The volume of a container is found to be 38.5 in³. Its volume in units of cm³ will be 630.902 cm³.
Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.
We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.
To create a formula to convert 38.49 in³ to cm³, we start with the fact that 1 inch is 2.54 centimetres, which means that you multiply inches by 2.54 to get centimetres. We can therefore make the following equation:
inches × 2.54 = centimeters
(inches × 2.54)³ = centimeters³
inches³ × 16.387064 = centimeters³
in³ × 16.387064 = cm³
Now that we have the in³ to cm³ formula, we can calculate and convert 38.5 in³ to cm³. Here is 38.5 in³ converted to cm³, along with the math and the formula:
= in³ × 16.387064
= 38.5 × 16.387064
= 630.902 cm³
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how does each inverse function from part a relate to its original function? describe the relationship in terms of the context for each situation.
The inverse function is the reverse of the original function and relationship between the two functions is determined by the mapping between the inputs and outputs of the original function.
In mathematics, the inverse function is a inverse function of a function is the reverse of the original function.
To understand the relationship between an inverse function and its original function, consider the following example. Suppose we have a function that maps the height of an object to its weight.
The original function would take the height as an input and output the corresponding weight. The inverse function, on the other hand, would take the weight as an input and output the corresponding height.
It is important to note that not all functions have an inverse. A function is only considered to have an inverse if it is a one-to-one mapping, meaning that each input has a unique output.
In summary, If the original function is a one-to-one mapping, then it has an inverse function that can be found by swapping the inputs and outputs.
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ms. losch has a piece of rope long that she cuts into pieces for an experiment in her first-grade class. each piece of rope is to be long. how many long pieces of rope can she cut from the original piece of rope?
Ms. Losch can cut the original piece of rope into as many pieces as she wants, provided that each piece is the same length as the original.
If the original piece of rope is 12 inches long, she can cut it into 12 one-inch long pieces, 6 two-inch long pieces, 4 three-inch long pieces, 3 four-inch long pieces, 2 six-inch long pieces, or 1 twelve-inch long piece.
It is important to note that the pieces of rope must all be the same length, so if she wants to make any combination of the lengths, she must make sure that the total length of the pieces of rope adds up to the original length.
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A rhombus is a quadrilateral with 4 congruent sides.
Explain why quadrilateral ACBD is a rhombus.
Answer: It is because the length of the diagonals are not equal.
Step-by-step explanation: Note: The diagonals of a square are equal
write a real world deseription for the Algebraic expression 4.95x + 3
Answer:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
Step-by-step explanation:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
So you pay 4.95x + 3 for your drink and x sandwiches
The algebraic expression 4.95x + 3 can be described as the total cost of a product that has a fixed price of 3 dollars, and an additional price of 4.95 dollars per unit of the product. In this case, x represents the number of units purchased, and the expression represents the total cost of the purchase.
The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. What is the region of overlap called?
A. vertex
B. boundary line
C. intersection
D. test point
All the shaded regions of the overlap inequalities represents the located solution region of the system of linear inequalities , the overlap region is called intersection ( option C ).
Graph is attached.
Let us consider the system of linear inequalities are x + y > 1 and x -y <1.Represents both the system of inequality on the graph.Plot x + y > 1, region above x >1, y > 1 represents the inequality.Plot x - y < 1 region x < 1 , y > -1 represents the inequality.Shaded region of both the inequalities intersect each other represents the solution region of the system of inequalities.Solution region is the shaded region which get overlap.Graph is attached.
Therefore, the solution region is represented by the shaded region called (option C) intersection area of the system of linear inequalities.
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problem 6. a population of bacteria, growing according to the malthusian model, doubles itself in 10 days. if there are 1000 bacteria present initially, how long will it take the population to reach 10,000?
Here the population growth is as per the Malthusian model. As per the calculations, the bacterial population will reach 10000 after 33 days.
Here the bacterial growth is as per the exponential growth curve. So the equation is,
[tex]P_{t} = P_{0} e^{rt}[/tex]
[tex]P_{t}[/tex] is the population at n
[tex]P_{0}[/tex] is the initial population
r is the time
t is the rate
Population doubles after 10 days.
