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3 years ago

5

G+6>5 solve the inequality please

2 answers:

melomori [17]3 years ago

5 0

<span>Subtract 6 from both sides.</span>

Gnoma [55]3 years ago

4 0

Subtract 6 from both sides and get g is greater than -1.

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Let x denote the courtship time for a randomly selected female–male pair of mating scorpion flies (time from the beginning of in

gavmur [86]

Complete Question:

a) Is it plausible that X is normally distributed?

b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?

Answer:

a) It is plausible that X is normally distributed

b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269

Step-by-step explanation:

a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.

b) Probability that the sample mean courtship time is between 100 min and 125 min

$\mu = 120\\n = 50$

$P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})$

$SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56$

$P(100 < \bar{X}$

From the probability distribution table:

$P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986$

$P(100 < \bar{X}$

6 0

3 years ago

Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

Jamie purchased a DVD that was on sale for 15% off. The sales tax in her county is 5%. Let y represent the original price of the

Triss [41]

Answer:

1.05(0.85y)

Step-by-step explanation:

15% off so .85y and a 5% tax so 1.05(.85y)

6 0

3 years ago

Read 2 more answers

M Enter the number that belongs in<br> the green box

gladu [14]

Answer:

m<C = 180 - (90+32)

= 180 - 122

= 58°

4 0

2 years ago

Can you guys help me again lol-

BartSMP [9]

Answer:

$93 per hour ?

125-405 = 280

280÷3= 93 per hour

4 0

3 years ago

Read 2 more answers