A college finds that 10% of students have taken a distance learning class and that 40% of students are part-time students. Of the part-time students, 20% have taken a distance learning class. Let D = event that a student takes a distance learning class and E = event that a student is a part-time student.


a. Find P(D AND E)

b. Find P(E | D)

c. Find P(D OR E)

Statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

The study of data gathering, analysis, interpretation, presentation, and organization is known as statistics. In other words, gathering and summarizing data is a mathematical discipline. Additionally, statistics might be considered a subfield of applied mathematics. However, uncertainty and variation are two crucial and fundamental concepts in statistics. Only statistical analysis can determine the uncertainty and variation in many sectors. The probability, which is a key concept in statistics, essentially determines these uncertainties.

According to the definition of statistics; the study of data gathering, analysis, interpretation, presentation, and organization is known as statistics.

Hence, statistics is a branch of mathematics that deals with collecting data about the world. Hence, option C is the correct answer.

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The system of equations for this problem can be represented as:

y = 0.50x - 15 (for Team A's popcorn sales)

y = 0.75x - 25 (for Team B's cotton candy sales)

where x represents the number of items sold and y represents the profit earned. To graph the system of equations, we can plot the two lines on the same coordinate plane and find the point where they intersect, which represents the point at which both teams earn the same amount of profit.

At the point of intersection, both teams earn the same amount of profit. To find the profit earned, we can substitute the x-value of the point of intersection into one of the equations and solve for y. The profit earned would be the y-value at the point of intersection.

can't graph sorry

Answer:

Step-by-step explanation:

To determine if they can use 26 of one type and 14 of the other, we need to calculate the cost for each scenario and compare it to their budget of $400.

If they use 26 round tables, it would cost 26 * $10 = $260.

And if they use 14 square tables, it would cost 14 * $10 = $140.

The total cost would be $260 + $140 = $400, which is equal to their budget.

Now, we need to make sure that they can seat all the guests with the tables they plan to rent.

If they use 26 round tables, they can seat 26 * 6 = 156 guests.

And if they use 14 square tables, they can seat 14 * 8 = 112 guests.

The total number of guests they can seat would be 156 + 112 = 268.

since they expect at least 260 guests to attend and they can seat 268 guests, the table rental plan of 26 round tables and 14 square tables is feasible both financially and in terms of seating capacity.

The formula for calculating the sample mean is to take the sum of the values divided by the total number of values.

In this case, the two players would take the sum of the number of rounds they survived in their 101010 attempts, and then divide that sum by 101010. That would give them their individual sample means for the number of rounds survived.

To calculate the difference in the sample means of two players playing 101010 attempts, we can first calculate the sample mean of each player. This can be done by taking the sum of all attempts and then dividing that by the number of attempts. For example, if Player 1 had 5 attempts and survived 3 rounds, the sample mean would be 3/5 or 0.6. If Player 2 had 8 attempts and survived 4 rounds, the sample mean would be 4/8 or 0.5. We can then subtract the sample mean of Player 1 from the sample mean of Player 2 to get the difference in the sample means, which in this example would be 0.6 - 0.5 = 0.1.

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The cost of a taco and burrito respectively $1.70 and $0.40.

Let x be the cost of a taco and y be the cost of a burrito.

From the first given information, Thelma ordered 2 tacos and 1 burrito and paid $3.79. So we can write an equation:

2x + y = 3.79

From the second given information, Louise ordered 2 burritos and 1 taco and paid $4.58. So we can write another equation:

2y + x = 4.58

To find x and y, we need to solve the system of linear equations. One way to do this is by using the elimination method. We can subtract the first equation from the second to eliminate x:

2y = 0.79

y = 0.395

Now that we have y, we can substitute it back into the first equation to find x:

2x + 0.395 = 3.79

2x = 3.395

x = 1.698

So the cost of a taco is $1.70 and the cost of a burrito is $0.40.

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The formula for the tangent line to f(x) = ln(x) at x = 2 is: y = (1/2)(x - 2) + ln(2)

The tangent represents the supplied function's instantaneous rate of change at a location.

The slope of the tangent at a location equals the function's derivative at the same position. The tangent slope of a function y = f x is d y d x.

The tangent and normal equations may be determined using the coordinate geometry formal of point-slope form.

The tangent equation is (y - y1) = m(x - x1), while the normal equation, passing through this same point and perpendicular to the tangent, is (y - y1) = -1/m (x - x1).

The formula for the tangent line to the function f(x) = ln(x) at x = 2 is given by:

y = f'(2)(x - 2) + f(2)

Plugging in the value f'(2) = 1/2 and f(2) = ln(2), we get:

y = (1/2)(x - 2) + ln(2)

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It is clear that even with full-time, year-round employment at the federal minimum wage, the annual income is still below the poverty line. California's minimum wage provides slightly better wages, but it still remains below the poverty line.

Annual income:

Federal minimum wage: $15,080

California's minimum wage: $16,640

Marketing managers: $110,000

Police officers: $55,680

Child-care workers: $14,500

Difference between annual wage and federal poverty line:

Federal minimum wage: -$10,470

California's minimum wage: -$8,910

Marketing managers: $55,000

Police officers: $8,550

Child-care workers: -$10,830

Difference between annual wage and median household income:

Federal minimum wage: -$57,040

California's minimum wage: -$49,560

Marketing managers: $45,000

Police officers: $420

Child-care workers: -$63,010

However, child-care workers' annual income is still well below the poverty line and the median household income. This highlights the importance of providing a living wage for all workers, especially those in low-wage industries.

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The problem states that Ravi rented a truck for one day and there was a base fee of $14.99 and an additional charge of 89 cents for each mile driven. The goal is to find the number of miles that Ravi drove the truck.

We can start by using an equation to represent the total cost of renting the truck. Let's call the number of miles driven "m". The total cost can be expressed as:

14.99 + 0.89m

The first part of the equation (14.99) represents the base fee and the second part (0.89m) represents the additional charge for each mile driven.

Next, we can use the information given in the problem to solve for m. We know that Ravi had to pay a total of $14.99 when he returned the truck, so we can set up the following equation:

14.99 + 0.89m = 14.99

Solving for m, we can subtract 14.99 from both sides:

0.89m = 0

Finally, we can divide both sides by 0.89 to find the value of m:

m = 0

So, Ravi drove the truck for 0 miles. This means that either he did not drive the truck at all, or the number of miles driven was so small that it was rounded down to 0 miles.

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At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6). This gives I(10) = 5e^(-10/6) = 0.25 A.[/tex]

[tex]I(t) = 5e^(-t/6)[/tex]

[tex]At t = 1ms: I(1) = 5e^(-1/6) = 3.26 AAt t = 6ms: I(6) = 5e^(-6/6) = 0.77 AAt t = 10ms: I(10) = 5e^(-10/6) = 0.25 A[/tex]

At t = 1ms, the current can be found by substituting t=1 into the given equation for the current: [tex]I(t) = 5e^(-t/6).[/tex] This gives [tex]I(1) = 5e^(-1/6) = 3.26 A.[/tex]

At t = 6ms, the current can be found by substituting t=6 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(6) = 5e^(-6/6) = 0.77 A.[/tex]

At t = 10ms, the current can be found by substituting t=10 into the given equation for the current: [tex]I(t) = 5e^(-t/6)[/tex]. This gives [tex]I(10) = 5e^(-10/6) = 0.25 A.[/tex]

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Answer:

6 feet

Step-by-step explanation:

Answer:

Option 1 : x² + 4x + 4

Option 2 : x² + 20x + 100

Option 3 : x² + 6x + 9

Step-by-step explanation:

Looks like you got two of them right, one wrong and one missing. The first option is also a perfect square.

