Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane.

Answer:

8/10

Step-by-step explanation:

add the numerator but keep the denominators the same

you could also simplify to 4/5

Answer:

2/10 + 6/10

= 8/10

=4/5

Therefore the answer is 4/5

Answer: The price after 3 years is £6904.15

Step-by-step explanation:

After 1 year,  8500*0.9= 7650

7650*0.95=7267.5

7267.5*0.95=6904.125

The price after 3 years is £6904.15

The optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2. To solve the given linear programming (LP) model using the graphical method, we need to graphically represent the feasible region and find the optimal solution by maximizing the objective function.

Step 1: Graph the Constraints

We start by graphing each constraint individually on a coordinate plane.

The first constraint is x - y ≥ 0, which represents the line y = x. We can draw this line on the plane.

The second constraint is x + 2y ≤ 4. To graph this, we can rewrite it as 2y ≤ -x + 4 and then solve for y, which gives y ≤ (-1/2)x + 2. We can plot this line on the graph as well.

The third constraint x ≥ 0 represents the x-axis, and the fourth constraint y ≥ -1 represents the horizontal line y = -1.

Step 2: Identify the Feasible Region

The feasible region is the area where all constraints are satisfied. It is the intersection of the shaded regions formed by the constraints.

Step 3: Identify the Optimal Solution

To find the optimal solution, we need to maximize the objective function Z = x - 2y. The objective function is represented by a line with a positive slope.

By sliding the objective function line parallel to itself from left to right or right to left, we can observe the points of intersection between the objective function line and the feasible region. The point that gives the maximum value of Z within the feasible region is the optimal solution.

Step 4: Determine the Optimal Solution

By visually inspecting the graph, we can see that the objective function line will intersect the feasible region at the corner point (2, 0). This is the optimal solution for the given LP model.

Therefore, the optimal solution is x = 2, y = 0, and the maximum value of Z is Z = 2 - 2(0) = 2.

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The angular measure L is : 47°

Angles are formed when two lines meet.

Analysis:

Firstly, we calculate for m using cosine rule.

\(m^{2}\) = \(510^{2}\) + \(820^{2}\) -2(510)(820) cos 20

\(m^{2}\) = 260100 + 672400 -83600(0.9396)

\(m^{2}\) = 146618.56

m = \(\sqrt{146618.56}\) = 382.9cm

using sine rule to find ∠L

382.9/sin20 = 820/sinL

sinL = 820sin20/382.9

sinL = 820(0.342)/382.9

sinL = 0.732

L = sin inverse of 0.732 = 47°

In conclusion, ∠L is 47°

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The slope of the second function has decreased by 4.75.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given the first function y = 5x – 2

Now equation of any line is given as y = mx + c

By comparing it m = 5

Now the second function  y = 1/4x – 2,

Slope = 1/4

So it is clear that function 2 has the same except for the slope.

Hence "The slope of the second function has decreased by 4.75".

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Answer:

The least number of stamps required is \(9\)

Step-by-step explanation:

Let the number of \(3\) cent stamps be \(x\) and \(4\) cent stamps be \(y\)

We have

\(3x+4y=33\)

The minimum number is obtained when more  \(4\) cent stamps are used

Here \(y\) cannot be greater than \(8\) since \(\frac{33}{4} <9\)

Substitute \(y=8\)

\(3x+4\times 8=33\\\\3x=1\\\\x=\frac{1}{3}\)

Not possible since \(x\) is not a fraction

Substitute \(y=7\)

\(3x+4\times 7=33\\\\3x=5\\\\x=\frac{5}{3}\)

Not possible since \(x\) is not a fraction

Substitute \(y=6\)

\(3x+4\times 6=33\\\\3x=9\\\\x=\frac{9}{3}\\\\=3\)

Possible

Hence minimum number of stamps is

\(=x+y\\\\=3+6\\\\=9\)

Answer:

the number of more people watched each screen on sunday is 103

Step-by-step explanation:

The computation of the number of more people watched each screen on sunday is shown below:

= Sunday - saturday

= (1576 ÷ 4) - (1164 ÷ 4)

= 394 - 291

= 103 more people

hence, the number of more people watched each screen on sunday is 103

Answer:

Step-by-step explanation:

A - Since there are parenthesis on 30 and 10, you would want to find the difference between 30 and 10 first, and then multiply it by 5, hence getting you 5 times the difference of 30 and 10.

