What is the second derivative of Sin²x​

Answers

Answer 1

The second derivative of sin2x is d/dx(sin 2x) = 2 cos 2x.

Answer 2

\(\textbf{First derivative:}\\\\~~\dfrac{d}{dx}(\sin^2 x) \\\\\\= 2 \sin x \cdot \dfrac{d}{dx} (\sin x)\\\\\\=2 \sin x \cos x\\\\\\=\sin 2x\\\\ \textbf{Second derivative:}\\\\\dfrac{d^2}{dx^2} (\sin^2 x)\\\\\\=\dfrac{d}{dx}(\sin 2x)\\\\\\=\cos 2x \dfrac{d}{dx}(2x)\\\\\\=2 \cos 2x\\\\\text{Hence, the second derivative of the given function is}~ 2 \cos (2x).\)


Related Questions

g What is the probability of a diffusing atom jumping from one site to another at 500C and 1000 C

Answers

The probability of a diffusing atom jumping from one site to another is influenced by temperature. It is typically described by the Arrhenius equation:

P = \(Ae^{(-Q/RT)}\)

Where:

P is the probability of a jump

A is the pre-exponential factor

Q is the activation energy

R is the gas constant

T is the absolute temperature in Kelvin

To calculate the probability at 500°C and 1000°C, we need to convert these temperatures to Kelvin:

\(T_{500C}\) = 500 + 273.15

= 773.15 K

\(T_{1000C}\) = 1000 + 273.15

= 1273.15 K

Assuming we have values for the pre-exponential factor (A) and activation energy (Q), we can substitute these values into the Arrhenius equation to calculate the probabilities at the given temperatures. However, without specific values for A and Q, we cannot provide a numerical answer.

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suppose quadrilaterals a and b are both squares. determine whether the statement below is true or false. select the correct choice.a and b are scale copies of one another.

Answers

The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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Simplify b(a + b) - a(a - b).

Answers

b(a+b)-a(a-b)
ab+b^2-a^2+ab

Answer
2ab+b^2-a^2

under the bounded rationality model of problem solving and decision making:

Answers

The statement that best summarizes the bounded rationality model of problem solving and decision making is 'Managers are comfortable making decisions without identifying all options'. Therefore, the correct option is B.

This is because the bounded rationality model recognizes that managers have limitations in their cognitive ability to process all information and alternatives, and therefore they use heuristics and simplified decision-making processes. However, this does not mean that they completely ignore options or do not consider the consequences of their decisions. Instead, they focus on the most relevant information and use their experience and judgment to make the best possible decision given the constraints they face.

Therefore, while option A) is partially correct, it does not capture the essence of the bounded rationality model. Option C) is too idealistic and implies that managers have unlimited time and resources to generate all possible options, which is not realistic. Option D) is not accurate as the bounded rationality model does not rely solely on statistical rules for decision making. Hence, the correct answer is option B.

Note: The question is incomplete. The complete question probably is: Which statement best summarizes the bounded rationality model of problem solving and decision making? A) Managers critically view the world as complex and multivariate. B) Managers are comfortable making decisions without identifying all options. C) Managers generate a wide array of decision options and select the one that meets all decision criteria. D) Managers follow statistical rules for decision making.

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What is a disadvantage of electron microscopes compared to light microscopes?

They do not have a very high power of resolution.
They cannot be used to view live specimens.
They can only be used by doctors.
They can only see surface details.

Answers

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

What is ""statistical conclusion validity""? what was the main threat to statistical conclusion validity discussed in class?

Answers

Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.

The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.

Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.

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what is the variable in 5 + 12w

Answers

the variable in this question would be........................ W

you are welcom

The variable in 5+12w is w

A bag contains 20 pink candies, 8 red candies, and 12
green candies. Without looking, Sarah pulls out a piece of
candy. Which color of candy is least likely to be pulled
out?

Answers

Answer:

The red marbles.

Step-by-step explanation:

It is because Red has the least amount of marbles, therefore it is most likely for you to not pull out a red marble.

A lighthouse has circumference 47.1m. Workout the diameter of the lighthouse.

Answers

Answer:

14.99m= d

Step-by-step explanation:

C = πd                       Use this equation to find the circumference of a circle

47.1 = πd                   Divide both sides by π

14.99= d

The three legs of a triangle measure 18, 46, and 3x-5. What are the possible values of x?
a.28 b.11 c. 45 d. 13

The three legs of a triangle measure 18, 46, and 3x-5. What are the possible values of x?a.28b.11c. 45d.

