Find the Shaded area

Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The value of k equivalent for the reaction expressed in scientific notation is 1.2 × 10⁻³. Then the correct option is D.

The equation in which chemically react with each other is called chemical reaction and if this reaction is shown mathematically then it is called a chemical equation.

The given chemical equation will be

\(\rm H_2 + F_2 \xrightarrow[equil.]{at\ 600} 2HF\)

[HF] = 5.82 x 10⁻² m

[H₂] = 8.4 x 10⁻³ m

[F₂] = 8.4 x 10⁻³ m

The value of k equivalent for the reaction expressed in scientific notation will be

\(\rm k_{eq} = \dfrac{8.4*10^{-3}*8.4*10^{-3}}{5.82*10^{-2}}\\\\k_{eq} = 1.2 *10 ^{-3}\)

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Answer:

D

Step-by-step explanation:

Edge 2022

Answer:

7918

Step-by-step explanation:

If you round Earth's diameter, I believe that it is 7,918 miles.

The Probability that at least one trip will last less than one hour =7/8

It refers to the ratio of favorable outcome to the total possible outcome.

The possibility of happening an event is probability.

Probability of staying in the alternative time for more than an hour is 8

each trip is likely to last for more than one hour so probability of at least one trip will last more than an hour =1/8

Now, probability of at least one trip will last less than one hour = 1-1/8

                                                                                                    7/8

hence, the result is 7/8

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The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

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

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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The given function is

f(x) = - 2|x+5| + 2

The x intercept is the value of x when f(x) = 0

Substituting f(x) = 0 into the function, we have

0 = - 2|x+5| + 2

Subtract 2 from both sides

0 - 2 = - 2|x+5| + 2 - 2

- 2 = - 2|x+5|

Divide both sides by - 2. It becomes

- 2/- 2 = - 2|x+5|/- 2

1 = |x+5|

x + 5 = 1 or x + 5 = - 1

x = 1 - 5 or x = - 1 - 5

x = - 4 or x = - 6

x intercepts are x = - 6, x = - 4

Writing the x intercepts as points, they are

(- 6, 0) and (- 4, 0)

The y intercept is the value of f(x) when x = 0

substituting x = 0 into the function, we have

f(0) = - 2|0+5| + 2

f(0) = - 2|5| + 2 = - 2(5) + 2 = - 10 + 2

f(0) = - 8

y intercept = (0, - 8)

The answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.To use a u-substitution to evaluate 0∫π/3 cos⁴xsinx dx, we will use the following steps:

Step 1: Choose a u-substitution that simplifies the integral. In this case, we will let u = cosx, which will allow us to rewrite the integral as 0∫1 u⁴(1-u²)du.

Step 2: Substitute the expression for u into the integral, and simplify. Using the substitution u = cosx, we have:

0∫π/3 cos⁴xsinx dx = 0∫1 u⁴(1-u²)du

Step 3: Evaluate the integral using standard integration techniques. Integrating u⁴(1-u²) with respect to u, we get:

∫ u⁴(1-u²)du = (1/5)u⁵ - (1/3)u³ + C

Step 4: Evaluate the integral from 0 to 1 using the substitution u = cosx. Substituting back, we have:

0∫π/3 cos⁴xsinx dx = (1/5)cos⁵x - (1/3)cos³x ∣₀ᴰ³/₃

Evaluating this expression at the limits of integration, we get:

(1/5)(cos⁵(π/3) - cos⁵(0)) - (1/3)(cos³(π/3) - cos³(0))

Simplifying, we get:

(1/5)(27/64 - 1) - (1/3)(3√3/8 - 1)

= -1/120 (27 - 64) - √3/24 + 1/3

= -5/24 - √3/24

Therefore, the answer to the integral 0∫π/3 cos⁴xsinx dx using a u-substitution is -5/24 - √3/24, or approximately -0.315.

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Answer: D x>-7 and x<4

Step-by-step explanation:

The compound inequality of 3x + 12 > -9 and 9x - 3 < 33 can be written as after simplification as x > -7  and x < 4, so option D is correct.

A relationship that compares two numbers or other mathematical expressions in an unfair manner is known as inequality. When comparing the sizes of two numbers on the number line, it is most usually utilized.

