Interest rate 6% is:

ABCD Is a rectangle that represents a park.

Andru [333]

Answer:

Shortest distance from A to C = 102.9005 m.

Step-by-step explanation:

It is given that, ABCD is a rectangular park.

The length of the park is 80 m.

The breadth of the park is 50 m.

The diameter of the circle = 15 m.

We have to calculate the shortest distance from A to C across the park.

The distance AC = $\sqrt{50^{2}+80^{2} }$ = 94.339 m.

As one has to pass only through the lines shown, he cannot pass through the circle.

So, we have to subtract the diameter of 15 m from AC

=> 94.339 m - 15 m = 79.339 m.

One must pass through either half of the circumference of the circle.

Since, diameter of circle = 15 m, its radius(r) = $\frac{15}{2}$ = 7.5 m.

The circumference of the circle = 2×π×r = 47.123 m.

Half of the circumference = $\frac{47.123}{2}$ = 23.5615 m.

Distance from A to C passing through circumference = 79.339 m + 23.5615 m = 102.9005 m.

As we have to calculate the shortest distance from A to C, one cannot pass from A to C either through B or D,

since the distance ABC or ADC = 50+80 = 130 m.

Therefore, shortest distance from A to C = 102.9005 m.

3 0

3 years ago

Read 2 more answers

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a 5 8 per hour, so that the number o

timurjin [86]

Answer:

(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.

(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.

(c) P (X ≥ 20) = 0.5298 and P (X ≤ 10) = 0.0108.

Step-by-step explanation:

Let the random variable X = number of aircraft arrive at a certain airport during 1-hour period.

The arrival rate is, λt = 8 per hour.

(a)

For t = 1 the average number of aircraft arrival is:

$\lambda t=8\times 1=8$

The probability distribution of a Poisson distribution is:

$P(X=x)=\frac{e^{-8}(8)^{x}}{x!}$

Compute the value of P (X = 6) as follows:

$P(X=6)=\frac{e^{-8}(8)^{6}}{6!}\\=\frac{0.00034\times262144}{720}\\ =0.12214$

Thus, the probability that exactly 6 small aircraft arrive during a 1-hour period is 0.12214.

Compute the value of P (X ≥ 6) as follows:

$P(X\geq 6)=1-P(X$

Thus, the probability that at least 6 small aircraft arrive during a 1-hour period is 0.8088.

Compute the value of P (X ≥ 10) as follows:

$P(X\geq 10)=1-P(X$

Thus, the probability that at least 10 small aircraft arrive during a 1-hour period is 0.2834.

(b)

For t = 90 minutes = 1.5 hour, the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 1.5=12$

The expected value of the number of small aircraft that arrive during a 90-min period is 12.

The standard deviation is:

$SD=\sqrt{\lambda t}=\sqrt{12}=3.464$

The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.

(c)

For t = 2.5 the value of λ, the average number of aircraft arrival is:

$\lambda t=8\times 2.5=20$

Compute the value of P (X ≥ 20) as follows:

$P(X\geq 20)=1-P(X$

Thus, the probability that at least 20 small aircraft arrive during a 2.5-hour period is 0.5298.

Compute the value of P (X ≤ 10) as follows:

$P(X\leq 10)=\sum\limits^{10}_{x=0}(\frac{e^{-20}(20)^{x}}{x!})\\=0.01081\\\approx0.0108$

Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.

8 0

2 years ago

Help with 2 plz I really need help

Kazeer [188]

the whole triangle is call an acute equilibrium triangle if that's the answer your looking for if not I need to see the whole question

4 0

2 years ago

Right △EFG has its right angle at F, EG=8 , and FG=2 .

d1i1m1o1n [39]

Answer:

Tan E = 2 / 7.75

Sin G = 7.75 / 8

Sec G = 4

Step-by-step explanation:

Find the attached document for better illustration of the triangle

Assuming the hypothenus of the triangle is 8 = EG since it's the longest side of the triangle.

FG = 2 = opposite side of the triangle.

We can use pythagorean theorem to find the adjacent of the triangle since we already know two sides.

EG² = FG² + EF²

EF² = EG² - FG²

EF² = 8² - 2²

EF² = 64 - 4

EF² = 60

EF = √(60)

EF = 7.7459 = 7.75

To find the respective trignometric ratio, we can use the relation SOH CAH TOA

Sine = opposite / hypothenus

Cosine = adjacent/ hypothenus

Tangent = opposite/ adjacent

A. tan E

Tan E = opposite/ adjacent

Tan E = 2 / 7.75

Tan E = 0.2580

B. Sin G = opposite / hypothenus

Sin G = 7.75 / 8

Sin G = 0.9687

C. Sec G = 1 / cos G

Cos G = adjacent / hypothenus

Sec G = 1 / (adjacent / hypothenus)

Sec G = hypothenus/ adjacent

Sec G = 8 / 2

Sec G = 4

5 0

3 years ago

What is the value of x in the equation 1,331x^4-216=0?

yarga [219]

The value of x will be obtained as follows:
1331x^4-216=0
1331x^4=216
divide through by 1331
x^4=216/1331
x=(216/1331)^(1/4)
x=(6^3/11^3)^(1/4)
x=(6/11)^(3/4)

8 0

2 years ago