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evablogger [386]

3 years ago

15

Determine the coordinates of the point shown. A coordinate grid shown. There are increments of 0.5 for each grid line on each of

the two axes. A point is located at 3 grid lines to the right and 5 grid lines down from the origin. (3, −5) (1, −2) (1.5, −2.5) (−2.5, 1.5)

1 answer:

Leni [432]3 years ago

3 0

Grid lines to the right represent positive numbers for the first coordinate. 3 of them will put you on a grid line with a value of 3×0.5 = 1.5.

You now know enough to select the correct answer, ...

... (1.5, -2.5)

_____

You can confirm this is the correct answer by figuring the second coordinate. Down represents negative numbers, so down 5 units is -(5×0.5) = -2.5. This matches the second coordinate of the chosen answer.

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A line passes through the point (2, 10) and has a y-intercept of 4. What is the equation of the line?

KatRina [158]

Answer:

$y=3x+4$

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is equal to 0)

<u>1) Determine the slope (m)</u>

$m=\frac{y_2-y_1}{x_2-x_1}$ where two points that the line passes through are $(x_1,y_1)$ and $(x_2,y_2)$

We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.

Plug these points into the equation

$=\frac{10-4}{2-0}\\=\frac{6}{2}\\=3$

Therefore, the slope of the line is 3. Plug this into $y=mx+b$

$y=3x+b$

<u>2) Determine the y-intercept (b)</u>

The y-intercept is given; it is 4. Plug this back into $y=3x+b$

$y=3x+4$

I hope this helps!

3 0

3 years ago

Simplify (2/3x3/5)-(3/4x1/6)

ira [324]

Answer:

11/40

Step-by-step explanation:

2/5 − 3/4 (1/6)

2/5 − 1/8

= 11/40

4 0

3 years ago

Fractions to Decimals 2/2 = 0.2...

MAXImum [283]

It would equal 1.0 because 2/2 is 1.

8 0

3 years ago

The difference of two supplementary angles is 32 degrees. what are the angles

Masteriza [31]

Supplementary means 180

180-32=148 hope this helps

6 0

3 years ago

Read 2 more answers

A company is reviewing a batch of 24 products to determine if any are defective. On average, 3.2% of products are defective.

Svetach [21]

Using the binomial distribution, it is found that:

0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.
0.0066 = 0.66% probability that 4 or more defective products are found in this batch.

-----------------

For each product, there are only two possible outcomes, either it is defective, or it is not. The probability of a product being defective is independent of any other product, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the<u> probability of exactly x successes on n repeated trials.</u>

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of a success on a single trial.

-----------------

24 products means that $n = 24$
3.2% are defective, thus $p = 0.032$

-----------------

The probability that <u>2 or fewer are defective</u> is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{24,0}.(0.032)^{0}.(0.968)^{24} = 0.4582$

$P(X = 1) = C_{24,1}.(0.032)^{1}.(0.968)^{23} = 0.3635$

$P(X = 2) = C_{24,2}.(0.032)^{2}.(0.968)^{22} = 0.1382$

Thus

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4582 + 0.3635 + 0.1382 = 0.9599$

0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.

-----------------

The probability that <u>4 or more are defective</u> is:

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{24,0}.(0.032)^{0}.(0.968)^{24} = 0.4582$

$P(X = 1) = C_{24,1}.(0.032)^{1}.(0.968)^{23} = 0.3635$

$P(X = 2) = C_{24,2}.(0.032)^{2}.(0.968)^{22} = 0.1382$

$P(X = 3) = C_{24,3}.(0.032)^{3}.(0.968)^{21} = 0.0335$

Thus

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.4582 + 0.3635 + 0.1382 + 0.0335 = 0.9934$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.9934 = 0.0066$

0.0066 = 0.66% probability that 4 or more defective products are found in this batch.

A similar problem is given at brainly.com/question/23780714

6 0

3 years ago