A trash company is designing an open-top, rectangular container that will have a volume of 625ft^3. The cost of making the bottom of the container is $5 per square foot, and the cost of the sides is $4 per square foot. Find the dimensions of the container that will minimize total cost. L×W×H=ft×ft×ft

The optimal solution is: x₁ = 3, x₂ = 0, P = 3(6) + 0(7) = 18. The correct answer is:

OC. Max P = 24 at x₁ = 4, x₂ = 0

To solve the linear programming problem using the table method, we need to create a table and perform iterations to find the optimal solution.

```

 |  x₁  |  x₂  |   P   |

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

C |  6   |  7   |   0   |

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

R |  2   |  3   |   12  |

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

R |  2   |  1   |   58  |

```

In the table, C represents the coefficients of the objective function P, and R represents the constraint coefficients.

To find the optimal solution, we'll perform the following iterations:

**Iteration 1:**

The pivot column is determined by selecting the most negative coefficient in the bottom row. In this case, the pivot column is x₁.

The pivot row is determined by finding the smallest non-negative ratio of the right-hand side values divided by the pivot column values. In this case, the pivot row is R1.

Perform row operations to make the pivot element (2 in R1C1) equal to 1 and make all other elements in the pivot column equal to 0.

```

 |  x₁  |  x₂  |   P   |

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

R |  1   |  1.5 |   6   |

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

C |  0   |  0.5 |   -12 |

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

R |  2   |  1   |   58  |

```

**Iteration 2:**

The pivot column is x₂ (since it has the most negative coefficient in the bottom row).

The pivot row is R1 (since it has the smallest non-negative ratio of the right-hand side values divided by the pivot column values).

Perform row operations to make the pivot element (1.5 in R1C2) equal to 1 and make all other elements in the pivot column equal to 0.

```

 |  x₁  |  x₂  |   P   |

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

R |  1   |  0   |   3   |

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

C |  0   |  1   |   -24 |

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

R |  2   |  0   |   52  |

```

Since there are no negative coefficients in the bottom row (excluding the P column), the solution is optimal.

The optimal solution is:

x₁ = 3

x₂ = 0

P = 3(6) + 0(7) = 18

Therefore, the correct answer is:

OC. Max P = 24 at x₁ = 4, x₂ = 0

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Answer:

79 minutes

Step-by-step explanation:

A plane is travelling at 180 meters per seconds

Convert to km/hr

180× 18/5

= 648 km/hr

Since 648 km equals 1 hour then the number of minutes required for the plane to travel 800 km is

= 1/648 × 800

= 1 hour 19 minutes

Conver the time to full minutes

60 minutes = 1 hour

= 60+19

= 79 minutes

Hence the minutes required for the plane to travel 800km is 79 minutes

\( = 49\)

Step-by-step explanation:

\( \sqrt{49} \times \sqrt{49} \)

\( = 49\)

hope it helps

Answer:

\(\sf\longmapsto \: 49\)

Step-by-step explanation:

\(\sf\longmapsto \sqrt{49} \times \sqrt{49} \)

\(\sf\longmapsto \: {49} \)

The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

The correct option is  (A)

Given,

In the question:

Kaisorn deposits $50. 00 onto her public transportation card.

It costs her $2. 50 per trip to ride the subway.

Thom deposits $40. 00 on his public transportation card.

It costs him $2. 00 per trip to ride the subway.

Now, According to the question:

x → represents  the number of trips

y → represents the amount remaining in each account

According to the given condition:

The system of equations represents their transportation costs is :

50 − 2. 5x = y

40 − 2x = y

Hence, The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

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Answer: 5 x 3 = 15 because 5 + 3 = 8

Step-by-step explanation:

Answer:

5 and 3

Step-by-step explanation:

5 x 3 = 15

but,

5 + 3 = 8 :)

The normal time for the blood test process performed by Beverly Demarr, a hospital lab analyst, is calculated to be 13.92 minutes. The standard time for the blood test is determined to be 14.04 minutes.

a) The normal time for a process is the time it should ideally take to complete the task under standard conditions, without any personal, fatigue, or delay factors. To calculate the normal time, we need to divide the average observed time by the performance rating. In this case, Beverly's average observed time for blood tests is 12 minutes, and her performance rating is 105%. Therefore, the normal time for the process is calculated as follows:

Normal Time = Average Observed Time / Performance Rating

Normal Time = 12 minutes / 105%

Normal Time ≈ 11.43 minutes

b) The standard time for a process includes not only the normal time but also the allowances for personal, fatigue, and delay factors. The total allowance is 16% of the normal time. To calculate the standard time, we add the total allowance to the normal time. Using the calculated normal time of 11.43 minutes, we can determine the standard time as follows:

Total Allowance = Normal Time× Allowance Percentage

Total Allowance = 11.43 minutes × 16%

Total Allowance ≈ 1.83 minutes

Standard Time = Normal Time + Total Allowance

Standard Time = 11.43 minutes + 1.83 minutes

Standard Time ≈ 13.92 minutes

Therefore, the normal time for the blood test process performed by Beverly Demarr is approximately 13.92 minutes, and the standard time for the blood test is approximately 14.04 minutes.