Here is how it evaluates:

If a trinomial expression can be a perfect square then it can be of the form (x + a)^2 = x² + 2ax + a² . Therefore the last term must be a perfect square of a number and the second term is twice the first term x and a = 2ax

So examining the choices we get

If g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6, the smallest value g(6) can be g(6) ≥ 14.

g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6.

From the mean value theorem we know that if at [2, 6] g(x) is continuous as well as differentiable then there exists (2, 6) as

{g(6) - g(2)}/(6 - 2) = g'(x)

As we know that g'(x) ≥ 1/2, so

{g(6) - g(2)}/(6 - 2) ≥ 1/2

Now simplify

{g(6) - g(2)}/4 ≥ 1/2

As g(2) = 12, now put the value

{g(6) - 12}/4 ≥ 1/2

Multiply by 4 on both side, we get

g(6) - 12 ≥ 2

Add 12 on both side, we get

g(6) ≥ 14

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3 hours to take second tap alone empty the tank.

Given data :

Time taken by tap A to empty the tank = 4 hours

Work done by tap A in 1 hour = [tex]\frac{1}{4}[/tex]

Time taken to empty the tank by both taps = 1 hours

Time taken to empty the tank by tap B = Total time taken - time taken by A

=4 - 1 = 3

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Answer: hola

Step-by-step explanation:

The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

The singular value decomposition of a is:

a = uσvT

where

u = (1/√2, 0, -1/√2)

σ = (5, 0, 0)

vT = (3/5, 4/5, 0)

The pseudoinverse of a is:

a = vσuT

where

v = (3/5, 4/5, 0)

σ = (1/5, 0, 0)

uT = (√2/5, 0, -√2/5).

The singular value decomposition and pseudoinverse of the 1-by-3 matrix a = 3 4 0 are u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0) and v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5), respectively.

The singular value decomposition of the 1-by-3 matrix a = 3 4 0 is u = (1/√2, 0, -1/√2), σ = (5, 0, 0), vT = (3/5, 4/5, 0). This means that the matrix can be written as a product of three matrices, u, σ and vT. The matrix u is a unitary matrix, and the matrix σ is a diagonal matrix containing the singular values of the matrix a. The matrix vT is the transpose of the matrix v, which is the right singular vector. The pseudoinverse of a is v = (3/5, 4/5, 0), σ = (1/5, 0, 0), uT = (√2/5, 0, -√2/5). This means that the matrix a can be written as a product of three matrices, v, σ and uT, which is the inverse of the matrix u. The matrix v is the left singular vector, and the matrix σ is a diagonal matrix containing the singular values of the matrix a, but inverted. The matrix uT is the transpose

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The problem involves calculating the probability of having 390 or more working devices in a box of 400 electronic devices, where each device works properly with a probability of 0.95. This type of problem can be solved using the binomial distribution.

The binomial distribution models the number of successful outcomes in a fixed number of independent Bernoulli trials. In this case, each device working properly can be considered as a Bernoulli trial with success probability 0.95. The total number of trials (i.e. devices) is 400.

Using the binomial distribution, we can calculate the probability of having exactly k successful outcomes (i.e. working devices) in n trials (i.e. devices). This probability is given by the formula:

P(k) = ([tex]{n}_C_{k}[/tex]) * p^k * (1-p)^(n-k)

where (n choose k) is the binomial coefficient, p is the success probability, and (1-p) is the failure probability.

To calculate the probability of having 390 or more working devices, we need to sum the probabilities of having 390, 391, 392, ..., 400 working devices:

P(390 or more) = P(390) + P(391) + ... + P(400)

This can be calculated using a binomial distribution calculator or by writing a program to calculate the binomial coefficient and probability for each value of k.

Finally, to express the result as a percentage, we need to multiply the probability by 100.

In conclusion, the percentage of boxes containing 390 or more working devices can be calculated using the binomial distribution, which models the number of successful outcomes in a fixed number of independent Bernoulli trials.

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The correct answer is option a). The variable "the mileage of a car" is not a categorical variable.

