Per year price drop is -41.50$
The cost of an MP3 player in the year 2003 is = $ 499
The cost of an MP3 player in the year 2009 is = $ 249.99
The price drop per year will be –
We need to subtract the base year price from that of the current year price and divide that by the difference between the base year and the current year
The year that serves as the standard against which subsequent values are measured is referred to as the base year.
The term "current year" refers to the fiscal year that has already begun but has not yet completed its cycle.
So,
(499-249.99) / (2003-2009)
249.01 / -6 = -41.50 $
Hence per year price drop is -41.50$
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PROOF Write the specified type of proof. two-column proof
Given: RSTUV is a pentagon.
Prove: m ∠ S+m \VS T U+m∠ T U V +m ∠ V+m ∠ V R S=540
According to the given data the specified type of proof. two-column proof are:
m∠ S + m∠ 1 + m∠ 2 + m ∠3 + m ∠4 + m∠ 7 + m∠ 6 + m∠ V + m∠ 5 = 540 (Add. Prop.) m ∠S + m ∠STU + m ∠TUV + m∠ V + m∠ VRS = 540 (Subst.)What exactly is two-column proof?A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned in the right column.
What exactly is proof geometry?Geometric proofs are assertions that demonstrate the truth of a mathematical notion. Proof must comprise numerous phases in order to be proven true. These steps consist of reasons and declarations. Geometric proofs come in a variety of forms, include two-column proofs, paragraph proofs, and flowchart proofs.
According to the given data:Given: RSTUV is a pentagon.
Prove: m ∠ S+m \VS T U+m∠ T U V +m ∠ V+m ∠ V R S=540
1. RSTUV is a pentagon. (Given)
2. m∠ S + m ∠1 + m ∠2 = 180;
m ∠3 + m ∠4 + m∠ 7 = 180;
m ∠6 + m ∠V + m∠ 5 = 180 ( Sum Thm.)
3. m∠ S + m∠ 1 + m∠ 2 + m ∠3 + m ∠4 + m∠ 7 + m∠ 6 + m∠ V + m∠ 5 = 540 (Add. Prop.)
4. m ∠VRS = m ∠1 + m∠ 4 + m ∠5;
m∠ TUV = m∠ 7 + m ∠6;
m ∠STU = m ∠2 + m∠ 3 ( Addition)
5. m ∠S + m ∠STU + m ∠TUV + m∠ V + m∠ VRS = 540 (Subst.)
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Malika was given a gift card for a coffee shop. Each morning, Malika uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and the original amount of money on the gift card was $45. Make a table of values and then write an equation for A,A, in terms of x,x, representing the amount money remaining on the card after buying xx cups of coffee.
The expression representing the amount remaining will be 45 - 2.50x.
Table of values
At x = 1 Amount = 42.50
At x = 2 Amount = 40.
How to illustrate the information?From the information, Malika uses the card to buy one cup of coffee. Each cup of coffee costs $2.50 and the original amount of money on the gift card was $45.
Therefore, the expression representing the amount remaining will be:
A = 45 - (2.50 × x)
A = 45 - 2.50x
At x = 1 Amount remaining will be:
= 45 - 2.50
= 42.50
At x = 2
A = 45 - 2.50x
A = 45 - 2.50(2)
= 40
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What is an equation of a parabola opening left with vertex (0,0) and focus (-3,0) ?
A parabola is defined as a curve where each point is equidistant from:
fixed point (focus) and
fixed line (director).
The properties of a parabola can be defined as given below:
Rays parallel to the axis of symmetry are reflected straight from the surface to the focal point.
Because the vertex of the parabola is at (0,0) and the focus is at (-3,0).
This means that the parabola axis is the negative x-axis.
The parabola equation is x^2 =4ay and a=3.
So, the parabola equation is x^2 =12y.
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Determine whether y varies directly with x . If so, find the constant of variation.
y=4 x+1
The required value of constant of variation, k does not exist for which x and y vary directly.
What is the constant of proportion?
A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.
Solving for the value of constant of variation
When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion —-- 1
Given relation is y = 4x + 1
On comparing it with equation 1, we get, that y does not vary directly with x
Hence, the required value of constant of variation does not exist.
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A veterinarian recorded a cat’s resting heart rate to be 120 beats over a 45-second time period. Complete the table to find the number of heartbeats in different amounts of time. Then find the constant of proportionality in beats per minute. number of hearveats
Number of Minutes Number of Heartbeats
0.25
0.5
0.75
1
Answer:
1. 0.6 (continues)
2. 1.3 (continues)
3. 2
4. 2.7
The height of a thrown ball is a quadratic function of the time it has been in the air. The graph of the quadratic function is the parabolic path of the ball. The vertex of the graph is (1, 20) and the path of the ball includes the point (0, 4). What is an expression that defines this function? Write the quadratic equation in vertex form and in the form y = ax^2 + bx + c.
An expression that defines this quadratic function is ax² + bx + c = 0.
An expression that defines the quadratic equation in vertex form is equal to y = -16(x - 1)² + 20 and y = -16x² + 32x + 4.
Given the following data:
Vertex, (h, k) = (1, 20).Point (x, y) = (0, 4).What is a quadratic function?A quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. Also, the standard form of a quadratic function is given by;
ax² + bx + c = 0
Mathematically, the standard equation with the vertex for any parabola is given by:
y = a(x - h)² + k.
where:
h and k are the vertex.a is a point.Substituting the given parameters into the formula, we have;
y = a(x - h)² + k.
4 = a(0 - 1)² + 20.
4 = a + 20
a = -20 + 4
a = -16.
Therefore, an expression that defines this quadratic function is equal to ax² + bx + c = 0.
For the quadratic equation in vertex form, we have:
y = -16(x - 1)² + 20.
y = -16(x - 1)(x - 1) + 20.
y = -16(x² - x - x + 1) + 20.
y = -16(x² - 2x + 1) + 20.
y = -16x² + 32x - 16 + 20.
y = -16x² + 32x + 4.
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According to the Handbook for Public Playground Safety, the ratio of the vertical distance to the horizontal distance covered by a slide should not be more than about 4 to 7 . If the horizontal distance allotted in a slide design is 14 feet, approximately how long should the slide be?
The length of the slide should be approx. 16 ft long.
Pythagoras Theorem states that sum of square of two sides of triangle is equal to the square of longest side of the right angle triangle..
From the given figure
we will use ratio to find the vertical distance
given that vertical/horizontal=4/7
[tex]\frac{vertical.distance}{horizontal.distance} =\frac{vertical.distance}{horizontal.distance}[/tex]
[tex]\frac{4}{7} =\frac{v}{14}[/tex]
By cross multiplying we get v=8 feet.
As we can see in the figure that Vertical distance, Horizontal distance and the Slide forms a Right angled Triangle.
Pythagoras Theorem can be used to find the length of the slide.
Applying Pythagoras Theorem in ΔABC
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
given that AB=14 and BC=8
Substituting in the above equation we get
[tex](14)^{2} +8^{2} =AC^{2} \\\\ 196+64=AC^{2} \\ \\ 260=AC^{2}[/tex]
[tex]AC=\sqrt{260}=16.12[/tex]
approx. 16 feet
Therefore , the length of the slide should be approx. 16 ft long.
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дост
IS
8. A patio is rectangular. Its length is 8.39 meters, and its width
is 5.4 meters.
What is the approximate perimeter of the patio? Round your answer to the
nearest whole number.
140
28 m is the approximate perimeter of the rectangle patio.
What is a rectangle, exactly?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.p = 2w + 2l
therefore, p = 8.39 * 2 + 5.4 * 2
p = 16. 78 + 10.8
p = 27.58
perimeter = 28 meters
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The band boosters sell cider and doughnuts at home football games.
Last week they sold 318 cups of cider at $0.75 per cup and 12 dozen
doughnuts at $1.25 per doughnut. What were the total sales?
318* 0.75= $238.5
12*12=144 doughnuts total
144*1.25= $180
238.5+180= $418.50
the total sales were $418.50
Relations, Domains
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
The domain are -3, -1, 1 . The range is -2, 0, 2 .
What is relation and domain?A relation is a rule that relates an element from one set to the other set.The domain is the set of all first elements of the ordered pairs. The range on the other hand is the set of all second elements of the ordered pairs.A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x, y) is in the relation.The range of a relation is the set of the second coordinates from the ordered pairs.Note that both functions and relations are defined as sets of lists. In fact, every function is a relation. However, not every relation is a function. In a function, there cannot be two lists that disagree on only the last element.To know more about Relation visit:
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Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.
Multiply -
60/21 by 7/30
2. Joel needs to solve the equation below.
Which describes the step he should take?
n² = 16
a. Divide both sides by 2
b. Take the square root of both sides
c. Square both sides
d. None of the above
Answer: B
Step-by-step explanation:
Since n is being squared, to get rid of the square you would need to square root it.
which number sentence does the following number line represent?
1 + (-5) = 6
5 + 1 = 6
1 + (-6) = -5
-5 + 6 = 1
The number expression that represents the number line option (C)
1 + (-6) = -5 is correct.
What is a number line?
It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
A number line can be used to add and subtract integers. When adding positive numbers we move to the right and when adding negative numbers we move to the left.
When subtracting positive numbers we move to the left and when subtracting negative numbers we move to the right.
We can frame a number expression using the number line:
1 + (-6) = -5
1 - 6 = -5
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It begins at 1 and moves backward 6 before ending at -5.
The number phrase 1 + (-6) = -5 on the number line represents the (C) choice correctly.
