37.70/12
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Find the discriminant of $3x^2 + \left(3 + \frac 13\right)x + \frac 13$.
The discriminant, D of the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex] when calculated is 64/9
How to determine the discriminant of the equationThe quadratic equation is given as
[tex]3x\² + 3 \frac 13x + \frac 13[/tex]
The discriminant of a quadratic equation of the form ax² + bx +c = 0 is given by the expression b² - 4ac
In this case, we have the quadratic equation [tex]3x\² + 3 \frac 13x + \frac 13[/tex], which can be written in the standard form as
[tex]3x\² + \frac {10}3x + \frac 13[/tex]
Comparing with the standard form ax² + bx + c = 0,
we have a = 3, b = 10/3 and c = 1/3
The discriminant of this quadratic equation is therefore:
D = b² - 4ac
[tex]D = (\frac{10}{3})\² - 4 \cdot 3 \cdot \frac{1}{3}[/tex]
D = 64/9
Hence, the discriminant of [tex]3x\² + 3 \frac 13x + \frac 13[/tex] is 64/9
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I heed a lot of help Guys
Answer: The graph is translated to the left 9 units
Step-by-step explanation:
When the thing is negative it will move to the right it will be positive. When it's negative it will move to the left than it will be negative.
name the property the equation illustrates-4x-1/4=1
The prοperty the equatiοn illustrates-4x-1/4=1 is multiplicatiοn inverse.
What is an equatiοn?The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.
οr,
A mathematical expressiοn cοmpοsed οf twο expressiοns jοined tοgether by the equal sign.
Given equatiοn is (-4)×(-1/4) = 1.
The name οf prοperties are
Distributive Prοperty: a(b+c) = ab + bc
Cοmmutative Prοperty: ab =ba
Assοciative Prοperty :a(bc) = (ab)c
Identity Prοperty a×b=1
Inverse Prοperty: a×b=1
These characteristics hοld true in mathematical and algebraic expressiοns just as they dο in prοpοsitiοnal language.
In the Inverse Prοperty, the prοduct οf a number and its inverse is equal tο 1.
The given equatiοn represents Inverse Prοperty.
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If two points on a line are A(4, 6) and B(8, −8), the rise is __________, and the run is __________, so the slope of the line is __________.
Jason wants to walk the shortest distance to get from the parking lot to the beach. How far is the spot on the beach from the parking lot?
How far will his place on the beach be from the refreshment stand?
A: 24 m; 32 m
B: 38 m; 12 m
C: 24 m; 18 m
D: 34 m; 16 m
the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
The answer is C: 24 m; 18 m. To find the shortest distance from the parking lot to the beach, one should measure the distance between the two locations. The distance between the parking lot and the beach is 24 m. To find the distance between the beach and the refreshment stand, one should measure the distance between the two locations. The distance between the beach and the refreshment stand is 18 m. Therefore, the shortest distance from the parking lot to the beach is 24 m and the distance between the beach and the refreshment stand is 18 m.
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Work out the value of 4 squared + 3 cubed
help if can for 10+ points
Answer:
43
Step-by-step explanation:
We can simplify the expression:
[tex]4^2 + 3^3[/tex]
by rewriting exponents as multiplication of their base.
[tex]4^2 + 3^3[/tex]
[tex]= (4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
Then, we can simplify using the order of operations (PEMDAS).
[tex](4\cdot 4) + (3\cdot 3 \cdot 3)[/tex]
[tex]= 16 + (9 \cdot 3)[/tex]
[tex]= 16 + 27[/tex]
[tex]\boxed{= 43}[/tex]
problem i need help now
Answer:
Step-by-step explanation: 55 i think
Answer:
2%?
Step-by-step explanation:
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was 2/5. How many games did they lose?
