You can use the formula V = lwh to find the volume of a box.


a. Write a quadratic equation in standard form that represents the volume of the box.


b. The volume of the box is 6 ft3. Solve the quadratic equation for x.


c. Use the solution from part (b) to find the length and width of the box.


Describe any extraneous solutions

The surface area  of the given volume of the rectangular prism is equal to 13.86 square centimeters.

Volume of the rectangular prism is 6 cubic centimeters.

Let the dimensions of the rectangular prism be length (l), width (w), and height (h).

Volume of the rectangular prism = l x w x h

⇒ l x w x h = 6

Use the given volume to find one of the dimensions .

Then use that information to find the surface area.

To calculate the surface area at least two of the dimensions known.

Let us assume that the height (h) is 1 centimeter.

⇒l x w x 1 = 6

⇒ l x w = 6

Use this equation to solve for one of the dimensions.

⇒ l = 6/w

Substituting this value of l into the surface area formula, we get,

Surface area = 2lw + 2wh + 2lh

⇒Surface area = 2(6/w)w + 2w(1) + 2(6/w)(1)

⇒Surface area = 12/w + 2w + 12/w

⇒Surface area = 2w + 24/w

Value of w that gives the minimum surface area,

Take the derivative of the surface area formula with respect to w and set it equal to 0,

d/dw (2w + 24/w) = 0

⇒ 2 - 24/w^2 = 0

Solving for w, we get,

⇒w = √(12)

Substituting this value of w back into the surface area formula, we get,

⇒ Surface area = 2(√(12)) + 24/√(12)

⇒Surface area = 4√3 + 4√3

⇒Surface area = 8√3

⇒ Surface area = 13.86 square centimeters

Therefore, the surface area of the rectangular prism is approximately 13.86 square centimeters.

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The dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

We can use the following steps:

Step 1: Write the volume formula for the cylinder.
The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the volume is given as 181 in³, we have:

181 = πr²h

Step 2: Solve for h in terms of r.
Divide both sides by πr²:

h = 181 / (πr²)

Step 3: Write the surface area formula for the cylinder without a top.
The surface area (S) of a cylinder without a top is given by the formula S = 2πrh + πr², where r is the radius and h is the height.

Step 4: Substitute h from step 2 into the surface area formula.
Replace h with 181 / (πr²) in the surface area formula:

S = 2πr(181 / (πr²)) + πr²

Step 5: Simplify the surface area formula.
After simplifying the surface area formula, we get:

S = (362 / r) + πr²

Step 6: Minimize the surface area.
To minimize the surface area, differentiate S with respect to r and set the derivative equal to 0:

dS/dr = -362/r² + 2πr = 0

Step 7: Solve for r.
To find the value of r that minimizes the surface area, solve the equation for r:

r³ = 181/π

r = (181/π)¹/³

Step 8: Find the height h.
Substitute the value of r back into the equation for h from step 2:

h = 181 / (π((181/π)¹/³)²)

Step 9: Calculate the dimensions.
Calculate the dimensions r and h using the values obtained in step 7 and step 8:

r ≈ 2.82 inches
h ≈ 7.10 inches

So, the dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.

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As an estimation of the exchange rates, 16 Euros is approximately equal to 12 Pounds.

To convert Euros to Pounds, we first need to determine the conversion rate between these two currencies. From the information provided, we know that 3 Pounds is approximately equal to 4 Euros. Using this information, we can establish a conversion factor by dividing 3 Pounds by 4 Euros:

Conversion factor = 3 Pounds / 4 Euros = 0.75 Pounds per Euro

Now that we have the conversion factor, we can use it to convert 16 Euros to Pounds. To do this, we simply multiply the amount in Euros (16) by the conversion factor (0.75 Pounds per Euro):

16 Euros * 0.75 Pounds per Euro = 12 Pounds

So, as an estimation, 16 Euros is approximately equal to 12 Pounds. Keep in mind that exchange rates between currencies can fluctuate over time, so it's always a good idea to double-check the current rate before making any financial transactions.

