The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.
How is altitude measured and what does it mean?Utilizing the measurement of air pressure, altitude may be calculated. The pressure decreases with increasing altitude. An instrument is referred to as a pressure analyzer or pneumatic altimeter when a barometer is given a nonlinear calibration to display altitude.
This may be calculated by dividing the cloud's speed (552 metres per minutes) by the distance it must travel (17.5 minutes). We now know the distance to be 9,616 meters.
The speed of said cloud and the length of time it is going are four pieces of information that must be known in order to determine the minimum distance the cloud might cover in 17.5 minutes. We must increase the cloud's stated speed of 552 meters a minute by the distance it is going across, which in itself is 17.5 minutes. As a result, we now have 9,616 meters overall.
Another way to see this is to picture the cloud beginning at place A (9,200 meters) or terminating at point B. (9,616 meters). The distance between points A and B will be covered in 17.5 minutes if the cloud is moving at a pace of 552 meters per minute.
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hat is the probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck?
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck is 1/221.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
The probability that an ace appears at the 9th place, and a queen appears at the 10th place in the deck can be calculated as:
There is a total of 52 cards in a deck and 4 aces and 4 queen cards.
So, the probability is
4/52 * 4/51 = 1/221
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a ship leaves port at noon and has a bearing of the ship sails at 20 knots. how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.?
On solving the provided question we can say that the equation gives us 101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).
The location of the ship will be in (S, W) coordinates.
[tex]120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)[/tex]
The ship will have traveled 101.77 miles south and 63.59 miles west.
83.59). The distance from port will be ...
[tex]d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4[/tex]
The bearing and distance are ...
S 39.4° W
131.7 nautical miles
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I need help bru im from Chicago need help
Answer:
3.20
Step-by-step explanation:
use a linear approximation (or differentials) to estimate the given number. (1.999)5
The approximate value of [tex](1.999)^5[/tex] is 31.92.
Describe linear approximation :A linear approximations in maths is the use of a linear function to estimate a generic function. They are frequently used to create first order methods for solving or approximating equation solution in the method of finite difference.
To estimate [tex](1.999)^5[/tex]
we’ll find the linearization of f(x) = [tex]x^5[/tex]
at a = 2. Since
f′(x) = 5[tex]x^4[/tex]
, f(2) = 32, and
f′(2) = 80,
we have L(x) = 32+80(x−2). Thus,
[tex]x^5[/tex] ≈ 32 + 80(x − 2) when x is near 2,
so (1.999)5 ≈ 32 + 80(1.999 − 2) =
32 − 0.080 = 31.92.
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in the hardy boys adventure while the clock ticked, the pendelum of the grandfather clock at the purdy place is 44 inches long and swings through an arc of 6. find the length of the arc taht the pendelum traces
On solving the provided question we can say that equation of pendulum traces an arc, s, that is roughly 4.61 inches long.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
6° = 6° X [tex]\pi /180 = \pi /30[/tex]
s = r∅
s = 44 X [tex]\pi /30[/tex]
s = 4.61
Hence, The pendulum traces an arc, s, that is roughly 4.61 inches long.
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one person drives 70,000 miles in a car that averages 30 miles per gallon (mpg). how much gasoline are they using?
The person is using approximately 2,333.333 gallons of gasoline.
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
To calculate the amount of gasoline used, you can use the formula:
gasoline used = total miles driven / mpg
Where total miles driven is 70,000 miles and mpg is 30.
Plugging these values into the formula, we get:
Gasoline used = 70,000 miles / 30 mpg = 2,333.333 gallons
So the person is using approximately 2,333.333 gallons of gasoline.
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Merchandise inventory includes: (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)\
Therefore , solution of unitary method problem The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance.
What exactly is a unitary method?The unitary approach is a method of problem solving that entails first calculating the percentage of a single set there is, then doubling that value to arrive at the solution. The unit technique, to put it simply, is used to extract a typical programming value from a given many. For instance, the price of 40 pens is 400 rupees ($1.01), meaning Rs. It's feasible that the method used to achieve this will be controlled in only one nation.
Here,
The finished goods kept in inventory are those that will be sold to clients.
All items that are owned by a business and kept for sale are included in the merchandise inventory.
a retail business:
purchases and sales of goods generate its net income.
It can also purchase goods from producers and market them to retailers.
It can also be a retailer or a wholesaler, purchasing goods from producers and selling them to clients.
The term "current asset" refers to merchandise inventory.
Therefore , The cost of the items purchased, the cost of shipping and handling, the cost of transit insurance, and the cost of storage are all included in the merchandise inventory account.
