What is the numerator of the simplified sum?

Answer:

36/6

Step-by-step explanation:

12 x 3= 36.

2 x 3= 6.

Answer:

C. \(\frac{36}{6}\)

Step-by-step explanation:

Statistical process control technique that permits only 3.4 defects per million opportunities is Six Sigma.

Six Sigma is a statistical technique that emphasizes the necessity of a standardized approach to enhancing and optimizing the efficiency of the production and management processes by reducing the variation and waste within them. It concentrates on controlling a process to ensure that the results of a process are consistent and reliable by using statistical methods. The objective of the Six Sigma process is to produce 3.4 errors or defects per million opportunities. If the process is better than Six Sigma, it is considered more consistent and predictable.
Six Sigma's statistical approach to process control encompasses a range of tools and methods. Six Sigma's primary objective is to increase revenue and profits by developing and delivering high-quality products and services while eliminating defects and reducing waste.
Six Sigma aims to improve quality by detecting and reducing the reasons for variations in production processes. It accomplishes this by developing quality management practices that enable it to assess quality, establish goals, and implement best practices to achieve those goals.
In conclusion, Six Sigma is a process control approach that emphasizes statistical methods for process control and improvement. Six Sigma is used to reduce variability and eliminate waste, and its goal is to achieve 3.4 defects per million opportunities.

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Answer:

where is the information?

Step-by-step explanation:

Answer:

3. positive correlation but not causal relationship

Step-by-step explanation:

A positive correlation is when one factor increases, the other factor increases as well.

A negative correlation is when one factor increases, the other factor decreases.

A causal relationship is when one factor causes the other factor change in a certain way (i.e. increase or decrease).

More people buy ice cream as the day becomes hotter and sunnier. This also applies to people choosing to wear sunglasses. Therefore, there is a positive correlation between the two (because both increase). However, this is not a causal relationship because the cause of both is the hotter and sunnier day.

I hope this helps! If you have any question, feel free to as. :)

Answer:

2 1/4 cups i think

Step-by-step explanation:

On solving the question we can say that Therefore, the solutions to the inequality given inequality are: x < 4 or x > 6.

An inequality in mathematics is a relationship between two expressions or values ​​that are not equal. Imbalance therefore leads to inequality. An inequality establishes a connection between two values ​​that are not equal in mathematics. Equality is different from inequality. The inequality sign () is most commonly used when two values ​​are not equal. Various inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be solved by changing both sides until only variables remain. But many things contribute to inequality.

two inequalities

4x - 6 < 10

4x < 16

x < 4

2x - 4 > 8

2x > 12

x > 6

Therefore, the solutions to the given inequality are:

x < 4 or x > 6.

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a. Effective annual interest rate is 24.53%

b. Effective annual interest rate is 34.86%

c. Effective annual interest rate is 16.35%

d. Effective annual interest rate is 149.15%

a. The effective annual interest rate the firm earns when a customer does not take the discount can be calculated using the following formula:

Effective Annual Interest Rate = (1 + Discount % / (100 - Discount %))³⁶⁵/Number of Days Credit is Given - 1

Plugging in the values from the given terms, we get:

Effective Annual Interest Rate = (1 + 2% / (100 - 2%))³⁶⁵/45 - 1

Effective Annual Interest Rate = 24.53%

Therefore, the firm earns an effective annual interest rate of 24.53% when a customer does not take the discount.

b. If the discount is changed to 3%, the effective annual interest rate the firm earns can be calculated using the same formula:

Effective Annual Interest Rate = (1 + Discount % / (100 - Discount %))³⁶⁵/Number of Days Credit is Given - 1

Plugging in the new discount percentage, we get: Effective Annual Interest Rate = (1 + 3% / (100 - 3%))³⁶⁵/45 - 1

Effective Annual Interest Rate = 34.86%

Therefore, the firm earns an effective annual interest rate of 34.86% if the discount is changed to 3%.

c. If the credit period is increased to 65 days, the effective annual interest rate the firm earns can be calculated using the same formula:

Effective Annual Interest Rate = (1 + Discount % / (100 - Discount %))³⁶⁵/Number of Days Credit is Given - 1

Plugging in the new number of days credit is given, we get:

Effective Annual Interest Rate = (1 + 2% / (100 - 2%))³⁶⁵/65 - 1

Effective Annual Interest Rate = 16.35%

Therefore, the firm earns an effective annual interest rate of 16.35% if the credit period is increased to 65 days.

d. If the discount period is increased to 20 days, the effective annual interest rate the firm earns can be calculated using the same formula:

Effective Annual Interest Rate = (1 + Discount % / (100 - Discount %))³⁶⁵/Number of Days Credit is Given - 1

Plugging in the new number of days the discount is offered, we get:

Effective Annual Interest Rate = (1 + 2% / (100 - 2%))³⁶⁵/25 - 1

Effective Annual Interest Rate = 149.15%

Therefore, the firm earns an effective annual interest rate of 149.15% if the discount period is increased to 20 days.

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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They can buy between 3 and 13 pairs of earrings.

The correct answer is: 115 ≤ 9(3) + 6(11) + 6x ≤ 175;

To set up an inequality to model the problem, we can start by calculating the total cost of the bracelets and necklaces.

The cost of 9 bracelets at $3 each is 9 \(\times\) 3 = $27.

The cost of 6 necklaces at $11 each is 6 \(\times\) 11 = $66.

Therefore, the total cost of the bracelets and necklaces is $27 + $66 = $93.

Let's represent the number of pairs of earrings they can buy as "x". The cost of each pair of earrings is $6.

Now, we can set up the inequality to represent the given condition:

$115 ≤ 9 \(\times\) 3 + 6 \(\times\) 11 + 6x ≤ $175

Simplifying the inequality, we have:

$115 ≤ 27 + 66 + 6x ≤ $175

Combining like terms, we get:

$115 ≤ 93 + 6x ≤ $175

To isolate "x", we can subtract 93 from all parts of the inequality:

$115 - 93 ≤ 6x ≤ $175 - 93

This simplifies to:

22 ≤ 6x ≤ 82

Now, divide all parts of the inequality by 6:

22/6 ≤ x ≤ 82/6

This gives us:

3.67 ≤ x ≤ 13.67

Since we cannot have a fraction of pairs of earrings, we round down the lower limit and round up the upper limit:

3 ≤ x ≤ 14

Therefore, they can buy between 3 and 14 pairs of earrings.

So, the correct answer is:

115 ≤ 9(3) + 6(11) + 6x ≤ 175; They can buy between 3 and 14 pairs of earrings.

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Answer:

\(\frac{2}{5}\)

Step-by-step explanation:

the rate of change is calculated as\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

where (x₁, y₁ ) and (x₂, y₂ ) are any 2 ordered pairs from the table

using (x₁, y₁ ) = (20, 16 ) and (x₂, y₂ ) = (10, 12 ) , then

rate of change = \(\frac{12-16}{10-20}\) = \(\frac{-4}{-10}\) = \(\frac{4}{10}\) = \(\frac{2}{5}\)

Answer:

Option B

m<1 + m<2 = 180-m<3

Explanation:

This is how you will find the third interior angle of a triangle when two angles are already given.

The number of ways to select 3 pages in ascending index order depends on the total number of pages available.

To find the number of ways to select 3 pages in ascending index order, we can use the concept of combinations . In combinatorics, selecting objects in a specific order is often referred to as permutations. However, since the order does not matter in this case, we need to consider combinations instead.

The number of ways to select 3 pages in ascending index order can be calculated using the combination formula. Since we are selecting from a set of pages, without replacement and order doesn't matter, we can use the formula C(n, k) = n! / (k!  (n-k)!), where n is the total number of pages and k is the number of pages we want to select.

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Answer:

The line to graph is y=-\(\frac{2}{3}\) -1

Step-by-step explanation:

In order to graph the line, it needs to be in slope-intercept form. We can make an equation in slope intercept form by using the point-slope form, which is y-y₁=m(x-x₁).

1. Plug info into point-slope form:

y-(-5)=-\(\frac{2}{3}\)(x-6)

2. Simplify:

y+5=-\(\frac{2}{3}\) x+4

3. Simplify even further:

y=-\(\frac{2}{3}\) -1

To graph the line, make a point a (0,-1). From here, go down 2 points and to the right 3 points. Continue the pattern and connect the points with a line.

If Earle Bailey has 20 songs to choose from but can play only 7 in the next half‑hour, then there are 77520 possible playlists.

