According to the solution we have come to find that, the length of the box is [tex](V/2)^{1/3}[/tex].
what is volume?
Volume is the measure of the amount of space occupied by a three-dimensional object or region of space. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³), depending on the unit of length used to measure the dimensions of the object. The formula for calculating the volume of a geometric shape depends on the shape, but generally involves multiplying the dimensions of the shape together, such as the length, width, and height of a rectangular prism, or the radius and height of a cylinder.
Let's start by defining the variables:
Let's call the height of the box "h".
The length and width are each twice as long as the height, so we can write: length = 2h and width = 2h.
The volume of the box is given as "V".
We can use the formula for the volume of a rectangular box to write:
V = length × width × height
V = (2h) × (2h) × h
V = 4h^3
Now we can solve for h in terms of V:
4h³ = V
h³ = V/4
h = [tex](V/4)^{(1/3)[/tex]
This gives us the formula for the height of the box in terms of its volume V.
If we are given the volume V and asked to find the length of the box, we can use the formula for length in terms of height:
length = 2h
length = 2(V/4[tex])^{(1/3)[/tex]
length = (2V/4[tex])^{(1/3)[/tex]
length = (V/2[tex])^{(1/3)[/tex]
So, the length of the box is [tex](V/2)^{1/3}[/tex].
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Joseph and Deb deposit $600.00 into a savings account which earns 5% interest compounded
continuously. They want to use the money in the account to go on a trip in 1 year. How much
will they be able to spend?
Round your answer to the nearest cent.
Answer:
We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:
A = Pe^(rt)
where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.
Substituting the given values, we get:
A = $600.00e^(0.05*1)
Using a calculator, we get:
A ≈ $632.57
Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.
Find the slope of the line.
A decreasing line that has a Y intercept of zero and passes through the point, four, negative 3.
Examine the diagram. A triangle has angles 1, 2, 3. Angle 4 is an exterior angle to angle 3. For the angles shown in the diagram, which statements are true? Select all that apply. The sum of m∠3 and m∠4 is 180°. The sum of the measures of the adjacent interior angle and one of the remote interior angles is equal to the measure of the exterior angle. ∠3 is supplementary to ∠1. m∠4 = m∠1 + m∠2. m∠1 + m∠2 + m∠3 = 180°
The statements that are true regarding the diagram given are:
m∠3 + m∠4 = 180° (angles on a straight line)m∠4 = m∠1 + m∠2 (external angle theorem)m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).What is the Triangle Sum Theorem?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
We have in the diagram that in the diagram given, the statements that are all true are:
m∠3 + m∠4 = 180° (angles on a straight line)
m∠4 = m∠1 + m∠2 (external angle theorem)
m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).
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A volleyball team wants to order a team T-shirt. The Red Nose company charges $3.50 per shirt plus a $79 flat fee. The green Machine company charges $5 per shirt plus a $40 flat fee. Let T be the total cost and R be the number of shirts
show your full work
Red Nose: t = 4.50r + 55
Green Machine: t = 5r + 40
Find the total number of shirts that would make the total cost for each company the same
Number of shirts:
Cost:
Answer:
To find the total number of shirts that would make the total cost for each company the same, we can set the two equations equal to each other and solve for the number of shirts:
Red Nose: t = 3.50r + 79
Green Machine: t = 5r + 40
3.50r + 79 = 5r + 40
Subtracting 3.50r from both sides, we get:
79 = 1.50r + 40
Subtracting 40 from both sides, we get:
39 = 1.50r
Dividing both sides by 1.50, we get:
r = 26
So the total cost for each company would be the same if 26 shirts are ordered.
To find the total cost for each company when 26 shirts are ordered, we can substitute 26 for r in each equation:
Red Nose: t = 3.50(26) + 79 = $192
Green Machine: t = 5(26) + 40 = $170
Therefore, if 26 shirts are ordered, the total cost would be $192 for Red Nose and $170 for Green Machine.
Solve the problems. Show your work.
7
1. Mr. Nguyen had 7/8
pint of water in his water bottle. Then, he drank 2/3
pint. How much water is left in the bottle?
Answer:
7/8 - 2/3 = 5/8 pint of water left in the bottle.
the unit rate for this relationship is 1 gallon per 18.25 minutes
The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.
So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:
(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons
Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be approximately 6.58 gallons.
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The complete question is :
What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?