\(\pink{\bigstar}\) Amount of apple juice Will added \(\large\leadsto\boxed{\tt\purple{1 \frac{5}{12}}}\)

➪ Amount of grape juice Will added = 1/4

➪ Amount of juice in total after adding the apple juice = 1⅔

Therefore, it is clear that the amount of apple juice Will added to the cup will be the difference in total amount of juice and amount of grape juice.

Hence,

➪ \(\sf 1 \frac{2}{3} - \dfrac{1}{4}\)

➪ \(\sf \dfrac{5}{3} - \dfrac{1}{4}\)

• Taking an L.CM:-

➪ \(\sf \dfrac{20 - 3}{12}\)

➪ \(\sf \dfrac{17}{12}\)

➪ \(\large{\bold\red{1 \frac{5}{12}}}\)

Therefore, the amount of apple juice added is \(\large{\bold 1 \frac{5}{12}}\)

The key attributes of linear functions are that they have a constant slope and a constant y-intercept. The domain and range of linear functions are all real numbers.

The key features of quadratic functions are that they have a parabolic shape and they have two roots. The domain and range of quadratic functions are all real numbers.

The key attributes of linear functions can be seen in their graph. A linear function graph is a straight line. The slope of the line tells us how much the y-value changes for every change in the x-value. The y-intercept tells us the value of y when x is 0.

The domain and range of linear functions are all real numbers. This means that the x-value and the y-value can be any real number.

The key features of quadratic functions can be seen in their graph. A quadratic function graph is a parabola. The parabola opens up or down depending on the coefficient of the x^2 term. The roots of the quadratic function are the points where the graph crosses the x-axis.

The domain and range of quadratic functions are all real numbers. This means that the x-value can be any real number, but the y-value cannot be less than or equal to 0.

The key attributes of exponential functions are that they have an exponential growth or decay rate and they have an initial value. The domain and range of exponential functions depend on the base of the exponent.

If the base of the exponent is greater than 1, then the function has an exponential growth rate. This means that the y-value increases rapidly as the x-value increases. If the base of the exponent is less than 1, then the function has an exponential decay rate. This means that the y-value decreases rapidly as the x-value increases.

The domain and range of exponential functions depend on the base of the exponent. If the base of the exponent is greater than 1, then the domain is all real numbers and the range is all positive real numbers. If the base of the exponent is less than 1, then the domain is all real numbers and the range is all real numbers less than or equal to 1.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

y - 2 = (1/2)(x - 4).

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Answer:

4min

Step-by-step explanation:

half full = 4min. disregard the doubles every min.

Answer:

7 minutes

Step-by-step explanation:

Y is a random variable on (Ω, F, P).

To show that y is a random variable on (Ω, F, P), we need to show that the pre-image of any Borel set B in R under y is an event in F. In other words, we need to show that {w : y(w) ∈ B} is in F for any Borel set B in R.

Let y be any real-valued function on Ω. Then, for any Borel set B in R,

{w : y(w) ∈ B} = y^{-1}(B),

where y^{-1}(B) denotes the pre-image of B under y. Since y is measurable, we have y^{-1}(B) ∈ F for any Borel set B in R. Therefore, y is a random variable on (Ω, F, P).

Alternatively, we can use the definition of a random variable to show that y is a random variable. Let y be any real-valued function on Ω. Then, for any Borel set B in R,

{w : y(w) ∈ B} = {w : y(w) ≤ x} ∩ {w : y(w) ≥ x},

where x is any real number such that B = (-∞, x] ∪ (x, ∞). Since y is measurable, {w : y(w) ≤ x} and {w : y(w) ≥ x} are events in F for any real number x, and hence their intersection {w : y(w) ∈ B} is also an event in F. Therefore, y is a random variable on (Ω, F, P).

