Dylan is wrapping a birthday present for his sister. The box the gift is in has a length of 6 inches, a width of 5 inches, and a height of 3 inches. What is the minimum amount of wrapping paper Dylan will need to completely cover the box?

Given that the volume of a rectangular box is a product of its length, breadth, and height, we define our problem using the given volume of 108 cubic inches and the formula for the surface area of an open box. To find the dimensions that will use minimal material requires the application of calculus and optimization techniques.

In this problem, we know that the volume of the open rectangular box is 108 cubic inches. The volume of a rectangular box can be calculated with the formula V = xyz where x, y, and z are the length, width, and height. If we let the dimensions of the box be x, y, and z inches respectively, it means that the volume V = 108 = x*y*z.

The amount of material used or the surface area S of an open box (a rectangular box without a top) is given by the formula S = xy + 2xz + 2yz. Here, our task is to minimize this surface area.

To minimize the surface area, we need to employ calculus, specifically the concept of optimal control. However to apply calculus, we need to express S in terms of one variable. We can get this by expressing y in terms of x and z using the volume formula. This leads to a complex optimization problem that involves calculus.

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A circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that, flowers are spaced every 6​ inches, are needed to surround a circular garden with a 50​-foot ​radius.

As we know that, their is 12 inches in 1 foot.

1 foot = 12 inches

50 foot = 50 × 12 inches

50 foot = 600 inches

Circumfereeence of circle is obtained as,

C= 2πr

C=2×3.14×600

C=3768

If the floweres are spaced ​ flowers, spaced every 6​ inches, the number of are needed to surround a circular garden with a 50​-foot ​radius,

n = C / 6

n=3768 / 6

n=628

Thus, a circular garden with a 50-foot radius needs 628 flowers spaced every 6 inches.

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The correct step is to square the binomial (n - 3)² before combining like n terms.

Brayden is working on simplifying the expression 4n – (n - 3)². The correct initial step is not to distribute the negative inside the parentheses, but rather to square the binomial. This involves applying the binomial square formula [tex](a - b)^2 = a^2 - 2ab + b^2[/tex], to the expression inside the parentheses. Therefore, simplification should start with (n - 3)² resulting in [tex]n^2 - 6n + 9[/tex]. After this, Brayden should combine like n terms by adding or subtracting them to simplify the expression further.

Answer:

length is 18 and width is 10

Answer:

Your Answer is 4 CM

Step-by-step explanation:

Answer:

The value of the expression is 504.

Step-by-step explanation:

We are given the expression [tex]9P3[/tex].

Now, [tex]9P3[/tex] represents the permutations of 9 objects which are taken 3 at a time.

Also, its value is given by,

[tex]9P3=\dfrac{9!}{(9-3)!}\\\\9P3=\dfrac{9!}{6!}[/tex],

where ! represents the factorial given by,

[tex]n!=n(n-1)(n-2)...3.2.1[/tex]

Thus, evaluating the expression, we get,

[tex]9P3=\dfrac{9!}{6!}\\\\9P3=\dfrac{9\times 8\times 7\times 6!}{6!}\\\\9P3=9\times 8\times 7\\\\9P3=504[/tex]

The first step to solve this problem is to compute for the total minutes allowable in his cell phone plan. To compute for this, you have to divide the number of minutes consumed by the fraction of the time consumed.

200 minutes / 33 1/3% = 600 minutes

To compute for the remaining minutes left for this month, you have to deduct the consumed minutes to the total allowable minutes in his plan.

600 minutes – 200 minutes = 400 minutes left

Maya's bank can hold 1733 pennies.

To find out how many pennies Maya's bank can hold, we can set up an equation using the given information. Let's start with the fact that Maya's bank is 3/10 full before adding 520 pennies. This means that 3/10 of the bank's capacity is equal to 520 pennies. We can use this information to find the total capacity of the bank.

Since 3/10 of the bank's capacity is equal to 520 pennies, we can set up the equation (3/10)x = 520, where x represents the total capacity of the bank in pennies.

To solve for x, we can multiply both sides of the equation by 10/3 to cancel out the fraction. This gives us x = (10/3) * 520 = 1733.33. Since we cannot have a fraction of a penny, we round down to the nearest whole number. Therefore, Maya's bank can hold 1733 pennies.

The y intercept in the equation y=75x+50 shows that he was given $50 for his birthday which is option D.

Equation is like a relationship between two variables in equal to form which is simplified in order to get the value of both variables.

The given equation is y=75x+50 where y is the amount of money in the account and x is the number of deposits. Put the value of x=0 and we get y=50 means when deposit is 0 means no deposits then the amount of money in account is equal to 50 which concludes that Mario was given 50 on his birthday.

Hence y intercept in the equation y=75x+50 shows that he was given $50 for his birthday.

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Jalla's hourly wage, when rounded to the nearest cent, is $11.79.

To round Jalla's wage to the nearest cent, we must look at the numbers following the decimal. In this case, Jalla's hourly wage is $11.791. Decimal rounding rules tell us that if the number following the decimal is equal to 5 or more, round up; otherwise, round down. In this case, the number after the decimal is 9, more than 5, so we round the second decimal place up. Therefore, rounding to the nearest cent, Jalla earns $11.79 per hour, her rounded wage.

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Answer:

a. A rotation of 180° around the origin.

Step-by-step explanation:

A rotation of 180° around the origin would give us the same result as a reflection over the y-axis followed by a reflection over the x-axis. When we perform this rotation, we take each of its points through the transformation (x,y) ---> (-x, -y). This means that we would multiply the coordinates of each of the points on the shape by a negative. This is equivalent to reflecting a shape over the x-axis and the y-axis.

The area is the product of length and width, which is to say that the length and width are factors of the area.

Assuming the dimensions are integers, you want factors of 84 that differ by 5.

... 84 = 1×84 = 2×42 = 3×28 = 4×21 = 6×14 = 7×12

The last of these pairs differ by 5, so ...

Answer:

The answer is l=12, w=7

Step-by-step explanation:

Nancy can sell the wooden ramp for $486 based on the surface area.

The area of Rectangle is length times of width.

The area of each rectangular face is length times width, so the top and bottom faces have an area of:

2 x (8 feet x 3 feet) = 48 square feet

The side faces also have an area of:

2 x (8 feet x 6 feet) = 96 square feet

The area of each triangular face is one-half the product of the base and the height, so the front and back faces have an area of:

2 x (0.5 x 3 feet x 6 feet) = 18 square feet

The total surface area of the ramp is the sum of the areas of all the faces:

48 + 96 + 18 = 162 square feet

If each square foot of wood of the ramp is sold for $3, then the ramp would sell for:

162 square feet x $3/square foot = $486

Therefore, Nancy can sell the wooden ramp for $486 based on the surface area.

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Answer: [tex]\frac{7}{20}[/tex]

Step-by-step explanation:

From the given table, The number of times arrow comes results in section 1= 28

The total number of times spinner spins =80

Now, the experimental probability of the arrow stopping over Section 1 is given by:-

[tex]\text{P(Section 1)}=\frac{28}{80}=\frac{7}{20}[/tex]

Hence, the  experimental probability of the arrow stopping over Section 1 is [tex]\frac{7}{20}[/tex]