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Find the common difference or ratio.
20, 10,__,2.5,__
At a carnival, the object of a game is to throw a dart at the board and hit region III.
d. What is the probability that it hits region IV?
The probability that it hits region IV is 30%.
Probability:
Probability means the possibility of the particular event.
And it can be calculated as,
P(A) = n(A)/n(S)
Where,
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes
n(S) is the total number of events in the sample space.
Given,
At a carnival, the object of a game is to throw a dart at the board and hit region III.
Here we need to find the probability that it hits region IV.
Consider the board was look like the following figure.
Then based on the given figure,
First, we have to find the total area of the board and the area of the required region.
And then we have to compare it to calculate the Probability.
So, the total area of the board is,
=> total area of the board = (10 + 30)(10 + 15)
=> total area of the board = 1000 in²
Now, the The area of the region IV is
=> Area = (10)(30)
=> Area = 300 in²
Therefore, the probability that it hits region IV is
=> P = 300/1000
=> P = 30/100
=> P = 30%
Therefore, the probability that it hits region IV is 30%.
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An example is a counterexample to a general statement if it makes the statement false. Show that each of the following statements is false by finding a counterexample.
The opposite of each whole number is a whole number.
An example is a counterexample to a general statement if it makes the statement false is given by an example of the opposite of each whole number is not a whole number, it is an integer.
As given,
Given statement:
Opposite of each whole number is a whole number
Consider whole number=2
Opposite of 2 is -2
-2 is not a whole number it is an integer.
Therefore, an example is a counterexample to a general statement if it makes the statement false is given by an example of opposite of each whole number is not a whole number.
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V=1/3πr2(h-1) solve for h with work shown please
Answer:
which mountain is known as Nepal Himal?
Write the expression as a number in scientific notation. quantity 8 times 10 squared end quantity times quantity 3.2 times 10 to the fifth power end quantity all divided by quantity 4 times 10 cubed 7.2 x 107 7.2 x 104 6.4 x 107 6.4 x 104
Scientific notation exists as a method of writing very large or very small numbers. The expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].
What is meant by scientific notation?Utilizing scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
To express exceedingly high numbers in a shorter manner, scientists have created a shorthand. Scientific notation is the name of this technique. The foundation of scientific notation is the base-10 powers. The coefficient is defined as the initial number, 1.23.
Given: (8 ×10²) × (3.2 ×[tex]$$10^5[/tex])/4 × 10³
simplifying the above equation, we get
= 800 × 320000/4000
= 64000
= 6.4 × [tex]$$10^4[/tex]
Therefore, the expression as a number in scientific notation is 6.4 × [tex]$$10^4[/tex].
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Answer:
6.4 x 10^4
Step-by-step explanation:
A wide receiver starts from his 15-yard line on the right hash mark and runs a route that takes him 12 yards to the left and down field for a gain of 17 yards. Write a translation vector to describe the receiver's route.
A translation vector describing the receiver's path < -12, 17 >.
What is termed as translation vector?The distance vectors that almost all atoms in the grouping are translated through just to form another cluster inside the solid are defined by translation vectors.
Tv can be in either Cartesian or internal coordinates. If a Tv is described in Cartesian coordinates, it is directly used. If it is defined in internal coordinates, it is converted to Cartesian coordinates as well as the Cartesian coordinates of atom 1 (real or dummy) are subtracted from it at run time. If atom 1 is at the origin, i.e. (0.0, 0.0, 0.0), then the coordinates defined by Tv are indeed the translation vectors; this simplifies visualizing this same translation vectors using a GUI because a line drawn from atom 1 to Tv would represent this same translation vector.Now, as per the stated question;
The horizontal (lateral, x) change is represented by the number 12. This same player runs 12 yards to the left.
The vertical (up/down, y) transition is represented by the number 17. In addition, the player runs 17 yards up the field.
When you put it all together, you get < -12, 17 >.
Therefore, the receiver's route is defined by translation vector < -12, 17 >.
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What to do if B is negative in a transformation? Does it become a positive fraction or stay a negative fraction when reflected over the y axis?
Step-by-step explanation:
what is B in your question ? you did not tell us.
since you mention "fraction", I assume B is the slope of a line ?
if that is the case, please remember, the slope is (y coordinate change / x coordinate change) when going from one point of the line to another.
the way you phrased it I assume the slope was originally negative.
that means either the y difference or the x difference was negative (but not both, otherwise it would have been a positive fraction again).
let's look at what happens, when things get reflected across the y axis :
things go from the left side (negative x values) to the right side (positive x values) of the y axis or vice versa.
and things stay on the same side of the x axis (either above the x-axis with positive y values, or below the x-axis with negative y values).
so, that reflection causes the x values to flip their sign, but the y values stay the same.
so, if y was originally negative, then x must have been positive. after the reflection x is now negative too, that makes the y/x fraction -/- = +/+ positive.
if y was originally positive, then x must have been negative. after the reflection x is now positive too, that makes the y/x fraction +/+ positive.
therefore, in every case, the reflected slope fraction must be positive.
