Camile realizes she is charged more based on the volume of the box and not the weight which box would fit her requirements and be the best choice to save her on shipping cost? Explain your reasning

Answer:

  5 meters

Step-by-step explanation:

You want to know the width of a rectangular living room that is 12 m along one side and 13 m along the diagonal.

The diagonal of a rectangle is the hypotenuse of each of the right triangles it creates by dividing the rectangle in half. If one side length is 12 and the diagonal is 13, these measures are part of the {5, 12, 13} Pythagorean triple.

The width of the living room is 5 meters.

__

Additional comment

You can use the Pythagorean theorem to find the missing length:

  13² = 12² +w²

  169 -144 = w²

  w = √25 = 5

The width of the living room is 5 meters.

Other Pythagorean triples you see in algebra, trig, and geometry problems are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41} and their multiples.

The fewest number of minutes it will take Jeremy and Michael to solve 10 Rubik's cube is 16 with a speed such that Jeremy solve one in 4 minutes and Michael solves 5 in 12 minutes.

To solve the following word problem,

Time taken by Jeremy to solve one cube = 4 minutes = 240 seconds

Time taken by Michael to solve 5 cubes = 12 minutes

Time taken by Michael to solve 1 cube = [tex]\frac{12}{5}[/tex] minutes = 144 seconds

Since one solves the cube alone, they do it individually,

For the first 12 minutes,  Michael solves 5 cubes and Jeremy solves 3 cubes ([tex]\frac{12}{3}[/tex])

Then, to solve 2 or more cubes Michael takes 288 seconds

And if Michael and Jeremy each solve one cube it takes them 144 seconds and 240 seconds respectively.

Therefore, the second situation is responsible for solving in the least time which comes out to be 12 minutes + 4 minutes (240 seconds) is 16 minutes.

Learn more about word problems:

https://brainly.com/question/13818690

#SPJ4

Answer: is option (3) -4x²-6.

Step-by-step explanation: First, we need to add the two given polynomials:

4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3

Now, we need to multiply this sum by 2:

2(-2x^2 - 3) = -4x^2 - 6

Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4

The calculated volume of the figure is 761.97 cubic inches

From the question, we have the following parameters that can be used in our computation:

The volume of the figure is calculated as

Volume = Cylinder + Cone - Hollow cylinder

So, we have

Volume = 3.14 * (8/2)^2 * 18 + 1/3 * 3.14 * (8/2)^2 * 5 - 3.14 * (2)^2 * 18

Evaluate

Volume = 761.97

Hence, the volume is 761.97 cubic inches

Read more about volume at

https://brainly.com/question/463363

#SPJ1

The graph of the solution set can be seen in the image at the end.

Here we have the inequality:

-(6 + 1/2)y + 9 > -17

First, we need to isolate the variable y, then we will get:

9 + 17 > (6 + 1/2)y

26 > 6.5y

26/6.5 > y

4 > y

The graph of this will be an open circle at y = 4, and an arrow that goes to the left, the graph can be seen in the image at the end.

Learn more about inequalities at:

https://brainly.com/question/24372553

#SPJ1

Answer: 2/3

Step-by-step explanation: 1/2 converted to 6ths is 3/6 add them together and it’s 4/6 simplify that and it’s 2/3

To proof that ΔLMQ ≅ ΔNPQ; we use the given statement "∠L is congruent to ∠N"

To complete the proof that ΔLMQ is congruent to ΔNPQ, we have to follow the following steps.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

We will apply ASA method to proof that ΔLMQ ≅ ΔNPQ;

∠L is congruent to ∠N

Length LM is congruent to length NP

Looking at the options, only one was stated. (∠L is congruent to ∠N).

Learn more about congruent triangles here: https://brainly.com/question/2938476

#SPJ1

The estimated area is about 22.5 square units

To estimate the perimeter of a patio, you need to measure the length of each side and then add those lengths together.

