You work in the quality assurance department for a bottling company. A water bottle is supposed to contain 750
milliliters (mL) of water, and the company sets a tolerance of +5 mL.

What is the least amount of water that is considered acceptable?

1. 740 mL
2. 745 mL
3. 750 ml
4. 755 mL
5. 760 mL

Answer:

Sunglower I really want to help, but personally I do not know the answer, but if this answer is going percentage wise, the answer would be 1.6004

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

The given parabolic equation is y = 4x - x² and the point is (1, 3). We are to determine the slope of the tangent line at (1, 3) and then obtain an equation of the tangent line.  we must first calculate the derivative of the given equation.

We can do this by using the power rule of differentiation. The derivative of x² is 2x. So the derivative of y = 4x - x² is dy/dx = 4 - 2x.Since we want to find the slope of the tangent line at (1, 3), we need to substitute x = 1 into the equation we just obtained. dy/dx = 4 - 2x = 4 - 2(1) = 2. Therefore, the slope of the tangent line at (1, 3) is 2.We can now write the equation of the tangent line. We know the slope of the tangent line, m = 2, and we know the point (1, 3).

We can use the point-slope form of the equation of a line to obtain the equation of the tangent line. The point-slope form of the equation of a line is given as: y - y₁ = m(x - x₁)where m is the slope, (x₁, y₁) is a point on the line.Substituting in the values we have, we get:y - 3 = 2(x - 1)We can expand this equation to obtain the slope-intercept form of the equation of the tangent line:y = 2x + 1Therefore, the equation of the tangent line to the parabola y = 4x - x² at the point (1, 3) is y = 2x + 1.

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Answer:

I think infinite since it goes on past these numbers.

Step-by-step explanation:

Answer:

Infinity solutions

Step-by-step explanation:

This inequality has infinite solutions because the number line goes from 3 to infinity. this means that there is an uncountable number of solution which means the answer to this question is E.

-3 is less than 2

< is the symbol

The cost of one yard of green fabric is $10.

Let's assume that the cost of one yard of green fabric is represented by the variable x. Since the blue fabric costs $3 more per yard, the cost of one yard of blue fabric can be expressed as (x + $3).

La Tanya buys 4 yards of blue fabric, so the total cost of the blue fabric is 4(x + $3). She also buys 7 yards of green fabric, so the total cost of the green fabric is 7x.

The total cost of the fabrics is given as $122, so we can set up the equation:

4(x + $3) + 7x = $122

Simplifying the equation:

4x + $12 + 7x = $122

11x + $12 = $122

11x = $122 - $12

11x = $110

Dividing both sides by 11:

x = $110 / 11

x = $10

Therefore, the cost of one yard of green fabric is $10.

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The circumference of a circle with a diameter of 36 inches is approximately 113.1 inches.

The circumference of a circle can be found using the formula: C = πd, where C represents the circumference and d represents the diameter. In this case, the given diameter is 36 inches.

Using the value of π (pi) as approximately 3.14159, we can substitute the values into the formula:

C = πd

C = 3.14159 * 36

C ≈ 113.09724

Rounding to the nearest tenth, the circumference of the 36-inch diameter circle is approximately 113.1 inches.

The circumference of a circle with a diameter of 36 inches is approximately 113.1 inches.

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Answer:

40%

Step-by-step explanation:

6 votes, from the 15 members total. This is 6/15, which is 0.4, which is 40%. :)

Answer:

B

Step-by-step explanation:

V26 is closer to 5 because it's only one number away.

The number among the option that is closest to 5 is √26.

The number closest to 5 is the number that is almost 5.

The option are express in surd form, therefore, lets express in real numbers(decimal form) Real numbers are rational or irrational numbers. Therefore,

√23 = 4.79583152331

√26 = 5.09901951359

√22 = 4.69041575982

√28 = 5.29150262213

Therefore, using the decimal form, the closest number to 5 is √26

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Answer:

m=-2/3

Step-by-step explanation:

two points from graph:(-1,1) and (-4,3)

m=y2-y1/x2-x1

m=3-1/-4-(-1)

m=2/-3

m=-2/3

Using the values provided in the ordered pair, The linear inequality is satisfied by putting the ordered pair values and checking if the statement is true or false.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two.

ordered pair=(1,2)

linear inequality equation,

\(4x_{1}-x_{2} > 0\)

using value from ordered pair,

\(4*1 - 2 > 0\)

\(2 > 0\)

which is true. That is it satisfies the given linear inequality.