(Type a whole number)
Answer:
Ratio of 2/5 can be added like 2+5=7
And then
154÷7=22
22×2=44
22×5=110
They lost 110 games
Find an equation of the line with gradient 4 and that passes through the point
(-5, -5)
Answer:
y = 4x + 15
Step-by-step explanation:
Using 'y=mx+c' form,
Since m = 4,
y = 4x + c
Substituting (-5, -5) into the above equation:
-5 = -20 + c
c = 15
Hence,
y = 4x + 15
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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
0 , x<0
f(x) = ((x^2)/4) , 0 <= x <= 2
1 , 2<= x
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) P(X %u2264 1)
(b) P(0.5 %u2264 X %u2264 1)
(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)
(f) Calculate E(X)
(g) Calculate V(X) and %u03C3x
(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For [tex]0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.[/tex] Hence, the correct option is (a) P(X ≤ 1).
Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:
[tex]cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x[/tex]
To use the cdf to obtain the following.P(X ≤ 1)
So, the probability distribution function is the derivative of the cumulative distribution function.
∴ f(x) = d/dx(F(x))
Also, from the cdf, we know that:
[tex]f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.[/tex]
f(x) = 1 when x ≥ 2.
Using the above conditions, we have to calculate the following:
(a) P(X ≤ 1)
Here, P(X ≤ 1) = F(1).
When[tex]0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)[/tex]
Thus, for[tex]0 ≤ x ≤ 2, F(x) = (x^3/12).[/tex]
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Simplify (5+1)^2-(11+3^2) divided by 4
Answer:
(5+1)^2 = 6^2 = 36
3^2 = 9
Next, we can substitute these values into the expression:
(5+1)^2 - (11+3^2) = 36 - (11+9) = 16
Finally, we can divide by 4:
16/4 = 4
Therefore, the simplified expression is 4.
Step-by-step explanation:
A car moving at a constant speed passed a timing device at t= 0. After 7 seconds, the car has traveled 812 ft. er of seconds t after passing the timing device.
Answer: y= 116x
Step-by-step explanation:
Use dimensional analysis to convert 9 tsp to tablespoons
Using the dimensional analysis, 9 tsp is equivalent to 3 tbsp.
A conversion factor is a numerical ratio that relates two units of measurement for the same quantity
To convert 9 tsp to tablespoons using dimensional analysis, we can use the conversion factor that 1 tablespoon is equal to 3 teaspoons. We can set up the following proportion
1 tablespoon / 3 teaspoons = x tablespoons / 9 teaspoons
where x is the number of tablespoons we want to find. To solve for x, we can cross-multiply and simplify:
1 tablespoon × 9 teaspoons = 3 teaspoons × x tablespoons
9 tablespoons = 3x
x = 9 tablespoons / 3
x = 3 tablespoons
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Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free. You know that the wait times for customers are normally distributed with a mean of 20 minutes and a standard deviation of 4 minutes. Use statistics to decide the maximum wait time you would advertise to customers so that you only give away free meals to at most 1% of the customers.
a. Determine an estimate of an advertised maximum wait time so that 1% of the customers would receive a free meal. Round to one decimal place. __________ minutes
b. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 1% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below. Choose File
c. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:
An advanced explanation of the normal distribution
Why the normal distribution might apply to this situation
Describe the specific normal distribution for this situation (give the mean and standard deviation)
Explain how the graph created in part b. represents the waiting times of the customers.
Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a "nice" wait time to be used in the actual advertising campaign.
Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.
The proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal.
To answer the vice president's request, the proposed maximum wait time should be 24.2 minutes so that 1% of the customers receive a free meal. This can be seen in the graph below, which illustrates the normal distribution of customer wait times with a mean of 20 minutes and a standard deviation of 4 minutes. In this graph, the area of the curve between 0 and 24.2 minutes represents the customers who will receive a free meal, and the area to the right of 24.2 minutes represents the customers who will not receive a free meal.
The normal distribution is a common probability distribution which follows a symmetric, bell-shaped curve. It is often used to describe real-world phenomena such as customer wait times in restaurants, since it is an effective tool for modeling variation in large datasets. The normal distribution can be determined by two parameters: the mean and the standard deviation. The mean represents the average wait time, while the standard deviation describes how the wait times vary.