If $14,000 is invested at 7% annual interest, which is compounded continuously, what is the account balance after 12 years, assuming no additional deposits or withdrawals are made?
the account balance after 12 years of continuous compounding at 7% annual interest, assuming no additional deposits or withdrawals are made, would be $32,447.44.
The formula for continuous compounding is:
A = P[tex]e^(rt)[/tex]
where:
A = the final amount
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate
t = the time in years
Plugging in the given values, we get:
A = 14000[tex]e^(0.0712)[/tex]
A = 14000*[tex]e^0.84[/tex]
A = 14000*2.31796
A = $32,447.44
Compound interest is a type of interest that is calculated not only on the initial principal amount, but also on the accumulated interest from previous periods. In other words, interest is added to the principal amount, and then interest is calculated on the new total amount.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
Y=38(1.09)^x
The exponential equation represents a growth, and the rate of increase is 9%.
Is it a growth or a decay?The general exponential equation is written as:
y = A*(1 + r)^x
Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).
Here we have:
y = 38*(1.09)^x
We can rewrite this as:
y = 38*(1 + 0.09)^x
So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:
100%*0.09 = 9%
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How many solutions does it have ?
Y =4
Y =4x-1
Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
You mix gas and oil to obtain 2 and 1/2 gallons of mixture for an engine. The mixture is 40 parts gasoline and 1 part oil. How much gasoline must be added bring the mixture to 50 parts gasoline and 1 part oil?
We need to add a volume of 39.69 fluid ounces of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.
What is mensuration?Mensuration is the branch of mathematics concerned with the measurement of geometric figures and parameters such as length, volume, shape, surface area, and lateral area.
According to information in the question:
The mixture is 40 parts gasoline and 1 part oil, there are 40 + 1 = 41 parts in total.
Let, the amount of oil in the mixture "x".
We know that there are 2 and 1/2 gallons of the mixture, which is the same as 2.5 * 128 = 320 fluid ounces.
So, the equation which can be formed is
x/41 * 320 = the amount of oil in the mixture (in fluid ounces)
Solving for "x":
x/41 * 320 = x/41 * 50 + 320 - (x/41 * 50)
Multiplying both sides by 41:
x * 320 = 50x + 41(320 - 50x)
Simplifying:
320x = 41(320)
x = 41 * 10 = 410 (fluid ounces of oil in the mixture)
Thus, amount of gasoline in the mixture is
40 parts gasoline / 41 parts total * 320 fluid ounces = 311.22 fluid ounces of gasoline.
Let the gasoline we need be "y", so a equation can be formed as follows
(311.22 + y)/(41 + y) * 320 = 410
Solving for y:
(311.22 + y)/(41 + y) = 410/320
Multiplying both sides by (41 + y) * 320:
311.22 + y = 410/320 * (41 + y) * 320
Simplifying:
311.22 + y = 205.625 * (41 + y)
311.22 + y = 8434.375 + 205.625y
Solving for y:
204.625y = 8123.155
y = 39.69 (fluid ounces of gasoline to add)
Therefore, we need to add 39.69 fluid ounces volume of gasoline to the mixture to bring it to 50 parts gasoline and 1 part oil.
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I need a satisfying conditions question answered thank you sm
The linear function can be written as:
f(x) = -x/3 + 17/3
How to find the linear function?A general linear function can be written as:
f(x) = ax + b
Where a is the slope, and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂), then the slope of the linear function is:
a= (y₂ - y₁)/(x₂ - x₁)
Here we know the pairs:
f(-4) = 7
f(5) = 4
So we have the points (-4, 7) and (5, 4), then the slope is:
a = (4 - 7)/(5 + 4) = -3/9 = -1/3
Then we can write:
f(x) = -x/3 + b
now we can use one of the given points, like f(5) = 4, replacing that there we will get:
4 = -5/3 + b
4 + 5/3 = b
12/3 + 5/3 = b
17/3 = b
So the function is:
f(x) = -x/3 + 17/3
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A group of 125 students went on a field trip to a museum. Mr. Shan asked a random sample of 50 students which exhibit was their favorite. Ten students favored the insect exhibit, 15 students favored the space exhibit, and 25 students favored the dinosaur exhibit. Based on the survey results, which inferences about the entire group of 125 students are true? Select TWO correct answers. 1.One-fifth of students favored the insect exhibit. 2.The dinosaur exhibit is most favored. 3.The insect exhibit is favored more than the space exhibit. 4.Only 24% of students favored the space exhibit. 5.Fifty students favored the dinosaur exhibit.
