Since the Top-Notch Middle School had athletes from all the grades playing on a sports team, the ratio 15:73 represents the following: C. The ratio 15:73 represents the ratio of 7th grade football players to total athletes.
How to explain the given ratio?In order to interpret and explain the meaning of the given ratio 15:73, we would first of all determine the total number of athletes from all grades in Top-Notch Middle School as follows;
Total number of athletes, T = 2 + 4 + 7 + 1 + 6 + 5 + 7 + 4 + 4 + 8 + 15 + 10
Total number of athletes, T = 73 athletes.
For the number of Basketball athletes, we have:
Number of Basketball athletes, B = 2 + 4 + 7
Number of Basketball athletes, B = 13 Basketball athletes.
Ratio of B to T = 13:73.
For the number of Baseball athletes, we have:
Number of Baseball athletes, B = 1 + 6 + 5
Number of Baseball athletes, B = 12 Baseball athletes.
Ratio of Ba to T = 12:73.
For the number of Football athletes, we have:
Number of Football athletes, B = 8 + 15 + 10
Number of Football athletes, B = 33 Football athletes.
Ratio of F to T = 33:73.
For the ratio of Football athletes in 7th grade to total number of athletes, we have:
Ratio of F7 to T = 15:73.
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In a game of chance, two fair dice are thrown. If the sum of the two dice is seven, you get paid out $90. If the sum of two dice is a six or an eight, you must pay $90(No money is exchanged for all other sums). How much money would you expect to win or lose, on average, per game?
You are expected to lose $ 10 on an average per game
How to determine the amount of money you would winTotal outcome = 36Event of sum of 7 = 6Amount per sum of 7 = $ 90Amount won per game =?Probability of sum of 7 = 6 / 36
Probability of sum of 7 = 1 / 6
Amount won per game = (1 / 6) × 90
Amount won per game = $ 15
How to determine the amount of money you would loseTotal outcome = 36Event of sum of 6 = 5Event of sum of 8 = 5Event of sum of 6 or 8 = 5 + 5 = 10Amount per sum 6 or 8 = $ 90Amount lose per game =?Probability of sum 6 or 8 = 10 / 36
Probability of sum 6 or 8 = 5 / 18
Amount lose per game = (5 / 18) × 90
Amount lose per game = $ 25
How to determine your expect earning on an avarge per gameAmount won per game = $ 15Amount lose per game = $ 25Expected earnings =?Expected earnings = Amount won per game - Amount lose per game
Expected earnings = 15 - 25
Expected earnings = -$ 10
Thus, you are expected to lose $ 10 on an average per game
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Borrwed 25000 at ir10.5%
for ten years accured interest
Find the value of t for which (4,6,3, t) is a linear combination of (1,3,-4,1), (2,8,-5,-1) and (-1,-5,0,2)
The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
How to find a vector as a linear combination of other vectors
In this question we must solve for t such that (4, 6, 3, t) is a linear combination of vectors (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2), which means that non-zero coefficients have to be found by algebraic handling:
(4, 6, 3, t) = α₁ · (1, 3, - 4, 1) + α₂ · (2, 8, - 5, - 1) + α₃ · (- 1, - 5, 0, 2)
Which is equivalent to this system of linear equations:
α₁ + 2 · α₂ - α₃ = 4
3 · α₁ + 8 · α₂ - 5 · α₃ = 6
- 4 · α₁ - 5 · α₂ = 3
α₁ - α₂ + 2 · α₃ - t = 0
Whose solution is (α₁, α₂, α₃, t) = (38, - 31, - 28, 13). The value of t for which (4, 6, 3, t) is a linear combination of (1, 3, - 4, 1), (2, 8, - 5, - 1) and (- 1, - 5, 0, 2) is equal to 13.
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Find the measure of MON
Answer: 77 degrees
mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.
The average amount of electricty consumed by a household in a day is strongly correlated to the average daily temperature for that day. This relationship is given by y=0.503x+3.31 where x is the temperature in F and y is the amount of electricity consumed in kilowatt-hours (kWh).
What does the y-intercept of this function represent?
A. the average amount of electricity consumed for each degree Fahrenheit
B. the average electricity consumption for a daily average temperature of 0 F
C. the minimum amount of electricity consumed
D. the change in temperature for each increase in electricity consumption
The y-intercept of this function represents C. the minimum amount of electricity consumed
How to interpret the y-intercept?The function is given as:
y = 0.503x + 3.31
The y-intercept of a function represents the minimum or the initial value of the function
This means that the y-intercept of this function represents C. the minimum amount of electricity consumed
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Question 4 (Essay Worth 10 points)
(07.03, 07.05 HC)
Use the function f(x) = 2x²-5x+3 to answer the questions.
Part A: Completely factor f(x). (2 points).
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points) HELP ASAP
Part A
[tex]f(x)=(x-1)(2x-3)[/tex]
Part B
[tex](x-1)(2x-3)=0\\\\x=1, \frac{3}{2}[/tex]
So, the x-intercepts are [tex](1,0)[/tex] and [tex]\left(\frac{3}{2}, 0 \right)[/tex]
Part C
As [tex]x \to \infty[/tex], [tex]f(x) \to \infty[/tex] because the leading coefficient is positive.
As [tex]x \to -\infty[/tex], [tex]f(x) \to \infty[/tex] because the degree is even and the leading coefficient is positive.
Part D
Plot the x-intercepts on the graph, and then find the value of [tex]f(x)[/tex] at [tex]x=\frac{5}{4}[/tex] (the midpoint of the two roots) to plot the vertex. Then, draw a curve through these three points that approaches infinity as [tex]x \to \pm \infty[/tex]
3 p2 9 p = 6 Add 6 to both sides to set the right side to o 3 p2 9 p 6=04 Divide everything by 3 p2 3 p 2 =0 ( P 1)(p 2) = 0 P 1 = 0 OR P 2 = 0 P=-1 P= -2
The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
Finding the solution of a quadratic equation
The given equation is:
[tex]3p^2-9p=6[/tex]
This can be re-written as:
[tex]3p^2-9p-6=0[/tex]
Solve for p by factorization
[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]
Equate each of the factors to zero
3p - 6 = 0
3p = 6
p = 6/3
p = 2
p - 1 = 0
p = 1
Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2
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there are 60 minutes in one hour and 60 seconds in one minute. Using this information, explain how you could convert 20 miles per hour to feet per second
The conversion is given as 1, 760 feet per second
How to convert the valueWe need to convert 20miles per hour to feet per second
First, we should convert miles to feet
1 mile = 5280 feet
Then,
20 miles = x
Cross multiply
20 × 5280 = x
x = 105, 600
Per hour = I hour = 60 seconds
To find the conversion, we divided the conversion to feet by that of the time
= 105, 600/60
= 1, 760 feet per second
Thus, the conversion is given as 1, 760 feet per second
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Estimate the difference of the decimals below by rounding to the nearest
whole number.
61.621
7.173
Answer:
55
Step-by-step explanation:
61.621 rounded to the nearest whole number is 62. We know this by looking at the whole number "61" and rounding its last digit by the digit to the right of it, depending if its <5 or >5. In this case, the right ones digit is "6", being greater than 5 means we can round 61.621 to 62.
The same applies to 7.173, given that "1" is less than 5, we don't round down (because we are rounding up), instead we replace remaining digits with 0, leaving us with 7.
To find the difference means to subtract;
62-7 = 55.
For a population with a mean of μ = 72 and a standard deviation of σ = 8, find the z-score corresponding to the sample mean M= 80 and sample size n = 22 scores.
The z score corresponding to the sample is -6.25
z-score of a populationThe formula for calculating the z-score is expressed as
z = x- μ/σ
Given the following parameters
x = 22 (sample size)
Mean μ = 72
standard deviation σ = 8
Substitute
z = 22-72/8
z = -50/8
z = -6.25
Hence the z score corresponding to the sample is -6.25
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Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′. (-1, 3)
B′
(-2, 2)
C′
(-2, 1)
D′
(-1, 1)
Answer:Rules for rotating points about the origin
1. The point (a,b) rotated 90° counterclockwise about the origin
becomes (-b,a).
A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)
A (a,b)-----------------A′ (-b,a)=(-1, 3)----------->A( 3,1)
B (a,b)-----------------B′ (-b,a)=(-2, 2)----------->B( 2,2)
C (a,b)-----------------C′ (-b,a)=(-2, 1)----------->C( 1,2)
D (a,b)-----------------D′ (-b,a)=(-1, 1)----------->D( 1,1)
Step-by-step explanation:
Which statement correctly describes the diagram?
On a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
1. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
2. Triangle B is a reflection of triangle A across the y-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
3. Triangle B is a reflection of triangle A across the y-axis. Triangle C is not a reflection of triangle A.
4. Triangle B is a reflection of triangle A across the x-axis. Triangle C is a reflection of triangle A across the line y = x + 3.
The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.
Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.
From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.
Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".
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Answer:
A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..
Step-by-step explanation:
goodluck
Indicate the equation of the given line in standard form. Show all of your work for full credit.
