=====================================
Work Shown:
[tex](\text{x}-7)^2 = 36\\\\\sqrt{(\text{x}-7)^2} = \sqrt{36}\\\\\text{x}-7 = \pm\sqrt{36}\\\\\text{x}-7 = \pm6\\\\\text{x}-7 = 6 \ \text{ or } \ \text{x}-7 = -6\\\\\text{x} = 6+7 \ \text{ or } \ \text{x} = -6+7\\\\\text{x} = 13 \ \text{ or } \ \text{x} = 1\\\\[/tex]
-------------
Check:
Plug in x = 13
[tex](\text{x}-7)^2 = 36\\\\(13-7)^2 = 36\\\\(6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\[/tex]
This confirms x = 13
Now check x = 1
[tex](\text{x}-7)^2 = 36\\\\(1-7)^2 = 36\\\\(-6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\[/tex]
The value x = 1 is confirmed as well.
Both solutions are confirmed.
2. How many points
of intersection are there
on the graph
of
y=x² + 3x-2
y -x=4
There is one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
To find the point of intersection, we need to set the two equations equal to each other and solve for x and y.
y = x² + 3x - 2
y - x = 4
x² + 3x - 2 - x = 4
x² + 2x - 6 = 0
(x-3)(x+2)=0
x =3 or x=-2
When x = 3, we substitute it into the first equation y = x² + 3x - 2
y = 3² + 3(3) - 2
y = 9 + 9 - 2
y = 16
When x = -2, we substitute it into the first equation y = x² + 3x - 2
y = -2² + 3(-2) - 2
y = 4 -6 -2
y = -4
So the point of intersection is (3,16) or (-2,-4)
Hence there is only one point of intersection on the graph of y = x² + 3x - 2 and y - x = 4
A bakery sells different packages of muffins. The number of muffins, , and the price in dollars, , of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
The bakery is considering adding a new package of muffins. Which of these combinations would make the relation NOT a function? Select TWO that apply.
A relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
What are combinations?Combinations are mathematical procedures that count how many different ways a collection of items could be arranged when the order in which they are chosen is immaterial.
Combos' components can be chosen in any hierarchy.
Combinations and permutations can coexist.
Hence, the ordered pair is given:
(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)
For a relation to be a function, all of the x-values must be unique (i.e. no repetition)
From the list of alternatives, options (b) and (d), with x values (6, 7) and (d), already exist in the ordered pair (4,5)
In light of this, (b) and (d) would stop the connection from being a function.
Therefore, a relation might or might not be a function. The connection would cease to be a function because of b. (6, 8) and d. (4, 3).
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Correct question:
A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
{(1,2),(2,3),(4,5),(6,7),(12,13)}
The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.
a. (10,13)
b. (6,8)
c. (8,12)
d. (4,3)
e. (24,18)
When we are concerned with whether we are correct in inferring that a cause produced an effect, we are concerned with the:
The concept here is the Research method, it is the main extent to which a concept, conclusion, or measurement is well-founded The answer is validity.
Research methods are strategies, processes, or ways used to collect data or substantiation for analysis to uncover new information or better understand the content.
Validity is the lesser degree to which an idea, conclusion, or action is reasonable and likely to directly reflect reality. The word" valid" comes from the Latin Validus, which means strong.
The validity of a dimension instrument is the extent to which the instrument measures what it's intended to measure. Validity refers to the relationship between the study thing and the data the experimenter chooses to use to quantify that thing. Some confines similar to physical strength, aren't naturally related to intelligence.
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0.75 * ( x+4)=9. what does x equal?
Answer:
x = 8
Step-by-step explanation:
0.75 * ( x+4) = 9
0.75x + 3 = 9
0.75x = 9 - 3
0.75x = 6
x = 6 / 0.75
x = 8
Josh drank 70 ounces of water yesterday.how many cups of water did he drink
Answer:
8.75
Step-by-step explanation:
Does someone mind helping me with this problem? Thank you!