Answer:1 and 2
Step-by-step explanation:
so, they asked 50 students and then that was later broke down to smaller groups.
10,15,25
so, for every 10 students will be one. 1 vote= 10 students.
also, the dinosaur had the greatest number of votes so that explains answer 2.
In circle C with the measure of minor arc BD=42°, find mBED.
Answer: mBED = 2(42°) = 84°
Step-by-step explanation:
We are asked to find the measure of the central angle ∠BED in the circle given that the measure of the minor arc BD is 42°.
We can use the formula that states that the measure of a central angle is equal to twice the measure of its intercepted arc. That is,
m∠BED = 2*mBD
We can substitute the value of mBD, which is 42°, into our equation.
m∠BED = 2*42°
m∠BED = 84°
Therefore, the measure of the central angle ∠BED is 84°.
What is the surface area?
26 ft
36 ft
33 ft
Answer:
To calculate the surface area of an object, we need to know its shape. Please provide more information on the object's shape or context of the problem to calculate its surface area.
Find the critical numbers and absolute extrema for….
Final Answer: The critical number is x = DNE. The absolute maximum is x = 0.2, and y = -125.The absolute minimum does not exist on the interval.
To find the critical numbers?we need to find the values of x where the derivative of y equals zero or does not exist. So, we first find the derivative of y: y' = 10x^{(-3)}
The derivative is defined for all x in the interval [0.2, 2], so there are no points where the derivative does not exist.
To find where y' = 0, we set the derivative equal to zero and solve for x: [tex]10x^{(-3)} = 0[/tex] x = DNE There are no critical numbers since the derivative does not equal zero at any point in the interval.
Next, we check the endpoints of the interval: [tex]y(0.2) = -5/ (0.2^2) =[/tex] [tex]-125y(2) = -5/(2^2) = -1.25[/tex] Since y is a decreasing function on the interval,
the absolute maximum occurs at the left endpoint x=0.2: Absolute maximum: [tex]y(-0.2) = -125[/tex]
Since y is an unbounded function as x approaches zero, there is no absolute minimum on the interval [0.2, 2].
Final Answer: The critical number is x = DNE.The absolute maximum is x = 0.2, and y = -125.The absolute minimum does not exist on the interval.
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what's the square root of 144
[tex]\sqrt{144} =12\\12*12=144[/tex]
1. Identify and clearly label the slope and y-intercept for each equation in slope intercept form. Choose the correct answer from the choices below.
Y=-5
A. Slope is-5 and the y-intercept is (0,0)
B.Slope is zero and the y-intercept is (0,-5)
C. Slope is zero and the y-intercept is (0,0)
D. Slope is -5 and the y-intercept is (0,-5)
Slope is zero and the y-intercept is (0,-5)
What is slope ?
In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.
In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.
The formula for calculating slope is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation Y = -5 to y = mx + b, we can see that:
The slope, m, is 0, since there is no x-term in the equation.
The y-intercept, b, is -5, since that is the constant value in the equation.
Therefore, the correct answer is:
B. Slope is zero and the y-intercept is (0,-5)
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Help with number 4!!!
Answer:forgot the explanation
Step-by-step explanation: give me a equation to solve
Pls help meee!!
Anybody!!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
Shebane rolls a standard six sides number cube. Find p
Answer:
2/3
Step-by-step explanation:
A six sided number cube :
Sample space = 1,2,3,4,5,6
Non composite numbers on a six sided number cube = 1,2,3,5
Probability of an event = required outcome / Total possible outcomes
Required outcome = number of non composite number = 4
Total possible outcomes = sample space = 6
P(not composite)= 4/6 = 2/3
Can somebody find me a pencil to write please
Try going to the store and they should be surprisingly cheap.
Answer: here it is.
Step-by-step explanation:
which of these animals can travel at the greatest distance from sea level?
Answer:
Dragonflies
Step-by-step explanation:
They can fly on top of the water, but also, they have the fastest turns per second for their wings.
I need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1
Suppose a city with population 100,000 has been growing at a rate of 7% per year. If this rate continues, find the population of this city in 19 years.
Answer:b
Step-by-step explanation:
trust it’s b
What values of y and z make
The value of y and z are 11 and 11.
