the equation above models h, the height of a firework shell in feet, t seconds after launch. what is the height in feet, of the firework shell 2 seconds after launch?​

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Answer:

-1.3333333333333

Step-by-step explanation:

The distance from point P to line L is equal to the length of the component of vector AP that is orthogonal to vector AB: Distance = abs(-16 / sqrt(29)) = 16 / sqrt(29)

(a) To find a unit vector in the same direction as 3i + 2j, we need to divide the vector by its magnitude.

Magnitude of 3i + 2j = \(sqrt((3^2) + (2^2)) = sqrt(13)\)

So, a unit vector in the same direction as 3i + 2j is:

u = (3i + 2j) / sqrt(13)

(b) To find a unit vector in the opposite direction to 6i - 3j + 12k, we can negate the vector and then divide it by its magnitude.

Magnitude of 6i - 3j + 12k =\(sqrt((6^2) + (-3^2) + (12^2)) = sqrt(189) =\)3sqrt(21)

So, a unit vector in the opposite direction to 6i - 3j + 12k is:

v = -(6i - 3j + 12k) / (3sqrt(21))

(c) To find a unit vector in the same direction as the vector from point A(-2, 0, 4) to point B(3, 3, 3), we need to subtract the coordinates of A from B to get the vector AB, and then divide it by its magnitude.

Vector AB = B - A = (3 - (-2))i + (3 - 0)j + (3 - 4)k = 5i + 3j - k

Magnitude of AB = \(sqrt((5^2) + (3^2) + (-1^2)) = sqrt(35)\)

So, a unit vector in the same direction as AB is:

w = (5i + 3j - k) / sqrt(35)

For the second part of your question:

Given line L passing through points A(1, 1, 0) and B(-2, 3, -4), we can find the distance from point P(-3, 1, 7) to line L using the formula you mentioned.

Vector AB = B - A = (-2 - 1)i + (3 - 1)j + (-4 - 0)k = -3i + 2j - 4k

Vector AP = P - A = (-3 - 1)i + (1 - 1)j + (7 - 0)k = -4i + 0j + 7k

Now, we find the component of vector AP that is orthogonal to vector AB.

Component of vector AP orthogonal to vector AB = (Vector AP dot Vector AB) / (Magnitude of AB)

(Vector AP dot Vector AB) = (-4)(-3) + (0)(2) + (7)(-4) = 12 - 28 = -16

Magnitude of AB = \(sqrt((-3)^2 + 2^2 + (-4)^2) = sqrt(29)\)

Component of vector AP orthogonal to vector AB = -16 / sqrt(29)

Finally, the distance from point P to line L is equal to the length of the component of vector AP that is orthogonal to vector AB:

Distance = abs(-16 / sqrt(29)) = 16 / sqrt(29)

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The linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

The given equation is x² + 2x* + 2x² - 12x + 10 = 0.

It needs to be linearized around its equilibrium position.

Linearizing the given equation around its equilibrium position x0, we have;

f(x) = f(x0) + f'(x0)(x - x0)

Where f(x) = x² + 2x* + 2x² - 12x + 10

The equilibrium position is the point where f(x) = 0.

Hence, f(x0) = 0.

Thus, x² + 2x* + 2x² - 12x + 10 = 0⇒ 3x² - 6x = -10⇒ x² - 2x + (2.33) = 0(x-1)² = 0.77x - 0.77 or

x = 1 + (0.77)/(2) or x = 1.39

Hence, the equilibrium position x0 = 1.39.

Substitute x0 = 1.39 in the equation and simplify to get f'(x0):

f(x) = x² + 2x* + 2x² - 12x + 10

f(x) = 3.84 - 8.34 + 10

f'(x0) = f'(1.39) = -4.8

Therefore, the linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

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Answer:

-96x^5y^2

Step-by-step explanation:

I think that this is the answer I hope it helps and hope its right. A sight I often use for math is Math

way

Answer:

$-648x^2y^8$

Step-by-step explanation:

hope this helps Brianlesty pleasE?

Answer:

11-d

12-g

13-h

14-c

15-j

16-e

17-b

18-f

19-k

20-a

Step-by-step explanation:

Just plot the coordinates

Here are the answers:

D

G

H

C

J

E

B

F

K

A

Based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

The population in statistics refers to the total set of people or things that we are attempting to analyse and make conclusions about. Typically, this group is too big to see or measure directly, so we use statistical methods to infer some of its features from a smaller collection of people or things, known as a sample. A representative portion of the population was selected for the sample in order to learn more about the population as a whole. The purpose of statistical analysis is to draw conclusions about the population using data from the sample.

The number of weeks in a month= 4.

Using the given table the estimated number of sales for the month are:

Salted caramel: 51 x 4 = 204

Gingerbread: 31 x 4 = 124

Mint: 99 x 4 = 396

Hence, based on the past week's sales data, the baker can expect to sell Option C 220 caramel, 130 gingerbread, and 420 mint choco chip cookies.

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Answer:

\(1.003*10^{25}\)

Step-by-step explanation:

We'll be using Avogadro's number which defines the amount of atoms in a mole.
To find the mole amount, we use the atomic mass to find the molar mass because the atomic mass represents how many grams are in a single mole of any element

2 Hydrogen atoms have an atomic mass of 2.016 g

1 Oxygen atom has an atomic mass of 15.999 g

Adding these two numbers gives us H2O's molar mass, which is 18.015 g/mol (grams per mole).

Now we take the supplied mass of 300g and divide it by the mm (molar mass) to find the amount of moles we have. 300/18.015 = 16.653

We have 16.653 moles in 300g of H2O.

Now we have to multiply 16.653 by Avogadro's number, \(6.022 * 10^{23}\)

This gives us: \(1.003*10^{25}\)

The expression that best estimates 6 3/4 divided by 1 2/3 is 7/2. 6 3/4 (or 6.75) divided by 1 2/3 (or 1.66...) comes out to 4 1/20 (or 4.05). The closest value to this in the options available is 7/2 (or 3.5). This answer is only .55 away from the correct value, while the rest of the options are far less close.

Answer:

7/2 or

7 dived by 2

Step-by-step explanation:

bruh A

Answer:

The answer is b. 4*3 2/5.

Step-by-step explanation:

It states 4 times the amount Ruby mixed. Ruby mixed it 3 2/5 solution. So you would right out 4 x 3 2/5.

Answer:

14 cubic inches

Step-by-step explanation:

First, we have to find the radius from the circumference. We know that the circumference can be found using the equation c = 2pi(r). Set c equal to 7.1, and solve for r by dividing by 2pi.

Now, we have a radius of 1.13. Using this, we can plug the radius and the height into the equation used to find the volume of a cone: v = pi(r^2)(h/3)

This leads us to 14.04, or 14, when rounded to the nearest tenth of a cubic inch.

The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115

According to the statement

we have to find that the what percent of the population has an iq over 115.

And from given information,

the mean iq score is 100 and the standard deviation is 15.

And

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

And by use of this formula, we find the percentage of the population has an iq over 115.

Then the result will comes as 100%.

hence, 100%-Norm.Dist(value,mean,sd,true)

So, The 100%-Norm.Dist(value,mean,sd,true) percent of the population has an iq over 115.

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Answer:

\(x=-6\)

Step-by-step explanation:

So we have the equation:

\(-34=7(x+8)+8x\)

First, distribute the 7 into the (x+8) and simplify:

\(-34=7(x)+7(8)+8x\\-34=7x+56+8x\)

Combine the like terms 7x and 8x by adding them together:

\(-34=56+15x\)

Subtract 56 from both sides to isolate the x:

\(-34-56=15x+56-56\\15x=-90\)

Divide both sides by 15 to get x:

\(x=-90/15=-6\)

Answer:

A=17

Step-by-step explanation:

The domain of the function  |10 - x|  is  (-∞, +∞).

The absolute value function |10 - x| takes the value of (10 - x) and returns its non-negative magnitude.

In other words, it gives us the distance between (10 - x) and zero on the number line.

Since the distance between any two points on the number line is always a non-negative value, the absolute value function is defined for all real numbers.

There are no restrictions on the values of x for which we can evaluate the absolute value.

Therefore, the domain of the function f(x) = |10 - x| is (-∞, +∞), which means that it is defined for all real numbers.

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Answer:

To write a system of inequalities that has the point (6, 6) as a solution but not (6, -6), we can use the fact that the point (6, 6) is above the graph of the quadratic function, but the point (6, -6) is below the graph. Therefore, we can write a system of inequalities that includes the condition that the y-value must be greater than the value of the quadratic function at a given x-value.

For example, we could use the quadratic function y = x^2 and write the following system of inequalities:

y > x^2

y > 6

The first inequality states that the y-value must be greater than the value of the quadratic function at a given x-value. The second inequality is added to ensure that the y-value is greater than 6, which is necessary for the point (6, 6) to be a solution.

Since the point (6, 6) satisfies both of these inequalities, it is a solution to the system. However, the point (6, -6) does not satisfy the first inequality, since the y-value is less than the value of the quadratic function at x = 6. Therefore, it is not a solution to the system.

Overall, the system of inequalities would be as follows:

y > x^2

y > 6

We must solve for x using the addition principle, the equation is as follows

In conclusion, the answer is x = -9

The slope of the line is 4/5.

Option C is the correct answer.

We have,

The slope of the line that passes through the points (3, -1) and (-2, -5) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the coordinates, we get:

slope = (-5 - (-1)) / (-2 - 3) = -4 / (-5) = 4/5

Therefore,

The slope of the line is 4/5.

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Answer:

the answer to the problem is 1/2

Answer:

Step-by-step explanation:

If the (X) in this means times then

1/15

The value of solution of expression is,

⇒ 1 / 15

We have to given that;

Expression is,

⇒ 1/5 × 1/3

Now, We can multiply the numbers as;

⇒ 1/5 x 1/3

⇒ 1 / (5×3)

⇒ 1 / 15

Thus, The value of solution of expression is,

⇒ 1 / 15

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Answer: I’m pretty sure they are similar because they have the same interior degree.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

You take the area of the rectangle and then subtract the area of the triangle.

Area of a rectangle is bh = 4*2= 8

Area of a triangle is 1/2*bh = 1*2 = 2/2 = 1

8-1 = 7

The difference between any two successive integer squares is equal to the total of all these two integers, as demonstrated by the completed proof.

Let x represent any integer to prove algebraically.

This means that x+1 should be the following integer.

The claim demands evidence;

(x+1)² - x² = x+(x+1)

Consider the left hand side;

= x² + x + x + 1² - x²

= 2x+1 (Left Hand Solution)

Similarly, the right side.

= x + (x + 1)

= 2x + 1

Thus, subtracting the difference between two consecutive squared integers equals adding the two integers that since LHS=RHS equality is clear.

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Answer:

The theoretical probability of being dealt exactly two 2's in a 5-card hand from a standard 52-card deck is:

\(= \dfrac{2162}{32487}\\\\\approx 0.06655 \text{ in decimnal}\)

Step-by-step explanation:

The problem can be solved by using the combinatorics formula. The number of ways of drawing a subset of r items from a population of n items is given by

\(^nC_r = \dfrac{n!}{r! (n-r)!}\)

where n! is the factorial of n, r! the factorial of r and (n-r)! = factorial of (n-r)

The general formula for k! = k x (k - 1) x (k - 2) x ..... x 3 x 2 x 1

The number or ways in which you can get two 2's in a deal of 5 cards is given by

\(^5C_2 = \dfrac{5!}{ 2! (5 - 2)! } \\\\= = \dfrac{5!}{2! \times 3! }\\\\= 10\)

Once we have been dealt 2 2's we have to compute how many ways we can get the remaining 3 cards. Since we are looking for exactly two 2's we cannot draw another 2

The number of cards left that we can draw the remaining three cards = 52(total cards) -2(two 2's already drawn) - 2(two 2's that cannot be drawn)

= 48 cards

We can draw 3 cards from 48 cards in \(^{48}C_3\)  ways
\(^{48}C_3 = \dfrac{48!}{ 3! (48 - 3)! }\\\\\\= \dfrac{48!}{3! \times 45! }\\\\= 17296\)

Therefore the total number of ways of drawing exactly two 2's
= 10 x 17296 = 172960

The number of ways in which we can draw 5 cards from 52 cards is given by
\(^{52}C_5 = = \dfrac{52!}{5! (52 - 5)! }\\\\= \dfrac{52!}{5! \times 47! }\\\\= 2598960\)

P(exactly two 2's in a 5-card hand)
\(= \dfrac{172960}{2598960}\\\\ \\= \dfrac{2162}{32487}\\\\\)

or, in decimal
\(\approx 0.06655\)

The volume of the display case is 2161 1/8 cubic inches.To find the volume of a rectangular prism-shaped display case, we multiply its length, width, and height.

Given that the display case is 30 1/2 inches wide, 10 1/2 inches long, and 32 1/4 inches tall, we can calculate the volume as follows:

Volume = Length * Width * Height

Using the given measurements:

Volume = 10 1/2 inches * 30 1/2 inches * 32 1/4 inches

To simplify the calculation, we can convert the mixed numbers to improper fractions:

Volume = (21/2) inches * (61/2) inches * (129/4) inches

Next, we multiply the fractions:

Volume = (21/2) * (61/2) * (129/4) = 17289/8

The resulting fraction, 17289/8, is an improper fraction. To convert it back to mixed number form:

Volume = 2161 1/8 in³.

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Each adult pays $9 and each child under 12 pays $4.50.

To find the cost of the buffet for each adult and child at a pizza restaurant, we can set up a system of equations using the given information. Let a be the cost for each adult and c be the cost for each child. Using the bills for Todd's family and Margot's family, we get the equations 2a + 3c = 40.5 and 3a + 4c = 57.5.

Solving this system of equations gives us a = $9 and c = $4.50. Therefore, each adult pays $9 and each child under 12 pays $4.50 for the buffet. It is important to set up and solve the system of equations correctly in order to find the cost for each category.

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Answer:

Answer is in the pic I promise nothing bad

Step-by-step explanation:

In scientific notation, the number 6,267,000 is expressed as 6.267 × 10⁶, where the coefficient is 6.267 and the power of 10 is 6.

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

The first step is to move the decimal point to the right or left so that only one nonzero digit remains to the left of the decimal point. In this case, we can move the decimal point six places to the left, as follows:

6,267,000 ⇒ 6.267000

Since we moved it six places to the left, the power of 10 will be positive 6.

Finally, we write the number in scientific notation using the coefficient and the power of 10:

6.267000 × 10⁶

6.267 × 10⁶

In scientific notation, the number 6,267,000 is expressed as 6.267 × 10⁶.

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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