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2 years ago

Find the domain (d) range(r) and asymptote (a) of the graph f(x)=5^x+6

Mathematics

1 answer:

Temka [501]2 years ago

7 0

Answer:

D= R

R =(6,∞)

A: y=6

Step-by-step explanation:

We are asked to Find the domain (D ) range(R) and Asymptote (A) of the graph $f(x)=5^x+6$

Our function $f(x)=5^x+6$ is an translated function of

$f(x)=5^x$ which is an exponential function. Therefore the basic properties remains the same.

Any exponential function is defined for all values of x and Hence

however, The range of exponential functions is always positive from 0 to infinity . however here we have 6 added to out parent exponential function and hence the Range of exponential function is always be

Range = (6,∞)

Asymptote : Asymptote of our parent exponential function is y = 0, but in our function $f(x)=5^x+6$ , the asymptote will be y=6

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The Venn Diagram below models probabilities of three events, A,B, and C.

Keith_Richards [23]

Answer: dependent

Step-by-step explanation:

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2 years ago

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A person sights a boat from 235 feet above sea-level as shown. If the angle of depression from the man to the boat is 21 , then

Evgen [1.6K]

Answer:

B = 612.2 ft

Step-by-step explanation:

Solution:-

- The elevation of person, H = 235 ft

- The angle of depression, θ = 21°

- We will sketch a right angle triangle with Height (H), and Base (B) : the boat's distance to the edge of the cliff and the angle (θ) between B and the direct line of sight distance.

- We will use trigonometric ratios to determine the distance between boat and the edge of the cliff, using tangent function.

tan ( θ ) = H / B

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2 years ago

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You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence

Alla [95]

Answer:

$122 \leq \mu \leq 138$

The 95% confidence interval would be given by (122;138)

And the correct interpretation for this case is:

c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % where by a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.06$