Given:

3x + 12 > -9 and 9x - 3 < 33

Solve the inequalities as shown below,

Subtract 12 on both sides and in the second inequality add 3 on both sides

3x + 12 > -9 and 9x - 3 < 33

3x + 12 - 12 > -9 -12 and 9x - 3 + 3 < 33 + 3

3x > -21 and 9x  < 36

x > -7  and x < 4

As can be seen that the value can be greater than -7 but less than 4,

Thus, x (-7, 4).

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Step-by-step explanation:

Not true....is they are perpendicular  the slopes have the relation

  m   and    - 1/m    where m is the slope

slope 2 has a perpendicular slope = - 1/2

Answer:

1

Step-by-step explanation:

1. expand the terms on the right side of the equation: 6=2y+4

2. subtract 4 from both side: 2=2y

3. divide both side by 2: 1=y

Answer:

y=1

Step-by-step explanation:

2(y+2)=6

2y+4=6

2y=6-4

2y=2

y=2/2

y=1

Answer:

B

Step-by-step explanation:

There is two wholes and one half.

Complete question is;

Roger and Rita each drive at a constant speed between Phoenix and San Diego. Each driver’s distance for the same section of the trip is displayed below. Who had a head start, and how many miles was the head start?

A) Rita had a 28-mile head start.

B) Roger had a 26-mile head start.

C) Roger had a 25-mile head start.

D) Rita had a 22-mile head start.

Answer:

A) Rita had a 28-mile head start.

Step-by-step explanation:

Let's assume that Roger travelled a distance of 60 miles

And that;

Rita travelled a distance of 32 miles

We are told that they travelled between Phoenix and San Diego.

Thus, it means that if they have different distances but covered same section of the trip, it means the one with higher distance started before the section of the trip.

Thus, it means that Rita had a head start of Roger since she covered only 32 miles.

Thus;

Rita had a head start of; 60 - 32 = 28 miles

Answer:

The 90% confidence interval

(74.71, 82.63)

Step-by-step explanation:

Confidence Interval Formula is given as:

Confidence Interval = μ ± z (σ/√n)

Where

μ = mean score

z = z score

N = number of the population

σ = standard deviation

The mean is calculated as = The average of their scores

N = 6 students

(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6

Mean score = 472/6

= 78.666666667

≈ 78.67

We are given a confidence interval of 90% therefore the

z score = 1.645

Standard Deviation for the scores =

s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1

= 5.886047531

= 5.89

The confidence interval is calculated as

= μ ± z (σ/√N)

= 78.67 ± 1.645(5.89/√6)

= 78.67 ± 3.9555380987

The 90% confidence interval

is :

78.67 + 3.9555380987 = 82.625538099

78.67 - 3.9555380987 = 74.714619013

Therefore, the confidence interval is approximately between

(74.71, 82.63)

There are 8,400 5-letter words that can be formed with 3 different Consonants, 2 different vowels, and contain the letter "b," even if they have no meaning.

To find the number of 5-letter words that can be formed with 3 different consonants and 2 different vowels, we need to consider the choices for each position in the word.

First, let's consider the placement of the consonants. Since we need to use 3 different consonants, we have 27 - 5 = 22 consonants to choose from. For the first position, we have 22 choices, for the second position, we have 21 choices (as we've used one consonant already), and for the third position, we have 20 choices (as we've used two consonants already).

Next, let's consider the placement of the vowels. Since we need to use 2 different vowels, we have 5 vowels to choose from. For the fourth position, we have 5 choices, and for the fifth position, we have 4 choices (as we've used one vowel already).

To find the total number of words, we multiply the number of choices for each position:

Total number of words = (Number of choices for consonants) * (Number of choices for vowels)

                    = 22 * 21 * 20 * 5 * 4

                    = 61,600

Therefore, there are 61,600 5-letter words that can be formed with 3 different consonants and 2 different vowels, even if they have no meaning.

To find the number of these words that contain the letter "b," we need to consider the placement of the letter "b" among the consonants. Since we have already chosen 3 different consonants, the letter "b" can only be placed in one of these positions. Therefore, the number of words that contain the letter "b" is equal to the number of choices for the other consonants and vowels.

