Explain why 1/12+1/12+1/12 is the same as 1/4
Answers
Explanation of why 1/12+1/12+1/12 equals 1/4 through adding fractions with common denominators.
Adding fractions:
Convert all fractions to have a common denominator.
Add the numerators together.
Keep the denominator the same.
Therefore, 1/12 + 1/12 + 1/12 = 3/12 = 1/4.
Related Questions
Lesson 8 homework practice solve percent problems
Answers
To solve percent problems, we can use equivalent fractions, cross-multiply, solve for the unknown, or convert percent to a fraction and simplify. In context, a 24% positive rate among students indicates that 24 out of every 100 students are positive.
Explanation:In mathematics, specifically in percentage calculation, there are several methodologies to solve problems. One very common way, as mentioned in the reference material, is by setting up equivalent fractions with 100 as the denominator, and cross-multiplying. For example, if you have the fraction 9/37 representing some scenario (like 9 successful attempts out of 37), you can set up an equation like 9/37 = x/100, where 'x' is the equivalent percentage. Cross-multiply and solve for 'x' to get x = (9/37) * 100, giving you the percentage.
Also, note that a percent can be converted to a fraction by writing the value of the percent as a fraction with a denominator of 100. Simplify the fraction, if possible.
In context, if 24% of students are positive, that means for every 100 students, 24 would be positive. If only 70 are surveyed, then (24/100)*70 = 16.8 students, but since we can't have a part of a student, we would round it to 17 students are positive for this sample size.
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if the area of a rectangle is 42 feet. what could be possible lengths and widths of the rectangle? 42=__×___
Answers
because 6×7=42
I hope this helps!
We know that it is a rectangle, so its length will be longer than its width, unlike a square.
Here are some possible widths:
42 = 7 × 6
42 = 14 × 3
42 = 21 × 2
42 = 42 × 1
These are the factors of 42.
Membership in the Volunteers Club increased by 15% from last year. If the number of members last year was m, complete a simplified expression to represent the number of members this year. Enter your answer in the box.
Answers
m ---> 100%
x ----> 115%
Clearing the value of x we have:
x = (115/100) * (m)
x = 1.15 * (m)
Answer:
a simplified expression to represent the number of members this year is:
x = 1.15 * (m)
Identify the graph that displays the altitude of a skydiver as he is taken up in a plane and then jumps.
Answers
Answer:
A is your answer
Graph Below
Joe’s current age is five times Mary’s age ten years ago. If Mary is currently m years old, what is Joe’s current age in terms of m?
Answers
Answer:
5m + 10
That should be it, you may need to simplify.
Sorry if its wrong, but i think this is it.
Step-by-step explanation:
A space shuttle orbits earth at a rate of about 4,375 miles in 15 minutes. At the rate, how far does the space shuttle travel around earth in 1 hour?
Answers
Hope this helps
There min in and 1hour so
291.6 times 60= 17,596
The shuttle will go 17,596 miles in an hour.
what is the proportion 5.2/8=y/6
Answers
.. y/6 = 0.65
Multiply by 6 to find the value of y that makes it true as
.. y = 3.9
In a basic sine curve, where can the zeros NOT be found?
a. middle
b. beginning
c. maximum point
d. end
Answers
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we know that
[tex]f(x)=\sin x[/tex]
It is an odd function.
It has a period of 2π because the sine wave repeats after every 2π units.
It value lies between -1 and 1.
And we know that
[tex]\sin 0^\circ=0^\circ[/tex]
And 0 occurs exactly middle of -1 and 1.
So, the zeroes can be found in the middle, beginning and at the end.
But at maximum point, there will be no zero.
As when it attains its maximum point, it won't touch x-axis.
Hence, Option 'C' is correct.
during the new year celebration there are orange, green purple, and blue fireworks. In how many different orders can the different colors of fireworks appear?
Answers
If they cannot be repeated, there are 24 possible combinations.