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An apple pie with diameter 10 inches is cut into six equal slices. The arc length of one slice is approximately 5.23 inches.

An  arc of a circle is a segment of the circumference of a circle.

The formula for the length of an arc is given by:

Length of arc = central angle / 360⁰  x circle circumference.

The circumference of a circle is given by:

C = 2π r

Where r is the radius of the circle. Hence,

Length of arc = central angle / 360⁰  x 2π r

In this problem, it is assumed that the apple pie has a circular shape with 10 inches diameter.

Information available in the problem:

radius = 10/2 inches. = 5 inches.

Since, 1/6 circle has central angle 60⁰, hence:

Length of arc = 60⁰ / 360⁰  x  2π r

Length of arc = 1/6 x  2π r

Length of arc = 1/6 x  2π x 5 = 5.23 inches

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Answer:900

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

because 800 is above 500 so round it to 1000

Answer:

350 millimeters

Step-by-step explanation:

3.5 millimeters x 100 = 350 millimeters

The percent change in the price is  -6.67

The percentage change will be given by the formula:

Percent change = 100%*(new price - old price)/old price

We know that:

old price = 15 pounds.

new price = 14 pounds

Replacing that we will get:

percent change = 100%*(14 - 15)/15 = -6.67%

The price is 6.67% smaller.

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Answer:

what exactly is this question

Step-by-step explanation:

The value of c guaranteed by MVT is 29/20.

Mean-Value Theorem (MVT) states that if a function is continuous on the interval [a, b] and differentiable on the interval (a, b), then there exists at least one point c in (a, b) such that:

\(\[\frac{f(b)-f(a)}{b-a}=f^{\prime}(c)\]\)

The solution to the given problem is as follows:

Given,

\(\[f(x) = x^2 - 6x^2 - 5\]\)

We have to find the value of c for the interval [-2, 3].Thus, a = -2, b = 3, and f(x) is continuous on [-2, 3] and differentiable on (-2, 3).Now, we have to find the value of c, using Mean-Value Theorem (MVT).

By MVT,

\(\[\frac{f(b) - f(a)}{b - a} = f'(c)\]\)

Differentiating f(x), we get,

\(\[f'(x) = 2x - 12x\]\)

Therefore\(,\[\frac{f(b) - f(a)}{b - a} = f'(c)\]\)

Plugging in the values of f(b), f(a), and f'(c), we get:\(\[\frac{f(b) - f(a)}{b - a} = \frac{(3)^2 - 6(3)^2 - 5 - [(-2)^2 - 6(-2)^2 - 5]}{3 - (-2)}\]\)

On solving, we get:\(\[\frac{f(b) - f(a)}{b - a} = \frac{8}{5}\]\)

Now, we have to find the value of c.

Using MVT, we have:\(\[\frac{8}{5} = 2c - 12\]\\\\\\\\On solving, we get:\\\\\\\[c = \frac{29}{20}\]\)

Therefore, the value of c guaranteed by MVT is 29/20.

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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The distance and displacement are the same because both determine the total path traveled by the object.

It is also true that the total path length covered by a subject is equal to the displacement and as well as the distance if it has moved along in a straight line.

The distance between two places of an item in motion is known as displacement. Therefore, it relies on both the starting position and the ending position. Displacement is also the shortest distance between the initial and ultimate places.

Thus, The distance and displacement are the same because both determine the total path traveled by the object.

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No, the formula of distance and displacement is not same.

In order to find the solution, we must know that what is meant by distance and displacement.

The formula of speed distance time is mathematically given as,

=> Speed = Distance/Time

And the term displacement is referred as the change in position of an object and it is the smallest distance between two positions.

Here we have also know that it is a vector quantity and it has magnitude and direction both.

The formula to calculate the displacement is written as

=> displacement = velocity x time

While we looking into the definition, we have identified that both terms are not equal.

And the formula of each of them are also differs.

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Answer:

 -12 b + 6 c + 18

Step-by-step explanation:

-4 b + 8 c + 12 - 8 b - 2 c + 6

After simplification, the correct value is,

⇒ 6 (- 2b + c + 3)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We haver to given that;

The expression is,

⇒ -4b + 8c + 12 - 8b - 2c + 6.

Now, We can simplify by combine like terms as;

⇒ -4b + 8c + 12 - 8b - 2c + 6.

