Using the Empirical Rule, approximate the following percentages for Parts A - E.
The distribution of weights of newborn babies in one region is bell-shaped with a mean of 3000 grams and standard deviation of 500 grams. For all questions below, show all relevant work.


Part A :Approximately, what percentage of newborn babies weigh more than 3000 grams?
Part B : Approximately, what percentage of newborn babies weigh more than 2000 grams?
Part C : Approximately, what percentage of newborn babies weigh less than 4000 grams?
Part D : Approximately, what percentage of newborn babies weigh between 2000 and 4000 grams?
Part E : What is the range of birth weights that would contain the middle 68% of newborn babies' weights?

The perimeter of the Rhombus ABCD that is given above would be = 60.

To calculate the perimeter of the rhombus, the following steps needs to be taken as follows:

But;

AE = a = 9

BE = b = 12

AB = c = ?

Using the Pythagorean formula;

C² = a²+b²

C = 9²+12²

= 81+144

= 225

c = √225 = 15

The perimeter = 4× 15 = 60

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Among the given four countries the one which has the largest land area is Algeria, and the total land area in k[tex]m^2[/tex] of the four countries is 5017000 k[tex]m^2[/tex].

Given the land area of Ethiopia is 1.13×[tex]10^6[/tex] k[tex]m^2[/tex] = 1130000 k[tex]m^2[/tex].

The land area of Algeria is 2.38×[tex]10^6[/tex] k[tex]m^2[/tex] = 2380000k[tex]m^2[/tex].

The land area of Nigeria is 9.24×[tex]10^5[/tex] k[tex]m^2[/tex] =924000k[tex]m^2[/tex].

The land area of Kenya is 5.83×[tex]10^5[/tex] k[tex]m^2[/tex] =583000 k[tex]m^2[/tex].

Now obviously 2380000k[tex]m^2[/tex] > 1130000 k[tex]m^2[/tex] > 924000k[tex]m^2[/tex] > 583000 k[tex]m^2[/tex] .

Hence, Algeria has the largest land area.(a)

Total land area will be, (1130000+2380000+924000+583000 )k[tex]m^2[/tex] = 5017000 k[tex]m^2[/tex].

Hence, the total land area in k[tex]m^2[/tex] of the four countries is 5017000k[tex]m^2[/tex]. (b)

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By calculating this average, we can approximate the slope of the tangent line to the curve at P (16, 7).

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates (change in y) divided by the difference in x-coordinates (change in x) between the points P and Q.

For x = 16.1:

Coordinates of Q: (16.1, √(16.1) + 3)

Slope of PQ = (y-coordinate of Q - y-coordinate of P) / (x-coordinate of Q - x-coordinate of P)

Slope of PQ = (√(16.1) + 3 - 7) / (16.1 - 16)

Slope of PQ = (√(16.1) - 4) / 0.1

Similarly, we can find the slope of PQ for the other given values of x:

For x = 16.01: Slope of PQ = (√(16.01) - 4) / 0.01

For x = 15.9: Slope of PQ = (√(15.9) - 4) / (-0.1)

For x = 15.99: Slope of PQ = (√(15.99) - 4) / (-0.01)

Based on the given values, we can observe that as x approaches 16, the values of the slopes of PQ get closer to a certain value. This suggests that the slope of the secant line PQ tends to converge to a specific value as x approaches 16.

Therefore, we can infer that the slope of the tangent line to the curve at P (16, 7) is the limit of the slopes of PQ as x approaches 16. To get an estimate of the slope of the tangent line, we can take the average of the slopes of PQ for x = 16.1 and x = 15.9:

Slope of the tangent line at P ≈ (slope of PQ for x = 16.1 + slope of PQ for x = 15.9) / 2.

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The width of the walkway around the community garden is 19.5 feet.

To find the width of the walkway around the community garden, we can subtract the area of the garden from the total area of the garden and walkway combined.

Let's denote the width of the walkway as 'w'.

The area of the garden is given as 12 feet wide by 15 feet long, so its area is:

Area of the garden = 12 feet * 15 feet = 180 square feet

The total area of the garden and walkway combined is given as 648 square feet.