Here's a step-by-step guide to help you:

Determine the shape of your patio: Before you can estimate the perimeter, identify whether your patio is a rectangle, square, circle, or any other shape. The method for calculating the perimeter will vary depending on the shape.

Measure the sides:

a. For rectangular or square patios: Measure the length (L) and width (W) of the patio using a measuring tape. Ensure that the measurements are taken in the same unit (e.g., feet, meters, etc.).

b. For circular patios: Measure the diameter (D) or radius (R) of the patio. The radius is the distance from the center of the circle to any point on its edge.

c. For irregularly-shaped patios: Break the patio down into smaller, regular shapes (like rectangles, squares, or triangles), and measure each side of these smaller shapes.

Calculate the perimeter:

a. For rectangular or square patios: Use the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

b. For circular patios: Use the formula P = 2πR or P = πD, where P is the perimeter, R is the radius, and D is the diameter. π (pi) is approximately 3.14159.

c. For irregularly-shaped patios: Add up the side lengths of each smaller shape that you've broken the patio into. The sum of these lengths will give you the total perimeter.

(look at the image)

Read more about estimation here:

https://brainly.com/question/28416295

#SPJ1

Roehr Corporation Additional Paid-in Capital--Common account will increase by $110,000 by issuing 20,000 shares of $0.50 par common stock for $6 per share.

When a corporation issues common stock, the par value of the stock is recorded in the Common Stock account, and any amount received above the par value is recorded in the Additional Paid-in Capital--Common account. In this case, Roehr Corporation The par value of the common stock is

Total par value = Par value per share x Number of shares

= $0.50 x 20,000

= $10,000

The total amount received from issuing the stock is $6 per share x 20,000 shares = $120,000.

The additional paid-in capital is calculated as the difference between the total amount received and the total par value:

Additional paid-in capital = Total amount received - Total par value

= $120,000 - $10,000

= $110,000

Therefore, the answer is (B) $110,000.

Learn more about Paid-in Capital:

https://brainly.com/question/22556463

#SPJ4

Answer:

Step-by-step explanation:

THE ANSWER IS 21

Answer:

The same line.

Step-by-step explanation:

We have to decide whether the lines are perpendicular, neither parallel nor perpendicular, parallel, or the same line. We can check if a line is perpendicular by finding the slope. The line is perpendicular if the slope of one line is the negative reciprocal of the second line.

Let's try to solve for the Y-intercept (where X = 0) of both of these functions.

y + 3x = -4

y + 3(0) = -4

y + 0 = -4

:. y = -4

And now the other one:

y = -3x-4

y = -3(0) - 4

:. y = -4

Since y = -4 in both cases, well, now we have our answer. The answer is it's the same line, so the fourth answer is correct. All the other ones - perpendicular, neither parallel nor perpendicular, and parallel - are incorrect by process of elimination. We don't actually have to keep going from here. But we can (although I won't).

(a) Total number of trips = 270

(b) There are 33 different visits that could make.

We have the information:

There are 18 major sea islands in the queen Elizabeth islands of Canada. There are 15 major lakes in Saskatchewan, Canada.

Let us say that A indicates the major sea Islands and B indicates the major lakes.

Taking both the cases as events, we will use multiplication principle.

Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

(a) A × B = 18 × 15

Total number of trips = 270

(b) |A| = 18

|B| = 15

A ∩B = θ         (as we cannot visit both an island and lake)

Addition Principle: There are |A| + |B| ways to choose an element form

A ∪ B , when A and B are the finite sets with A ∩B = θ

|A ∪ B| = |A| + |B| = 18 + 15 = 33

Thus, There are 33 different visits that could make.

Learn more about Addition principle at:

https://brainly.com/question/12904549

#SPJ4

Using percentages we know that Terrel has the best free throw statistics which is 70.83%.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

So, in the given situation where we need to get whose statistics are the best.

We need to calculate the percentages in all cases as follows:

Jack: 18/39*100 = 46.15%

Henry: 54%

Terrel: 17/24*100 = 70.83%

Riley: 9/23*100 = 39.13%

Since Terrel has the highest %, so he has the best free throw statistics.

Therefore, using percentages we know that Terrel has the best free throw statistics which is 70.83%.

Know more about the percentage here:

https://brainly.com/question/24877689

#SPJ1

Answer: Luis will spend a total of $22,868.48 on his lease.

Step-by-step explanation: To calculate the total cost of Luis's lease, we need to multiply the monthly cost by the number of months in the lease:

Total cost = monthly cost x number of months

The number of months in 4 years is 4 x 12 = 48 months.

Therefore, the total cost of Luis's lease is:

Total cost = $475.86/month x 48 months

Total cost = $22,868.48

So Luis will spend a total of $22,868.48 on his lease.

The function that possesses a period of 16 units, a midline at y=3, and a maximum at y=8 is f(x) = 5 sin(π/8 x) + 3

The sine function with a period of 16 units, a midline at y=3, and a maximum at y=8 can be written in the form:

y = A sin(Bx) + C

where A is the amplitude, B is the frequency (related to the period), and C is the vertical shift (related to the midline).

The frequency is related to the period by the formula: B = 2π/period.

So, in this case,

B = 2π/16 = π/8.

So, we have

y = A sin(π/8x) + C

Using the list of options as a guide the sine function that satisfies these conditions is f(x) = 5 sin(π/8 x) + 3

Read more about sinusoidal function at

https://brainly.com/question/12050240

#SPJ1

A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = [tex]x^2[/tex] * h = 8500

Solving for h, we get:

h = 8500 / [tex]x^2[/tex]

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = [tex]2x^2[/tex] + 4x(8500 / [tex]x^2[/tex]) = 2[tex]x^2[/tex]+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/[tex]x^2[/tex] = 0

Multiplying both sides by [tex]x^2[/tex] and solving for x, we get:

x = (8500/2[tex])^(1/3)[/tex] ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / [tex]x^2[/tex] ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

Learn more about square base,

https://brainly.com/question/3028557

#SPJ4

A) The Surface Area = [tex]X^2 + 34000/X[/tex]

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

[tex]X^{2Y} = 8500[/tex]

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = [tex]X^2 + 4XY[/tex]

We can substitute the value of Y from the equation for volume, giving:

Surface Area = [tex]X^2 + 4X(8500/X^2)[/tex]

Surface Area = [tex]X^2 + 34000/X[/tex]

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = [tex]20.5^2 + 4(20.5)(8500/20.5^2)[/tex]= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

[tex]X^2Y = 8500[/tex]

[tex](20.5)^2 Y = 8500[/tex]

[tex]Y = 8500/(20.5)^2 = 16.87[/tex] inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

for such more questions on surface area

https://brainly.com/question/26403859

#SPJ11

Step-by-step explanation:

[tex] - 3 = \frac{3}{4} (2) + b[/tex]

[tex] - \frac{6}{2} = \frac{3}{2} + b[/tex]

[tex]b = - \frac{9}{2} [/tex]

[tex]y = \frac{3}{4} x - \frac{9}{2} [/tex]

Alternately, starting at (2, -3), go up 3 units, then right 4 units, to (6, 0). Draw a line that goes through these points.

The equation of the circle centered at (4, -5) with radius 7 is (x - 4)²+ (y + 5)² = 49.

A circle is a two-dimensional form that may be described as a collection of points (locus) that are equally spaced apart from a central fixed point. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points at a certain radius from the centre.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)²= r²

In this case, the center of the circle is (4, -5), and the radius is 7. So the equation of the circle is:

(x - 4)² + (y - (-5))² = 7²

(x - 4)² + (y + 5)² = 49

Therefore, the equation of the circle centered at (4, -5) with radius 7 is (x - 4)² + (y + 5)² = 49.

To know more about radius, visit:

https://brainly.com/question/21298138

#SPJ1

For a survey to put an estimate the proportion of voters who support gun control, the minimum sample size is 752 that is minimum 752 people need to be included in the sample.

