x + y = y + x
a. True
b. False

The velocity of the ball when t = 8 seconds is -236 ft/s.

To find the velocity when t = 8 for the given equation y = 20t - 16t^2, we need to calculate the derivative of y with respect to t. The derivative of y represents the rate of change of y with respect to time, which corresponds to the velocity.

Let's go through the steps:

1. Start with the given equation: y = 20t - 16t^2.

2. Differentiate the equation with respect to t using the power rule of differentiation. The power rule states that if you have a term of the form x^n, its derivative is nx^(n-1). Applying this rule, we get:

  dy/dt = 20 - 32t.

  Here, dy/dt represents the derivative of y with respect to t, which is the velocity.

3. Now we can substitute t = 8 into the derivative equation to find the velocity at t = 8:

  dy/dt = 20 - 32(8) = 20 - 256 = -236 ft/s.

Therefore, when t = 8, the velocity of the ball is -236 ft/s. The negative sign indicates that the ball is moving downward.

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Answer:

x^2 -12x+36

Step-by-step explanation:

(x - 6)^2

(x-6)(x-6)

FOIL

x^2 - 6x-6x+36

Combine like terms

x^2 -12x+36

(i) The degree of precision of a quadrature formula is the highest degree of polynomial that the formula can exactly integrate.

(ii) To find the constants co, ci, and x1 that give the highest possible degree of precision, we need to choose a quadrature formula that is exact for polynomials of the highest possible degree.

Let's assume that we are trying to find a formula that is exact for polynomials of degree 1 (i.e., linear polynomials). We can set up two equations using this assumption:

∫ 1 dx = c0 + c1   (since the formula must be exact for constant functions)
∫ x dx = c0*0 + c1*x1   (since the formula must be exact for linear functions)

Solving for c0 and c1, we get:

c0 = 1/2
c1 = 1/2
x1 = 1

Therefore, the quadrature formula that has the highest possible degree of precision is:

∫ f(x) dx = (1/2) f(0) + (1/2) f(1)

This formula is exact for linear polynomials and has a degree of precision of 1.

(i) The degree of precision of a quadrature formula is the highest degree of a polynomial, p(x), for which the quadrature formula gives an exact result when applied to the integral of p(x) dx over a given interval.

(ii) To find the constants c0, c1, and x1 so that the quadrature formula ∫f(x)dx = c0f(0) + c1f(x1) has the highest possible degree of precision, we'll follow these steps:

Step 1: Start with the quadrature formula
∫₀¹ f(x)dx = c0f(0) + c1f(x1)

Step 2: Test polynomials of increasing degree until the formula fails to be exact.
For n=0: f(x) = 1
∫₀¹ 1 dx = c0(1) + c1(1) => 1 = c0 + c1

For n=1: f(x) = x
∫₀¹ x dx = c0(0) + c1(x1) => 1/2 = x1*c1

Step 3: Solve for the unknowns using the equations obtained from the test polynomials:
From the equation for n=0: c1 = 1 - c0
Substitute this expression for c1 in the equation for n=1:
1/2 = x1 * (1 - c0)

Step 4: Choose values that satisfy the above equation:
Let c0 = 1/2 and c1 = 1/2
1/2 = x1 * (1/2) => x1 = 1

So, the constants are c0 = 1/2, c1 = 1/2, and x1 = 1. The highest degree of precision achieved by this quadrature formula is 1 because the formula works exactly for polynomials of degree 0 and 1, but not for higher degrees.

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Answer:

They both have paper

Step-by-step explanation:

Crayons have paper wrapped around them and a newspaper is made of paper. & they both can be recycled

Answer:

208/8=26

Step-by-step explanation:

Each friend would get 26 beads.

Answer:

-8

Step-by-step explanation:

You answer is: 28 + 3\(x\)

Since $28 is a one-time fee and does not have to be paid again for each and every ride, it does not need a variable in front of.

But for every ride you want, you pay $3 so you need the variable "\(x\)" which represents how many times you ride.

