The general formula to describe the variation: M varies jointly with the cube root of the difference B and b is [tex]M=k \sqrt[3]{(B-b)}[/tex]
What is joint variation?
When two (or more) other variables are held constant, joint variation occurs when one variable directly fluctuates as each of the other variables.
Given that;
M varies jointly with the cube root of the difference B and b
The difference of B and b (B-b)
let K be the the constant of proportionality
cube root of the difference B and b, [tex]\sqrt[3]{(B-b)}[/tex]
Then we have [tex]M=k \sqrt[3]{(B-b)}[/tex]
[tex]\[ M = k \cdot \sqrt[3]{B - b} \][/tex]
Explanation:In the given context, the formula [tex]\( M = k \cdot \sqrt[3]{B - b} \)[/tex] represents a joint variation between the variable M, the cube root of the difference between B and b, and a constant of proportionality (k).
Joint variation occurs when a variable is directly proportional to the product of two or more other variables, each raised to a specific power.
Breaking down the formula, [tex]\( \sqrt[3]{B - b} \)[/tex] signifies the cube root of the difference between B and b. This reflects the relationship where M is jointly influenced by both the magnitude and sign of the difference between B and b.
The constant of proportionality (k) is introduced to account for the specific numerical relationship between M and the cube root of the difference.
For a practical example, consider a scenario where M represents the volume of a gas, B is the initial pressure, and b is the final pressure. The formula captures how the volume varies jointly with the cube root of the pressure difference.
As the pressure difference increases, the cube root of the difference influences the volume of the gas, and the constant of proportionality ensures the appropriate scaling of this relationship.
The joint variation formula provides a concise representation of the complex relationship between the variables involved.
i am a polygon that connects with the bases of a polyhedron
What is the product of 0.04,-0.9,1.5
The product of the numbers 0.04,-0.9,1.5 is -0.054 because the multiplication of negative and positive quantities is negative.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
As we know, we can apply the arithmetic operation to any real numbers
Also, the number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
The numbers are:
0.04, -0.9, and 1.5
= 0.04x-0.9x1.5
First, multiply the first two numbers 0.04 and -0.9
= -0.036x1.5
(The multiplication of negative and positive quantity is negative)
= -0.054
Thus, the product of the numbers 0.04,-0.9,1.5 is -0.054 because the multiplication of negative and positive quantity is negative.
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Martin says the area of a tile with a length of 1 foot by a width of 1 foot has an area of 1 square foot. And, to find 1 2 12 of this area, he would need to find 1 2 12 of the width and 1 2 12 of the length, and then multiply those two values. Unfortunately, his method is incorrect. Show at least one equation to show why this method would not work, and briefly state a method that will find 1 2 12 of 1 square foot.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
If two figures are similar. then the ratio of its areas is equal to the scale factor squared
In this problem we have a tile with a length of 1 foot by a width of 1 foot
The area of the tile is equal to
[tex]A=LW[/tex]
substitute the values
[tex]A=(1)(1)=1\ ft^{2}[/tex]
Let
z-------> the scale factor
x------> the area of 1/2 tile
y------> the area of the original tile
so
[tex]z^{2} =\frac{x}{y}[/tex]
substitute
[tex]z^{2} =\frac{(1/2)}{1}[/tex]
[tex]z=\frac{\sqrt{2}}{2}[/tex] -----> scale factor
therefore
To find the area of 1/2 tile must multiply the dimensions of the tile by the scale factor
so
[tex]L=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]
[tex]W=1*\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}\ in[/tex]
Calculate the area
[tex]A=\frac{\sqrt{2}}{2}*\frac{\sqrt{2}}{2}=\frac{1}{2}\ ft^{2}[/tex]
Martin's method is incorrect because to find the area of 1/2 tile, he multiplies the dimensions by 1/2
so
[tex]L=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]
[tex]W=1*\frac{1}{2}=\frac{1}{2}\ in[/tex]
the area will be
[tex]A=\frac{1}{2}*\frac{1}{2}=\frac{1}{4}\ ft^{2}[/tex]
If Sally walked 1⁄2 kilometer in 1⁄4 hour, how fast, in kilometers per hour, was she walking?
Answer:
Sally walks at a speed of 2 kilometers per hour.