In this case, the normal distribution has a mean of 20 minutes and a standard deviation of 4 minutes. This means that the average wait time is 20 minutes and that the wait times may vary by up to 4 minutes. The area of the graph between 0 and 24.2 minutes can be seen as the customers who will receive a free meal, as these customers waited longer than the advertised maximum wait time. The area of the graph to the right of 24.2 minutes represents the customers who will not receive a free meal, as these customers did not wait longer than the advertised maximum wait time.
By proposing a maximum wait time of 24.2 minutes, the company will not be losing out on any profit. This is because only 1% of customers will be receiving a free meal, and the cost of this will be more than offset by the increased customer satisfaction due to faster service.
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The function y=100(1. 05)^x represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened
The given function of the cost represents exponential growth.
Exponential growth: what is it?A form of growth known as exponential growth occurs when the rate of expansion is proportionate to the present value. This implies that the rate of growth increases as the present quantity increases. An exponential function, such as the one in this question (y = abx, where an is the starting value, b is the growth factor, and x is the number of time periods), may be used to describe exponential growth. In natural and social processes, such as population expansion, economic growth, and the spread of illnesses, exponential growth is frequently seen. Yet, there are always resource constraints and other factors that will ultimately reduce or stop the expansion, therefore exponential growth cannot last eternally.
The given function is y=100(1. 05)^x.
To find cost for certain year we substitute different value of x.
From the function we observe that as the value of x increases the function increases continuously.
Hence, the given function of the cost represents exponential growth.
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The complete question is:
Find the slope of a line with the cordnates of (6,1) and (-3,5)
Answer:
Answer:
Slopem=−49
As a decimal:
m = -0.444444
Step-by-step explanation:
Slope m with two points
Graph of the line for y = mx + b
Point Slope Form y - y1 = m(x - x1)
Slope Intercept Form y = mx + b
Standard Form Ax + By = C
y-intercept, when x = 0
x-intercept, when y = 0
PLEASE HELP!!!! DUE TOMORROW AND GRADED!!!! I WILL GIVE BRAINLIEST
Answer:
f(-3) = 6
Step-by-step explanation:
You want the value of f(-3) given a graph of f(x).
Reading a graphTo find the value of f(-3), locate -3 on the x-axis. Follow the vertical grid line to where it intersects the graph of f(x). Follow the horizontal grid line from there to the axis marked f(x), and read the value on the vertical scale.
The attachment shows this process, and that the value of f(-3) is 6.
__
Additional comment
Unless there is information to the contrary, the usual assumption is that each grid line represents one unit. Positive is to the right of the vertical axis, and up from the horizontal axis. Then x=-3 is 3 grid lines left of the vertical axis.
The notation f(x) means the value of function f depends on the value x. The expression f(-3) is the function value when x=-3. Here, it is found by reading the graph. In other situations, it might be found from a table or by evaluating an algebraic expression.
Write the ratio in its simplest form: 2m: 8cm : 40mm
The simplest form of the ratio 2m : 8cm : 40mm is
50mm : 2mm : 1mm
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
For we to simplify the ratio , we have to convert the unit to the least form. The least form of the unit is millimeter
2m = 2× 1000mm = 2000mm
8cm = 8 × 10 = 80mm
40mm = 40mm
therefore the ratio will be in form of
2000mm : 80mm ; 40mm
divide through by 10
200mm : 8mm : 4mm
divide through by 4
50mm : 2mm : 1mm
therefore the simplest form of the ratio 2m: 8cm : 40mm is 50mm : 2mm : 1mm
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The area of the triangular section is (4, 6, 12, 24) square units. The area of the entire figure is (12, 48, 60, 120) square units
The area of the triangular section is 12 square units and the area of the entire figure is 60 square units.
We know that the Area of triangle is defined as the product of its height to its base.
Area of triangle = height × base
From the figure, we can see that Height is = 4 units and the base is = 6 units,
So, the area of the triangular section is = 1/2 × base × height,
⇒ (1/2) × 6 × 4
⇒ 12 square units
The entire figure consists of two figure , one is a rectangle and the other part is a triangle,
So, the area of the entire figure is = Area of rectangle + area of triangle
⇒ 4×12 + 12
⇒ 48 + 12
⇒ 60 square units
Therefore, the area of the entire figure is 60 square units.