Number of words with the letter "b" = (Number of choices for consonants without "b") * (Number of choices for vowels)

                                 = 21 * 20 * 5 * 4

                                 = 8,400

Therefore, there are 8,400 5-letter words that can be formed with 3 different consonants, 2 different vowels, and contain the letter "b," even if they have no meaning.

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Answer:  0.000039

Step-by-step explanation: i us calculator

Answer:

0.000039.

Step-by-step explanation:

3.9 / 100,000

Move the decimal point 5 places to the left ( as there are 5 0's in 100,000)

filling in the zeroes as you move alomg.

So its  0.000039

Answer:

7.937005

Step-by-step explanation:

You can't simplify it, but you can solve it.

By replacing each hexadecimal digit with its corresponding four binary digits, we obtain the binary representation of n.

To show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits, we need to understand the number systems involved and the relationship between them.

The hexadecimal system is a base-16 number system, while the binary system is a base-2 number system. In the hexadecimal system, digits from 0 to 9 represent values from 0 to 9, and letters A to F represent values from 10 to 15. In the binary system, digits can only be 0 or 1.

To demonstrate the relationship between the two systems, let's take a positive integer and examine its hexadecimal and binary representations.

Let's consider a positive integer n and its hexadecimal representation:

n = (xn xn-1 ... x3 x2 x1 x0) base-16

In the hexadecimal representation, each digit represents a power of 16. The rightmost digit (x0) represents \(16^{0}\), the next digit (x1) represents \(16^{1}\), the next digit (x2) represents \(16^{2}\), and so on.

To obtain the binary representation of n, we can translate each hexadecimal digit into a block of four binary digits. The correspondence between the hexadecimal and binary digits is as follows:

Hexadecimal Binary

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

A 1010

B 1011

C 1100

D 1101

E 1110

F 1111

By replacing each hexadecimal digit with its corresponding four binary digits, we obtain the binary representation of n. Each hexadecimal digit represents a block of four binary digits, which aligns with the binary system's base-2 nature.

Therefore, we have shown that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.

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Answer:

D. 0.00003471

Step-by-step explanation:

The values of  unknown variable on equating the matrices are w =±9 ,

k =-6 , f= -7

A matrix is arrangement of numbers in the form of rows and columns  such that a rectangular array is formed . if number of rows is m and number if columns is n then we say that the matrix is of order m*n .

Let [ a  b ] and [ c   d ] be two 1*2 matrices

Equating these two matrix [ a  b ]  =  [ c   d ] means that entries of both the matrix are identical a=c  and b =d , entries at same places (row and column wise ) in both matrix have to be identical.

Given that  two matrices [ -12  -w²  2f  3 ] and [ 2k  -81  -14  3 ] are equal and we need to find the unknown variables w, f, k

If   [ -12  -w²  2f  3 ]  =   [ 2k  -81  14  3 ] then their terms are identical

 AS  -12 = 2k

Dividing both sides by 2

⇒ k = -12/2 = -6

As - w² = -81

⇒ w² = 81

Taking square root  both sides

⇒ w = ± 9

As  2f = -14

Dividing both sides by 2

⇒ f = -14/2 = -7

The values of the variable w, f, k after equating both the matrices are

k = -6 , w = ±9 , f = -7

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Choice B) Jacket world has the better deal.

Choice D) Both stores are offering a 25% discount on the jacket.

Choice E) The difference in sale prices at the two stores is $7.50

===========================================================

Explanation:

25% = 0.25

25% of $190 = 0.25*190 = 47.50

190 - 47.50 = 142.5

This indicates the price at Jacket World is $142.5 instead of $150

Therefore, choice A is false.

---------------------

Choice B on the other hand is true because $142.50 at Jacket World is a lower price compared to $150 at Clothes Are Us. Jacket World has the better deal.

---------------------

Because choice B was shown to be true, there's no way choice C can be true as well. Otherwise, we'd have a contradiction. So we can rule out choice C.

---------------------

Let's find the percentage discount for Clothes Are Us.

The original price is $200 and its sale price is $150. So you save 200-150 = 50 dollars.

