a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.

Answers

Answer 1

The side length of the original cube is, 8.60 feet.

What is volume?

The amount of three-dimensional space that is occupied is measured by volume. It is frequently expressed quantitatively using SI-derived units, other imperial units, or US customary units. Volume and the notion of length are connected.

Given:

A 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft^3.

Let x = the side of the cube then

x^3 = original volume of the cube and

8x^2 = volume of the 8 feet slice

Therefore,

x^3 - 8x^2 = 44

Subtract 44 on both sides,

x^3 - 8x^2 - 44 = 44 - 44

x^3 - 8x^2 - 44 = 0

After solving x ≈ 8.59553

⇒ x = 8.60

Hence, the side length of the original cube is 8.60 feet.

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Related Questions

amanda chicopee bought a new car and drove 8,000 miles in the first four months. at the same rate, how many miles will amanda drive in 3 years?

Answers

If Amanda stays on her current course, she will go 72,000 km in three years.

Given data,

In the first four months after purchasing a new car, Amanda Chicopee covered 8,000 kilometers. How many miles will Amanda log in three years if she continues on her path?

Here,

She drove 8000 km in 4 months.

⇒ In 1 month = 8000/4 = 2000 km

To find how many miles in 3 years,

⇒ In 36 months = 2000 * 36

                          = 72000 km

Hence, 72000 km will Amanda log in three years if she continues on her path.

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Find the tenth term of the
sequence.
4, 3, 0, -5, - 12, ...

Answers

Answer:

-76

each term is being subtracted from the preceding the next odd number

Ellis's backyard has a 6.25m by 6.25m patio. She would like to build a 1.5m wide extension around 3 sides of the patio. She will buy 0.25m b 0.25m tiles that come 25 to a package. How many packages does Ellis need to buy to build the extension?

Answers

Answer:

21

Step-by-step explanation:

The amount added to each of the 3 sides is a rectangle 6.25 m by 1.5 m.

Then there are two square corners added that each one is 1.5 m by 1.5 m.

Total added area = 3 × 6.25 m × 1.5 m + 2 × 1.5 m × 1.5 m

Total added area = 28.125 m² + 4.5 m²

Total added area = 32.625 m²

The area of each tile is:

0.25 m × 0.25 m = 0.0625 m²

A box of tiles has 25 tiles. The total area covered by a box of tiles is:

25 × 0.0625 m² = 1.5625 m²

The number of boxes need is:

32.625 m² / 1.5625 m² = 20.88

Since 20.88 boxes are needed, but she needs to buy full boxes, she needs 21 boxes of tiles.

Answer: 21

URGENT PLEASE HELP: Ryan planted flowers in a rectangular garden. The width of the garden is (x-8) feet and the length of the garden is 3 feet longer than the width. Write an expression for the area of the
garden.
An expression for the area of the garden is
(Type an expression using x as the variable.)

Answers

Answer:

-8 + 3 + x =  x - 5

Step-by-step explanation:

This is because X does not have a value & both 8 & 3 are constants making them computable

caitlin won a bag full of money. she has 49 bills in all. she counts $1,430. there are twenty dollar bills and fifty dollar bills in the bag. how many of each bill does caitlin have?

Answers

Answer:

30 I think but I'm not positive

Step-by-step explanation:

6x-4y=18 -x-6y=7 solve

Answers

Answer:

Solution = (2, 1.5)

Step-by-step explanation:

Step 1: Solve for y in 6x - 4y = 18

    1. 6x - 4y = 18 → -4y = -6x + 18 → y = 1.5x - 4.5

Step 2: Substitute 1.5x - 4.5 for y in -x - 6y = 7

    2. -x - 6(1.5x - 4.5) = 7

Step 3: Solve for x

    3. -x - 9x + 27 = 7 → -10x + 27 = -20 → -10x = -20 → x = 2

Step 4: Substitute 2 for x in -x - 6y = 7

    4. -(2) - 6y = 7

Step 5: Solve for y

    5. -2 - 6y = 7 → -6y = 9 → y = -1.5

Hope this helps you out :)

1. Write the slope-
intercept form
(y=mx+b) of the line
with a slope of -1/2and
one ordered pair (-6, 4).

Answers

Your mom was in my bed last night talking about you

a piece of wire 10 m long is cut into two pieces. one piece is bent into an equilateral and the other is bent into a circle. how should the wire be cut so that the total area enclosed is (a) a maximum? (b) a minimum?

Answers

For maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

What is the area of any geometrical shape?

The area of a shape is the “space enclosed within the perimeter or within the boundary” of the given shape. We calculate the area for different shapes using math formulas.