There are 24 different orders in which the different colors of fireworks can appear.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
If there are four colors of fireworks (orange, green, purple, and blue), then the number of different orders in which they can appear can be found by calculating the number of permutations of four objects, which is:
4! = 4 x 3 x 2 x 1 = 24
Therefore,
There are 24 different orders in which the different colors of fireworks can appear.
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Gracie can purchase 5 oranges for $4 but she only wants one what is the cost of one orange
Answers
what you do is you divide 5 by 4 so 5 divided by 4= 1.25
hope this helps!
Karina read a total of 20 2/4 pages in her science and social studies books combined she read 12 3/4 pages in her science book how many pages did she read in her social studies book?
Answers
Final answer:
To find out how many pages Karina read in her social studies book, you subtract the number of pages read in the science book from the total pages read. After doing the math, Karina read 8 1/4 pages in her social studies book.
Explanation:
Karina read a total of 20 2/4 pages in both her science and social studies books combined. It is mentioned that she read 12 3/4 pages in her science book. To find out how many pages she read in her social studies book, one must subtract the pages read in the science book from the total pages read.
The subtraction of mixed numbers involves the following steps:
First, make sure the fractions have the same denominator.
Then, subtract the fractions.
If necessary, borrow from the whole number and reduce the fractions further.
Finally, subtract the whole numbers.
In this case:
Total pages - Science book pages = Social Studies book pages
20 2/4 - 12 3/4 = 7 5/4 or 8 1/4 pages (since 5/4 is equal to 1 and 1/4).
Therefore, Karina read 8 1/4 pages in her social studies book.
write each fraction in simplest form. if the fraction is already in simplest form, write simplified
A.
[tex] \ \frac{4}{14} [/tex]
B.
[tex] \frac{15}{20} [/tex]
C.
[tex] \frac{21}{35} [/tex]
Answers
B. 15/20 = 3/4
C. 21/35 = 3/5
Answer:
4/14 = 2/7
15/20 = 3/4
21/35 = 3/5
Step-by-step explanation:
An airplane is flying at an altitude of 10,000 feet when it receives clearance to land at the airport. The angle of depression from the airplane to the airport is 4o. What is the horizontal (ground distance) from the airport to the airplane's position?
Answers
[tex]tan(40)= \frac{10000}{leg} [/tex]
[tex]leg= \frac{10000}{tan(40)} [/tex]
[tex]leg=11917.54[/tex]
We can conclude that the horizontal (ground distance) from the airport to the airplane's position is 11,917.54 feet.
Find the product of (4x − 3)(2x2 − 7x + 1).
Answers
=(4x − 3)(2x2 − 7x + 1)
=(4x*2x2) + (4x*-7x) + (4x*1) + (-3*2x2) + (-3*-7x) + (-3*1)
multiply each set of parentheses
=8x3 - 28x2 + 4x - 6x2 + 21x-3
combine like terms
ANSWER:
=8x3 - 34x2 + 25x - 3
Hope this helps! :)
without graphing decide whether the system of linear equations below has one solution, no solution, or infinitely many solutions. y=3x-8. 4y=12x-5
Answers
Answer:
B. no solution
Step-by-step explanation:
Multiplying the first equation by 4 gives ...
4y = 12x -32
This is inconsistent with the second equation, ...
4y = 12x -5
There can be no common point on these parallel lines, hence no solution.
Answer:
You will revise your narrative, indicating four instances in which you have added adjectives and/or adverbs.
You will also submit a reflection paragraph.
View the grading rubric as you complete your assignment. This is your guide to a super submission.
Add adjectives and adverbs. Mark your new additions with an (Adj) or (Adv).
Make other revisions suggested in your Discussion-Based Assessment.
Write a reflection paragraph discussing changes you made during the revision process. Explain how you feel these changes improved your narrative.
Submit your (1) final draft and your (2) reflection paragraph.
Save your work to your computer or drive.
Submit your work in 03.10 Kick It Up a Notch.
