A group of students recycled 7 2/3 pounds of glass and 9 3/4 pounds of paper. How many pounds of glass and paper did the students recycle alltogether?

Answer:

 286 possible outcomes.

Step-by-step explanation:

We have been given total 13 identical marbles

We need to select 10 out of 13

We will use combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

here,n=13 and r=10 on substituting the values in the formula we get:

[tex]^13C_{10}=\frac{13!}{10!(13-10)!}[/tex]

[tex]^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}[/tex]

[tex]\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}[/tex]

[tex]\Rightarrow 286[/tex]

So, there are 286 possible outcomes.

Possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].

Further explanation:

The formula of combination can be expressed as,

[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]

Given:

A bag contains [tex]13[/tex] identical marbles.

Calculation:

Suzy randomly picks [tex]10[/tex] marbles from a bag of [tex]13[/tex] identical marble.

The number of possible outcomes that she can select [tex]10[/tex] marbles can be obtained as,

[tex]{\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}[/tex]

Substitute [tex]13[/tex] for [tex]n[/tex] and [tex]10[/tex] for [tex]r[/tex] in equation [tex]{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex] to obtain the possible outcomes that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles.

[tex]\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}[/tex]

Hence, possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Combination

Keywords: Suzy, picks, marbles, 13 identical marbles, 10 marbles, possible, outcomes, select, combination, randomly picks, a bag contains 13 marbles.

Answer:

The answer on edge 2021 is 1.667

Step-by-step explanation:

I got a 50% and it showed the answer

The value of b in the quadratic regression equation is 1.667.

The value of b in the given quadratic regression equation is 1.667.

To find the value of b, you can look at the coefficient of the linear term in the quadratic equation ,, In this case, the linear term is 1.667x, so the value of b is 1.667.

Arithmetic is the answer

To find the possible integer lengths for diagonal AC in quadrilateral ABCD, the Triangle Inequality Theorem is used. Possible integer values for AC are constrained between the sum and the difference of the lengths of the sides forming triangles ABC and CDA, resulting in potential lengths of 4, 5, 6, and 7.

The question pertains to finding all possible integer values for the diagonal AC of a quadrilateral ABCD given the lengths of the sides. To determine the possible lengths of AC, we need to inspect the properties of triangles that could form within the quadrilateral upon drawing this diagonal. The quadrilateral could possibly be a rectangle, a square, or a parallelogram, but without further information, we assume it is an irregular quadrilateral.

By using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, we can determine possible values for AC. Since ABCD is a quadrilateral with sides AB = 3, BC = 6, CD = 4, and DA = 4, diagonal AC can create two triangles, ABC and CDA. For triangle ABC, the sum of sides AB and BC is 9, so AC must be less than 9. Similarly, for triangle CDA, the sum of sides CD and DA is 8, so AC must be less than 8. Therefore, the maximum value for AC is 7. However, AC must also be greater than the difference of the sides, 3 for triangle ABC and 0 for triangle CDA. This leaves us with possible integer values of 4, 5, 6, and 7 for AC.

The square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.

The equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where:

a is the coefficient of the x² term

b is the coefficient of the x term

c is the constant term

In the equation x² - x = 2, we have:

a = 1

b = -1

c = 2

Plugging these values into the quadratic formula, we get:

x = (1 ± √((-1)² - 4(1)(2))) / 2(1)

Simplifying the expression, we get:

x = (1 ± √(1 - 8)) / 2

Evaluating the square root, we get:

x = (1 ± √(-7)) / 2

Since the square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.

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Answer:

A. Jenny's initial height above the surface of the water

Step-by-step explanation:

Given : The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. [tex]-16x^2 +12x+10.[/tex]

To Find: Which statement best describes the term 10?

Solution:

[tex]h(x)=-16x^2 +12x+10.[/tex]

Substitute x = 0 i.e.time = 0 seconds

[tex]h(x)=-16x^2 +12x+10.[/tex]

[tex]h(0)=-16(0)^2 +12(0)+10.[/tex]

[tex]h(0)=10[/tex]

so, at time 0 the height was 10

So, 10 is the initial height.

Thus Option A is correct.

A. 10 is Jenny's initial height above the surface of the water.

Answer:

1,313,000

Step-by-step explanation:

The task involves evaluating the line integral of a vector field along a path to determine the work done by the field. Since the path does not traverse in the x-direction, only the y and z components of the vector field contribute to the integral. The calculation involves parameterizing each segment and summing up the individual integrals.

The student's question involves finding f · dr along a path c in a vector field. The vector field is given as f = ay i + bz j + cx k, and the path c is a triangle with vertices at (7, 0, 0), (7, 0, 2), and (7, 6, 2). The dot product of a vector field with a differential displacement vector (dr) represents the work done by the field along that path.

To find the integral of f · dr along the path c, we would parameterize each segment of the path and evaluate the line integral. However, since the vector field has constants multiplied by either i, j, or k, and the path only moves parallel to the y and z axes, the components involving x do not contribute to the integral. Therefore, for each segment of the path, we will only consider the y and z components of the vector field. The line integral along the path is then the sum of the integrals over each segment of the triangle.

In this example, since the x-component of the field does not change and the path does not move in the x direction, the integral over the x components will be zero.

Calculation Steps:

Answer:

The answer is 896pi in.^2

Step-by-step explanation:

It may seem confusing as you get an answer in the thousands by plugging in the formula, but remember they are asking you to find the answer in "terms of pi". This means you have to divide the answer by 3.14.

2814/3.14 = 896pi in^2

Hope this helped!

Answer:

A minimum of 93 cm squared

Step-by-step explanation:

Answer:

I think the answer is 77.

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Given table:    Number of pages in book   Time needed to read book (hours)

                                               200                       18

                                               175                         15

                                               275                        21

                                               225                        18

                                               400                        30

                                               350                        26

The number of observations in the above table = 6

When we create a scatter-plot from the table of values the number of points should be plotted  =6.

Hence, the number of points should be plotted when creating a scatter-plot from the given table of values =6

Final answer:

The amount of salt in the tank, described by the differential equation, reaches 5 pounds after 50 minutes with an initial amount of 10 pounds and a rate of change defined by the given equation.

Explanation:

Let's start with the given differential equation: A'(t) = (2 gal/1 min) * (0 lb/1 gal) - (1 gal/1 min) * A(t) / (50 + (2 - 1)t gal).

By simplifying the equation, we get A'(t) + A(t) / (50 + t) = 0. Multiplying through by (50 + t) gives (50 + t)A'(t) + A(t) = 0. Recognizing that ((50 + t)A(t))' equals zero, we integrate to find (50 + t)A(t) = C, where C is a constant.

With the initial condition A(0) = 10, we find 10 = C / (50 + 0), which simplifies to C = 500. So, the equation describing the amount of salt in the tank is A(t) = 500 / (50 + t).

To determine when the tank will be filled, we solve 50 + t = 100, which gives t = 50 minutes. Plugging this into A(t) yields A(50) = 500 / (50 + 50) = 5 lb.

This linear programming problem can be solved by graphing the given inequalities to determine the feasible region. If this region is empty, there are no solutions. If the function is unbounded in this region, the maximal value can be infinitely large.

To solve this linear programming problem, we first need to identify its feasible region which is defined by its constraints. The constraints of this problem are as follows:

By graphing these inequalities we can identify the feasible region as the intersection of these inequalities. If the feasible region is empty, it means that there is no solution that satisfies all the constraints. If the objective function p = x - 2y is unbounded, it means that the maximum value of p can be infinitely large within this feasible region. By investigating both these situations, we should be able to determine whether an optimal solution exists or not.

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