The given data is as follows:

Total number of songs = 20

Number of songs in the playlist  = 7

So, it is given that we need to select 7 songs out of 20. This can be done using combinations.

Decimal notation is another appropriate way to describe fractional values in the calculation. This implies that base 10 is being used for the fractional indication. Both fractions and decimals can be altered.

The dissimilarity is that fractions and decimals are registered using different notations. We can visually determine how considerably of a full number we are operating to decimal notation.

Let us assume that n = 20 and r= 7

C( n, r ) = ?

C( n, r ) = C (20 , 7)

C( n, r ) = 20! / ( 7! (20-7)!)

C( n, r )  =  20! / ( 7! × 13! )

C( n, r )  = 77520

Therefore we can conclude that there are 77520 possible playlists.

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Answer:

The circle has a radius of 7 units.

Step-by-step explanation:

Center of the circle is at origin i.e. \(P(0,0)\) Where P is the point where center of the circle lies.

A line with a positive slope, cuts the circle at point (0,7)

Let \(Q(0,7)\) be the point where the line intersects the circle.

Please refer to the attached diagram for circle.

Clearly, it means that there is a point on circle which is at (0,7).

Radius of a circle is the distance between the center of circle and any point on circle.

We can use distance formula for finding the circle's radius:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Here, the two points are P(0,0) and Q(0,7)

\(x_1 = 0\\y_1 = 0\\x_2 = 0\\y_2 = 7\\\)

Putting the values and finding out radius:

\(Radius = \sqrt{(0-0)^2+(7-0)^2}\\\Rightarrow Radius = \sqrt{7^2}\\\Rightarrow Radius = 7\ units\)

Hence, the correct option is Circle has a radius equal to 7.

Answer:

It's B

The circle has a radius equal to 7.

Step-by-step explanation:

Just trust me

Answer:

The multiplication sentence is 4/9*3/8=1/6

then for the rectangular fraction model draw two rectangles and in the first one draw 9 boxes and shade in 4. Then, in the second one draw 8 boxes and shade 3.

Step-by-step explanation:

This is an example:

The multiplication sentence is,

''For the rectangular fraction model draw two rectangles and in the first one draw 9 boxes and shade in 4. Then, in the second one draw 8 boxes and shade 3.''

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Draw a rectangular fraction model to explain your thinking.

Here, The expression is,

⇒ 4/9 × 3/8

Now, We can write the multiplication sentence as,

''For the rectangular fraction model draw two rectangles and in the first one draw 9 boxes and shade in 4. Then, in the second one draw 8 boxes and shade 3.''

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Based on your knowledge of context-dependent memory, you recommend that Delores studies in an environment similar to the exam setting to enhance memory recall and performance.

Context-dependent memory refers to the phenomenon where memory recall is improved when the external environment during learning or encoding matches the environment during retrieval. To leverage this effect for effective studying, you advise Delores to recreate the exam setting as much as possible while studying. This means studying in a quiet place, similar to the exam room, and using similar materials such as textbooks or online resources.

By studying in a context similar to the exam environment, Delores can enhance memory retrieval during the actual exam. The familiarity of the surroundings, sensory cues, and overall context can trigger associations and facilitate the retrieval of information learned during studying. This can result in better performance and improved memory recall, as the brain is primed to retrieve information within the same context it was learned.

It's important to note that context-dependent memory is just one strategy among many, and different individuals may have different preferences and learning styles. Delores should also consider other effective study techniques such as active learning, spaced repetition, and self-testing to optimize her exam preparation.

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Answer:

D

Step-by-step explanation:

Given

x + 3 = - 2 ( subtract 3 from both sides )

x = - 5

While the study found an association between diet soda and weight gain, it does not necessarily mean that it causes weight gain. There could be other explanations for this association.

One possible explanation is that people who are already overweight or at risk of gaining weight are more likely to consume diet soda to control their calorie intake. These individuals may also be more likely to engage in other behaviors contributing to weight gain, such as consuming high-calorie foods and engaging in a sedentary lifestyle.

Another explanation is that the artificial sweeteners used in diet soda may interfere with the body's natural ability to regulate calorie intake, leading to increased cravings for high-calorie foods and, ultimately, weight gain. However, more research is needed to understand the impact of artificial sweeteners on weight gain fully.