We have a survey which is planned to estimate the proportion of voters who support gun control. Margin of error, MOE = 3% = 0.03

Confidence level = 90% = 0.90

No information about the proportion of the voters that is p,so let's assume, p= 0.5

Level of significance, α = 1 - CI

= 1 - 0.90 = 0.10

We have to determine the sample size of people. Using the following formula for computes minimum sample size required to estimate population proportion within the required margin of error, [tex]n ≥ p( 1-p) (\frac{z_c}{MOE})²[/tex]

where, n --> sample size

[tex]z_c[/tex]--> critical value of z

using the Z-distribution table, the value of z for 90% confidence interval is 1.64.

Substitute all known values in above formula, [tex]n ≥ 0.5( 1- 0.5) (\frac{1.64}{0.03})²[/tex]

= 751.54 ~ 752( people must be a integer no.)

Hence, required minimum sample size is 752.

For more information about sample size, visit :

https://brainly.com/question/30528695

#SPJ4

the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.

How to solve the question?

The given equation is 2x² + x + 4k.

(a) For the equation to have two real solutions, the discriminant b² - 4ac must be positive.

Therefore, for this equation, b² - 4ac > 0

=> 1 - 4(2)(4k) > 0

=> 1 - 32k > 0

=> k < 1/32

Hence, all values of k less than 1/32 will give the equation 2x² + x + 4k two real solutions.

(b) For the equation to have one real solution, the discriminant b² - 4ac must be zero.

Therefore, for this equation, b² - 4ac = 0

=> 1 - 4(2)(4k) = 0

=> 1 - 32k = 0

=> k = 1/32

Hence, only the value of k equal to 1/32 will give the equation 2x² + x + 4k one real solution.

(c) For the equation to have no real solutions, the discriminant b² - 4ac must be negative.

Therefore, for this equation, b² - 4ac < 0

=> 1 - 4(2)(4k) < 0

=> 1 - 32k < 0

=> k > 1/32

Hence, all values of k greater than 1/32 will give the equation 2x² + x + 4k no real solutions.

In conclusion, the values of k for which the equation 2x² + x + 4k has (a) two real solutions are k < 1/32, (b) one real solution is k = 1/32, and (c) no real solutions are k > 1/32.

To know more about equations visit :-

https://brainly.com/question/2972832

#SPJ1

A graph of four points with integer coordinates that are each 3 units away from (2, 3) is shown in the image attached below.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).

Where:

In order to write an equation that models the four points with integer coordinates that are each 3 units away from (2, 3), we would have to apply a set of translation to f(x) by 3 units:

A (5, 3)

B (-1, 3)

C (2, 6)

D (2, 0)

Read more on coordinates here: https://brainly.com/question/27129207

#SPJ1

Answer:

I found a video that provides the answer key for the Ankara Güçlendiren

Step-by-step explanation:

The polynomials that are equivalent to  (x-3y+72)2 are

A polynomial is described as an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

A polynomial equation in two variables is an equation of the form

p(x, y) = q(x, y) where both p(x, y) and q(x, y) are polynomials in two variables.

Learn more about polynomial at:

https://brainly.com/question/4142886

#SPJ1

The distance from Earth to Mercury is approximately 5.7 x 107 miles, which is less than the fuel capacity of Spigot to travel 125% of the distance from Earth to Mars. Therefore, Spigot has enough fuel to travel from Earth to Mercury and return to Earth before refueling. The correct option is D.

Distance refers to the amount of space between two points, objects, or locations. It is typically measured in units such as meters, kilometers, miles, feet, or yards. Distance can be measured in a straight line or along a curved path, depending on the context.

Distance is often used in conjunction with time to calculate speed and velocity. For example, the distance traveled by a car in a certain amount of time can be used to calculate its speed.

Learn more about distance on

https://brainly.com/question/26550516

#SPJ1

Answer:

Let's use a system of equations to solve the problem.

