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4 years ago

Solve using the elimination method: X-3y=7 3x + 3y=9

Mathematics

1 answer:

sergij07 [2.7K]4 years ago

7 0

Answer:

$x=4\\\\y=-1$

Step-by-step explanation:

Given Equation:

$x-3y=7$ Equation:1

$3x + 3y=9$ Equation:2

Dividing Equation:2 by '3' both the sides:

$x+y=3$

or $x=3-y$ Equation:3

Putting the vale of 'x' in Equation:1

$x-3y=7$

$(3-y)-3y=7\\\\3-y-3y=7\\\\3-4y=7\\\\$

Subtracting '3' both sides

$-4y=7-3\\\\-4y=4$

$y=\frac{4}{-4}$

$y=-1$

Putting value of 'y' in Equation:3

$x=3-y$

$x=3-(-1)\\\\x=3+1\\\\x=4$

The solution of the equations is :

$x=4\\\\y=-1$

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During a 5-year period, 48% of snowstorms in a certain city caused power outages. Thirty dash nine of the snowstorms did not

beks73 [17]

Answer:

Step-by-step explanation:

48% of snowstorms caused power outages, which means 52% did not.

Therefore, 39 is 52% of all snowstorms.

39 = 0.52x

x = 75

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3 years ago

A factory employs over 3000 workers, of whom 30% are women. If the 15 members of the union executive committee were chosen from

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Answer:

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3 years ago

A softball pitcher has a 0.675 probability of throwing a strike for each pitch and a 0.325 probability of throwing a ball. If th

Dafna11 [192]

Answer:

The probability that exactly 19 of them are strikes is 0.1504

Step-by-step explanation:

The binomial probability parameters given are;

The probability that the pitcher throwing a strike, p = 0.675

The probability that the pitcher throwing a ball. q = 0.325

The binomial probability is given as follows;

$p(x) = _{n}C_{x}\cdot p^{x}\cdot q^{1-x}$

Where:

x = Required probability

Therefore, the probability that the pitcher throws 19 strikes out of 29 pitches is found as follows;

The probability that exactly 19 of them are strikes is given as follows;

$\binom{29}{19}(0.675)^{19}0.325^{10} = \frac{29!}{19!\times 10!}\times (0.675)^{19}\times 0.325^{10} = 0.1504$

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8 0

3 years ago

We have five samples of data: sample A with 30 successes of 50 cases, sample B with 600 successes of 1000 cases, sample C with 3

faust18 [17]

Answer:

C. with 3000 successes of 5000 cases sample

Step-by-step explanation:

Given that we need to test if the proportion of success is greater than 0.5.

From the given options, we can see that they all have the same proportion which equals to;

Proportion p = 30/50 = 600/1000 = 0.6

p = 0.6

But we can notice that the number of samples in each case is different.

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size

po = Null hypothesized value

p^ = Observed proportion

Since all other variables are the same for all the cases except sample size, from the formula for the test statistics we can see that the higher the value of sample size (n) the higher the test statistics (z) and the highest z gives the strongest evidence for the alternative hypothesis. So the option with the highest sample size gives the strongest evidence for the alternative hypothesis.

Therefore, option C with sample size 5000 and proportion 0.6 has the highest sample size. Hence, option C gives the strongest evidence for the alternative hypothesis

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4 years ago

If a triangle has an area of 192 mm2, and the

Debora [2.8K]

Answer:32mm

Step-by-step explanation:

area of triangle = 1/2 *base * height

192mm2 = 1/2 *b* 12mm

192 =6b

base=192/6

base= 32mm

3 0

3 years ago