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Complete Question:

As an estimation we are told £3 is €4.

Convert €16 to pounds.

Answer:80%

Step-by-step explanation:

a) The mean monthly rainfall amount for City A is 334.17 inches and for City B is 5.83 inches.

b) The MAD for City A is 464.28 inches and for City B is 0.46 inches.

c) The median for City A is 5 inches and for City B is 6 inches.

(a) To find the mean monthly rainfall amount for each city, we need to add up all the rainfall amounts and divide by the number of months:

For City A: (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 334.17 inches

For City B: (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 5.83 inches

(b) To find the mean absolute deviation (MAD) for each city, we need to find the absolute deviations from the mean for each data point, then calculate the average of those absolute deviations:

For City A:

Mean = 334.17 inches

Absolute deviations from the mean: |5 - 334.17| = 329.17, |2.5 - 334.17| = 331.67, |6 - 334.17| = 328.17, |2008.5 - 334.17| = 1674.33, |5 - 334.17| = 328.17, |3 - 334.17| = 331.17

MAD = (329.17 + 331.67 + 328.17 + 1674.33 + 328.17 + 331.17) / 6 = 464.28 inches

For City B:

Mean = 5.83 inches

Absolute deviations from the mean: |7 - 5.83| = 1.17, |6 - 5.83| = 0.17, |5.5 - 5.83| = 0.33, |6.5 - 5.83| = 0.67, |5 - 5.83| = 0.83, |6 - 5.83| = 0.17

MAD = (1.17 + 0.17 + 0.33 + 0.67 + 0.83 + 0.17) / 6 = 0.46 inches

(c) To find the median for each city, we need to arrange the data points in order and find the middle value:

For City A: {2.5, 3, 5, 5, 6, 2008.5}

Median = 5 inches

For City B: {5, 5.5, 6, 6, 6.5, 7}

Median = 6 inches

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Answer:

B.

Resources, as in details of the problem and then you do check the answers and present the solution.

When approximating mixed fraction 5 6/13 to the nearest whole number, the rounded value is 5.

To round the mixed fraction 5 6/13 to the nearest whole number, we examine the fractional part, which is 6/13. The general rule for rounding mixed fractions is to consider the fractional part and round up if it is greater than or equal to 1/2, and round down if it is less than 1/2.

In this case, 6/13 is approximately 0.4615. Since it is less than 1/2, we need to round down to the nearest whole number. Therefore, when rounding 5 6/13 to the nearest whole number, the answer is 5.

A mixed fraction consists of a whole number part and a fractional part. When rounding a mixed fraction, we focus on the fractional part to determine the appropriate rounding direction. If the fractional part is exactly 1/2, it is typically rounded up to the next whole number.

However, in the case of 5 6/13, the fractional part is less than 1/2, so we round down. Rounding down gives us a more accurate approximation that is closer to the original value. In this instance, rounding 5 6/13 down to 5 provides a whole number estimate that is slightly smaller but still reasonably close to the initial mixed fraction.

Rounding serves as a useful tool in situations where precise values are not necessary and a simpler approximation is sufficient for practical purposes.

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The group of friends can consist of at most 9 people, given the budget constraint and pricing can go to the amusement park.

The inequality to determine the number of people who can go to the amusement park can be written as: 38.75p + 16.25 ≤ 365.

Where p represents the number of people and the left-hand side of the inequality represents the total cost of admission and parking for p people.

The inequality is set up such that the total cost cannot exceed the given budget of $365.

To solve this inequality, we can first subtract 16.25 from both sides: 38.75p ≤ 348.75. Then, divide both sides by 38.75: p ≤ 9

To determine the maximum number of people who can go to the amusement park with a given budget,

we can write and solve an inequality based on the cost of parking and admission per person.

In this case, the inequality is 38.75p + 16.25 ≤ 365, and the solution is p ≤ 9.

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The solution to the system of linear equations is (x, y) = (13, -4).