How to determine the valuesWe can see from the diagram that the two triangles are of equal lengths.
To determine the value of the variables, we have to note that;
In triangle QRS, the adjacent sides is y + 20
In triangle VX, the adjacent side is y = 31
Now, equate the values
y + 20 = 31
collect like terms
y = 31 -20
y = 11
Also, the hypotenuse sides are equivalent, then
y + 3z + 28 = 6y + z - 5
collect the like terms
y - 6y + 3z - z = -5 - 28
add or subtract the values
-5y + 2z = -33
Substitute the values
2z = -33 + 55
2z = 22
z = 11
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f(x) = 2x - 1 g(x) = 7x + 8 find (gof) (x)
Answer:
(gof)(x) = 14x + 1
Step-by-step explanation:
We can think of (gof)(x) as g(f(x)). Writing it in this form shows that we must start with the inner function and work our way to the outer function.
Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.
f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1
Now, this output becomes the input for g(x):
g(2x-1) = 7(2x - 1) + 8
14x -7 + 8
(gof)(x) = 14x + 1
The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is skewed right. However, records indicate that the mean time is 16.4 minutes, and the standard deviation is 4.2 minutes. Complete parts (a) through (c).
Question content area bottom
Part 1
(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
A.
The sample size needs to be greater than or equal to 30.
B.
The sample size needs to be less than or equal to 30.
C.
Any sample size could be used.
D.
The normal model cannot be used if the shape of the distribution is skewed right.
Part 2
(b) What is the probability that a random sample of n=35 oil changes results in a sample mean time less than 15 minutes?
The probability is approximately enter your response here.
(Round to four decimal places as needed.)
Part 3
(c) Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 35 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
There is a 10% chance of being at or below a mean oil-change time of enter your response here minutes.
(Round to one decimal place as needed.)
Part 1: a. A. The sample size needs to be greater than or equal to 30.
Part 2: The probability is approximately 0.0013.
Part 3: There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.
What is sample size?The number of individuals or items in a population that are selected for study.
A. The sample size needs to be greater than or equal to 30.
This is due to the Central Limit Theorem, which states that the sample size of a normal distribution must be 30 or more to produce reliable results.
If a sample size is less than 30, the results may be skewed and not accurately represent the true population mean and standard deviation.
B. The probability is approximately 0.0013.
This probability can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.
The z-score for a sample mean of 15 minutes =-3.3,
which translates to a probability of 0.0013 using the z-score table.
C. There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.
This can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.
The z-score for a 10% chance= -1.28,
which translates to a mean oil-change time of 14.9 minutes.
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Find the coordinates of the point 13
of the way from A to B.
If you know the coordinates for points between A and B, that you can use this method to determine the dimensions of the spot that is located (0, 1/3) between A and B.
What do coordinates number mean?A set of integers called coordinates are used to locate a spot or a shape in a two-dimensional plane. The x-coordinate as well as the y-coordinate are two integers that describe a point's location on a [tex]2D[/tex] plane.
To find the coordinates of the point that is [tex]1/3[/tex] of the way from point A to point B. we can use the midpoint formula, which states that the coordinates of the midpoint of the line segment joining two points [tex](x1, y1)[/tex]and [tex](x2, y2)[/tex] are:
[tex]((x1 + x2)/2, (y1 + y2)/2)[/tex]
In this case, let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2). Then the point that is 1/3 of the way from A to B has coordinates:
[tex]((2/3) × x1 + (1/3) × x2, (2/3) × y1 + (1/3) × y2)[/tex]
Therefore, So if you have the coordinates of points A and B, you can plug them into this formula to find the coordinates of the point 1/3 of the way from A to B.
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Given the following information, fill in the blanks.
x = 14.5, μ> 13, n = 50, o = 5.1 and a = 0.01
Round to TWO decimal places.
Critical Value: type your answer...
z-value: type your answer...
P-value: type your answer...
Reject or fail to reject? choose your answer...
✨
Answer: 46
Step-by-step explanation: i took quiz i swear the answer is
D.
At Cameron Elementary, 2 out of every 3 teachers are women. If there are 45 teachers
teaching at Cameron, how many of those are men? (2pts)
Answer: 15 of those teachers are men
Step-by-step explanation: 2 out of 3, is of course written as 2/3
if 2/3 are women, this means 2/3 of 45 is 30, meaning 30 of the teachers are women, so if 30/45 are women, the remaining 15 are men