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Please assist with C ii
Solve the equation 1-2/x^2 = -x-1
x = ?
The value of x in the expression 1 - (2/x²) = - x - 1 is ± √2, 4.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, An expression 1 - (2/x²) = - x - 1.
- (2/x²) + x = 2.
Multiplying each term by x².
- 2 + x³ = 2x².
x³ - 2x² = 2.
x²(x - 2) = 2.
x² = 2 ⇒ x = ± √2 Or x - 2 = 2 ⇒ x = 4.
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Please help, i know you have to use pythagoras and the hypotenuse is 8.44 but i dont know how to get one of the sides
======================================================
Explanation:
Check out the diagram below.
I've defined the following points:
A = center of the circle, and center of the squareB, C, D, and E = vertices of the square that are on the circleF = midpoint of segment CDNow focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.
The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.
[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]
This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.
------------
We now know the hypotenuse of triangle ACF.
Use Pythagoras (aka Pythagorean Theorem) to have the following steps:
[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]
The final answer is 5.97With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.
Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.
In short, we're rounding to the nearest hundredth.
--------------------
Check:
x = 5.97 is the square's side length.
It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.
Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.
Use that radius to find the area of the circle.
A = pi*r^2
A = pi*(4.22142748)^2
A = 55.984594705958
A = 56.0
I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.
Jerome has $3,000 to invest in an account that yields 2.1% annual interest which is compounded quarterly. If he leaves the money untouched in the account for 4 years, how much money will he have?
Jerome will have $3261.93 after 4 years
How to calculate how much money Jerome will have?
The formula for compound interest is A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for.
In this case, P = $3,000, n = 3, r = 2.1% = 0.021, t = 4 years. Thus:
A = P(1 + r/n)^(nt)
A = 3000(1 + 0.021/3)^(3×4)
A = 3000(1 + 0.021/3)^(12)
A = $3261.93
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The area and perimeter of arectangular field are 60m² and 32 m respectively. Find the length and breadth of the fueld
Ekaterina’s favorite expression is 4x – 4. Alban’s favorite expression is 8x – 24. What value of x makes these two expressions equal?
Answer:
x = 5
Step-by-step explanation:
You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:
4x - 4 = 8x - 24
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 8x and add 4 to both sides of the equation:
4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)
4x - 8x = -24 + 4
-4x = -20
Next, divide -4 from both sides of the equation:
(-4x)/-4 = (-20)/-4
x = -20/-4
x = 5
5 is your answer.
Check:
Plug in 5 for x in both given expressions:
4x - 4
4(5) - 4
= 20 - 4
= 16
-
8x - 24
8(5) - 24
= 40 - 24
= 16
~
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what is the value of t? 7+8t-9=62
Answer:
t = 8
Step-by-step explanation:
8t - 2=62
8t =62+2
8t = 64
t = 64÷8
t = 8
Answer: t = 8
Step-by-step explanation:
What is the equation of the line in slope-intercept form that passes through point (4, 5) and is parallel to the line y = −2x − 2?
Answer:
y = -2x + 13
Step-by-step explanation:
In order to write an equation of the line in slope-intercept form, we first have to look at the equation:
y = mx + b
We know that m represents slope, and b represents the y-intecept, in other words, what y is equal to when x is equal to zero.
We already have y and x, (4,5), and the slope of the line, since the two lines are parellel, they share the same slope. So now, we have to pulg those values into the equation and solve for b:
(4,5)
y = 5
x = 4
m = -2
y = mx + b
(5) = (-2)(4) + b
5 = -8 + b
13 = b
So, equation of the line in slope-intercept form that passes through point (4, 5), is y = -2x + 13
Remeber that you can always graph to check your work!
I hope this helps! :)
please help me on this math question
Answer:
The formula for compound interest is: A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (the amount Alex has at the end of 7 years)
P = the initial investment (£4000)
r = the annual interest rate (x/100)
n = the number of times interest is compounded per year (let's assume it is compounded annually)
t = the number of years invested (7)
Plugging in the given values and solving for x:
5263.73 = 4000(1 + x/100)^7
So x = ((5263.73/4000)^(1/7))-1*100
x = 6.33% (approximately)
So, the interest rate is 6.33%.
How do you know if there are no solutions?
If you attempt to solve an equation and the result is false, the problem has no solutions.
If both sides of a linear equation have unique constant values but the same variable term, then the problem has no solutions.
For instance, in the equation [tex]3x+8=1+3x[/tex],
the variable term is the same, [tex]3x[/tex], but the constant terms, 8 and 1, are on opposite sides of the equation. It, therefore, lacks solutions. Try the equation to determine why.
