Number of years to make a worth of $45000 with Depreciation rate of 12% and Total worth $45000 is 4 years
Years= 4 year
What is Depreciation?The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used. It allows companies to earn revenue from the assets they own by paying for them over a certain period of time.
Given that:
limousine costs $75000
Depreciation rate = 12% per year= 0.12
Total worth= $45000
By using the formula for year we have
total worth = cost of object [tex](1- Depreciation \;rate)^{year}[/tex]
45000= 75000x [tex](1-0.12)^{year}[/tex]
0.6= [tex](0.88)^{year}[/tex]
Now taking log on both side we have
log 0.6= year x log0.88
-0.2218 = year x -0.05551
year= 4.049
year≈ 4 year(rounding off nearest year)
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Which line is parallel to the line y= x + 7 ?
Answer: y=x+
Step-by-step explanation:
In order for two lines to be paralell, their slopes must be the same but their y intercepts must be different. Therefore, any line that looks like y=x+ (anything but 7) will be paralell.
A juggler throws a ball from an initial height of 4 feet with an initial vertical velocity of 30 feet per second, the height of the ball can be modeled by h= -16t^2 +vt+s where t is the time in seconds the ball has been in the air, v is the initial vertical velocity, and s is the initial height. Write an equation that gives you the height of the feet of the ball as a function of time since it left the jugglers hand? Then calculate if the juggler misses the ball how many seconds does it take to hit the ground?
Answer:
1. h = -16t² + 30t + 4
2. 2 s
Step-by-step explanation:
1. Write an equation that gives you the height of the feet of the ball as a function of time since it left the jugglers hand?
Since the height moved by the ball, h is given by
h = -16t² + vt + s
Since v = initial vertical velocity = 30 ft/s and s = initial height = 4 ft, then
substituting the values of the variables into the equation for h, we have
h = -16t² + vt + s
h = -16t² + 30t + 4
2. Then calculate if the juggler misses the ball how many seconds does it take to hit the ground?
The ball hits the ground when h = 0
So, h = 0 ⇒
-16t² + 30t + 4 = 0
dividing through by -2, we have
8t² - 15t - 2 = 0
Factorizing, we have
8t² - 16t + t - 2 = 0
8t(t - 2) + (t - 2) = 0
(8t + 1)(t - 2) = 0
8t + 1 = 0 or t - 2 = 0
8t = -1 or t = 2
t = -1/8 or t = 2
Since t cannot be negative, t = 2 s
So, the ball hits the ground after 2 s.
After takeoff, a plane flies in a straight line for a distance of 4000 feet in order to gain an altitude of 800 feet. Find the angle of elevation from the ground to the plane.
Need help please, thank you!
Answer:
The angle of elevation from the ground to the plane is 11.5 degrees
Step-by-step explanation:
Given -
Horizontal distance from the point of takeoff to which the plane flies in a straight line = 4000 feet
The vertical distance travelled from the ground to the plane is 800 feet
Angle of Elevation
[tex]Sin X= \frac{800}{4000} \\X = Sin^{-1}\frac{800}{4000}\\X = 11.5[/tex]
The angle of elevation from the ground to the plane is 11.5 degrees
A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 3 cm. If silver is priced at $7.00 per cm", how much will the silver cost to make one solid sphere?
Use 3.14 for , and do not round your answer.
Answer: [tex]\$791.28[/tex]
Step-by-step explanation:
Given
The radius of the sphere is 3 cm
Silver cost [tex]\$7[/tex] per [tex]cm^3[/tex]
The volume of a sphere is [tex]\frac{4\pi}{3}r^3[/tex]
Put the values
[tex]\Rightarrow \dfrac{4\pi}{3}\times 3^3\\\\\Rightarrow \dfrac{4\times 3.14}{3}\times 3\times 3^2\\\\\Rightarrow 113.04\ cm^3[/tex]
The price of this sphere is
[tex]\Rightarrow 113.04\times 7=\$791.28[/tex]
center (3,-2), radius =5
Answer:
(x-3^2+y+2^2 =25
Step-by-step explanation:
4. What is the value of x in the equation 512x3 = 8?
A 3/4
B 3 1/4
C 4
D 1/4
Answer1/4 hope this help
Step-by-step explanation:
How many milliliters equal to 8.25 liters 
Answer: 8,500
Step-by-step explanation:
Answer:
8250 mL
Step-by-step explanation:
Multiply the volume value by 1000
Derek put 10 crickets in his pet lizard’s cage. After one day, Derek’s lizard had eaten 20% of the crickets he had put in the cage. By the end of the next day, the lizard had eaten 25% of the remaining crickets. How many crickets were left in the cage at the end of the second day?
Answer:
6 crickets
Step-by-step explanation:
First day: 20% of 10 is (.20)(10) = 2, so there were 10 - 2 = 8 crickets left.
Second day: 25% of 8 is (.25)(8) = 2, so there were 8 - 2 = 6 crickets left.
In the diagram below of triangle GHIGHI, JJ is the midpoint of \overline{GI} GI and KK is the midpoint of \overline{HI} HI . If JK=-21+9xJK=−21+9x, and GH=-2x+18GH=−2x+18, what is the measure of \overline{GH} GH ? G H
Answer:
25.5
Step-by-step explanation:
2( -21+9x)=2x+18
-42+18x=2x+18
+42 +42
18x=2x+60
-2x -2x
16x=60
60/16=3.75
x=3.75
GH=2x+18
2(3.75)+18
7.5+18=25.5
GH=25.5
Lesson 6 Homework Practice Select an Appropriate Display
URGENT!!!!!!
Dan's car depreciates at a rate of 17% per year.
By what percentage has Dan's car depreciated after 4 years?
Give your answer to the nearest percent.
Answer:
an=yearn−year−0.17n+0.34
Step-by-step explanation:
Answer:
68%
Step-by-step explanation:
17% × 4
68%
pls help this needs to be answered by today.
Anybody know geometry?
hi as a person who is taking geometry, i think i can help
Answer:
7x-3=5x+1 ->x=2
Step-by-step explanation:
to find the x, you would put both equations together like how it is shown above, then try and get x to one side
7x-3=5x+1
+3 +3
7x=5x+4
-5x -5x
2x=4
/2 /2
x=2
Connor makes 3 batches of muffins . Each batch has 12 muffins . Connor eats 2 muffins . What is m, the number of muffins Connor has left
A car travels according to the table of value shown.what equation can be used to predict the distance (d) the car travels in the number of hours (h)
Answer:
Vajsjke
Step-by-step explanation:
ggzodxkdfdjhs
A ladder is leaning against a building. Find the height at which the ladder is touching the building
Answer:
13.9 ft
Step-by-step explanation:
Since the triangle is a right triangle we can use pythagoreom theorm.
16^2=8^2+a^2 (a is the unknown side)
256= 64+a^2
192= a^2
Square root both sides and you get around 13.9 ft
Help please?
.........................
What is (1/2+i √3/2)^5?
Answer:
Hello! I know I am late but here is the answer for anyone else who might need it.
D. 1/2-i√3/2
Step-by-step explanation:
I got it right on edge. Hope this helps!
The value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
What is binomial theorem?
The expression of the form (a+b)^n is expand by binomial theorem.
The expansion is [tex](a+b)^{n}=\sum_{r=0}^{n}{ }^{n} C_{r} a^{n-r} b^{r}[/tex].
What is the value of given expression?Use a=1/2 and b=[tex]b=\frac{i\sqrt{3} }{2}[/tex] into the expansion of binomial.
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\sum_{k=0}^{5}\left(\begin{array}{l}5 \\k\end{array}\right)\left(\frac{1}{2}\right)^{5-k}\left(\frac{\sqrt{3} i}{2}\right)^{k}[/tex]
When k=0 then, [tex]\left(\begin{array}{l}5 \\0\end{array}\right)\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{5 !}{(5-0) ! 0 !}\left(\frac{1}{2}\right)^{5-0}\left(\frac{\sqrt{3} i}{2}\right)^{0}=\frac{1}{32}[/tex]
When k=1 then, [tex]\left(\begin{array}{l}5 \\1\end{array}\right)\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 !}{(5-1) ! 1 !}\left(\frac{1}{2}\right)^{5-1}\left(\frac{\sqrt{3} i}{2}\right)^{1}=\frac{5 \sqrt{3} i}{32}[/tex]
When k=2 then, [tex]\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=\frac{5 !}{(5-2) ! 2 !}\left(\frac{1}{2}\right)^{5-2}\left(\frac{\sqrt{3} i}{2}\right)^{2}=-\frac{15}{16}[/tex]
When k=3 then, [tex]\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=\frac{5 !}{(5-3) ! 3 !}\left(\frac{1}{2}\right)^{5-3}\left(\frac{\sqrt{3} i}{2}\right)^{3}=-\frac{15 \sqrt{3} i}{16}[/tex]
When k=4 then, [tex]\left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{5 !}{(5-4) ! 4 !}\left(\frac{1}{2}\right)^{5-4}\left(\frac{\sqrt{3} i}{2}\right)^{4}=\frac{45}{32}[/tex]
When k=5 then, [tex]\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{5 !}{(5-5) ! 5 !}\left(\frac{1}{2}\right)^{5-5}\left(\frac{\sqrt{3} i}{2}\right)^{5}=\frac{9 \sqrt{3} i}{32}[/tex],
Now we will add all the results to get the expansion of given expression,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{32}+\frac{5 \sqrt{3} i}{32}-\frac{15}{16}-\frac{15 \sqrt{3} i}{16}+\frac{45}{32}+\frac{9 \sqrt{3} i}{32}[/tex]
On simplifying,
[tex]\left(\frac{1}{2}+\frac{\sqrt{3} i}{2}\right)^{5}=\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex]
Therefore, the value of given expression is [tex]\frac{1}{2}-\frac{\sqrt{3} i}{2}[/tex].
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Find an equivalent ratio 24:9
F 6 to 2
H 36 to 13.5
G 5:12
J 6:5
Kyle is practicing for a 3 mile race. His normal time is 23 minutes and 26 seconds. Yesterday it took him 21 minutes and 38 seconds. How much faster was Kyle's time yesterday than his normal time?
Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.
How much faster was Kyle's time yesterday than his normal time?To find the difference in time between Kyle's normal time and yesterday's time, we need to subtract his normal time from yesterday's time:
(21 minutes 38seconds)−(23 minutes 26 seconds)
(21 minutes 38 seconds)−(23 minutes 26 seconds)
We can first convert both times to seconds to make the subtraction easier:
=(21×60+38)seconds
−(23×60+26)seconds
=(21×60+38) seconds−(23×60+26) seconds
=(1298 seconds)−(1406 seconds)
=(1298 seconds)−(1406 seconds)
=−108 seconds
=−108 seconds
The result is negative because Kyle's yesterday's time is faster than his normal time. To find the positive difference, we can multiply by -1:
∣−108∣ =108seconds
∣−108∣= 108 seconds
Therefore, Kyle's yesterday's time was 108 seconds, or 1 minute and 48 seconds, faster than his normal time.
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are 3ab and -8ba like terms?
true or false
Answer:
True
hope this helps
have a good day :)
Step-by-step explanation:
what is the length, in feet, of the hypotenuse of a right triangle with legs that are 6 feet long and 7 feet long, respectively
Answer:
9.22 feet
Step-by-step explanation:
To find the sides of a right triangle, we use the Pythagorean Theorem:
a² + b² = c²
a and b are each one side. c is the hypotenuse.
Let's plug in what we know.
a² + b² = c²
(6)² + (7)² = c²
Evaluate the exponents.
36 + 49 = c²
Add.
85 = c²
Take the square root of both sides.
√85 = √c²
√85 = c
9.22 = c
The hypotenuse is about 9.22 feet long.
Hope this helps!
Solve- 5x - 2(2x - 7) = 2(3x - 1) + [tex]\frac{7}{2}[/tex]
Pls help mehhh
The scale factor of a model car is the actual car is 300. If the model car is 2 in tall, how all is the car
Answer:
600
Step-by-step explanation:
The length of the actual car is 600.
What is a scale factor?Scale factor is that it is a number that multiplies times a given quantity to produce a smaller or larger version of the original number. The ratio of any two corresponding lengths in two similar geometric figures.
For the given situation,
The scale factor of a model car = 2
The length of the model car = 300
The length of the actual car = [tex]300(2)[/tex]
⇒ [tex]600[/tex]
Hence we can conclude that the length of the actual car is 600.
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Find the volume of the solid. Round your answer to the nearest tenth.
Answer:
31.71 mm
Step-by-step explanation:
#1: Find V of cube
(L)(W)(H) = V
(3)(3)(3) = V
27= V
#2: Find V of the half sphere.
3 (diameter) × π = 9.42 (rounded)
9.42/2 (since 9.42 is the volume for a whole sphere)
=4.71
#3: 4.71+27= 31.71
:)
Geometry questionnn!
Answer:
88 units
Step-by-step explanation:
[tex] In\: \triangle OBR \:\&\: \triangle OWN[/tex]
BR || WN (Given)
Therefore,
[tex] \angle OBR \cong \angle OWN[/tex] (Alternate angles)
[tex] \angle BOR \cong \angle WON[/tex] (Vertical angles)
[tex] \therefore \triangle OBR \sim \triangle OWN[/tex] (AA postulate)
[tex] \therefore \frac{OR}{ON} =\frac{BR}{WN} [/tex] (csst)
[tex] \therefore \frac{OR}{56} =\frac{24}{42} [/tex]
[tex] \therefore \frac{OR}{56} =\frac{4}{7} [/tex]
[tex] \therefore OR =\frac{4\times 56}{7} [/tex]
[tex] \therefore OR ={4\times 8} [/tex]
[tex] \therefore OR =32 [/tex]
RN = OR + ON
RN = 32 + 56
RN = 88 units
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 14. What percentage of people has an IQ score greater than 114?
Answer:
15.87%
Step-by-step explanation:
We start with getting the z score
Mathematically , we have this as;
z-score = (x-mean)/SD
where x = 114
z-score = (114-100)/14 = 14/14 = 1
So we want to calculate the probability values that are greater than 1
We can use the standard normal distribution table
so we have P(z> 1) = 0.15866
in percentage, we multiply by 100 and that gives 15.866 which is 15.87 people
A 16 oz package of brown rice costs 79 cents and a 32 oz package of
brown rice costs $2.09. Which package is a better deal?
I have to get this done by tonight please help me!!
Answer:
The 16oz is a better deal
Step-by-step explanation:
32 = 2 * 16
buying 2 packages of 16 oz cost
0.79 * 2 = 1.58
1.58 < 2.09
The 16oz is a better deal
Answer:
The 16 oz package.
Step-by-step explanation:
Make the 16 oz a 32 oz so we can compare the prices
Mutiply 0.79 X 2 = 1.58
The 16 oz is because you can buy it twice making it a 32 oz for less than the orginal 32 oz.
(Compared side by side)
2.09 > 1.58
hope this helped!
Please help FIND DB.....
Margaret and Bethany have a lemonade stand for one week each summer.
Each day they spend $1.50 on the ingredients necessary to make 20 cups
of lemonade. They sell each cup of lemonade for $0.25. How much do the
girls, after expenses, earn on a day that they sell 18 cups of lemonade? *
$6.00
$4.50
$3.50
$3.00
Answer:
6.00
Step-by-step explanation: