Which of the following equations is written correctly for: 40 is 92% of what number

Which expression can be used to find the volume of the sphere

Zina [86]

Answer:

The formula is

$\frac{4}{3} \pi \times {r}^{3}$

5 0

3 years ago

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.

Ulleksa [173]

Answer:

0.52763 is the probability that the time between the next two calls will be 54 seconds or less.

0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.

Step-by-step explanation:

We are given the following information in the question:

The time between telephone calls to a cable television service call center follows an exponential distribution with a mean of 1.2 minutes.

The distribution function can be written as:

$f(x) = \lambda e^{-\lambda x}\\\text{where lambda is the parameter}\\\\\text{Mean} = \mu = \displaystyle\frac{1}{\lambda}\\\\\Rightarrow 1.2 = \frac{1}{\lambda}\\\\\lambda = 0.84 \\f(x) = 0.84 e^{0.84 x}$

The probability for exponential distribution is given as:

$P( x \leq a) = 1 - e^{\frac{-a}{\mu}}\\\\P(a \leq x \leq b) = e^{\frac{-a}{\mu} -\frac{-b}{\mu}}$

a) P( time between the next two calls will be 54 seconds or less)

$P( x \leq 0.9)\\= 1 - e^{\frac{\frac{-54}{60}}{1.2}} = 0.52763$

0.52763 is the probability that the time between the next two calls will be 54 seconds or less.

b) P(time between the next two calls will be greater than 118.5 seconds)

$p( x > \frac{118.5}{60}) = P(x > 1.975)\\\\ = 1 - P(x \leq 1.975) \\\\= 1 -1+ e^{\frac{-1.975}{1.2}}\\\\= 0.19285$

0.19285 is the probability that the time between the next two calls will be greater than 118.5 seconds.

6 0

3 years ago

Determine the time necessary for P dollars to double when it is invested at interest rate r compounded annually, monthly, daily,

kipiarov [429]

9514 1404 393

Answer:

annually: 9.01 years
monthly: 8.69 years
daily: 8.67 years
continuously: 8.66 years

Step-by-step explanation:

For interest compounded in discrete intervals, the formula is ...

A = P(1 +r/n)^(nt)

We want to find t for P=1 and A=2, so we have ...

2 = (1 +r/n)^(nt)

ln(2) = nt·ln(1+r/n)

t = ln(2)/(n·ln(1+r/n))

A table of values for r=0.08 is attached.

__

For continuous compounding, the formula is ...

A = Pe^(rt)

t = ln(A/P)/r = ln(2)/0.08 ≈ 8.66434 . . . . years

__

annually: 9.01 years
monthly: 8.69 years
daily: 8.67 years
continuously: 8.66 years

5 0

2 years ago

Find the distance of the line segment joining the two points (-4 /2 - /12) and (/32, 2/3)

astraxan [27]

Answer: $4\sqrt{3}$ .

Step-by-step explanation:

Distance formula : Distance between points (a,b) and (c,d) is given by :-

$D=\sqrt{(d-b)^2+(b-a)^2}$

Distance between points $(-4\sqrt{2},\sqrt{12}) \text{ and }(-\sqrt{32}, 2\sqrt{3})$ .

$D=\sqrt{(2\sqrt{3}-(-\sqrt{12}))^2+(-\sqrt{32}-(-4\sqrt{2}))}\\\\=\sqrt{(2\sqrt{3}+\sqrt{2\times2\times3})^2+(-\sqrt{4\times4\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}-\sqrt{2^2\times3})^2+(-\sqrt{4^2\times2}+4\sqrt{2})^2}\\\\=\sqrt{(2\sqrt{3}+2\sqrt{3})^2+(-4\sqrt{2}+4\sqrt{2})^2}\\\\=\sqrt{(4\sqrt{3})^2+0}\\\\=4\sqrt{3}\text{ units}$

Hence, the correct option is $4\sqrt{3}$ .

3 0

3 years ago

Which basic geometric figure is labeled with either one capital letter or three capital letters?

tester [92]

Answer-

An angle is labeled with either one capital letter or three capital letters

Solution-

Point-

As a point is 0 dimensional, so you just need 1 point to define a point.

Line-

As a line is 1 dimensional,so you need 2 points to define a line.

Plane-

A plane is 2 0r 3 dimensional, so you need 3 points to define a plane.

Angle-

An angle measures the amount of turn. An angles is labeled with a single letter at the vertex, as long as it is perfectly clear that there is only one angle at this vertex. Otherwise, it is named according to the intersecting lines with 3 letters.

3 0

3 years ago