So, [tex]2000 = 1000e^{r*10} \\\\\frac{2000}{1000} = e^{10r}\\\\ 2 = e^{10r\\}\\\\[/tex]
Taking logarithms on both sides
[tex]ln(2) = lne^{10r}\\\\10r = 0.693\\ \\r = 0.0693[/tex]
So the rate is 0.0693.
When population reaches 10000,
[tex]10000 =1000e^{0.0693t}[/tex]
[tex]\frac{10000}{1000} =e^{0.0693n}[/tex]
[tex]10 = e^{0.0693*t}\\ \\ln(10) = ln(e^{0.0693t}\\ \\2.3 = 0.0693t\\\\t = 2.3/0.0693\\= 33.18[/tex]
So the number of days to reach population of 10000 is 33.18≈ 33 days.
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An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. The other side is 13 more than 4 times the length of the bottom of the triangle. The last side is 8 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
The perimeter of the triangle is the distance around the triangle.
We need to apply our ability to convert word problems in to mathematical expressions.
we were told that the bottom of the triangle is units.
From the diagram perimeter
Four times the length of the bottom will be .
12 more than 4 times the bottom will be
Hence another side of the triangle is
Finally we were told that the last side is 3 more than the bottom, that will be
Step-by-step explanation:
Are the two triangles similar? If so, how do you know
Answer:
Yes, through AA
Step-by-step explanation:
The angles of a triangle = 180
One angle is a right angle, which is 90. They give us an angle of 52.
Subtracting 180-90 = 90
Then subtracting 90-52 gives you 38
If you look at the other triangle... what's the given angle? It's 38
180-90=90
90-38 = 52
That 52 looks familiar
A produce tore offer red and green apple. In one morning they old 48 apple total. If 20 of the apple they old were red, what i the ratio of green apple old to red apple old?
The ratio of green apples sold to red apple old is:
7:5
If the store sold a total of 48 apples and 20 of them were red, then the number of green apples sold is:
48 apples - 20 red apples = 28 green applesTo find the ratio of green apples to red apples, we divide the number of green apples by the number of red apples and express the result as a fraction:
28 green apples / 20 red apples = 7/5So the ratio of green apples to red apples is 7:5, or written as a fraction, 7/5. This means for every 5 red apples sold, the store sold 7 green apples.
The ratio of green apples to red apples is a way of comparing the number of green apples to the number of red apples sold in a specific time period.
It provides a way to understand the proportion of green apples relative to red apples, and can be useful for the store to track the popularity of different types of apples.
Complete Question:
"A produce store offer red and green apple. In one morning they sold 48 apple total. If 20 of the apple they sold were red, what is the ratio of green apple sold to red apple sold?"
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On Monday, the balance in your checking account is -$149. The bank charges you a $15 fee for having a negative balance. The next day you make two deposits of $117 and $59. What is your new balance?
After making the deposits, your new balance will be $12
Given :
ray TV bisects ZUTW
ray TV is an altitude in A TUW
Prove:
Δ TUW is isosceles
Answer:
To prove that triangle TUW is isosceles, we can use the fact that ray TV bisects angle ZUT and is an altitude in triangle TUW.
Since ray TV bisects angle ZUT, it splits the angle into two congruent angles, ZTV and TVU. This means that angle ZTV is congruent to angle TVU.
Since ray TV is an altitude in triangle TUW, it forms a right angle with the base of the triangle, which is line segment TU. This means that angle TVU is a right angle, and therefore, angle ZTV is a right angle as well.
Since angle ZTV and angle TVU are congruent right angles, we know that the two sides that form these angles, UT and TU, are congruent. This means that side UT is congruent to side TU, and therefore, triangle TUW is isosceles.
which of the following scenarios contain biased samples? select all that apply. select all that apply: to estimate the mean project completions of technicians in his company, donald collects data by recording completions from the warehouse area. kenneth wants to estimate the mean market shares of his company. he collects data by selecting a random group of coworkers within one department. to estimate the male to female ratio of the residents of her city, janice collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents. amy wants to estimate the mean accidents of coworkers at her company. she collects data by recording the accidents of every 25th coworker on the list of coworkers after a randomly selecting first coworker.
The scenarios that contain biased samples is Kenneth wants to estimate the mean market shares of his company. he collects data by selecting a random group of coworkers within one department. to estimate the male to female ratio of the residents of her city, janice collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents.