Let x be the number of regular admission tickets sold, and y be the number of fast pass tickets sold.

From the problem, we know that:

x + y = 104 (equation 1)

and

8x + 22y = 1280 (equation 2)

We can use equation 1 to solve for x in terms of y:

x = 104 - y

Substituting this expression for x into equation 2, we get:

8(104 - y) + 22y = 1280

Simplifying and solving for y, we get:

832 - 8y + 22y = 1280

14y = 448

y = 32

So the student sold 32 fast pass tickets.

To find the number of regular admission tickets sold, we can substitute y = 32 into equation 1 and solve for x:

x + 32 = 104

x = 72

So the student sold 72 regular admission tickets.

Therefore, the student sold 72 regular admission tickets and 32 fast pass tickets.

There are almost 8 different dessert options that can be served.

Given that there are four fruit alternatives (watermelon, cantaloupe, pineapple and mango) and two ice cream selections (lemon or piquin chilli), the question asks how many different dessert options are offered. We can utilise the multiplication principle of counting. In this case, there are 4 ways to choose a fruit and 2 ways to choose an ice cream flavor. Using the multiplication principle, we can multiply these choices to find the total number of dessert options:

4 (fruit options) x 2 (ice cream options) = 8

Therefore, there are 8 different dessert options that can be served.

To know more about principle of counting, here

brainly.com/question/29078133

#SPJ4

--The complete Question is, Today's dessert is any of these fruits: watermelon, cantaloupe, pineapple or mango, accompanied by lemon or piquin chili ice cream. How many different desserts can be served? --

The digit 5 in 89.059 is greater than the digit 5 in 78.365.

To compare the digit 5 in the numbers 89.059 and 78.365, we need to look at the place value of the digit 5 in both numbers. In 89.059, the digit 5 is in the thousandth place, while in 78.365, the digit 5 is in the hundredth place.

Since the digit 5 in the thousandth place has a greater place value than the digit 5 in the hundredth place, it means that the digit 5 in 89.059 is greater than the digit 5 in 78.365.

To understand this concept better, consider the place value system of decimal numbers, where each digit represents a specific place value. The rightmost digit represents the units, the next digit to the left represents the tens, and so on.

Moving leftwards, each digit's place value increases by a factor of 10. Thus, the digit 5 in the thousandth place has a place value of 0.001, which is greater than the place value of the digit 5 in the hundredth place, which is 0.01. Therefore, the digit 5 in 89.059 is greater than the digit 5 in 78.365.

To know more about number place value follow

https://brainly.com/question/28726939

#SPJ1

The width of the rectangle is x + 4

Since the area of the rectangle is x^2 + 15x + 44, the product that give the value can be solved by factorization

To factorize the expression x^2 + 15x + 44, we need to find two numbers whose product is 44 and whose sum is 15. These numbers are 11 and 4, because 11 times 4 is 44 and 11 plus 4 is 15.

Now we can write the expression as:

x^2 + 11x + 4x + 44

Grouping the terms in pairs:

(x^2 + 11x) + (4x + 44)

Factoring out the greatest common factor from each pair:

x(x + 11) + 4(x + 11)

Now we can see that we have a common factor of (x + 11):

(x + 11)(x + 4)

Therefore, the factored form of x^2 + 15x + 44 is:

(x + 11)(x + 4)

the width of the rectangle is x + 4

Learn more about area of rectangle at

https://brainly.com/question/13048427

#SPJ1

Answer:

3/5 = 60% = 0.6

In the bottom row, 3/5 is the wrong fraction. 2/3 is the correct fraction.

Step-by-step explanation:

Let A(x1,y1)=(-3,1), B(x2,y2)=(5,6)  be the points of a line segment.

Mid point = [tex]\sf{ \dfrac{x1+x2}{2} , \dfrac{y1+y2}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-3+1}{2} , \dfrac{1+6}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-2}{2} , \dfrac{7}{2} }[/tex]