Answers

Answer:

9. 64

10. 21

11. A (I believe)

Step-by-step explanation:

The first two were simple math problems, however 11. was a bit more complicated and I used logic to find the numbers that best fit into the problem. I am not sure that it is the right answer and if I were you I would wait for someone else to answer this question.

The answer is going to be. A

Write the slope-intercept equation of a line that passes through the points (-2, 5) and (6, -4)

Answers

The slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

According to the question.

A line passes through the two points (-2, 5) and (6, -4).

As we know that, the slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

So, the slope of the line = -4 -5/(6 + 2) = -9/8

And, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4) is given by

y = (-9/8)x + b

Since, the line passes through (-2, 5) and (6, -4). So, both the points must statisfy the above equation.

⇒ 5 = (-9/8)(-2) + b

⇒ 5 = 9/4 + b

⇒ b = 5 - 9/4

⇒ b = (20 - 9)/4

⇒ b = 11/4

Therefore, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

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Consider the following. cos(x) + vy = 6 (a) Find y' by implicit differentiation. (b) Solve the equation explicitly for
y and differentiate to get y' in terms of x. y' (c) Check that your solutions to parts (a) and (b) are consistent by
substituting the expression for y into your solution for part (a). y'

Answers

(a) The derivative of y with respect to x, y', is given by -sin(x) + v(dy/dx) + y(dv/dx) = 0. (b) Solving the equation for y and differentiating gives y' = [(cos(x))(dv/dx)]/v^2. (c) Substituting the expression for y into the solution from part (a) confirms the consistency of the solutions.


To find the derivative of y with respect to x, we can use implicit differentiation. Let's go through the steps:

(a) To find y', we differentiate both sides of the equation cos(x) + vy = 6 with respect to x.
Differentiating cos(x) with respect to x gives us -sin(x).
For the term vy, we need to use the product rule. Let u = v and v = y.
Differentiating u = v with respect to x gives us du/dx = dv/dx.
So, differentiating vy with respect to x gives us v(dy/dx) + y(dv/dx).
Since we are differentiating with respect to x, the term dv/dx is the derivative of v with respect to x.
Now, we can put these results together to find y':
-sin(x) + v(dy/dx) + y(dv/dx) = 0

(b) To solve the equation explicitly for y, we rearrange the equation cos(x) + vy = 6 to isolate y.
Subtracting cos(x) from both sides gives vy = 6 - cos(x).
Dividing both sides by v gives y = (6 - cos(x))/v.
To find y' in terms of x, we need to differentiate y = (6 - cos(x))/v with respect to x.
Using the quotient rule, we have:
y' = [(v(0) - (6 - cos(x))(dv/dx))/(v^2)]
Simplifying, we get:
y' = [(cos(x))(dv/dx)]/v^2

(c) To check the consistency of our solutions, we substitute the expression for y from part (b) into the equation from part (a).
cos(x) + v[(6 - cos(x))/v] = 6
Canceling out v on the right side gives:
cos(x) + (6 - cos(x)) = 6
Simplifying, we have:
cos(x) - cos(x) + 6 = 6
0 + 6 = 6
This is a true statement, confirming the consistency of our solutions.
So, the final expression for y' is [(cos(x))(dv/dx)]/v^2.

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Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).​

Answers

Answer:

The domain of \(f(x)\) is \(Dom \{f(x)\} = \mathbb{R}-\{1\}\).

Step-by-step explanation:

Let \(f(5\cdot x ) = \frac{x-5}{5\cdot x-1}\), which is rearranged by algebraic means:

1) \(f(5\cdot x ) = \frac{x-5}{5\cdot x-1}\)  Given

2) \(f(5\cdot x) = \frac{x\cdot 1 - 5}{5\cdot x -1}\) Modulative property

3) \(f(5\cdot x) = \frac{5^{-1}\cdot (5\cdot x)-5}{5\cdot x -1}\) Existence of multiplicative inverse/Associative and commutative properties.

4) \(f(x) = \frac{5^{-1}\cdot x - 5}{x-1}\) Composition of functions.

5) \(f(x) = \frac{(5^{-1}\cdot x-5)\cdot (5\cdot 5^{-1})}{x-1}\) Existence of multiplicative inverse/Associative property.