Step-by-step explanation:
solve the following system using substitution x+4y=21 4x-y=16
Answers
4x-y=16
Isolate one of the variables
x + 4y = 21
subtract 4y from both sides
x = -4y + 21
Plug that into the other equation
4x - y = 16
4(-4y + 21) - y = 16
-16y + 84 - y = 16
combine like terms
-17y + 84 = 16
subtract 84 from both sides
-17y = -68
divide both sides by -17
y = 4
Plug that into the equation
x+4y=21
x + 4(4) = 21
x + 16 = 21
subtract 16 from both sides
x = 5
Hope this helps!
Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?
Answers
A=LxW
L: The lenght of the rectangle (L=2W).
W: The width of the rectangle.
2. Let's substitute L=2W into the formula A=LxW:
A=LxW
A=2WxW
A=2W²
3. When we clear "W", we obtain:
W²=A/2
W=√(A/2)
4. We already know the value of "A", so:
W=√(50 ft²/2)
W=√(25 ft²)
W=5 ft
5. Now, we must substitute the value of "W", into L=2W:
L=2W
L=2(5 ft)
L=10 ft
6. The perimeter of a rectangle is:
P=2L+2W
7. We know the value of "L" and "W", therefore:
P=(2x10 ft)+(2x5 ft)
P=20 ft+10 ft
P=30 ft
What is the perimeter of the porch?
The answer is: 30 ft
The width of the porch is 5 feet and the length is 10 feet. The perimeter of the porch is 30 feet.
Explanation:To find the perimeter of the porch, we first need to find the dimensions of the porch. Let's assume the width of the porch is x feet. According to the problem, the length of the porch is two times the width, so the length would be 2x feet. Since the area of the porch is 50 square feet, we can set up the equation: x * 2x = 50. Simplifying this equation, we get 2x^2 = 50. Divide both sides by 2 to isolate x^2: x^2 = 25. Taking the square root of both sides, we find that x = 5. Therefore, the width of the porch is 5 feet and the length is 2 * 5 = 10 feet.
To find the perimeter, we use the formula: perimeter = 2 * (length + width). Substituting the values, we get perimeter = 2 * (10 + 5) = 2 * 15 = 30 feet. So, the perimeter of the porch is 30 feet.
Keshawn is constructing the inscribed circle for △PQR . He has already used his compass and straightedge to complete the part of the construction shown in the figure. Which construction could be his next step? Construct the angle bisector of ∠XQR . Construct the line through points P and X. Construct the perpendicular bisector of PQ¯¯¯¯¯ . Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Answers
Answer:
Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Step-by-step explanation:
what is the difference of the rational expressions below? 13x/5 - 4x/5
a. 9x/5
b. 17x/5
c. 52x/5
d. 52x/25
Answers
a. 9x/5
What you must do in this case is a sum of fractions.
Step 1:
Common factor 5 in the denominator
Step 2:
Perform subtraction of numerator
Step 3:
Rewrite the expression.
See attached image.
Answer:
a. 9x/5
movie mania charges a subscription fee of $30 and an additional fee of 5 per movie
Answers
[tex]M_m: y=\frac{30+5x}{x} [/tex],
per movie.
Movie time is earning
[tex]M_t: y=\frac{25+6x}{x}[/tex],
per movie.
Anna wants her customers to pay more than they would at Movie Time but less than Movie Mania.
The answer would be D :
[tex]y\ \textgreater \ \frac{6x+25}{x}\\ y\ \textless \ \frac{5x+30}{x}[/tex]
An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are β = 7° and θ = 10.5° (see figure). How far apart are the ships? (Round your answer to one decimal place.) ft
Answers
The ships are 21.5 feet apart.
We have,
Let's denote the distance between the observer and Ship 1 as x and the distance between the observer and Ship 2 as y.
Using the angles of depression, we can establish the following relationships:
tan(β) = x / 350
tan(θ) = y / 350
We need to find the distance between the ships, which is the difference between x and y.
