Show and explain how replacing one equation by the sum of that equation and a multiple of the other produces a system with the s

Answer:
x > - 11/10
(I’m not certain if this is correct, but if it is, I’m happy to help!)

The third number amounts to 180. To explain, let the third number equal 9x where x is an integer. The prime factorization of 48 is 2*2*2*2*3, while 264 equals 2*2*2*3*11. Then, 9x can be rewritten as 3*3*x, leading to 2*2*2*2*3*3*11*x equaling 7920y for some integer y. Thus, 1584x equals 7920y which simplifies to x = 7920y / 1584 = 5y. With the GCD being 12, x must include 4 as a factor. Since x is a multiple of 5, one possibility is 20, making y equal to 4. Hence, if x = 20, the third number becomes 9*20 = 180, which can be confirmed.

Response:

The first time they meet again at the starting point happens after 336 seconds.

Venu completes 7 laps, while Tanuj finishes 6 laps.

Detailed explanation:

Venu and Tanuj require 48 seconds and 56 seconds, respectively, to finish one lap.

To reconvene at the starting point, the time must be a multiple of both 56 and 48.

Thus, the earliest time they can meet again at the starting position is when they first clash.

This aforementioned first meeting time represents the smallest number divisible by both 56 and 48, which is 336 seconds or equivalently 5 minutes and 36 seconds.

Number of laps by Venu

Number of laps by Tanuj

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

Answer:

Using integer tiles, you would either add five sets of negative two tiles or take away two sets of five positive tiles. On the number line, you would jump 5 spaces to the left

Step-by-step explanation:

I hope this is helpful :)