a particular fruit's weights are normally distributed, with a mean of 494 grams and a standard deviation of 8 grams. if you pick 17 fruits at random, what is the probability that their mean weight will be between 489 grams and 500 grams? (round answer to four decimal places)

Angle 1 and Angle 5 are the supplementary angle relationships.

acc to our question-

Therefore, ∠1 and ∠5 are supplementary angles.

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The explicit formula for the given sequence is an = 3n + 1. The tenth term is 31.

To find the explicit formula for the sequence, we observe that each term is obtained by adding 3 to the previous term. This indicates that there is a linear relationship between the terms.

Let's denote the nth term as an. We can express the nth term in terms of n as follows:

an = a1 + (n - 1)d,

where a1 is the first term, n is the term number, and d is the common difference between consecutive terms.

In our given sequence, the first term a1 is 4 and the common difference d is 3. Substituting these values into the formula, we have:

an = 4 + (n - 1)3,

an = 4 + 3n - 3,

an = 3n + 1.

Now, to find the tenth term, we substitute n = 10 into the explicit formula:

a10 = 3(10) + 1,

a10 = 30 + 1,

a10 = 31.

The explicit formula for the sequence is an = 3n + 1, and the tenth term is 31.

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Answer:

Step-by-step explanation:

A person invested $2,500 in an account growing at a rate allowing the money to double every 11 years. How long, to the nearest tenth of a year would it take for the

value of the account to reach $3,800?

The formula for exponential growth given as:

A(t) = Ao (1/2)^t/t½

A(t) = Amount after time t = $3,800

Ao = Initial amount invested = $2500

t = Time in years

t½ = Time it takes to double = 11 years

Hence,

3800 = 2500(1/2)^t/11

Divide both sides by 2500

3800/2500 = 2500(1/2)^t/11/2500

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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The length of major arc ACD in the circle with center D is given as (325/36)π feet

An equation is an expression that shows the relationship between two or more numbers and variables.

The length of major arc ACD = [(360 - 35) / 360) * 2π(10/2) = (325/36)π feet

The length of major arc ACD in the circle with center D is given as (325/36)π feet

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The length of the chord located 0.7 cm from the centre of a circular ring with a 2.5 cm radius is approximately 3.5 cm.

To calculate the length of the chord, we can use the following formula:

Chord Length = 2 x √(r^2 - d^2)

Where r is the radius of the circular ring and d is the distance between the chord and the centre of the circle.

In this case, r = 2.5 cm and d = 0.7 cm. Plugging these values into the formula, we get:

Chord Length = 2 x √(2.5^2 - 0.7^2) ≈ 3.5 cm (rounded to the nearest tenth)

Therefore, the length of the chord is approximately 3.5 cm. This hidden watermark technique is a simple but effective security measure that can help prevent counterfeiting or tampering with important documents. By incorporating a unique and difficult-to-replicate watermark, the jewellery company can protect its brand identity and ensure the authenticity of its official documents.

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If we have a 90 in class but get a zero that is worth 15 points, 0 will be that grade.

I know it takes 3 '15' to get 'C' from 0. Knowing this, getting zero is not recommended.

Here is the information we need to know to answer the question correctly.

For example:

3 allocations of 100 each .

3 x 15 = 45

45 / 3 = 15%

But now 0:

The same 3 allocations of 15 each AND these 0...

3 x 15 = 45

45 / 4 = 11.25%  which is a 25 point drop at zero.

Let's say we have 10 allocations of 15 each...

10 x 15 = 150

150 / 10 = 15%

But we have 15 allocations of the same Questions each, which is 0.

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Answer:

0.8 is the probability that a single detection system will detect a missile attack.

Step-by-step explanation:

Answer:

40, 284 omelets

Step-by-step explanation:

Given that:

In the first week of June = 10345 omelets were sold

In the second week = 1096 fewer omelets are sold than in week one

i.e.  10345 - 1096 = 9249 omelets

In the third week = 2000 more were sold than week one.

i.e. 2000 + 10345 = 12345 omelets

In the fourth week = 2000 fewer omelets were sold than week one.

i.e. 10345 - 2000 = 8345 omelets

Thus, the total quantity of Omelet sold in the month of June is:

= (10345 + 9249 + 12345 + 8345) omelets

= 40, 284 omelets

Net realizable value (NRV) is a term used in accounting to represent the estimated selling price of an asset minus the estimated costs of completing and disposing of the asset.

