Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob’s bag. Bob then randomly selects one ball from his bag and puts it into Alice’s bag. What is the probability that after this process the contents of the two bags are the same? (Hint: you can simplify your solution using "without loss of generality".)

Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

Answer:

x = 2, 6

Step-by-step explanation:

differentiate f(x) using the power rule

f'(a\(x^{n}\) ) = na\(x^{n-1}\) and f'( constant) = 0

given

f(x) = x³ - 12x² + 6x - 8

f'(x) = 3x² - 24x + 6

equate f'(x) to - 30

3x² - 24x + 6 = - 30 ( add 30 to both sides )

3x² - 24x + 36 = 0 ( divide through by 3 )

x² - 8x + 12 = 0 ← in standard form

(x - 2)(x - 6) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 6 = 0 ⇒ x = 6

solution is x = 2, 6

Answer: 18.75 inches

Step-by-step explanation:

Let the height of the model be represented by x. Therefore, based on the information given in the question, we can form an equation which will be:

3/x = 32/200

Cross multiply

32 × x = 200 × 3

32x = 600

x = 600/32

x = 18.75

Therefore, the height of the model is 18.75 inches

Answer:Hi B)

Step-by-step explanation:

Answer:

4850 boxes

Step-by-step explanation:

97 out of 100 boxes have no defects, can be translated into 97% of boxes have no defects. Using this number, we can find 97% of 5,000 to make an estimate of how many boxes will not have defects
.97(5,000)=4850

The inequality that can be used to solve for x, the height of the wall, is \(x^2 + 15x - 166 ≤ 0.\)

To solve for x, the height of the wall, we need to set up an inequality based on the combined area of the wall and the paintings.

The area of the wall can be represented as (15 + x) ft multiplied by the width x ft, which gives us an area of (15 + x) * x square feet.

The combined area of the wall and the three paintings is the area of the wall plus the sum of the areas of the three paintings, which are each 3 ft by 4 ft. So the combined area is (15 + x) * x + 3 * 4 * 3 square feet.

We want the combined area to be at most 202 square feet, so we can set up the following inequality:

\((15 + x) * x + 3 * 4 * 3 ≤ 202\)

Simplifying the inequality:

(15 + x) * x + 36 ≤ 202

Expanding the terms:

15x + x^2 + 36 ≤ 202

Rearranging the terms:

\(x^2 + 15x + 36 - 202 ≤ 0x^2 + 15x - 166 ≤ 0\)

Now we have a quadratic inequality. We can solve it by factoring or by using the quadratic formula. However, in this case, since we are looking for a range of values for x, we can use the graph of the quadratic equation to determine the solution.

By graphing the quadratic equation y =\(x^2 + 15x\)- 166 and finding the values of x where the graph is less than or equal to zero (on or below the x-axis), we can determine the valid range of x values.

Therefore, the inequality that can be used to solve for x, the height of the wall, is \(x^2 + 15x - 166 ≤ 0.\)

for more such question on inequality visit

https://brainly.com/question/30238989

#SPJ8

Answer:

y = 1/2x - 6

Step-by-step explanation:

y2 - y1 / x2 - x1

-2 - (-5) / 8 - 2

3 / 6

= 1/2

y = 1/2x + b

-5 = 1/2(2) + b

-5 = 1 + b

-6 = b

Answer:

Step-by-step explanation:

Radius = half the diameter = AB/2

The restricted value on the range of function f(x) is given as follows:

3.

From the horizontal dashed line, the function never assumes a value of y = 3, hence the restricted value on the range of function f(x) is given as follows:

3.

Learn more about domain and range at https://brainly.com/question/26098895

#SPJ1

Answer:

3

Step-by-step explanation:

The range of a function is the set of all possible output values (y-values).

The given diagram shows the graph of a rational function with a horizontal asymptote at y = 3 (indicated by the dashed line).

An asymptote is a line that the curve gets infinitely close to, but never touches.

Therefore, as there is an asymptote at y = 3, the curve of the function will never touch the line y = 3, and consequently the value of y = 3 is restricted from the range of the function.

Answer:

Where is the number I need to round to?

(Please don't give me a bad rating i'm trying to help :) )

Thus,  the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.

