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4 years ago

Which statement is true about the domain of y = 3(2^-x)? Explain.

1 answer:

8 0

We want to determine the domain of ${y=3 \cdot 2^{-x}=3 \cdot ({2^{-1}})^x=3 \cdot ({ \frac{1}{2}})^x$

any function of the form $y=f(x)=a \cdot b^x$ is called an "exponential function",
the only condition is that b is positive and different from 1, and a is a nonzero real number.

The domain of such functions is all real numbers.

That is for any x, the expression 3(2^-x) "makes sense".

Answer: The domain is all real numbers

You might be interested in

A random sample of 100 people from City A has an average IQ of 120 with a SD of 18. Independently of this, a random sample of 15

Sloan [31]

Answer:

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

$p_v =P(z>1.837)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the average IQ on city A is signficantly higher than city B at 5% of singificance.

Step-by-step explanation:

$\bar X_{A}=120$ represent the mean for sample 1

$\bar X_{B}=116$ represent the mean for sample 2

$s_{A}=18$ represent the sample standard deviation for 1

$s_{B}=15$ represent the sample standard deviation for 2

$n_{A}=100$ sample size for the group 2

$n_{B}=150$ sample size for the group 2

$\alpha$ Significance level provided

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if residents of City A smarter on average, the system of hypothesis would be:

Null hypothesis: $\mu_{A}-\mu_{B}\leq 0$

Alternative hypothesis: $\mu_{A} - \mu_{B}> 0$

We don't have the population standard deviation's, but the sample sizes are large enough we can apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{A}-\bar X_{B})-\Delta}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.837)=1-P(Z$

5 0

3 years ago

What is the solution to the equation 1/3(9x - 6) = 2x 3 ? x =

coldgirl [10]

X is equal to -2/3
if you ever need anymore help with things like this you can go to mathway . com

8 0

3 years ago

To function properly, a water outflow pipe must drop 1 inch for every 22 inches of horizontal distance.

Hitman42 [59]

a. Calculate the slope for this drain pipe.
1/22
b. A rainwater pipe 30 feet long must run under the edge of a roof. What is the minimum vertical distance the pipe must drop between its ends?

Turn 30 feet to inches so 30 * 12 = 360 inches
Now times 1/22 x 360 = 16.32 inches . If they want it in feet just change 16.32 to feet by dividing 16.32 / 12

c. A design calls for a drainage pipe to cross a building 45 feet wide as it drops 25 inches. Is this pip steep enough to function properly? Explain.
Change 45 feet to inches so 45 * 12 = 540

Now times 540 * 1/22 = 24.54 inches so 25 inches would be steep enough since it droops 25 inches.

7 0

3 years ago

Read 2 more answers

Consider the following system of equations, −2x−9y=12−2x−7y=8 The value of x is

joja [24]

The value of x is 23 and the value of y is -6

x = 23

y = -6

You're welcome.

6 0

3 years ago

What is to answer to 10x-x+5=41