A bag contains 222 red marbles, 333 green marbles, and 444 blue marbles. If we choose a marble, then another marble without putting the first one back in the bag, what is the probability that the first marble will be green and the second will be red?

Answer:

1:8 or 1/8

Step-by-step explanation:

That's your answer.....

Answer:

b = 6

Step-by-step explanation:

7b - 15 = 5b - 3

7b = 5b + 12               Add 15 to both sides

2b = 12                       Subtract 5b from both sides

b = 6                           Divide 2 from both sides

Answer:

\(b = 6\)

Step-by-step explanation:

1.) We need to manipulate the equation to get b by itself.

2.) ​ Subtract 5b from each side. Combine like terms. Add 15 to each side. Combine like terms. Divide each side by 2. Simplify.

The tangent plane approximation at h(4.001,0.997) is 72.026, where h(x, y) = x³ + 2xy.

Plane is h(x, y) = x³ + 2xy.

Substitute the value of x and y in the plane

h(4, 1) = (4)³ + 2(4)(1)

h(4, 1) = 64 + 8

h(4, 1) = 72

Partial Differentiation with respect to x

hₓ = ∂h/∂x

hₓ = 3x² + 2y

at (4, 1)

hₓ = 3(4)² + 2(1)

hₓ = 3(16) + 2

hₓ = 48 + 2

hₓ = 50

Partial Differentiation with respect to x

\(h_{y}\) = ∂h/∂y

\(h_{y}\) = 2x

at (4, 1)

\(h_{y}\) = 2(4)

\(h_{y}\) = 8

tangent plane is

z = h(4, 1) + hₓ(x - x₀) + \(h_{y}\)(y - y₀)

z = 72 + 50(x - 4) + 8(y - 1)

z = 72 + 50x - 200 + 8y - 8

z = 50x + 8y - 136

at (x, y) = (4.001, 0.997)

z = 50(4.001) + 8(0.997) - 136

z = 200.05 + 7.976 - 136

z = 72.026

To learn more about tangent plane link is here

brainly.com/question/30260323

#SPJ4

To describe y as the sum of two orthogonal vectors, x1 in the span{u} and x2 orthogonal to u , we follow two steps procedure:

1.First, find a vector x1 in the span{u} that is the projection of y onto u. To do this, use the formula:
  x1 = (y • u / ||u||^2) * u, where • represents the dot product and || || represents the magnitude of the vector.

2.Next, find the vector x2 that is orthogonal to u. Since y can be represented as the sum of x1 and x2, you can find x2 by subtracting x1 from y:
  x2 = y - x1

3.Now, you have y as the sum of two orthogonal vectors x1 and x2, with x1 in the span{u} and x2 orthogonal to u.

Learn more about   at orthogonal vectors  brainly.com/question/29423004

#SPJ11

Answer:

Step-by-step explanation:

X = shirts

Y = trousers

3x + 2y = 155

Now

y + 10 = x

Make y + 10 = x equal y

-10. -10

y = x - 10

Replace y with this equation in our other equation.

3x + 2(x - 10) = 155

Do the math:

This equals x = 35

Now put x = 35 in the other equation

Y + 10 = 35

Do the math:

y = 25

$35 per shirt

$25 per trousers

Now for the bar model, the total is 155

Make a fraction of 35/155

Make a long bar. Split it into 5 parts.

Label three parts 35 and two 25

Make the 35 parts slightly bigger.

It should look like this

Answer:

7.5

Step-by-step explanation:

If 'quter' is quarter, then 30(1/4) is 7.5

A quarter of 30 is 7.5

All you gotta do is divided 30 by 4 cause a quarter is half of the half. It's the 1/4th part of the whole.

Answer:

h= 24 inches

Step-by-step explanation:

(Volume)= (Base Area) * (Height)

6,912= 288h

h=

Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

In mathematics, a variable is a symbol or letter that represents a quantity that can vary or change. Variables are used to express mathematical relationships and to represent unknown values.

For example, in the equation "y = 2x + 3", "x" and "y" are variables. "x" represents an unknown value that can vary, while "y" represents the output value that is dependent on the input value of "x".

Variables can take on different values depending on the context of the problem being solved. In algebra, variables are commonly used to solve equations and to represent unknowns in formulas.

It's important to note that variables are not the same as constants, which are values that remain fixed throughout a mathematical expression or equation.

by the question.

The appropriate measure of variability for the data represented by the box plot is the interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, and it is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, the box extends from 17 to 21, with a line at 19, which means that Q1 is 17 and Q3 is 21. Therefore, the IQR is:

IQR = Q3 - Q1 = 21 - 17 = 4

So, the appropriate measure of variability for the data is the IQR, and its value is 4.

Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

To know more about the variable, visit:

https://brainly.com/question/15740935

#SPJ1

Answer:

504

Step-by-step explanation:

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

m < 3 = 40 degrees

Step-by-step explanation:

Measure of angle one and measure of angle three are the same because they are opposite angles (i cant remember the exact term)

Answer:

square root 75

Step-by-step explanation:

khan

Using the normal distribution, the mean of T is of 30 seconds.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

The mean of T is 10 seconds

A normal distribution has two parameters: Mean  and standard deviation .

The given parameters are the mean completion time of each step, μ = 10 seconds

The standard deviation, σ = 5 seconds.

For the total completion, there are 3 instances, hence ,n = 3(10)

Thus, the mean of T is of 30 seconds.

Learn more about standard normal distribution here:

https://brainly.com/question/10984889

#SPJ1

a) Mark earns $110 at the rock concert,  b) i) Mary's annual income is $66,000, c) Danny's regular salary is $400 and his overtime salary is $75. His total salary is $475.

a) Mark sells 200 programs, so he earns an additional $0.45 for each program. Therefore, his earnings from selling programs is 200 * $0.45 = $90. In addition, he earns a fixed amount of $20 for showing up. Therefore, his total earnings at the rock concert is $20 + $90 = $110.

b) i) Mary's annual income is her monthly salary multiplied by 12 since there are 12 months in a year. Therefore, her annual income is $5,500 * 12 = $66,000.

ii) Mary's gross earnings per pay period would depend on the pay frequency. If we assume a monthly pay frequency, her gross earnings per pay period would be equal to her monthly salary of $5,500.

iii) If Mary is paid semi-monthly, her earnings per pay period would be half of her monthly salary. Therefore, her earnings per pay period would be $5,500 / 2 = $2,750.

iv) If Mary is paid weekly, we need to divide her monthly salary by the number of weeks in a month. Assuming there are approximately 4.33 weeks in a month, her earnings per pay period would be $5,500 / 4.33 = $1,270.99 (rounded to the nearest cent).

c) To calculate Danny's regular salary and overtime, we need to consider his regular working hours and overtime hours.

Regular working hours: 8 hours on Monday + 8 hours on Tuesday + 8 hours on Wednesday + 8 hours on Thursday = 32 hours.

Overtime hours: 10 hours on Wednesday (2 hours overtime) + 10 hours on Friday (2 hours overtime) = 4 hours overtime.

Regular salary: Regular working hours * hourly rate = 32 hours * $12.50/hour = $400.

Overtime salary: Overtime hours * hourly rate * overtime multiplier = 4 hours * $12.50/hour * 1.5 = $75.

Therefore, Danny's regular salary is $400 and his overtime salary is $75. His total salary would be the sum of his regular salary and overtime salary, which is $400 + $75 = $475.

Learn more about divide here:

https://brainly.com/question/15381501

#SPJ11

The situation that describes the use of an ATM is option C, where Abby entered a PIN to begin a transaction and received an amount of cash.

An ATM, or Automated Teller Machine, is a self-service banking machine that allows users to perform various financial transactions, including withdrawing cash, depositing money, checking account balances, and transferring funds. To use an ATM, the user typically needs to have a debit card or ATM card linked to their bank account, and they need to enter a unique Personal Identification Number (PIN) to access their account.

Once the user enters the correct PIN, they can choose the type of transaction they want to perform, such as withdrawing cash, and the machine dispenses the requested amount of cash.

Therefore, option C is the correct answer that describes the use of an ATM.

To know more about ATM  click on below link :

https://brainly.com/question/24198010#

#SPJ11

The number line highlighted such that  all the numbers that can be values of x so |x| < 7 is attached accordingly.

A number line is a graphic depiction of numbers on a straight line in mathematics. A number line has numbers that are consecutively set at identical distances throughout its span. It may be stretched in any direction indefinitely and is commonly depicted horizontally.

Number lines are significant because they show numbers in context. Primarily because they allowed negative numbers to be expressed in a meaningful fashion.

Learn more about number lines;
https://brainly.com/question/16191404
#SPJ1

Answer:

Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

x

3

+

11

=

32

3

(

x

+

11

)

=

32

3

(

x

+

11

)

=

32

3

x

+

11

=

32

3

x

+

11

=

32

Step-by-step explanation:

Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

What Does Solve for x Mean?

