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coldgirl [10]
3 years ago
6

Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested i

n living. (2 points)

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
3 0
Check the picture below.

to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line <span>y = 3x − 6.

and then you do a "true" or "false" check.

now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.

so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.

y < 3x - 6

y = 0,  x = 0  thus

0 < 3(0) - 6

0 < -6   <--- now, is that really true? is 0 lesser than -6? not quite, is false.

recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.

because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.

we can run a quick check on that btw, say on point 4,4

y =4,   x = 4  thus

4 < 3(4) - 6

4 < 12 - 6

4 < 8    <---- yeap, is true, 4 is lesser/smaller than 8.

hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike </span>⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.

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(MC)
Juli2301 [7.4K]

Answer:

Square root 112 Units.

Step-by-step explanation:

See the image attached for the work.

6 0
3 years ago
Simplify a polynomial: (3x–4y)²–(3x–4y)(3x+4y)
Vika [28.1K]

Step-by-step explanation:

(3x-4y)×(3x-4y-(3x+4y))

(3x-4y)×(3x-4y-3x-4y)

(3x-4y)×(-8y)

-8y×(3x-4y

8 0
3 years ago
Read 2 more answers
A-One Talent Agency has 108 clients. 42 of the clients play piano and 51 of the clients play guitar.
Butoxors [25]

Thwre are 28 clients who don not play any of the instrument using the principle of Venn distribution.

<u>Using a Venn diagram analogy</u> :

  • Total number of client, U = 108
  • Piano, P = 42
  • Guitar, G = 51
  • Piano and Guitar, (PnG) = 13
  • None =?

<u>From the information given</u> :

  • P only = 42 - 13 = 29
  • G only = 51 - 13 = 38

<u>The total number of clients can be related thus</u> :

  • Total = P only + G only + PnG + None

108 = 29 + 38 + 13 + None

108 = 80 + None

None = 108 - 80

None = 28

Therefore, the number of clients who do not play any of the instruments is 28

Learn more :brainly.com/question/12570490

7 0
3 years ago
PLEASEEEEE HELPPPPP!!!!
Dmitry_Shevchenko [17]

Step One

Find AM

Formula

AM = MN - AN

Givens

MN = 67.2

AN = 32

Solution

AM - 67,2 - 32

AM = 35.2

Step Two

Set up a solution

67.2/35.2 = 81.9/x            Cross Muliply

67.2 * x   =    81.9 * 35.2   Combine the right

67.2 * x = 2882.88            Divide by 67.2

x = 2882.88/67.2

x = 42.9                             Answer

3 0
3 years ago
Which statement is not true for a binomial distribution with n = 15 and p = 1/20 ? a) The standard deviation is 0.8441 b) The nu
malfutka [58]

Answer:

d) The highest probability occurs when x equals 0.7500

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability, given by the following formula:

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

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

In this problem, we have that:

n = 15, p = \frac{1}{20}

a) The standard deviation is 0.8441

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15*0.05*0.95} = 0.8441

This is correct

b) The number of trials is equal to 15

n is the number of trials and n = 15. So this option is correct.

c) The probability that x equals 1 is 0.3658

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

P(X = 1) = C_{15,1}.(0.05)^{1}.(0.95)^{14} = 0.3658

This option is correct.

d) The highest probability occurs when x equals 0.7500

False. The number of sucesses is a discrete number, that is, 0, 1, 2,...,15. P(X = 0.75), for example, does not exist.

e) The mean equals 0.7500

E(X) = np = 15*0.05 = 0.75

This option is correct.

f) None of the above

d is false

3 0
3 years ago
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