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4 days ago

The function P(t) gives the number of insects in a population at time t. The birth rate for the insects is 6.7 % per unit of tim

e and the death rate is 2 % per unit of time. Give the rate of change of the population with respect to time in terms of P.

Mathematics

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Assume that a study of 500 randomly selected airplane routes showed that 482 arrived on time. Select the correct interpretation

babunello [11817]

Answer: C. Significant at 0.036

Step-by-step explanation:

Given:

Total samples selected Ns= 500

Airplanes that arrived on time Na = 482.

Airplanes that arrived late Nl = 500 - 482 = 18

Calculating the probability of an airplane arriving late:

P(L) = Nl/Ns

P(L) = 18/500

P(L) = 0.036

An event is deemed significant if its probability is equal to or less than 0.05.

As P(L) < 0.05

P(L) = Significant at 0.036

4 0

3 months ago

When the sun is at a certain angle in the sky, a 50-foot building will cast a -foot shadow. What is the length of the shadow in

Svet_ta [12734]

Answer:

0.40 feet

Step-by-step explanation:

For the first scenario, a 50-foot building casts a shadow of 1 foot. Let the angle of elevation of the sun from the shadow be denoted as θ.

Then:

Tan θ = $\frac{opposite}{adjacent}$

Tan θ = $\frac{50}{1}$

Tan θ = 50

⇒ θ = $Tan^{-1}$ 50

= 88.8542

= $88.85^{o}$

The elevation angle is roughly $88.85^{o}$ .

For a 20-foot pole,

Tan θ = $\frac{opposite}{adjacent}$

Tan $88.85^{o}$ = $\frac{20}{x}$

x = $\frac{20}{Tan 88.85^{o} }$

= 0.4015

= 0.40 feet

The length of the pole's shadow is 0.40 feet.

4 0

2 months ago

1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v

Svet_ta [12734]

Answer:

(1) The necessary proportion of spirit to varnish stands at 1:3.

(2) A total of 80 ml of mineral spirit is required.

(3) The ratio of the heights to the widths of the tapestries is 3:2.

Step-by-step explanation:

(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.

Therefore, $\frac{spirit}{varnish}=\frac{25}{75}$

$=\frac{1}{3}$

Consequently, the proportion of spirit to varnish is 1:3.

(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.

Let the total solution quantity be $x$ .

Thus, $240:x=3:4$ .

⇒ $\frac{240}{x}=\frac{3}{4}$

⇒ $3x=240*4$

⇒ $x=\frac{240*4}{3}$

⇒ $x=320$

This means the total solution amounts to 320 ml.

Now, calculating Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.

(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.

Thus, the dimensions become 15m long and 10m wide.

Now, the proportion of Height to Width is 15:10

⇒ $\frac{Height}{Width} =\frac{15}{10}$

⇒ $\frac{Height}{Width} =\frac{3}{2}$

Thus, the proportion of the heights of the tapestries to their widths is 3:2.

8 0

2 months ago