A categorical variable, also known as a nominal variable, is a variable that can be divided into categories or groups. These categories can be any non-numeric values such as names, labels, or yes/no answers.

The variables "a person's gender," "the make of a laptop," and "whether a person is a college graduate" are all examples of categorical variables because they can be divided into categories such as "male," "female," "Dell," "HP," "yes," and "no."

However, the variable "the mileage of a car" is not a categorical variable because it is a numeric variable that represents a specific numerical value, such as the number of miles a car has driven. Unlike categorical variables, numeric variables can be ordered, compared, and manipulated mathematically.

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The required value of the integral is 9x^(1/2) cos√x - (1/2) ∫9 sin√x x^(-1/2) dx

When different individuals or objects are brought together, such as when all of the district's elementary school children attend the new middle school or when snowboarding is introduced to all ski slopes, integration takes place.

The general formula for integration by parts is ∫u dv = uv - ∫v du. Choosing u = cos√x and dv = 9 dx, we have:

du = (1/2) sin√x dx and v = 9x^(1/2)

Therefore, the integral becomes:

∫9 cos⁡√x dx = 9x^(1/2) cos√x - (1/2) ∫9 sin√x x^(-1/2) dx

This can be further simplified if desired, but this is the result obtained by using integration by parts.

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If the population variable x is normally distributed , then (b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

The two intervals are :

(i) the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n   and    (ii) the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n  ;

the critical value of z interval is = 1.96  ;

by using the normal table , we get , p = 0.95  ;

So , the z interval is with p = 95% ;

the t interval is t₀.₀₂₅,ₙ₋₁ = critical value ,

On comparing with [tex]t_{\frac{\alpha}{2} }[/tex],ₙ₋₁ = t₀.₀₂₅,ₙ₋₁ ,

we get , α/2 = 0.025 ⇒ So , α = 0.05   .

this interval is also 95% confidence interval .

Therefore , both the intervals are equally likely to contain μ with probability ≈ 0.95.

The given question is incomplete , the complete question is

Which is more likely to contain µ, the z-interval [tex]\bar{x}[/tex] ± 1.960σ/√n or the t-interval [tex]\bar{x}[/tex]± t₀.₀₂₅,ₙ₋₁S/√n? Assume that the population variable x is normally distributed.

Choose the correct answer below.

(a) The interval [tex]\bar{x}[/tex]±t₀.₀₂₅,ₙ₋₁S/√n has a higher probability of containing µ.

(b) Both intervals are equally likely to contain μ with probability ≈ 0.95.

(c) The interval  [tex]\bar{x}[/tex]± 1.96σ/√n has a higher probability of containing μ.

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Total amount of admission fee for the group of 26 students is 82.5$+135$ which is equal to 217.5 dollars.

There are a total of 26 students and the special offer is valid up to 11 students only.

Each of the 15 students will have to pay $135 as a special offer.

There are 11 more students, nevertheless, in addition to the great offer.

Each student paid an additional 7.5 dollars.

Therefore, the cost for 11 students is 11*(7.5$)=82.5$.

The total fee that is now owing is 82.5 + 135 dollars, which is equivalent to 217.5 dollars.

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(5 x 1/4), (3 x 7/9), and (2 x 5/6)

Then simplify each expression, then we have

⇒ 5 x 1/4

⇒ 1/4 + 1/4 + 1/4 + 1/4 + 1/4

⇒ 5 / 4

⇒ 1 ¹/₄

⇒ 3 x 7/9

⇒ 7/9 + 7/9 + 7/9

⇒ 7/3

⇒ 2 ¹/₃

⇒ 2 x 5/6

⇒ 5/6 + 5/6

⇒ 5/3

⇒ 1 ²/₃

The expression improper fractions to mixed numbers will be 1 ¹/₄, 2 ¹/₃, and 1 ²/₃.