[tex]3x+8=1+3x\\8=1[/tex]
following mathematics, the term is not possible. so, here equation has no solutions. so how we can know that equation has no solution if mathematical inequality is wrong.
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!!! 20 POINTS !!!
It will take you t seconds to carry the water, which you will do y times a day. What is the total amount of
time you will be carrying water?
How many hours would you spend carrying water in a year?
Answer:
To find the total amount of time you will be carrying water, we can use the following formula : Total time = t x y (t represents the time taken to carry water in seconds and y represents the number of times you will carry water per day)To find how many hours you would spend carrying water in a year, we can use the following formula:Total hours = (total time in seconds) / (3600 seconds in an hour)
Note: Remember to convert the result from seconds to hours.
It's important to mention that you need to know the value of t and y to be able to calculate the total time and the total hours.
If you have the values, you can substitute them in the equations above and get the answer.
I need help with this problem ?
Answer:
398.32
Step-by-step explanation:
647.82 - 249.50 = 398.32
3. Pencils are sold at a unit rate of 36 pencils per box.
Use the variables and number in the box to write an equation to
represent the proportional relationship. The letter b represents the
number of boxes, and p represents the total number of pencils.
Use the unit rate as the constant of proportionality.
Numbers and letters cannot be used more than once. Write
each number or letter in the appropriate box.
36
b
Р
HINT, H
The unit rates
constant of p
the equation
where m is th
proportional
The constant of proportionality for the proportional equation is 36.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Box = b
Number of pencils in one box.
p = 36
Now,
The proportional equation for b and p.
p ∝ b
p = mb
where m is the constant of proportionality.
Now,
b = 1
p = 36
p = mb
36 = m x 1
m = 36
Thus,
The constant of proportionality is 36.
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An inurance company ell a $500,000 five-year term policy to a female. The monthly policy i m dollar. If the peron die 20 month after taking out the policy, expre the inurance company profit algebraically
The profit of the insurance company is -20x, where x is the monthly premium.
What is algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to describe and analyze the relationship between numbers, variables, and operations. Algebra is used to solve equations and simplify expressions, and it is useful in a wide range of applications such as engineering, economics, and science. Algebra also helps us understand and explore abstract concepts such as equations, functions, and graphs. Algebraic thinking is a valuable skill that can help us to make sense of the world around us.
Let x = monthly premium
The insurance company's profit = (500,000 - 20x) - 500,000 = -20x
Therefore, the profit of the insurance company is -20x, where x is the monthly premium.
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A set of data with a normal distribution has a mean of 16.4 and a standard deviation of 3.2. 68% of the data falls between what two numbers?
68% of the data falls between one standard deviation from the mean which is 13.2 and 19.6
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The empirical rule states that 68% of the data falls within one standard deviation, 95% within two standard deviation from the mean and 99.7% falls within three standard deviation from the mean.
Given a mean of 16.4 and a standard deviation of 3.2.
68% of the data falls one standard deviation from the mean = 16.4 ± 3.2 = (13.2, 19.6)
68% of the data falls between 13.2 and 19.6
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function f(x) = 4(1.5)x?
Answer:
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5
Step-by-step explanation:
For each pair of triangles below, state
whether the triangles are congruent, not
congruent or if it is impossible to tell.
a)
65°
27 cm
38 cm
19 cm
65°
27 cm
43°
43°
b)
80°
58°
42°
42°
80°
58%
C)
12 cm
82°
12 cm
37°
37%
82°
Answer: all are congruent
Step-by-step explanation:
a. The pair of triangles are not congruent.
b. It is impossible to tell about congruency.
c. The pair of triangles are congruent.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
These triangles can be slides, rotated, flipped and turned to be looked identical.
a. The given triangles are not congruent.
The triangle has same measures but the side lengths are different.
So the pair of triangles are not congruent.
b. The given pair of triangles are might be congruent if they have side lengths same.
But in the given triangles the side lengths are not measured.
So it is impossible to tell.
c. The given pair of triangles have same measures and same side lengths.
By AAS rule the pair of triangles are congruent.
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angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each. How many books and magazines did angelina buy
In all, she purchased 1 book and 6 periodicals, taking into account the inequality.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, Angelina spent $23.65 on books and magazines when she went to chapters. She bought a total of 7 items. The books cost $5.95 each and the magazine cost $2.95 each.
Let "b" be the number of total book and "m" be the number of magazine she bought.
