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Xelga [282]
2 years ago
7

Solve the following equation simultaneously 1/x-5/y=7, 2/x+1/y=3​

Mathematics
1 answer:
maria [59]2 years ago
6 0

Answer:

  (x, y) = (1/2, -1)

Step-by-step explanation:

Subtracting twice the first equation from the second gives ...

  (2/x +1/y) -2(1/x -5/y) = (3) -2(7)

  11/y = -11 . . . . simplify

  y = -1 . . . . . . . multiply by y/-11

Using the second equation, we can find x:

  2/x +1/-1 = 3

  2/x = 4 . . . . . . . add 1

  x = 1/2 . . . . . . . multiply by x/4

The solution is (x, y) = (1/2, -1).

_____

<em>Additional comment</em>

If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.

A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).

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It's 60 m because 2 cm is 20 mm, and if each mm is 3 m then 20*3 is 60
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Find the missing length.
algol [13]

Answer:

3 \sqrt{13}

Step-by-step explanation:

{6}^{2}  +  {9}^{2}

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3 \sqrt{13}

6 0
3 years ago
. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes
jok3333 [9.3K]

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

P(X = r) = nCr * p^{r}  * (1 - p)^{n - r}

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

5 0
3 years ago
(6 to the power of 3 times 3 to the power of 3) to the power of 2
frosja888 [35]

Answer:

True

Step-by-step explanation:

(6³ * 3³)² = 18⁶

Multiply inside the parenthesis.

(18³)² = 18⁶

When you put powers to powers, they multiply, eg:

(x³)⁴ = x³°⁴ = x¹²

18⁶ = 18⁶

True.

4 0
3 years ago
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