A company manufactured a 16-oz box of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

Answer:

6 sections.

Step-by-step explanation:

Malcom uses a marker to draw a straight line on a piece of paper.

The line is [tex]\frac{2}{3}[/tex] feet long.

He wants to divide the line into sections of [tex]\frac{1}{9}[/tex] feet long.

The number of sections would be = [tex]\frac{\frac{2}{3}}{\frac{1}{9} }[/tex]

             = [tex]\frac{2}{3}[/tex] × [tex]\frac{9}{1}[/tex]

            = [tex]\frac{18}{3}[/tex]

            = 6 sections

There would be 6 sections.

The chain rule allows you to find the derivative of a function that is a composition of other functions. With an example, we calculated dz/dt with z = y^3 and y = 2t+1. While calculators can help, understanding the process is key.

The chain rule in calculus is a theorem that allows you to find the derivative of a composite function. If a variable z depends on the variable y, which itself depends on another variable t, then z, is a function of t. The chain rule could be mathematically expressed as dz/dt = (dz/dy) × (dy/dt).

For instance, if z = y^3 and y = 2t+1, we can calculate dz/dt by first finding the derivatives dz/dy and dy/dt, which are 3y² and 2, respectively. We then substitute y = 2t+1 into dz/dy to get dz/dy = 3(2t+1)². Therefore, using the chain rule, dz/dt = 3(2t+1)² × 2.

While your request mentions a calculator, knowing these steps should enable you to perform the operation using most scientific calculators. However, understanding the process is very important before relying on technology.

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The final expression for [tex]\frac{dz}{dt}[/tex] incorporates the partial derivatives and the derivatives of x and y with respect to t.

Given the function z = xy⁷ - x²y, where x = t² + 1 and y = t² - 1, we are to find [tex]\frac{dz}{dt}[/tex].

[tex]\frac{dz}{dt}[/tex] = ([tex]\frac{dz}{dx}[/tex]) × ([tex]\frac{dx}{dt}[/tex]) + ([tex]\frac{dz}{dy}[/tex]) × ([tex]\frac{dy}{dt}[/tex]).

Let's find [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex]:

⇒ [tex]\frac{dx}{dt}[/tex] = d(t² + 1) ÷ dt = 2t

⇒ [tex]\frac{dy}{dt}[/tex] = d(t² - 1) ÷ dt = 2t

⇒ [tex]\frac{dz}{dx}[/tex] = y⁷ - 2xy

⇒ [tex]\frac{dz}{dy}[/tex] = 7xy⁶ - x²

x = t² + 1, y = t² - 1

⇒ [tex]\frac{dz}{dx}[/tex] = (t² - 1)⁷ - 2(t² + 1)(t² - 1)

⇒ [tex]\frac{dz}{dy}[/tex] = 7(t² + 1)(t² - 1)⁶ - (t² + 1)²

Finally, we combine these to find [tex]\frac{dz}{dt}[/tex]:

⇒ [tex]\frac{dz}{dt}[/tex] = ([tex]\frac{dz}{dx}[/tex]) × ([tex]\frac{dx}{dt}[/tex]) + ([tex]\frac{dz}{dy}[/tex]) × ([tex]\frac{dy}{dt}[/tex]).

Substituting everything into this formula:

⇒ [tex]\frac{dz}{dt}[/tex] = [(t² - 1)⁷ - 2(t² + 1)(t² - 1)] × 2t + [7(t² + 1)(t² - 1)⁶ - (t² + 1)²] × 2t

Complete question:

Use the Chain Rule to find [tex]\frac{dz}{dt}[/tex].

z = xy⁷ - x²y, x= t² + 1, y = t² - 1

Answer:

Option B is correct that is 8.

Step-by-step explanation:

Given Expression : [tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]

We use a law of exponent here to simplify it,

[tex](x^a)^b=x^{ab}[/tex]

Consider,

[tex](16^{\frac{3}{2}})^{\frac{1}{2}}[/tex]

[tex]=16^{\frac{3}{2}\times\frac{1}{2}}[/tex]

[tex]=16^{\frac{3}{4}}[/tex]

[tex]=(2^4)^{\frac{3}{4}}[/tex]

[tex]=2^{4\times\frac{3}{4}}[/tex]

[tex]=2^3[/tex]

[tex]=8[/tex]

Therefore, Option B is correct that is 8.

