The two cars will draw level at a distance of 12 kilometers from the starting point, taking their speed and into consideration, as further explained below.
How to find the distanceSince both cars are traveling towards the same destination, the distance between them will decrease over time until they draw level. Let's call the distance between the starting point and the meeting point "d" kilometers. We can use the formula:
distance = rate × time
Since car A has a three-minute head start, car B will have to travel for three minutes less than car A. Let's call the time it takes for car B to catch up to car A "t" hours. Then:
time for car A = t + 3/60 hours
time for car B = t hours
We want to find the distance between the starting point and the meeting point, which is the same for both cars. So we can set up an equation based on their distances:
distance traveled by car A = distance traveled by car B
(rate for car A) × (time for car A) = (rate for car B) × (time for car B)
60 × (t + 3/60) = 70 × t
3 = 10t
t = 3/10 hours
Now that we know the time it takes for car B to catch up to car A, we can use either car's rate and time to find the distance between the starting point and the meeting point. Let's use car A's rate and time:
distance = rate × time
distance = 60 × (t + 3/60)
distance = 60 × (3/10 + 1/20)
distance = 60 × (4/20)
distance = 12 kilometers
Therefore, the two cars will meet 12 kilometers from the starting point.
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At the beginning of the period, the Cutting Department budgeted direct labor of $37,260 and supervisor salaries of $43,370 for 4,140 hours of production. The department actually completed 4,500 hours of production.
Determine the budget for the department assuming that it uses flexible budgeting.
Answer:
To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.
First, we need to calculate the variable cost per hour of production:
Variable cost per hour = Direct labor / Hours of production
Variable cost per hour = $37,260 / 4,140 hours
Variable cost per hour = $9
Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:
Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs
Flexible budget = ($9 x 4,500 hours) + $43,370
Flexible budget = $40,500 + $43,370
Flexible budget = $83,870
Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.
Use the variable c to represent Chau's height.
[tex]\left[\begin{array}{ccc}Answr:\\=&=&=\\1&6&.\end{array}\right][/tex]
Step-by-step explanation & Answer
In order to find chau’s height we would only need to subtract:
40 - 24 = ?
? = 16
But it determines what you are putting it in as well.
You can put it in, feet, meters, or inches.
So I do not know but looking at the question it seems like I do not need to know. ( Saying thing because you might actually have the measurements but I do not know / I cannot see. )
Thus the answer to your problem is, 16
In a grocery store, a $12 case of soda is discounted 20%. How much will you save?
Answer: 9.60
Step-by-step explanation:
Labeled price = $ 12
Discount = 20% of labeled price = 12 x 20%
= 12 x 2 / 10 = 24 / 10 = $ 2.4
Sale price = Labeled price - Discount.
Sale price = $ 12 - $ 2.40 = $ 9.60
Thus the sale price of the case of soda is 9.60 $
Help with math problems
Answer:
70
Step-by-step explanation:
If two cards are chosen from a standard deck of cards one at a time and placed in your hands as you choose them, the probability of choosing a 7 and a jack is what?
As a result, the probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.
What is probability?Probabilistic theory is a branch of mathematics that evaluates the probability of a certain occurrence or proposition occurring or being true. A danger is a number in the range between 0 and 1, whereas 1 signifies certainty and a probability of around 0 reflects how likely an event seems to be to occur. Probability seems to be a mathematical function for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences between equally as likely possibilities that result in a specific event.
The probability of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is as follows:
As a result, the odds of selecting a jack from the remaining cards are 4/51.
The product of these probabilities is the likelihood of selecting a 7 and a jack in sequence:
P(7) = P(7) x P(jack|7 not picked) = 4/52 x 4/51
When we simplify this expression, we get:
P(Jack and 7) = 16/2652
As a result, the likelihood of selecting a 7 and a jack from a regular deck of cards, one at a time and without replacement, is about 0.006 or 0.6%.
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13 The diagram shows a wall. 2.8 m The area of the wall is 39.2 m² Work out the length of the wall. N length 2.1 m Not drawn accurately [3 marks]
After answering the presented question, we can conclude that As a rectangle result, the wall's length is approximately 18.67 metres.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. It can also be described as a fundamental rule hexagon or one in which all of the angles are equal. Another option for the parallelogram is a straight angle. Four of the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
To begin, we can use the formula for the area of a rectangle, which is:
length x width Equals area
We know the wall's area is 39.2 m2, and we want to know how long it is. We are also given the wall's breadth, which is 2.1 m.