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The given question is incomplete, the complete question is
The area of the triangular section is ___ square units, and the area of the entire figure is ___ square units. Refer to the figure given below.
Question two, please help
2/10
Answer:
C,D
Step-by-step explanation:
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
Randy's claim is not correct Therefore, he cannot purchase 3.5 pounds of chicken salad for $23.50
To determine if Randy's claim is correct, we can use the given linear graph and points to find the equation of the line that represents the relationship between the amount of chicken salad purchased and the cost.
We can use the two points (1, 7.5) and (3, 22.5) to find the slope of the line:
slope = (change in y) / (change in x)
slope = (22.5 - 7.5) / (3 - 1)
slope = 15 / 2
slope = 7.5
Now we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line:
y = 7.5x + b
To find b, we can use one of the points on the line, such as (1, 7.5):
7.5 = 7.5(1) + b
b = 0
So the equation of the line is:
y = 7.5x
Now we can use this equation to check if Randy's claim is correct. If he can purchase 3.5 pounds of chicken salad for $23.50, we can plug in x = 3.5 and see if y = 23.5:
y = 7.5x
y = 7.5(3.5)
y = 26.25
Since y = 26.25 is not equal to $23.50
Therefore, Randy's claim is not correct
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The given question is incomplete, the complete question is:
Randy claims that he can purchase 3. 5 pounds of chicken salad for $23. 50. Is he correct? Explain.
Find the unit rate for each, then tell which is the least expensive brand.
Bugsy-B: $9.99 for 64 ounces, How many dollars per ounce?
Tazi-D: $2.25 for 16 ounces, how many dollars per ounce?
Answer: Tazi-D
Bugsy-B: 0.16 per ounce
Tazi-D: 0.14 per ounce
Step-by-step explanation:
divide the $ by the ounce for both.
A family is traveling a total distance of 532 miles. If the family travels at an average speed of 57 miles per hour, which equation represents the number of miles remaining, m, after h hours?
m = 532 - (57 * h) represents the number of miles remaining after h hours of traveling at an average speed of 57 miles per hour.
The equation m = 532 - (57 * h) is used to represent the number of miles remaining, m, after h hours of traveling at an average speed of 57 miles per hour. The equation works by taking the total distance, 532 miles, and subtracting the product of the average speed, 57 miles per hour, and the amount of hours traveled, h. The result of the equation is the number of miles remaining, m. For example, if the family has been traveling for four hours, the equation would be m = 532 - (57 * 4). Solving the equation, m = 344, meaning the family has 344 miles left to travel. This equation allows the family to easily determine how many miles they have left to travel, given the average speed and amount of time traveled.
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a particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. with the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx
The work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
A particle of mass 0.58 kg is subject to a force that is always pointed towards east or west but whose magnitude changes sinusoidally with time. With the positive x-axis pointed towards the east, the x-component of the force is given as follows: fx(t) = (2.6 N) sin(2.2t)where t is in seconds.
The work done by the force as the particle moves from x = 0 m to x = 2.2 m: For a sinusoidal force that changes with time, the work done is given by W = ∫F dx where F is the force, and dx is the displacement. For this problem, the force is given by fx(t) = (2.6 N) sin(2.2t)dx is the displacement, which is given by dx = x2 – x1 where x2 = 2.2 m, and x1 = 0 m.
Substituting for F and dx, we get W = ∫02.2(2.6 sin(2.2t)) dx= 2.6 ∫02.2 sin(2.2t) dx= 2.6 [(-1/2.2) cos(2.2t)]02.2= 1.18 (cos(4.84) – 1)≈ -0.53 J. So, the work done by the force as the particle moves from x = 0 m to x = 2.2 m is approximately -0.53 J.
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What is the area of this trapezoid? Enter your answer in the box.
Answer:153
Step-by-step explanation
we can see height is equal to 9. if we consider height and 10sm as sides of rectangle, we can say top of trapezoid is equal to 10 as well.
Area of trapezoid is A=(a+b)/2*h
h-height=9
a-top=10
b-bottom=10+7+7=24
A=(10+24)/2*h=34/2*9=17*9=153
Alex picked 15 ⅘ kilograms of red apples and 9 ⅗ kilograms of green apples. What is the total mass of the apples Alex picked?