To find x and y, we can rearrange the equations as follows:
x = 350 * tan(β)
y = 350 * tan(θ)
Now, we can calculate the distances x and y using the given angles of depression:
x = 350 * tan(7°)
x ≈ 42.9 feet
y = 350 * tan(10.5°)
y ≈ 64.4 feet
The distance between the ships is the difference between x and y:
Distance = y - x
Distance ≈ 64.4 - 42.9
Distance ≈ 21.5 feet
Therefore,
The ships are 21.5 feet apart.
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He radius r of a circle is increasing at a rate of 6 centimeters per minute. find the rate of change of the area when r = 35 centimeters. cm2/min
Answers
The rate of change of the area when the radius is 35 centimeters is 420π cm2/min.
Explanation:To find the rate of change of the area, we can use the formula for the area of a circle: A = πr2. We are given that the radius (r) is increasing at a rate of 6 centimeters per minute. We need to find the rate of change of the area when r = 35 centimeters.
First, differentiate the area formula with respect to time (t) using the chain rule:
dA/dt = 2πr(dr/dt)
Substitute the given values into the formula: dA/dt = 2π35(6) = 420π cm2/min.
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The rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
Explanation:The subject of this question is related to the rate of change in the context of a circle's area, which is a topic in calculus. Given that the radius r of a circle is increasing at a rate of 6 centimeters per minute, we are to find the rate of change of the area when r = 35 centimeters.
The area A of a circle is given by the equation A = πr². If we differentiate this equation with respect to time t, we get dA/dt = 2πr(dr/dt). We know that dr/dt, the rate of change of the radius, is 6 cm/min. Substituting r = 35 cm and dr/dt = 6 cm/min into the derivative equation, we get dA/dt = 2π*35*6 = 420π cm²/min.
So, the rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
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What is the following product?
3 sqrt24 * 3sqrt 45
Answers
The product of 3√24 and 3√45 is approximately 295.77.
Explanation:To find the product, we can first simplify the individual square roots.
√24 = √(4 * 6) = 2√6
√45 = √(9 * 5) = 3√5
Substitute the simplified terms: 3 * 2√6 * 3 * 3√5 = 18√30
Factor out a 9: 18√30 = 9 * 2√(10 * 3)
Simplify the remaining square root: 9 * 2√30 ≈ 9 * 2 * 5.477 = 295.77 (rounded to two decimal places).
Therefore, the product of 3√24 and 3√45 is approximately 295.77.
Tomas created a function table using the equation y = x + 4. Which table is correct?
Answers
1) How to make a table
For the function y = x + 4, the variable x is the input and the variable y is the output.
A table consists of a sequence of pairs x, y.
You choose the x-values and calculate th y-values using the function.
For expample if you choose x = 3 as your input, then the output is given by the function y = x + 4, so you subsititute x = 3 and obtain y = 3 + 4 = 7.
And the table is represented as in the example below.
What you have to do is checking if all the values of the table given satisfy the equation y = x + 4.
2) Table (example):
x y = x + 4
-20 -16
-19 -15
-18 -14
-17 -13
-16 -12
-15 -11
-14 -10
-13 -9
-12 -8
-11 -7
-10 -6
-9 -5
-8 -4
-7 -3
-6 -2
-5 -1
-4 0
-3 1
-2 2
-1 3
0 4
1 5
2 6
3 7
4 8
5 9
6 10
7 11
8 12
9 13
10 14
11 15
A grocer had 40 crates of tomatoes. Each crate contained 124 tomatoes. She threw away 24 rotten tomatoes and repack the rest into bag of 8 tomatoes each. How many bags of tomatoes were there?
Answers
4,960 - 24 = 4,936
4,936 / 8 = 617
There are 617 bags of tomatoes.
124*40=4960 tomatoes
24 are rotten
4960-24=4936
4936/8=617 bags
A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10-6 seconds. How much time would the program take to complete 2.5 × 103 mathematical operations?
Answers
x = 1.5 * 10^-6 * 2500
x = 0.00375 or 3.75 * 10^-3 second.
Good question.
You forgot A, B, C, and D but the correct answer is option D, 3.75 x 10 ^ -3 seconds
HELP!!