Area of the garden and walkway = 648 square feet

Now, we can set up an equation to find the area of the walkway:

Area of the walkway = Area of the garden and walkway - Area of the garden

Area of the walkway = 648 square feet - 180 square feet

Area of the walkway = 468 square feet

Since the walkway surrounds the garden on all sides, we can calculate its width by dividing the area of the walkway by the length of the garden plus twice the width of the walkway:

Width of the walkway = Area of the walkway / (Length of the garden + 2 * Width of the walkway)

Width of the walkway = 468 square feet / (15 feet + 2w)

Now we can substitute the given values and solve for 'w':

468 square feet / (15 feet + 2w) = w

Multiply both sides by (15 feet + 2w):

468 square feet = w(15 feet + 2w)

Rearrange the equation:

2w^2 + 15w - 468 = 0

Now, we can solve this quadratic equation for 'w' using factoring, completing the square, or the quadratic formula.

In this case, factoring is the most convenient method:

(2w - 39)(w + 12) = 0

Setting each factor to zero gives us two possible solutions:

2w - 39 = 0 or w + 12 = 0

Solving each equation for 'w' gives us:

2w = 39 or w = -12

w = 39/2 = 19.5

Since the width cannot be negative, the width of the walkway is 19.5 feet.

Therefore, the width of the walkway around the community garden is 19.5 feet.

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The LU factorization of the matrix is:

[-5 0 4]                     [1   0   0] [ -5 0 4 ]

[10 2 -5]      =     [1  0  0] [ 0  2  3 ] [ 0  2 3 ]

[10 10 16]                   [-2 5/2 1] [ 0  0 9 ]

To compute the LU factorization of a matrix, we need to decompose it into an upper triangular matrix U and a lower triangular matrix L, where L is a unit lower triangular matrix (i.e., its diagonal entries are all 1).

We begin with the given matrix:

[-5 0 4]

[10 2 -5]

[10 10 16]

First, we use row operations to transform the matrix into an upper triangular matrix. Let's use Gaussian elimination to reduce the matrix to row echelon form.

Let's add 2 times the first row to the second row to eliminate the entry in the (2,1) position:

[-5 0 4]

[0 2 3]

[10 10 16]

Next, let's add 2 times the first row to the third row to eliminate the entry in the (3,1) position:

[-5 0 4]

[0 2 3]

[0 10 24]

subtract 5 times the second row from the third row to eliminate the entry in the (3,2) position:

[-5 0 4]

[0 2 3]

[0 0 9]

We now have an upper triangular matrix U. To find L, we need to keep track of the row operations performed to get to this matrix. Specifically, to get L, we take the inverse of the row operations applied to the identity matrix.

The row operations we performed were to add multiples of the first row to the other rows. So, to get L, we apply the inverse row operations and write the multipliers as entries in L below the diagonal:

[1   0   0]

[-2  1   0]

[-2  5/2 1]

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Answer:

∠ 1 = 110° , ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is

6x + 20 + 4x + 10 = 180

10x + 30 = 180 ( subtract 30 from both sides )

10x = 150 ( divide both sides by 10 )

x = 15

Then

∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°

∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°

The domain of the function C(m) is the set of all possible values for the number of minutes used, m. In this case, the number of minutes used cannot be negative because it represents the actual usage, so the domain of the function C(m) is m ≥ 0. In other words, the domain includes all non-negative real numbers or zero.

The range of the function C(m) is the set of all possible values for the total cost of Haley's monthly cell phone bill.

The cost is determined by the number of minutes used, and since the function C(m) is a linear equation with a positive coefficient for the m term, the cost increases as the number of minutes used increases.

Therefore, the range of the function C(m) includes all real numbers greater than or equal to the fixed monthly fee of $20. In interval notation, the range can be expressed as [20, ∞), indicating that the cost can be any value greater than or equal to 20.

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The inequality is x < -1

An inequality is a mathematical statement that represents the relation between two expressions that are not equal.

Symbol used to denote inequalities are signs such as

≠ ‘not equal to’,

> ‘greater than’,

< ‘less than’

≥ ‘greater than or equal to’

≤ ‘lesser than or equal to’

From the given diagram, the circle is resting at -1 but the circle is not shaded. This means that -1 is not included in the inequality.

Furthermore, the arrow is pointing towards the left side of the number line which means only numbers lesser than -1 (towards the left of -1) are included. Therefore, the inequality is

x < -1

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The probability of exactly 15 out of 25 randomly selected adult smartphone users using their smartphones in meetings or classes is calculated using the binomial probability formula.

The formula is given by:

P(X = k) = (nCk) * [tex]p^k * (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials or selections,

k is the number of successes,

p is the probability of success in a single trial,

(1 - p) is the probability of failure in a single trial,

nCk is the binomial coefficient, also known as "n choose k."