The total mass of the apples Alex picked is 25 2/5 kilograms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants
To find the total mass of the apples Alex picked, we need to add the mass of the red apples and the mass of the green apples.
First, let's convert the mixed numbers to improper fractions to make the addition easier:
15 ⅘ = 15 + 8/10 = 15 + 4/5 = 75/5 + 4/5 = 79/5
9 ⅗ = 9 + 6/10 = 9 + 3/5 = 45/5 + 3/5 = 48/5
Now we can add the fractions:
79/5 + 48/5 = (79 + 48)/5 = 127/5
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case:
127/5 = 25 2/5
Therefore, the total mass of the apples Alex picked is 25 2/5 kilograms.
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Q9) Rashmi obtains 480 marks out of 600. Rajan obtains 560 marks out of 700. Whose performance is better?
Answer:
Step-by-step explanation:
Let us first make the denominators equal, so
600 x 700 = 420000
[tex]\frac{480}{600} * \frac{700}{700} \\\\= \frac{336000}{420000}[/tex]
Similarly,
[tex]\frac{560}{700} * \frac{600}{600} = \frac{336000}{420000}[/tex]
By comparison, both of them are equal.
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Arthur can paint a wall in 45 minutes alone. Cheyenne can paint a wall in 1 hour alone. One
room has 4 walls. How many minutes will it take them to paint 3 rooms together?
The time needed to paint 3 rooms together is given as follows:
308.4 minutes.
How to obtain the time needed?The time needed is obtained applying the proportions in the context of the problem.
First we use the together rate, which is the sum of each separate rate, for the time needed to paint a single wall, hence:
1/x = 1/45 + 1/60
1/x = 7/180
7x = 180
x = 180/7
x = 25.7 minutes per wall.
The number of walls in 3 rooms is given as follows:
3 x 4 = 12 walls.
Thus the time needed to paint the 3 rooms is given as follows:
25.7 x 12 = 308.4 minutes.
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The path of a firecracker is modeled by the equation h(t) = -t^2 + 19t + 14, where h(t) is the hight, in feet, of the firecracker at any given time, t. What is the hight of the firecracker after 4 seconds from launch.
A. 63 feet
B. 68 feet
C. 70 feet
D. 74 feet
the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to plug in t = 4 into the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This gives us h(4) =[tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. Therefore, the height of the firecracker after 4 seconds from launch is 68 feet.
To find the height of the firecracker after 4 seconds from launch, we need to use the equation h(t) =[tex]-t^2[/tex] + 19t + 14. This equation models the path of the firecracker, with h(t) being the height in feet of the firecracker at any given time, t. When we plug in t = 4, we get h(4) = [tex]-4^2[/tex] + 19(4) + 14 = -16 + 76 + 14 = 68 feet. So, the height of the firecracker 4 seconds after launch is 68 feet. This equation allows us to calculate the height of the firecracker at any given time, making it a useful tool for predicting the trajectory of the firecracker.
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PLS HELP! ITS DUE TOMORROW BY 11:59pm
The ratios of the side lengths of B to A, C to B, and D to C are the same. How much more space do the boxes occupy when stored separately in a closet than when they are stacked inside each other in the closet?
1.) Yes, it will fit because the volume of the baseball is 13.36 cubic inches and the volume of the box is 64 cubic inches which is greater than the volume of the baseball.
2) The ratio of the side length of box B to the side length of box A is 1.472 inches: 6 inches.
What is circumference?The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.
To check whether the baseball is will still fit in the box we will check the maximum value of circumference.
[tex]2\pi r = 9.25[/tex]
Make r the subject formula
r= 1.472 inches
Volume of the baseball = [tex]\frac{4}{3\pi x^3}[/tex]
Expand:
13.35 inches^3 < 64 inches^3
So, it will fit inside the box.
2.) [tex]\sqrt[3]{216} = 6[/tex]
Therefore, V = a^3
The length of each side of the box is 6 inches.
The ratio of the side length of box B to the side length of box
A:
1.472 in : 6 inches
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