Answers
Answer:
2
Step-by-step explanation:
SV = TU
x+3 = 4x-3
6=3x
x=2
Hello!:
In a parallelogram:
--> the sides parallel to each other are equal in length
--> so sides SV and TU are equal lengths
--> which in equation form
[tex]SV=TU\\x+3=4x-3\\4x-x=3+3\\3x=6\\x=2[/tex]
Thus if SV = x + 3, then:
[tex]SV=x+3=2+3=5[/tex]
The length of SV is 5
Answer: 5
Related Questions
Which of the following is most likely the next step in the series?
#
C.
H
•
H
Answers
Answer:i don't know maybe C
The Smiths paid Maeve $6 an hour to babysit. The Blacks paid her $8 an hour. During one week, Maeve babysat for the Smiths for four hours and for the Blacks for three hours. How much did she earn in total that week?
Maeve earned
Answers
Answer:
48$
Step-by-step explanation:
6 times 4 equals 24 and 8 times 3 equals 24. 24 plus 24 equals 48.
Answer:
$ 48
Step-by-step explanation:
Smiths payment:
To find the amount Maeve earned for 4 hours, multiply the unit rate (per hour $6) by 4.
Payment made to Maeve for 1 hour = $ 6
Payment made to Maeve for 4 hour = 6 * 4
= $ 24
Blacks payment:
To find the amount Maeve earned for 3 hours, multiply the unit rate (per hour $8) by 3.
Payment made to Maeve for 1 hour = $ 8
Payment made to Maeve for 3 hours = 3 * 8
= $ 24
To find the total earnings, add the amount given by Smith and Black
Maeve earnings = 24 + 24
= $ 48
If algebra tiles have the dimensions shown here, what would you call this tile collection?
In other words, what is the total area of all of the pieces?
Answers
The algebraic equation of the total area of all of the pieces is 4x + 6y + 6x² + 2xy + y².
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
We have given,
Collection of tiles of the same dimensions.
x, x², y, y², and xy.
The question examines the calculation,
Total Area = 1* x * 4 + 1 * y * 6 + x * x * 6 + x * y * 2 + y * y *1
= 4x + 6y + 6x² + 2xy + y²
Area = 4x + 6y + 6x² + 2xy + y².
Therefore, The algebraic equation of the total area of all of the pieces is 4x + 6y + 6x² + 2xy + y².
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Mikoy is currently 34 years old. His daughter is 22 years younger than him. In how many years will Mikoy’s age be 24 years less than three times as old as his daughter?
Answers
Answer:
three times
Step-by-step explanation:
Please find the attachment for detail
p=(mv+x)=q+z
Solve for p
Solve for v
Answers
Answer:
Solve for p:
p = q + z
Solve for v:
v = (p - q - z) / m
Step-by-step explanation:
You provided an algebraic equation with multiple variables: p, m, v, x, q, and z. To solve for a specific variable, we need to isolate that variable on one side of the equation and all the other variables on the other.
To solve for p:
p = mv + x = q + z
The variable "p" is already on one side of the equation, so we don't need to do anything else.
To solve for v:
v = (p - q - z) / m
We need to isolate v on one side. Therefore we can subtract q and z from both sides to obtain the equation v = (p - q - z) / m, where v is the isolated variable on one side of the equation, and all the other variables are on the other side.
Solve x^2-7x=-12
Need help
Answers
Answer:
x=4 and x=3
Step-by-step explanation:
which equation is graphed along with the parent function?
Answers
Equation graphed along with the parent function is, g(x) = ∛(x-3) + 4
The correct option is B.
What is graph of a function?The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).
Given that;
Graph of a parent function.
And, Equation is graphed along with the parent function.
Here, The Parent function is,
f(x) = ∛x
Hence, By the graph,
There is 3 unit horizontal shift to positive side, and 4 unit vertical shift to upwards in parent function
Thus, The function drawn along with it is;
g(x) = ∛(x-3) + 4
Hence, g(x) = ∛(x-3) + 4 is the equation, graphed along with the parent function.
