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4 years ago

Is 450 divisible by 5, 9, and 10? explain

Mathematics

2 answers:

oksano4ka [1.4K]4 years ago

7 0

Yes 450 can be equivalent to 45 * 10
45 is divisible by 5 and 9
while 10 is divisible by 10

timurjin [86]4 years ago

6 0

Yes, if you divide 450 by 5 you should get 90, if you divide it by 9 you should get 50, and if you divide it by 10, you should get 45... if you plug it into a calculator then its really easy, if you dont have one available, just remember if it ends in 0 you should be able to divide it by 5 and 10.

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A coin is tossed 71 times and 34 heads are observed. Is the coin fair? Use a 98% level confidence interval to base your inferenc

Fofino [41]

Answer:

a) $\hat p=\frac{34}{71}=0.48$ estimated proportion of heads observed.

b) $Se= \sqrt{\frac{0.479(1-0.479)}{71}}=0.0593$

c) $z_{\alpha/2}=2.33$

d) $0.479 - 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.341$

e) $0.479 + 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.617$

f) In order to be fair the coin needs to have included the 0.5 on the interval, and for this case it's included, so we can say that at 2% of significance we can say that the coin is fair.

Step-by-step explanation:

Notation and definitions

$X=34$ number of heads observed.

$n=71$ random sample taken

$\hat p=\frac{34}{71}=0.479$ estimated proportion of heads observed.

$p$ true population proportion of heads observed.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The point estimator for the population proportion of heads is: Answer with two decimal precision.

$\hat p=\frac{34}{71}=0.48$ estimated proportion of heads observed.

The standard error in this estimate is: Answer with four decimal precision.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And the standard error is given by:

$Se= \sqrt{\frac{\hat p(1-\hat p)}{n}}$

$Se= \sqrt{\frac{0.479(1-0.479)}{71}}=0.0593$

The correct table value for the 98% level confidence interval is: Answer with two decimal precision

For the 98% confidence interval the value of $\alpha=1-0.98=0.02$ and $\alpha/2=0.01$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.33$

The lower end point of the CI is: Answer with three decimal precision.

And replacing into the confidence interval formula we got:

$0.479 - 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.341$

The upper end point of the CI is: Answer with three decimal precision.

$0.479 + 2.33 \sqrt{\frac{0.479(1-0.479)}{71}}=0.617$

And the 90% confidence interval would be given (0.341;0.617).

Based on the confidence interval, it is plausible that the coin is fair.

In order to be fair the coin needs to have included the 0.5 on the interval, and for this case it's included, so we can say that at 2% of significance we can say that the coin is fair.

4 0

4 years ago

The 7th grade has 220 tudents. There are 3/5 girls. How many boys are there in 7th grade

Helga [31]

Answer:

Step-by-step explanation:

Let's see - if there are 3/5 girls, there must be 2/5 boys. Assuming everyone in the class is binary, of course.

So 2/5 of 220 is the number of boys. When you see "of," always think multiplication!

2/5 of 220

2/5 * 220 = 88 boys in 7th grade

3 0

4 years ago

An item is regularly priced at 29. Joe bought it at a discount of 45% off the regular price.

Luden [163]

Answer:

$13.05

Step-by-step explanation:

The prize will be $13.05 after the discount.

29x45%=13.05

29x0.45=13.05

6 0

3 years ago

Alberto conducted an experiment by rolling a fair six-sided number cube 60 times. He rolled a 2 fifteen times. Which statement a

Setler [38]

Answer:

Experimental probability is the probability of what actually happens in the given experiment.

We know that a fair six-sided cube is rolled 60 times and the outcome 2 has occurred 15 times out of 60 times.

Therefore, the experiment probability in the given experiment is:

Experimental probability of rolling 2

$\frac{15}{60}=\frac{1}{4}$

Now, the theoretical probability is the probability of what is expected from the random experiment. We know that a cube has 6 sides and the theoretical probability of getting 2 is given below:

Theoretical probability of rolling a 2

$\frac{1}{6}$