Inequality from the given data
m + b = 7
since, Angelina spent $23.65 on books and magazines
thus,
5.95 * b + 2.95 * m = 23.65
from equation 1
5.95b + 2.95(7 - b) = 23.65
5.95b + 20.65 - 2.95b = 23.65
3 b = 3
b = 1
from any equation
m = 6
Therefore, she total bought 1 book and 6 magazines according the given inequality.
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evaluate the double integral_d (x^2 + 2y) dA, D is bounded by y = x, y = x^3, x ≥ 0
After evaluating the double integral, the result, 0.27, is determined by the stated statement.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or maybe a new function, the inverse of which comprises the original result (indefinite integral). The value produced after integrates or adding the words of a function that is split into an unending number of terms is referred to as an integral value in general.
The double integral is an example.
[tex]\iint_D\left(x^2+2 y\right) d A[/tex] where d is enclosed by the lines y = x & y = x³.
In the region D, x varies from 0 to 1, and y varies from y = x³ to y = x
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=\int_{x=0}^1 \int_{y=x^3}^x\left(x^2+2 y\right) d y d x[/tex]
[tex]=\int_{x=0}^1\left[x^2 y+y^2\right]_{x^3}^x d x[/tex]
[tex]=\int_{x=0}^1\left[x^2\left(x-x^3\right)+\left[x^2-\left(x^3\right)^2\right]\right] d x=\int_{x=0}^1\left[x^3-x^5+x^2-x^6\right] d x[/tex]
[tex]\left.=\frac{x^4}{4}-\frac{x^6}{6}+\frac{x^3}{3}-\frac{x^7}{7}\right]_0^1[/tex]
= [tex]\frac{1}{4}-\frac{1}{6}+\frac{1}{3}-\frac{1}{7}[/tex]
= 23/84
= 0.27
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=0.27[/tex]
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find the inequality represented by the graph
X, Y and Z form the vertices of a triangle, where
∠
YXZ = 57°,
∠
YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP
Answer:
Step-by-step explanation:
For each of the following wages, determine the Social Security tax that would be withheld. Use $106,800 for maximum taxable earnings. i. $23,660 ii. $89,000 iii. $166,090 a. i. $146.69 ii. $551.80 iii. $1,029.76 b. i. $1,466.92 ii. $5,518.00 iii. $10,297.58 c. i. $146.69 ii. $551.80 iii. $662.16 d. i. $1,466.92 ii. $5,518.00 iii. $6,621.60 Please select the best answer from the choices provided A B C D
The correct answer is C) i. $146.69 ii. $551.80 iii. $662.16.
What is social security tax ?
Social Security tax is a payroll tax that is imposed on both employees and employers to fund the Social Security program in the United States. The tax is used to provide benefits to retired and disabled workers, as well as to the families of deceased workers. The tax is imposed on wages and salaries earned by employees.
A. i. $146.69 ii. $551.80 iii. $1,029.76
B. i. $1,466.92 ii. $5,518.00 iii. $10,297.58
C. i. $146.69 ii. $551.80 iii. $662.16
D. i. $1,466.92 ii. $5,518.00 iii. $6,621.60
The Social Security tax rate is 6.2% for the employee and 6.2% for the employer, for a total of 12.4%. However, the employee portion of the tax is only applied to the first $142,800 of earnings in 2021. Any earnings above this amount are not subject to the employee portion of the Social Security tax.
The correct answer is C) i. $146.69 ii. $551.80 iii. $662.16.
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Answer:
its D
Step-by-step explanation:
because of PEMDAS
How do you solve ratio word problems in 7th grade?
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
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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A cube with side length 5h^2 is sTacked on another cube with side length 3k . What is the total volume of the cubes in factored form?
(5h^2)^3 + (3k)^3
(5h^2 + 3k) + (25h^4 - 15 h^2k + 9k^2)
(5h^2 + 3k) + (25h^4 + 15 h^2k + 9k^2)
(5h^2 + 3k)^3
The correct option is Option A: (5h^2)^3 + (3k)^3
The total number of cubic units that the cube totally occupies is the definition of a cube's volume. A cube is a solid three-dimensional object with six square faces. Volume is simply the total amount of space an object takes up. A thing with a bigger volume would take up more room.
Total Volume = V₁ + V₂
V₁ = Volume of Cube 1
V₂ = Volume of Cube 2
Volume of Cube = (Side Length)³
V₁ = (5h²)³
V₂ = (3k)³
∴ Total Volume = (5h²)³ + (3k)³
And this cannot be simplified further.
Therefore, the correct option is Option A: (5h^2)^3 + (3k)^3
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