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The complete question is this,
Which equation is graphed along with the parent function?
g(x)= ^3 √x+3 +4
g(x)= ^3 √x-3 +4
g(x)= ^3 √x-4 +3
g(x)= ^3 √x+4 +3
When you solve the equation x^3−4x^2+3x=0,
how many roots are greater than 1/3
?
Answers
Answer:
0
Step-by-step explanation:
[tex] {x3 \: - 4 {x \: }^{2} + 3x \: = 0}^{} [/tex]
solve for x
[tex]x 1 = 0 \\ x2 \: = 1 \\ x3 \: = 3[/tex]
joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 5050 total rooms. Joe had already reserved and paid for 16 1616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 88 rooms and costs $ 900 $900dollar sign, 900. Let B BB represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: Choose 1 answer: (Choice A) A 16 + 8 B ≤ 50 16+8B≤5016, plus, 8, B, is less than or equal to, 50 (Choice B) B 16 + 8 B ≥ 50 16+8B≥5016, plus, 8, B, is greater than or equal to, 50 (Choice C) C 16 + B ≤ 50 16+B≤5016, plus, B, is less than or equal to, 50 (Choice D) D 16 + B ≥ 50 16+B≥5016, plus, B, is greater than or equal to, 50 2) What is the least amount of additional money Joe can spend to get the rooms they need? dollars
Answers
If Joe can only reserve rooms in blocks, and each block contains 8 rooms and costs $900 , then inequality describes this scenario is (b) 16 + 8B ≥ 50 .
the number of rooms that Joe has already reserved = 16 rooms ;
the number of additional blocks that Joe reserved is = 8 blocks
they need at least 50 total rooms , which means that the total number of rooms that Joe has reserved, including the blocks he needs to reserve.
The expression "16 + 8B" represents the total number of rooms that Joe has reserved, as he has already reserved 16 rooms and each block contains 8 rooms.
Therefore, The inequality represents the constraint that Joe must meet in order to ensure that the company has enough rooms for the trip is 16 + 8B ≥ 50 .
Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms.
He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900 , "B" represent the number of additional blocks that Joe reserves
Which inequality describes this scenario?
(a) 16 + 8B ≤ 50
(b) 16 + 8B ≥ 50
(c) 16 + B ≤ 50
(d) 16 + B ≥ 50
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9. The temperature is 80 degrees at noon, and the high and low temperatures during the day
are 90 and 70 degrees, respectively. Assuming t is the number of hours since noon, find a
function for the temperature, D, in terms of t.
Answers
https://brainly.com/question/25317034Assuming t is the number of hours since noon, a slope equation for the temperature, D, in terms of t is 80 ± 10t.
What is the slope?The slope refers to the change in y value resulting from a change in x.
The slope is also described as the quotient of the rise and run.
The slope refers to the rate of change along the regression line.
Temperature at noon = 80 degrees
High temperature during the day = 90 degrees
Increase in temperature from noon = 10 degrees (90 - 80)
Low temperature during the day = 70 degrees
Decrease in temperature from noon = -10 degrees (70 - 80)
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Please help me with this question.
Answers
The exact value of trigonometric function is ,
sin(60°+45°)= [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]
cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex] = [tex]\frac{\sqrt2+\sqrt6}{4}[/tex].