Round...
1. 24.263 to the nearest tenth.
Answer: 24.3
Step-by-step explanation:
A tenth would be the first decimal place.
Since the digit after the digit we need to round is above 5, then we need to round up.
The two turns into a 3.
I would really appreciate if you give brainliest.
Cement is poured into a hemisphere that is 6cm across. What is the volume of cement used?
hope the picture makes sense. I think it's right (no expert) if u want me to explain just ask. the answer is circled. usually the question would ask you to round so i wrote the full version
Complete the statement of the distance formula.
DISTANCE FORMULA The distance AB between two points A(x₁, y₁) and B(x₂, y₂) in a
coordinate plane is given by the equation:
AB =
Answer:
[tex] \sqrt{(x2 - x1) ^{2} } + (y2 - y1) {}^{2} [/tex]
I WILL GIVE BARINLIEST TO THE FIRST PERSON WHO ANSWERS MY QUESTION!!!!!
Can someone please help me? I really need the help right now.
Which of the following is equal to g(x)?
A. 2(x + 2)
B. 2x + 2
C. 2x - 2
D. 2(x - 2)
( Also I am bo*red...Can someone talk to me.....Anyone...Idc who you are....Unless your cr33py then I care)
Using translation concepts, the formula for function g(x) is given by the following option:
D. g(x) = 2^(x - 2)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
From the graph of the functions, we have that:
f(x) = 2 when x = 1.g(x) = 2 when x = 3.f(x) = 4 when x = 2.g(x) = 4 when x = 4.This means that g(x) is a shift right of 2 units of f(x), that is:
g(x) = f(x - 2).
Hence:
g(x) = 2^(x - 2)
The formula for function g(x) is given by the following option:
D. g(x) = 2^(x - 2)
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What is the answer to this problem?
Answer:
The length is 120 yards, the width is 60 yards.
Step-by-step explanation:
[tex]l = 2w[/tex]
[tex]2(w + 2w) = 360[/tex]
[tex]3w = 180[/tex]
[tex]w = 60[/tex]
[tex]l = 120[/tex]
Factories: a factory produces 6 motorcycles in 9 hours. Write a proportion and solve it to find how many hours it takes to produce 16 motorcycles.
Answer: x=24
6:9, 16 is to x = 16:x
6/9=16/x
multiply both sides by x
6x/9=16
multiply both sides by 9
6x=144
divide by 6
x=24
Answer:
6 motorcycles/ 9 hours = 16 motorcycles/x hours
to complete a proportion you need to multiply the cross products
9(16)=6x
144=6x
144/6=6/6 x
24=x
it will take 24 hours to produce 16 motorcycles
PLEASEE HELPP MEE
EHTS THE ANSWER WITH THE WORKK
5x - 4 = 1/2 (4x + 8 )
Answer:
х=8/3 solution on screen
Step-by-step explanation:
Good luck
help pls
-4|w-1|=-8
solve for w
Answer:
w= 3, -1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
w can be either 3 or -1
Step-by-step explanation:
-4 |w-1| = -8
Divide both sides by -4
List both cases
|w-1| = 2 |w-1| = -2
w = 3 w = -1
Physical science
Your dog takes off from your house after seeing a cat run across the street. If your dog started from rest and achieved 5.5 m/s in 3 seconds, what is the acceleration of your dog?
The acceleration of the dog is approximately 1.83 meter per second² .
Acceleration is defined as the rate of change of velocity . The change in velocity per unit time is acceleration.
The formula to calculate acceleration is given by acceleration = velocity ÷ time.Negative acceleration is called deceleration.Acceleration can be uniform or non-uniform.In the given problem the dog started from rest and achieved the final velocity of 5.5 m/s.
Let us use Newton's laws to write the equation:
v = u + at , where v is the final velocity , u is the initial velocity , a is acceleration and t is time.
The dog starts from rest so the initial velocity is 0.
given v=5.5 /s and t = 3 seconds
putting the values we get:
v = u + a t
or , 5.5 = 0 + 3a
or, a = 5.5/3 meters per seconds²
or, a = 1.8333... m/s²
or, a ≈ 1.83 m/s²
The acceleration of the dog is 1.83 m/s²
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Find the distance between pair of parallel lines with the given equations.
y=-6 y=1
The distance between pair of parallel lines with the given equation
y=-6 y=1 is 7 units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The two lines have the coefficient of x, zero. So, the slopes are 0.
Therefore, the lines are horizontal lines passing through y = −6 and y = 1.
The perpendicular distance between the these horizontal lines is
1 - (-6) = 7 units.
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