As a result, we can rearrange the formula to find the length:
width = Area length
length = 39.2 2.1 cm
a length of 18.67
As a result, the wall's length is approximately 18.67 metres.
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Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
b + 12r
Answer:
Parts of the expression:
b: a variable representing a quantity that can vary or change.
12: a constant representing a fixed value.
r: a variable representing a quantity that can vary or change.
Word expression:
"Add twelve times the quantity of r to b."
Step-by-step explanation:
The length of a rectangle is 7 inches more than its width. The area of the rectangle is equal to 2 inches more than 2 times the perimeter. Find the length and width of the rectangle.
The width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.
What is area of a rectangle?The region contained inside the rectangle's perimeter is referred to as the area of the rectangle. In other terms, the area of a rectangle is the whole area that a rectangle encloses. Depending on the provided dimensions, this may be determined using the area of rectangle formula and a number of other techniques.
Let us suppose the width = x.
Then, length is given as:
l = x + 7
The area of the rectangle is:
A = lw
Substituting the values:
A = (x + 7)x
The perimeter of the rectangle is:
P = 2(l + w)
P = 2(x + 7 + x)
P = 2(2x + 7)
P = 4x + 14
Also, we have:
A = 2P
Substituting the values of area and perimeter:
4x + 14 = (x + 7)x
Simplifying the expression:
x^2 + 7x = 8x + 30
x^2 - x - 30 = 0
(x-6)(x+5) = 0
Since, width cannot be negative value we have:
x = 6.
l = 7 + 6 = 13 inches.
Hence, the width of the rectangle is x = 6 inches and the length of the rectangle is 13 inches.
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Use the graphs of f and g to find (fg)(−2).
In this the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.
What is a coordinate plane?A coordinate plane is a two-dimensional surface composed of two number lines, one horizontal (x-axis) and one vertical (y-axis). It is used to graph points, lines, and other shapes. Each point is identified by a pair of numbers which indicate its position along the x and y axes. The x and y axes intersect at the origin and divide the plane into four quadrants.
The graph of fg can be found by first graphing both f and g on the same coordinate plane. From there, the graph of fg can be found by taking each point on the graph of f and multiplying it by the corresponding point on the graph of g. In this example, the point (x,y) on the graph of f is multiplied by the corresponding point (x,y) on the graph of g to form a new point (x,yz). This new point is then placed on the graph of fg.
Using the graphs of f and g provided, we can determine that (fg)(-2) = -8. To find this, first locate the point (-2,3) on the graph of f. Then, locate the corresponding point (-2,2) on the graph of g. The product of these two points is (-2,6). This means that (fg)(-2) = -8.
In summary, to find (fg)(-2) using the graphs of f and g, first graph both f and g on the same coordinate plane. Then, take each point on the graph of f and multiply it by the corresponding point on the graph of g. In this example, the point (-2,3) on the graph of f multiplied by the corresponding point (-2,2) on the graph of g yields the product (-2,6), which is equal to -8.
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Describe the set of values that is greater than the quadratic function with zeros –5 and –13 and include the
point (–9, –32).
y>2(x+5)(x+13)
y>2(x−5)(x−13)
y≥- 8\77 (x+5)(x+13)
y≥- 8\77(x−5)(x−13)
The set of values that is greater than the quadratic function with zeros -5 and -13 and includes the point (-9, -32) is: y > 2(x+5)(x+13)
Define the term quadratic function?A quadratic function is a type of function in mathematics that can be represented by a quadratic equation, which is a polynomial equation of the second degree. It is an equation, for example, y = ax2 + bx + c, where a, b, and c are constants and x is the variable, that involves a variable raised to the power of two.
The factored form of the quadratic function with zeros -5 and -13 is as follows:
f(x) = a(x + 5)(x + 13)
where a is a constant.