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Answer:

15 pi.

Step-by-step explanation:

2/5=6/x

x=15

This is how I would answer it, but there is an error with the question. The measure of the central angle of an arc is supposed to be equal to the length of the arc.      

Answer:

x=36

Step-by-step explanation:

\(60^{2} = 48^{2} + x^{2} \\x^{2} =60^{2} - 48^{2}\\x^{2} =3600 - 2304\\x=36\)

The volume of the triangular prism as described is; 15 cubic foot.

A triangular pyramid simply refers to any geometric solid with a triangular base, and all three lateral faces are also triangles with a common vertex

It follows from the formula for calculating the volume of a triangular prism that;

Volume = (1/3) × base area × height.

Consequently,

volume of the prism is; = (1/3) ×9 × 5

Volume = 15 cubic foot

Therefore, volume of the triangular prism as described is; 15 cubic foot.

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Answer:

Whichever distance you can count the metric units and see that the x value is 7 on

Step-by-step explanation:

Whichever distance you can count the metric units and see that the x value is 7 on

According to the solving the area of the square is 68.0625.

As is common knowledge, a square is a four-sided, two-dimensional figure. It is also referred to as a quadrilateral. The total quantity of unit squares forming a square is referred to as the square's area. In other words, it is described as the area that the square takes up.

The box formed after cutting the square from each corner will have the dimensions as,

length = 104 - 2x, width = 39 - 2x, height = x.

∴ volume of the box = length × width × height

∴ v = (104 - 2x)(39 - 2x)(x) -----(i)

∴ v = (104 - 2x) (39x - 2\(x^{2}\))

∴ v = 104(39x - 2\(x^{2}\)) -2x(39x - 2\(x^{2}\))

∴ v = 4056x - 208\(x^{2}\) - 78\(x^{2}\) + 4\(x^{3}\)

∴ v = 4\(x^{3}\) - 286\(x^{2}\)  + 4056x

let f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x  -----(ii)

To, find x for which f(x) is maximum,

⇒we should apply second derivative test ,

According to this test, first we should find critical points at which f'(x) = 0.

then if f''(x) < 0 for that critical point then f(x) is maximum at that critical point.

∴ let us consider, f'(x) = 0.

now, f(x) =  4\(x^{3}\) - 286\(x^{2}\)  + 4056x

⇒ f'(x) = 12\(x^{2}\) - 572x + 4056.  -----(iii)

⇒ f'(x) = 4(3\(x^{2}\) - 143x + 1014)

⇒ f'(x) = 0.

⇒  f'(x) = 4(3\(x^{2}\) - 143x + 1014) = 0

⇒ x = (-b ± \(\sqrt{b^{2} - 4ac }\))/2a    ; where a = 3, b = -143, c = 1014.

∴ x = (-(-143) ± \(\sqrt{(-143)^{2} -4(3)(1014)}\))/2×3

∴ x = (143 ± \(\sqrt{8281}\))/6.

∴ x = \(\frac{143 + 91}{6}\)  , x = \(\frac{143 - 91}{6}\)

⇒ x = 39, 8.25

the square of length 8.25 inch should be cut from each side to det contained with the maximum volume.

Area of the square is = \(x^{2}\) = \(8.25^{2}\)

∴ Area = 68.0625

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17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.

Answer:

(22, 0)

Step-by-step explanation:

Answer:

x=-4

Step-by-step explanation:

These two angles have to equal 180 because they are opposite of each other. Therefore, the equation will be 129+x+x+59=180. You add all common terms. 2x+188=180. You want to isolate x so you have to subtract both sides by 188. Therefore, the equation will be 2x=-8. Divide both sides by 2 to isolate x. x=-8/2. This is equal to x=-4.

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The simple interest using the formula i = prt is $9,000.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account.

Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Simple interest is preferable for borrowers since, without compounding, overall interest costs will be lower.

So, the simple interest will be:

We know that Oliver borrowed $1500.

The interest rate was 12%.

The time period was 6 months.

We have the formula: i = prt

Now, substitute the values and calculate as follows:

i = prt

i = 1500 × 12 × 6/12

i = 1500 × 12 × 1/2

i = 1500 × 6

i = 9,000

Therefore, the simple interest using the formula i = prt is $9,000.

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