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bagirrra123 [75]

3 years ago

8

Jose's school spent $1284 on 9 sticksof memory and a new hard drive. The hard drive cost $168. Which is the reasonable estimate

of the cost of one stick of memory?

1 answer:

vekshin13 years ago

5 0

It would be 1284 divided by 9 and then u round it which is 1284 / 9 =142.666 which can be rounded up to 140 or 143

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Theresa has two brothers,Paul and Steve, who are both the same height. Paul says he is 16 inches shorter than 1 1/2 times Theres

shepuryov [24]

Answer:

Theresa's height is 60 inches

Step-by-step explanation:

The given parameters are;

The height of Paul = The height of Steve

Paul's height = $1\dfrac{1}{2}$ times Theresa's height - 16 inches

Steve's height = $1\dfrac{1}{3}$ times Theresa's height - 6 inches

Let 'T' represents Theresa's height, we have;

Paul's height = $1\dfrac{1}{2}$ ×T - 16

Steve's height = $1\dfrac{1}{3}$ ×T - 6

Paul's height = Steve's height

Therefore;

$1\dfrac{1}{2}$ ×T - 16 = $1\dfrac{1}{3}$ ×T - 6

$1\dfrac{1}{2}$ ×T - $1\dfrac{1}{3}$ ×T = 10

$#\dfrac{3}{2}$ ×T - $\dfrac{4}{3}$ ×T = 10

$\dfrac{1}{6}$ ×T = 10

T = 10 × 6 = 60

Theresa's height, T = 60 inches

5 0

2 years ago

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

2 years ago

(7 + 7i)(2 − 2i)

Ostrovityanka [42]

The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

$\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)$

$\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)$

$\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}$

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

=21-21i

After converting into the exponential form:

$\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}$

From part (b) and part (c) both results are the same.

Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

3 0

1 year ago

Write a inequality to represent a number is at most two

Arturiano [62]

Answer:

x≤2

Step-by-step explanation:

8 0

2 years ago

Help pleasee , thank you so much in advance

Tanzania [10]

Pretty sure the answer would be 32. It’s basic subtraction I think.

3 0

2 years ago

Read 2 more answers