i didn't listen when my teacher was showing us this as a review so i don't remember how to do it can someone give answer and explain if possible

Answer:

3:4

Step-by-step explanation:

3:4 because that's 15/20 reduced

If you want to guarantee that two cards are from the same suit, you need only draw five cards (since there is no way you can draw five cards without at least two of them being the same suit)

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

learn more about probability here :

brainly.com/question/11234923

#SPJ4

Answer:

3

Step-by-step explanation:

Angle bisector divides the angle into two equal angles,

So,

x + 7 = 2 ( 3x - 4 )

x + 7 = 6x - 8

6x - 8 = x + 7

6x - x = 7 + 8

5x = 15

x = 15 / 5

x = 3

a.we get, `A = √(2α³/π)`.

b.`⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

c.we can say that the variational principle is valid in this case.

(a) Let's find the normalization constant A.

We know that the integral over all space of the absolute square of the wave function is equal to 1, which is the requirement for normalization.  `∫⟨ψ|ψ⟩dx= 1`

Hence, using the given trial wavefunction, we get, `∫⟨ψ|ψ⟩dx = ∫ |A/(x^2+α²)|²dx= A² ∫ dx / (x²+α²)²`

Using a substitution `x = α tan θ`, we get, `dx = α sec² θ dθ`

Substituting these in the above integral, we get, `A² ∫ dθ/α² sec^4 θ = A²/(α³) ∫ cos^4 θ dθ`

Using the identity, `cos² θ = (1 + cos2θ)/2`twice, we can write,

`A²/(α³) ∫ (1 + cos2θ)²/16 d(2θ) = A²/(α³) [θ/8 + sin 2θ/32 + (1/4)sin4θ/16]`

We need to evaluate this between `0` and `π/2`. Hence, `θ = 0` and `θ = π/2` limits.

Using these limits, we get,`⟨ψ|ψ⟩ = A²/(α³) [π/16 + (1/8)] = 1`

Therefore, we get, `A = √(2α³/π)`.

Hence, we can now write the wavefunction as `ψ(x) = √(2α³/π)/(x²+α²)`.  

(b) Using the wave function found in part (a), we can now determine the expectation value of energy using the time-independent Schrödinger equation, `Hψ = Eψ`. We can write, `H = (p²/2m) + (1/2)mω²x²`.

The first term represents the kinetic energy of the particle and the second term represents the potential energy.

We can write the first term in terms of the momentum operator `p`.We know that `p = -ih(∂/∂x)`Hence, we get, `p² = -h²(∂²/∂x²)`Using this, we can now write, `H = -(h²/2m) (∂²/∂x²) + (1/2)mω²x²`

The expectation value of energy can be obtained by taking the integral, `⟨H⟩ = ⟨ψ|H|ψ⟩ = ∫ψ* H ψ dx`Plugging in the expressions for `H` and `ψ`, we get, `⟨H⟩ = - (h²/2m) ∫ψ*(∂²/∂x²)ψ dx + (1/2)mω² ∫ ψ* x² ψ dx`Evaluating these two integrals, we get, `⟨H⟩ = (3/4)hω - (h²/4ma²)` where `a = α/√(mω/h)`.

(c) Since we have an approximate ground state wavefunction, we can expect that the expectation value of energy ⟨H⟩ should be greater than the true ground state energy.

Hence, the value obtained in part (b) should be greater than the true ground state energy obtained by solving the Schrödinger equation exactly.

Therefore, we can say that the variational principle is valid in this case.

To know more about time-independent Schrödinger equation,visit:

https://brainly.com/question/31642338

#SPJ11

The length of ST is 3.61 units.

The length of TU is 3.16 units.

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by:

d=√((x₂ – x₁)² + (y₂ – y₁)²)

Length of ST:

The coordinates of S and T are:

S(0, 0) : x₁ = 0 , y₁ = -5

T(2, 3) : x₂  = 2 , y₂  = -2

Using the distance formula with the given values:

d=√((x₂ – x₁)² + (y₂ – y₁)²)

d=√((2 – 0)² + (-2 – (-5))²) = 3.61 units

Thus, the length of ST is 3.61 units.

Length of TU:

The coordinates of S and T are:

T(0, 0) : x₁ = 2 , y₁ = -2

U(2, 3) : x₂  = 3 , y₂  = -5

Using the distance formula with the given values:

d=√((x₂ – x₁)² + (y₂ – y₁)²)

d=√((3 – 2)² + (-5 – (-2))²) = 3.16 units

Thus, the length of ST is 3.16 units.

Learn more about the distance between two points on:

brainly.com/question/17704491

#SPJ1

Carter must go north to get back to City Hall.

First carter needs to travel 5 blocks north and 2 blocks west from his current position.