In this case, the values are:

n = 25 (total number of adult smartphone users selected)

k = 15 (number of smartphone users using their smartphones in meetings or classes)

p = 0.41 (probability of using smartphones in meetings or classes)

Using these values in the formula, we can calculate the probability:

P(X = 15) = (25C15) * 0.41^15 * (1 - [tex]0.41)^{(25 - 15)[/tex]

Calculating the binomial coefficient:

(25C15) = 25! / (15! * (25-15)!) = 3268760

Substituting the values:

P(X = 15) = 3268760 * 0.41^15 * (1 - 0.[tex]41)^{(25 - 15)[/tex]

Calculating this expression will give you the final probability.

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Answer:

Step-by-step explanation:

They are wanting to find out what the size of the state is.  I look at the units.

Population density is in People/mi²

Population is people

and they are looking for _____ mi²

Population density = population / size of state

Let's rework that equation so we can solve for size of state

size of state = population/population density

size of Texas = (29145505 people) / (108.51 people/mi²)

size of Texas = 268597 mi²

We can conclude that point A is located at the origin (0, 0).

There is only one possible location for point A is at the origin.

Let's revisit the given information to determine the possible location of point A.

Point C has the same y-coordinate as point B.

This means that the y-coordinate of point C is equal to the y-coordinate of point B.

The distance between point B and point C is equal to the distance between point C and the y-axis.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point C and the y-axis is also "d".

Point A has the same x-coordinate as point C.

This implies that the x-coordinate of point A is equal to the x-coordinate of point C.

The distance between point A and point C is twice the distance between point B and point C.

Let's assume the distance between point B and point C is represented by "d".

According to the information given, the distance between point A and point C is 2d.

Based on this information, we can analyze the relationships between the points:

Since the distance between point B and point C is equal to the distance between point C and the y-axis, we can infer that point B lies on the y-axis.

The x-coordinate of point B is 0.

As point C has the same y-coordinate as point B, the y-coordinate of point C is also determined to be the same as the y-coordinate of point B.

Since point A has the same x-coordinate as point C, the x-coordinate of point A will also be 0.

The distance between point A and point C is twice the distance between point B and point C.

As the distance between point B and point C is "d", the distance between point A and point C is 2d.

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The distance travelled by the roller coaster to get on top is 415.8 ft.

The Distance travelled by the roller coaster on the downhill track is 212.6 ft.

The Pythagorean Theorem describes the relationships between the sides of a right triangle. The square of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the two sides.

The hypotenuse during uphill is;

Hypotenuse = √(360² + 208²)

Hypotenuse = 415.8 ft

The hypotenuse during downhill can be calculated as follows:

Hypotenuse = √(44² + 208²)

Hypotenuse = 212.6 ft

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Complete question is;

Suppose a roller coaster climbs 208 feet higher than its starting point, moving horizontally 360 feet. When it comes down, it moves horizontally 44 feet.

a. How far will it travel to get to the top of the ride?

b. How far will it travel on the downhill track?

To change fractions with a denominator of 2 to whole numbers, multiply each fraction by 2, because multiplying both the numerator and denominator by the same number results in an equivalent fraction with a denominator of 1, effectively converting it to a whole number.

To change a list of inputs that are fractions with a denominator of 2 to whole numbers, we can apply the rule of multiplying each fraction by 2. The reason for this is based on the fundamental concept of equivalent fractions.

When we multiply a fraction by a certain number, we are essentially multiplying both the numerator and denominator by that number. In this case, since we want to convert fractions with a denominator of 2 to whole numbers, we need to find a number that, when multiplied by 2, results in a denominator of 1.

By multiplying each fraction in the list by 2, the denominator will become 1 (2 multiplied by 2 is 4, which simplifies to 1).

Since any number divided by 1 is equal to that number itself, the fractions will be converted to whole numbers.

For example, let's consider the fraction 3/2.

When we multiply it by 2, we get (3/2) [tex]\times[/tex] 2 = (32)/(22) = 6/4.

Simplifying 6/4 gives us 3/2 again, but now the denominator is 1.

Therefore, by applying the rule of multiplying each fraction by 2, we can convert a list of fractions with a denominator of 2 to whole numbers.

This rule works because it effectively cancels out the denominator of 2, resulting in equivalent fractions with a denominator of 1, which are whole numbers.

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/ mean do or does when a 3rd person is present

The probability that it will rain on exactly three of the six days they are there is 0.242.

