The diagonal V2 of the square will be √2 feet.
What are squares?
A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.
The most important properties of a square are listed below:
All four interior angles are equal to 90°.All four sides of the square are congruent or equal to each other.The opposite sides of the square are parallel to each other.The diagonals of the square bisect each other at 90°.The two diagonals of the square are equal to each other.The square has 4 vertices and 4 sides.The diagonal of the square divides into two similar isosceles triangles.The length of diagonals is greater than the sides of the square.Area of square=(side)²
Perimeter of square=4*side
Now,
as side=1 foot
By applying Pythagorean theorem,
Diagonal²=side²+side²
therefore,
V2²=1²+1²
=2
V2= √2 feet
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Find the solution to the system of equations.
Answer: (-5, -2)
Step-by-step explanation:
We will substitute the first equation into the second and then solve for x. Then we will substitute x into the equation and solve for y.
Given:
5x + 3y = -31
Substitue:
5x + 3(x + 3) = -31
Distribute:
5x + 3x + 9 = -31
Combine like terms:
8x + 9 = -31
Subtract 9 from both sides of the equation:
8x = -40
Divide both sides by 8:
x = -5
Given:
y = x + 3
Substitute x into the equation and solve for y.
y = (-5) + 3
Combine like terms:
y = -2
We can also graph it. The point of intersection is the solution, see below.
Find x please help asap
Answer:
68888jours 9999999888
the half-life of radon (rn-222) is 3.82 days. how much (what fraction) of a sample remains after 11.46 days?
Radon-222 was initially present in a sample of 3.82 mg. Only 0.375 mg of the radon-222 in the sample were still present after 11.46 days, after which three half-lives had gone.
As per the data given in the above question are as bellow,
A material has a half-life when it takes a particular length of time for half of it to disappear or change.
11.46 days have 3 half lives because 11.46 x 3.82 Equals 3.
We thus split the 3 mg sample in half three times.
3 ÷ 2 = 1.5
1.5 ÷ 2 = 0.75
0.75 ÷ 2 = 0.375
After 11.46 days, there will only be 0.375mg of radon-222 left.
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find the soulotion to this in eqaulity a
> –3
A graph of the solution to this inequality a > -3 is shown on the number line attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).In this exercise, we would use an online graphing calculator to plot the given inequality a > -3 as shown on the number line (graph) attached below.
In conclusion, the circle on the number line (graph) is open because of the greater than (>) symbol and it increases to the right of the number line.
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Complete Question:
Find the solution to this inequality a > –3.
janet gross salary is 24000 per month her tax free allowances are shown in the table below national insurance 2 1\2 ,personal allowances is 20000 what is her total tax allowances for the year
Janet's total tax allowances for the year are $27,200.
How are the tax allowances determined?The first step is to convert the monthly gross salary to the annual gross salary by multiplying it by 12.
The insurance allowance is computed by applying the rate to the annual gross salary.
The personal and insurance allowances are added to determine the total tax allowances.
Generally, tax allowances reduce the taxpayer's taxable income.
Gross salary per month = $24,000
Annual gross salary = $288,000 ($24,000 x 12)
Personal allowances per year = $20,000
National insurance = 2¹/₂%
= $7,200 ($288,000 x 2¹/₂%)
Total allowances for the year = $27,200 ($20,000 + $7,200)
Thus, Janet is entitled to a total tax allowance of $27,200 for the year.
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Kate is firing off her homemade rockets for a project in physics class. The
maximum height of any of her rockets can be represented by the equation
h-701-162, where h is the height (in feet) of the rocket after t seconds.
The domain and range for the function for the maximum height of the rockets Kate fires is; h = 70·t - 16·t² are;
Domain; 0 ≤ t ≤ 4.375
Range; 0 ≤ h ≤ 39.06
What is a mathematical function?A function is a rule that defines the relationship between input variables and output variables, such that the each value from the set of input variables are assigned to exactly on variable from the set of output variables.
The possible specified function in the question is; h = 70·t - 16·t², and the possible required details is the domain and range that best represent the situation.