It is a conservative estimate of the asset's value and takes into account any anticipated costs or losses. NRV is not the same as fair value because fair value represents the price at which an asset could be exchanged between knowledgeable and willing parties in an arm's length transaction.

Net realizable value (NRV) is a concept used in accounting to determine the value of assets, particularly inventory or accounts receivable. It represents the estimated amount of cash the company expects to receive from the sale of an asset after deducting any direct costs associated with its sale.

These costs may include selling expenses, distribution costs, or any other costs incurred to make the asset ready for sale. NRV is a conservative estimate that reflects the expected realizable value of an asset in the current market conditions.

On the other hand, fair value represents the price at which an asset could be exchanged between knowledgeable and willing parties in an arm's length transaction.

Fair value considers market conditions, supply and demand factors, and other relevant information to determine the value of an asset. It does not take into account any specific costs associated with selling or disposing of the asset.

While net realizable value and fair value may share some similarities in terms of estimating the value of assets, they are not the same. NRV focuses on the estimated proceeds after deducting direct costs, while fair value considers the value in a hypothetical transaction between knowledgeable parties.

Therefore, the two concepts can provide different values for the same asset depending on the specific circumstances and considerations involved in their calculation.

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The final equation in the system, and it can be used to solve for either x or y is x + 1.5y = 3

The pivot operation is used to solve linear equations. The operation starts by selecting a pivot element from a matrix. This pivot element is usually the first non-zero element in the first column of the matrix. The pivot element is then multiplied by a scalar to create a new equation. This new equation is then added to or subtracted from the other equations in the system to eliminate the coefficient of the pivot element. This process is repeated until the system of equations is solved.

For example, consider the following system of equations:

2x + 3y = 6

4x + 6y = 12

The first non-zero element in the first column is 2, so this will be our pivot element. To use the pivot operation, we multiply 2 by a scalar and add this new equation to the other equation. Let's use the scalar 4. This gives us:

8x + 12y = 24

Now we subtract this equation from the other equation to eliminate the coefficient of the pivot element:

2x + 3y = 6 - 8x - 12y = 24

This leaves us with:

-6x - 9y = 18

We now have an equation with only one variable. To solve for this variable, we can divide both sides by -6, giving us:

x + 1.5y = 3

This is the final equation in the system, and it can be used to solve for either x or y.

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

≈ £ 4584.38

Step-by-step explanation:

Firstly, we need to find the number of litres that Mr. Leonard needs to fill up his tank:

We know that there is already 450 litres in the 1200 litre tank, so he must need 1200 - 450 = 750 litres.

I'm not quite sure what the variable p means, but I'm going to assume that p represents the number of litres and that 81.5 is the price per litre in pounds.

So:

Total price = 81.5p

Total price = 81.5(750)

Total price = £61125

We have to remember though that the question is asking for the discount and not the discounted price, so:

61125 × 7.5%

61125 × 0.075 = 4584.375

≈ £ 4584.38

Answer:

C

Step-by-step explanation:

In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.

The evolution of the function call (things '(11 -2 31)) is as follows:

(things '(11 -2 31)) -> (things '(-2 31)) -> (things '(31)) -> (things '()) -> '() the final result of the given call is '().

The given function is a recursive function called "things" that takes a list as input. It checks if the list is empty (null), and if so, it returns an empty list. Otherwise, it checks if the first element of the list (car x) is greater than 10. If it is, it adds 1 to the first element and recursively calls the "things" function on the rest of the list (cdr x). If the first element is not greater than 10, it subtracts 1 from the first element and recursively calls the "things" function on the rest of the list. The function then returns the result.