Let's imagine that Carter's starting point (City Hall) is at the center of a coordinate system, where the positive x-axis points east and the positive y-axis points north. Carter's movements can then be represented as vectors in this coordinate system:

We can add up all of these vectors to find Carter's final position relative to City Hall:

(0, 5) + (5, 0) + (-7, 0) + (0, -5) = (-2, 0)

This means that Carter is now 2 blocks west of City Hall (since the x-coordinate is negative), and he needs to travel 5 blocks north to get back to City Hall.

Therefore, Carter must go north to get back to City Hall.

Learn more about coordinate system here : brainly.com/question/10930749

#SPJ1

Answer:

\((4 {x}^{3})^{2} \\ = 4 ^{2} (x ^{3} )^{2} \\ = 16 ({x ^{3} )}^{2} \\ = {16x}^{3 \times 2} \\ = 16x ^{6} \\ \\ \infty \infty \infty \infty \infty \infty \infty \infty \)

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

Learn more about rate: https://brainly.com/question/24304697

#SPJ1

Answer:

The correct option is;

Triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime negative 1 comma 1, and C prime negative 1 comma negative 3

Step-by-step explanation:

The given parameters are;

The equation of the line t over which ΔABC is reflected is given by y = x

The coordinates of the vertices of ΔABC are given as follows;

A(-1, 1), B(1, -1), and C(-3, -1)

The reflection of a preimage (x, y) across the line y = x gives an image with coordinates at (y,  x)

Therefore, the coordinates of the vertices of the image ΔA'B'C' after the reflection of the preimage ΔABC over the line, y = x are given as follows;

Coordinates of preimage → Reflection across y = x → Coordinates of image

A(-1, 1) \({}\)                       Reflection across the line y = x          A'(1, -1)

B(1, -1) \({}\)                       Reflection across the line y = x          B'(-1, 1)

C(-3, -1) \({}\)                     Reflection across the line y = x          C'(-1, -3)

Therefore, the correct option is triangle A prime B prime C prime graphed on a coordinate plane with vertices at A prime 1 comma negative 1, B prime negative 1 comma 1, and C prime negative 1 comma negative 3.

Answer:

A

Step-by-step explanation:

There is no dialation of the figure. Simply a rigidmotion. There is no need to change the shape, merely the sign befre the number.

Answer: the first one

Step-by-step explanation:

...

The correct statement for the given relation being a function is -

B: No, because for each output there is not exactly one input.

What is a relation?

In mathematics, a relation describes the connection between two distinct collections of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their components.

To determine if the relation is a function, we need to check if there is exactly one output (y-value) for each input (x-value).

Looking at the mapping diagram, we see that the input value of 1 and -3 has arrows pointing to one output value which is 0.

Similarly, the input value -1 and 3 has arrows pointing to one output value which is 2.

Therefore, there is not exactly one input for the output value of 0 and 2.

Thus, the relation is not a function because for at least one output there is not exactly one input.

Therefore, this relation cannot be considered a function.

To learn more about relation from the given link

https://brainly.com/question/26098895

#SPJ1

The volume of the pyramid with a square base, where the perimeter of the base is 10.3 m and the height of the pyramid is 15.1 m, is approximately 31.5 cubic meters.

To find the volume of a pyramid with a square base, we need to know the length of one side of the square base. Since the perimeter of the base is given as 10.3 m, we can find the length of one side by dividing the perimeter by 4 (since a square has four equal sides).

Length of one side of the square base = Perimeter / 4 = 10.3 m / 4 = 2.575 m.

Now we have the dimensions of the pyramid:

Base side length = 2.575 m

Height = 15.1 m.

The volume of a pyramid is given by the formula:

Volume = (1/3) * base area * height.

Since the base of the pyramid is square, the base area is equal to the square of one side length:

Base area = (side length)^2 = (2.575 m)^2 = 6.630625 m^2.

Now, we can calculate the volume using the formula:

Volume = (1/3) * base area * height = (1/3) * 6.630625 m^2 * 15.1 m.

Volume ≈ 31.46003 m^3.

Rounding to the nearest tenth of a cubic meter, the volume of the pyramid is approximately 31.5 m^3.

For more such question on volume. visit :

https://brainly.com/question/27535498

#SPJ8

0.85

1) Since the exponential model of decay points out, in this case, a devaluation. then, we can write the following for a 15% decay:

Note that 1, refers to 100%. And a to the initial value.

2) So the base is 0.85 and a is the initial value. This function will provide us the devaluating value over time.