The given information can be represented as follows:P(Rain on any given day) = 4/9

The hiking club is camping for 6 days and the probability of rain on any given day is given as 4/9.

We are to find the probability that it will rain exactly three days out of the six days they are camping.

The number of ways that it can rain exactly three days out of the six days is given by:C(6,3) = 6!/(3!3!) = 20The probability of rain for any one of the 20 ways of getting exactly three days of rain is:

P(Rain on three days and no rain on three days) = (4/9)³(5/9)³

The probability of getting exactly three days of rain out of six is given by: P(exactly three days of rain) = 20(4/9)³(5/9)³ = 0.242, rounded to the nearest thousandth.

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The previous year's total revenue for the small business was approximately $25,130.43.

The total revenue of the small business the previous year can be calculated by finding the value that is 15% more than the revenue of $28,900 this year.

To determine the previous year's revenue, we can set up the equation:

Previous Year's Revenue + 15% of Previous Year's Revenue = $28,900

Let's solve the equation to find the previous year's revenue:

Let x be the previous year's revenue.

x + 0.15x = $28,900

Combining like terms, we have:

1.15x = $28,900

Dividing both sides by 1.15, we get:

x = $28,900 / 1.15 ≈ $25,130.43

Therefore, the previous year's total revenue for the small business was approximately $25,130.43.

We set up the equation by adding 15% of the previous year's revenue to the previous year's revenue. This is done to find the total revenue that is 15% more than the previous year's revenue. By solving the equation, we find that the previous year's revenue was approximately $25,130.43.

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Answer: 6 cookies

Step-by-step explanation:

4.5 dozen is 54 cookie

Dividen 54 by the 9 parents is 6 cookie so each partner need to make at least 6 cookie

Apart from division or a fraction, the symbol '/' can also represent a ratio or indicate a relationship between two quantities.

In addition to representing division or a fraction, the symbol '/' can have different meanings depending on the context in which it is used. Here are a few common interpretations of the '/' symbol:

Ratio: The '/' symbol can indicate a ratio between two quantities. For example, if we say the ratio of boys to girls is 3/2, it means there are three boys for every two girls.

Per: The '/' symbol can be used to express "per" or "each." For instance, when we see a speed limit sign that says "60 km/h," it means "60 kilometers per hour."

Similarly, in sports statistics, we might see "10 goals/season," which means an average of 10 goals per season.

Probability: In probability theory, the '/' symbol can represent the probability of an event.

For example, if we say the probability of rolling a six on a fair die is 1/6, it means there is a one in six chance of rolling a six.

Quotient: While '/' is commonly used to represent division, it specifically represents the quotient in mathematical expressions.

For instance, in the expression 6/3, '/' indicates that we are finding the quotient of 6 divided by 3, which is equal to 2.

Symbolic Representation: In certain cases, the '/' symbol can be used as a shorthand or symbol to represent a concept or operation in specific fields or contexts.

For instance, in computer programming, '/' is often used to indicate file path or directory structure.

It is important to consider the context in which '/' is used to determine its meaning, as it can vary across different disciplines and applications.

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Answer:

The coordinates of point D are (-7, -5).

Step-by-step explanation:

Since ABCD is a rectangle, opposite sides are parallel and have the same length. We are given points A(-7, -2), B(3, -2), and C(3, -5).

We can find the length and direction of the sides AB and BC:

AB = B - A = (3 - (-7), -2 - (-2)) = (10, 0)

BC = C - B = (3 - 3, -5 - (-2)) = (0, -3)

Now, we can find the coordinates of point D by moving along the direction of side BC from point A:

D = A + (direction of BC) = (-7, -2) + (0, -3) = (-7, -5)

So, the coordinates of point D are (-7, -5).

By rearranging the equation M - q = (1/6)g, we can isolate the variable g and find that g = 6M - 6q.

To solve the equation M - q = (1/6)g for g, we can isolate the variable g by moving the terms involving g to one side of the equation.

Let's rearrange the equation step by step:

Start with the given equation: M - q = (1/6)g

To isolate the term involving g, we can add q to both sides of the equation: M - q + q = (1/6)g + q

Simplify the equation: M = (1/6)g + q

Next, we can subtract q from both sides of the equation: M - q = (1/6)g + q - q

Simplify further: M - q = (1/6)g

To isolate g, we can multiply both sides of the equation by 6: 6(M - q) = 6(1/6)g

Simplify the equation: 6M - 6q = g

Therefore, the solution for g is g = 6M - 6q.