What is bias in sampling?When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. the thing that makes sampling bias significant is that Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population.
The market shares only reflect one department, and no other employees have an equal chance of being chosen to represent all sales in the company, hence the sample from option B is skewed.
Therefore, option B is correct.
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Please answer asap! I need answer for the blank spaces ! Thanks!
Answer: 1 quarter or 0.25 cents.
Step-by-step explanation: According to the illustration shown, we can infer that the coin we are looking for is for 1 value. So, if we subtract the amount shown (total) from the other coins (pennies in this case), 0.27 - 0.02 = 0.25 which is equivalent to the coin of the quarter (worth $0.25 USD) So, the blanks would look like this:
1 quarters
0 dimes
0 nickles
2 pennies
I hope this helped!
Which of the following points lies on the graph of the function y = 2 times 3 Superscript x?
The point lies on the graph of the function will be (2, 18). Then the correct option is A.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The exponent equation is given below.
y = 2(3)ˣ
At x = 2, the value of the variable 'y' is given as,
y = 2(3)²
y = 2(9)
y = 18
The point lies on the graph of the function will be (2, 18). Then the correct option is A.
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The missing options are given below.
A. (2, 18)
B. (2, 11)
C. (2, 8)
D. (2, 12)
In ΔOPQ, p = 9.7 inches,
�
m∠Q=93° and
�
m∠O=82°. Find the length of q, to the nearest 10th of an inch.
Answer:
To find the length of q, we can use the Law of Cosines formula:
q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))
where p and o are the lengths of sides PQ and PO, and Q is the measure of the included angle between them.
Since we know that p = 9.7 inches and ∠Q = 93°, we can use the Law of Sines to find o:
sin(Q) = o/q
=> o = q * sin(Q)
=> o = 9.7 * sin(93)
Using this formula and rounding to the nearest tenth, we can find that o = 11.7 inches.
Now we can use the Law of Cosines to find q:
q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))
=> q = sqrt(9.7^2 + 11.7^2 - 2 * 9.7 * 11.7 * cos(93))
Rounding to the nearest tenth, we get that q = 17.2 inches.
Answer:
111.1
Step-by-step explanation:
Fred has a recipe for 30 biscuits.
Here is a list of ingredients for 30 biscuits.
Self-raising flour:
230g
150g
100g
Butter:
Caster sugar:
Eggs:
2
Fred wants to make 45 biscuits.
(a) Complete his new list of ingredients for 45 biscuits.
Answer:
*1.5
Step-by-step explanation:
45/30＝1.5
use all ingredients *1.5 then get the ans
eg. 230g*1.5＝345g
150*1.5＝225
5. The area of a rectangular plot 50m long is 1500 sqm. Find the width of the rectangular plot.
Answer:
area = length * width
1,500 = 50 m * width
width = 1,500 / 50
width = 30 meters
Step-by-step explanation:
Given points F(3, 1), G( 8, 2), H(2, 4), and J(1, 6).
a. Find the slope of FG and the slope of HJ.
b. Explain if FG and HJ are parallel, perpendicular or neither.
The slope of FG is equal to 1/5 while the slope of HJ is equal to -2.
Lines FG and HJ are neither parallel nor perpendicular because their slopes are different and not an inverse of each other.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
For the slope of line FG, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (2 - 1)/(8 - 3)
Slope (m) of line FG = 1/5.
For the slope of line HJ, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 4)/(1 - 2)
Slope (m) of line HJ = -2/1.
Slope (m) of line HJ = -2.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by m₁ × m₂ = -1 while m₁ = m₂ for an two lines that are parallel.
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solve the initial value problem. (9ye^9xy-5/y)dx (9xe^9xy 5x/y^2)dy=0, y(3)=3 the implicit solution is:
The initial value problem [tex](9ye^9xy-5/y)dx (9xe^9xy 5x/y^2)dy=0, y(3)=3[/tex] can be approximated using numerical methods such as the Euler method.
To find the initial value problem is a differential equation of the form:
[tex](9ye^(9xy) - 5/y) dx + (9xe^(9xy) - 5x/y^2) dy = 0[/tex]
with the initial condition y(3) = 3.
