Answer: People attended the two performances are 683
What makes something common?
A whole number that is a factor of two or more numbers is referred to as a common factor. Example: The common factors of 30 and 20 are 2, 5, and 10. A factor that everyone whole numbers share is 1, or 1.
What is a greatest common factor?
It is the biggest number that two numbers are divisible by.
For example, if you did 12 and 24
The factors of 12 are:
1, 2, 3, 4, 6, 12
The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24
Their greatest common factor would be 12 since, it is the greatest number that each number can be divisible by.
Step-by-step explanation:
Number of people attend Friday event = 728
Number of people attend Saturday event = 728 - 45 = 683
Hence the answer is 683
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a-2b + c = -6
a = -5c-12
-a + 6b+ 4c = 3
a - 2b + c = -6 (1)
a = -5c - 12 (2)
-a + 6b + 4c = 3 (3)
Putting (2) into (1) & (3) gives
(-5c -12) - 2b + c = -6 (5)
-(-5c - 12) + 6b +4c =3 (6)
Neatening it up gives
-2b - 4c = 6 (7)
6b + 9c = -9 (8)
Using simulataenous equations, we want to cancel out either b or c. b in this case is easier. Multiplying (7) makes that possible
(7) * 3
gives
-6b - 12c = 18 (9)
Adding (8) & (9) gives
-3c = 9
c = -3
Now we know c we can use that to calculate b in one of the previous equations.
Using (7)
-2b -4(-3) = 6
-2b = -6
b = 3
Now, b & c are known, we can use these in any equation with a to get the final unknown.
Using (1)
a - 2(3) + (-3) = -6
a = 3
Plugging a,b&c back into each (1) (2) & (3) to check you get the right answer is also a good sanity check that you've not made any mistakes in your previous working!
6x²-5xy-4y factoring
Answer:
(3x-4y) (2x+1)
two mountain peaks are known to be 25 kilometers apart. a person located at a vista point such that a right angle is spanned when he looks from one peak to the other is told that the distances from the vista point to each peak differ by 5 kilometers. how far is the vista point from each mountain peak?
Pythagoras was a philosopher and a teacher. Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides: a2+b2=c2.
Explain about the Right angle?
An angle with a measure of exactly 90 degrees (or /2) is referred to as a right angle. The proper angles are frequently demonstrated in everyday life. For instance, the edges of the cardboard or the corner of a book.
The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A point is surrounded by four right angles. According to our definition of a degree, a "complete turn" around a point is 360°, making each right angle one-fourth of that, or 90°.
One mountain it should be 30 Kilometers and other mountain should be 40 kilometers
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{Question 11} Please help, need these by today! Thanks so much :) {Click on picture}
Answer:
-1.25 or -5/4
Step-by-step explanation:
I think it would be this because I remember that the slope formula is y2-y1/x2-x1 so using that you get 8-3/9-13 which simplifies to -5/4 which then turns into -1.25 when fully simplified. I think this is right.
Can someone explain this to me please on how I get it?
Answer: I think its the second one
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
2.5 x 7 = 17.5
10^-10 x 10^-6 = 10^(-10-6) = 10^-16
17.5 x 10^-16
1.75 x 10^-16 x 10
1.75 x 10^(-16+1)
1.75 x 10^-15
8/15 times 3/10 equals?
When earning compound interest on money you invest, which statement is true?
A.
As time goes on and your bank account grows, you earn more interest.
B.
As time goes on and your bank account grows, you earn less interest.
C.
As time goes on and your bank account grows, you earn the same amount of interest.
D.
As time goes on and your bank account grows, you stop earning interest.
Answer:
Step-by-step explanation:
Effective annual interest rate is an investment’s annual rate
of interest when compounding occurs more than a year.
The effective interest rate is calculated as if compounded
annually. The effective rate is calculated in following way…..
r = effective annual rate
i = nominal rate
n = number of periods
= (1+i/n)^n -1
For example, a nominal interest rate 6% compounded
monthly is equivalent to an effective interest rate of 6.17%
So, option A is the correct answer.
HELP! Xochitl went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. Determine the price of each bag of popcorn and the price of each drink.
Each bag of popcorn costs $__ and each drink costs $__.
The cost of bag of popcorn is $7.5 and that of one drink is $5.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.
Assume that the cost of one popcorn bag is $[x] and one drink is $[y]. Then we can write -
6x + 4y = 65
9x + 8y = 107.5
Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.
Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.
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All of the quadrilaterals in the shape below are squares . Find the area of the shaded region
The side length of 6 units for the intermediate large square and 4 units for the smallest square, give the area of the shaded region as 32 square unites.
What is the area of a shape?The area of a shape or figure is the two dimensional space occupied by the boundary line of the shape.