To find the directional derivative of the function g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j, we need to use the formula for directional derivative:

dvg(6, 0) = ∇g(6, 0) ⋅ v

where ∇g is the gradient of g, which is given by:

∇g = (∂g/∂u)i + (∂g/∂v)j
   = (2ue^(-v))i - (u^2e^(-v))j

Evaluating the gradient at (6, 0), we get:

∇g(6, 0) = (2(6)e^(0))i - ((6)^2e^(0))j
         = 12i - 36j

Now we can substitute these values into the formula for directional derivative:

dvg(6, 0) = ∇g(6, 0) ⋅ v
         = (12i - 36j) ⋅ (3i + 4j)
         = 36 - 144
         = -108

Therefore, the directional derivative of g(u, v) = u^2e^(-v) at the point (6, 0) in the direction of the vector v = 3i + 4j is -108.

Know more about the directional derivative

https://brainly.com/question/30048535

#SPJ11

Answer:

1 inch = 54.7

Answer:

6 lb 12 oz is the answer

Step-by-step explanation:

Just did the subtraction

This is the formula you are looking for Logb x = Loga x/Loga b

If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be  984N.

As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.

We are required to calculate the force required to compress this spring by 1.2 cms

To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as

[F = (k * x)]

Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and

(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.

To learn more about Spring Constants, click on the link below.

https://brainly.com/question/14652640

#SPJ4

Using translation concepts, the statement that correctly describes the graph g(x) = f(x - 11) is given by:

A. It is the graph of f(x) translated 11 units to the right.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, we have that g(x) = f(x - 11), that is, x -> x - 11, which means that f(x) was shifted 11 units to the right and option A is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

The baker bought 8 pounds of apples and 4 pounds of bananas.

Step-by-step explanation:

a+b=12.

0.75a+1.05b=10.20

First, multiply 2 my 10.

75a+105b=1020.

Then multiply 1 by 75.

75a+75b=900.

Then subtract.

75a+105b=1020

75a+75b=900.

75a-75a+105b-75b=1020-900

30b=120

b=4

Substitute into (1)

a+4=12

a=8.

Hope this helps :)

The 60th term of the arithmetic sequence -29, -49, -69, ... is -1209.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

We can see that the common difference between any two consecutive terms is -20.

To find the 60th term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term, n is the number of the term, and d is the common difference.

In this case, we have:

a1 = -29

d = -20

n = 60

So, we can substitute these values into the formula:

a60 = -29 + (60-1)(-20)

a60 = -29 + 59(-20)

a60 = -29 - 1180

a60 = -1209

Therefore, the 60th term of the arithmetic sequence -29, -49, -69, ... is -1209.

To know more about sequence visit:

https://brainly.com/question/12246947

#SPJ1

output of the given input/output relationships is 36 and 25.

To illustrate a function, an input-output table can be used, as in the example below. The same function rule connects every pair of numbers in the table. To find each output number, multiply each input number (-value) by 3. ( -value).

Input-output analysis table: what is it?

The table of input-output analysis measures the flows of outputs from one industry as inputs into another (in rows) (in columns). In the input-output analysis paradigm, the original demand shift and its direct, indirect, and induced implications can be used to examine the overall economic impact of an event.

output = input +29

input= 7

output = input +29=7+29=36

input= -4

output = input +29= -4+29=25.

To know more about input-output visit:-

https://brainly.com/question/28352674

#SPJ1

Answer:

I think the IQR is 100

Step-by-step explanation:

You would have to find the first and third quartiles first. After that you would subtract the third quartile by the first to get the IQR

The lower bound of the 95% confidence interval is given as follows:

7.981 mm.

The level of confidence of the statement is of 95%.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 100 - 1 = 99 df, is t = 1.9842.

The parameters for this problem are given as follows:

\(\overline{x} = 8.1, s = 0.6, n = 100\)

Hence the lower bound of the interval is given as follows:

8.1 - 1.9842 x 0.6/10 = 7.981 mm.

More can be learned about the t-distribution at https://brainly.com/question/17469144

#SPJ4

Answer:58

Step-by-step explanation:

The  value of angle B is determined as 42 degrees.

The value of angle B is calculated by applying Sine rule as shown below;

Sin C / length C = Sin B / length B

From the given triangle,

C = 75 degrees

B = ?

length opposite angle C = 13 yd

Length opposite angle B = 9 yd

The  value of angle B is calculated as follows;

Sin B / 9 = Sin 75 / 13

13 sin B / 9 = Sin 75

13 sin B = 9 sin 75

sin B = 9/13 x sin 75

Sin B = 0.6687

B = arc sin (0.6687)

B = 42⁰

Learn more about sine rule here: https://brainly.com/question/20839703

#SPJ1

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

To learn more about Ratio:

https://brainly.com/question/13419413

The general solution of the system of differential equations d/dt x = [-37 -56; 30 45] is:
x(t) = c1*[-4t; t]*e^(5t) + c2*[-7t; t]*e^(3t), where c1 and c2 are constants determined by the initial conditions.