6) \(f(x) = \frac{(x-25)\cdot 5^{-1}}{x-1}\)  Commutative, associative and distributive properties/\(a\cdot (-b) =-a\cdot b\)/Definition of subtraction

7) \(f(x) = (x-25)\cdot [5^{-1}\cdot (x-1)^{-1}]\) Definition of division/Associative property

8) \(f(x) = (x-25)\cdot (5\cdot x -5)^{-1}\)  \(a^{c}\cdot b^{c} = (a\cdot b)^{c}\)/Distributive property/\(a\cdot (-b) =-a\cdot b\)/Definition of subtraction

9) \(f(x) = \frac{x-25}{5\cdot x - 5}\) Definition of division/Result

The domain of a polynomial-based rational function consists in all values of the real set except values where denominator equals zero. The value of \(x\) such that rational function becomes undefined is:

1) \(5\cdot x - 5 = 0\)  Given

2) \(5\cdot (x-1) = 0\) Distributive property

3) \([5\cdot (x-1)]\cdot 5^{-1} = 0\cdot 5^{-1}\) Compatibility with multiplication

4) \((x-1)\cdot (5\cdot 5^{-1}) = 0\) Commutative and associative properties/\(a\cdot 0 = 0\)

5) \(x-1 = 0\) Existence of multiplicative inverse/Modulative property

6) \(x+[1+(-1)] = 1+0\) Compatibility with addition/Commutative and associative properties

7) \(x = 1\) Existence of additive inverse/Modulative property/Result

Hence, the domain of \(f(x)\) is \(Dom \{f(x)\} = \mathbb{R}-\{1\}\).

can you plz solve for x

can you plz solve for x

Answers

Answer:

90+36+7x+5=180 ( sum of all angles of a triangle)

131+7x=180

7x=180-131

x=49/7

hence the value of x=7

7x+5+36+90=180
7x+131=180(combined like term)
-131 -131
7x=49
7x/7= 49/7
X=7

in an examination
18 candidates passed math
17 candidates passed physics
11 candidates passed both subjects
find:the total number of candidates that passed math only
the total number of candidates that passed physics only
the total amount of candidates that sat for the examination​

Answers

Answer:

7 candidates passed maths only

6 candidates passed physics only

23 students sat in examination

Step-by-step explanation:

The figure is a parallelogram. True or false?​

The figure is a parallelogram. True or false?

Answers

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Which expression is equivalent to?

Which expression is equivalent to?

Answers

Answer:

The answer is D x(9 root y^2

I NEED HELP WITH MORE WORK I HATE MY GEOMETRY TEACHER THE TEXTBOOK TEACHES BETTER THAN HER LOL

idk how to increase given points but i can give 5 stars and thanks u dont have to answer all of them ^-^


What is the value of x in each figure?

I NEED HELP WITH MORE WORK I HATE MY GEOMETRY TEACHER THE TEXTBOOK TEACHES BETTER THAN HER LOLidk how
I NEED HELP WITH MORE WORK I HATE MY GEOMETRY TEACHER THE TEXTBOOK TEACHES BETTER THAN HER LOLidk how
I NEED HELP WITH MORE WORK I HATE MY GEOMETRY TEACHER THE TEXTBOOK TEACHES BETTER THAN HER LOLidk how

Answers

The figure to the left is 41. The middle figure is 59. The figure to the right is 15

8(q-2) = 44+5(2q-12)

Answers

The value of q in the given equation is 0.

This is a problem from an algebraic equation, we can solve this problem by following a few steps.

The given equation is,

8(q-2) = 44+5(2q-12)

Let's simplify the equation.

8(q-2) = 44+5(2q-12)

Or, 8q- 16= 44+ 10q- 60

Now, we have to organize the equation.

8q- 10q= 44- 60+ 16

Or, -2q = 0

Or, q = 0/2        ( dividing both side by 2 )

Or, q = 0

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The complete question is:

Find the value in the given equation,

8(q-2) = 44+5(2q-12)

what is the average total lung capacity (tlc) of an average man and how much is the average total lung capacity of a man like tom sietas?

Answers

The average total lung capacity (TLC) of an average man is around 6 liters. However, the average total lung capacity of a man like Tom Sietas cannot be determined precisely as it depends on factors like height, weight, age, and physical condition.

What is lung capacity? Lung capacity refers to the total amount of air that your lungs can hold. Lung capacity is measured by a spirometer, a machine that measures the amount of air that you can breathe in and out. The total lung capacity (TLC) is the sum of four different volumes that include the tidal volume, inspiratory reserve volume, expiratory reserve volume, and residual volume.What is Tom Sietas’ total lung capacity?Tom Sietas is a German freediver who set a world record for holding his breath for 22 minutes and 22 seconds underwater in 2012. He is known for his exceptional lung capacity and has been reported to have a total lung capacity of 14 liters, which is more than double the average TLC of an average man. However, this figure may vary depending on several factors like height, weight, age, and physical condition.