Please find attached a possible drawing of the figure in the question created with MS Word
From the drawing, we have;
Side length of the ;large square containing the other squares = 6 + 4 = 10
Area of the largest square, A₁ = 10 × 10 = 100
Side length of the second largest square = 6
Area of the second largest square, A₂ = 6 × 6 = 36
Side length of the two small squares = 4
Area of the two small squares, A₃ = 4 × 4 = 16
Therefore;
Area of the shaded region = A₁ - A₂ - 2·A₃
Which gives;
Area of the shaded region = 100 - 36 - 2×16 = 32
The area of the shaded region is 32
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In exercises 5 and 6, find m∠1, m∠2, and m∠3
5)
1= 102
2= 102
3= 78
ask any questions in the comments below if needed:)
Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha’s songs were played on 2 more commercials than movies, and her total earnings on the royalties from all the commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha’s songs were played. Define the variables that you use to write the system
The equations that Nakeishia can use to determine the number of commercials and the number of movies on which Nakeisha’s songs were played include:
30m + 110(m + 2) = 760
How to illustrate the information?Let the movies be represented by m
Since Nakeisha’s songs were played on 2 more commercials than movies, this will be m + 2.
Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. This will be:
30m + 110(m + 2) = 760
This represents the equation.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
The slope is [tex]\frac{-3}{5}[/tex]
Step-by-step explanation:
You know the slope is negative if you start on the left side and move right along the line. You are moving down hill. Down hill is a negative slope.
Kory has a collection of 314 stickers organized in a sticker book. There are 7 stickers on each page. How many pages of the album have exactly 7 stickers?
Rewrite the expression as the sine, cosine, or tangent of a double-angle. Then find the exact value of the trigonometric expression without the use of a calculator.
2cos² (-22.5 °)-1
Use the appropriate double-angle formula to rewrite the given expression as the sine, cosine, or tangent of the corresponding double-angle.
2cos² (-22.5 °)-1= _____
(Do not evaluate. Type your answer in degrees. Do not include the degree symbol in your answer)
Find the exact value of the trigonometric expression without the use of a calculator.
2cos²(-22.5 °)-1= _____
(Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)
The value of 2cos² (-22.5°)-1 is 1/√2.
What is double angle in trigonometry?In trigonometry, double angle identities or double angle trig identities are a set of trigonometric identities for angles of form 2θ. There are three double angle identities for each of sine, cosine and tangent ratios.
Given that, 2cos² (-22.5°)-1
2cos²x -1 = cos2x
2cos² (-22.5°)-1 = cos2(-22.5°)
cos(-45°)
∵ cos(-x) = cosx
∴ cos(-45°) = cos(45°)
cos(45°) = 1/√2
Hence, The value of 2cos² (-22.5°)-1 is 1/√2.
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A voter polling research group determined that 30% of the voters in a county would vote for the
democratic candidate with a +4% margin of error. If they anticipate only 12,000 people will turn
out to vote in this election, which would represent the lowest possible number of voters for the
democratic candidate.
The lowest possible number of voters for the democratic candidate are,
3120 to 4080.
What is election?
A populace selects a person or people to hold public office through a formal group decision-making process called an election. Since the 17th century, elections have been the primary means by which modern representative democracies have been governed.
Given: A voter polling research group determined that 30% of the voters in a county would vote for the democratic candidate with a +4% margin of error.
They anticipate only 12,000 people will turn out to vote in this election.
If 12000 voters participate in the election, then 30% of them are, 3600.
Now we must add and subtract 4% of the total voters to 3600 people.
4% of the total voters = 480.
So,
3600 + 480 = 4080
3600 - 480 = 3120
Therefore, 3120 to 4080 voters represent the lowest possible number of voters for the democratic candidate.
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The 3-rd term of the arithmetic progression is equal to 1. The 10-th term of it is three times as much as
the 6-th term. Find the first term and the common difference. (Hint: Use the formula for the n-th term
of the progression and write what is given in the problem using this formula.)
Answer:
First term: 3
Common difference: -1
Step-by-step explanation:
3rd term: 1
6th term: x
10th term: 3x
Formula for the nth term using the common difference d and the first term a1:
an = a1 + (n - 1)d
Third term: a3 = a1 + (3 - 1)d = a1 + 2d = 1
6th term: a6 = a1 + (6 - 1)d = a1 + 5d = x
10th term: a10 = a1 + (10 - 1)d = a1 + 9d = 3x
a1 + 2d = 1 Eq. 1
a1 + 5d = x Eq. 2
a1 + 9d = 3x Eq. 3
Eq. 2 - Eq. 1
3d = x - 1
Eq. 3 - Eq. 2
4d = 2x
x = 2d
3d = x - 1
Substitute 2d for x.