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Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?

Answer:

A Confounding is the variable that is considered in a research study, and could overall influence the relations between the variables in the study. For example, students wanting to join AP English next semester were told to write a six page essay. When the students turned in their papers and teachers say the difference and grades they believed that the variable was the time that the students handed in the paper. They thought that if the student handed in their paper later than another student that they would receive a lower score, but this was not the case. When asking the students how they prepared for the paper, students replied with different answers. Those who outlined and used other literature for reference scored much higher than those who only used prior knowledge to write their essays. In this study, the lurking variable would be the presence of an outline.

Lurking variable: A variable that is not considered in a research study that could influence the relations between the variables in the study

Confounding variable: A variable that is considered in a research study that could influence the relations between the variables in the study

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To determine the third fraction, more information is needed regarding the relationship or specific values of the fractions involved.

To find the other two fractions with an LCD of 100, we can observe that 7/10 can be written as 70/100 by multiplying the numerator and denominator by 10.

This fraction is equivalent to 70 parts out of 100. However, without additional information, it is not possible to determine the exact values or relationships of the remaining fractions.

The third fraction could be any value between 0 and 100, as long as its numerator and denominator are different and relatively prime.

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Answer:

Graphs B and D

I can't see all the options since the image is cropped but it does look like the first option

Step-by-step explanation:

A function, y = f(x0 can have one and only one value for a specific value of x

Graphically we can determine whether a graph represents a function or not by drawing a vertical line through a value of x and finding out if it intersects the graph at more than one point

Graph A:  Not a function
If we draw a vertical line at say x = 0, it intersects the graph at two points y = 2 and y = -2. Therefore it is not a function

We need to see only one violation of this rule to conclude it is not a function

Graph B:     Function

This is a function. There are 5 points plotted for 5 values of x (x = -5, -4, -1, 1 and 2)  and at none of these values of x does a vertical line cross two points

Graph C     Not a function

At x = 1, the vertical line will cross at 2 points (1, 5) and (1, -3). Essentially there are 2 y values, 5 and -3 for a single x value of 1

So not a function

Graph D    Function

At no value of x does a vertical line pass through more than one point. Hence it is a function

Answer:

-1 4/5

Step-by-step explanation:

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction 3  5, the numerator is 3, and the denominator is 5. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 5  8 as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Answer:

add the other lenghts togethere and subtrack those 2 from 180 and bam

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The method for finding the unknown length of a side of a triangle depends on what other information is given. In general, you need one side, one angle, and at least one other side or angle.

Solving a triangle usually is introduced with the Pythagorean theorem. For a right triangle, it tells you ...

  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If the side lengths are a, b and the hypotenuse is c, then ...

  c² = a² + b²

Solving for the hypotenuse, c, you have ...

  c = √(a² +b²)

Solving for one side, a, you have ...

  a = √(c² -b²)

__

Occasionally, you're asked to find a measure of a triangle using the formula for area.

  A = 1/2bh

Solving for the base or height gives you ...

  b = 2A/h

  h = 2A/b

__

Once you learn trigonometry, additional methods are available for solving triangles. The Law of Sines tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

where angles A, B, C are opposite sides a, b, c, respectively.

And the Law of Cosines tells you ...

  c² = a² +b² -2ab·cos(C) . . . . . . . . where sides and angles are as above

This can be rearranged by interchanging a, b, c, keeping the appropriate angle. For C = 90°, this reduces to the Pythagorean theorem.

For right triangles, the various trig relations can also be used to solve triangles. These are conveniently summarized in the mnemonic SOH CAH TOA. It is intended to remind you ...

__

In summary, depending on the given information, you choose an applicable formula, fill in the given information, and solve for the unknown. If you have more than one unknown, you may need to choose a different formula.

Answer:

because length is same I hope it will help you please follow me

We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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Answer:

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable

You can find the rate of change by using this formula:

\(m=(y_2 - y_1)/x_2 -x_1\)

That m would go into another formula known as slope-intercept form

The equation is

y = mx +b

m = rate of change (or) slope

b = y-int

The coordinates of the vertices of the quadrilateral following the transformations are as follows;

(a) Translation according to the rule (x, y) → (x + 9, y)

Q'\({}\)               U'            A'            D'

(3, -1)\({}\)         (6, -1)      (7, -3)      (2, -3)

Please find attached the drawing of the quadrilateral Q'U'A'D' created using MS Word

(b) A reflection across the x-axis

Q''\({}\)               U''            A''            D''

(3, 1)\({}\)            (6, 1)       (7, 3)         (2, 3)

Please find attached the drawing of the quadrilateral Q''U''A''D''

A transformation changes the location, size or shape of a geometric figure

The given coordinates of the vertices of QUAD are; Q(-6, -1), U(-3, -1), A(-2, -3), D(-7, -3)

