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2 years ago

Tell whether (-9,2) is a solution of x+3y≥-2

Mathematics

2 answers:

jok3333 [9.3K]2 years ago

8 0

Step-by-step explanation:

Substitute the point (-9, 2) into the inequality:

$-9+3(2)\geq 2$

Simplify:

$-3\geq -2$ False.

-3 isn't greater than or equal to -2.

(-9, 2) is not a solution of $x+3y\geq -2$

WARRIOR [948]2 years ago

3 0

Answer:

Not a solution

Step-by-step explanation:

Plug the coordinates and check

$x+3y\geq-2\\\\(-9)+3(2)\stackrel{?}{\geq}-2\\\\-9+6\stackrel{?}{\geq}-2\\\\-3\stackrel{?}{\geq}-2\\\\-3\ngeq-2$

Therefore, $(-9,2)$ is not a solution of $x+3y\geq2$

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The U.S. government has devoted considerable funding to missile defense research over the past 20 years. The latest development

Bad White [126]

Answer:

a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

b) $X \sim Bin(n =20, p=0.8)$

c) $P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

d) $P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

e) $E(X) = np = 20*0.8 = 16$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

Part a

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

Part b

$X \sim Bin(n =20, p=0.8)$

Part c

For this case we just need to replace into the mass function and we got:

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

Part d

For this case we want this probability: $P(X\geq 15)$

And we can solve this using the complement rule:

$P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

Part e

The expected value is given by:

$E(X) = np = 20*0.8 = 16$

5 0

3 years ago

Two numbers are in the ratio 2:3 and their sum id 45 then find both number

Goryan [66]

Answer:

Step-by-step explanation:

Let the two numbers be 2x and 3x.

According to the question,

2x+3x=45

5x=45

x=45/5

x=9

so th required numbers are 18 and 27 as

2x=2*9=18

3x=3*9=27

8 0

3 years ago

Read 2 more answers

What is the y-intercept of the line described by the equation below? y = 7x + 4

zlopas [31]

Answer:

The y-intercept is 4

Step-by-step explanation:

y=mx+b

m=the slope

b=the y-intercept

Hope this helps .-.

8 0

3 years ago

Write an inequality for the given graph.

Aliun [14]

Y=MX+B

M = slope

B = y intercept (number that intersects with the line in the y axis)

y=-3/4x+2

It starts on the y intercept (2) then we travel to the next point (4 on the x axis)

So we travel 3 spaces down (-3) landing on the origin (0,0) then four spaces to the right (4). Getting the slope of -3/4 (rise over run)

Then just plug in these into the equation

y = -3/4 + 2

5 0

3 years ago

Give the slope and the y-intercept of the line y=9x+7 . Make sure the y-intercept is written as a coordinate.

nekit [7.7K]

Answer:

The slope is 9

The y intercept is (0,7)

Step-by-step explanation:

y=9x+7

The equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 9

The y intercept is (0,7)

7 0

3 years ago