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AysviL [449]
2 years ago
6

A box contains

Mathematics
1 answer:
Rama09 [41]2 years ago
6 0

The probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

<h3>How to determine the probability</h3>

Note that the ratios =  5:4:2:3

toffee: coffee: orange: mint chocolates = 5:4:2:3:1

Total ratio = 15

Probability of picking a hazelnut chocolate = ratio of hazelnut chocolates/ total ratio

Probability of picking a hazelnut chocolate  = \frac{1}{15}

The number of hazelnut chocolates in the box is gotten from the ratio which is 1

Therefore, the probability of picking a hazelnut chocolate is 1/5 and the number of hazelnut chocolates in the box is 1

Learn more about probability here:

brainly.com/question/24756209

#SPJ1

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Ocean tides can be modeled by a sinusoidal function. Suppose that there is a low and high tide every 12 hours, and that high tid
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(a)y=5sin(\frac{\pi}{6}(x+2))+5

(b) 7.5ft above the low tide.

Step-by-step explanation:

(a) To find the function that computes the height of the tide, you need to select the form of the sinusoidal function. For example, use the form:

y=Asin(B(x-C))+D

Where A is the amplitude, B the frequency, C the phase shift and D the vertical shift.

The  amplitude is half the distance between the highest and the lowest tide:

A=10/2=5ft

The frequency is related to the period T by:

B=\frac{2\pi}{T}

The period is 12 hours, then

B=\frac{2\pi}{12}=\frac{\pi}{6}

The high tide is at 1:00 a.m. and 1:00 p.m. , this is the moment when sin(B(x-C))=1, if sin(\frac{\pi}{2})=1 then B(x-C) must be equal to \frac{\pi}{2} when x=1:

B(x-C)=\frac{\pi}{2}\\\frac{\pi}{6}(1-C)=\frac{\pi}{2}\\\frac{1}{6}(1-C)=\frac{1}{2}\\(1-C)=\frac{6}{2}\\-C=3-1\\C=-2

The vertical shift is the sum of the lowest value, the height of the low tide (lt) and the amplitude:

D=5+lt

The function is:

y=5sin(\frac{\pi}{6} (x+2))+5+lt

Because the function must be the height above low tide height, subtract this heigh from the function:

y=5sin(\frac{\pi}{6} (x+2))+5+lt-lt

y=5sin(\frac{\pi}{6} (x+2))+5

(b) Use x=11 in the function

y=5sin(\frac{\pi}{6} (11+2))+5=2.5+5=7.5ft above the low tide.

3 0
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