To solve the system of linear equations using Gaussian elimination, we need to eliminate one variable from one of the equations. Here, we can eliminate x from the second equation by subtracting twice the first equation from the second equation:

x + 2y = 5    (equation 1)

2x + 3y = 6    (equation 2)

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

  -2x - 4y = -10   (2 * equation 1)

        y = -4

Now, we can substitute the value of y into the first equation to solve for x:

x + 2(-4) = 5

x - 8 = 5

x = 13

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Answer:

H

Step-by-step explanation:

You take each given side and multiply them all together

18.4 x 8.8 x 11 = approx 1782

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part I: The payment amount for payment number 2 is $1055.69 (same as the first payment).

Part II: Interest due for payment number 2 = (Unpaid Balance after payment 1) * (Monthly Interest Rate) = $189,671.31 * (4.8% / 12) = $758.68.

Part III: Note reduction for payment 2 = Payment Amount - Interest Due = $1055.69 - $758.68 = $297.01.

Part IV: Unpaid balance for payment number 2 = (Unpaid Balance after payment 1) - (Note Reduction for payment 2) = $189,671.31 - $297.01 = $189,374.30.

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Answer: 2

sqrt 41

Step-by-step explanation:

distance formula is just d=√((x2 – x1)² + (y2 – y1)²)

√(-2+8)^2+(-5-3)^2

√(-10)^2+(-8)^2

√100+64

2√41

Answer:

In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.

Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.

Step-by-step explanation:

If both confidence intervals were correctly calculated (6. 53, 7. 95) is the 90 percent level. Therefore, the correct option is A.

To determine which confidence interval corresponds to the 90 percent level and the 98 percent level, we can look at the width of the intervals. The interval with the larger width is the one with a higher confidence level because it accounts for more possible variation in the data.

The first interval (6.53, 7.95) has a width of 7.95 - 6.53 = 1.42.

The second interval (6.20, 8.28) has a width of 8.28 - 6.20 = 2.08.

Since the second interval has a larger width, it corresponds to the higher confidence level of 98 percent. Therefore, the first interval corresponds to the 90 percent confidence level. The correct answer is option A. (6.53, 7.95) is the 90 percent level.

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The domain of a function is the set of all possible inputs for the function. In this case, the function is h(t)=80t-16t². Since time cannot be negative, the domain of h(t) is all real numbers greater than 0. Then,  required answer for the provided question is Option A.

To evaluate the maximum height reached by the rocket, now to calculate the derivative of the function h(t)=80t-16t² and set it equal to zero.
This will provide  the time at which the rocket reaches its maximum height. Therefore, here we can place  time back into the original function to evaluate the maximum height.
h(t)=80t-16t²
h'(t)=80-32t
0=80-32t
32t=80
t=2.5 seconds

Then the rocket touches its maximum height after 2.5 seconds.
To evaluate the maximum height, place t=2.5 into h(t):
h(2.5)=80(2.5)-16(2.5)²
=100 feet

Hence, the maximum height touched by the rocket is 100 feet.

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Answer: Your answer is 9y(y^3 - 4) (y^3 + 4

(The fours are not being subtracted with the exponent 3. They are separate)

The fraction is equivalent to a whole number  are 9/3, -16/8, 7/0, 0/5

A fraction can simply be described as the part of a whole variable, a whole numbers, or a whole element.

In mathematics, there are different types of fractions. These fractions are listed thus;

From the information given, we have that;

Equivalent expressions or fractions are fractions with the same solutions

Then, we have;

9/3

Divide the values

3

-16/8

-2

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The mechanic used 412 - 411.375 = 0.625 gallons of motor oil during the day.

To solve this problem, we need to convert both measurements to the same unit.

1 gallon = 8 pints (since there are 8 pints in a gallon)

So the mechanic started with:

412 gallons * 8 pints/gallon = 3,296 pints

And ended with:

5 pints

To find how much motor oil the mechanic used during the day, we can subtract the ending amount from the starting amount:

3,296 pints - 5 pints = 3,291 pints

To convert this back to gallons, we divide by 8:

3,291 pints / 8 pints/gallon = 411.375 gallons (rounded to three decimal places)

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Answer:

d

Step-by-step explanation:

so b = 4

and the slope is rise over run = 5/2

Answer:

D) [tex]y=\frac{5}{2}x+4[/tex]

Step-by-step explanation:

The line equation of a line is:

[tex]y=mx+b[/tex] with m being the slope and b being the y-intercept.

We can see from the graph that the y-intercept is 4, as that's where the line intercepts the y-axis, and when x=0.

To find the slope, we first need to pick 2 points: (0,4) and (2,9).

The formula for slope is:

[tex]\frac{rise}{run}[/tex]

The rise is how many units you go up/down from one point to another.  The run is how many units you go left/right from one point to another.
We can see that we go up 5 units and we go right 2 units.  This means our slope is 5/2.

The completed line equation is:

[tex]y=\frac{5}{2}x+4[/tex], which means D is the correct option.

Hope this helps! :)

The solution to this system of equations are x = -5 and y = 8.

In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

x + y = 3                .........equation 1.

x - 3y = -29                .........equation 2.

By subtracting equation 2 from equation 1, we have:

(x - x) + (y - (-3y) = 3 - (-29)

y + 3y = 3 + 29

4y = 32

y = 32/4 = 8

x = 3 - y

x = 3 - 8

x = -5

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One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.

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Thus, approximately 33.33% of the data values are between 25 and 45.

A box-and-whisker plot, also known as a box plot, is a graphical representation of a set of data that shows the distribution of the data along a number line. The plot is composed of a box that represents the middle 50% of the data, along with two "whiskers" that represent the lowest and highest values in the data set. The box is drawn between the first and third quartiles of the data, with a line inside the box representing the median value. The distance between the first and third quartiles is known as the interquartile range (IQR), which can be used to identify outliers in the data. Box-and-whisker plots are useful for comparing the distribution of data between different groups or data sets.

Here,

To find the percentage of the data values that are between 25 and 45 on the given box-and-whisker plot, we need to find the area of the box that is between the lower quartile (Q1) and the median (Q2). From the plot, we can see that the lower quartile (Q1) is at 30, and the median (Q2) is at 40. The interquartile range (IQR), which is the distance between Q1 and Q3, is 20.

Therefore, the box extends from 30 to 40, which is a distance of 10. The total length of the plot is 30 (from 25 to 55), so the percentage of data values between 25 and 45 is:

10/30 * 100% = 33.33%

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Complete question:

The box-and-whisker plot below represents some data set. What percentage of the data values are between 25 and 45?

The surface area of the rectangular prism with the given dimensions is 540yd².

To find the surface area (sa) of the rectangular prism with the given dimensions, we need to calculate the area of each face and add them together.

The formula for the area of a rectangle is length multiplied by width (A = l x w).

Face 1 has a length of 5yd and a width of 37yd, so its area is 5 x 37 = 185yd².
Face 2 has a length of 5yd and a width of 20yd, so its area is 5 x 20 = 100yd².
Face 3 has a length of 5yd and a width of 51yd, so its area is 5 x 51 = 255yd².

To find the total surface area, we add the areas of all three faces:

sa = area of face 1 + area of face 2 + area of face 3
sa = 185yd² + 100yd² + 255yd²
sa = 540yd²

Therefore, the numerical value of the surface area of the rectangular prism with the given dimensions is 540yd².

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Answer:

a_48000cm^3

b_48000000mm^3

Step-by-step explanation:

first of all, let's find the base area:

Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2

then, to find the volume, we need to multiplicate the base area to the height of the prism:

V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3

Distribute

50+30(2x+10)

50+30×2x+30×10

50+60×+300

add the number

50+300+60×

350+60x

60x+350

common factors

10(6x+35)

To evenly distribute 1425 stamps into 7 piles, you would divide 1425 by 7. This gives you a quotient of 203 with a remainder of 4. This means that each pile would contain 203 stamps and there would be 4 stamps left over.

To understand this better, you can visualize the process of dividing 1425 stamps into 7 equal piles. You could start by putting 203 stamps into the first pile. Then, you would add another 203 stamps to the second pile. You would continue this process until you had 7 piles, each containing 203 stamps. However, you would be left with 4 stamps that couldn't be evenly distributed.

This type of division is called integer division because it results in a whole number quotient and potentially a remainder. In this case, the quotient represents the number of stamps that can be evenly distributed among the piles, and the remainder represents the leftover stamps that cannot be evenly distributed.

Overall, to divide 1425 stamps into 7 piles, each pile would contain 203 stamps, with 4 stamps remaining.

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When the diameter of the balloon is 50 cm, the radius of the balloon is increasing at a rate of approximately 0.0254 cm/s

We are given that the volume of a spherical balloon is increasing at a rate of 100 cm³/s. We need to find how fast the radius of the balloon is increasing when the diameter is 50 cm.

Let's first find the expression for the volume of the balloon in terms of its radius.

V = 4/3 πr³

Differentiating with respect to time (t), we get:

dV/dt = 4πr² (dr/dt)

We are given that dV/dt = 100 cm³/s. When the diameter of the balloon is 50 cm, the radius is 25 cm.

Substituting these values, we get:

100 = 4π(25)² (dr/dt)

Simplifying, we get:

dr/dt = 100 / (4π(25)²)

dr/dt ≈ 0.0254 cm/s

Therefore, when the diameter of the balloon is 50 cm, the radius of the balloon is increasing at a rate of approximately 0.0254 cm/s

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ccabo de 25 años será la edad del padre tres veces mayor que la edad del hijo.El número es 36.Hay 8 hombres, 16 mujeres y 72 niños.Hay 27 cerdos y 8 pavos

Sea x el número de años transcurridos. La edad del padre será 35 + x y la edad del hijo será 5 + x. La ecuación que representa la situación es: 35 + x = 3(5 + x). Resolviendo la ecuación, tenemos:

35 + x = 15 + 3x

2x = 20

x = 10

Por lo tanto, después de 10 años, la edad del padre será tres veces mayor que la edad del hijo.

Sea x el número desconocido. La ecuación que representa la situación es: 2x - (1/2)x = 54. Resolviendo la ecuación, tenemos:

(4/2)x - (1/2)x = 54

(3/2)x = 54

x = 36

Por lo tanto, el número desconocido es 36.

Sea x el número de hombres. Según la información dada, el número de mujeres es el doble, es decir, 2x, y el número de niños es el triple, es decir, 3(x + 2x) = 9x. La ecuación que representa la situación es: x + 2x + 9x = 96. Resolviendo la ecuación, tenemos:

12x = 96

x = 8

Por lo tanto, hay 8 hombres, 16 mujeres y 72 niños en la reunión.

Sea x el número de cerdos y y el número de pavos. Según la información dada, tenemos las siguientes ecuaciones: x + y = 35 (por el total de cabezas) y 4x + 2y = 116 (por el total de patas). Resolviendo este sistema de ecuaciones, obtenemos:

x + y = 35

4x + 2y = 116

Multiplicamos la primera ecuación por 2:

2x + 2y = 70

Restamos la segunda ecuación de la primera:

2x + 2y - (4x + 2y) = 70 - 116

-2x = -46

x = 23

Sustituyendo el valor de x en la primera ecuación, tenemos:

23 + y = 35

y = 12

Por lo tanto, hay 23 cerdos y 12 pavos en la granja.

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The equivalent expressions are p−3q=11 and 3p+q=3. Option A

It is important to note that equivalent equations are defined as equations that have the same solution but are different in the way with which the values are arranged.

From the information given, we have that;

3 times (p minus q) = 2 times p + 11

This equation is represented as;

3(p - q) = 2(p) + 11)

expand the bracket, we get;

3p - 3q = 2p + 11

collect the like terms

3p - 2p - 3q =11

Subtract the values

p - 3q = 11

Then,

4 times p + q = p + 3

4p + q = p + 3

collect like terms

4p - p + q = 3

3p = q = 3

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