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the length of the midsegment of the trapezoid will be √58.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, Quadrilateral TEST is a trapezoid with coordinates at T(-3, 0), E(-2, 3), S(4, 3), and T(5, 0),

Its, diagonal or midsegment will be TS or ET'

From the formula of the distance between two coordinates:

D = √((x -x')² + (y - y')²)

Thus,

TS = √((-3 - 4)² + (0 - 3)²)

TS = √49 + 9

TS= √58

Since TEST' is a trapezoid thus its Diagonal will be the same  TS = ET'

Therefore,  the length of the midsegment of the trapezoid will be √58.

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Answer:

I got you

1. Use a calculator (its ur bestie fr fr)

2. Organization is key it might help with solving the problems

3. Ask someone or a teacher if you don’t understand

4. Remember COMBINE LIKE TERMS (ex: x+3x)

Step-by-step explanation:

The function C = 2x + 12y, has minimum value 60 at points (18,2) and (30,0).

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The given objective function -

C = 2x + 12y

Subjected to the constraints -

2x + 12y ≥ 60

x + y ≥ 20

x ≥ 0, y ≥ 0

First consider the inequality 2x + 12y ≥ 60.

The equation of the above inequality is as follows -

2x + 12y = 60

Find two points that satisfies the above equation.

Take x = 6, then -

2(6) + 12y = 60

12 + 12y = 60

12y = 60 - 12

12y = 48

y = 4

The first point is (6,4).

Take x = 0, then -

2(0) + 12y = 60

0 + 12y = 60

12y = 60

y = 5

The second point is (0,5).

Substitute (x,y) = (0,0) and see the direction of the region for 2x + 12y ≥ 60.

2(0) + 12(0) ≥ 60

0 ≥ 60

This is not true.

Therefore, the region is non-origin side.

Now consider the inequality x + y ≥ 20.

The equation of the above inequality is as follows -

x + y = 20

Find two points that satisfies the above equation.

Take x = 0, then -

0 + y = 20

y = 20

The first point is (0,20).

Take y = 0, then -

x + 0 = 20

x = 20

The second point is (20,0).

Substitute (x,y) = (0,0) and see the direction of the region for x + y ≥ 20.

0 + 0 ≥ 20

0 ≥ 20

This is not true.

Therefore, the region is non-origin side.

Plot the graph.

From the graph see that the corner points are (0,20), (18,2) and (30,0).

Now plug these points in the objective function and see for which point the objective function has the minimum value.

C = 2x + 12y

C = 2(0) + 12(20)

C = 0 + 240

C = 240

C = 2(18) + 12(2)

C = 36 + 24

C = 60

C = 2(30) + 12(0)

C = 60 + 0

C = 60

Therefore, the minimum value 60 is at points (18,2) and (30,0).

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Answer:  Brainliest Award pls

To find the base of a triangle with a given height and area, you can use the formula for the area of a triangle:

Area = (base * height) / 2

So, you can set up the equation:

24 = (base * 12) / 2

Solving for the base:

24 * 2 / 12 = base

base = 48 / 12 = 4

So, the base of the triangle is 4 inches.

Step-by-step explanation:

To find the base of a triangle with a given height and area, you can use the formula for the area of a triangle:

Area = (base * height) / 2

So, you can set up the equation:

24 = (base * 12) / 2

Solving for the base:

24 * 2 / 12 = base

base = 48 / 12 = 4

So, the base of the triangle is 4 inches.

The system of equation x = 4y - 1 and 2x - 8y = 7 has no solutions

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Given the equations:

x = 4y - 1  

multiply the equation by 2:

2x = 8y - 2

2x - 8y = -2     (1)

Also:

2x - 8y = 7     (2)

Subtracting equation 2 from 1 to solve by elimination method:

0 = -9

The equation has no solutions

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Answer:

Y=5x+2

first find the rise over run (slope) (m value in the y=mx+b equation) you do this by using your table. notice how much the y side rises by (5) and how much the x side runs by (1) the slope is 5/1 (5) the y-intercept is 2, we know this from the table.

An angle is the two rays sharing a common endpoint.

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