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Xelga [282]
3 years ago
14

Please help I am struggling

Mathematics
1 answer:
likoan [24]3 years ago
4 0

☆ The relation between x and y is <u>y</u><u> </u><u>=</u><u> </u><u>a</u><u> </u><u>cos</u><u> </u><u>x°</u><u> </u><u>+</u><u>b</u><u> </u>

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

<h3>→ 1 = b </h3>

<u>Putt</u><u>ing</u><u> the</u><u> </u><u>val</u><u>ue</u><u> of</u><u> </u><u>b</u><u> </u><u>in</u><u> </u><u>equation</u><u> </u><u>1</u><u>s</u><u>t</u><u> </u><u>.</u><u> </u>

→ 9 = a + 1

→ <u>a</u><u> </u><u>=</u><u> </u><u>8</u><u> </u><u>.</u><u> </u>

<u>Now</u><u> </u><u>taki</u><u>ng</u><u> the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>x</u><u> </u><u>acc</u><u>ording</u><u> to</u><u> the</u><u> </u><u>ques</u><u>tion</u><u> </u><u>.</u>

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

<h3>y = 4√2 +1 </h3>

So the answer is <u>4</u><u>√</u><u>2</u><u>+</u><u>1</u><u> </u>

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The equations y=x22−8 and y=2x−2 are graphed below. What are the solutions to the equation x22−8=2x−2?
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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
  • standard deviation \sigma = 2.1.

In other words,

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

and the probability in question is X \le 13.

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.)

P(X\le 13) = P(Z \le 0.857143) \approx 0.8051.

"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.

As a result,

P(X\le 13) = 0.804317.

Number of green beans that are shorter than 13 centimeters:

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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  • Probability of success p: 0.804317.

Let Y be the number of green beans out of this 150 that are shorter than 13 centimeters. Y\sim\text{B}(150,0.804317).

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121

The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.

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Step-by-step explanation:


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