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here the given is
a) sin(60°+45°)
Now using formula sin(t+s)= sin t cos s+ cos t sin s then
=> sin60°cos45°+cos 45°sin60°
=> [tex]\frac{\sqrt3}{2}\times\frac{\sqrt2}{2}+\frac{1}{2}\times\frac{\sqrt2}{2}[/tex]
=> [tex]\frac{\sqrt6}{4}+\frac{\sqrt2}{4}[/tex]
=> [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]
b) cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex]
Now using formula cos(t-s)=cos t cos s + sin t sin s then
=> [tex]cos\frac{\pi}{3} cos\frac{\pi}{4}+ sin\frac{\pi}{3}sin\frac{\pi}{4}[/tex]
=> [tex]\frac{1}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt3}{2}\times\frac{\sqrt2}{2}[/tex]
=> [tex]\frac{\sqrt2}{4}+\frac{\sqrt6}{4}[/tex]
=> [tex]\frac{\sqrt2+\sqrt6}{4}[/tex]
Hence the exact value of trigonometric function is ,
sin(60°+45°)= [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]
cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex] = [tex]\frac{\sqrt2+\sqrt6}{4}[/tex].
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You use a garden hose to fill a wading pool. If the water level rises 14 centimeters every 3 minutes and you record the data point of (6,y), what is the value of y? Use slope to justify your answer.
Answers
The value of y is 28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The water level rises 14 centimeters every 3 minutes.
This means,
14 cm = 3 minutes
This can be written as,
(3, 14)
Now,
14 cm = 3 minutes
Multiply with 2 on both sides.
2 x 14 cm = 6 minutes
28 cm = 6 minutes
This can be written as,
(6, 28)
Thus,
The y value is 28.
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Gavyn was thinking of a number. Gavyn doubles it and adds 4.4 to get an answer of 85.8. Form an equation with x from the information.
Answers
Answer:2x+4.4=85.8
Step-by-step explanation:
pretty sure this is the answer
Gavyn doubles the number and adds 4.4 so -> 2x+4.4 and that equals to 85.8
so it's 2x+4.4=85.8
Answer:
Step-by-step explanation:
If the original number is x, then we can say:
2x+4.4=85.8
2x=85.8-4.4
2x=81.4
x=40.7
To check,
40.7*2=81.4
81.4+4.4=85.8
Hence, x is 40.7
Your family has a new swimming pool which has a volume of 60m³. Determine the number of gallons of water that will be needed to fill the empty swimming pool to 94% of its capacity. Write your answer rounded to 3 decimal values.
Answers
Answer: To convert cubic meters (m³) to gallons, we can use the conversion factor 1 m³ = 264.172 gallons.
First, we need to find the amount of water needed to fill the pool to 94% of its capacity. We can do this by multiplying the volume of the pool (60 m³) by 94% (0.94).
60 m³ * 0.94 = 56.4 m³
Now we can use the conversion factor to convert the volume in cubic meters to gallons:
56.4 m³ * 264.172 gallons/m³ = 14,958.2 gallons
So the number of gallons of water that will be needed to fill the empty swimming pool to 94% of its capacity is 14,958.2 gallons.
Rounded to 3 decimal values is 14,958.2 gallons.
Step-by-step explanation:
Puppies Galore is selling puppies for $149.50. There is a sale going on that offers 45% off. What is the total selling price of one puppy?
Answers
Answer: $81.92
Step-by-step explanation:
First you must convert the 45% to a decimal.
0.45
You must multiply 0.45 by the total cost and then subtract what you get.
What is the percent of change from 400 to 600?
Answers
The percent of change from 400 to 600 is 33.34%.
What is Percentage Increase?
The final increase in quantity is expressed as a percentage by the term "percentage increase". A quantity's growth from its starting value to its final value through time is compared using the percentage increase formula. The final value minus the initial value, divided by the initial value, and multiplied by 100 are how this formula is mathematically expressed.The formula for percentage increase is given as, [tex]\% \text Increase = \frac{\text FV - IV}{FV} \times 100[/tex], where FV is the Final Value and IV is the Initial Value.It is given that the percent of change is from 400 to 600.
There is an increase from 400 to 600, so the percent of change is an increase.
[tex]\% \text Increase = \frac{\text FV - IV}{FV} \times 100[/tex]
Here, the final value (FV) = 600 and initial value (IV) = 400.