Substituting the given point (-9, -32) into the quadratic function, we get:
-32 = a(-9 + 5)(-9 + 13)
-32 = -16a
a = 2
So, the quadratic function in factored form is:
f(x) = 2(x + 5)(x + 13)
we need to find the range of values that satisfy this inequality:
y > a(x + 5)(x + 13)
Therefore, the set of values that is greater than the quadratic function with zeros -5 and -13 and includes the point (-9, -32) is: y > 2(x+5)(x+13)
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In 1940, the average size of a privately owned farm in a particular country was 170 acres. In a recent year, the average size of a privately owned farm in the country had increased to 432 acres. What is this percent increase?
Answer:
154%
Step-by-step explanation:
First, we need to calculate the increase in size of the privately owned farm:
increase = new value - old value
increase = 432 - 170
increase = 262
Next, we can use the formula to calculate the percent increase:
percent increase = (262 / 170) x 100%
percent increase = 1.54 x 100%
percent increase = 154%
Therefore, the percent increase in the size of privately owned farms in the country is 154%.
Write the equation of the line that has a slope of 4 / 3 and passes through the point ( 0, - 3 ).
Answer: y = 4/3x -3
Step-by-step explanation:
can someone help?
Write an equation for the transformed logarithm shown below, that passes through (0,0) and (-5,3)
The equation for the logarithmic function that passes through (0,0) and (-5,3) is given as follows:
y = log2(-x + 1)
How to define the logarithmic function?First we must consider the vertical asymptote of the logarithmic equation, which is given as follows:
x = 1.
As the function is defined for the values to the left of the vertical asymptote, the function was reflected over the y-axis, hence:
y = logb(-x + 1) + d.
When x = -1, y = 1, hence we can have a logarithm of base 2 with a vertical shift of zero, hence:
y = log2(-x + 1)
Which is the logarithmic function for the function graphed in this problem.;
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K
Use the information shown on the auger shell. What is the value of x?
8.8 mm
11 mm
20 mm
Using the information shown on the auger shell. The value of x is found as 16.
Explain about the proportion of the numbers?Fractions and ratios can both be stated as reciprocals of one another. Similar rules apply to proportions, which are just the equivalence of two ratios.
Fractions and ratios both convey the relationship between two different quantities.A percentage is an algebraic assessment of two numbers.According to proportion, two sets of provided numbers are referred to as directly proportional to one another if they increase or decrease in the same ratio. A proportion is actually an equation that equalizes two ratios. One boy and 3 girls, for example, might just be defined by a ratio of 1: 3.For the given values in question:
8.8 mm
11 mm
20 mm
Value of x.
Using proportion of the numbers:
8.8 / 11 = x / 20
x = 8.8*20 / 11
x = 16
Thus, using the information shown on the auger shell. The value of x is found as 16.
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Consider the function
f(t)=1−2t+4t2.
Give the largest value of t such that the percentage rate of change equals 100. Give your answer to one decimal place.
Answer:
The percentage rate of change of a function f(t) is given by:
(Δf / f) x 100
where Δf is the change in f and f is the original value of the function.
To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:
(Δf / f) x 100 = 100
Simplifying, we get:
Δf / f = 1
This means that the change in f is equal to the original value of f.
So, we need to solve the equation:
f(t + Δt) - f(t) = f(t)
where Δt is the change in t.
Substituting the given function, we get:
[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2
Simplifying, we get:
-8tΔt + 8Δt^2 = 1
Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.
Ignoring the term Δt^2, we get:
-8tΔt = 1
Solving for Δt, we get:
Δt = -1 / (8t)
Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:
-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1
Simplifying, we get:
1 / t^2 = 1
Solving for t, we get:
t = 1
Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.
PLEASE HELP FAST!
A marble is selected from a bag containing eight marbles numbered 1 to 8.
The number on the marble selected will be recorded as the outcome.
Consider the following events.
Event A: The marble selected has a a number less than 4
Event B: The marble selected has an even number
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
Answer:
Look explain
Step-by-step explanation:
Give the following outcomes for each of the events with a set of 1,2,3,4,5,6,7,8:
Event A: The number can be 1,2,3 because it has to be less than 4
Event B: The number can be 2,4,6,8 because those are the only even numbers
Both Event A&B: The marble must be even and between 1,2,3 so only 2 is correct and must be marble #2
I hope this helps :)
Choose the best answer. ________Functions have a constant rate of change and when graphed form a straight line. _______functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape"
Best answer for the statement are Linear, Nonlinear.