For example, if you ride the roller coaster once, your total amount, in dollars, will be:

T = 28 + 3 * (1)

T = $31

But if you ride the roller coaster 3 times, your cost, in dollars, will be:

T = 28 + 3 * (3)

T = 28 + 9

T = $37

Answer:

4. A 5. B

Step-by-step explanation:

A hypothesis is an educated guess. When you write a report you should use an if, then statement.

An observation is a fact, not an opinion.

From the calculation, all three inequalities are satisfied, which means that the given measurements produce one triangle.

To determine whether the given measurements produce one triangle, two triangles, or no triangle at all, we can use the Law of Sines and the Triangle Inequality Theorem.

Given:

a = 10

b = 13.6

A = 33°

Determine angle B:

Angle B can be found using the equation: B = 180° - A - C, where C is the remaining angle of the triangle.

B = 180° - 33° - C

B = 147° - C

Apply the Law of Sines:

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

a/sin(A) = b/sin(B) = c/sin(C)

We can rearrange the equation to solve for side c:

c = (a * sin(C)) / sin(A)

Substituting the given values:

c = (10 * sin(C)) / sin(33°)

Determine angle C:

We can use the equation: C = arcsin((c * sin(A)) / a)

C = arcsin((c * sin(33°)) / 10)

Apply the Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we need to check if a + b > c, b + c > a, and c + a > b.

If all three inequalities are satisfied, it means that the measurements produce one triangle. If one of the inequalities is not satisfied, it means no triangle can be formed.

Now, let's perform the calculations:

B = 147° - C (from step 1)

c = (10 * sin(C)) / sin(33°) (from step 2)

C = arcsin((c * sin(33°)) / 10) (from step 3)

Using a calculator, we find that C ≈ 34.65° and c ≈ 6.16.

Now, let's check the Triangle Inequality Theorem:

a + b > c:

10 + 13.6 > 6.16

23.6 > 6.16 (True)

b + c > a:

13.6 + 6.16 > 10

19.76 > 10 (True)

c + a > b:

6.16 + 10 > 13.6

16.16 > 13.6 (True)

All three inequalities are satisfied, which means that the given measurements produce one triangle.

In summary, with the given measurements of a = 10, b = 13.6, and A = 33°, we can determine that one triangle can be formed. The measures of the angles are approximately A = 33°, B ≈ 147° - C, and C ≈ 34.65°, and the lengths of the sides are approximately a = 10, b = 13.6, and c ≈ 6.16.

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Answer:

200x-160

Step-by-step explanation:

The null space of A is spanned by the vector x = (t, -t, -t, -t), where t is a real number

Vectors are an important mathematical tool for representing data, equations, and other mathematical objects. In this problem, we are given a matrix A and asked to find a non-zero vector x in the null space of A.

The matrix A = | | 1-1-1-1 | can be reduced to row-echelon form using row operations. The resulting matrix is A = | | 1 0 0 0 | , which has a single non-zero row, indicating that the null space of A is one-dimensional.

Therefore, the non-zero vector x in the null space of A can be written as x = (t, -t, -t, -t), where t is a real number.

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A 2x2 matrix with no real eigenvalues can be represented as [a, b; -b, a] where a and b are complex numbers, with b ≠ 0. An example of such a matrix is [1, i; -i, 1], where i represents the imaginary unit.

In a 2x2 matrix, the eigenvalues are the solutions to the characteristic equation. For a matrix to have no real eigenvalues, the discriminant of the characteristic equation must be negative, indicating the presence of complex eigenvalues.

To construct such a matrix, we can use the form [a, b; -b, a], where a and b are complex numbers. If b is not equal to 0, the matrix will have complex eigenvalues.

For example, let's consider [1, i; -i, 1]. The characteristic equation is det(A - λI) = 0, where A is the matrix and λ is the eigenvalue. Solving this equation, we find the complex eigenvalues λ = 1 + i and λ = 1 - i, indicating that the matrix has no real eigenvalues.

