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3 years ago

What restrictions are there on the range of the function H(w) below

2 answers:

5 0

The x-axis serves as a horizontal asymptote for all exponential functions. Exponential functions are of the form f(x) = ax . The domain consists of all real numbers. However, the range only consists of all numbers greater than zero. This is because no matter how large x gets, the graph will shoot upwards towards infinity. If x becomes a negative, we know that we will get f(x) = 1/a2 . The larger the negative number, the closer the function approaches zero. So, for exponential functions we will always have that restriction that the range will only include positive numbers. I hope this answers your question. I believe the statement is true.

olga_2 [115]3 years ago

4 0

Answer:

Apex: H(w) > 0

Step-by-step explanation:

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The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

KatRina [158]

Answer:

a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. 0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean:

$\mu = 47$

(95% of data) range from 19 to 75 beats per minute.

This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So

$4\sigma = 75 - 19$

$4\sigma = 56$

$\sigma = \frac{56}{4} = 14$

a. What is the probability that the heart rate is less than 25 beats per minute?

This is the p-value of Z when X = 25. So

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

$Z = \frac{25 - 47}{14}$

$Z = -1.57$

$Z = -1.57$ has a p-value of 0.0582.

0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. What is the probability that the heart rate is greater than 60 beats per minute?

This is 1 subtracted by the p-value of Z when X = 60. So

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

$Z = \frac{60 - 47}{14}$

$Z = 0.93$

$Z = 0.93$ has a p-value of 0.8238.

1 - 0.8238 = 0.1762

0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. What is the probability that the heart rate is between 25 and 60 beats per minute?

This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So

0.8238 - 0.0582 = 0.7656

0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

3 0

3 years ago

when added to the number that is produced by doubling the number x the result is equal to 8 times the number that is 5 less than

Olenka [21]

X is 4
4+4=8
4is less than 5

6 0

4 years ago

Read 2 more answers

Find x if x-8=2(x+4)

Fofino [41]

Answer:

$x=-16$

Step-by-step explanation:

$x-8=2(x+4)\\x-8=2x+8\\-x=16\\x=-16$

4 0

3 years ago

Read 2 more answers

A car manufacturer estimates that 25% of the new cars sold in one city have defective engine

photoshop1234 [79]

Answer: 672 cars will have defective engine mounds

Step-by-step explanation: 25% of 2,688 is 672

8 0

3 years ago

In 2007, the first generation of the i-phone sold for $499. The average cost of an i-phone today is $999. At a press conference

Gwar [14]

Answer: the statement made by Tim Cook is TRUE

Step-by-step explanation:

Given that;

in 2007 cost of 1st gen iphone = $499 (base year price)

cost of iphone today = $999 (current year price)

Using the Consumer Price Index

the Consumer Price Index = (cost pf product in current years/cost of product base year) × 100

we substitute

CPI = (999/499) × 100

CPI = 200.2004

so the CPI is 100.2004% higher in the current year than in the base year

Checking the inflation rate

IR = (( CPI this year- CPI last year)/CPI last year) × 100

CPI last year (base year) = 100

CPI current year is = 100.2004

IR = (( 100.2004 - 100)/100) × 100

IR = 0.002004 × 100

IR = 0.2004%

THEREFORE the statement made by Tim Cook is TRUE

3 0

3 years ago