Answer:
x=71; y=19
Step-by-step explanation:
x+y = 90 so x =90-y = 14+3y
so 90=14+4y
90-14 = 4y
76=4y
y=19
x=71
Answer:
x = 71
y = 19
Step-by-step explanation:
I solved by graphing and got (71,19) as included in the image. A more mathematical way to solve is by substitution. You try to find x with one of the equations, plug in x and then solve for y.
x + y = 90
x = 90 - y
90 - y = 14 + 3y
90 - y + y= 14 + 3y + y
90 = 14 + 4y
90 - 14= 14 + 4y - 14
76= 4y
19 = y
x + y = 90
x + (19) = 90
x + 19 - 19= 90- 19
x = 71
Eagle Airlines flies charter planes all over the world. Susan, one of the airlines' top pilo
routes in Europe and North Africa. Susan's plane uses 2 kilograms of fuel for every kil
she flies.
There is a proportional relationship between the distance Susan flies (in kilometers), x
the amount of fuel her plane uses (in kilograms), y.
Graph this relationship. Select two points to draw a line.
What is the slope of the line?
The proportional relationship that models this situation is given as follows:
y = 2x.
The graph is given by the image presented at the end of the answer.
How to model the proportional relationship?A proportional relationship is modeled as follows:
y = kx.
In which k is the constant of proportionality.
Susan's plane uses 2 kilograms of fuel for every unit she flies, hence the constant is given as follows:
k = 2.
The relationship is:
y = 2x.
The domain is:
x >= 0, as the number of units flied cannot be negative.
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Please help me. Answer ASAP!! all info you need to solve the problem is in the photo
If f(0) = 18 and f(1) = 13 then f(0) be the largest value.
What is meant by function?A function is a relationship between a number of inputs where each input has exactly one output, according to one definition.
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions denoted the idealized relationship between two changing quantities.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). If f exists typically utilized to denote a function (x).
Let the function f(x) = 18 - 5x
a) f(-4) = 18 - 5(-4) = 38
b) f(0) = 18 - 5(0) = 18
f(1) = 18 - 5(1) = 13
Therefore, f(0) be the largest value.
The complete question is:
Given the function f(x) = 18 - 5x
a. What is the value of function f given an input of -4 ?
b. Which is larger, f(0) or f(1)? Show your work to justify your answer.
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What is the solution to 9|x + 8| > 45?
x < –3 or x > 13
–3 < x < 13
x < –13 or x > –3
–13 < x < –3
The inequality model of the question will be -13 > x > -3
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
9|x + 8| > 45
now when we remove the modulus there will be two terms.
|x + 8| > 45/9
|x + 8| > 5
-5>x + 8>5
-5-8>x >5-8
-13 > x > -3
Hence, the inequality model will be -13 > x > -3
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complete the description of the piecewise function graphed below
The supplied input should simply be replaced in the function definition for that precise interval.
What best describes a piecewise function?An equation or set of equations, rather than a single equation, defines a piecewise-defined function. For a specific interval, each equation is valid.
Find out to which of the above intervals (or inequalities) the supplied input belongs before evaluating a piecewise function at any given input. The function definition for that specific interval should therefore just have the specified input replaced.
When a rule or relationship changes as an input value passes specific "boundaries," we refer to these instances as piecewise functions. For instance, scenarios where the price per piece of a specific item is decreased once the quantity requested exceeds a given amount are frequent in business.
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PLEASE ANSWER DUE TOMORROW
The measurement of angles formed by intersecting line segments UT and WV are -
∠TXV = 25°
∠UXW = 25°
∠TXW = 155°
∠UXV = 155°
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Two line segments UT and WV are given.
The line segment UT and WV are intersecting each other at a point X.
Due to the intersection many angles are formed.
To find the measure of the angles, use the protractor.
The first angle is ∠TXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UT.
The measure of ∠TXV is approximately 25°.
The second angle is ∠UXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠UXW is approximately 25°.
The third angle is ∠TXW.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line WV.
The measure of ∠TXW is approximately 155°.
The fourth angle is ∠UXV.
Keep the protractor's midpoint at point X.
Then turn the protractor so that it aligns with line UV.
The measure of ∠UXV is approximately 155°.
Therefore, all the four angles are obtained.
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Find two numbers that the quotient is between.
4,096 divided by 61
The quotient is between _ and _
Answer:
Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)
Step-by-step explanation:
see image
The quotient from 4,096 divided by 61 is between 66 and 67.
How do the values compare? Order the values from least to greatest.
30
314
4
-1
14
4
314
14
14
-2.
