What is .1664 as fraction?

A loan processing office receives 4 loan requests every hour. The office has 2 departments. It takes the first department on ave

jenyasd209 [6]

Answer:

On average how many requests are in the first department (including those who are waiting) is 1.32.

Step-by-step explanation:

In this case, use the Little's law of queuing theory.

The Little's law states that the average number of customers in a fixed system (L) is equal to the average effective arrival rate (λ) multiplied by the average time a customer spends in the system (W).

The number of requests per hour in the 1st department is, λ₁ = 4.

It is provided that 20% are rejected directly by the 1st department without going into the 2nd department.

Then the number of requests per hour is, λ₂ = $4\times 80\%=4\times0.80=3.2$

The average time a customer spends in the 1st department,

W₁ = 20 minutes = 0.33 hours.

The average time a customer spends in the 1st department,

W₂ = 60 minutes = 1 hour

On average how many requests are in the first department (including those who are waiting) is:

L = λ₁ × W₁

= 4 × 0.33

= 1.32

Thus, on average how many requests are in the first department (including those who are waiting) is 1.32.

6 0

4 years ago

A recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, w

charle [14.2K]

Answer:

90% confidence interval for the mean time per week spent listening to the radio is $11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }$ .

Step-by-step explanation:

We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average amount of time spent listening to music = 11.5

s = sample standard deviation = 9.2 hours

n = sample of students = 51

$\mu$ = population mean per week spent listening to the radio

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.676 < $t_5_0$ < 1.676) = 0.90 {As the critical value of t at 50 degree of

freedom are -1.676 & 1.676 with P = 5%}

P(-1.676 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.676) = 0.90

P( $-1.676 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }$ , $11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }$ ]

= [9.34 hours , 13.66 hours]

Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].

4 0

4 years ago

Please help y'all I'd greatllyyy appreciate itt!!!!!!!!!!! (no links)

SIZIF [17.4K]

<h3>Answer: D) The triangles are not similar</h3>

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Explanation:

We can immediately rule out choice C because we don't have info about all three pairs of sides. So that's why we can't use the SSS rule.

We may be able to use SAS however. This rule says that if we know a pair of sides are proportional, and if the angles between them are congruent, then we have similar triangles.

However, note the jump from XZ = 2 to XW = 8 is "times 4" while the jump from XY = 3 to XV = 9 is "times 3". The two multipliers don't match up. We would need them to be the same for the sides to be proportional.

Put another way, the equation

8/2 = 9/3

is a false equation

If we tried the equation

8/3 = 9/2

then that's also false. No matter what combos we try, the sides aren't proportional.

So ultimately, we can't use SAS either. This eliminates choice B.

Consequently, it means that we know the triangles aren't similar. If they were similar, then we'd be able to use SAS to prove them to be so.

Therefore, we do have enough information to conclude that the triangles are not similar.

This is why choice D is the final answer.

4 0

3 years ago

The length of the major axis of the ellipse below is 17 and the length of the red line segment is 6. How long is the blue line s

KatRina [158]

Answer:

Option B. 11

Step-by-step explanation:

See the attached figure

As the figure about an ellipse

So, The sum of distance between A and the foci will be equal the major axis

AB = 6 and the major axis = 17

∴ AB + AC = major axis

∴ 6 + AC = 17

∴ AC = 17 - 6 = 11

So, the length of the blue line segment = 11

5 0

3 years ago

What is the time period and rate if $12000 is borrowed for 2 years at 4% p.a. compounded quarterly?

maria [59]

Answer: t = 2, r = 4%, A = $12,994.28

Step-by-step explanation:

The formula for compound interest is: $A=P_o\bigg(1+\dfrac{r}{n}\bigg)^{nt}$ where

A is the accrued amount
P₀ is the principal (initial amount invested)
r is the rate (convert percent into a decimal)
n is the number of times per year the interest is compounded
t is the number of years the principal is invested

The information provided in the given problem is:

P₀ = 12,000
r = 4% ⇒ 0.04
n = quarterly ⇒ 4
t = 2

$A = 12,000\bigg(1+\dfrac{0.04}{4}\bigg)^{4\cdot 2}\\\\.\quad =12,000(1+0.01)^{8}\\\\.\quad =12,000(1.01)^{8}\\\\.\quad =12,994.28$

8 0

3 years ago