4. What are the values of x and y?
A) x=9/4, y=3/4
B) x=9/4, y=15/4
C) x=15/4, y=5/4
D) x=3/4, y=15/4
THANK YOU
Answers
Ratio of short to long sides:
.. x/3 = 3/4
.. x = 9/4
Ratio of hypotenuse to long sides:
.. y/3 = 5/4
.. y = 15/4
The 2nd selection is appropriate.
Scientist determine that Antarctica average winter temperature was 34.44 Celsius the difference between the temperature and Antartica highest record temperature was 49.44 degrees what was the highest record temperature
Answers
Then the highest recorded temperature is
-34.44 °C +49.44 °C = 15 °C . . . . . . . . . . about 59 °F
an artist painted a 6 foot tall painting, then decide to also create a smaller version. if she uses a scale of 4 inches=1.5 feet, what will be the height of the smaller painting
Answers
x----------------- > the height of the smaller painting
y-----------------> the height of the tall painting-----------> 6 ft
the scale factor is-------------- > x/y
(x/y)=(4 in)/(1.5 ft)
x=y*[(4 in)/(1.5 ft)]-------> 6*(4 in)/(1.5 ft)=16 in
the answer is x=16 in
Final answer:
To determine the height of the smaller version of the painting using the scale of 4 inches = 1.5 feet, we first convert the original height to inches (6 feet = 72 inches) and then use a proportion to find that the height of the smaller painting is 16 inches.
Explanation:
The student's question involves using a scale to determine the height of a smaller version of a painting. The scale given is 4 inches = 1.5 feet. To begin, we convert the original height of the painting from feet to inches since the scale is in inches. The original height of 6 feet is equivalent to 72 inches (because 1 foot is equal to 12 inches).
Next, we set up a proportion using the scale:
4 inches / 1.5 feet = x inches / 6 feet
Now we solve for x, which represents the height of the smaller painting in inches:
4 / 1.5 = x / 6
4 / 1.5 * 6 = x
x = 4 * 6 / 1.5
x = 24 / 1.5
x = 16 inches
Thus, the height of the smaller version of the painting will be 16 inches.
Formulate a decision model to determine whether there are any arbitrage opportunities with the spot currency rates given in table 1. note that an arbitrage opportunity could involve several currencies. if there is an arbitrage opportunity, your model should specify the exact set of transactions to achieve it. to us dollar pound ffranc dmark yen us dollar - 0.63900 5.37120 1.57120 98.8901 pound 1.56480 - 8.43040 2.45900 154.7733 from ffranc 0.18560 0.11860 - 0.29210 18.4122 dmark 0.63610 0.40630 3.42330 - 62.9400 yen 0.01011 0.00645 0.05431 0.01588 - table 1: cross-currency spot rates
Answers
Final answer:
To determine if there's an arbitrage opportunity, convert an amount through various currencies in the table and see if you end with more than you started. If more is ended up with, there's an opportunity, specifying the currencies and transactions. If not, the market is in equilibrium, and rates will adjust to prevent arbitrage.
Explanation:
To identify an arbitrage opportunity within the given spot currency rates, one must find a sequence of exchanges that results in more currency than initially started with, after accounting for the currency exchange rates in table 1. The decision model for discovering an arbitrage opportunity typically involves converting an amount from one currency to another across several pairs and ending up with more than one started with in the original currency. The following steps outline the process to determine if arbitrage is possible:
Start with a denomination of one currency (e.g., $1).
Convert this amount into another currency using the provided spot rates.
Repeat the conversion process for subsequent currencies.
Finally, convert back to the original currency.
If the final amount is greater than the starting amount, an arbitrage opportunity exists. In such a scenario, the model should indicate the currencies involved and the specific transactions to execute the arbitrage. However, if no sequence of transactions results in profit, then no arbitrage opportunity is present given the rates provided. The absence of arbitrage ensures that the markets are in equilibrium, and the exchange rates will adjust to eliminate any potential for arbitrage as per the efficient market hypothesis.