Assume that there are 18 board members: 11 females, and 7 males including Carl. There are 3 tasks to be assigned. Note that assigning the same people different tasks constitutes a different assignment

. (1) Find the probability that both males and females are given a task.

(2) Find the probability that Carl and at least one female are given tasks.

Answer:

D

Step-by-step explanation:

Given

- 3 ÷ - \(\frac{2}{5}\)

Leave the first number, change division to multiplication and turn the fraction upside down, that is

= - 3 × - \(\frac{5}{2}\)

= \(\frac{3(5)}{2}\)

= \(\frac{15}{2}\)

= 7 \(\frac{1}{2}\) → D

The value of  ∛64 will be equal to 4.

In mathematics, a number r is said to be the nth root of a number x if it is raised to the power n. where n is a positive integer, also referred to as the root's degree. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The radical expression will be solved as,

∛64 = ∛ ( 4 x  4 x 4 )

∛64 = ∛ ( 4³ )

∛64 = 4

Hence, the solution for ∛64 will be 4.

To know more about radical expression follow

https://brainly.com/question/738531

#SPJ1

Answer:ifk

Step-by-step explanation:

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

To learn more on logarithms: https://brainly.com/question/30226560

#SPJ1

Answer:

5 1/4 mph

Step-by-step explanation:

21 divided by 4= 5 1/4

Answer:

Average Speed = 5.25 mph

Step-by-step explanation:

Given:

Distance = 21 miles

Time = 4 hours

Required:

Average Speed

Formula:

Average Speed = Total Distance Covered / Total Time Taken

Solution:

Average Speed = 21/4

Average Speed = 5.25 mph

Answer:

(x+12)

Step-by-step explanation:

x2 + 8x - 48

x2 + 12x - 4x - 48

(x-4)(x+12)

The factors of the expression are:

(x + 12) and (x - 4).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To determine which of the options is a factor of x² + 8x - 48,

We can use either factoring or the quadratic formula.

First, let's try factoring:

x² + 8x - 48 = 0

We need to find two numbers that multiply to -48 and add to 8.

One possible pair of numbers is 12 and -4:

(x + 12)(x - 4) = 0

Now we can see that x = -12 or x = 4 are the solutions to the equation. None of the options given match these solutions.

Therefore,

The factors of the expression are:

(x + 12) and (x - 4).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ7

Answer:

13/16 is the answer. Bad handwriting but try to understand .

The 95% confidence interval is from 50.7 to 58.5.

To calculate the 95% confidence interval, we'll need the sample mean, margin of error, and critical value. The critical value is determined by the confidence level and sample size. For a 95% confidence interval with a sample size of 30 or more, we can use the z-score of 1.96.

The formula for a confidence interval is: Confidence Interval = Sample Mean ± (Critical Value × Standard Error)where Standard Error = Standard Deviation / √n Given, Sample Mean = 54.6Margin of Error = 3.9Critical Value (z-score) = 1.96Using these values and plugging them into the formula, we get: Confidence Interval = 54.6 ± (1.96 × 3.9)Confidence Interval = 54.6 ± 7.644The lower limit of the interval is 54.6 - 7.644 = 46.956The upper limit of the interval is 54.6 + 7.644 = 62.244

To know more about confidence interval refer to-

brainly.com/question/24131141#

#SPJ11

The correct answer is C. A family may own both a minivan and an SUV. The events are not disjoint, so the addition rule does not apply.

The addition rule of probability states that if two events are disjoint (or mutually exclusive), meaning they cannot occur simultaneously, then the probability of either event occurring is equal to the sum of their individual probabilities. However, in this case, owning a minivan and owning an SUV are not mutually exclusive events. It is possible for a family to own both a minivan and an SUV at the same time.

When using the addition rule, we assume that the events being considered are mutually exclusive, meaning they cannot happen together. Since owning a minivan and owning an SUV can occur together, adding their individual probabilities will result in double-counting the families who own both types of vehicles. This means that simply adding the percentages of families who own a minivan (53%) and those who own an SUV (24%) will overestimate the total percentage of families who own either a minivan or an SUV.

To calculate the correct percentage of families who own either a minivan or an SUV, we need to take into account the overlap between the two groups. This can be done by subtracting the percentage of families who own both from the sum of the individual percentages. Without information about the percentage of families who own both a minivan and an SUV, we cannot determine the exact percentage of families who own either vehicle.

Learn more about probability here:

brainly.com/question/31828911

#SPJ11

Answer:

Monkey says NO

Step-by-step explanation:

Monkey says A^2 + B^2 = C^2. Monkey do math, gets C = 8.5. So close, monkey sad. Not right triangle.

The correct statement is that Ursula has incurred the finance charge of 46.17% about for the loan amounting to $6400. So, the correct option matching the statement is not as quoted in the options above.

Finance charge can be calculated by summarizing and comparing the principal amount with the annuity amount derived by the formula of compound interest.

Hence, the correct option is that Ursula has borne the financial charge as 46.17% of her principal.

To know more about finance charge, click the link below.

https://brainly.com/question/298229

Answer:

A

Step-by-step explanation:

The line has to go down when x move to the right due to the negative slope. So B and C cannot be right.