Substituting the given values in the above formula, we get
[tex]\% \text Increase = \frac{600-400}{600} \times 100\\\implies \% \text Increase = \frac{200}{600} \times 100\\\implies \% \text Increase = 33.34 \%[/tex]
Therefore, the percent of change from 400 to 600 is 33.34%.
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Find Power Set B = {a, b, c, d, e, f, g}
Answers
Answer:
The power set of a set B = {a, b, c, d, e, f, g} is the set of all possible subsets of B.
In mathematical notation, the power set of B is represented as P(B).
The number of elements in the power set of B is 2^n, where n is the number of elements in B. In this case, n = 7, so the number of elements in P(B) = 2^7 = 128.
The power set of B is:
{{}, {a}, {b}, {c}, {d}, {e}, {f}, {g}, {a, b}, {a, c}, {a, d}, {a, e}, {a, f}, {a, g}, {b, c}, {b, d}, {b, e}, {b, f}, {b, g}, {c, d}, {c, e}, {c, f}, {c, g}, {d, e}, {d, f}, {d, g}, {e, f}, {e, g}, {f, g}, {a, b, c}, {a, b, d}, {a, b, e}, {a, b, f}, {a, b, g}, {a, c, d}, {a, c, e}, {a, c, f}, {a, c, g}, {a, d, e}, {a, d, f}, {a, d, g}, {a, e, f}, {a, e, g}, {a, f, g}, {b, c, d}, {b, c, e}, {b, c, f}, {b, c, g}, {b, d, e}, {b, d, f}, {b, d, g}, {b, e, f}, {b, e, g}, {c, d, e}, {c, d, f}, {c, d, g}, {c, e, f}, {c, e, g}, {d, e, f}, {d, e, g}, {e, f, g}, {a, b, c, d}, {a, b, c, e}, {a, b, c, f}, {a, b, c, g}, {a, b, d, e}, {a, b, d, f}, {a, b, d, g}, {a, b, e, f}, {a, b, e, g}, {a, c, d, e}, {a, c, d, f}, {a, c, d, g}, {a, c, e, f}, {a, c, e, g}, {a, d, e, f}, {a, d, e, g}, {b, c, d, e}, {b, c, d, f}, {b, c, d, g}, {b, c, e, f}, {b, c, e, g}, {b, d, e, f}, {b, d, e, g}, {c, d, e, f}, {c, d, e, g}, {a, b, c, d, e}, {a, b, c, d, f}, {a, b, c, d, g}, {a, b, c, e, f}, {a, b, c, e, g}, {a, b, d, e, f}, {a, b, d, e, g}, {a, c, d, e, f}, {a, c, d, e, g}, {b, c, d, e, f}, {b, c, d, e, g}, {a, b, c, d, e, f}, {a, b, c, d, e, g},{a, b, c, d, f, g},{a, b, c, e, f, g},{a, b, d, e, f, g},{a, c, d, e, f, g},{b, c, d, e, f, g},{a, b, c, d, e, f, g}}
The number of cars sold by a car dealer last month. Is it qualitative or quantitative
Answers
pls help me with math matching i’ll give you brainlist
Answers
The matching of equations with their characteristic is as shown:
a) Neither parallel nor perpendicular lines
b) these are perpendicular lines
c) these are parallel lines
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Rewrite the equations that need to be in y=mx+b form, then compare the slopes ( m values )
a) y= -4x +5 , y=(-1/4)x - 6
Neither parallel nor perpendicular lines
b) y=3x+5 , y= (-1/3)x - 7
The slopes are m and -1/m , these are perpendicular lines
c) The slopes are equal
So, these are parallel lines
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.6(2x +4.5y) -.3y = m(x+ny) solve for n
Answers
Answer:
n=0.2(6x+12y-5mx)/my
Step-by-step explanation:
A state imposes a 5% sales tax on items of clothing that cost more than $175. The tax applies only to the difference of the price of the item and $175. A shopper has $400 to spend on a new suit. Write and solve an inequality to find the prices p of suits that the shopper can afford. Assume that p ≥ $175.
