g European roulette. The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A bal

We determine that the true average calorie content as estimated in the sampled population surpasses the actual calorie content. Step-by-step explanation: An article discussed a pilot study where each of the 58 participants was asked to estimate the calorie count of a 12 oz beer known to have 153 calories. The observed sample mean of calorie estimation was 193, with a sample standard deviation of 88. Let = true average estimated calorie level within the sampled population. Thus, Null Hypothesis, : 153 calories {indicating that the true average estimated calorie content does not exceed the actual amount}. Alternative Hypothesis, : > 153 calories {indicating the true average estimation exceeds the actual}. The appropriate test statistic would be a one-sample t-test statistic, as we lack knowledge of the population standard deviation; Test Statistic = ~t =

where, sample mean estimated calorie level = 193 calories, s = sample standard deviation = 88, and n = sample size = 58. Therefore, the test statistic = ~t = 3.462. The t-table indicates a critical value of 1.6725 for 57 degrees of freedom at a 0.05 significance level. Since our test statistic of 3.462 > 1.6725, we have sufficient evidence to reject the null hypothesis; thus, affirming that the true average estimated calorie content in the sampled population exceeds the real content.

You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)

A(n)=a(1)+(n-1)d=
a(n)=2+(n-1)2=2+2n-2=2n

Answer:

Option C is the right choice.

Step-by-step explanation:

The given coordinates define a rectangle, and our objective is to show that the diagonals JL and KM are congruent.

We know that rectangles possess four right angles.

To prove the congruence of the diagonals JL and KM, we will utilize the Pythagorean theorem.

In triangle KLM, KL has a length of b units while LM has a length of a units. By applying the Pythagorean theorem

In triangle JML, JM is b units long, and LM remains a units long. We again can apply the Pythagorean theorem

Thus, we find that and option C is the correct choice.

Let X denote <span>the baby’s weight.
Let y represent </span>the doctor’s weight.
Let z stand for the nurse’s weight.

From the equations: x + y = 78 implies y = 78 - x
and x + z = 69 gives z = 69 - x
then we have x + y + z = 142

Substituting y = 78 - x and z = 69 - x into the equation x + y + z = 142

x + y + z = 142
x + 78 - x + 69 - x = 142
-x + 147 = 142
-x = -5
x = 5

Conclusion

<span>the baby’s weight was 5 kg</span>