The confidence intervals for Bugs Bunny and Baby Shark are [32.3%, 35.7%] and [24.7%, 27.3%] respectively, with a margin of error of 5%. Since these intervals overlap, one cannot say with certainty that more people clearly support Bugs Bunny over Baby Shark in the population based on the poll results. Further research or a larger sample size would be needed to determine the true support for each candidate.

In a heated election, people will vote for their all-time favorite cartoon. Before the election, a poll was taken to see the results and it showed that 34% of the people said they will vote for Bugs Bunny, and 26% said they will vote for Baby Shark. The poll had an error of +/- 5%. Based on this result, one cannot say that in the population, more people clearly support Bugs Bunny over Baby Shark, as the confidence intervals for the two groups overlap.

Find out more about Bugs Bunny

brainly.com/question/22776315

#SPJ4

The length of each side is given as 36 meters. Plugging this value into the formula. The square-shaped land, with each side measuring 36 meters, has an area of 1,296 square meters.

To find the area of a square, we use the formula A = ℓ^2, where A represents the area and ℓ represents the length of one side.

In this case, the length of each side is given as 36 meters. Plugging this value into the formula, we have:

A = 36^2.

Simplifying the equation, we get:

A = 1,296.

Therefore, the area of the square-shaped land is 1,296 square meters. The result is obtained by squaring the length of one side (36 meters) to find the total area within the square.

Learn more about area of a square here:

https://brainly.com/question/27776258

#SPJ11

Answer:

You input the equation they give you into the table to get an outcome. The Equation they gave you is x=y. simply, what ever X is, thats what y is. x=y. On the table it says that X is 3. If x is 3 then y is three because they are equal. if X is 7 then Y is 7. its the same throughout the whole table. To write it as an ordered pair you write (X,Y) if x is three y is three so the ordered pair would look like (3,3)

Answer:

dV/dt = 13,5 [Km³/h]

Step-by-step explanation:

The volume f the cube is:

V = x³                 where x is a side of the cube, then tacking derivatives with respect to  time on both sides of the equation

dV/dt = 3*x² dx/dt

dx/dt = 2 km/h

at the time when the side x =  1,5 Km

dV/dt = 3* (1,5)²*2   [km³/h]

dV/dt = 13,5 [Km³/h]

Answer:

2

Step-by-step explanation:

Say you have 1 apple and 1 banana. Count them like 1,2,3. That’ll give you two.

Answer:

1+1 is 2

Step-by-step explanation:

you learned that in kindergarten

If α + β > 1, then depending on the precise values of and, (-1) and (-1) can either be positive or negative. Without additional knowledge about the signs of (-1) and (-1) the concavity of the Cobb-Douglas function cannot be calculated in this situation.

To determine whether the Cobb-Douglas function is concave, we need to examine the second-order partial derivatives of the function with respect to its variables, x₁ and x₂.

Let's start by finding the first-order partial derivatives of the Cobb-Douglas function:

∂y/∂x₁ = α(x₁)^(α-1)(x₂)^β

∂y/∂x₂ = β(x₁)^α(x₂)^(β-1)

Now, let's find the second-order partial derivatives:

∂²y/∂x₁² = α(α-1)(x₁)^(α-2)(x₂)^β

∂²y/∂x₂² = β(β-1)(x₁)^α(x₂)^(β-2)

∂²y/∂x₁∂x₂ = αβ(x₁)^(α-1)(x₂)^(β-1)

The Hessian matrix is formed using these second-order partial derivatives:

H = | ∂²y/∂x₁² ∂²y/∂x₁∂x₂ |

| ∂²y/∂x₁∂x₂ ∂²y/∂x₂² |

For concavity, the determinant of the Hessian matrix must be negative (since α and β are positive constants):

det(H) = (∂²y/∂x₁²) * (∂²y/∂x₂²) - (∂²y/∂x₁∂x₂)²

det(H) = [α(α-1)(x₁)^(α-2)(x₂)^β] * [β(β-1)(x₁)^α(x₂)^(β-2)] - [αβ(x₁)^(α-1)(x₂)^(β-1)]²

det(H) = αβ(x₁)^(α+β-2)(x₂)^(α+β-2)[α(α-1)(x₂)^β - β(β-1)(x₁)^α]

Since α + β < 1, we know that α + β - 2 < -1. This means that (x₁)^(α+β-2) and (x₂)^(α+β-2) are positive and decreasing functions of x₁ and x₂, respectively.

Now, let's consider the expression inside the square brackets: α(α-1)(x₂)^β - β(β-1)(x₁)^α.

If α + β < 1, we can observe that both α(α-1) and β(β-1) are positive, and since α and β are less than 1, the expression is also positive.

Therefore, the determinant of the Hessian matrix is negative, det(H) < 0, implying that the Cobb-Douglas function is concave when α + β < 1.