To find the general solution of the system of differential equations d/dt x = [-37 -56; 30 45], we can first find the eigenvalues and eigenvectors of the matrix:

det([-37-lambda -56; 30 45-lambda]) = (-37-lambda)(45-lambda) - (-56)(30) = lambda^2 - 8lambda - 15 = (lambda-5)(lambda-3)

So the eigenvalues are lambda_1 = 5 and lambda_2 = 3.

To find the eigenvectors, we can solve for the nullspaces of the matrices A-lambda_1*I and A-lambda_2*I, where I is the identity matrix and A is the coefficient matrix:

For lambda_1 = 5, we have:

[-42 -56; 30 40] * [x1; x2] = [0; 0]

Solving this system of equations, we get x1 = -4x2. So any vector of the form [x1; x2] = [-4t; t] is an eigenvector corresponding to lambda_1 = 5.

For lambda_2 = 3, we have:

[-40 -56; 30 42] * [x1; x2] = [0; 0]

Solving this system of equations, we get x1 = -7x2. So any vector of the form [x1; x2] = [-7t; t] is an eigenvector corresponding to lambda_2 = 3.

Therefore, the general solution of the system of differential equations d/dt x = [-37 -56; 30 45] is:

x(t) = c1*[-4t; t]*e^(5t) + c2*[-7t; t]*e^(3t)
where c1 and c2 are constants determined by the initial conditions.

The correct question should be :

Find the general solution of the system of differential equations d/dt x = [-37 -56; 30 45].

To learn more about differential equations visit : https://brainly.com/question/1164377

#SPJ11

Answer:

he owed $4

Step-by-step explanation:

Ben borrowed twenty dollars to spend, and 20 is above 16, so his savings is immediately gone. He owes four dollars because that's how much he needs even after using up his savings.

Answer:

B.

at most 199 miles

Step-by-step explanation:

To find how many miles Emily drove, we need to use the equation

Total cost = flat fee + miles driven * cost per mile

Substituting in the numbers

121 ≥ 21.50 + m * .5

121≥ 21.50 +.50m

Subtract 21.50 from each side.

99.50 ≥ .5m

Divide each side by .5

199 ≥m

Emily drove less than or equal to 199 miles

Answer:

Below.

Step-by-step explanation:

a. (x - √5)(x + √5)

= x(x + √5) - √5(x + √5)

= x^2 + √5x - √5x - 5

= x^2 - 5.

b. 10 - 3x^2

= (√10 - √3x) (√10 + √3x)

(a) Ahmad's factorization is correct.

(b)  (√10 - √3x)(√10 + √3x)

Given equation as

x² - 5 = (x - √5)(x + √5)

A Perfect Square is defined as when multiplying an integer by itself, we get a perfect square, which is a positive integer. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.

Solution of (a)

Taking RHS from the given equation

⇒ (x - √5)(x + √5)

⇒ x(x + √5) - √5(x + √5)

⇒ x² + √5x - √5x - 5

⇒ x² - 5.

So, RHS = LHS

Hence, Ahmad's factorization is correct.

Solution of (b)

⇒ 10 - 3x²

According to Ahmad's strategy  

⇒ √10(√10 + √3x) - √3x(√10 + √3x)

⇒ (√10 - √3x)(√10 + √3x)

Learn more about perfect square here:

https://brainly.com/question/385286

#SPJ2

Answer:

Below!

Step-by-step explanation:

Given square root:

\(\sqrt41\)

Let's note a few perfect square roots.

\(1 = \sqrt{1 \times 1} = \sqrt{1}\)

\(2 = \sqrt{2 \times 2} = \sqrt{4}\)

\(3 = \sqrt{3 \times 3} =\sqrt{9}\)

\(4 = \sqrt{4 \times 4} =\sqrt{16}\)

\(5 = \sqrt{5 \times 5} =\sqrt{25}\)

\(6 = \sqrt{6 \times 6} =\sqrt{36}\)

\(7 = \sqrt{7 \times 7} =\sqrt{49}\)

\(8 = \sqrt{8 \times 8} =\sqrt{64}\)

And so on...

When looking at the perfect square roots we identified, we can say that:

\(\sqrt{36} < \sqrt{41} < \sqrt{49}\)

Therefore,

\(6 < \sqrt{41} < 7\)

We can conclude that \(\sqrt{41}\) is between 6 and 7.

Let's check the squares of first 10 number

41 lies between 36 and 49

Hence