The line has to pass through (0,3), that's the y-intercept, so A and D can still both be right.

For every step to the right, the line has to move 2 down (slope -2). Only A does that. D moves 0.5 down for every step to the right.

Answer:

y= -2x +13

Step-by-step explanation:

By simple algebra, Jane is 57 9/20 inches taller.

If one object or person's height exceeds that of another, the taller object or person is said to exist. There is a two-object or two-person limit. Taller is a relative term. For instance: Hoppy stands at 7 feet.

You can begin this issue by first figuring out Dwight's height. At 54 3/4 inches, he would be 1 1/2 inches taller than Chloe:

54 3/4 plus 1 1/2 equals 55 + (3/4 + 1/2) equals 55 + (3/4 + 2/4) equals 55 + 5/4 equals 56 1/4 inches.

Dwight stands at 56 1/4 inches.

Dwight is 1 1/5 inches shorter than Jane, so

56 1/4 plus 1 1/5 is 57 plus (1/4 plus 1/5) is 57 plus (5/20 plus 4/20) is 57 plus 9/20 is 57 9/20 inches.

Jane stands at 57 9/20 inches.

To know more about algebra visit:-

brainly.com/question/24875240

#SPJ4

Answer:

for all the plato users...

Step-by-step explanation:

To determine if the given set is a subspace of $P_n$, we need to check if it satisfies the three conditions for being a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Let's consider the set of polynomials of the form $p(t) = at^2$, where $a \in \mathbb{R}$.Firstly, let's check if the set is closed under addition. Take two arbitrary polynomials $p_1(t) = a_1t^2$ and $p_2(t) = a_2t^2$ in the set. Then, their sum is $p_1(t) + p_2(t) = (a_1 + a_2)t^2$, which is still in the set of polynomials of the form $at^2$. Therefore, the set is closed under addition.

Next, we need to check if the set is closed under scalar multiplication. Take an arbitrary polynomial $p(t) = at^2$ in the set and a scalar $c \in \mathbb{R}$. Then, $cp(t) = cat^2$, which is still in the set of polynomials of the form $at^2$. Thus

To learn more about  polynomial click here:

brainly.com/question/32088107

#SPJ11

To calculate the least radius of gyration and the slenderness ratio of a hollow rectangular section with given dimensions and material thickness, we need to follow the formulas and steps involved. The least radius of gyration is a measure of the distribution of material around the centroid of a section, while the slenderness ratio provides information about the stability of the section under axial loading.

1. To calculate the least radius of gyration, we use the formula:

 r_min = sqrt((I / A))

  where I is the moment of inertia of the section and A is the cross-sectional area. For a hollow rectangular section, the moment of inertia can be calculated using the formula:

  I = ((b1 * h1^3) - (b2 * h2^3)) / 12

  where b1 and b2 are the outer and inner dimensions of the section, and h1 and h2 are the outer and inner heights of the section. The cross-sectional area A can be calculated as:

  A = (b1 * h1) - (b2 * h2)

2. To calculate the slenderness ratio, we divide the effective length of the section by the least radius of gyration:

  Slenderness ratio = L / r_min

  Given that the effective length is 6m, and considering the dimensions provided in millimeters (30cm x 15cm), we convert 60mm to meters (0.06m).

By substituting the given values into the formulas and performing the calculations, we can find the least radius of gyration and the slenderness ratio for the hollow rectangular section.

To learn more about radius of gyration; -brainly.com/question/30763368

#SPJ11

A negative exponent indicates that the base should be inverted or flipped, and the exponent should become positive. Therefore, -45 in positive exponent form would be: 1/ (45²1) or 1/45

What is a negative component?

A negative exponent is a mathematical notation indicating that the number or variable should be inverted or flipped, and the exponent should be made positive. In other words, a negative exponent represents the reciprocal of the number or variable raised to the corresponding positive exponent.

For example, 2²-3 is read as "2 to the power of negative 3" and represents 1/(2²3), which is equal to 1/8. Similarly, x²-2 is read as "x to the power of negative 2" and represents 1/(x²2), which is the reciprocal of x squared.

Negative exponents are used in various mathematical and scientific applications, such as in calculations involving very small or large numbers, in scientific notation, and in the rules of exponents.

To know more about Negative Component visit:

https://brainly.com/question/29009712

#SPJ1

Complete question:

Write -45 in positive exponent form.

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

To know more about probability visit

https://brainly.com/question/13604758

#SPJ11

Answer:

There are 39 seats I think.

Step-by-step explanation:

548 divided by 14 is a decimal but rounded it to the nearest full number.

Answer:

Step-by-step explanation:

(3x-6)(3x+9)(3x+12)

27x^2+135x^2-54x-648

The equation of the ellipse satisfying the given conditions does not exist.

To find the equation of the ellipse with the given conditions, we can start by noting that the foci of the ellipse are located at (-4, 0) and (4, 0). The length of the major axis is given as 10 units.

The general equation of an ellipse with center (h, k) is:

((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1

Where "a" is the length of the semi-major axis and "b" is the length of the semi-minor axis.

Since the foci lie on the x-axis, the center of the ellipse is at the origin (0, 0). The distance from the center to each focus is given by "c".

We can determine "c" by using the distance formula between the two foci:

c = √((4 - (-4))^2 + (0 - 0)^2)

c = √(8^2)

c = 8

Since the length of the major axis is 10 units, the distance from the center to each vertex is "a", which is half of the length of the major axis:

a = 10 / 2

a = 5

Now, we can find "b" using the relationship between "a", "b", and "c" in an ellipse:

b = √(a^2 - c^2)

b = √(5^2 - 8^2)

b = √(25 - 64)

b = √(-39)

However, since "b" cannot be imaginary in this case, we can conclude that there is no real solution that satisfies the given conditions. Therefore, the equation of the ellipse satisfying the given conditions does not exist.

Learn more about ellipse here

https://brainly.com/question/30727620

#SPJ11

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

To know more about differential equation:

https://brainly.com/question/2273154

#SPJ4

No Solutions

5 − 4 + 7x + 1 = 0x + 0

One Solution

5 − 4 + 7x + 1 = 1x + 2

Infinitely Many Solutions

5 − 4 + 7x + 1 = 7x + 5

We have,

No Solutions

5 − 4 + 7x + 1 = 0x + 0

One Solution

5 − 4 + 7x + 1 = 1x + 2

Infinitely Many Solutions

5 − 4 + 7x + 1 = 7x + 5

In each case,

The equation is completed by setting the coefficients of "x" and the constants on both sides equal to each other, ensuring that the equation holds true for all values of "x".

The different choices of coefficients and constants determine whether the equation has no solution, one solution, or infinitely many solutions.

Thus,

No Solutions

5 − 4 + 7x + 1 = 0x + 0

One Solution

5 − 4 + 7x + 1 = 1x + 2

Infinitely Many Solutions

5 − 4 + 7x + 1 = 7x + 5

Learn more about solutions of equations here:

https://brainly.com/question/545403

#SPJ1

Using standard basis vectors, the cross product of (7-5) and (4) is (0, 0, 8).

To calculate the cross product of the vectors (7-5) and (4) using standard basis vectors, we can use the formula for the cross product in three-dimensional space:

(a1, a2, a3) × (b1, b2, b3) = (a2b3 - a3b2)i + (a3b1 - a1b3)j + (a1b2 - a2b1)k

In this case, we have (7-5) × (4) = (2) × (4).

Substituting the values into the formula, we get:

(7-5) × (4) = (2 × 0 - 0 × 4)i + (0 × 4 - 2 × 0)j + (2 × 4 - 0 × 0)k

Simplifying the expression, we have:

(7-5) × (4) = (0)i + (0)j + (8)k

Therefore, the cross product of (7-5) and (4) using standard basis vectors is (0, 0, 8).

To know more about the cross product refer here:

https://brainly.com/question/29097076?#

#SPJ11

Yes, that is correct. The notation P(z < a) represents the probability that a standard normal distribution variable Z is less than a particular value "a".

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to happen. The probability of an event A is typically denoted as P(A) and is calculated as the number of ways that event A can occur divided by the total number of possible outcomes. Probability is used in a wide range of fields, including mathematics, statistics, physics, finance, and engineering.

what is statistics?

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It includes a variety of methods for collecting data, such as surveys, experiments, and observational studies. Statistical methods are used to summarize and analyze the data, and to draw conclusions and make predictions about the population from which the data is sampled. The results of statistical analyses can be used in a variety of fields, including business, social sciences, natural sciences, and engineering.

To know more about probability visit:

brainly.com/question/32004014

#SPJ11

The data is best modeled by a Quadratic function, and based on the graph, the store owner should continue stocking the product.

Because it decreases in value until the minimum value, then it increases again.

After that, the graph will continue to increase, that is, it will have no more turning points as it is a quadratic function, hence the store owner should continue storing the product.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

The probability that the patient is indeed infected is 83.3% (accurate to at least 4 decimal places).

Let P(A) be the probability that the patient is infected and P(B) be the probability that the test result is positive.P(A) = 0.05 (Given)P(B|A) = 0.99 (Given)P(B|not A) = 0.10 (Given)Now, we have to find P(A|B). We can find this using Bayes Rule.

Bayes Rule: P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)] substitute the values and calculate:P(A|B) = (0.99)(0.05) / [(0.99)(0.05) + (0.10)(0.95)]≈ 0.8333So, the probability that the patient is indeed infected is 83.3% (accurate to at least 4 decimal places).

See more about probability at: https://brainly.com/question/24756209

#SPJ11

Answer:

B

Step-by-step explanation:

Answer:

Area = 36 squ. unit

Step-by-step explanation:

According to the Question,

by using these points a quadrilateral is formed with two opposite sides 7 and 5 and with height 6 (Refer in the diagram).

Area = 1/2 * (sum of opposite side) * height

Area = 1/2 * (7+5) * 6

Area = 3*12

Area = 36 squ. unit

Answer:

36

Step-by-step explanation: