Elena writes the equation 6x + 2y = 12. Write a new equation that has:

Answer:

The small puzzle took 16% of the total time while the large puzzle took 84%.

Step-by-step explanation:

The result is 8. Vanilla makes up 26%, which translates to 13 from 50, whereas chocolate at 42% gives 21. The difference is 21-13=8.

Answer:

(a) P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) P(X ≥ 13.01) = 0.3075

Step-by-step explanation:

To address this problem, one needs to grasp the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems involving normally distributed samples are resolved through the application of the z-score formula.

In a data set with a mean and standard deviation , the z-score for a measurement X is defined as:

The Z-score indicates how many standard deviations the measurement deviates from the mean. After determining the Z-score, one can consult the z-score table to find the relevant p-value for that score. This p-value represents the probability that the measure's value is less than X, which indicates the percentile of X. By subtracting this p-value from 1, we obtain the likelihood that the measure's value exceeds X.

Central Limit Theorem

According to the Central Limit Theorem, for a normally distributed random variable X with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated by a normal distribution, characterized by mean and standard deviation .

The Central Limit Theorem can also be applicable to a skewed variable, provided that n is 30 or more.

In this case, we are given that:

(a) Compute P(12.99 ≤ X ≤ 13.01) when n = 16.

In this scenario, we find

This probability equates to the p-value of Z at X = 13.01 minus the p-value of Z at X = 12.99.

X = 13.01

According to the Central Limit Theorem

has a p-value of 0.6915

X = 12.99

yields a p-value of 0.3075

0.6915 - 0.3075 = 0.3840

P(12.99 ≤ X ≤ 13.01) = 0.3840

(b) What is the probability that the sample mean diameter is greater than 13.01 when n = 25?

P(X ≥ 13.01) =

This is obtained by subtracting the p-value of Z when X = 13.01 from 1. Hence

has a p-value of 0.6915

1 - 0.6915 = 0.3075

P(X ≥ 13.01) = 0.3075

Step-by-step explanation: We have the dimensions of a rectangular field given in feet. We are informed that an extension of feet is made to each side. Therefore, the new dimensions can be calculated accordingly. Hence, they are presented as .

Since the ball achieves a peak height of 18 meters at 1 second, it will begin descending thereafter. Therefore, we anticipate that the height will drop below 18 m after 1.5 sec.

f(x) = –10x2 + 20x + 8
f(x) = –10(1.5^2) + 20(1.5) + 8
f(x) = 15.5 m

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