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Answer:

x is greater than or equal to -26

Step-by-step explanation:

We can use distributive property to solve the equation.

-6(x+4) in distributive property is:  -6x-24

-6x-24 is less than or equal to -5x+2

+6x                                             +6x

-24 is less than or equal to x+2

-2                                              -2

-26 is less than or equal to x

This means x is greater than or equal to -26

On the graph you would put a closed circle on -26 and point to the right.

Hope this helps! Good luck on your quiz!

The probability that Adam and Betty meet at some point is $1-\frac{1}{16}=\boxed{\frac{15}{16}}$.

To find the probability that Adam and Betty meet while walking on the grid, we can consider their paths. Adam will always move up or right, while Betty will always move down or left. This means that their paths will always be perpendicular, and they will only meet if they intersect at some point.

Let's consider the first minute. Adam can either move up or right, and Betty can either move down or left. There are four possible outcomes: Adam moves up and Betty moves down, Adam moves up and Betty moves left, Adam moves right and Betty moves down, or Adam moves right and Betty moves left.

Out of these four outcomes, only one leads to Adam and Betty meeting: if Adam moves right and Betty moves down, they will meet at the point $(1,3)$. So the probability of them meeting in the first minute is $\frac{1}{4}$.

Now let's consider the second minute. Adam will be one unit away from $(1,3)$, and Betty will be one unit away from $(1,3)$. There are four possible outcomes again, but only one leads to them meeting: if Adam moves up and Betty moves down, they will meet at the point $(1,2)$. So the probability of them meeting in the second minute is $\frac{1}{4}$.

We can continue this process for each minute. At each step, there is only one outcome that leads to them meeting, and the probability of that outcome is $\frac{1}{4}$. So the probability of them meeting after $n$ minutes is $\left(\frac{1}{4}\right)^n$.

Now we need to find the probability that they meet at any point in time. We can do this by taking the complement of the probability that they never meet. The only way they will never meet is if their paths never intersect, which means that Adam always stays to the right of Betty or always stays above Betty.

The probability of this happening is the same as the probability that Adam flips tails $4$ times in a row, or Betty flips heads $2$ times in a row. This probability is $\left(\frac{1}{2}\right)^4=\frac{1}{16}$, since there are $2^4$ possible outcomes for Adam and $2^2$ possible outcomes for Betty.

So the probability that Adam and Betty meet at some point is $1-\frac{1}{16}=\boxed{\frac{15}{16}}$.

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The value of the integral ∭ E x 2 + y 2 dV a in cylindrical coordinates is (7π/20).

In mathematics, we frequently encounter the problem of evaluating triple integrals over a three-dimensional region E. This question examines the use of cylindrical coordinates to solve this type of issue. The integral we must evaluate in this question is

∭ E x 2 + y 2 dV a.

E is the area that exists within the cylinder x 2 + y 2 = 4 and between the planes z = 2 and z = 7.

Therefore, we can say that the integral in cylindrical coordinates is as follows:

∭ E x 2 + y 2 dV = ∫∫∫ E ρ³sin(θ) dρ dθ dz.

To solve this issue, we must first define E in cylindrical coordinates. E can be defined as

E = {(ρ,θ,z) : 0 ≤ θ ≤ 2π, 0 ≤ ρ ≤ 2, 2 ≤ z ≤ 7}.

As a result, the limits of ρ, θ, and z are as follows: 0 ≤ θ ≤ 2π, 2 ≤ z ≤ 7, and 0 ≤ ρ ≤ 2.

Substituting x = ρ cos θ, y = ρ sin θ, and z = z in x 2 + y 2 = 4, we get ρ = 2.

Using these values in equation (1), we get

∭ E x 2 + y 2 dV = ∫ 0² 2π ∫ 2⁷ ∫ 0 ρ³sin(θ) dρ dθ dz.