3d = 2d - 1
d = -1
a1 + 2d = 1
a1 + 2(-1) = 1
a1 = 3
Check:
Here are the first 10 terms:
3, 2, 1, 0, -1, -2, -3, -4, -5, -6
The third term is 1. Correct
The tenth term (-6) is 3 times the 6th term (-2). Correct
Answer:
First term: 3
Common difference: -1
How many solutions exist for the system of equations below?
[3x+y=18
3x+y=16
Answer:2
Step-by-step explanation:
What is a mathematical equation
There are several methods to formulate a mathematical equation. A model, in its simplest basic form, is a quantitative declaration that two major theoretical findings are comparable.
What is the mathematical equation?A mathematical equation can be defined in a variety of ways. In its most basic form, a model is a mathematical assertion that indicates that two theoretical results are equal. 3x + 5 = 14, for example, is an equation inside which 3x + 5 and 14 are two formulas separated by an 'equal' sign. In mathematics, the most fundamental and elementary algebraic equations are comprised of one or more parameters.
Type of the mathematical equations are as follows:
Linear equationQuadratic equationCubic equationPolynomial equationRational equationA math statement is not the same as a maths problem. Between two arithmetic statements, a solution will always employ the equivalent (=) symbol.
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Answer: Equations can vary!
Step-by-step explanation: 1. Equations can be as simple as a math sentence with always an equal sign, make sure it balances, for example, 1+1=2
2. Equations can be complicated sometimes, with variables, but still you have to BALANCE both sides EQUALLY. One question is: 1+x=3
It seems simple and it is, and yeah you've actually done lots of equations throughout your life. Ever heard of algebra, it consists of equations, have you ever seen this 1+?=3? That's an equation with a variable that is represented as, or sometimes a box. You might take a look and say easy. I know, but the traditional steps are to take one on both sides first, but never forget what you do on one side you ALWAYS have to do to the other side. This is an easy equation question, there are going to be much more complex ones in the future.
Consider the quadratic equation: x^2-8x=9. What would this equation look like after completing the square on the left side?
The left-hand side of the equation become (____)^2 (enter a binomial in the box)
The right-hand side of the equation becomes ___ (enter a number)
The left-hand side of the equation becomes (x - 4)² while the right side of the equation is 25
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a quadratic equation is given by:
0 = Ax² + Bx + C
Where A, B and C are constants.
Given the quadratic equation:
x² - 8x = 9
To solve the quadratic equation using the completing square method, add to both sides the square of half the coefficient of x, hence:
x² - 8x + (-4)² = 9 + (-4)²
(x - 4)² = 9 + 16
(x - 4)² = 25
The solution to the equation is (x - 4)² = 25
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[(1 1/4−3/4)⋅(−2/3)^3]÷(−4)
Which statements are true about FIve-sixths and Seven-tenths? Check all that apply.
40 is a common multiple of 6 and 10
False:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
Multiples of 10: 10, 20, 30, 40...
(2) The fraction 5/6 is greater than 7/10
True:
Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.
(5/6) x (5/5) = 25/30
(7/10) x (3/3) = 21/30
25/30 > 21/30 ∴ 5/6 is greater than 7/10
(3) The fraction 42/60 is an equivalent form of 7/10
True:
Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.
(7/10) x (6/6) = 42/10
42/10 = 42/10 ∴ 7/10 = 42/10
(4) The only value that can be used as a common denominator is 60.
False:
While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.
(5) Ten is a multiple of 6.
False:
Multiples of 6: 6, 12, 18, 24, 30...
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A coin and a die are tossed simultaneously.
a) What is the probability that the result is tails and an odd number?
b) What is the probability of getting tails or an odd number?
c) What are the probabilities of getting tails, or of getting an odd number, but not both simultaneously?
The probabilities are given as follows:
a) Tails and odd number: 1/4.
b) Tails or odd number: 3/4.
c) Tails or odd number, but not simultaneously: 1/2.
How to obtain the probabilities?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For each event, the probabilities are given as follows:
Tails: 1/2.Odd number on the dice: 1/2.Hence the probability of both events is of:
p = 1/2 x 1/2 = 1/4.
The or probability is composed as follows:
Tails and odd: 1/4.Tails and even: 1/2 x 1/2 = 1/4.Heads and off: 1/2 x 1/2 = 1/4.Hence the ´probability is of:
3 x 1/4 = 3/4.
Removing the simultaneous event, the probability is of:
3/4 - 1/4 = 2/4 = 1/2.
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Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 257 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball.
a. What is the distribution of X? X ~ N(Correct,Correct)
b. Find the probability that a randomly hit fly ball travels less than 284 feet. Round to 4 decimal places.
c. Find the 70th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet
Hint:
a. distribution of X is (257,45)
b. Probability that a randomly hit fly ball travels less than 284 feet is 0.2257
c. The 70th percentile for the distribution of distance of fly balls is 290 feet.