In summary, by following the steps outlined above, we have solved the equation M - q = (1/6)g for g, and the solution is g = 6M - 6q.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

The amount of money increases by $125,000 due to the decrease in the reserve rate. The correct answer is B. It increases the amount by $125,000.

When the Federal Reserve decreases the reserve rate, it allows banks to hold a smaller portion of their deposits as reserves and lend out a larger portion. This change stimulates lending and increases the money supply in the economy through the process of fractional-reserve banking.

In this scenario, the initial deposit of $15,000 can be multiplied by the money multiplier, which is the reciprocal of the reserve rate. Initially, with a reserve rate of 6%, the money multiplier is 1/0.06 = 16.67. Therefore, the initial deposit can lead to a maximum increase in the money supply of $15,000 x 16.67 = $250,050.

When the reserve rate is decreased to 4%, the money multiplier becomes 1/0.04 = 25. Therefore, the same initial deposit of $15,000 can now result in a maximum increase in the money supply of $15,000 x 25 = $375,000.

The difference between the two scenarios is $375,000 - $250,050 = $124,950, which is approximately $125,000. Hence, the amount of money increases by $125,000 due to the decrease in the reserve rate.

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The ratio given can be written in the lowest simplified form as 14:11

Given the ratio

To write in the form 1 : n, we need to divide to its simplest term, To do this we divide by 2.

Hence, we have :

Looking at the ratio we have, it can no longer be divided further by a cook factor.

Hence, the ratio would be written as 14:11

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The 97% confidence interval for the mean amount of monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

We shall use the following steps to find the 97% confidence interval:

First, we compute the margin of error using the formula:

Margin of error = Z * (σ / √n)

Where:

Z = the z-score

σ = standard deviation

n = sample size

Given:

Z = the z-score for a 97% confidence interval (which is 1.96 using the z-table).

σ = $215.

n = 120.

Putting the values:

Margin of error = 1.96 * (215 / √120)

= 1.96 * (215 / 10.95)

= 1.96 * 19.64

= $38.48

Next, we add and subtract the margin of error from the sample mean to find the confidence interval.

Confidence interval = $1575 +/- $38.48

= $1613.48 and $1536.52

Hence, the bank manager can be 97% confident that the average monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

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Answer:

(-∞, -4]

Step-by-step explanation:

4x - 1 < -15

4x < -14

x < -14/4

x < -7/2

So the solution to the inequality is x < -7/2. This means that all integer values of x that make the inequality true are the integers less than -7/2. In interval notation, we can write this as:

(-∞, -4]

Answer: [-∞, -4]

Step-by-step explanation:

Given inequality

4x - 1 < -15

Add 1 on both sides

4x - 1 + 1 < -15 + 1

4x < -14

Divide 4 on both sides

4x / 4 < -14 / 4

x < -3.5

Since, -3.5 is not an integer and the interval needs to be less than -3.5.

The closest integer that is less than -3.5 is -4.

Therefore, all integers [-∞, -4] fulfill this inequality.

Hope this helps!! :)

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Answer:

introduction of a business invironment

When a process is in control but does not meet specification, it is referred to as a Type II error, also known as a producer's risk or a beta error.

In statistical process control, a process is considered to be in control when it is stable, predictable, and the variation is within acceptable limits. However, even when the process is in control, there is still a possibility that it may produce outputs that do not meet the desired specifications or requirements.

A Type II error occurs when the process fails to detect and identify these non-conforming outputs, leading to the acceptance of defective products or services. In other words, it means that the process is not sensitive enough to identify deviations from the specification, resulting in the production of items that do not meet the desired quality standards.

Type II errors can have various consequences depending on the context. It can lead to increased costs due to rework, scrap, or customer dissatisfaction. It can also have implications for safety, reliability, or performance in critical applications.

To minimize Type II errors, it is important to continually monitor and improve the process, enhance the sensitivity of quality control measures, and ensure that appropriate inspection and testing methods are in place to detect deviations from specifications.

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The equations solved by the graph are y = x + 3 and y = x - 3

From the question, we have the following parameters that can be used in our computation:

The graph of systems of equations

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

Using the points on the graph, we have

Line 1: y = mx + 3

Line 2: y = mx - 3

Using the common points, we have

Line 1: -m + 3 =  -4

Line 2: -m - 3 = -4

When evaluated, we have

Line 1: m = 1

Line 2: m = 1

So, we have

Line 1: y = x + 3

Line 2: y = x - 3

Hence, the equations solved by the graph are y = x + 3 and y = x - 3

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