Divide that over the original price to find the discount: 50/200 = 0.25 = 25%

Therefore, Clothes Are Us has the same discount percentage as Jacket World. Both have a 25% discount. Choice D is true.

---------------------

Comparing the two sale prices of $150 (Clothes Are Us) and $142.50 (Jacket World), the difference in price is 150-142.50 = 7.50; this means choice E is a true statement.

Answer:

Samee

Step-by-step explanation:

Answer:

TIAGZ

and Billie Eilish

DABABY

Step-by-step explanation:

Answer:

Answer is D.

\(y=9(\frac{1}{3} )^x\\ y=9(\frac{1}{3} )^2\\\\y=1\\\\\)

Step-by-step explanation:

The road distance between Wrexham and Corwen can be found to be 21 miles

The miles in total that Elyas travelled to and from work each week would be 270 miles.

The road distance between Wrexham and Corwen can be found at the intersection between Wrexham and Corwen on the table which is 21 miles.

The miles between Mold and Oswestry by the same method would be 27 miles. This means that the total miles traveled by Elyas :

= 27 miles x 2 going and coming x 5 days a week

= 270 miles

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Answer:1=a, 2=b, 3=c

Step-by-step explanation:

just smart like that

Answer:

(not D) unknown letter, but graph shown in pic

Step-by-step explanation:

i myself am not too sure how this works but i had a friend who does know help me out (he doesnt have brainly)

heres what the correct answer should look like

The derivative of f in the direction of u = <4, 4, 4> is 48√3.

The derivative of a function represents the rate at which the function changes with respect to its independent variable(s). It measures the slope or steepness of the function at a specific point.

To find the directions in which the function increases and decreases most rapidly at point P0(1, 1, 1), we need to calculate the gradient vector (∇f) at that point and identify its components. The gradient vector will point in the direction of the steepest increase in the function.

Given the function f(x, y, z) = 2ln(xy) + 2ln(yz) + 2ln(xz), we can calculate the partial derivatives with respect to each variable:
∂f/∂x = 2/y + 2/z
∂f/∂y = 2/x + 2/z
∂f/∂z = 2/x + 2/y

Now, we evaluate the partial derivatives at point P₀(1, 1, 1):
∂f/∂x = 2/1 + 2/1 = 4
∂f/∂y = 2/1 + 2/1 = 4
∂f/∂z = 2/1 + 2/1 = 4

So, the gradient vector at P0(1, 1, 1) is (∇f) = <4, 4, 4>. The components of this vector indicate that the function increases most rapidly in all directions at that point.

To find the derivatives of the function in those directions, we can take the dot product of the gradient vector (∇f) with a unit vector in each direction at that point.
u = <4, 4, 4> / √(1² + 1² + 1²) = <4/√3, 4/√3, 4/√3>

To find the derivative of f in the direction of u, we take the dot product:
∇f · u = <4, 4, 4> · <4/√3, 4/√3, 4/√3> = 16/√3 + 16/√3 + 16/√3 = 48√3

So, the derivative of f in the direction of u = <4, 4, 4> is 48√3.

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There would be no change in the interval width that is Option-C is correct when the sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.

Given that,

The sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.

We have to find how will this impact the confidence interval's width.

We know that,

Therefore, There would be no change in the interval width that is Option-C is correct when the sample mean was discovered to be 37 miles rather than the first reported 35 miles after a second run of the data.

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The solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Solve as shown below,

(a) 8 × 3 = 24

(b) –7 × 5 = -35

(c) –6 × (–9) = -(-54) = 54

(d) 8 ÷ (–2) = 8 × 1 / (-2) = - 4

(e) –24 ÷ (–3) = -24 ×  1 / (-3) = 8

(f) –36 ÷ 6 = -36 × 1 \ 6 = -6

Therefore, the solution to the problem are 8 × 3 = 24, –7 × 5 = -35, –6 × (–9) = 54, 8 ÷ (–2) = -4, –24 ÷ (–3) = 8, –36 ÷ 6 = -6.

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Answer:

C

Step-by-step explanation:

big number

Answer:

D

Step by step explanation:

08*10^2=800

4,000,000/800=5,000