What do you mean by normal distribution?
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.
It is given that we have a normal distribution with mean of 257 feet and standard deviation of 45 feet.
X be the distance in feet for a fly ball.
a. As mean of the normal distribution is 257 and standard deviation is 45 feet
Therefore, distribution of X is (257,45)
b. Probability that a randomly hit fly ball travels less than 284 feet,
P(X < 284) =
The z-score can be calculated as
z = (x - μ)/σ = (284-257)/45 = 27/45 = 0.6
So, the equivalent z-score form can be given as:
P(X < 284) = P(Z < 0.6) = 0.2257
c. The 70th percentile of the distribution of fly balls is given by a raw score such that:
P(X < x)=70%⇒ x = ?
Using formula , z = (x - μ)/σ ⇒ x = zσ + μ
P(Z < z) = 0.7000
Now, we can use the cumulative standard normal distribution table:
z = 0.7000 + 0.04 = 0.74
Finally, the required random variable can be computed as:
x = zσ + μ = 0.74 × 45 + 257 = 33.3 + 257 = 290.3
That means P(X < 290.3) feet =70%
Therefore, the 70th percentile of the distribution of fly balls is approximately 290 feet
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.
19.
The driver rested after traveling 440
miles in 8 hours. If he traveled at the same
rate the next day, how many miles could he
go in 12 hours?
Answer:
∴ He can travel 660 miles in 12 hours on the next day.
Step-by-step explanation:
Since the rate of travelling is equal on both days,
8 hours = 440 miles travelled
2 hours = 110 miles travelled
∴ 12 hours = 660 miles travelled
What is the slope of the line below?
Answer:
The slope of the line is 1/2.
15,246
In the number above, which digit has the
greatest value?
Explain.
In the given number, the digit that has the greatest value is 1.
We are given a number. The number is a natural number. Natural numbers are the numbers used in mathematics for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering. The number contains five digits. We need to find the digit that has the greatest value. We know that as we go left, the place value of the digit increases by a factor of 10. So, the place value of the number is maximum for the digit that is present at the leftmost position in a number.
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In exercises 3 and 4, find the value of x.
3)
x= 16
4)
x= 51
please ask any questions in the comments below if needed
Answer: 3. 16=X 4. X=51
Step-by-step explanation:
Okay so for number 3, both angles are the same because of the parallel lines, so you can have the angles be equal to each other. Then just do the math. Giving you 16 as the answer
For 4 the angles added up together equal 180 because of the parallel lines. So you have to make them add up and then equal to 180, at the ending the answer is 51.
please help asap
math question
The exponential function of the given graph is y = 4ˣ
Exponential function:
the general form of the exponential function is written as,
y = aˣ
Where
a > 0 and a ≠ 1.
Here a is called the base and x is called the exponent.
Given,
Here we have the graph and the point (2,16)
Now, we have to find the exponential function form this graph and point.
We already know that the general form of the exponential function is
y = aˣ
Here we have point (2,16), now we have to apply this point value on the general form in order to find the value of a,
So, when we apply the point values, then we get,
16 = a²
Now, move the power value to the other side, then we get,
a = √16
a = 4
Therefore, the exponential function of the given graph is,
y = 4ˣ
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PLEASE HELP ME THIS IS OVER DO
The graph of a relation that is a function is the last option that is in the attachment below.
How to Determine a Relation that is a Function?A graph that represents a relation that is a function is a graph whose x-values each have exactly one corresponding y-value. That is to say, no two y-values correspond to one x-value in the graph of a relation that represents a function.
All of the graphs represents relations that have different y-values that correspond to an x-value except the graph at the bottom far right, whose diagram is attached below.
The graph attached below has exactly one y-value that corresponds to each x-value on the graph. Therefore, the relation is a function.
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Raquel simplified the first step of the expression (5+6)+18➡️16+18
The mistake that Raquel made in simplifying the expression is given as follows:
The square is applied only to the number 3, not to the sum of 5 and 3.
Hence the correct simplified version is:
(5 + 3²) + 18 = (5 + 9) + 18 = 32.
How to simplify the expression?The expression for this problem is given as follows:
(5 + 3²) + 18.
The parenthesis takes precedence, hence the first operation to be solved is of:
5 + 3².
Then the square is the operation that takes precedence, hence the expression is given as follows:
5 + 3² = 5 + 9.
Here is where Raquel's mistake lays, as only the number 3 is squared, the number 5 is not, hence 3 is squared and then added to 5.
Then the correct result of the expression is obtained as follows:
5 + 9 + 18 = 32.
Missing InformationThe problem is given by the image shown at the end of the answer.
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