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Paladinen [302]
3 years ago
11

a new parking lot is being built for a medical office. the expression representing the number of parking spots in the new lot is

15x/4-9 where x represents the number of parking lots in the first row. how many spots are in the parking lot if there are 32 parking spots in the first row?
Mathematics
2 answers:
nexus9112 [7]3 years ago
5 0
111 parking spots. 15x32 = 480 480 divided by 4 is 120 and 120 - 9 = 111
marusya05 [52]3 years ago
5 0

Answer:

The number of spots in the parking lot if there are 32 parking spots in the first row =111.

Step-by-step explanation:

We are given that a new parking lot is being built for a medical office.

We are given that

The expression representing the number of parking spots in the new lot =\frac{15x}{4}-9

Where x= The number of parking lots in the first row

We have to find number of spots in the parking lot when parking spots in the first row is 32.

The number of parking spots in the first row =x=32

Substitute the value of x in the given expression then we get

Number of spots in the parking lot =\frac{15\times 32}{4}-9

Number of spots in the parking lot=\frac{480}{4}-9

The number of spots in the parking lot=120-9

The number of spots in the parking lot=111.

Hence, the number of spots in the parking lot if there are 32 parking spots in the first row=111.

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Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains liters of a dye solution with a
Alja [10]

Answer:

t = 460.52 min

Step-by-step explanation:

Here is the complete question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 g/liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate.Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution

Let Q(t) represent the amount of dye at any time t. Q' represent the net rate of change of amount of dye in the tank. Q' = inflow - outflow.

inflow = 0 (since the incoming water contains no dye)

outflow = concentration × rate of water inflow

Concentration = Quantity/volume = Q/200

outflow = concentration × rate of water inflow = Q/200 g/liter × 2 liters/min = Q/100 g/min.

So, Q' = inflow - outflow = 0 - Q/100

Q' = -Q/100 This is our differential equation. We solve it as follows

Q'/Q = -1/100

∫Q'/Q = ∫-1/100

㏑Q  = -t/100 + c

Q(t) = e^{(-t/100 + c)} = e^{(-t/100)}e^{c}  = Ae^{(-t/100)}\\Q(t) = Ae^{(-t/100)}

when t = 0, Q = 200 L × 1 g/L = 200 g

Q(0) = 200 = Ae^{(-0/100)} = Ae^{(0)} = A\\A = 200.\\So, Q(t) = 200e^{(-t/100)}

We are to find t when Q = 1% of its original value. 1% of 200 g = 0.01 × 200 = 2

2 = 200e^{(-t/100)}\\\frac{2}{200} =  e^{(-t/100)}

㏑0.01 = -t/100

t = -100㏑0.01

t = 460.52 min

6 0
3 years ago
Point S is on line segment RT. Given RT=4x, ST = 5x-10, and RS = 6 determine the numerical length of ST.
Art [367]

Answer:

ST=10

Step-by-step explanation:

8 0
3 years ago
Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a h
Kipish [7]

Answer:

The home would be worth $249000 during the year of 2012.

Step-by-step explanation:

The price of the home in t years after 2004 can be modeled by the following equation:

P(t) = P(0)(1+r)^{t}

In which P(0) is the price of the house in 2004 and r is the growth rate.

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.

This means that r = 0.047

$172000 in 2004

This means that P(0) = 172000

What year would the home be worth $ 249000 ?

t years after 2004.

t is found when P(t) = 249000. So

P(t) = P(0)(1+r)^{t}

249000 = 172000(1.047)^{t}

(1.047)^{t} = \frac{249000}{172000}

\log{(1.047)^{t}} = \log{\frac{249000}{172000}}

t\log(1.047) = \log{\frac{249000}{172000}}

t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}

t = 8.05

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The home would be worth $249000 during the year of 2012.

8 0
3 years ago
S/4-6.8=-9.8 what does s equal
Hatshy [7]
S/4-6.8=-9.8
S/4= -9.8+6.8
S/4= -3
S=-3*4
S= -12
4 0
3 years ago
What is the quadratic function that is created with roots at 2 and 4 and a vertex at (3, 1)?
Arada [10]
Hello,

y=k*(x-2)(x-4)
and is passing throught (3,1)
==>1=k*(3-2)(3-4)==>k=-1

y=-(x-2)(x-4) is an answer
4 0
3 years ago
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