The line containing the diagonal, BD, of a square whose vertices are A(-3, 3), B(3, 3), C(3, -3), and D(-3, -3). Find two equations, one for each diagonal.
The linear equations are given as follows:
For diagonal AC: [tex]x + y = 0, -3 \leq x \leq 3[/tex].For diagonal BD: [tex]x - y = 0, -3 \leq x \leq 3[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For diagonal AC, the line contains points (-3,3) and (3,-3), hence the line is:
y = -x.
In standard form:
[tex]x + y = 0, -3 \leq x \leq 3[/tex].
For diagonal BD, the line contains points (3,3) and (-3,-3), hence the line is:
y = x.
In standard form:
[tex]x - y = 0, -3 \leq x \leq 3[/tex].
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IfX+9=11,
then the value of 7 X = ......
The answer is 14.
First, we need to find X using the first statement.
X + 9 = 11X = 11 - 9X = 2Now, we have to substitute this in the required expression.
7X7(2)14A group of neighbors is holding an end of summer block party. They buy p packs of hot
dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party.
Write an equation to describe this situation.
How many packs of hot dogs did the neighbors buy?
Answer:
7 packs of hots dogs if they had 56 for the party 8 divided by 56 is 7
The equation is 8p=56. Hence p=7 and they bought 7 packs of hot dogs. Hope it helps : )
The graph of a line passes through the two points below
(2,-4);(-3,1)
Which of these can be used to determine the slope of the line
The expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
What are slopes?The slope of a line is the gradient or the average rate of change of the line or a line equation
Note that linear equations are equations that have constant average rates of change, slope or gradient
How to determine the slopes?The two points are given as
(2,-4);(-3,1)
The slope of a line is calculated using
m = (y2 - y1)/(x2 - x1)
Substitute the coordinates of the points in the above equation
m = (1 + 4)/(-3 - 2)
Evaluate the numerator
m = 5/(-3 - 2)
Evaluate the denominator
m = 5/-5
Rewrite the quotient as
m = -5/5
Evaluate the quotient
m = -1
Hence, the expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
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someone please help me with this
Answer:
x = 60 degrees
Step-by-step explanation:
1. We know that a triangle has a total angle of 180. If we look at the image closely, triangle GEH can be found, and since we know two angles, which are 40 and 80, we can find the other angle. 180 - (40+80) = 60. Angle GEH is 60 degrees.
2. If angle GEH is 60 degrees, angle EFD will also be 60 degrees, since they have the same angle side. To prove this, we can use alternate interior angles. This means that if a line crosses two parallel lines, the inner angles made have the same size.
3. Since angle EFD is x, we can find that x is equal to 60 degrees.
The cost price was $10000 she made a down payment of 2500 and agreed to pay the balance in 24 monthly installments of $350 how much did Jen pay for microwave?
Answer:
in total she spent 10900
Step-by-step explanation:
We know she made a down payment of 2500 dollars and she agreed to pay the balance in 24 monthly installments of 350 dollars. Thus we can do simple multiplying of 24 x 350 which gives us 8400. We also need to add in her down payment which is 2500 so in total we got 10900
what is the inverse of the function f(x)=x/5-2
Answer:
[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]
Step-by-step explanation:
Given function:[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]
Put f(x) = y
[tex]\displaystyle y=\frac{x}{5} -2[/tex]
Swap x and y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Now, solve for y
[tex]\displaystyle x = \frac{y}{5} -2[/tex]
Add 2 to both sides
[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]
Multiply 5 to both sides
[tex]5(x+2)=y[/tex]
Distribute
[tex]5x + 10 =y[/tex]
Put y = f⁻¹(x)
[tex]\boxed{f^{-1}(x)=5x+10}[/tex]
[tex]\rule[225]{225}{2}[/tex]
25 POINTS, QUICKLY PLEASE!
1. Which system is represented in the graph?
A. y > x2 + 4x – 5, y > x + 5
B. y < x2 + 4x – 5, y < x + 5
C. y ≥ x2 + 4x – 5, y ≤ x + 5
D. y > x2 + 4x – 5, y < x + 5
2. Which type of function describes f(x)?
A. Exponential
B. Logarithmic
C. Rational
D. Polynomial
Answer:
1) y > x² + 4x - 5, y > x + 5
2) Rational
Step-by-step explanation:
For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:
For a line, if the shade is above it then the value of y will be greater or equal to:
Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"
Therefore, the inequality for parabola is y > x² + 4x - 5
For a line, it does not have solid graph so the inequality is ">"
Therefore, the inequality for line is y > x + 5
-----------
The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.
That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.