14
1-2-11
Answer: -2, -1, 4, 4, 14, 14, 14, 30, 314, 314
The values are arranged in increasing order from least to greatest.
Check the picture below.
what is the measure of arc BC?
130 degrees
180 degrees
65 degrees
32.5 degrees
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
What is Area of circle ?
Area of circle can be defined as the product of pi and the square of radius of a circle.
Using the property that angle subtended by an arc on center is double than on circumference, you can find measure of arc BC.
The angle subtended by arc BC on center of circle is of 2 times 65 = 130
Given,
The angle subtended by arc BC on circumference is 65 degrees.
We have to find Length of arc BC
Relation between angle at center and angle at circumference by an arc:
"Angle subtended by an arc of a circle on its center is double than angle subtended by it on circumference"
Therefore , angle subtended by arc BC on center of circle is of 2 times 65 = 130 .
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At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
please help
The equation that represents the proportional relationship is: k = 7.25.
What is a Proportional Relationship Equation?A proportional relationship is a relationship between two variables such that one variable is a constant multiple of the other. A proportional relationship can be represented by an equation of the form y = kx where y and x are the variables, and k is the constant of proportionality. This equation can also be written as y/x = k.
From the given information, we have:
Constant of proportionality (k) = 21.75 / 3
k = 7.25
To write the equation, substitute k = 7.25 into y = kx:
y = 7.25x
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Here is some information about the goals scored in some hockey games.
Each game has four quarters.
Goals in hockey games
9
8
7
Number
6
of goals 5
4
3
2
1
The mean number of home
goals scored is 2. 5
The mean number of away
goals scored is 1. 8
How many home and away
games have been played
in total?
0
1st
3rd
4th
+
2nd
Quarter
Away goals
Key:
Home goals
If the mean number of home goals is 2.5 and away goals is 1.88 , then the number of home and away games have been played in total is 32 games .
From the histogram , we get that ,
the total number of home goals is = 9 + 6 + 8 + 7 = 30 goals ;
the total number of away goals is = 2 + 7 + 4 + 5 = 18 goals ;
the mean number of home goals is = 2.5 ;
the mean number of away goals is = 1.8 ;
we know formula that⇒ Mean Goal = (total goals)/(number of games) ;
For Home goals :
⇒ 2.5 = 30/n ⇒ n = 30/2.5 = 22 games .
For Away goals :
⇒ 1.8 = 18/n ⇒ n = 18/1.8 = 10 games .
So , total number of games is = 10 + 22 = 32 games ,
Therefore , In total the total number of home and away games played is 32 games .
The given question is incomplete , the complete question is
Here is some information about the goals scored in some hockey games. Each game has four quarters. the histogram is given below :
The mean number of home goals scored is 2.5 ;
The mean number of away goals scored is 1.8 ;
How many home and away games have been played in total ?
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3. In the MN Daily 3 lottery, players are given a ticket based upon 3 digits that they pick. If their
3 digits match the winning digits in the correct order, then the player wins $500. If the digits
don't match, then the player loses. The game costs $1 to play. What is the expected value for
a player of this lottery game. (Hint find the probability of winning the Daily 3)
On average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.
How to find the expected value?To find the expected value of the Daily 3 lottery game, we need to calculate the probability of winning and the expected payout for winning.
The probability of winning the Daily 3 game with a single ticket is 1/1000, since there are 1000 possible 3-digit number combinations and only one of them is the winning combination.
The expected payout for winning is $500, since this is the prize for matching the winning digits in the correct order.
To calculate the expected value, we can use the formula:
Expected Value = (Probability of Winning) x (Payout for Winning) - (Cost of Playing)
Plugging in the values we found, we get:
Expected Value = (1/1000) x ($500) - ($1)
= $0.50 - $1
= -$0.50
This means that, on average, a player can expect to lose $0.50 for every ticket they play in the Daily 3 lottery. Therefore, the Daily 3 lottery game is not a good investment, as the expected value is negative, and players are likely to lose money in the long run.
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The same type of dinner plate is sold in two different packs. Small pack contents 3 plates £5. 25. Large pack contents 12 plates £21. 24 which size packet is the better value for money?
Large pack with 12 plates has better value of money with $1.77 for each plate comparison to smaller pack with $1.75 for each plate.
Number of plates in smaller pack is equal to 3 .