The domain of the above function is the set of possible input (t) values, which is found by the time it takes the rocket to land after flight as follows;
At ground level, h = 0, therefore;
h = 70·t - 16·t² = 0
(70 - 16·t)·t = 0
A possible solution is therefore, t = 0
The other solution is found as follows;
(70 - 16·t) = 0
70 = 16·t
16·t = 70
t = 70/16 = 4.375
The other solution or time at which the rocket is at ground level is t = 4.375
The domain is therefore; 0 ≤ t ≤ 4.375The range is the set of possible h values, which is obtained as follows;
The maximum point of the quadratic function, f(x) = a·x² + b·x + c, is the point, x = -b/2·a. Therefore, comparison between the function, f(x) = a·x² + b·x + c, and h = 70·t - 16·t², we get;
a = -16
b = 70
c = 0
The maximum height reached, therefore is obtained at the point, at which; t = -70/(2 × (-16)) = 2.1875
The maximum height, [tex]h_{max}[/tex], is therefore;
[tex]h_{max}[/tex] = 70 × 2.1875 - 16 × 2.1875² = 76.5625
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joan earns 8% commission on her sales this month Joan had $6000 in sales what was her commission
The amount of commission that Joan earns this month on sales will be $480.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Joan earns an 8% commission on her sales this month Joan had $6000 in sales.
Let 'x' be the commission. Then the equation is given as,
x / $6,000 = 0.08
x = 0.08 · $6,000
x = $480
The amount of commission that Joan earns this month on sales will be $480.
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in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55
Six friends are going to run a relay race that is 3.12 miles long. Each friend will run an equal distance. How many miles will each friend run? (I WILL GIVE BRAINLIEST!!)
In a relay race each friend run a distance of 0.52 miles.
How to find distance?The distance of the race divided by the runners' times will give you their average velocities.
We are given that
Total distance covered in a race = 3.12 miles
Total number of persons = 6
Each person runs equal parts of the race.
We have to find the miles run by each person.
To find the distance covered by each person we will divide the total distance by total number of persons who took part in a race.
Each person runs = Total distance/ Total number of persons
Each person runs= 3.12 / 6 miles
Each person runs = 0.52 miles
Hence, each person runs 0.52 miles.
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A girl of height 0.9 m is walking away from the base of a lamp-post and covered 4.8 m. If the lamp is 3.6 m above the ground, find the length of her shadow.
If the lamp is 3.6 m above the ground, the length of her shadow is 1.2 m.
What is proportionality?In algebra proportionality is equality between two ratios. In the mathematical expression a/b = c/d, a and b are in the same proportion as c and d.
Height of the girl = 0.9 m.
Height of the lamp = 3.6 m.
Distance between the lamp and the girl = 4.8 m.
Let the length of her shadow = x m.
From proportionality relation:
3.6 : 4.8 = 0.9 : x
3.6/4.8 = 0.9/x
3.6x = 4.8 × 0.9
x = (4.8 × 0.9) ÷ 3.6
x = 1.2
Hence, the length of her shadow is 1.2 m.
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20 ft
8 ft
20 ft
12 ft
Find the area
Evaluate the following: −3 − (−8)
Answer: The answer is 5
Step-by-step explanation:
-3-(-8)
-3+8
5
Answer: 5
Step-by-step explanation:
First the negative 3 adds to 8. Because if you see “- -“ it will be +. So we just have -3 + 8 = 5
A company manufactures and sells shirts the daily profit. The company makes depends on how many shirts they sell the profit in dollars when the company sells X shirts can be found using the function F (X)equals 6X -90 find the interpret the given function values and determine inappropriate domain for the function f(-9)
profit of
of the problem.
=
f(27)
profit of
of the problem.
=
f(17.5) =
profit of
of the problem.
meaning if the company sells |
dollars. This interpretation
meaning if the company sells
dollars. This interpretation
, meaning if the company sells
dollars. This interpretation
shirts, they would make a
in the context
shirts, they would make a
in the context
shirts, they would make a
in the context
The increase in earnings brought on by producing one extra unit is known as the marginal profit. The proper domain for functions is the integers (0, 1, 2, ...).
Explain about the Marginal profit?By dividing marginal revenue by marginal cost, one can compute marginal profit. Because it can help determine whether to raise or lower the level of output, marginal profit analysis is useful.