Define Linear functionsA linear function is a type of mathematical function that has the following form:
f(x) = mx + b
where "m" and "b" are constants. "m" represents the slope of the line, or the rate at which the function changes .
Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".
Therefore, the best answer to complete the sentence is:
Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".
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What is the value of the expression 9x^2−12x+4 when x=3?
Answer: 9·9 -36 +4.
Step-by-step explanation: 9x² -12x +4 for x=3. 9·3² -12·3 +4 = 9·9 -36 +4.
Write a word phrase that represents the expression
Answer:
Where is the expression bro
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
Answer: It looks like it could be III I'm not sure thought I hope it was right
Step-by-step explanation:
Use the diagram below to answer the questions.
What are two other names for line WQ?
QW
What is another name for plane V?
What are three points that are collinear? What is a fourth point that is not collinear with those three points?
What is a point that is not coplanar with R, S, and T?
Answer:
Step-by-step explanation:
b-y=55
Point T has coordinates (-7, -3). If it's reflected across the line x = 2, what will be the coordinates of its image?
(7, -3)
(11, -3)
(7, 3)
(-7, 7)
The image after the reflection over the line x = 2 is (11, -3)
What will be the coordinates after the reflection?Here we have the point T which has coordinates (-7, -3), and we apply a refletion across the line x = 2.
This reflection will only chane the value of x in our point, such that the initial value x = -7
Is at the same distance of the line x = 2 than the final x-value
The distance between these values is:
d = |-7 - 2| = 9
Then the new x-value will be:
x = 2 + 9 = 11
Thus, the image after the reflection is (11, -3)
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Please Help ASAP - 100 pts + Brainliest if the answer is correct!
The sum of the infinite geometric series is: ²/₅
How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
where;
a is first term
r is common ratio
The first term is; a = ⁴/₁₅
Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃
r = ²⁰/₂₇ ÷ ⁴/₉ = ⁵/₃
Thus;
[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)
[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃
= ²/₅
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Answer:
How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9) = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5
The attendance at a concert was 335. Admission was $2.50 for adults and $1.25 for children. The receipts were $675. How many adults and children attended the concert? (Show steps)
In response to the question, we may say that 205 adults and 130 kids equation respectively attended the concert, for a total of 205 adults and 130 kids.
What is equation?The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programmed. An example would be 2x - 4 = 2.
Assume that "x" represents the proportion of adults who attended the performance and "y" represents the proportion of children.
The problem statement informs us that:
x + y = 335 —-(1) (1) (There are 335 persons present in all.)
The total amount of money gathered is $675 (2.5x + 1.25y).
1.25x + 1.25y = 418.75 —-(3) (3)
2.5x - 1.25x = 675 - 418.75
1.25x = 256.25
x = 205
205 + y = 335
y = 130
205 adults and 130 kids respectively attended the concert, for a total of 205 adults and 130 kids.
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Find an equation of the ellipse that has center (-1,-5) , a minor axis of length 2, and a vertex at (5,-5).
According to the given conditions, the equation of the ellipse is [tex]{\frac{(x+1)^2}{25}+(y+5)^2=1}$.[/tex]
What is equations ?An equation is a mathematical statement that shows the equality between two expressions. In other words, it is a way to describe a relationship between two or more variables or quantities.
According to given information :The center of the ellipse is (-1,-5), which means that the center of the ellipse is shifted from the origin. We can find the equation of the ellipse using the standard form equation:
[tex]$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$[/tex]
where (h,k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.
Since the minor axis has length 2, we know that b=1. We also know that the vertex on the minor axis is (5,-5), which means that the semi-major axis has length 5. Therefore, a=5.
Substituting these values into the standard form equation, we get:
Simplifying, we get:
[tex]$\frac{(x+1)^2}{25}+(y+5)^2=1$[/tex]
Therefore, according to the given conditions, the equation of the ellipse is [tex]{\frac{(x+1)^2}{25}+(y+5)^2=1}$.[/tex]
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i neeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeedddd help
Answer:
divide the numbers and you'll get 1×10^5
quick Math Answer ok
Answer:
See below.
Step-by-step explanation:
For this problem, we are asked to find x, the hypotenuse.
