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3 years ago

Please help I am struggling

Mathematics

1 answer:

likoan [24]3 years ago

4 0

☆ The relation between x and y is y = a cos x° +b 

Taking 1st condition from the table .

→ x = 0 and y = 9

→ y = a + cos 0° + b

→ 9 = a + cos 0° + b

☆ We know that cos 0° = 1

→ 9 = a(1) + b

<h3>→ a + b = 9. equation 1st </h3>

Now taking other condition

→ x = 90° and y = 1

→ y = a cos 90° + b

→ 1 = a cos 90° + b

☆ We know that cos 90° is 0

→ 1 = a(0) + b

Putting the value of b in equation 1st . 

→ 9 = a + 1

→ a = 8 . 

Now taking the value of x according to the question .

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

So the answer is 4√2+1 

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Answer:

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be $X$ centimeters.

$X$ follows a normal distribution with

mean $\mu = 11.2$ and
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In other words,

$X\sim \text{N}(11.2, 2.1^{2})$ ,

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Z-score table approach:

Find the z-score of this measurement:

$\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143$ . Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that $Z$ will be less than or equal to the z-score in question. (In case the question is asking for the probability that $Z$ is greater than the z-score, subtract the value from table from 1.)

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"Technology" Approach

Depending on the manufacturer, the steps generally include:

Locate the cumulative probability function (cdf) for normal distributions.
Enter the lower and upper bound. The lower bound shall be a very negative number such as $-10^{9}$ . For the upper bound, enter $13$
Enter the mean and standard deviation (or variance if required).
Evaluate.

For example, on a Texas Instruments TI-84, evaluating $\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )$ gives $0.804317$ .

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Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

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