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Answer:

40.9ft

Step-by-step explanation:

The perimeter is when you add all the sides together.

8 + 10 + 10 + 4 + 8.9 = 40.9ft

Answer:D

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

10% of 300=30

30*6= 180 (to get 60 percent you multiply 10% by 6)

60%=180

The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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Answer:

50%

Step-by-step explanation:

In order to change a decimal into a percent, move the decimal to the right twice and add a percent sign

0.5 = 5.0 once

5.0 = 50.0 twice

And add a percent sign 50%

Answer:

Your answer would be 50%

Step-by-step explanation:

you would move the 5 to the left 2 times let me show you.  

0.5 = 05. then 05. = 50. which would be 50%

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Solve for dy/dx:   dy/dx = (-2x) / (2y) = -x / y which gives the slope of tangent line using implicit differentiation

To find the slope of a tangent line using implicit differentiation, follow these steps:

1. Start with the given equation that represents the relationship between x and y in the form of an equation involving both variables, for example: F(x, y) = 0.

2. Differentiate both sides of the equation with respect to x using the chain rule whenever necessary. Treat y as a function of x and apply the derivative rules accordingly.

3. After differentiating, have a resulting equation involving both x, y, and their derivatives (dy/dx). Rearrange the equation if necessary to isolate dy/dx on one side.

4. Solve for dy/dx to find the derivative of y with respect to x. This will give the slope of the tangent line at any given point on the curve defined by the implicit equation.

Note: The resulting expression for dy/dx may involve both x and y variables. To find the slope of the tangent line at a specific point, substitute the coordinates of that point into the expression for dy/dx.

Here's an example to illustrate the process:

Given the implicit equation: \(x^2 + y^2 = 25\)

1. Start with the equation: \(x^2 + y^2 = 25.\)

2. Differentiate both sides with respect to x:

  2x + 2y * (dy/dx) = 0

3. Rearrange the equation to isolate dy/dx:

  2y * (dy/dx) = -2x

4. Solve for dy/dx:

  dy/dx = (-2x) / (2y)

         = -x / y

Now, have the expression for the slope of the tangent line in terms of x and y. To find the slope at a specific point, substitute the coordinates of that point into the expression.

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xx+1=132=131=xx=x=131/x

Answer:

Step-by-step explanation:

uh all i can tell you is good luck

Step-by-step explanation:

5/9 × (x - 32) = 1.8 × x + 32 = 9/5 × x + 32

5×(x - 32) = 9×9/5 × x + 32×9

5×5×(x - 32) = 9×9×x + 32×9×5

25x - 32×25 = 81x + 32×45

32×(-25 - 45) = 56x

4×(-70) = 7x

x = 4×(-10) = -40

-40° is the same temperature in Celsius and in Fahrenheit.

Multiply the number of chairs by the price of the chair:

34 x 205 = 6,970

Total spent = $6,970

Step-by-step explanation:

Simplifying

36 = byx

Solving

36 = bxy

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-1bxy' to each side of the equation.

36 + -1bxy = bxy + -1bxy

Combine like terms: bxy + -1bxy = 0

36 + -1bxy = 0

Add '-36' to each side of the equation.

36 + -36 + -1bxy = 0 + -36

Combine like terms: 36 + -36 = 0

0 + -1bxy = 0 + -36

-1bxy = 0 + -36

Combine like terms: 0 + -36 = -36

-1bxy = -36

Divide each side by '-1xy'.

b = 36x-1y-1

Simplifying

b = 36x-1y-1

Answer:

y = \(\frac{36}{bx}\)

Step-by-step explanation:

Given

36 = byx ( isolate y by dividing both sides by bx )

\(\frac{36}{bx}\) = y