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Mama L [17]
3 years ago
14

How to determine if an expression is rational or irrational?

Mathematics
1 answer:
Neporo4naja [7]3 years ago
4 0
If it is rational, it has a terminating decimal or a repeated decimal number (ex. 56, or 1.25, or 3.666...)

If it is irrational, it is an ongoing number with no pattern (ex. 3.14159265... Which is pi)
You might be interested in
. 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
2 years ago
A seamstress is paid $9.55 for every pair of pants made. how many pants would have to be made to receive $525.00 a week?
Svetlanka [38]
Let the number of pants have to be made be x.

So,

9.55 * x = 525.00

x = \frac{525}{9.55} ≈ 54.97 

Thus, the number of pants have to be made are 54.
8 0
3 years ago
Round 3:38 to the nearest ten
aev [14]

Answer:3

Step-by-step explanation:

Round 3.38 to the nearest ten

Rounding up to the nearest 10, we look at the digits on the left hand side of the decimal point. If the number on the right of the decimal point is less than 5, we ignore it.if it is greater than 5, we add one to the last digit on the right hand side.

In this case, the first digit on the left hand side is less than 5, so we ignore it. Rounding up to the nearest ten,the 0.38 is ignored.

Therefore, it becomes 3.0 = 3

To the nearest ten

7 0
3 years ago
a triangle garden is being formed with stones. the three sides measure 4 meters by 6 meters by 7 meters. which of the following
postnew [5]

all sides of a triangle are equal

3 0
2 years ago
Why can't 1.07 pounds of sugar be compared to 1.23 cups of sugar?
Anuta_ua [19.1K]

Answer:

A pound is a measure of weight and a cup is a measure of volume.

Step-by-step explanation:

5 0
3 years ago
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