Now, let's see the evolution resulting from the call (things '(11 -2 31)):

1. (things '(11 -2 31))

  Since the list is not empty, we move to the next if statement.

  The first element (car x) is 11, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '(-2 31)).

2. (things '(-2 31))

  Again, the list is not empty.

  The first element (car x) is -2, which is not greater than 10, so we subtract 1 from it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '(31)).

3. (things '(31))

  The list is still not empty.

  The first element (car x) is 31, which is greater than 10, so we add 1 to it and recursively call the "things" function on the rest of the list.

  The recursive call is (things '()).

4. (things '())

  The list is now empty, so the function returns an empty list.

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(a) In matrix notation, the given functions can be expressed as:

1. W1 = ZMY

2. W2 = M2Y

(b) The expectation of the random vector W is:

E[W] = ZM1μ for W1, and

E[W] = M2μ for W2.

(c) The covariance matrix of W is:

Cov(W) = ZM1CM1T ZT + M2CM2T.

(a) In matrix notation, the given functions can be expressed as follows:

1. W1 = Z(y1 + y2 + y3 + y4)

2. W2 = (y1 + y2) - (y3 + y4)

To represent these equations in matrix form, we can define the following matrices and vectors:

Y = [y1, y2, y3, y4]T, where T denotes the transpose operation.

M1 = [0, 0, 0, 1]

M2 = [1, 1, -1, -1]

Then, we can rewrite the functions as:

1. W1 = ZMY

2. W2 = M2Y

(b) To find the expectation of the random vector W, we need to calculate E[W] using the linearity of expectations. Since Z is a constant, we have:

E[W1] = ZE[MY] = ZM1E[Y] = ZM1μ,

E[W2] = E[M2Y] = M2E[Y] = M2μ,

where μ is the mean vector of Y.

(c) To find the covariance matrix of W, we need to calculate Cov(W) using the property Cov(X) = E[(X - E[X])(X - E[X])T]. Thus, we have:

Cov(W1) = ZM1Cov(Y)M1T ZT,

Cov(W2) = M2Cov(Y)M2T.

To compute Cov(Y), we require the covariance matrix of Y, denoted as C. Therefore, we have:

Cov(W) = ZM1CM1T ZT + M2CM2T.

This represents the covariance matrix of the random vector W.

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Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

the anser and the

Step-by-step explanation:

Answer:

If im wrong just say but i think it B

Step-by-step explanation:

Polynomial function R is the difference of two​ degree-2 polynomial functions P and Q. the possible degree of Polynomial R is

A polynomial function is a function in an equation, such as the quadratic equation or the cubic equation, that only uses non-negative integer powers or only positive integer exponents of a variable.

A polynomial function of degree 2 is a quadratic function.

The degree of polynomials can only increase during multiplication, when polynomials are added or subtracted the result will have a degree which is at most the degree of the functions operated on.

Polynomial of degree zero are constants and hence is possible in the case

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complete question

Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees for R? Explain.

Select the correct choice below and fill in the answer box to complete your choice.

(Type an integer or a decimal. Use a comma to separate answers as needed)

A. The possible degree(s) is/are    because it must be equal to the greater of the degrees of P and Q.

B. The possible degree(s) is/are    because it must be equal to the lesser of the degrees of P and Q.

C. The possible degree(s) is/are     because it must be less than the degree of either P or Q

D. The possible degree(s) is/are    because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel

The following parts can be solved by the concept of Sets.

(a) KnF is definitely compact and closed.

(b) Fc U Kc is definitely closed, but not necessarily compact.

(c) K\F is definitely closed, but not necessarily compact.

(d) KnFc is definitely neither compact nor closed.

(a) KnF:

Since K is compact and F is closed, their intersection KnF is also closed, as the intersection of any finite number of closed sets is closed. Moreover, since K is compact, every open cover of K has a finite subcover, and thus, KnF is compact by the finite intersection property.

(b) Fc U Kc:

Fc is closed since the complement of a closed set is open, and Kc is closed since K is compact (and thus, closed) and the complement of a closed set is open. The union of two closed sets is also closed, so Fc U Kc is closed. However, Kc may not be compact, so Fc U Kc is not necessarily compact.

