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zavuch27 [327]
2 years ago
15

Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

Mathematics
1 answer:
Eddi Din [679]2 years ago
4 0

9514 1404 393

Answer:

  x = -6 or 6

Step-by-step explanation:

The square root is always positive, so the equation simplifies to ...

  \sqrt{4x^2}-\sqrt{x^2}=6\\\\2|x|-|x|=6\\\\|x|=6\\\\x=\{-6,\ 6\}

_____

The graph shows the solutions to f(x) = 0, where f(x) = √(4x²) -√(x²) -6.

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The thumb length of fully grown females of a certain type of frog is normally distributed with a mean of 8.59 mm and a standard
PilotLPTM [1.2K]

Answer:

21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 8.59, \sigma = 0.63

Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

This is 1 subtracted by the pvalue of Z when X = 9.08. So

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

Z = \frac{9.08 - 8.59}{0.63}

Z = 0.78

Z = 0.78 has a pvalue of 0.7823

1 - 0.7823 = 0.2177

21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

8 0
3 years ago
Spongebob and Patrick will be renting paddleboards while on vacation. Shop A rents
Alenkasestr [34]

Answer:

shop B

Step-by-step explanation: 3.80*2=7.6

5 0
3 years ago
gary started measuring change in temperature every hour. in the first hour it went up by 1 degree. during the second hour it wen
DochEvi [55]

Answer:

the answer is 1+ (-13)= -12

5 0
3 years ago
Can somebody help me?
kari74 [83]

Answer:

6

Step-by-step explanation:

Arc length = radius * central angle

s = rθ

A circle is 2π radians, so 1/3 of that is 2/3 π.

Given that s = 12 and θ = 2/3 π:

12 = r (2/3 π)

r = 18/π

r ≈ 6

7 0
3 years ago
Jessica‘s mom is 30. Jessica‘s daughter is zero years old. Jessica‘s mom had Jessica at 15 years old. Jessica is 15 years old. J
TiliK225 [7]

Answer:

135y/o

105years apart

Step-by-step explanation:

Assuming that every mother in the family has their child at 15, Jessica‘s great great great great great great grandma is 135 (45 +15years for every 'great')

Jessica is fifteen (fifteen years younger than her mom, who is 30), so she and her great great great great great great grandma are 105 years apart.

4 0
2 years ago
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