A state imposes a 5% sales tax on items of clothing that cost more than $175. The tax applies only to the difference of the price of the item and $175. A shopper has $400 to spend on a new suit. Write and solve an inequality to find the prices p of suits that the shopper can afford. Assume that p ≥ $175.
A state imposes a 5% sales tax on items of clothing that cost more than $175. The tax applies only to the difference of the price of the item and $175. A shopper has $400 to spend on a new suit. Write and solve an inequality to find the prices p of suits that the shopper can afford. Assume that p ≥ $175.
A state imposes a 5% sales tax on items of clothing that cost more than $175. The tax applies only to the difference of the price of the item and $175. A shopper has $400 to spend on a new suit. Write and solve an inequality to find the prices p of suits that the shopper can afford. Assume that p ≥ $175.
A state imposes a 5% sales tax on items of clothing above $175. The tax applies only to the difference between the price of the item and $175. A shopper has $400 to spend on a new suit. Write and solve an inequality to find the prices p of suits that the shopper can afford.
Answers
The solution of the inequality means p = { range of values greater than $175 up until $400 }
We need to write and solve an inequality to find the prices p of coats that the shopper can afford.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Given that the value of price, p of coats the shopper can afford is greater than $175.
p > 175 can be translated as 175 < p
The shopper has $400 to spend on a winter coat such, p ≤ $400 .
The two inequalities can therefore be combined to yield a single inequality thus;
175 < p ≤ $400
The solution for prices of coat, p that the shopper can afford ranges between;
p = { range of values greater than $175 up until $400 }
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You are going down a road with 2% grade
you are going down 1 feet every (blank) feet horizontally.
the slope of the road as a reduced fraction is
Answers
im stuck on the same thing
pls help I really need this ASAP
Answers
What is the height of the triangular prism if the Surface Area is 180 inches squared
Answers
Answer:
4 in
Step-by-step explanation:
Surface area = 1/2 ( 5x12) *2 + 5 x h + 13 * h + 12 x h
60 + 30h = 180
h = 4 in
just a quick addition to "jsimpson11000" posting above
keeping in mind that for a triangular prism, the base is always the triangular face.
Check the picture below.
[tex]5h~~ + ~~12h~~ + ~~\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(12)(5) \right]}~~ + ~~13h~~ = ~~180 \\\\\\ 60+30h=180\implies 30(2+h)=180\implies 2+h=\cfrac{180}{30} \\\\\\ 2+h=6\implies \boxed{h=4}[/tex]
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it
Answers
The axis of symmetry for the function f(x) is x = 8 , and h(x) is x = 3
What is the axis of symmetry of a quadratic function?The axis of symmetry is a hypothetical straight line that splits a form into two identical halves, making one half the mirror image of the other. Both pieces are overlaid when folded along the axis of symmetry.
A straight line called the axis of symmetry is what gives an object its symmetrical form and exactly the same reflections are produced on each side of the axis of symmetry on the graph.
From the given information:
f(x) = -4(x - 8)² + 3
Use the vertex form, y = a ( x − h )² + k, to determine the values of a, h, and k.
a = -4, h = 8, k = 3Since the value of a is negative, the parabola opens down, and the vertex (h, k) is (8, 3).
The distance (p) from the vertex and the focus of the quadratic equation can be calculated by using the formula:
P = 1/4a
Replacing the value of a from above:
P = 1/4(-4)
P = -1/16
The focus of a parabola can be determined by adding the p to the y-coordinate k if the parabola opens up or down. Thus, (h, k + p) = (8, 47/16).
Thus, the axis of symmetry is finally estimated by finding the line that passes through the vertex and the focus;
Axis of symmetry x = 8
For the graphical function of h(x); we use the following points on the graph to determine the equation of the parabola: (1,-2), (3,2), (5,-2)
Thus, h(x) = -x² + 6x - 7
Rewriting the function in its vertex form, we have:
y = - (x - 3)² + 2
Using the vertex form;
a = -1, h = 3, k = 2The vertex (h,k) = (3,2). The axis of symmetry (x) is the line that passes through the vertex and the focus, x = 3.
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Question 1
2
The winner of the 95th annual hotdog eating contest consumed 207 hotdogs (and buns!) in 10 minutes.
You are determined to break this record, so you would have to consume 208 hotdogs and buns in 10 minutes.
How many hotdogs would you have to eat every minute to beat the last winner?
Type the number of hotdogs in the blank below (JUST the number).
Assuming you eat at the average rate needed to win the contest, how many total hotdogs will you consume in two minutes?
Type the number of hotdogs in the blank below (JUST the number).
Assuming you eat at the average rate needed to win the contest, how many total hotdogs will you consume in three minutes?
Type the number of hotdogs in the blank below (JUST the number).
Answers
The number of hotdogs would you have to eat every minute to beat the last winner is about 21 hotdogs per minute
How to determine the number of hotdogs?The statement reads that the 95th annual hotdog eating contest consumed 207 hotdogs (and buns!) in 10 minutes.
This implies that 208/10= 20.8 hotdogs (and buns) per minute to beat the record of 207 in 10 minutes or about 21 hotdogs per minute.
(2) In two minutes, you would be able to eat 21 hotdogs times 2 = 42 hotdogs
(3)At the average rate needed to win the contest, the number of total hotdogs will you consume in three minutes is 21 hotdogs times 3 = 63 hotdogs
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determine if b is in the span of the other given vectors. if so, express b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter dne in both answer blanks.) -1 -2 -6
a1 = 3 a2 = -3 b= 9
-1 6 2
Answers
Yes, b(-6, 9, 2) is in the span of the other given vectors [tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6).
b as a linear combination of the other vectors [tex]a_1[/tex] and [tex]a_2[/tex]
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
A vector is a quantity that has magnitude and direction.
We say that a vector u spans vectors v, w if u = av + bw where a and b are scalars.
As per the given data:
[tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6), b = (-6, 9, 2)
We need to write vector b as a linear combination of vectors [tex]$a_1[/tex] and [tex]a_2$[/tex].
Let c and d be scalars.
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
(-6, 9, 2) = c(-1, 3, -1) + d(-2, -3, 6)
(-6, 9, 2) = (-c - 2d, 3c - 3 d, -c + 6d)
-6 = -c - 2d........(i),
9 = 3c - 3d ...... (ii),
2 = -c + 6d .......(iii)
b = c [tex]a_1[/tex] + d [tex]a_2[/tex]
On solving equations (i) and (ii), we get c = 4, d = 1
Now, we will check if c = 4, and d = 1 satisfy equation (iii).
= - c + 6d
= -4 + 6(1)
= -4 + 6
= 2
As it satisfies this equation, so b is a linear combination of [tex]$a_1[/tex] and [tex]a_2[/tex]
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Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors. (if b cannot be written as a linear combination of the other two vectors, enter done in both answer blanks.) a1=[-1 3 -1],a2=[-2 -3 6],b=[-6 9 2]
Consider a job offer with the given starting salary and the given annual raise. Starting salary Aannual raise $36,500 $1200 (a) Determine the salary during the sixth year of employment.
(b) Determine the total compensation from the company through six full years of employment.
Answers
The salary after sixth year of employment will be $45918.34. The total compensation after six years are $250914.15.
The amount raised over a period of time is given by the equation ,
Xₙ = X₀ (1+r)ⁿ
Xₙ is the final amount or number
X₀ is the initial amount or number
r is the rate
n is the number of years or period of time.
Here the annual rise is given as $1200. So we can calculate the rate.
r = 1200/36500 = 0.039
The salary rise during the sixth year, Xₙ = 36500 ×(1+0.039)⁶
= 45918.34
Total salary in all six years = 36500 + [36500×(1+0.039)¹] + [36500× (1+0.039)²] + [36500× (1+0.039)³] + [36500×( 1+0.039)⁴] +[36500×(1+0.039)⁵] + [36500× (1+0.039)⁶]
=250914.15
So the 6th year salary is $45918.34 and total compensation for 6 years will be 250914.15.