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A number f is rounded to the nearest integer is 27. Complete the upper and lower bounds of f

Answers

The upper bound of f is 28 and the lower bound is 27.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

When a number is rounded to the nearest integer, it can be either rounded up or down, depending on whether the decimal part is greater than or equal to 0.5 or less than 0.5, respectively.

In this case, since the number f is rounded to 27, we know that its decimal part must be between 0.5 and 0.0, inclusive.

To find the upper and lower bounds of f, we can consider the two possible cases:

Case 1: f is rounded up to 27

In this case, the decimal part of f is greater than or equal to 0.5. Let d be the decimal part of f. Then we have:

f = 27 + d (rounded up to the nearest integer)

Since d is greater than or equal to 0.5, we know that:

0.5 ≤ d < 1

Therefore, the upper bound of f is:

f ≤ 27 + 1 = 28

Case 2: f is rounded down to 27

In this case, the decimal part of f is less than 0.5. Let d be the decimal part of f. Then we have:

f = 27 + d (rounded down to the nearest integer)

Since d is less than 0.5, we know that:

0 ≤ d < 0.5

Therefore, the lower bound of f is:

f ≥ 27 + 0 = 27

therefore, the upper bound of f is 28 and the lower bound is 27.

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(a) . -3b ²+76b-25
(b). 4c ²+10c+4

Answers

Answer:I don’t understand

Step-by-step explanation:

y = ( x - 3 )² + 2

what is the vertex :
what is the Axis of Symmetry :
Does it opens up or down :
Is it Maximum or Minimum :
what is the Max/Min Value :
what is the y-intercept :
what is the Standard Form :

Answers

Answer:

19

Step-by-step explanation:

Which of the following choices presents a correct order of the processes of letter of credit payment listed below? I. Exporter receives the payment II. Exporter's bank ensures exporter that payment will be made III. Letter of credit issued to exporter's bank IV. Sales contract V. Shipment of goods a. IV -> III -> II -> I -> V b. IV -> III -> II -> V-> I
c. III -> IV -> II -> I-> V d. III -> IV -> II -> V-> I
e. II -> IV -> III -> I-> V

Answers

The correct order of the processes of letter of credit payment is:

IV -> III -> II -> V -> I. b

Explanation:

The first step is to establish a sales contract (IV) between the importer and the exporter.

Then, the importer's bank issues a letter of credit (III) to the exporter's bank, which guarantees payment to the exporter if the terms of the sales contract are met.

The letter of credit is in place, the exporter's bank ensures the exporter that payment will be made (II).

The exporter then ships the goods (V) to the importer.

The importer receives and verifies the goods, the exporter's bank receives payment from the importer's bank and the exporter receives the payment. (I)

Establishing a sales contract (IV) between the importer and the exporter is the first stage.

Then, if the conditions of the sales contract are satisfied, the importer's bank sends a letter of credit (III) to the exporter's bank, guaranteeing payment to the exporter.

The exporter's bank guarantees that payment will be made because the letter of credit is in place (II).

The items (V) are subsequently delivered to the importer by the exporter.

The exporter's bank gets payment from the importer's bank, the exporter receives the money when the importer receives and inspects the items. (I)

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in a park, 25 children play every day in the evening. 12 children like to play cricket, 8 like to play football and 4 like to play soccer. how many children in the park do not like to play either cricket or football or soccer?

Answers

There is only one child in the park who does not like to play either cricket or football or soccer.

Additionally, you should ignore any typos or irrelevant parts of the question .Here's how you can solve the given problem :Given that ,In a park, 25 children play every day in the evening.

12 children like to play cricket.8 children like to play football.4 children like to play soccer.Total children who like to play either of these three sports = \(12 + 8 + 4 = 24.\)

Therefore, the number of children who do not like to play any of these sports = Total number of children - Number of children who like to play any of these sports= \(25 - 24= 1\).

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The right rectangular prisms are similar. which statements are correct? check all that apply. the angles in the smaller prism measure 90 degrees. the perimeter of the rectangular bases changes by a factor of 2. the surface area changes by a factor of 8. the larger prism has twice the volume of the smaller prism. the area of the rectangular bases changes by a factor of 4.

Answers

The true statement about the right rectangular prisms include:

The angles in the smaller prism measure 90 degrees.The perimeter of the rectangular bases changes by a factor of 2.The rectangular bases changes by a factor of 4.

