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AVprozaik [17]
3 years ago
12

Lilianna has $68. She needs at least $194 for a new cell phone. Write an inequality to fit this situation. What's the least amou

nt of additional money she needs to buy the new cell phone?
Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Answer:

The least amount of additional money that Lilianna needs is \$126

Step-by-step explanation:

Let

x------> the least amount of additional money

we know that

x+\$68\geq\$194 -----> inequality that represent the situation

Solve for x

x\geq\$194-\$68

x\geq\$126

The minimum amount of money that Lilianna needs is  $126

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The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota
Dafna1 [17]

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

a.

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

b.

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

8 0
3 years ago
I don’t understand this
egoroff_w [7]

Answer: OPTION A

Step-by-step explanation:

The distance between any number is always positive so we should apply the absolute value.

The distance between numbers=number 1-number2 (or vise versa, and that is why we need absolute value)

In your question, the two numbers are 3/4 and 2. Applying to the expression above, the distance between two numbers should be |3/4-2| or |2-3/4|.

The only option in your case is |3/4-2| and this is it.

Hope this helps!! :)

Please let me know if you have any question

5 0
3 years ago
Please help. Thank you.
damaskus [11]
(10x + 4) + (5x-4) ≈ 180

solve for x and you get x≈12 
 
plug 12 in to 5x-4 and you get 56 
7 0
3 years ago
Find the angles please please
IceJOKER [234]
Angle BAC
cosφ⁻¹ = (10² + 17² - 11²)/(2*10*17) = 37.9 ≈ 38°
Angle ACB
cosφ⁻¹ = (10² + 11² - 17²)/(2*10*11) = 108.0°
Angle ABC
cosφ⁻¹ = (11² + 17² - 10²)/(2*11*17) = 34.0°
See you !
6 0
3 years ago
What is the solution to the system of equations? -3x-y+z=6 -3x-y+3z=0 x-3z=3
valentina_108 [34]

Answer:X/3X=3

We move all terms to the left:

X/3X-(3)=0

Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R

We multiply all the terms by the denominator

X-3*3X=0

Wy multiply elements

X-9X=0

We add all the numbers together, and all the variables

-8X=0

X=0/-8

X=0

Step-by-step explanation:

4 0
3 years ago
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