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elena55 [62]
3 years ago
7

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordin

ate of P. What is the equation of the curve? (Use x as the independent variable.)
Mathematics
1 answer:
Bess [88]3 years ago
5 0

Answer:

y =5e^{2x}

Step-by-step explanation:

Given that a curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P.

Let y =f(x) be the equation of the curve

Since slope = 2y

we have

\frac{dy}{dx}= 2y\\\\y'     = 2dx\\ln y = 2x+C\\y = Ae^{2x}

To find A

It passes through (0,5)

Substitute x=0 and y=5

5=A

SO equation is

y =5e^{2x}

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Tom deposits $1000 into a savings account. That earns 5% simple interest. He has this account for 7 years. How much does it cont
Arada [10]

Answer:

$1350

Step-by-step explanation:

5% of 1000 is 50

50x7 is 350

1000+350=1350

3 0
2 years ago
The computer that controls a bank's automatic teller machine crashes a mean of 0.6 times per day. What is the probability that,
professor190 [17]

Answer:

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

Mean of 0.6 times a day

7 day week, so \mu = 7*0.6 = 4.2

What is the probability that, in any seven-day week, the computer will crash less than 3 times? Round your answer to four decimal places.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-4.2}*(4.2)^{0}}{(0)!} = 0.0150

P(X = 1) = \frac{e^{-4.2}*(4.2)^{1}}{(1)!} = 0.0630

P(X = 2) = \frac{e^{-4.2}*(4.2)^{2}}{(2)!} = 0.1323

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0150 + 0.0630 + 0.1323 = 0.2103

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

3 0
2 years ago
Use the cubic model y=10x^3-12x to estimate the value of y when x=3
likoan [24]
Y=10(3)^3-12(3)
y=270-36
y=234
7 0
3 years ago
Read 2 more answers
The mean number of hours of part-time work per week for a sample of 526526 college students is 2828. If the margin of error for
sveta [45]

Answer:

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

Step-by-step explanation:

A confidence interval has the following format.

\mu_{x} \pm M

In which \mu_{x} is the mean of the sample and M is the margin of error.

In this problem, we have that:

\mu_{x} = 28, M = 2.2

\mu_{x} - M = 28 - 2.2 = 25.8

\mu_{x} + M = 28 + 2.2 = 30.2

The 99% confidence interval for the mean number of hours of part-time work per week for all college students is between 25.8 and 30.2.

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D-%5Cfrac%7B2%7D%7B3%7D" id="TexFormula1" title="\frac{3}{4}-\frac{2}{3}"
Komok [63]
Lcf= 12


So we’d have
9 - 8
———
12

1
—-
12
8 0
2 years ago
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