Since this is an implicit solution, we cannot find an explicit solution for y in terms of x. However, we can use numerical methods to find approximate solutions for y. One such method is the Euler method.
In the Euler method, we start with an initial estimate for y(x), and then use the derivative information to find y(x + h), where h is a small step size. We then use the new estimate to find the next value, and so on.
To apply the Euler method to this problem, we start with the initial condition y(3) = 3, and then use the following formula to estimate y(x + h):
y(x + h) = y(x) + h * f(x, y(x))
where f(x, y) is the derivative information from the differential equation:
[tex]f(x, y) = -(9xe^(9xy) - 5x/y^2) / (9ye^(9xy) - 5/y)[/tex]
Using the Euler method, we can iteratively estimate y(x) for increasing values of x, until we reach a desired value of x or the accuracy is within an acceptable limit.
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Ernest measured a summer camp and made a scale drawing. The sand volleyball court is 4 centimeters wide in the drawing. The actual volleyball court is 8 meters wide. What is the drawing's scale factor?
The scale factor is greater than 1. The drawing scale factor is 200.
What are the measuring units?
A unit of measurement is a specific magnitude of a quantity that has been established and adopted by law or convention and is used as a benchmark for measuring other quantities of the same kind. A multiple of the unit of measurement can be used to express any other quantity of that type. A length, for instance, is a physical quantity.
Given that, the sand volleyball court is 4 centimeters wide in the drawing. The actual length of the volleyball court is 8 meters wide.
The sacle factor is the ratio of the actual length to new object.
The scale fator is
8 meter : 4 centimeters
= 800 centimeters: 4 centimeters
= 800 : 4
= 200 : 1
=200/1
= 200
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prove that sum of angles of a convex plygon of n sides is (n-2)pi, where n>3
The IH states that the sum of the angles in convex polygon C(which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A.
Using induction all convex polygons with n vertices have angles that add to (n - 2)·π, therefore let P(n) be that. We will demonstrate that P(n), where n≥3, holds for every n ∈ N. We demonstrate P(3), which states that any convex polygon with three vertices has an angle total of 180 degrees. Any triangle formed by such a polygon has angles that add up to 180°.
Assume that P(n) holds for some n ≥ 3 and that all convex polygons with n vertices have angles that add to (n-2) 180° for the inductive step. We demonstrate P(n+1), which states that each convex polygon with n+1 vertices has an angle sum of (n-1)·π. Let A represent any n+1-vertex convex polygon.
The IH states that the sum of the angles in convex polygon C (which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A. As a result, the total angle in A is (n-1) 180°. Thus, the induction is complete and P(n + 1) holds.
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Please help I have a learning disablity and need help.
The Ramirez family drove 1,764 miles across the United States on their vacation. If it took a total of 28 hours, write a multiplication equation to find their average speed in miles per hour.
Use R
as the variable to represent their unknown average speed.
ANswer here_________________
Answer:
The answer is 63 miles per hour.
The distance (d) is multiplication of speed x and time (t):
d = x * t
d = 1,764 mi
t = 28 h
x = ?
1,764 mi = x * 28 h
x = 1,764 mi / 28 h
x = 63 miles per hour
Step-by-step explanation:
Solving Systems and Missing Angles
*Show your work and write the rule used to solve each problem
4. The magnitude of angle S is 40°. Answer A.
5. The value of x is 48°. Answer B.
6. The true conclusion is Trevor is correct because the point (4 , 0) satisfies both equations. Answer B.
7. The system of equations has infinitely many solutions. Answer D.
Two parallel lines cut by a transversal form several angles. Look at the top image on the left. Two types of alternate angles have the same magnitude of the angle
Alternate interior anglesThe tangent line of two parallel lines is equals
Line equation number 1 : ax + by = c4. From the picture
PQ and RS are parallel∠Q and ∠S are alternate interior angles ∠S = ∠Q5. Look at the top image on the right.
∠B = 42°∠A and ∠B are alternate exterior angles ∠A = ∠B6. Solve the system of equations with the substitution method
x - 2y = 4 and y = 4 - xTrevor (4 , 0)Joey (0 , - 2)x - 2y = 47. The system of equations
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tell whether each equation has one zero or infinitely many solutions.
2. 1/2n + 7 = (n+14)/2
Answer:
n/2 + 7 is always equal to (n + 14)/2
Step-by-step explanation:
Both equations are the same, re-written.
Simplify the following:
n/2 + 7
Put each term in n/2 + 7 over the common denominator 2: n/2 + 7 = n/2 + 14/2:
n/2 + 14/2
n/2 + 14/2 = (n + 14)/2:
Answer: (n + 14)/2
Is each biconditional statement true or false?
Select True or False for each statement.
An angle is a right angle if and only if the measure of the angle is 90°. True/False
An angle measures 120° if and only if the angle is an obtuse angle. True/False
An angle measures 180° if and only if the angle is a straight angle. True/False
As far as we are aware, a straight angle is defined as 180 degrees then the bi-conditional assertion is true.
What is meant by bi-conditional assertion?It combines the conditions "if two line segments are congruent then they are of equal length" and "if two line segments are of equal length then they are congruent." Only when both conditionals are true does a biconditional hold. The symbol "or" is used to denote bi-conditionals.
A statement with two conditions is one that has the form "p if and only if q." In other words, if p, then q and if q, then p. "P iff q" or "p q" are other ways to express the biconditional "p if and only if q."
Since we have given that
1) If and only if the angle's measurement is 90 degrees, it is a right angle : True.
As is common knowledge, one angle in a right-angled triangle must be 90 degrees.
2) If and only if an angle is obtuse, it measures 120 degrees : True
Obtuse angle is a term used to describe angles that are more than 90° but less than 180°.
And 90°<120°<180°
3) Only if the angle is a straight angle does it measure 180 degrees : True
As far as we are aware, a straight angle is defined as 180 degrees.
As a result, every bi-conditional assertion is true.
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use log. 16＾k ＋4＾（k＋1）＝1/4＾3
a pool drained at a rate of 15 gallons every 2 minutes.How many cups of water drained out of the pool each second?
Answer: The answer is 0.125 cups.
Step-by-step explanation:
First, you need to find the unit rate of the draining.
7.5 gallons = one minute
Divide 7.5 by 60 seconds
After dividing, you should get 0.125 cups of water per second.
Therefore, the pool drained at a rate of 0.125 cups every second.
Hope this helps! :)
Please help. Consider x0y0z as 100000x+100y+10z or 100000x+100y+z
Answer:
To determine if the expression 100000x+100y+10z or 100000x+100y+z is divisible by 3, 7, 13, and 37, you can use the divisibility rules for each number.
Divisibility by 3: To check if a number is divisible by 3, you can add up the digits of the number, then check if the sum is divisible by 3.
Divisibility by 7: To check if a number is divisible by 7, you can subtract twice the last digit from the remaining number, then check if the result is divisible by 7.
Divisibility by 13: To check if a number is divisible by 13, you can subtract 10 times the last digit from the remaining number, then check if the result is divisible by 13.
Divisibility by 37: To check if a number is divisible by 37, you can subtract 30 times the last digit from the remaining number, then check if the result is divisible by 37.
By applying these divisibility rules to the expression 100000x+100y+10z or 100000x+100y+z, you can determine if it is divisible by 3, 7, 13, and 37.
Please help with this question
Answer:
352 inches squared
Step-by-step explanation:
The area of a triangle is 1/2 · base · height. There are 4 of the same triangles here, so it would be (1/2 · 8 · 18) · 4 to find the surface area of all 4 triangles, but you can't forget about the base. The area of a rectangle is length times width, so it would be 8 · 8. This means the formula for the entire surface area of this square pyramid is ((1/2 · 8 · 18) · 4) + (8 · 8). It can be simplified as follows:
((1/2 · 8 · 18) · 4) + (8 · 8)
((1/2 · 8 · 18) · 4) + 64
((4 · 18) · 4) + 64
(72 · 4) + 64
288 + 64
352
Please help, I need the answer as soon as possible!!!!
the value of a in this expression will be 1/2.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.4
The given expression [tex](\frac{m^{1/4} }{6m^{3/4} } )^-1[/tex]
=[tex](\frac{6m^{3/4} }{m^{1/4} } )[/tex]
=6 ([tex]m^{3/4-1/4}[/tex])
=6 ([tex]m^{1/2}[/tex])
a = 1/2
Hence the value of an in this expression will be 1/2.
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