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saul85 [17]
3 years ago
10

Write an equation in standard form for the line that passes through the given points (0,-3) and (7,0)

Mathematics
1 answer:
nata0808 [166]3 years ago
3 0

The equation in standard form that passes through (0, -3) and (7, 0) is 3x – 7y = 21

<u>Solution:</u>

Given, two points are (0, -3) and (7, 0)

We have to find that a line that passes through the given two points in standard form.

First let us find the slope of the line that passes through given two points.

The slope of the line "m" is given as:

\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }

\text { So slope of our line }=\frac{-3-0}{0-7}=\frac{-3}{-7}=\frac{3}{7}

Now, let us find the line equation using point slope form:

\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { is point on the line. }

\text { Then, line equation } \rightarrow y-0=\frac{3}{7}(x-7)

7(y – 0) = 3(x – 7)

7y = 3x – 21

3x – 7y = 21

Hence, the line equation in standard form is 3x – 7y = 21.

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3 years ago
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eimsori [14]

Answer:

8 small tables

Step-by-step explanation:

they told you they have 5 large tables that seat 10 guests and 98 guests are coming. You need to subtract 50 from 98 because after you multiple how many guests can sit at each large table by how many large tables they have it equals 50 so 98-50=48 then you need to divide 48 by six because each small table sits six people so 48/6=8 so you need 8 small tables.

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Anettt [7]

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.

  • Number of trials n: 150.
  • 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.

7 0
3 years ago
What factors of 48 are multiples of 4
docker41 [41]
4, 8, 12, 16, and 24
8 0
3 years ago
Read 2 more answers
4.5 (x - 9) = -13.5 plz help
arlik [135]
The answer should be x = 6
3 0
3 years ago
Read 2 more answers
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