Substituting the limits of ρ, θ, and z in equation (2), we obtain

∭ E x 2 + y 2 dV = ∫ 0² 2π ∫ 2⁷ [ρ⁴/4] ρ=0 dθ dz

∭ E x 2 + y 2 dV = ∫ 0² 2π ∫ 2⁷ ρ⁴/4 dθ dz

∭ E x 2 + y 2 dV = ∫ 0² 2π [(ρ⁵/20)] ρ=2 dz

∭ E x 2 + y 2 dV = (π/2) ∫ 2⁷ [ρ⁵/20] ρ=2 dz

∭ E x 2 + y 2 dV = (π/2) [z²/20] 7₂

∭ E x 2 + y 2 dV = (7π/20).

Therefore, the value of ∭ E x 2 + y 2 dV a in cylindrical coordinates is (7π/20).

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Part A

f(0)

that means the value of f(x) for x=0

looking at the table

For x=0 ----> f(x)=4

therefore

f(0)=4

Part B

f(x)=0

looking at the table

f(x)=0 when the value of x=1

therefore

f(1)=0

Part C

f^-1(0)

For f(x)=0 -----> the value of x=1

therefore

f^-1(0)=1

Part D

f^-1(x)=0

looking at the table

For x=0 -----> f(x)=4

therefore

f^-1(4)=0

Answer:

1 inch:2 feet

Step-by-step explanation:

The probability that a randomly selected household with a savings account has no checking account is approximately 0.149, or 14.9%.

To compute the probability that a randomly selected household with a savings account has no checking account, we can use Bayes' theorem. Let S denote the event that a household has a savings account, and C denote the event that a household has no checking account.

We want to find P(C | S), the probability that a household with a savings account has no checking account.

Using Bayes' theorem, we have:

P(C | S) = P(S | C) * P(C) / P(S)

We know that 40% of households with no checking accounts have savings accounts, so P(S | C) = 0.4. We also know that 21.5% of households have no checking accounts, 66.9% have regular checking accounts, and 11.6% have NOW accounts, so P(C) = 0.215.

Finally, we can use the law of total probability to find P(S), the overall probability of a household having a savings account:

P(S) = P(S | C) * P(C) + P(S | regular checking) * P(regular checking) + P(S | NOW) * P(NOW)

= 0.4 * 0.215 + 0.716 * 0.669 + 0.793 * 0.116

≈ 0.576

Substituting these values into the equation for Bayes' theorem, we get:

P(C | S) = 0.4 * 0.215 / 0.576

≈ 0.149

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Complete question is:

A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

Compute the probability that a randomly selected household with a savings account has no checking account.

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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Answer:

-1.5

Step-by-step explanation:

y=-1.5x-5

Answer:

5, 11

Step-by-step explanation:

the number is subtracting 4 adding 6 subtracting 4 adding 6

The equation y=1 represents a line Perpendicular to x=0.

The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.

So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.

Among the given options, the equation that represents a horizontal line is:

� = 1 y=1

Therefore, the equation y=1 represents a line perpendicular to x=0.

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Answer:

The answer would be 1/6

The probability that both jurors selected are female is 1/6.

For a criminal trial, 8 active and 4 alternate jurors are selected.

Two of the alternate jurors are male and two are female.

During the trial, two of the active jurors are dismissed.

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Total numbers of selected candidates is;

8 + 4 = 12

The judge decides to randomly select two replacement jurors from the 4 available alternates.

Therefore,

The probability that both jurors selected are female is;

\(= \dfrac{2}{12}\\\\= \dfrac{1}{6}\)

Hence, the probability that both jurors selected are female is 1/6.

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The expression that will help in finding the surface area of the net are

The external surface area of three-dimensional objects is referred to as the surface area, and is generally calculated in square units.

Calculating the surface area of certain 3D shapes requires one to use different formulas. depending on the shapes

The shapes encountered here are

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Answer:

\(q=70\)

Step-by-step explanation:

The total angle measure of supplementary angles (straight angles like this one) will always equal \(180\)°, so the following equation can be used:

\(180-52-58=q→180-110=q→70=q\)