If α + β > 1, then α(α-1) and β(β-1) can be either positive or negative, depending on the specific values of α and β. In this case, the concavity of the Cobb-Douglas function cannot be determined without additional information about the signs of α(α-1) and β(β-1).

learn more about  Cobb-Douglas function from given link

https://brainly.com/question/13938683

#SPJ11

If a number cube is rolled 25 times and 6 appears only four times, then the experimental probability of getting 6 is 4/25.

The experimental probability of an event happening is the number of times the event occurred divided by the total number of trials. In this case, a number cube is rolled 25 times and lands on 6 four times. Here are the steps to determine the experimental probability of landing on 6:

So, the experimental probability of landing on 6 is 4/25, which means that if we roll the number cube many more times, we would expect to get a 6 approximately 4 out of every 25 rolls.

To learn more about the experimental probability of a number cube,

https://brainly.com/question/3441188

https://brainly.com/question/24214402

The good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

An inferior good occurs when an increase in income causes a fall in demand.

An inferior good has a negative income elasticity of demand. (YED) Inferior goods are characterized by low quality – and are goods with better alternatives.

Suppose that good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

An inferior good is one whose demand drops when people's incomes rise. When incomes are low or the economy contracts, inferior goods become a more affordable substitute for more expensive goods.

Inferior goods are the opposite of normal goods, whose demand increases even when incomes increase.

Hence, the good has an income elasticity of demand of -2. 0. This means that the good is inferior goods.

Learn more about inferior goods here;

https://brainly.com/question/2410015

#SPJ4

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

For more such question on mean visit:

https://brainly.com/question/1136789

#SPJ8

The total number of cells after 9 hours is approximately 10671.

An exponential expression is a mathematical expression in which a number or variable is raised to a power, which is usually written as a superscript. The base is the number or variable being raised to a power, and the exponent is the number indicating how many times the base is multiplied by itself.

In the given question,

The initial growth of the bacterial cells can be modeled by an exponential function of the form:

N(t) = N0 * 3^(kt)

Where N(t) is the number of cells at time t, N0 is the initial number of cells, k is the growth rate, and t is the time elapsed.

Using the information given in the problem, we can find N0 and k as follows:

N0 = 1 (since the researchers started with one cell)

N(5) = 35

N(5) = N0 * 3^(5k) = 35

3^(5k) = 35

5k = log3(35)

k = log3(35)/5

Therefore, the function for the growth of bacterial cells is:

N(t) = 3^(t*log3(35)/5)

To find the total number of cells after 9 hours, we can substitute t=9 into the equation:

N(9) = 3^(9*log3(35)/5) ≈ 10671

Therefore, the total number of cells after 9 hours is approximately 10671.

To know more about exponential expression, visit:

https://brainly.com/question/26540624

#SPJ1

Answer:

264.

Step-by-step explanation:

12,000X2.2%=264.

Answer:

11200

Step-by-step explanation:

Answer:

66?

Step-by-step explanation:

18+18= 36

15+15= 30

30+36= 66

Answer:

7.5 for 6 pounds

Step-by-step explanation:

Answer:

c = 2

Step-by-step explanation:

6c + 3y = 18

6c + 3(2) = 18

6c + 6 = 18

6c = 12

c = 2

Step-by-step explanation:

When y =2, then

Hence, c=2

a) The effective rate of interest on a mortgage at 8.15 percent compounded semi-annually is 8.23 percent.

b) It will take approximately 54.4 years to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly.

a) To find the effective rate of interest, we use the formula: Effective Rate = (1 + (Nominal Rate / Number of Compounding Periods))^Number of Compounding Periods - 1.

For a mortgage at 8.15 percent compounded semi-annually, the nominal rate is 8.15 percent and the number of compounding periods is 2 per year.

Plugging these values into the formula, we get Effective Rate = (1 + (0.0815 / 2))^2 - 1 ≈ 0.0823, or 8.23 percent. Therefore, the effective rate of interest on the mortgage is 8.23 percent.

b) To determine how long it will take to save $1,000,000 for retirement with $200 monthly deposits at 6 percent interest compounded monthly, we can use the formula for the future value of an ordinary annuity: FV = P * ((1 + r)^n - 1) / r, where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.

Rearranging the formula to solve for n, we have n = log(FV * r / P + 1) / log(1 + r). Plugging in the values $1,000,000 for FV, $200 for P, and 6 percent divided by 12 for r, we get n = log(1,000,000 * (0.06/12) / 200 + 1) / log(1 + (0.06/12)) ≈ 54.4 years.

Therefore, it will take approximately 54.4 years to save $1,000,000 for retirement under these conditions.

Learn more about interest rate here:

https://brainly.com/question/32020793

#SPJ11