtraction from left to right:

= 30 + 70

= 100

2. Solving the expression using BODMAS

$20,000 1+0.07×12

a). for multiplication

0.07 × 12 = 0.84.

b) for addition

1 + 0.84 = 1.84.

Then,

$20,000: $20,000 × 1.84 = $36,800.

3. During Michael Jordan's NBA career (1984–2003), he averaged a free throw completion percentage of 83.5% in regular season play. If Jordan threw 8,772 free throws in his career, how many completed free throws did he make?

Calculating the number of completed free throws, the formula below will be used.

Number of completed free throws = (Free throw completion percentage / 100) × Total number of free throws attempted

Free throw completion percentage = 83.5%

Total number of free throws attempted= 8,772

So,

Number of completed free throws = (83.5 / 100) × 8,772

= 0.835 × 8,772

= 7,319.82 ( approximately 7,320).

Number of completed free throws = 7,320

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