Step-by-step explanation:
Given data
Walked distance (d): 1/2 kilometerElapsed time (t): 1/4 hourWe can find the speed (v) of Sally using the following expression
v = d/t = (1/2 km) / (1/4 h) = 2 km/h
Sally walks at a speed of 2 kilometers per hour.
Ms. Stapleton had 2,600 hens, ducks, and goats on her farm. 35% of them were hens, and 25% of them were goats. How many ducks did she have on her farm ?
the perimeter of a rectangle is p units. iF ITS LENGTH AND WIDTH ARE TRIPLED WHAT IS THE PERIMETER OF THE NEW RECTANGLE
The local parts shop buys a machine that costs $500000. Its value depreciates exponentially each year by 10%. What is the machines value after 5 years? Round your answer to the nearest integer.
The perimeter of a rectangle is 42 centimeters.What is the length and width if the width is 3 centimeters more than half the length? Please include work.
The rectangle's length is 12 cm, and the width is 9 cm, calculated by setting up a system of equations using the given perimeter and the relationship between length and width.
Explanation:To find the length and width of the rectangle when given its perimeter and a relationship between its length and width, we can set up a system of equations. First, let's denote the length of the rectangle as L and the width as W. According to the question, the width is 3 centimeters more than half the length, so we have W = ½L + 3.
Since the perimeter (P) of a rectangle is given by P = 2L + 2W, and we know the perimeter is 42 centimeters, we can set up an equation: 42 = 2L + 2(½L + 3). Simplifying this, we get 42 = 2L + L + 6 or 42 = 3L + 6. Subtracting 6 from both sides gives us 36 = 3L or L = 12 centimeters for the length.
Now we can find the width using the previous relationship W = ½L + 3. Substituting the value of L, we get W = ½(12) + 3 = 6 + 3 = 9 centimeters for the width.
Therefore, the length is 12 centimeters and the width is 9 centimeters.
The surface temperature on Mars can range from -17.2°C to -107°C. Which temperature is lower?
Solve the following equation. x + 6 = x + x 2 6 14 72
The solution to the given equation is 6. Therefore, the correct answer is option B.
The given equation is x+6=x+x.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, x+6=2x
Transpose x to other side of the equation, we get
2x-x=6
x=6
Therefore, the correct answer is option B.
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Which of the following is the inverse of y=6^x ?
A. Y=log 6x
B. Y=Log x6
C. YLog1/6X
D. Y=Log 6. 6x
replace x with y and y with x,
x=6^ythe answer is the option A.) Y=log 6x
Answer:
A
Step-by-step explanation:
edge 2021
Shelley is fresh out of college and looking for housing in Boston. She makes $37,000 a year and may have to move within two years to her company’s office in Dallas. What should Shelley value when looking for housing?
1. flexibility and short term cost
2. tax incentives and home appreciation
3. maintenance and homeowner’s fees
4. stability and long term costs
thank you for you help and time!!!
answer is 1
as Shelley has to live in Boston for only 2 years, she needs to consider that the owner is flexible enough to make 2 year rent agreement and the short term rent of the house.
Other choices are irrelevant. they may be applied while purchasing home with long term aim to stay in the place.
What is the probability of getting either a sum of 66 or at least one 66 in the roll of a pair of dice?
Max ran 50 meters in 10 seconds. molly ran 30 meters in 5 seconds. who ran faster
To find who ran faster, we have to find the speed of Max and Molly
The formula for speed is given as Distance/Time
Max's speed
Distance Max ran = 50 meters
Time = 30 seconds
Speed = 50 m/30s
= 1.67 meters/second
Molly's speed
Distance Molly ran = 30 meters
Time = 5 seconds
Speed = 30m/5s
= 6 meters/second
Therefore, Max ran faster than Molly with a speed of 1.67 meters/second.
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Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.
Answer:
its B
Step-by-step explanation:
4x (3x + 8y)-7y (5x-1) Simplify the expression above. Which of the following is correct?
What is the expression in factored form? x2 + 14x + 48
In triangle JKL and triangle PQR line JK = PQR line KL equals QR angle K equal angle Q then JKL must be congruent triangle PQR
Answer: True
Step-by-step explanation:
I don’t have one I know the answer because I am currently taking the quiz right now.
