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nasty-shy [4]
2 years ago
14

Which of the following is equivalent to (16 3/2)^1/2 ? O 6 O 8 O 12 O 64

Mathematics
1 answer:
Galina-37 [17]2 years ago
6 0

Step-by-step explanation:

=  { ({16}^{ \frac{3}{2} } )}^{ \frac{1}{2} }

=  { ({( {2}^{4}) }^{ \frac{3}{2} } )}^{ \frac{1}{2} }

=  {2}^{4 \times  \frac{3}{2} \times  \frac{1}{2}  }

=  {2}^{ \frac{12}{4} }

=  {2}^{3}

= 2 \times 2 \times 2

= 8

The answer is B.

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
What is the value of 2x3squared +x2squared when x = 3
irina [24]
I suspect this is what you mean, if let me know
2x(3)^2+x(2)^2
2(3)(9)+3(4)
54+12=66

6 0
3 years ago
What's so special about the relationship between<br> parallel and perpendicular
pishuonlain [190]
Parallel lines never touch they run side by side forever like the rails on railroad tracks
Perpendicular line cross or intersect
8 0
2 years ago
The volleyball team is having a carwash fundraiser. The cost of each car wash is $5. They sold some season ticket packages, whic
noname [10]

Answer:

They need to wash 72 cars

Step-by-step explanation:

2000 - 1640 = 360

360/5 = 72

5 0
2 years ago
If A = 3r^2h^2, and (rh) increases by 100%, then the new A is how many times greater than the old A? PLEASE HELP ME!!! (Specify
Maslowich

Answer: the answer is 3

Step-by-step explanation:

An increase of 100% in the value of (rh) means the value doubles. When that doubled value is squared, the new area is 4 times the old area.The question asks how many times GREATER the new A is than the old A. 4 times AS LARGE AS is a 300% INCREASE, which is 3 TIMES LARGER THAN.So the grammatically correct answer is 3 

3 0
1 year ago
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