2x-3/x divided 7/x^2
Answer:
2x-3/7x
Step-by-step explanation:
1. There are 50 contestants signed up for a TV show. There are 36 more female contestants than male contestants. How many female contestants have signed up to compete? Show your solution and explain how you plan to explain this to your students.
Considering the definition of an equation and the way to solve it, 43 female contestants have signed up to compete.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Amount of females contestantsBeing "m" the number of male contestants, and knowing that:
There are 50 contestants signed up for a TV show.There are 36 more female contestants than male contestants.the equation in this case is:
m + (m+36) = 50
Solving:
m + m = 50 - 36
2m= 14
m= 14 ÷ 2
m= 7
Since there are 36 more female contestants than male contestants, then m +36= 7 + 36= 43
Finally, 43 female contestants have signed up to compete.
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Solve the proportion
12
8
=
7.5
x
Answer:
9.8 is the final anwser
Step-by-step explanation so easy
A ______ function is a specific type of function that represents the relationship between two variables, usually x and y. The graph of this function is a line.
the answer choices are
dependent
independent
parallel
slope
perpendicular
rate
scale
y
change
linear
A music store sells music equipment at a 35%
markup. It a piece of equipment costs $150.00
what will the selling price be? I
The selling price of an equipment costing $150.00 with 35% markup is $202.50
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Given that the mark up is 35%, hence:
Markup = [(selling price - cost price)/cost price] * 100%
Substituting:
$202.50
Selling price = $202.50
The selling price of an equipment costing $150.00 with 35% markup is $202.50
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Choose the correct product of (6x - 2)(6 x + 2).
The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
How to determine the product?The expression is given as:
(6x - 2)(6 x + 2).
The above expression is a difference of two squares.
And this is represented as
(a - b)(a + b)= a^2 - b^2
So, we have
(6x - 2)(6 x + 2) = (6x)^2 - 2^2
Evaluate
(6x - 2)(6 x + 2) = 36x^2 - 4
Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
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The average heart rate of an adult human is 72 beats per minute. For an adult elephant, the average heart rate is 35 beats per minute.
A. Whose heart beats more times in one hour
B. Whose heart makes 1,000,000 beats in less time
Answer:
A. the adult human
B. the adult human
Step-by-step explanation:
A. There are 60 minutes in an hour, and the human's heart beats 72 bpm (beats per minute). If you multiply 60 by 72, you get 4,320 bpm. If you multiply 60 by 35, you only get 2,100 bpm.
B. If you use the same logic that 72 is greater than 35, than you can assume that the human hear makes 1,000,000 beats in less time. However, if you want to do the math, then simply divide 1,000,000 by 72. Then, divide 1,000,000 by 35. Whichever has the smaller number is the one that can make more heart beats in a faster time.
Instructions: Identify the vertices of the feasible region for the given linear programming constraints.
Optimization Equation: z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Fill in the vertices of the feasible region:
(0, )
(-3, )
(3, )
The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
How to identify the vertices of the feasible region for the given linear programming constraints?The optimization equation is given as
z=−3x+5y
The constraints are given as:
x+y≥−2
3x−y≤2
x−y≥−4
Next, we plot the constraints on a graph and determine the points of intersections
See attachment for the graph
From the attached graph, the points of intersections are
(-3, 1), (3, 7) and (0, -2)
So, we have:
(0, -2)
(-3, 1)
(3, 7)
Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)
So, the complete parameters are:
Optimization Equation:
z=−3x+5y
Constraints:
x+y≥−2
3x−y≤2
x−y≥−4
Vertices of the feasible region
(0, -2)
(-3, 1)
(3, 7)
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The equation of line / is y=3x/a +5, where a is a positive constant. If the value of a in this equation is doubled, then the resulting equation will represent a line whose slope is how many times the slope of line / ?
The resulting equation will represent a line whose slope is 1/2 times the slope of the line
How to determine the slope of the new line?The equation of the line is given as:
y = 3x/a + 5
The constant a is a positive constant.
So, when the value of a in the equation is doubled, we have:
y = 3x/2a + 5
A linear equation is represented as
y = mx + b
Where m represents the slope.
So, we have:
m1 = 3/a
m2 = 3/2a
Substitute m1 = 3/a in m2 = 3/2a
m2 = 1/2 * m1
Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line
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What is the ratio between 40,000 and 200?
The ratio between 40,000 and 200 is 200 : 1
How to determine the ratio?The numbers are given as:
40,000 and 200
Express as ratio
Ratio = 40000 : 200
Divide each number by 200
Ratio = 200 : 1
Hence, the ratio between 40,000 and 200 is 200 : 1
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