105,159 rounded to the nearest ten thousand

Answer:

B. The triangle.

Step-by-step explanation:

The number of sides decreases by one as you progress down the list.

Answer:

At the α = 0.10 level, there is no substantial evidence indicating that the average vertical jump for students at this school differs from 15 inches.

Step-by-step explanation:

A hypothesis test is necessary to verify the assertion that the average vertical jump of students diverges from 15 inches.

The null and alternative hypotheses are:

The significance level is set at 0.10.

The sample mean recorded is 17, and the sample standard deviation is 5.37.

The degrees of freedom are calculated as df=(20-1)=19.

The t-statistic is:

The two-tailed P-value corresponding to t=1.67 is P=0.11132.

<pSince this P-value exceeds the significance level, the result is not significant. Therefore, the null hypothesis remains unchallenged.

At the α = 0.10 level, there is no compelling evidence that the average vertical jump of students at this school deviates from 15 inches.

The likelihood that at least one trip occurs before Isabella's birth is 0.7627.

Step-by-step explanation:

In this scenario, Isabella has invented a time machine, but she lacks control over where she travels. Each use of the device holds a 0.25 probability of leading her to a time preceding her birth. Over the initial year of trials, she operates her machine 5 times. If we assume every journey has an equal chance of going back in time, we can calculate the odds that at least one of these trips occurs before she was born. Here's the calculation:

The probability of traveling to a time prior to her birth is 0.25.

The chance of not traveling back in time, given that the machine is used 5 times:

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The probability that at least one trip goes before Isabella's birth is equal to 1 minus the probability of not traveling back to that period:

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Consequently, the chance that at least one trip travels before Isabella's birth is 0.7627.

Response:

The more trials conducted, the stronger the observed theoretical trend becomes

Stepwise explanation:

Firstly, we need to define the probabilities,

-Theoretical probability quantifies success versus total possible outcomes of an experiment.

-Experimental probability calculates the ratio of the desired outcome relative to the total attempts made in the experiment.

Accordingly, the reasoning that best supports this is that as the experiment is repeated, the experimental probability aligns more closely with the theoretical probability, because repetition increases the likelihood of achieving predicted results.