The Nile River is 6,690 kilometers long. This is 1,160 kilometers longer than the Yangtze River. How long is the Yangzte River?

goblinko [34]

$D:x-2\ \textgreater \ 0 \wedge 2x-3\ \textgreater \ 0 \wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2 \wedge x\ \textgreater \ \dfrac{3}{2}\wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2\\\\
\ln (x-2) +\ln (2x-3)=2\ln x \\
\ln (x-2)(2x-3)=\ln x^2\\
(x-2)(2x-3)=x^2\\
2x^2-3x-4x+6=x^2\\
x^2-7x+6=0\\
x^2-x-6x+6=0\\
x(x-1)-6(x-1)=0\\
(x-6)(x-1)=0\\
x=6 \vee x=1\\
1\not \in D\\
\boxed{x=6}$

4 0

3 years ago

5. What is the mode in this sequence of numbers? 5, 10, 16, 3, 8, 11, 7, 10,2 I a. 8 b. 5 c. 11 d. 10

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

c, because 3+8 is 11 so c would be correct

5 0

3 years ago

Most college-bound students take either the SAT(Scholastic Assessment Test) or the ACT (which originally stood for American coll

Jlenok [28]

Answer:

Luis would need to have a SAT score of 574.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Nicole's z-score:

ACT scores have a mean of about 21 with a standard deviation of about 5, which means that $\mu = 21, \sigma = 5$