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Ms brous has some overdue library books. The function t(b)=4b+5 with t being the total the amount she paid in fees and b being the number of books
A) state the independent and dependant variables
B) use the input/output table to find some of the ordered pairs of the function (can't attach but the b values are 1-5)
C)determine if the domain is continuous or discrete. Explain.
D)find the domain and range of the function.
Answers
Answer:
A) The independent variable is the number of books (b) and the dependent variable is the total amount paid in fees (t).
Step-by-step explanation:
B) The input/output table for this function would be as follows:
b t
1 9
2 13
3 17
4 21
5 25
So some of the ordered pairs of the function are (1, 9), (2, 13), (3, 17), (4, 21) and (5, 25)
C) The domain of the function is discrete because it only includes specific values of b, the number of books. This is the only possible values of b are the natural numbers.
D) The domain of the function is all natural numbers b>=1, since it doesn't make sense for the number of books to be negative or zero. The range of the function is all natural numbers t>=5, since it doesn't make sense for the total amount paid to be negative or zero.
The article "Determination of Most Representative Subdivision" gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Data on the variable x = total length of streets within a subdivision are as follows.
1280 5320 4390 2100 1240 3060 4770 1050 360 3330 3380 340 1000 960 1320 530 3350 540 3870 1250 2400 960 1120 2120 450 2250 2320 2400 3150 5700 5220 500 1850 2460 5850 2700 2730 1670 100 5770 3150 1890 510 240 396 1419 2109
(a) Fill in a stem-and-leaf display for these data using the thousands digit as the stem. Do not truncate numbers. For example, number 2380 has stem-"2" and leaf-"380". (Enter solutions from smallest to largest. Separate the numbers with spaces.)
0 100 240 340 360 396 396 450 500 510 530 540 960 960
(b) Fill in the table below. (Round your answer to four decimal places if needed.)
Class Interval Frequency Relative Frequency
0 - <1000
2000 - < 3000
4000 - < 5000
5000 - < 6000
(c)
What proportion of subdivisions has total length less than 2000?
What proportion of subdivisions has total length between 2000 and 4000? (Round your answer to four decimal places if needed.)
Answers
a) The data is not symmetric
b) The complete table:
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298c) Proportion of subdivisions has total length less than 2000 is 0.49
Proportion of the subdivisions has total length between 2000 and 4000 is 0.36
a) To draw the stem and leaf plot we take the thousandth place digit as stem and the leaf is obtained by remaining digits.
Stem Leaf
0 360, 340, 960, 530, 540, 960, 450, 500, 100, 510, 240, 3961 280, 240, 050, 000, 320, 250, 850, 670, 890, 4192 100, 400, 120, 250, 320, 400, 460, 700, 730, 1093 060, 330, 380, 350, 870, 150, 1504 390, 7705 320, 700, 220, 850, 770The data is not symmetric
b) To draw the histogram first we form the frequency distribution and the relative frequency using the formula
Relative Frequencies are given by
Relative frequency = Frequency / Total frequency
Class interval Frequency Relative Frequency
0-1000 12 0.255319151000-2000 11 0.234042552000-3000 10 0.212765963000-4000 7 0.148936174000-5000 2 0.04255319 5000-6000 5 0.10638298= 47
Histogram attached at end of solution
The histogram is approximately positively skewed.
c) Proportion of lengths less than 2000 = sum of relative frequency from 0 to 2000
= 0.26 + 0.23
Proportion of subdivisions has total length less than 2000 = 0.49
Proportion of length between 2000 and 4000 = sum of relative frequency between 2000 and 4000
= 0.21 + 0.15
Proportion of the subdivisions has total length between 2000 and 4000 = 0.36
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