Solve for x means finding the value of x for which the equation holds true. i.e when we find the value of x and substitute in the equation, we should get L.H.S = R.H.S

If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation.

Do you think x = 1 is the solution to this equation? Substitute it in the equation and see.

1 + 1 = 2

2 = 2

L.H.S = R.H.S

That’s what solving for x is all about.

How Do You Solve for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

Let’s start with a simple equation as, x + 2 = 7

How do you get x by itself?

Subtract 2 from both sides

⇒ x + 2 - 2 = 7 - 2

⇒ x = 5

Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7.

L.H.S = R.H.S

Answer:

No, but y = 8x is. There has to be an x after your number for it to be called a linear equation.

Answer:

B. 1.00 x 10 to the 4th power

Step-by-step explanation:

Given:

The dimensions of the square photo are 12'' × 12''.

The frame is 2 inches wider than the photo in both length and width.

To find:

The perimeter of the frame.

Solution:

We have,

Length of the photo = 12 inches

Width of the photo = 12 inches

The frame is 2 inches wider than the photo in both length and width. So,

Length of the frame = 12+2 inches

                                 = 14 inches

Width of the frame  = 12 inches

                                = 14 inches

The perimeter of a square is:

\(P=4a\)

Where, a is the side length.

Now, the perimeter of the square frame with side 14 inches is:

\(P=4(14)\)

\(P=56\)

Therefore, the perimeter of the square frame is 56 inches, Hence, option A is correct.

Answer:

In geometry, a circle is defined as a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center.” Never confuse a circle with a polygon. A circle is not a polygon because it is made up of curves.

Answer:

0.0381

Step-by-step explanation:

This is a binomial probability distribution problem. Thus;

p = 10% = 0.1

We are told that A random sample of 8 light bulbs are chosen and tested. Thus, n = 8

We want to find the probability that at least 3 are defective. This will be;

P(X ≥ 3) = P(3) + P(4) + P(5) + P(6) + P(7) + P(8)

P(X = x) = C(n, x) × p^(x) × (1 - p)^(n - x)

Thus;

P(3) = C(8, 3) × 0.1³ × (1 - 0.1)^(8 - 3)

P(3) = C(8, 3) × 0.1³ × 0.9^(5)

P(3) = 0.03306744

Repeating this same procedure, we have;

P(4) = 0.0045927

P(5) = 0.00040824

P(6) = 0.00002268

P(7) = 0.00000072

P(8) = 0.00000001

Thus;

P(X ≥ 3) = 0.03306744 + 0.0045927 + 0.00040824 + 0.00002268 + 0.00000072 + 0.00000001 = 0.03809179

Approximately 0.0381

Answer:

I think it's 1/2 because it might be right

Answer:5w=36

Step-by-step explanation:

The encrypted messages for the given encryption functions are:

(a) "MATH" encrypts to "POWD".

(b) "MATH" encrypts to "AOHU".

(c) "MATH" encrypts to "TPOO".

To encrypt the message "MATH" using the given encryption functions, we first need to translate the letters into numbers based on the given mapping. Using the mapping A=0,B=1,C=2,...,Z=25, the message "MATH" translates to the numbers [12, 0, 19, 7].

(a) Using the encryption function f(p) = (p+3) mod 26:

Applying the function to each number, we get [(12+3) mod 26, (0+3) mod 26, (19+3) mod 26, (7+3) mod 26] = [15, 3, 22, 10].

Translating the resulting numbers back into letters using the mapping, we obtain the encrypted message "POWD".

(b) Using the encryption function f(p) = (p+14) mod 26:

Applying the function to each number, we get [(12+14) mod 26, (0+14) mod 26, (19+14) mod 26, (7+14) mod 26] = [0, 14, 7, 21].

Translating the resulting numbers back into letters using the mapping, we obtain the encrypted message "AOHU".

(c) Using the encryption function f(p) = (p+7) mod 26:

Applying the function to each number, we get [(12+7) mod 26, (0+7) mod 26, (19+7) mod 26, (7+7) mod 26] = [19, 7, 0, 14].

Translating the resulting numbers back into letters using the mapping, we obtain the encrypted message "TPOO".

Therefore, the encrypted messages for the given encryption functions are:

(a) "MATH" encrypts to "POWD".

(b) "MATH" encrypts to "AOHU".

(c) "MATH" encrypts to "TPOO".

to learn more about numbers click here:

brainly.com/question/30752681

#SPJ11

Answer:

14

Step-by-step explanation:

The perimeter of the triangle is equal to 7 + √85 + √6 units (approx. 18.7 units).