Any quantity of output below the one at which marginal profit equals zero has a positive marginal profit, meaning that profit can be increased by producing more of that quantity. Conversely, any quantity of output above the one at which marginal profit equals zero has a negative marginal profit, meaning that profit can be increased by producing less of that quantity.
A company that manufactures and sells shirts. Daily profit of...
A company that manufactures and sells shirts. The daily profit the company makes depends on the number of shirts sold. The profit in dollars if a company sells x shirts can be found using the function f(x)=7x-40. Locates and interprets given function values to determine the appropriate domain for the function.
f(-10) = -110, which means that if the company sells -10 shirts, it will make a profit of -$110. This interpretation makes no sense in the context of the problem.
f(10) = 26.5, so if the company sells 9.5 of his shirts, he makes a profit of $26.5. This interpretation makes no sense in the context of the problem
f(9.5) = 26.5, so if the company sells 9.5 shirts, it makes a profit of $26.5. This interpretation makes no sense in the context of the problem.
Therefore, based on the above observations, it is clear that the proper domain for functions is the integers (0, 1, 2, ...).
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A town has a population of 20000 and grows at 5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41600?
If the town has a population of 20000 and grows at 5% every year , then the time required for the population to reach 41600 is 15 years .
To find out how long it will take for the town's population to reach 41600, we can use the formula :
⇒ A = P(1 + r)ⁿ
Where:
A = final population of town , P = initial population o town
r = percent increase (as a decimal)
let n = number of years for population to reach 41600 .
We know the final population is 41600, the initial population is 20000, the percent increase is 5% = 0.05 and we have to solve for n.
Substituting the values ,
we get ;
⇒ 41600 = 20000(1 + 0.05)ⁿ ;
⇒ 41600 = 20000(1.05)ⁿ ;
⇒ 41600/20000 = (1.05)ⁿ ;
taking "log" on both sides ,
we get ;
⇒ log(41600/20000) = n × log(1.05) ;
⇒ n = log(41600/20000)/log(1.05) ;
⇒ n = 15.0105 ≈ 15
Therefore , it will take approximately 15 years for the town's population to reach 41600, to the nearest tenth of a year.
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Please help just number 10 and 11 thank you.
Answer: 10. 3
Step-by-step explanation: 4x3=12, ad 3x3 is 9 so all the sides of the triangle are multiplied by 3
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Tony and Sue now have.
There are two phrases for how many sweet Sue and Tony have: 13-x and
How to find the calculation?Equivalent refers to the mathematical notion of equality between several terms and expressions with a comparable value.
Equivalent vs. Equal. Equivalent and equal are distinct terms in mathematics.
Equal means identical in every respect, as opposed to equivalent, which is similar but not the same.
18 + x/ 2 is the equivalent.
Sue has 18 delicious.
Tony has 18 delicious.
Sue gives Tony some candy. Sue Sweet is going to
18 - x Sue consumes 5 candies, thus his sweet will be
18 - 5 - x = 13 - x
Sue gave Tony x candy to take. His sweetness will
18 + x
Tony consumed half of his candy. His final treat will be
18 + x / 2
The phrase for Sue candies is 13 - x.
18 + x / 2 is the equation for Tony Sweets.
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A 50 fluid ounce bottle of laundry detergent washes 32 loads of laundry. A 100 fluid ounce bottle wash is 60 loads of laundry. Are they portional? Do these rates from a proportion? 
Answer:
No, they are not proportional
Step-by-step explanation
50*2=100
32*2=64, not 60
On parallelogram PQRS, P is located at (-1, 6) and S is located at (-7,-3). What is the
slope of segment QR?
P Р
R
rimblr an impronar fraction
How do I solve this?
According to the parallelogram, the slope of the segment QR is 3/2
In math the term called parallelogram is a closed quadrilateral with parallel and congruent opposite sides is referred to as a parallelogram and the opposite pairs of sides have the same slope and the sum of two adjacent angles is 180 degrees.