There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.
Represented as;
[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]
We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.
Substitute:
[tex]40^2+42^2=c^2[/tex]
[tex]3364 = c^2[/tex]
Square Root the Equation:
[tex]\sqrt{3364} = \sqrt{c^2}[/tex]
[tex]c = 58.[/tex]
The Hypotenuse is 58. Our final answer is Letter D.
PLEASE HELP
I bought a pie. It cost somewhere between £1.30 and £2.99. I gave a 24% tip, and the total price was still an exact number of a pence. When I paid with a £5 note I received five coins in my change (the fewest I could have been given for that amount). What were the two possible amounts of change I could have been given?
The two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.
What is combination ?
Combination refers to the number of ways a selection of items can be made from a larger set of items without regard to their arrangement. In other words, combinations are a way to calculate the total number of possible groups of items that can be formed, regardless of the order in which the items are selected. The formula for calculating the number of combinations is nCr, where n is the total number of items and r is the number of items being selected.
According to the question:
Let's start by finding the possible prices of the pie. Since the price must be an exact number of pence, we can convert the price range to pence by multiplying each value by 100:
£1.30 = 130 pence
£2.99 = 299 pence
We know that the price plus the 24% tip must be an exact number of pence. If we let x be the price of the pie in pence, then we can write this as:
x + 0.24x = 1.24x
Since 1.24 is not divisible by 5 (which we'll need for the change), we need to find two values of x that differ by a multiple of 5. One way to do this is to start with the lower bound and add multiples of 5 until we get a valid value:
x = 130: 1.24x = 161.2
x = 135: 1.24x = 167.4
x = 140: 1.24x = 173.6 (valid)
x = 145: 1.24x = 179.8
x = 150: 1.24x = 186.0 (valid)
x = 155: 1.24x = 192.2
x = 160: 1.24x = 198.4
So the possible prices of the pie are 140p and 150p. To find the possible amounts of change, we need to subtract each price from 500p (the value of the £5 note) and express the result as a combination of coins. For example:
Price = 140p, change = 360p = 3 x £1 + 1 x 50p + 1 x 10p
Price = 150p, change = 350p = 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p
Therefore, the two possible amounts of change are 3 x £1 + 1 x 50p + 1 x 10p and 3 x £1 + 1 x 20p + 1 x 10p + 1 x 5p, which simplify to £3.60 and £3.25 respectively.
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The 12 students in the Environmental Club represent 2% of the students in the seventh grade. How many students are in the seventh grade?
Hence, in response to the provided question, we can say that Therefore equation there are 600 pupils in the seventh grade.
What is equation?An algebraic equation is a method of connecting two quotes by using the equals symbol (=) to express equality. In algebra, an explanation is a definitive expression that verifies the equivalency of two formula. For example, the identical character divides the numbers 3x + 5 and 14. A linear equation might be used to recognize the connection that existing between the texts written on separate sides of a letter. The product and application both frequently the same. 2x - 4 equals 2, for example.
Let's call the total number of pupils in the seventh grade "x".
We know that the 12 students in the Environmental Club account for 2% of the seventh-grade students, which means:
12 = 0.02x
To find x, we must isolate it on one side of the equation. This can be accomplished by dividing both sides by 0.02:
12 ÷ 0.02 = x
This boils down to:
600 = x
Therefore there are 600 pupils in the seventh grade.
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what is the procedure, I need it for TODAY before 12pm
It is also important to communicate effectively with any individuals involved in the procedure to ensure that everyone is on the same page and working towards the same goal.
The procedure can refer to a variety of things depending on the context. If you are referring to a medical procedure, it is important to first consult with a healthcare professional to determine the specific procedure that is needed.
If you are referring to a legal or administrative procedure, it is important to review the guidelines and protocols set forth by the governing body or organization.
In general, the procedure typically involves a set of steps or instructions that must be followed in order to achieve a specific outcome. These steps may include gathering information, completing forms, submitting documents, or performing specific tasks.
It is important to carefully follow each step of the procedure to ensure that the desired outcome is achieved.
If you need a procedure completed by 12pm today, it is important to prioritize your tasks and ensure that you have all necessary resources and information available. Depending on the specific procedure, you may need to work quickly and efficiently in order to meet the deadline.
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