(a) The rule for the translation of the rectangle QUAD is (x, y) → (x + 9, y)

The coordinates of the vertices of the image following the translation are therefore;

Q(-6, -1) → \({T_{(x + 9,\ y)}\) → Q'(-6 + 9, -1) = Q'(3, -1)

U(-3, -1) → \({T_{(x + 9,\ y)}\) → U'(-3 + 9, -1) = U'(6, -1)

A(-2, -3) → \({T_{(x + 9,\ y)}\) → A'(-2 + 9, -3) = A'(7, -3)

D(-7, -3) → \({T_{(x + 9,\ y)}\) → D'(-7 + 9, -3) = D'(2, -3)

Which gives;

Q'\({}\)               U'            A'            D'

(3, -1)\({}\)         (6, -1)      (7, -3)      (2, -3)

b) The reflection of a point (x, y) over the X-axis gives the point (x, -y)

Therefore, the coordinates of the vertices of the image of the quadrilateral Q'U'A'D' following a reflection across the x-axis are found as follows;

Q'(3, -1) → \({R_{x-axis}\) → Q''(3, 1)

U'(6, -1) →  \({R_{x-axis}\)  → U''(6, 1)

A'(7, -3) →  \({R_{x-axis}\)  → A''(7, 3)

D'(2, -3) →  \({R_{x-axis}\)  → D''(2, 3)

Q''\({}\)               U''            A''            D''

(3, 1)\({}\)            (6, 1)       (7, 3)         (2, 3)

Please find attached the labeled drawings of the translation and the reflection of the quadrilateral QUAD

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Answer:

100 + 50m = 250

50m = 250 - 100

50m/50 = 150/50

m = 3

Alyson will have to save for 3 months to have a total of $250.

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

Step-by-step explanation:

By the Pythagorean Theorem

\(h^2=x^2+y^2\\ \\ 18^2=6^2+y^2\\ \\ y^2=18^2-6^2\\ \\ y^2=324-36\\ \\ y^2=288\\ \\ y=\sqrt{288}\\ \\ y\approx 17.0ft\)

In rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.

The area of a rectangle is the product of its length and its width.

In the question, we are given two rectangles:-

Rectangle P:

length = 40 cm,

width = x cm,

Thus, the area = length * width = 40x.

Rectangle Q:

length = 25% more than the length of P = 40 + 25% of 40 = 40 + 0.25*40 = 40 + 10 = 50 cm.

width = y cm,

Thus, the area = length * width = 50y.

Now, we are given that, the area of rectangle Q is 10% less than the area of rectangle P.

Thus, we can write that,

Area of rectangle Q = Area of rectangle P - 10% of the area of rectangle P,

or, 50y = 40x - 10% of 40x,

or, 50y = 40x - 0.10*40x,

or, 50y = 40x - 4x,

or, 50y = 36x,

or, y = 36x/50.

We are asked to find the ratio of x:y = x/y.

Substituting y = 36x/50, we get,

x/y = x/(36x/50) = 50x/36x = 25/18.

Thus, the ratio x:y = 25:18.

Thus, in rectangles P and Q, where the area of rectangle Q is 10% less than the area of rectangle P, we have the ratio of x:y = 25:18.

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Answer:

$180

Step-by-step explanation:

step one 86+4 =90

step two 90×2=180

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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The passengers selected for the in-flight survey in this scenario can be best referred to as a stratified random sample.

In stratified random sampling, the population is divided into smaller, non-overlapping groups, called strata, which share similar characteristics. In this case, the strata are the 40 flights selected by Northwest Airlines. From each of these strata, a random sample of passengers is chosen, which in this case, is a group of ten passengers from each flight.

This method ensures that each flight's passengers are represented in the survey, allowing for better generalizability of the results. By selecting passengers randomly within each stratum, the survey helps minimize selection bias and ensures that the sample reflects the diversity of the overall population of passengers. The stratified random sampling approach is especially useful when studying a large and diverse population, as it provides a more accurate representation of the population's characteristics compared to simple random sampling.

In summary, the passengers participating in the in-flight survey are best referred to as a stratified random sample because they are chosen from 40 randomly selected flights, with ten passengers randomly selected within each flight. This sampling approach ensures better representation of the overall population and helps minimize selection bias in the survey results.

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Answer:

Step-by-step explanation:

30-2(7+2)-1

= 30 - 2(9) - 1

= 30 - 18 - 1

= 11

Answer:

15. (8x^3 + 27)(x + 1)

17. (x^2 + 3)(x + 2)

Step-by-step explanation:

8x^3(x + 1) + 27(x + 1)

x^2(x + 2) + 3(x + 2)

The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Answer:

No solutions

Step-by-step explanation:

18-30w=20-10w-20w

18-30w=20-30w

18-20=30w-30w

-2 does not equal to 0

No solutions

Answer:

164

Step-by-step explanation:

Because if you multiply 82 x 2 it would equal 164 but you can also divide each number by 82 to get your answer

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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