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bearhunter [10]
3 years ago
11

Solve the system of equations using the Substitution Method (show work)

Mathematics
1 answer:
FromTheMoon [43]3 years ago
3 0
Since both equations have 3y, we will substitute 3y.
2x-3y = 20 eq 1
rearrange
2x - 20 = 3y
sub the value of 3y into eq2
11x + (2x-20) = -1
11x + 2x - 20 = -1
13x = 19
x =19/13

sub value of x into any equation
2(19/13) - 3y =20
38/13 - 20 = 3y
-222/13 = 3y
y = -74/13
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About 16 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probabil
Vinvika [58]

Answer:

(a) 0.0256

(b) 0.2944

Step-by-step explanation:

For solving this exercise we can apply the binomial distribution. The equation that give as the probability is:

P(x,n,p)=(nCx)*p^{x} *(1-p)^{n-x}

Where n is the number of identical events, p is the probability that the event has a success and x is the number of success in the n identical events.

Additionally, nCx is calculated as:

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

So, in this case we have 2 identical events because we are going to select two people randomly and the probability p of success is the probability that the person is allergic to pollen and this probability is 16%.

Then, for the first case, x is 2 because their are asking for the probability that both are allergic to pollen. Replacing the values of x, n and p we get:

P(2,2,0.16)=(2C2)*0.16^{2} *(1-0.16)^{2-2}

P(2,2,0.16)=0.0256

For the second case, their are asking for the probability that at least one is allergic to pollen, that means that we need to sum the probability that both are allergic to pollen with the probability that just one is allergic to pollen.

Using the same equation to calculate P(1,2,0.16) we get:

P(1,2,0.16)=(2C1)*0.16^{1} *(1-0.16)^{2-1}

P(1,2,0.16)=0.2688

So, the probability that at least one person is allergic to pollen is 0.2944 and it is calculated as:

0.0256 + 0.2688 = 0.2944

7 0
3 years ago
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Slove 4x - c = k for x
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2 years ago
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aivan3 [116]

Answer:

a)12 b)12 c)36

Step-by-step explanation:

a)find the least common multiple. the number of marbles is that number * n (where n is an integer)

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c)12*3 =?

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8 0
3 years ago
In 2004, a survey on computer crime indicated that 7% of reported unauthorized uses of business Web sites came from inside the c
masya89 [10]

Answer:

a) H0 : P = 0.07

   Ha : P ≠ 0.07

b) p -value = 0.1770

Step-by-step explanation:

P = 7% = 0.07

x (result ) = 7 , n = 163

p = x / n = 7 / 163 = 0.043

<u>a) Using a significance level ( ∝ ) of 0.05, estimate the appropriate hypothesis</u>

H0 : P = 0.07

Ha : P ≠ 0.07

conduct a  Z- test statistic

Z = ( p - P ) / \sqrt{\frac{P(1-P)}{n} }

  = ( 0.043 - 0.07 ) / \sqrt{\frac{P(1-P)}{n} }  =  - 1.35

Critical value ( Z₀.₀₂₅ ) = ± 1.96

<em>we fail to reject H0 given that | z | < Zcritical because there is not enough evidence to conclude that proportion change</em>

<u>b) Determine the p-value of the test </u>

P-value = P ( | Z | > Z )

             = 2 * P ( Z < -1.35 )

             = 0.1770

The p-value ( 0.1770 ) > ∝ ( 0.05 ) hence we fail to reject H0 ( i.e. the conclusion agrees with part a above )

8 0
3 years ago
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