What expression is equivalent to 3x + 14 + 3x + 10?

Prove that Tan x + Cos x = 1 /Sin x .Cos x

Anit [1.1K]

Answer:

tanx + cotx = $\frac{1}{sinxcosx}$

Step-by-step explanation:

Explanation

Take R.H.S = $\frac{1}{sinxcosx}$

= $\frac{sin^{2}x+cos^{2}x }{sinxcosx}$

= $\frac{sin^{2}x }{sinx cosx} + \frac{cos^{2} x}{sinxcosx}$

= $\frac{sinx}{cosx} + \frac{cosx}{sinx}$

= tanx + cotx

tanx + cotx = $\frac{1}{sinxcosx}$

5 0

3 years ago

Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636, the central limit theorem appl

lakkis [162]

Answer:

a) $\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)$

$\mu_{\bar X}=100$ $\sigma^2_{\bar X}=1$

b) $P(\bar X >101)=1-P(\bar X$

c) $P(\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$