On a graph, which characteristic shape is shown by exponential growth?
A. T-Shaped graph
B. S-Shaped graph
C. J-Shaped graph
D. Straight horizontal line
Answer:
C. J-Shaped graph
Step-by-step explanation:
A. T-Shaped graph
T- shaped graph can represents a rational function or quadratic function
B. S-Shaped graph
S shaped graph represents a cubic function. because it crosses x axis at two points.
C. J-Shaped graph
J shaped graph represents exponential function. the graph of J shape goes on increasing so its an exponential growth
D. Straight horizontal line
Straight line graph represents linear equation.
Anita divides 1438 by a multiple of 10. Her answer has a 3 in the tenths column. what number did she divide by?
Answer:
40
Step-by-step explanation:
Given that Anita divides 1438 by a multiple of 10
i.e. she might have divided by 10 or 20 or 30 .....
The tenth column is 3
So quotient value would be
30+d for some d in the unit column
It may be 31 or 32.....
Say it is 31, then 1438/31 =46.38 and
1438/39 = 36.87
i.e she must have divided by 40 only
Verify:
1438/40 =35 as quotient and 38 as remainder.
So she divided by 40
what are the mean,median ,mode and range of the data set given the altitude of lakes in feet -11, -28, - 17, -25, -28, -39, -6, and -46
The mean is the sum of data given to the total sample size.. The mean, median, mode, and range are -25, -28.-28, and 40 respectively
How to calculate the mean, median, mode and rangeThe mean is the sum of data given to the total sample size.
Mean = Sum of data/sample size
Mean = -11-28-17-25-28-39-6-46/8
Mean = -200/8
Mean = -25
Calculate the median
Median is the middle number after rearrangement
-46, -39, -28, -28, -25, -17, -11, -6
From the arrangement, the median of the data is -28
Calculate the mode
The mode is the value with the highest frequency. From the data given, the mode is -28
Range:
Range = highest value - lowest value
Range = -6 - (-46)
Range = 40
Hence the mean, median, mode and range are -25, -28.-28 and 40 respectively
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Follow the steps above and find c, the total of the payments, and the monthly payment. Choose the right answers. Jane Smart buys a new SUV. The price, including tax, is $22,500.00. She finances the vehicle over 60 months after making a $2,000 down payment. The true annual interest rate is 12%. What are Jane's monthly payments (principal plus interest)? To the nearest penny, c = $. Total of payments = amount financed + c = $. Total of payments ÷ number of payments = monthly payment = $.
To calculate Jane's monthly car loan payments, we must determine the amount financed, total of the payments, and monthly payment. After deducting the down payment from the price of the SUV, we find the amount financed. To calculate the total of the payments, we multiply the amount financed by the monthly interest rate. Finally, we divide the total of the payments by the number of months to find the monthly payment.
Explanation:To find the monthly payments for Jane Smart's car loan, we need to calculate the amount financed, the total of the payments, and the monthly payment.
First, we calculate the amount financed by subtracting the down payment from the price of the SUV: $22,500 - $2,000 = $20,500.Next, we calculate the total of the payments, which is the amount financed plus the interest. To calculate the interest, we multiply the amount financed by the true annual interest rate and divide by 12 to get the monthly interest rate: ($20,500 * 0.12) / 12 = $205.Then, we add the amount financed to the total interest to get the total of the payments: $20,500 + $205 = $20,705.Finally, we calculate the monthly payment by dividing the total of the payments by the number of months: $20,705 / 60 = $345.08 (rounded to the nearest penny).So, Jane's monthly payment for the SUV is $345.08.
please help me!!! will give brainlists!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
You have $3,750 to deposit. If you deposit the money in a savings account at your local bank, you will earn 1.75% annual interest and will be able to make ATM withdrawals at your bank’s ATMs. If you deposit the money in an online savings account, you will earn 3.25% interest, but you will be charged $4 every time you make an ATM withdrawal. Assuming that your ATM withdrawals do not reduce the amount of interest you earn, roughly how often must you make an ATM withdrawal for the local savings account to be a better deal than the online savings account?
To determine how often ATM withdrawals must be made for the local savings account to be a better deal than the online savings account, we compare the interest earned and ATM fees. By solving the inequality, it is found that more than $14.06 ATM withdrawals must be made in a year.
Explanation:To determine how often you must make ATM withdrawals for the local savings account to be a better deal than the online savings account, we need to compare the interest earned from each account and the fees associated with ATM withdrawals. Let's assume the time period is one year.
For the local savings account, you earn interest of 1.75% annually. So, if you deposit $3,750, you will earn ($3,750 * 1.75%) = $65.63 in interest.
For the online savings account, you earn interest of 3.25% annually. However, each ATM withdrawal incurs a fee of $4. Let's assume you make 'x' withdrawals in a year. So, the total interest earned would be ($3,750 * 3.25%) - ($4 * x).
We need to find the point where the interest earned from the online savings account is less than the interest earned from the local savings account. This can be calculated as:
($3,750 * 3.25%) - ($4 * x) < $65.63
Simplifying this inequality, we get:
0.0325 * $3,750 - $4 * x < $65.63
Adding $4 * x to both sides, we have:
0.0325 * $3,750 < $65.63 + $4 * x
Simplifying further, we get:
$121.87 < $65.63 + $4 * x
Subtracting $65.63 from both sides, we have:
$121.87 - $65.63 < $4 * x
Simplifying again, we get:
$56.24 < $4 * x
Dividing both sides by $4, we find:
$14.06 < x
So, you must make more than $14.06 ATM withdrawals in a year for the local savings account to be a better deal than the online savings account.
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Prove that the square of an odd number is of the form 8k+1 g
Show that n is odd →∃m∈ℤ,n2=8m+1
Let k be an integer so that n=2k+1. Then n2=(2k+1)2=4k2+4k+1=2(2k2+2k)+1.
But this isn't equal to 8m+1, so can I change that into 4(2m)+1?
Express the following sum in sigma notation:
1+4+7+10+13
The given series is an arithmetic series with a common difference of 3. The sigma notation for this series is [tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]
Explanation:The given series 1+4+7+10+13 is an arithmetic series, where the common difference between consecutive terms is 3. Sigma notation or summation notation is a way of expressing this long sum in a concise way. The rule for the nth term in your series is
[tex]\(a_n = 1 + 3 \cdot (n-1)\), where \(a_n\)[/tex]
stands for the nth term. So, the sigma notation for this series would be
[tex]\[\sum_{n=1}^{5} (1 + 3 \cdot (n-1)).\][/tex]
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Martin says the area of a tile with a length of 1 foot by a width of 1 foot has an area of 1 square foot. And, to find 1/2 of this area, he would need to find 1/2 of the width and 1/2 of the length, and then multiply those two values. Unfortunately, his method is incorrect. Show at least one equation to show why this method would not work, and briefly state a method that will find 1/2 of 1 square foot.
Answer:
His method is incorrect. By finding 1/2 the width and 1/2 the length, if we multiply them , we would get 1/4 of the original area.
Area = 0.5*l*0.5*w = 0.25*l*w = l*w/4
Let us establish
length = l
width = w
Original Area = l*w
Half the area = (a*l)*(b*w) = 0.5*(l*w)
This means that
a*b = 0.5
if b is equal to a, then
a = √0.5 = √2/2 = 0.707
Then, if a factor of a, where to be introduced in the lenght and width of the tile, we would obtain half the area.
A polar bear swims 390 meters at a constant rate in 150 seconds. What is the speed of the polar bear?
The speed of the polar bear is found by dividing the distance swam (390 meters) by the time it took (150 seconds). This results in a speed of 2.6 meters per second.
Explanation:The subject of your question is related to the calculation of speed, which falls under Physics. The polar bear swims 390 meters in 150 seconds. To find the speed, we apply the basic formula which is Speed = Distance/Time. Here, the distance is 390 meters, and the time is 150 seconds.
So if we divide 390 by 150, we get 2.6 meters per second. This means the speed of the polar bear is 2.6 m/s.
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On blueprint of a house, 48 millimeters represents 9 meters. The actual length of the living room is 6 meters. What is its length on the blueprint?
What is the area of the triangle in the coordinate plane? 26 units² 33 units² 36 units² 66 units²