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3 years ago

15

Marie is saving $75 each week so she can buy a new laptop which costs $1200. She has already saved $125. Find the minimum number

of weeks she will have to save in order to be able to make this purchase.

1 answer:

hjlf3 years ago

5 0

Answer:

Step-by-step explanation:

$125+75w\ge 1200\\ \\ 75w\ge 1075\\ \\ w\ge 14.33\\ \\ \text{So she must save for at least 15 weeks.}$

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A rectangular field 50m wide and ym long requires 260m fencing. find y

quester [9]

Answer:

5.2m

Step-by-step explanation:

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2 years ago

Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find

MrMuchimi

Answer:

0.0228
0.0231
100 years
0

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

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B) The continuous decay rate is the natural log of the growth factor, so is ...

ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

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C) For y=.10 (1/10 of the original amount) we find x to be ...

.1 = .5^(x/30)

ln(.1) = (x/30)ln(.5) . . . . . take the natural log

30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

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D) As x goes to infinity, y goes to zero.

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The relationship between growth rate and growth factor is ...

growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

8 0

3 years ago

A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose

VLD [36.1K]

Answer:

(a) P(A1 ∪ A2) = 0.35

Step-by-step explanation:

(a) A1 ∪ A2 :

We start by defining the events.

A1 : '' awarded project 1''

A2 : ''awarded project 2''

A3: ''awarded project 3''

In set theory we write the union of events A and B as A∪B.

A∪B means that the event A occurs,event B occurs or either both events occurs at the same time.

The probability is given by the equation :

P(A∪B) = P(A) + P(B) - P(A∩B) (1)

Where the event (A∩B) is the event where A and B occur at the same time

and P(A∩B) is the probability of (A∩B)

Using the equation (1) :

P(A1 ∪ A2) = P(A1) + P(A2) - P(A1∩A2)

P(A1 ∪ A2) = 0.22 + 0.25 - 0.12

P(A1 ∪ A2) = 0.35

7 0

3 years ago

Help pleaseee:)))) <br> If x equals -4, what does -x equal???

Citrus2011 [14]

I would say it equals 4 because if x=-4 than -x should equal 4 i may be wrong though

5 0

2 years ago

Dy/dx= y^4 and y(2)= -1. Y(-1)=

cupoosta [38]

It looks like you're asked to find the value of y(-1) given its implicit derivative,

$\dfrac{dy}{dx} = y^4$

and with initial condition y(2) = -1.

The differential equation is separable:

$\dfrac{dy}{y^4} = dx$

Integrate both sides:

$\displaystyle \int \frac{dy}{y^4} = \int dx$

$-\dfrac1{3y^3} = x + C$

Solve for y :

$\dfrac1{3y^3} = -x + C$

$3y^3 = \dfrac1{-x+C} = -\dfrac1{x + C}$

$y^3 = -\dfrac1{3x+C}$

$y = -\dfrac1{\sqrt[3]{3x+C}}$

Use the initial condition to solve for C :

$y(2) = -1 \implies -1 = -\dfrac1{\sqrt[3]{3\times2+C}} \implies C = -5$

Then the particular solution to the differential equation is

$y(x) = -\dfrac1{\sqrt[3]{3x-5}}$

and so

$y(-1) = -\dfrac1{\sqrt[3]{3\times(-1)-5}} = \boxed{\dfrac12}$

6 0

2 years ago