The value of x is 559.5.

An algebraic equation can be defined as mathematical statement in which two expressions are set equal to each other.

To solve the equation [tex]\(45(15x+20)7x=56(12x*24)+6\)[/tex], follow these steps:

First, distribute the multiplication on both sides of the equation:

[tex]\(45 \cdot 15x + 45 \cdot 20 - 7x = 56 \cdot 12x - 56 \cdot 24 + 6\)[/tex]

[tex]\(675x + 900 - 7x = 672x - 1344 + 6\)[/tex]

Next, combine like terms on both sides:

[tex]\(668x + 900 = 672x - 1338\)[/tex]

Now, move all terms involving [tex]\(x\)[/tex] to one side and constants to the other side:

[tex]\(668x - 672x = -1338 - 900\)[/tex]

[tex]\(-4x = -2238\)[/tex]

To find [tex]\(x\)[/tex], divide both sides by [tex]\(-4\)[/tex]:

[tex]\(x = \frac{-2238}{-4}\)[/tex]

[tex]\(x = 559.5\)[/tex]

So, the value of x is 559.5.

Answer:

The length of the other leg is 48 feet

Step-by-step explanation:

To find the length of the other leg, we will simply follow the steps below;

We will use the Pythagoras theorem formula to solve;

Write down the  Pythagoras theorem formula

opposite²  + adjacent² = hypotenuse²

Let the value of the other leg be x

From the question given;

hypotenuse = 50, a leg, say the opposite = 14

Lets substitute into our formula;

opposite²  + adjacent² = hypotenuse²

14²  +  x²  = 50²

196  + x² = 2500

subtract 196 from both-side of the equation

196 - 196 + x² = 2500 - 196

x² = 2304

Take the square root of both-side of the equation

√x² = √2304

x = 48 feet

The length of the other leg is 48 feet

Answer:

1) 8

2) 5

3) False

4) Option B

Step-by-step explanation:

1) We have to find the remainder when we divide (x² + 4) by (x - 2)

To get the remainder we will put x = 2 in (x² + 4)

= (2)² + 4

= 8

2). We have to evaluate f(-1) using substitution in f(x) = 2x³ - 3x² - 18x - 8

f(-1) = 2(-1)³ - 3(-1)²- 18(-1) - 8

      = 2(-1) - 3 + 18 -8

      = -2 - 3 + 18 - 8

      = 5

3) The point (1, 0) lies on the graph of p(x) = [tex]x^{4}-2x^{3}-x+2[/tex]

If this point lies on the graph then p(1) should be equal to zero.

p(1) = 1³ - 7(1)² + 7(1) - 9

     = 1 - 7 + 7 - 9

     = -8 ≠ 0

Therefore, It's false.

4). (x - 1) is a factor of p(x) = x³ - 7x² + 15x - 9

Now we will factorize it further when (x - 1) is a zero factor.

By Synthetic division

1 |  1    - 7     15    -9

           1      -6     9

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

    1     -6      9     0

Now we have got the expression as (x - 1)(x²- 6x + 9)

Or (x -1)(x² - 6x + 9) = (x - 1)(x - 3)(x - 3)

Therefore, Option B. is the answer.

The amount paid per movie is $4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Charge per movie = $5

The fifth movie charge = $0

Now,

The charge for 5 movies.

= 5 x 4 + 0

= 20

This means,

5 movies cost $20

The cost of one movie.

= 20/5

= $4

Thus,

The cost per movie is $4.

Learn more about expressions here:

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Final answer:

The distance between the points (-6,4) and (-8,6) is found using the Pythagorean Theorem, resulting in a distance of approximately 2.83 units.

Explanation:

The question asks for the distance between two points, (-6,4) and (-8,6), which can be found using the Pythagorean Theorem in a coordinate plane. The formula for finding the distance (d) between any two points (x₁,y₁) and (x₂,y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

Thus, substituting the given points into the formula, we get: d = √[(-8 + 6)² + (6 - 4)²] = √[(-2)²+ (2)²] = √[4 + 4] = √[8].

Therefore, the distance between the points (-6,4) and (-8,6) is √8, which is approximately 2.83 units.

Answer:

Sample response:  

2

5

is close to  

1

2

, and it is easy to find  

1

2

of 7 mentally. Half of 7 is 3.5, so Martin gave away about 3.5 pounds.

Step-by-step explanation:

-,-

The required angle can be found by solving the equation as 24°.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Suppose the measure of  required angle be x.

Then, its complement can be written as 90 - x.

As per the question, the following equation can be formed as,

x + 42 = 90 - x

⇒ 2x = 48

⇒ x = 24

Hence, the measure of the required angle is 24°.

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To calculate the total kilometers Rick will bike in 16 days, we find his daily distance by dividing 230 km by 4, which results in 57.5 km/day, and then multiply by 16 to get 920 km.

The subject of this question is Mathematics, and it seems appropriate for a Middle School student. To find out how many kilometers Rick will bike in 16 days, we need to start by calculating the number of kilometers he bikes per day. Rick bikes 230 km every 4 days, so we divide 230 km by 4 to get the daily distance:

230 km / 4 days = 57.5 km/day.

Now, to find the total distance Rick will bike in 16 days, we multiply the daily distance by the total number of days:

57.5 km/day times 16 days = 920 km.

So, Rick will bike 920 kilometers if he keeps the same pace for 16 days.

since line MO bisects, that means both angles are the same

6x-22 = 2x +34

6x = 2x +56

4x=56

x = 56/4 = 14

x=14

6(14)-22 = 62

2(14)+34 = 62

62+62 = 124

angle LMN = 124 degrees

Jesse saves $112.50 per week, Nick saves $51.25 per week, and Owen saves $56.25 per week.

To find out how much money each person saves per week, we need to set up a system of equations. Let's start by assigning variables to the amounts saved by each person. Let 'J' represent the amount saved by Jesse, 'N' represent the amount saved by Nick, and 'O' represent the amount saved by Owen.

2O = J   (Jesse saves twice as much as Owen)

N + 5 = O   (Owen saves $5 more than Nick)

J + N + O = 220   (The total amount saved by all three is $220)

Now, we can substitute the values in the equations to find the amounts saved by each person.

From the first equation, J = 2O. Substituting this value in the third equation gives us: 2O + N + O = 220. Simplifying, we get 3O + N = 220.

From the second equation, N + 5 = O. Rearranging, we get N = O - 5. Substituting this value in the third equation gives us: 3O + (O - 5) = 220. Simplifying, we get 4O = 225. Solving for O, we find that Owen saves $56.25 per week.

Substituting this value in the second equation, we find that Nick saves $51.25 per week. Finally, substituting the values in the first equation, we find that Jesse saves $112.50 per week.

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Final answer:

The question from the student is a mathematics problem on solving inequalities. We are asked to solve 'Twice the quantity of a number plus two is greater than the number plus five', which simplifies to n > 3, where 'n' is any number greater than three.

Explanation:

The student's question involves solving an inequality which is a concept in mathematics. The inequality is stating that 'Twice the quantity of a number plus two is greater than the number plus five.' This can be mathematically expressed as 2n + 2 > n + 5, where 'n' represents the number in question.

To solve this inequality, we would follow these steps:

Subtract 'n' from both sides of the inequality: 2n + 2 - n > n + 5 - n which simplifies to n + 2 > 5.

Next, subtract 2 from both sides: n + 2 - 2 > 5 - 2 which simplifies to n > 3.

This means any number greater than 3 satisfies the given inequality.

Transitivity of numbers with respect to comparison operators (<, >, =) is a fundamental principle in solving such inequalities. This principle allows us to state that if a number is greater than three, sequentially, it is also greater than two (2), one (1), and zero (0).

Answer:

Chart please

Step-by-step explanation: