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amm1812
3 years ago
5

Roger had $1200. He bought a phone with 0.4 of the money and a helmet with 0.5 of the remaining money. What is the amount of mon

ey Roger had left?
Mathematics
1 answer:
Paul [167]3 years ago
7 0

Answer:

the remaining money is $1189.22

Step-by-step explanation:

You might be interested in
A. Do some research and find a city that has experienced population growth.
horrorfan [7]
A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation N_{t} =N _{0}e^{rt}
where:
N(t) is the population after t years
N_{0} is the initial population 
t is the time in years 
r is the growth rate in decimal form 
e is the Euler's constant 
We now for our investigation that N(t)=238300, N_{0} =192157, and t=10; lets replace those values in our equation to find r:
238300=192157e^{10r}
e^{10r} = \frac{238300}{192157}
ln(e^{10r} )=ln( \frac{238300}{192157} )
r= \frac{ln( \frac{238300}{192157}) }{10}
r=0.022
Now lets multiply r by 100% to obtain our growth rate as a percentage:
(0.022)(100)=2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that N(t)=713777, N_{0} =951307, and t=10. Just like before, lets replace those values into our equation to find r:
713777=951307e^{10r}
e^{10r} = \frac{713777}{951307}
ln(e^{10r} )=ln( \frac{713777}{951307} )
r= \frac{ln( \frac{713777}{951307}) }{10}
r=-0.029
(-0.029)(100)= -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: N(t)=192157e^{0.022t}.
Final equation from point B: N(t)=951307e^{-0.029t}
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations N(t)=192157e^{0.022t} and N(t)=951307e^{-0.029t} and solve for t:
192157e^{0.022t} =951307e^{-0.029t}
\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1
e^{0.051t} = \frac{951307}{192157}
ln(e^{0.051t})=ln( \frac{951307}{192157})
t= \frac{ln( \frac{951307}{192157}) }{0.051}
t=31.36
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be 2(951307)=1902614. Now we can rewrite our equation as: N(t)=1902614e^{-0.029t}. The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
192157e^{0.022t} =1902614e^{-0.029t}
\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1
e^{0.051t} = \frac{1902614}{192157}
ln(e^{0.051t} )=ln( \frac{1902614}{192157} )
t= \frac{ln( \frac{1902614}{192157}) }{0.051}
t=44.95
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit. 

  
8 0
3 years ago
Please someone help me solve this i dpnt know the answer​
kozerog [31]
<h2><u>Answer With Explanation:</u></h2>

<u>Firstly, let's start with <XOZ: =55°</u>

We know that <ZOQ is 70° and angles on a line add up to 180° so we do 180-70=110 110 divided by 2 = 55 so the 2 angles (XOZ & XOP are 55)

<u>Secondly, <OMN, <MON & <ONM = All are 60°</u>

These 2 angles are joined to create an equilateral triangle which always adds up to 180°

So, there are 3 points to this triangle, therefore we divide 180 by 3 which is 60. The angles are 60°

<u>Thirdly, <QON: =55°</u>

This angle lies on the line XON which needs to add up to 180°

As we worked out before, <XOZ was 55°

So, <ZOQ was already given as 70°

We then do 55+70=125 then 180-125=55°

<QON is 55°

(I'm only in Grade 9 LOL)

4 0
2 years ago
Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her fri
Andru [333]

Answer:

Step-by-step explanation:

Total amount of apples that Nicole bought was 6 pounds.

Each pound of apple cost $1.50

This means that the total cost of the 6 pounds of apple that Nicole bought would be

6 × 1.5 = $9

The store had a discount of $2 off her total purchase. This means that the amount that was paid is

9 - 2 = $7

If Nicole and her friend then divided the cost of the purchase evenly, let x represent the amount that each of them would pay. Therefore, the expression that can be used to determine how much Nicole and her friend each paid for the apples would be

x = 7/2

6 0
3 years ago
Please help !! Which of the following are solutions to the equation below? check all that apply
Gala2k [10]
I thike so i would -4 must help u a lot
7 0
3 years ago
Read 2 more answers
Use the Pythagorean Theorem to find the measure of the space diagonal line in the box
madreJ [45]

Answer:

14.42inches

Step-by-step explanation:

Given the following

b = 5 in

c = 8in

we are to find the measure of the space diagonal line

Using the pythagoras theoreml

l^2 = b^2 + c^2

l^2 = 13^2 - 5^2

l^2 = 169 -25

l^2 = 144

l = 12in

To get the measure of the space diagonal line in the box, we will use the pythagoras theorem;

s^2 = l^2 + c^2

s^2 = 144 + 8^2

s^2 = 144 + 64

s^2 = 208

s= 14.42inches

Hence the required length ix 14.42inches

3 0
3 years ago
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