Given that a piece of wire 10m long is cut into two pieces so now we have two wires with lengths of 5m and 5m.

One wire is bent into an equilateral so the perimeter of that triangle would be 3 m.

Perimeter = 3 m

3*side = 3 m

side = 1 m

Now the area of the equilateral triangle = [tex]A=\frac{\sqrt{3}}{4}\times (side)^2[/tex]

                                                                    A = 0.4330 m² -----(I)

Now the circumference of the circle = 5 m

                      2π×r = 5

                          r = 5/2π

                          r = 0.7957 m.

Now the area of the circle = π×r²

                                            = 3.14 × (0.7957)²

                                            = 1.988 m² --------(II)

From (I) and (II), we can say that

Area of the equilateral triangle < Area of the circle

Hence, for maximum area the wire should be bent in the form of circle  and for minimum area the wire should bent into equilateral triangle.

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Can someone please help me? I need help
BTW this is algebra 2

Answers

Answer:

Step-by-step explanation:

1. is .4444444 or 4/9

All you do for this is enter -2 as x for 4(3)^x

2.  is x^24 or answer (4)

this is because you will multiply the exponents starting with -4 till you get 24.  

-4 x -1 = 4

4 x 6 = 24

3. sorry I have to go for this one, plug in any number into x and experiment with the 4 answers till one of them gives you the same solution

given the slope m of a line and a point (x, y) on that line, how can you determine the coordinates of another point on the line?

Answers

To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.

When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.

The equation of the line is written in the slope-intercept form, which is:

y = mx + b, where m represents the slope and b represents the y-intercept.

Finding the distance from the known endpoint to the midpoint and then applying the same transformation to the midpoint is the quickest way to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, so the new x-coordinate is 2-2 = 0.

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A recipe for cheesecake requires 3 cups of sugar per
batch.
A. Write an equation that can be used to determine y,
the number of cups of sugar required to make
cheesecake, based on x, the number of batches.
B. Use your equation to determine how many cups of
sugar are required to make 4 batches of cheesecake.
Pls hurry!!

Answers

Answer:

y = x × 3, 12

Step-by-step explanation:

If a recipe for cheesecake requires 3 cups of sugar per batch, we can use this equation:

y = x × 3

Using this, we can determine how many cups are needed when we need to make 4 batches.

y = 4 × 3 = 12

You need 12 cups of sugar for 4 batches.

Irina predicted that she would sell 75 books, but she actually sold 95 books. Which expression would find the percent error? Use the table below to help answer the question.

Answers

Answer:

21%

Step-by-step explanation:

Approximate number = 75 

exact number = 95error

approximate number - exact number| ÷ exact number error = |(75-95)| / 95 = |20| / 95 = 0.21percentage of error = 0.21 x 100% = 21%


The answer should be correct! Hope it helps!!! Mark as Brainliest. It would make my day! Thank you :)

he fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) use the data to test the hypothesis that the proportion is not 0.04. use ????α

Answers

The proportion is not equal to 0.04.

The test statistic

Z =  1.149

What is the random sample?

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

Since the calculated value of Z =  1.149 is less than 1.96 at 5% (0.05) level of significance.

The null hypothesis is accepted

Hence the proportion is not equal to 0.04

Given data a random sample of 300 circuits is tested, revealing 17 defectives.

The proportion of success

P = 17 / 300 = 0.056                                    

Null hypothesis:- H₀ = P ≠0.04

Alternative hypothesis:- H₁ = P =0.04

Q = 1-P = 1-0.04=0.96

Level of significance ∝ =0.05

The test statistic

[tex]z = \frac{p -P}{\sqrt{PQ/n} }[/tex]

now substitute all values, and we get

on calculation, Z =  1.149

Since the calculated value of Z =  1.149 is less than 1.96 at a 5% (0.05) level of significance.

The null hypothesis is accepted.

Hence the proportion is not equal to 0.04.

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Solve the system algebraically.

4x+2y=104x+2y=10

x=y+13x=y+13

Answers

The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equations are,

4x + 2y = 10

x = y + 13

Now,

Since, The system of equations are,

⇒ 4x + 2y = 10  ..(i)

⇒ x = y + 13  

⇒ x - y = 13    ..(ii)

Multiply by 2 in equation (ii) and add with (i);

⇒ 2x - 2y + 4x + 2y = 26 + 10

⇒ 6x = 36

⇒ x = 6

And, x - y = 13

⇒ 6 - y = 13

⇒ 6 - 13 = y

⇒ y = - 7

Thus, The solution of the system of equation are;

⇒ x = 6

⇒ y = - 7

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Nobody ANSERS MY QUESTONS pleas help me

Answers

Answer:

∠RPQ = 105

∠R = 45

Step-by-step explanation:

Question 1

By intersecting chord theorem ? = (175 + 35) / 2

? = (175 + 35) / 2

? = 210 / 2

? = 105

(See image below)

Question 2

By intersecting secant theorem ∠R = (140 - 50)/2

∠R = (140 - 50)/2

∠R = 90/2

∠R = 45

(See image below)

Intersecting chord theorem : Corresponding angle equals sum of corresponding arcs divided by two

Intersecting secant theorem : The inscribed angle equals major arc minus minor arc divided by two

he points ​(​12,10​) and ​(30​,25​) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.

Answers

The slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

What is a slope?

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. the slope is defined as the ratio of the rise to the run.

Given that points ​(​12,10​) and ​(30​,25​) form a proportional relationship.

The slope of the line passing through the two points will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 25-10 ) / ( 30-12 )

Slope = 15 / 18

Slope = 5 / 6

Therefore, the slope of the two points passing through points  (​12,10​) and ​(30​,25​) will be 5 / 6.

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For what type of variable does it make sense to construct a confidence interval about a population​ proportion?.

Answers

A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

Given,

We must determine the kind of variable needed in the given problem to build a confidence interval for a population proportion.

Considering that;

The percentage of the entire population that possesses a specific quality is known as the population proportion (which is qualitative in nature). Therefore, a qualitative variable with two alternative outcomes must be used to generate the confidence interval for the population proportion.

Therefore, the nature of the various types of variables is used to choose the correct option. A qualitative variable with two possible outcomes (Option D) is necessary to build a confidence interval for the population proportion.

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Question is incomplete. Completed question is given below;

What type of variable is required to construct a confidence interval for a population proportion?

A. Quantitative

B. Qualitative with any number of possible outcomes

C. Continuous

D. Qualitative with 2 possible outcomes

E. Discrete

F. Qualitative with 3 or more possible outcomes

10 degrees
below 0

Is it negative or positive or zero

Answers

Answer:

Step-by-step explanation:

It's -10 degrees

Please help need this done asap

Answers

2. 2x-7=3 Addition Property

3. 2x=10  Division Property

4. x = 5

Answer:

I hope I helped

I have not been taught on this topic yet but I manage to answer the question if the answer is wrong it isn't my fault I haven't been taught yet.

I wish you a happy day

Step-by-step explanation:

1.)4x – 7 = 2x + 3

4x – 2x – 7 = 2x – 2x + 3 (subtraction property)

2x – 7 = 3

2x – 7 +7 = 3 + 7(addition property)

2x = 10(division property)

x = 5(reflexive property)

help me please/............................................ . . . . . . . . . . . .

Answers

The value of x=11 and the value of an angle ∠RDB=45°.

What is meant by an angle?

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to the measurement of an angle or a rotation. This measurement is the ratio of the length of a circular arc to its radius.

By using the secant-secant theorem,

(13x+7-60)/2=5x-10

13x-53=10x-20

3x-53=-20

3x=33

x=11

m ∠RDB=5(11)-10

=45°

Hence, the value of x=11 and the value of an angle ∠RDB=45°.

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My question is below!

Answers

Answer:

Below

Step-by-step explanation:

s = small box number         volume =  6s

L = large box number         volume   = 15L

6s + 15 L =243    

  AND      s = L +2  

Find the Laplace transform F(s) = L{f(t)} of the function f(t) = sin^2 (wt), defined on the interval t >= 0. F(s) = L {sin^2 (wt)} = For what values of S does the Laplace transform exist

Answers

The laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

Given,

[tex]f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}[/tex]

applying laplace transform on both sides,

[tex]L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex]

The range for values of s for which F(s) exists is when F(s)≥0

[tex]\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0[/tex]

using formula to find roots,

[tex]s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi[/tex]

Thus,  the laplace transform of f(t) is [tex]F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}[/tex] and it's values exists for [tex]s=w\pm\sqrt{3}wi[/tex].

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customers is equally likely to report a food allergy, what is the probability that at least one customer will report a food allergy?

Answers

The probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

Given that.

The percentage of customers who will disclose a food allergy is 0.08

At Ying Ying's bakery, 121 people place orders on a single day.

We can utilize the binomial distribution if we believe that each of the 12 clients has an equal probability of reporting a food allergy.

Formula for Binomial probability distribution:

P(X=x)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

Where P(x)= probability of getting success in x trials,

n= sample size ,

p represents the probability that each event will succeed.

As stated, we have n=12

p=0.08

Let x signify that the client will disclose a food allergy.

Following that, the probability that at least one client will disclose a food allergy will be:

P(x≥1)=1-P(x<1)

=1-P(x=0)

=1-¹²C₀(0.08)⁰(1-0.08)¹²⁻⁰

=1-(1)(0.12)¹²

=1-0.3677

=0.6323

Therefore, the probability that at least one client will disclose a food allergy will be 0.6323 when the percentage of customers who will disclose a food allergy is 0.08.

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5/3 x + 1/3 x = 40/3 + 8/3 x

Answers

Solution
Isolate the variable by dividing each side by factors that don't contain the variable.
x=−20

The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers - 12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. We can use a simulation to see if this result is likely to happen by chance. How would you use random digits to imitate one repetition of the process? What variable would you measure?

Answers

We will use certain constraints to imitate the repetition of the process as mentioned below

To simulate one repetition of the procedure using random digits, we shall perform as follows:

from a line of the random digits table, ten one and two-digit numbers could be selected with the following conditions;

1. skipping repeated numbers

2. skipping numbers from 77    to 99  

here the numbers 01   to 12   i.e. first-class passengers in the group of selected random numbers are to be counted.

As we know, numbers represent first-class passengers while numbers to represent coach-class people.

Hence, using this we can use random digits

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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.

Answers

Option B, The center 95% of players had an average weight of 151 pounds.

Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.

So, let x represent a football player's weight.

X ≅ N(200, (25)²)

The minimal weight of the center 95% of the members is

P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)

P(X > 95) = P(-4.2 < z)

P(X > 95) = - P(z < -4.2)

P(X > 95) = 0.1512

The needed percentage is 0.1512 × 100 = 151.2 percent.

A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

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An investigator wants to estimate caffeine consumption in high school students. How many students would be required to estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.
Alpha = _____
Z = _____
p = _____
Effect Size = _____
n = _____

Answers

The value of alpha is 0.025. The Z-value is 1.96. The P(z) is 0.5. The effect size is 0.05. The Sample size for the study is 384.

What is confidence interval?

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. The 68-95-99.7 Rule states that 95% of values lie within two standard deviations of the mean, hence to get the 95% confidence interval, you add and subtract two standard deviations from the mean.

Here,

All the calculations attached in image.

z= 1.96

p = 0.5

q = 1-p = 0.5

E = 0.05

sample size =

(z^2).(pq)=(1.96^2).(0.5)(.0.5)

384.16,

round up

n for study =385

Alpha has a value of 0.025. There is a 1.96 Z-value. P(z) equals 0.5. The impact factor is 0.05. The Sample size for the study is 384.

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A landscape artist plans to draw a pair of mountains, so he takes some measurements and draws the figure below. (Note: the peaks are NOT right angles, and sides of the mountains are parallel). Find the measurement of x, y, and z. Explain your reasoning and show your work.

Answers

The angle measures in this problem are given as follows:

x = 88º. y = 55º.z = 37º.

How to obtain the angle measures?

The sides of the mountains are parallel, which means that the angles of these sides have the same measures, as follows:

y = 55º, as the measure on the first mountain is parallel to the measure of 55º in the second mountain.z = 37º, as the measure of 37º on the first mountain is parallel to the measure of z on the second mountain.

Then the measure of x is obtained considering that angles x, y and z form a ray, that is, the sum of their measures is of 180º, hence:

x + y + z = 180

x + 55 + 37 = 180

x = 180 - (55 + 37)

x = 88º.

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A pyramid has a square base with edges that measure 6 meters, and a slant height of 7. 5 meters. What is its surface area? 270 45 126 102.

Answers

The surface area of the given pyramid 126 m².

What do you mean by surface area?

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

According to data in the given question,

We have the given information:

A pyramid has a square base with edges that measure 6 meters, and a slant height of 7.5 meters.

Now, we need to determine the surface area of given pyramid,

The formula for a pyramid's surface area with a square base is:

[tex]SA=b^{2}+2*(bs)[/tex]

Where b is the base length and s is the slant height.

We have the following information for the stated situation,

b= 6 m

s= 7.5 m

Then, we will putting the given values in the above formula,

[tex]SA=b^{2}+2*(bs)[/tex]

[tex]SA=6^{2}+2*(6*7.5)\\SA=36+90\\SA=126m^{2}[/tex]

Therefore, the surface area is 126m².

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what is the statement of |4×+12|=0​

Answers

Step-by-step explanation:

4x+12=0

4x= -12

x = -3

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Other Questions
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