Here we have know that values of P is located at (-1, 6) and S is located at (-7,-3). Then the slope of QR is calculated by using the the slope formula for a line segment passing through two points,
It can be calculated as,
=> m = (-3 - 6) / (-7 - (-1)
When we simplify this one then we get,
=> m = -9/-6
=> m = 3/2
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What number line models the expression 1/8-(-3/4)
A number line that models the expression 1/8 - (-3/4) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Next, we would evaluate and add the given numbers together as follows:
Number = 1/8 - (-3/4)
Number = 1/8 + 3/4
Number = 7/8
In conclusion, you would start at 1/8 on the number line and move 3/4 places to the right.
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Select the correct answer from the drop-down menu.
What is the author's purpose for including the quote in paragraph 5 in the article?
The author includes the quote to give the reader
were at Mauna Loa.
F
a contrasting view
a first-hand account
an opinion
an objective summary
of how dangerous the conditions
In the essay “A Modest Proposal”, The author includes the quote to give the reader an objective summary of how dangerous the conditions were at Mauna Loa.
What is “A Modest Proposal”?Jonathan Swift, a satirist, suggested jokingly in an essay titled "A Modest Proposal" from 1729 that the people of Ireland sell their children as food. A radical or shocking notion is frequently introduced in an ironic way using the term a modest suggestion.
Swift's essay, which is hailed as a masterwork of irony, is officially titled "A Modest Proposal for Preventing the Children of the Poor People in Ireland from Being a Burden to Their Parents or Country, and for Making Them Beneficial to Their Public."
When a proposal takes the form of an essay, it typically proposes a fix for a social or political issue. The adjective "modest" denotes reason or modesty. Because the idea is genuinely absurd, it is humorously used in the title of "A Modest Proposal."
A modest proposal is frequently used in jest to make a point by taking something to its logical conclusion, which highlights a problem. Swift's article, which at the time caused controversy, has since become a satirical mainstay and has influenced a lot of authors.
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Answer:
first hand account
Step-by-step explanation:
I got a 100 on the test
PLEASE PLEASE HELPPP
Calculator
During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height
What is the volume of the water that filled one cone?
nter your answer as a decimal in the box. Use 3.14 for pi.
in³
1 2
3
A
4
5
6
7 8 9
10
The volume of One cone held 1.1017.36 inches3 of water when it was full.
A method for determining a cone's volume?A cone's volume is determined using the following formula:
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
A cone's volume is determined using the following ,
V = 1/3πr²h
R is the radius, and H is the height.
the aforementioned conditions
r = 12/2 = 6in
h =27in
Discover the volume V = 1/3(3.14)(6)2*27
V = 1.1017.36
In light of this, one cone held 1.1017.36 inches of water.
One cone held 1.1017.36 inches of water.
The complete question is,
Construction cones were soaked with water while a project was underway due to a strong downpour. A cone has a 12 inch diameter and a 27 inch height.
How much water was used to fill each cone?
Put a decimal in the box for your response. Pi is equal to 3.14; in3
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Find the quotient of 6y^4+10y^3-8y^2divided by 2y.
The quotient of 6y^4 + 10y³ - 8y² by 2y is given as follows:
6y³ + 10y² - 4y.
How to obtain the quotient?The dividend is given as follows:
6y^4 + 10y³ - 8y²
The common factors are given as follows:
Constants 6, 10 and -8: 2, which is the greatest common factor of the three numbers.Exponents 2, 3 and 4: 2, which is the lowest exponent.Hence the dividend can be simplified as follows:
2y²(6y² + 10y - 4).
Simplifying by 2y, the result of the quotient is given as follows:
y(6y² + 10y - 4) = 6y³ + 10y² - 4y.
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Karis ran 3 and 2/3rds miles on Monday. Benita ran 1/2 of the distance that Karis ran. How far did Benita run?
The required distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
This problem is related to the chapter fractions. The relation between the distances travelled by both the people is given, so that we can calculate the actual distance travelled by the second person.
Karis ran 3 2/3 miles on Monday.
It is said that Benita ran half of the distance ran by Karis.
So, the distance ran by Benita would be,
⇒ 3 2/3 × 1/2
⇒ 11/3 × 1/2
⇒ 11/6 miles
Thus, the distance travelled by Benita is calculated to be 11/6 miles when the relation between the distances travelled by Karis and Benita is given.
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if PQ+PR=72 cm, then what is the value of sinR? (look at the file)
The exact value of the sine of angle R is equal to 1 / 2.
