A car costsA car costs $30,000 when purchased as new and depreciates at a rate of 18% per year.Write an exponential decay model to represent the situation. Be sure to define the variables. Find the value of the car after 10 years
9514 1404 393
Answer:
v(t) = 30000×0.82^t . . . value in dollars after t years
v(10) ≈ 4123 . . . . dollars
Step-by-step explanation:
The general form of the decay model is ...
f(t) = f(0)×(1 -decay rate)^time
where the decay rate is a fraction between 0 and 1, and the time is expressed in the same time units as the decay rate. The multiplier f(0) is the initial value that is decaying.
In this problem, the initial value is $30,000 and the decay rate is 18% per year. So, we can write a function v(t), where v is the car's value in dollars, and t is the number of years after it starts depreciating.
v(t) = 30,000×(1 -0.18)^t
v(t) = 30,000×0.82^t
__
The car's value in 10 years is ...
v(t) = 30,000×0.82^10 ≈ 4123.44
The value of the car after 10 years is about $4,123.
what are the like terms in these?
3+5y-2g+7y
9g+5-2g+8x
Answer:
so the first one is 3+12y−2g
and the second one is 7g+5+8x
Step-by-step explanation:
im rlly rlly sorry if its wrong !!
A sphere has a Volume of 972 cubic feet. Find the radius of the sphere.
Answer:
6.15
Step-by-step explanation:
The numbers 1-6 are written on slips of paper and placed in a bag. Megan draws two numbers in a row withou replacement. What is the probability of Megan selecting an even number followed by a 3?
Answer:
2
Step-by-step explanation:
HELLPPP Fill in the blank
____ crystallizes from fluid lava and points to the north magnetic pole is the lava cools
One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 78 cm. Find the lengths of the sides of the kite
Answer:
[tex]9.4\:\mathrm{cm},\\9.4\:\mathrm{cm},\\29.6\:\mathrm{cm},\\29.6\:\mathrm{cm}[/tex]
Step-by-step explanation:
A kite consists of two pairs of congruent adjacent sides. Therefore, we have the following equation:
[tex]2x+2(4x-8)=78[/tex], where [tex]x[/tex] is the length of the shorter sides.
Solving, we get:
[tex]2x+8x-16=78,\\10x=94,\\x=\fbox{$9.4\:\mathrm{cm}$}[/tex].
Plugging in [tex]x=9.4[/tex] into [tex]4x-8[/tex], we get:
[tex]4(9.4)-8,\\37.6-8,\\\fbox{$29.6\:\mathrm{cm}$}[/tex].
Therefore, two sides have length [tex]9.4\:\mathrm{cm}[/tex] and two sides have length [tex]29.6\:\mathrm{cm}[/tex].
A piece of wire that is 28 inches long is cut into two pieces, each of which is then bent into the shape of a square. The larger square has side lengths that are three inches longer than the smaller square.
(a) If x is the side length of the smaller square and y is the side length of the larger square, write a system of equations that models this scenario.
(b) Solve the system of equations and determine the lengths of the two pieces of wire.
Answer:
1)
4(x+3)+4x=28
Solve
4x+12+4x=28
Combine
8x+12=28
Isolate
8x=16
Isolate
x=2
Substitute
4(2+3)=20
4*2=8
Now find each side
20/4=5
8/4=2
So one side is 5
Other side is 2
1 of 2
Find the length of the shortest side if the area of the rectangle is 144m2
х
x + 10
Answer:
Given,
Length and breadth of the rectangle are (x) and (x+10)
Area of the rectangle ( A ) = 144[tex]m^{2}[/tex]
We know ,
Area of rectangle ( A ) = L*B
or , 144 = x ( x+10 )
or , 144 = [tex]x^{2}[/tex] + 10x
or , [tex]x^{2}[/tex] + 10x - 144 = 0
Solving the equation , we get ,
x = 8 and -18
The side has to be positive so ,
x = 8 m , which is the shortest side !
Step-by-step explanation: We were given the area of the rectangle and length & breadth in expression . By using the formula of area of rectangle , we got the equation which then gave 8 and -18 as answers when solved and since the rectangle had positive sides 8 m was the correct value . Also its the shortest side and the other side is simply ( 8 + 10 ) which is 18 m but the question has only asked for the shortest side !
the barrel of a fountain pen, cylindrical in shape , is 7cm long and 5mm in diameter .a full barrel of ink in the pen will be used up in writting up 310 words on an average . how many words would use up on a bottle of ink containing one-fifth of a litre ?answer correct to the nearest 100 words.
Answer:
44 words
Step-by-step explanation:
Step one:
given data
The dimension is
7cm long and = 0.07mm
5mm in diameter
radius= 2.5mm
The volume = πr^2h
Volume= 3.142*2.5^2*0.07
Volume= 3.142*6.25*0.07
volume= 1.4 mm^3
If 1.4 mm^3 will write 310 words on an average
1/5(0.2mm^3) liter will write x
cross multiply we have
x= 0.2*310/1.4
x=62/1.4
x=44 words
Please help 30 points
The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
30 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
Mean for both coffee shops because the data distribution is symmetric
Median for both coffee shops because the data distribution is not symmetric
Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Answer: correct option is mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Step-by-step explanation:
According to the given data the correct statement is Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric.
Note that the two values of Shop B (10 and 11) are alot lower than the other values.
Thus the correct option is Mean for shop A and Median for shop B.
4) 1, -4, 16, -64, 256, ...
A) -3125, 15625, -78125
C) -32, 64, -128
B) 243, 729, 2187
D) -1024, 4096, -16384
Answer:
D) -1024, 4096,- 16384
Jill bought a lamp for $40. She sold it at a garage sale for $12. What was the approximate decrease?
Answer:
she was left with 28$ I'm in high school i think I'm right
Step-by-step explanation:
9.
Write the equations THEN solve by any method
Bowl-O-Rama charges 2.50 per game plus $2.00 for shoe rental and
Bowling Pinz charges $2 per game and $4.00 for shoe rental. For
how many games will the cost to the bowl be the same at both
places? What is the cost?
Answer: 4,12
Step-by-step explanation:
Bowl-O-Rama:
y = 2 + 2.50x
Bowling Pinz:
y = 4 + 2x
When you graph this, the solution is (4, 12). This represents that when you play 4 games for either company, both the prices will be the same, $12.
Answer:
$18.00
Step-by-step explanation:
Bowl-O-Rama: $4.50 times 4
Bowling Pinz: $6.00 times 3
The figure shows two equilateral triangles with a shared side. Can the triangles ΔIHJ and ΔIKJ be proven congruent?
Question 20 options:
A)
Yes, ΔIHJ ≅ ΔIKJ by AAA.
B)
No, ΔIHJ and ΔIKJ aren't congruent because SSA isn't a congruence theorem.
C)
Yes, ΔIHJ ≅ ΔIKJ by SSS.
D)
There isn't enough information.
The answer is Yes, ΔIHJ ≅ ΔIKJ by SSS.
Answer:
Step-by-step explanation:
D)
Yes, ΔIHJ ≅ ΔIKJ by SSS.
Just did this quiz got that one right.
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have? 6 ounces 12 ounces 18 ounces 27 ounces Please help cuz im in a pretest and my brain is ded
Complete question :
The graph below shows the percentages of ingredients in a salad mix.
A pie chart titled Percentages in salad mix. 40 percent is iceberg, 27 percent is romaine, 15 percent is spinach, 12 percent is arugula, 6 percent is carrots.
Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?
Answer:
18 ounces
Step-by-step explanation:
From the pie chart ;
The percentage of each Salad mixture in the mix is given ;
Romaine lettuce occupies 27% of the total salad mix ;
The total of amount of ounce of the entire salad mix is 64 ounce
Therefore, number of ounces of Romaine lettuce in the salad mix is ;
27% of 64
0.27 * 64
17.28
= 18 ounces
15.
Can someone help me?
Answer:
The radius, in inches, of the base of the cone will be:
r = 6 inches
Hence, option B is correct.
Step-by-step explanation:
Given
The Volume of a right circular cone V = 24 π cubic inches
The height of the cone h = 2 inches
To determine
The radius of the base of the cone r = ?
Using the formula involving Volume m, height h, and radius r of a right circular cone.
[tex]V\:=\frac{1}{3}h\:\pi \:\:r^2\:[/tex]
substituting V = 24 π, h = 2 to find the radius r
[tex]\left(24\pi \right)=\frac{1}{3}\left(2\right)\:\pi \:r^2[/tex]
switch sides
[tex]\frac{1}{3}\left(2\right)\pi r^2=\left(24\pi \right)[/tex]
[tex]\frac{1}{3}2\pi r^2=24\pi[/tex]
simplify
[tex]2\pi r^2=72\pi[/tex]
Divide both sides by 2π
[tex]\frac{2\pi r^2}{2\pi }=\frac{72\pi }{2\pi }[/tex]
[tex]r^2=36[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]
[tex]r=\sqrt{36},\:r=-\sqrt{36}[/tex]
Thus,
[tex]r=6,\:r=-6[/tex]
As we know that the radius can not be negative.
Therefore, the radius, in inches, of the base of the cone will be:
r = 6 inchesHence, option B is correct.
What must be included in an algebraic
expression?
A an equals sign
B at least one variable
C one or more numbers
D more than one operation
Answer:
B. you need atleast one variable for an algebraic expression.
an equals sign would make it an algebraic equation,
just a coefficient and a variable is the most basic algebraic expression. you don't need anything other than those for an expression. you can have more than one number, and more than one operation, but they don't have to be there.
Step-by-step explanation:
i hope this helps :))
Abigail’s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves.
Write an expression in two different ways to represent the amount their parents will pay Abigail and her sister for working the same number of hours
I dont get help me
Answer: (MAKE ME BRAINLIST PLEASE)
Answer: For Abigail W = $5t
For her younger sibling W= $3t
Bit by bit clarification:
How about we address the compensation with W
t as the time spent on work in hours
Abigail will be paid $5 every hour, her all out compensation will be
W(abg) = $5t
Her younger sibling will be paid $3 every hour, her complete compensation will be
W(lts) = $3t
i’m struggling help please
Answer:
Step-by-step explanation:
the slope would be y2-y1/x2-x1
so the distance is y and the time is x so what you are going to do is 30-18 over 5-3 which then means it would be 12/2 which equals 6
Find the value of x.
Hello!
[tex]\large\boxed{x = 6}[/tex]
The figure pictured contains two congruent triangles (ASA), so we can assume that:
JK ≅ JM
Therefore:
2x - 4 = 4x - 16
Subtract 2x from both sides:
2x - 2x - 4 = 4x - 2x - 16
-4 = 2x - 16
Add 16 to both sides:
-4 + 16 = 2x - 16 + 16
12 = 2x
Divide both sides by 2:
12/2 = 2x/2
x = 6.
Evelyn is working two summer jobs, making $18 per hour lifeguarding and making $11 per hour tutoring. In a given week, she can work a maximum of 15 total hours and must earn no less than $200. If Evelyn worked 8 hours lifeguarding, determine the maximum number of whole hours tutoring that she can work and still meet her requirements. If there are no possible solutions, submit an empty answer.
Answer:
Evelyn can work a maximum of [tex]7[/tex] hours tutoring.
Step-by-step explanation:
Evelyn earns [tex]\$\: 18[/tex] per hour lifeguarding and she worked [tex]8[/tex] hours lifeguarding.
So, total money earned by lifeguarding [tex]=\$\: 18\times 8=\$\:144[/tex].
She must earn no less than [tex]\$\:200[/tex].
So, money left to earn [tex]=\$\: 200-\$\:144=\$\:56[/tex].
Evelyn worked [tex]8[/tex] hours lifeguarding. She can work a maximum of [tex]15[/tex] total hours. So, she can work [tex]15-8=7[/tex] hours.
Evelyn earns [tex]\$\: 11[/tex] per hour tutoring.
So, total money earned by tutoring [tex]=\$\: 11\times 7=\$\:77[/tex].
Therefore, the total money earned [tex]=\$ \:144+\$\:77=\$\:221[/tex].
Hence, Evelyn can work a maximum of [tex]7[/tex] hours tutoring.
Answer:
The answer would be 7 hours tutoring. :)
Step-by-step explanation:
Which number sentence is represented by the number line?
Answer:
8
Step-by-step explanation:
it is 8
The staff takes 1/2 of an hour to assemble 1/8 of the booths. How long does it take the staff to assemble all of the booths?
Answer:
It takes all staff 3 hours
Step-by-step explanation:
So, first we write down all these important info. It takes half hour for staff to assemble one sixth (1/6) of the booths. First you need to take the fraction 1/6 a whole number by multiplying it by the denominator which in this case is 6 which will give you the answer 1. Next, you do the exact same thing for the other part. Multiply 1/2 by 6 to get 3.
The time to assemble the remaining fraction of the bottle is 3.5 hours.
Time to assemble one-eight of the bottles
The time taken for the staff to assemble one - eight (1/8) of the bottles is given as half (1/2) hour.
Remaining fractionThe remaining fraction of the bottle is calculated as follows;
[tex]= 1 - \frac{1}{8} \\\\= \frac{7}{8}[/tex]
Time to assemble the remaining fraction of the bottlesThe time to assemble the remaining fraction of the bottle is calculated as follows;
1/8 ----------------- 1/2 hour
7/8 ---------------- ?
[tex]\frac{7}{8} \times \frac{1}{2} \times \frac{8}{1} = 3.5 \ hours[/tex]
Learn more about time to complete work here: https://brainly.com/question/10929133
pls help :( i will give brainlist
Answer:
x=32 I used Jedi powers
Step-by-step explanation:
X+120+130+140+x-4+x+58=360(sum of quadrilateral is 360)
3x+250+140-4+58=360
3x+48-4=360
3x+444=360
3x=360-444
3x=-84
x=-85/3
x=-28
x-4
-28-4
-32
x+58
-28+58
30
It is correct answer
Given that GJ=70.2, JH=26, and GK=70.2, find the measure of JK
Answer:
52
Step-by-step explanation:
The two sides (GJ and GK) are congruent, and the angle of ∠GHJ is 90°.
It means JH ≅ HK.
JH = 26 so you multiply 2.
26 x 2 = 52
JK = 52
The measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
GJ=70.2, JH=26, and GK=70.2,
In the right angle triangle JHG:
GH = √(GJ² - JH²)
GH = √(70.2² - 26²)
GH = 65.20
Similarly, applying Pythagoras' theorem in the triangle GHK:
HK = √(GK² - GH²)
HK = √(70.2² - 65.20²)
HK = 26.01
JK = JH + HK
JK = 26 + 26.01
JK = 52.01 = 52
Thus, the measure of the side JK is 52 units if the GJ=70.2, JH=26, and GK=70.2 after applying the Pythagoras theorem.
Learn more about the right-angle triangle here:
brainly.com/question/3770177
#SPJ2
The bike store marks up the wholesale cost of all of the bikes they sell by 30%.
Andre wants to buy a bike that has a price tag of $125. The wholesale cost of this bike was $87.50.
Answer:
Suppose that the wholesale of a bike is A (A is the 100% in this case). If we have an increase of 30% for the sale price, we have the new price of:
Price = A + (30%/100%)A = A + 0.3*A = (1.3)*A
Then if we know that the price tag of the bike is $125, then we have:
$125 = (1.3)*A
$125/1.3 = A = $96.15
The wholesale cost of the bike is $96.15
Answer:
1. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike? $ 96.15
2. If the bike is discounted by 20%, how much will Andre pay (before tax)?
$ 100
I hope this helped <33 !
Anne is playing golf. On the first tee, she hits a slow shot down the Y = x -0.0 4X squared, we are why is the balls hide in the air and eggs is a horizontal distance in his drawer from the tea. The distance or measured in feet how far from the tea does the ball hit the ground
Answer:
25 ft
Step-by-step explanation:
The path of the golf ball is given by the equation.
[tex]y=x-0.04x^2[/tex]
The point on the ground where the ball will land on the ground is the point where [tex]y=0[/tex].
[tex]x[/tex] is horizontal distance
So
[tex]0=x-0.04x^2\\\Rightarrow x(1-0.04x)=0\\\Rightarrow 1-0.04x=0\\\Rightarrow x=\dfrac{1}{0.04}\\\Rightarrow x=25[/tex]
So, the ball will land 25 ft away from the tee.
least to greatest.
-2 3/4
-3/5
-1 3/4
Answer:
-2 3/4, -1 3/4, -3/5
Step-by-step explanation:
Interpret the remalnder to solve.
1. Hakeem has 100 tomato plants. He wants
to plant them in rows of 8. How many full
rows will he have?
Answer:
Step-by-step explanation:
Interpret the remainder to solve. 1. Hakeem has 100 tomato plants. He wants to plant them in rows of 8. How many full rows will he have? Think: 100 ÷ 8 is 12 with a remainder of 4. The question asks “how many full rows,” so use only the quotient. 2. A teacher has 27 students in her class. She asks the students to form as many groups of 4 ...
Keith needs to read 2 novels each month.
Let N be the number of novels Keith needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Keith needs to read in 19 months.
Equation:
Number of novels in 19 months: novels