1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
denpristay [2]
3 years ago
13

Shortern this expression pls​

Mathematics
1 answer:
pogonyaev3 years ago
4 0

Answer:

c =\frac{8}{3}

Step-by-step explanation:

Given

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Required

Shorten

We have:

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}}

Rationalize

c = \sqrt{\frac{4 + \sqrt 7}{4 - \sqrt 7} * \frac{4 + \sqrt 7}{4 + \sqrt 7}} +  \sqrt{\frac{4 - \sqrt 7}{4 + \sqrt 7}*\frac{4 - \sqrt 7}{4 - \sqrt 7}}

Expand

c = \sqrt{\frac{(4 + \sqrt 7)^2}{4^2 - (\sqrt 7)^2}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{4^2 - (\sqrt 7)^2}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{16 - 7}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{16 - 7}

c = \sqrt{\frac{(4 + \sqrt 7)^2}{9}} +  \sqrt{\frac{(4 - \sqrt 7)^2}{9}

Take positive square roots

c =\frac{4 + \sqrt 7}{3} +  \frac{4 - \sqrt 7}{3}

Take LCM

c =\frac{4 + \sqrt 7 + 4 - \sqrt 7}{3}

Collect like terms

c =\frac{4  + 4+ \sqrt 7 - \sqrt 7}{3}

c =\frac{8}{3}

You might be interested in
How does knowing the double 6+6=12 help solve the near double 6+7=13?
Yakvenalex [24]

Because, if 6 + 6 = 12, then in 6 + 7, 7 can be splitted into 6 + 6 + 1, and so you find it easier...!!

7 0
3 years ago
Can someone help me with this please it would be a big help
Anuta_ua [19.1K]
Answer in order

----------
answer
A. -4.6 - (0.4 + 7.2)

----------------
answer
B. -10 + (-90) + (-40)

--------
answer

associate property of addition

------------------

answer
Commutative <span>Property
</span>
--------------------

answer
-147
7 0
3 years ago
Name three numbers whose product is about 9,000
Fed [463]
1x9000
3x3000
2x4500 
I hope this is what you are looking for
5 0
3 years ago
Read 2 more answers
Help------------------------------------
Liula [17]

Answer:

7)141

8)65

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre
Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that p = 0.09

41 people arrested for DUI in Illinois are selected at random.

This means that n = 41

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1).

Then

P(X \geq 1) = 1 - P(X = 0)

In which

P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

E(X) = np = 41*0.09 = 3.69

d. What is the standard deviation of the number of repeat offenders?

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83

4 0
2 years ago
Other questions:
  • Find the total area for the regular pyramid.<br><br><br><br> T. A. =
    12·2 answers
  • What is a real world situation that can be modeled by the equation 1.25x = 0.75 + 50?
    15·2 answers
  • 11499 round to the nearest thousand
    15·2 answers
  • Hello i need help plz
    12·1 answer
  • Will Give Brainliest!<br><br><br>Find the function rule.
    11·1 answer
  • Please help me now ​
    9·1 answer
  • A $100 pair of headphones is marked down by 10% and you also have a 20% off coupon. What is the final price, before tax?
    15·1 answer
  • 40 divided by 28! HURRY!!
    10·1 answer
  • Problem 1.(32 points) A random sample of 100 Uber rides in Chicago has on average 5.4miles per ride. Assume the distribution of
    11·1 answer
  • Please someone help me out asap! Need this done
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!