How to determine the exact value of a trigonometric function
In this problem we find the representation of a right triangle, where two side lengths are known and the exact value of a trigonometric function must be found. First, determine the length of side PR:
PR = 72 cm - PQ
PR = 72 cm - 24 cm
PR = 48 cm
Second, determine the length of side PQ by Pythagorean theorem:
RQ = √[PR² - PQ²]
RQ = √[(48 cm)² - (24 cm)²]
RQ = 24√3 cm
Third, determine the exact value of a trigonometric function of angle R by definition of sine:
sin R = PQ / PR
sin R = (24 cm) / (48 cm)
sin R = 1 / 2
Fourth, determine the exact value of a trigonometric function of angle R by definition of cosine:
cos R = RQ / PR
cos R = (24√3 cm) / (48 cm)
cos R = √3 / 2
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true or false: if and are mutually exclusive and exhaustive with and , and is an event in , then
If A1 and A2, are mutually exclusive and exhaustive with P(A1)>0 and P(A2) >0, and B is an event in S. then P(B) = P(A1 ∩B) + P(A2∩ B). [TRUE]
IntersectionThe sets A and B are the sets of all objects that are members of set A and members of set B. In written notation form:
A ∩ B = {x | x ∈ A and x ∈ B}
Here's how to determine the separation of two sets:
One set which is another subset if A ⊆ B then A ∩ B = A and vice versa.
The sets are equal if A = B, then A ∩ B = (A = B).
Sets are mutually exclusive if A // B, then A ∩ B = … and vice versa.
The sets are not mutually exclusive.
UnionThe union of sets A and B is the set of all objects that are members of set A or members of set B. In written notation form:
A ∪ B = {x | x ∈ A or x ∈ B}
Here's how to determine the union of two sets:
A set that is a set in other parts if A ⊆ B, then A ∪ B = B and vice versa.
The set is equal if A = B then A ∪ B = (A = B).
Sets are mutually exclusive if A // B, then A ∪ B = {x | x ∈ A or x ∈ B} and vice versa.
The sets are not mutually exclusive if A ⊃⊂ B, then A ∪ B = {x | x ∈ A, x ∈ B or x ∈ (A ∩ B)}.
Your question is incomplete but most probably your full question was:
If A, and A, are mutually exclusive and exhaustive with P(A)>and P(A2) >0, and B is an event in s. then P(B) = P(ALB) + P(ANB). True False
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Ashley invested $59,000 in an account paying an interest rate of 3 (1/8)% compounded
daily. Fwam invested $59,000 in an account paying an interest rate of 2 (3/4)%
compounded annually. After 15 years, how much more money would Ashley have in
her account than Fwam, to the nearest dollar?
Answer:
5650
Step-by-step explanation:
3 (1/8)% =3.125% but compound daily = 3.125% /365 = 0.00856%
so everyday the money grows at 1.00856%, so compound 365 times, it'll become 1.00856%^365 =3.1742% annually equivalent.
so now you can compare the 2 - apples to apples.
so 3.1742%^15years * 59000 = $94,279.80
2.75%^15years * 59000 = $ $88,629.74
diff is 5650$
PLEASE HELP!!!!!!! PHOTO BELOW
State the equation of the graphed function.
The equation of the graphed function for this problem is given as follows:
y = x³ - 6x² - 7x - 6.
How to obtain the function?The function for this problem is obtained using the Factor Theorem, as a product of the linear factors of the function.
The zeros of the function are given as follows:
x = 1.x = 2.x = 3.Hence the linear factors are given as follows:
(x - 1).(x - 2).(x - 3).Then the function is given as follows:
y = a(x - 1)(x - 2)(x - 3).
In which a is the leading coefficient.
The y-intercept is at y = -6, hence the leading coefficient is given as follows:
-6a = -6
a = 1.
Hence the function is:
y = (x² - 3x + 2)(x - 3)
y = x³ - 6x² - 7x - 6.
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Can someone please help me with this
hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition
[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]
There are 25 pieces of candy in a bowl, and 15 of them are chocolate. What percentage of pieces of candy in the bowl are chocolate?
60% of the pieces of candy in the bowl are chocolate.
(15/25)*100 = 60%