Cost of smaller pack with three plates = $5.25
Cost of each plate in smaller pack = $5.25 / 3
= $1.75
Number of plates in larger pack is equal to 12 .
Cost of larger pack with twelve plates = $21.24
Cost of each plate in larger pack = $21.24 / 12
= $1.77
$1.77 is greater than $1.75.
Larger pack of plates have better value of money for each plate comparing the smaller pack.
Therefore, the larger pack has better value of money than the smaller pack .
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16 x 6 equals 92 How do I find 6?!?
The area of the rectangle would be 96 square inches.
Option (D) is correct.
What is the area of the rectangle?
The formula for the area of a rectangle is:
Area = length x width
where length is the distance along the longer side of the rectangle and width is the distance along the shorter side of the rectangle.
In the given figure,
The length of the rectangle = 8 + 8 = 16 inches.
Now by using the Pythagoras theorem, we can find the height
[tex]Height= \sqrt{(10)^2-(8)^2} \\\\=\sqrt{100-64}\\\\=\sqrt{36}\\\\=6[/tex]
So the base would be 6 inches.
Now we can find the area of the rectangle
Area = 16 * 6
Area = 96 square inches.
Hence, the area of the rectangle would be 96 square inches.
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Solve for x to the nearest tenth.
By calculating , The value of x is 5√5.
What is triangle?
Triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
From the given figure,
When we draw a line inside the figure than it becomes into rectangle and one another triangle.
so,
In the right angled triangle,
with base 10 and opposite side 5
We have to find the hypothenuse that is x .
so,
from pythagorean theorem
we can say that
Sum of squares of two sides is equal to square of hypothenuse
so,
10*10 + 5*5 = x*x
100+25 = x*x
x*x = 125
x = 5√5 .
Hence, The value of x is 5√5
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A boss wants to estimate the proportion of her employees who are satisfied with the company's
parking policy. She puts all 600 employees' names into a hat and picks 50 different names out of
the hat. Of the 50, 47 are satisfied with parking policy and 3 are not satisfied with it.
Which condition for constructing a l-sample z-interval for proportions has the boss failed to
satisfy?
For the given case The boss has failed to satisfy the condition of random sampling without replacement. This condition states that the samples must be taken randomly and with replacement, meaning that each sample is replaced after it has been selected.
In this case, the boss picked the 50 names out of the hat without replacing them, which means that the same names could have been picked more than once. This can lead to a sample bias, as the same names may be overrepresented in the sample. This lack of randomness can lead to an inaccurate estimate of the proportion of employees who are satisfied with the company's parking policy.
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The explicit rule for an arithmetic sequence is an = 8. 7 + (-1. 4)(n-1). What is the value of the 47th term? round to the nearest tenth, if necessary.
answer: A) -55. 7
The value of the 47th term of the given arithmetic sequence is -55.7
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same.
We are given the explicit rule for an arithmetic sequence as follows -
[tex]a_n[/tex] = 8.7 - 1.4(n-1)
We have to find the value of the 47th term in the series.
So, we have the value of n = 47
The equation will become -
[tex]a_{47}[/tex] = 8.7 - 1.4(47-1)
[tex]a_{47}[/tex] = 8.7 - 1.4(46)
[tex]a_{47}[/tex] = 8.7 - 64.4
[tex]a_{47}[/tex] = -55.7
Thus, the value of the 47th term of the given arithmetic sequence is -55.7
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Jude types 1,281 characters in 7 minutes. What is her typing rate in characters per minute?
Answer:
183 charters
7 goes into 12 1 time so 12-7=5
bring down the 8 so 7x8=56 so 58-56=2
being down the 1 and you have 21. 7 goes into 21 three times.
Answer:
183 characters per minute
Step-by-step explanation:
1281 divided by 7
Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef. The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese. How many different possible sandwiches does that leave Kim?
5
6
8
12
_______________________________________________________
Show your work!
The number of possible sandwiches does is 6.
What is combination ?
In arithmetic, a combination is a way of choosing gadgets from a set where the order of selection does no longer count. suppose we've got a hard and fast of 3 numbers P, Q and R. Then in what number of methods we can select two numbers from every set, is described via combination.
Given ,
Kim will choose 1 type of meat and 1 type of cheese for her sandwich. The meats offered are ham, turkey, or roast beef.