In this problem we need to determine the lengths of the three sides of the triangle based on the locations of the three vertices on the Cartesian plane and later to calculate of the perimeter. Each length is found by using an application of the Pythagorean theorem:

Side PQ

PQ = √[[- 3 - (- 3)]² + [- 1 - (- 8)]²]

PQ = 7

Side QR

QR = √[[- 9 - (-3)]² + [- 8 - (-1)]²]

QR = √85

Side PR

PR = √[[- 9 - (- 3)]² + [- 8 - (- 8)]²]

PR = √6

Then, the perimeter of the triangle is equal to 7 + √85 + √6 units (approx. 18.7 units).

To learn more on perimeters: https://brainly.com/question/7486523

#SPJ1

Answer:

None of the answer choices provided, but the closest option is 800 square yards, so that would be the best choice.

Step-by-step explanation:

To find the area of the playground, we need to divide it into two triangles and one rectangle.

The rectangle has a length of 12 yards and a width of 20 yards, so its area is:

Area of rectangle = length × width

Area of rectangle = 12 × 20

Area of rectangle = 240 square yards

One of the triangles has a base of 14 yards and a height of 20 yards, so its area is:

Area of triangle 1 = (base × height) / 2

Area of triangle 1 = (14 × 20) / 2

Area of triangle 1 = 140 square yards

The other triangle has a base of 26 yards (40 - 14) and a height of 20 yards, so its area is:

Area of triangle 2 = (base × height) / 2

Area of triangle 2 = (26 × 20) / 2

Area of triangle 2 = 260 square yards

Therefore, the total area of the playground is the sum of the areas of the rectangle and the two triangles:

Total area = Area of rectangle + Area of triangle 1 + Area of triangle 2

Total area = 240 + 140 + 260

Total area = 640 square yards

Therefore, the area of the playground is 640 square yards. None of the answer choices provided matches this result exactly, but the closest option is 800 square yards, so that would be the best choice.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the industry's output is Y = 3, and the profit of each firm  = -2.

a) Supply curve of an individual firm

The price received by the individual firm will be P. Its demand curve is given by

D(p) = 20 - p.

Each firm chooses output to maximize its profit. Profit maximization occurs when the price is equal to the marginal cost. Mathematically,

P = MC(y)

4y = P

y = P/4

Thus the supply curve of the firm is y = P/4

b) The smallest price at which the product can be sold. The product can be sold at the minimum of the supply curve, which is y = 0, given P ≥ 0. Therefore the smallest price is P = 0.

c) Equilibrium price and output

Equilibrium occurs when each firm is producing at its profit-maximizing output given the output of other firms. Let the number of firms in the industry be n. The output of the industry is Y = ny. The industry supply curve is given by

S(P) = nP/4

The equilibrium price intersects the industry supply curve with the demand curve. Thus the equilibrium price satisfies

S(P) = Y

nP/4 = 20 - P

=> P = 80/(4 + n).

The equilibrium number of firms is the number that makes the industry supply curve equal to the demand curve. Thus

20 - P = nP/4

=> P = 80/(4 + n)

=> n = (80 - 20P)/P

= 20/P - 4.

Thus the equilibrium number of firms is a function of P and can range between 1 and infinity, but it must be an integer. The equilibrium output of each firm is given by

y = P/4 = 20/(4n + n²)

The equilibrium output of the industry is given by

Y = n

y = 5/P = (n² + 4n)/80.

d) Equilibrium number of firms with new demand curve D(p) = 21 - p.

The intersection of this curve with the marginal cost curve is at p = 21/5. This is greater than the minimum possible price of 0. Thus there is a positive profit to be earned in this industry, and new firms can enter the market.

e) Equilibrium price and output with new demand curve with the new demand curve D(p) = 21 - p, the industry supply curve and the equilibrium price are as given in part (d). The equilibrium output of each firm is given by y = P/4 = 21/20, and the equilibrium output of the industry is given by Y = 21/4.

f) Equilibrium number of firms, price, output, and profit with demand curve D(p) = 24 - p. This demand curve intersects the marginal cost curve at p = 6. The minimum possible price is P = 0. Thus there is a range of prices from 0 to 6 where firms can profit positively.

The equilibrium number of firms will be the smallest integer such that the price is 6 or higher. This occurs when n = 2. At this equilibrium, the price is P = 6, the output of each firm is y = 3/2, the output of the industry is Y = 3, and the profit of each firm is (6)(3/2) - (2)(2(3/2)² + 8) = -2.

To know more about the demand curve, visit:

brainly.com/question/13131242

#SPJ11