(c) K\F:

K\F is closed because it is the complement of the open set F. However, K\F may not be compact, as K itself may not be compact. For example, if K is the real line and F is the open interval (0,1), then K\F is not compact.

(d) KnFc:

KnFc is neither compact nor closed. To see that it is not compact, consider the sequence {x_n} in K given by x_n = (1 + 1/n, 0). This sequence converges to the point (1, 0), which is outside of K, but every term of the sequence is in K. Thus, K is not closed. On the other hand, since F is closed, Fc is open and contains K, so KnFc is not closed either.

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The equation in the slope-intercept form will be y=35-0.7x

What is slope intercept form?

Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. It is frequently referred to as the y = mx + b form.

How to find the slope-intercept form of a line using two-point?

slope=m=(y2-y1)/(x2-x1)

To find the y-intercept, use the slope and one of the points (b).

The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

on observing the graph we can notice that the line passes through the points (0,35) and (50,0)

thus

x1=0

y1=35

x2=50

y2=0

substituting in the formula,

m= (0-35)/(50-0)

m=-35/50

m= -7/10

calculating b

b=35-(-7/10)*0

b=35

Finally, the equation of the line can be written in the form y = b + m x,

\(y=35-\frac{7x}{10}\)

0r

y=35-0.7x

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The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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Similar to that, we must construct a new matrix with 4 states—o, 1, 2, or at least 3 sesames—in order to obtain 3 sesames. Now, the likelihood of transition is always 1/6, and the likelihood of remaining is the complement of 1. Sesame is where we start.

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Let's determine the change in length of the material.

Given:
Axial load (P) = 250 N
Young's modulus (E) = 2.70 GPa = 2.70 x 10^9 Pa (converting GPa to Pa)
Poisson's ratio (ν) = 0.4

To find the change in length, we can use the formula for deformation under axial load:

ΔL = (P * L) / (A * E)

In this formula, ΔL represents the change in length, L is the original length, and A is the cross-sectional area of the material. However, we do not have information on the original length (L) or the cross-sectional area (A) of the material in your question.

Without the values for the original length and cross-sectional area, we cannot calculate the change in length of the material using the given data. If you can provide these missing values, I would be happy to help you find the change in length of the material under the axial load.

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Answer:

\(accelaration = \frac{change \: in \: veloity}{time} \\ = \frac{15 - 10}{5} \\ = \frac{5}{5} \\ = 1 \frac{m}{ {s}^{ - 2} } \)

Answer: acceleration = 1 m/s²

Concept:

Here, we need to know how to calculate the acceleration of a body.

a = Δv / Δt = (v₂ - v₁) / (t₂ - t₁)

v = velocity

t = time

unit = m/s²

Solve:

Given information

v₁ = 10 m/s

v₂ = 15 m/s

Δt = 5 seconds

Given expression

a = (v₂ - v₁) / (t₂ - t₁)

Substitute values into the expression

a = (15 - 10) / 5

Simplify values in parentheses

a = 5 / 5

Simplify by division

\(\boxed{a=1}\)

Hope this helps!! :)

Please let me know if you have any questions

The value of f(11) for the recursive rule and an explicit rule is 149.

An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed amount (referred to as the common difference). The nth term is often indicated by an, while the first term of the series is typically marked by a1. The following formula is used to determine the nth term in an arithmetic sequence:

a = a1 + (n-1)d

where d is the common distinction. In mathematics and other disciplines, arithmetic sequences are frequently employed to represent circumstances in which the pace or degree of change remains constant.

The recursive and explicit rule for the arithmetic sequence is given as:

an = a1 + (n-1)d

From the given graph f(1) = 19 and common difference = 32 - 19 = 13

The recursive rule is:

f(n) = f(n-1) + 13

The explicit rule is:

f(n) = 19 + 13(n-1)

Now, f(11) is calculated as:

f(11) = 19 + 13(11-1) = 19 + 130 = 149

Hence, the value of f(11) for the recursive rule and an explicit rule is 149.

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