The cheeses offered are American, Swiss, cheddar, or provolone. Kim dislikes roast beef and Swiss cheese.
factorial of n! = n*(n-1) !
The number of possible sandwiches does = 3!
=3*2 = 6.
Therefore, The number of possible sandwiches does is 6.
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A form of nickel has a half life of 91 years. How much of a 90 gram sample is left after 290 years? 
The amount of the 90gram-sample that will remain after 290 years is 9.88 grams
How to determine the number of half-lives?We'll begin by obtaining the number of half lives that has elapsed. This can be obtained as follow:
Step1
Half-life (t½) = 91yearsTime (t) = 290 yearsNumber of half-lives (n) =?n = t / t½
n = 290 / 91
n = 3.1868
Step 2
determine the amount remaining:
Original amount (N₀) = 90 gramsNumber of half-lives (n) = 3.1868Amount remaining (N) =?The amount remain can be obtained as follow:
N = N₀ / 2^n
N = 90 / 2^3.1868
=9.88
N=9.88 grams
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Use your formula 1/2(a+b)h, to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
The height of the trapezoid that has an area of 24 cubic cm is: 3 cm.
How to Calculate the Height of a Trapezoid?The formula for the area of a trapezoid is 1/2(a+b)h, where a and b are the lengths of the bases and h is the height.
Given that the area of the trapezoid is 24 cubic centimeters and the base lengths are 9 cm and 7 cm, we can plug in those values to the formula and solve for h:
24 = 1/2(9+7)h
24 = 1/2(16)h
24 = 8h
To find h, we divide both sides of the equation by 8:
h = 24/8
h = 3
So the height of the trapezoid is 3 cm.
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the value of philipine peso is less than the value of one US dollar
The mathematical statement that accurately depicts how value of philipine peso is less than the value of one US dollar is: p < d. The Option C is correct.
What is Less than Symbol all about?The Less-than symbol is used to compare two values where the first number is less than the second number, for example, in ascending order. The opening angle bracket is approximated by the less than symbol.
"<" is the symbol used to represent the less than inequality. The less than sign is a universally recognized math symbol composed of two equal measure strokes intersecting in an acute angle at the left.
For example: If given 2< 5: 2 is less than 5
Missing options "Which of the following mathematical statement represents the given situation? a. d = p b. p>d c. p <d d. none of these
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a bag contains 8 red marbles, 8 white marbles, and 10 blue marbles. you draw 5 marbles out at random, without replacement. what is the probability that all the marbles are red?
The probability of all 5 marbles being red is (8/26) x (7/25) x (6/24) x (5/23) x (4/22) = 0.000766.
This can also be written as P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22. This probability is very small, as the chances of randomly selecting only red marbles from the bag is low.
This calculation is based on the formula for combinations, which states that the probability of selecting r items from a group of n items is nCr x Pr, where nCr is the number of combinations of selecting r items from n items and Pr is the probability of selecting a specific item. In this case, n = 26 and r = 5, so the number of combinations of selecting 5 items from 26 items is 26C5. This is equal to 8x7x6x5x4/5x4x3x2x1, or 8x7x6x5x4/120. The probability of selecting a specific item is 1/26, as there are 26 items in the bag. Therefore, P(RRRRR) = 8/26 x 7/25 x 6/24 x 5/23 x 4/22.
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A movie club surveyed 200 high school students. The students were asked how often they go to the movies and whether they prefer action movies or dramas. Their responses are summarized in the following table
The percentage of students that prefer drama is 52%.
The percentage of students that go to the movies three times or more is 34%.
What are the percentages?
Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.
The percentage of students that prefer drama = (total number of students that prefer drama / total number of students surveyed) x 100
= [(70 + 34) / 200] x 100
= (104 / 200) x 100 = 52%
The percentage of students that go to the movies three times or more = (total number of students that go to the movies three times or more / total number of students surveyed) x 100
[(34 + 34) / 200] x 100
(68 / 200) x 100 = 34%
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Students will present a play in an
auditorium that has 550 seats. Each
student performing in the play must
sell 12 tickets to the performance.
The remaining 370 tickets will be
sold by other students in the school.
Which equation could be used
to
find x, the number of students
performing in the play?
Answer:
550 - 12x = 370