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2 years ago

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The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)? please

help!

1 answer:

Rom4ik [11]2 years ago

5 0

Answer:

I think the answer is option b

Step-by-step explanation:

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The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minu

pochemuha

Answer:

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

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:

$\mu = 265, \sigma = 50$

a) What is the probability that a battery lasts more than four hours?

4 hours = 4*60 = 240 minutes

This is 1 subtracted by the pvalue of Z when X = 240. So

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

$Z = \frac{240 - 265}{50}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.309

1 - 0.309 = 0.691

0.691 = 69.1% probability that a battery lasts more than four hours

b) What are the quartiles (the 25% and 75% values) of battery life?

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

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

$-0.675 = \frac{X - 265}{50}$

$X - 265 = -0.675*50$

$X = 231$

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

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

$0.675 = \frac{X - 265}{50}$

$X - 265 = 0.675*50$

$X = 299$

25% value = 231

75% value = 299

c) What value of life in minutes is exceeded with 95% probability?

The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

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

$-1.645 = \frac{X - 265}{50}$

$X - 265 = -1.645*50$

$X = 183$

8 0

2 years ago

Which shows how to solve the equation Three-fourths x = negative 6 for x in one step?

My name is Ann [436]

option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).

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

We have , The given expression as Three-fourths x = negative 6 , which can be written as $\frac{3}{4} (x) = -6$ . Now in order to solve this equation in one step , we must notice that coefficient of x must be 1 but it's $\frac{3}{4}$ , Let's make coefficient of x as 1 by multiplying both side of equations by 4/3:

$\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4} (x) = -6$

⇒ $\frac{3}{4}(\frac{4}{3} ) (x) = -6(\frac{4}{3} )$

⇒ $x = -6(\frac{4}{3} )$

⇒ $x = -2(4)$

⇒ $x = -8$

Therefore, x= -8 & correct option to solve the equation Three-fourths x = negative 6 for x in one step is <u>option A i.e. Three-fourths (four-thirds) x = negative 6 (four-thirds).</u>

7 0

1 year ago

Read 2 more answers

the parent function f(x) = x^3 and a translation, g(x), are shown on the graph. which represents g(x), the translated function?

tangare [24]

y=f(x)+g(x))

y=x³+g(x)

3 0

1 year ago

Carmen buys 4 daisies and some roses to make a flower arrangement. The number of daisies is 1/3 of the number of roses that she

Pani-rosa [81]

12, Carmen buys 12 roses

I got this by multiplying 4x3=12

3 0

2 years ago

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were m

aalyn [17]

This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

Answer: The initial deposit is $10,001

Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

Pv = present value

i = the interest rate

t = the time in years

e = a mathematical constant that is usually approximated by 2.7183

In this case, the Fv = 13,231.30

i = 3.5% or 0.035

t = 8 years

e = 2.7183

Pv = ? (The unknown variable).

13,231.30 = Pv × [2.7183^(0.035 × 8)]

13,231.30 = Pv × [2.7183^(0.28)]

13,231.30 = Pv × 1.323

Pv = 13,231.30/1.323

Pv = $10000.98

= $10,001

Therefore the initial deposit is $10,001

8 0

1 year ago