⇒ - 12b + 6c + 18

And, GCD of 12, 6, 18 = 6

Hence, Take 6 as common as;

⇒ - 12b + 6c + 18

⇒ - 2×6b + 6c + 3×6

⇒ 6 (- 2b + c + 3)

Therefore, The solution of the expression is,

⇒ 6 (- 2b + c + 3)

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The coordinates of the new triangle's vertices are (0, -1), (-4, -3), and

(-2, -1). Hence option A is true.

Used the rule of a point (x, y) when rotated over the y-axis of 90° clockwise rotation from point (0, 0),

(x, y) → (y, - x)

Given that the triangle BCD is shown in the image.

Here, the coordinates of the vertices of BCD are,

B = (1, 0)

C = (3, - 4)

D = (1, - 2)

Now apply the rotation rule, the coordinates of the new triangle's vertices are;

B' = (0, - 1)

C' = (- 4, - 3)

D' = (- 2, - 1)

Therefore, the option A is true.

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The function that is graphed is f(x) = |x - 3| + 1

The parent absolute function is:

f(x) = |x|

From the graph, we have the following transformations:

This is represented as:

(x, y) = (x - 3, y + 1)

So, we have:

f(x) = |x - 3| + 1

Hence, the function that is graphed is f(x) = |x - 3| + 1

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The statements that are true of medians in even and odd distributions are:

An even quantity of data values will forever maintain a pair of central numbers. In these circumstances, the middle numbers are attained by calculating the average among the two numbers amidst the set of data. As an illustration, in the series {1, 2, 3, 4}, the dual numeral at the core are 2 and 3.

The mean value between these integers is (2+3)/2=2.5, ultimately making it the center number of this cluster of data. Conversely, an odd number of data inserts shall eternally acquire only one midpoint, simply the figure located within the dataset's nucleus.

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Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

Given the following equation:

In the standard slope-intercept form, y = mx + b, m represents the slope of the equation.

If the slope is positive, it is increasing.

If the slope is negative, it is decreasing.

From the given equation, V = 23.4 + 2.8x, it appears that 2.8 is the slope in this equation. Since it is a positive number, it is increasing.

Therefore, we can say that:

The value of this investment is increasing at a rate of 2.8 thousand dollars per month.

Value of 158 Pounds is approximately 71.67 Kilograms. both are unit of measurement of weight.

To convert pounds (lbs) to kilograms (kg), you can use the conversion factor 1 lb = 0.45359237 kg. To convert 158 pounds to kilograms, you would multiply 158 by 0.45359237, which gives you 71.67 kilograms.

It is important to note that the pound and kilogram are both units of measurement for weight, but the pound is a unit commonly used in the United States, while the kilogram is the standard unit of measurement for weight in the International System of Units (SI).

When travelling or working with people from different parts of the world, it is important to be able to convert between these units of measurement to ensure accurate communication.

Additionally, it is important to have a good understanding of the difference between weight and mass, as weight is a measure of the force exerted on an object due to gravity, while mass is a measure of the amount of matter in an object, regardless of gravity.

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Answer:

Shopper spend $3 on Apples, $4 on Grapes and $3.5 on Oranges

Step-by-step explanation:

Cost of one pound of Apple = $2x

Cost of one pound of Grapes = $(6x-5)

Cost of one pound of Oranges = $(x+2)

A shopper purchases one pound each of  apples, grapes, and oranges and spends  $10.50.

It can be written as: \(2x+6x-5+x+2=10.50\)

We need to find how much the shopper spend on each fruit.

First we need to find value of x by solving equation

\(2x+6x-5+x+2=10.50\)

Solving:

\(2x+6x+x+2-5=10.50\\9x-3=10.50\\9x=10.50+3\\9x=13.5\\x=\frac{13.5}{9}\\x=1.5\)

The value of x is: x=1.5

Now finding cost of one pound each fruit by putting x=1.5

Cost of one pound of Apple = $2x = 2(1.5) = $3

Cost of one pound of Grapes = $(6x-5) = (6(1.5)-5)= $4

Cost of one pound of Oranges = $(x+2)=(1.5+2)=$3.5

So,

Cost of one pound of Apple  = $3

Cost of one pound of Grapes = $4

Cost of one pound of Oranges = $3.5

So, shopper spend $3 on apples, $4 on Grapes and $3.5 on Oranges

Answer:

B) No solution

Step-by-step explanation:

3x - 13 = 3(x-6)

3x - 13 = 3x - 18

-13 = -18

Since both sides are never equal to each other, there are no solutions