As a customer service representative Stan's yearly bonus would be 516 dollars.
What is Bonus ?A bonus is a financial compensation that is above and beyond the normal payment expectations of its recipient. Bonuses may be awarded by a company as an incentive or to reward good performance.
We have given that the amount of his yearly bonus in expression which is -1.5x + 546 dollars.
Where, 'x' = Number of complaints customer
We know that Stan gets 20 complaints,
To find his bonus we will solve this expression -1.5x + 546 by substituting 20 for x.
Bonus of Stan = -1.5x + 546
= (-1.5×20) + 546
= -30 + 546 = 516
Hence, the yearly bonus of Stan is 516 dollars.
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HELP FIND THE AVERAGE RATE OF CHANGE
The average rate of change of a function [tex]f(x)[/tex] as [tex]x[/tex] varies from [tex]x=a[/tex] to [tex]x=b[/tex] is given by the so-called difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
If we plot [tex]f(x)[/tex], this difference quotient would correspond to the slope of the line through two points [tex](a,f(a))[/tex] and [tex](b,f(b))[/tex] and intersecting with the curve [tex]y=f(x)[/tex].
(a) The average rate of change of height from 0 to 6.6 seconds is
[tex]\dfrac{H(6.6) - H(0)}{6.6 - 0}[/tex]
and is measured in m/s.
Consult the table for the values of [tex]H(t)[/tex] - it tells us [tex]H(0)=0[/tex] and [tex]H(6.6)=198[/tex]. So the average rate of change of height in this time is
[tex]\dfrac{198 - 0}{6.6 - 0} \dfrac{\rm m}{\rm s} = \boxed{30\dfrac{\rm m}{\rm s}}[/tex]
(b) Similarly, the average rate of change of height from 8.8 to 13.2 seconds is
[tex]\dfrac{H(13.2) - H(8.8)}{13.2-8.8} \dfrac{\rm m}{\rm s} = \dfrac{0 - 44)}{4.4} \dfrac{\rm m}{\rm s}= \boxed{-10 \dfrac{\rm m}{\rm s}}[/tex]
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
solve for -7x-3x+2=-8x-8
In linear equations, x = 5 is value of x .
What are instances of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.-7x-3x+2=-8x-8
-7x -3x + 8x = -8 - 2
-10x + 8x = -10
-2x = -10
x = 5
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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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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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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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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
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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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:
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]
V=1/3πr2(h-1) solve for h with work shown please
Answer:
which mountain is known as Nepal Himal?
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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Multiply -
60/21 by 7/30
Translate the sentence into an equation.
Twice the difference of a number and 3 is equal to 5.
Use the variable v for the unknown number.
Answer:
2(v-3) = 5
Step-by-step explanation:
2(v-3) = 5
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.
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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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
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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In captivity, a male lion grows to weight about 420 lbs with a standard deviation of 35 lbs. A zoo would like to have a lion that is in the largest 25% of male lions based on weight. How much should a male lion weigh for the zoo to obtain the male lion?
456.25 male lion weigh for the zoo to obtain the male lion.
what is Normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Given:
A male lion grows to weight about 420 lbs with a standard deviation of 35 lbs.
A zoo would like to have a lion that is in the largest 25% of male lions based on weight.
So,
z= (x- [tex]\mu[/tex])/[tex]\sigma[/tex]
Now substituting the value
1.036 = X-420/35
36.25= X- 420
X= 36.25 + 420
X= 456.25
Hence, 456.25 male lion weigh for the zoo to obtain the male lion.
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here for the solution We have here, that jet is equal to 0.52. Their score corresponding to 30 area under standard normal distribution. By using jet table to the right up ahead here, X is equal to zero multiplied by sigma plus mu. Here by substituting the value for the next step, we get 0.52 dataset, multiply by sigma. That is 35 plus mu, That is four 20. By simplifying this, we get the value is 4 83.2, which is approximately equal to 4 38.4. Which is our Answy for the answer is 4:38.4 is the correct choice for the answer. So here is the solution. The answer. Please go through this.
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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ASAP please
A rotating sprinkler is placed in one corner of a garden . If it has a reach of 8m and rotates through an angle of 30°, calculate the area of garden not being watered. Give your answer in terms of π
The area that is not covered by the sprinkler is 33.49 m².
The sprinkler is placed in one corner of the garden.
It has a reach of 8 m.
radius = r = 8 m
It means that it will form a segment of 90°.
So, the area it should cover will be:
Area that should be covered = 1 / 4 π r²
= 1 / 4 π (8)² m²
= 1/ 4 π (64) m²
= 16 ( 3.14 ) m²
= 50.24 m²
Now, it only rotates 30°.
It means that, it covers only 1 / 3 area.
So, the area actually covered = 1 / 3 × 50.24 m²
= 16.75 m²
The area that is not covered = 50.24 m² - 16.75 m²
The area that is not covered = 33.49 m²
Therefore, we get that the area that is not covered by the sprinkler is 33.49 m².
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Write a two-column proof.
Given: QR ≅ SR ≅ WR ≅ VR
Prove: QT ≅ WU
We can conclude that line QT ≅ WU.
What exactly is meant by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: QR ≅ SR ≅ WR ≅ VR
To Prove: QT ≅ WU
Line VRS ⊥ WRQAs ∠UWR and TQR = 90°.So, UW and QT ⊥ WRQTherefore, we can conclude that line QT ≅ WU.
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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.
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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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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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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5p − q − p; use p = 3, and q = 4
Step-by-step explanation:
5p − q − p; use p = 3, and q = 4
5*3-4-3
=15-7
=8
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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Find the distance between each pair of parallel lines with the given equations).
y=2 x-3
2 x-y=-4
Distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex] .
Two lines a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0 are said to be parallel if a₁=a₂ , b₁=b₂.
Distance between two two parallel lines is given by [tex]\frac{|c1-c2|}{\sqrt{a^{2} +b^{2} } }[/tex].
In the given question
2x-y-3=0 and 2x-y+4=0
Given the coefficient of x and y is same in both the line therefore they are parallel.
given, a(coefficient of x)=2 , b(coefficient of y= -1 , c₁=-3 , c₂=4.
Substituting the values in the distance formula we get
[tex]d=\frac{|-3-4|}{\sqrt{2^{2}+(-1)^{2} } }[/tex]
[tex]=\frac{7}{\sqrt{4+1} } =\frac{7}{\sqrt{5} }[/tex]
on rationalizing we get
[tex]d=\frac{7\sqrt{5} }{5}[/tex]
Therefore , the distance between parallel lines y=2x-3 and 2x-y=-4 is [tex]\frac{7\sqrt{5} }{5}[/tex].
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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.