How to illustrate the prism?

It should be noted that a prism simply means a shape that has two identical shapes that face each other.

Here, the angles in the smaller prism measure 90 degrees and the perimeter of the rectangular bases changes by a factor of 2.

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You buy an 8-year $1,000 par value bond today that has a 6% yield and a 6% annual payment coupon. In 1 year promised yields have risen to 7%. Your 1-year holding-period return was

Answers

In one-year, the promised yields have risen to 7%, then the 1-year holding-period return was : (a) 0.61%.

The "Par-value" of the bond (face value) is = $1,000;

Coupon rate = 6% (annual payment coupon)

Yield at purchasing time is = 6%

Yield after 1 year = 7%

Step 1: Calculate the present value of the redeemable value:

We know that PVIF at 7% for 7 years is 0.623,

So, Present value of redeemable value = (Par value) × PVIF = $1,000 × 0.623 = $622.75,

Step 2: Calculate the present value of coupon payments:

Coupon payment = (Coupon rate)×(Par value) = 6% × $1,000 = $60,

We know that PVAF at 7% for 7 years is 5.389,

So, Present value of coupon payments = (Coupon payment) × (PVAF) = $60 × 5.389 = $323.36,

Step 3: Calculate the price of bond after 1 year:

Price of bond = Present value of redeemable value + Present value of coupon payments,

Substituting the values,

We get,

Price of bond = $622.75 + $323.36 = $946.11

Step 4: Calculate the 1-year holding-period return:

Holding return = (Price in next year + Coupon interest - Price in current year) / Price in current year,

Holding return = ($946.11 + $60 - $1,000) / $1,000

Holding return = $6.11 / $1,000

Holding return = 0.00611 = 0.61%.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

You buy an 8-year $1,000 par value bond today that has a 6% yield and a 6% annual payment coupon. In 1 year promised yields have risen to 7%. Your 1-year holding-period return was

(a) 0.61%

(b) -5.39%

(c) 1.28%

(d) -3.25%

3.
PROBLEM: Vincent started his piano practice at 5:15 PM. He ended his practice when the
minute hand moved 90 in the clock circle. What time did he finish?
MAKE SENSE:
MODEL and SOLVE:
5:15 + 90

Answers

Answer:

6:45

Step-by-step explanation:

(r(x) ; ; ) where x be a set; r(x) is the set of rvalued functions on x with the operation :r(x) r(x) ! r(x) of addition of functions and : rr(x) !r(x) of multiplication by scalar.

Answers

These operations allow for combining functions within the set r(x) using addition and scaling them using scalar multiplication.

It seems like you're describing a set, denoted as r(x), which consists of r-valued functions on the set x. The set r(x) has two operations defined on it: addition of functions and multiplication by scalar.

Let's denote the addition of functions in r(x) as ⊕ (circle plus) and the multiplication by scalar as ⊗ (circle times). Given two functions f and g in r(x):

Addition of functions:

The operation ⊕ (circle plus) combines two functions from r(x) and produces another function in r(x). It can be represented as:

f ⊕ g = h, where h is a function in r(x) resulting from adding f and g pointwise.

Multiplication by scalar:

The operation ⊗ (circle times) takes a scalar value and a function from r(x) and produces another function in r(x). It can be represented as:

c ⊗ f = j, where j is a function in r(x) resulting from multiplying each value of f by the scalar c.

These operations allow for combining functions within the set r(x) using addition and scaling them using scalar multiplication.

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Dr. Porterfield has a choice of bread (pink, purple), meat (ham, turkey, beef) and Cheese (American, Swiss, Portugues, Japanese) at a sandwich shop. What is the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese

Answers

Answer:

The probability is 0.08\(\overline 3\)

Step-by-step explanation:

The choice of bread Dr Porterfield has = Pink, purple

The number of types of breads = 2

The choices of meat = Ham, turkey, beef

The number of types of meat = 3

The choice of cheese = American, Swiss, Portuguese, Japanese

The number of types of cheese = 4

The probability of selecting purple bread from pink or purple = 1/2

The probability of selecting beef or turkey from the 3 choices of meat = 2/3

The probability of selecting Japanese cheese from the fourvtypes of cheese = 1/4

Therefore, the probability he will select a sandwich on purple bread with either beef or turkey and has Japanese cheese = (1/2) × (2/3) × (1/4) = 2/24 = 1/12 = 0.08\(\overline 3\)

Other Questions
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