A number cube is rolled and a coin is flipped.

Hello, Can someone please explain on how to do this? thank you!

Marrrta [24]

Steps:

1) determine the domain

2) determine the extreme limits of the function

3) determine critical points (where the derivative is zero)

4) determine the intercepts with the axis

5) do a table

6) put the data on a system of coordinates

7) graph: join the points with the best smooth curve

Solution:

1) domain

The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0

=> x > 3 <-------- domain

2) extreme limits of the function

Limit log (x - 3) when x → ∞ = ∞

Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote

3) critical points

dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)

4) determine the intercepts with the axis

x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4

y-intercept: The function never intercepts the y-axis because x cannot not be 0.

5) do a table

x                          y = log (x - 3)

limit x → 3+            - ∞

3.000000001        log (3.000000001 -3) = -9

3.0001    log (3.0001 - 3) = - 4

3.1                       log (3.1 - 3) = - 1

4                          log (4 - 3) = 0

13                       log (13 - 3) = 1

103                     log (103 - 3) = 10

lim x → ∞             ∞

Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.

7 0

3 years ago

Read 2 more answers

PLEAAASE HELP ME ON #5 PLEAAASE IM DESPERATE IM RLLY SYRESSSEDDD TAKE 45 PTS

Lina20 [59]

I believe the answer should be x equals 37

4 0

3 years ago

Read 2 more answers

Franklin Porter purchased a waterbed for $4,500. He made a 20 percent down payment and financed the remainder. What amount did h

ira [324]

To find the amount that Franklin financed, you will calculate the amount he put down and subtract that from the original price because that is what he still owes.

0.2 x $4500 = $900
$4500 - $900 = $3600.

Porter financed $3600.

You also multiply 0.8 x $4500 because this represents the part out of 100% he still owes. You will get the same answer this way.

3 0

3 years ago

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is

frozen [14]

Answer:

The decision rule for rejecting the null hypothesis is $t < -1.721$

Step-by-step explanation:

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 410 gram setting. It is believed that the machine is underfilling the bags.

At the null hypothesis, we test if the mean weight of the bag is the desired value of 410, that is:

$H_0: \mu = 410$

At the alternate hypothesis, we test if the bag is underfilled, that is, the mean weight is below the desired value, so:

$H_0: \mu < 410$

Type of test:

As we test if the mean is less than a value, we have a left-tailed test.

We have the standard deviation for the sample, which means that the t-distribution is used.

We have 22 - 1 = 21 degrees of freedom, with a level of significance of 0.05.

Using a calculator, the critical value is $t_c = -1.721$

Determine the decision rule for rejecting the null hypothesis.

We reject the null hypothesis if the test statistic is less than the critical value, so the decision rule for rejecting the null hypothesis is $t < -1.721$

3 0

3 years ago

I need this ASAP!!<br><br><br> calculate the rate of change on this graph

Vilka [71]

Answer: The slope is 2

Step-by-step explanation: For questions like these, find 2 points on the graph that are on whole numbers, for example (10,60) and (20,80). Then use the formula y2-y1/x2-x1 to solve for the slope, which would be the same thing as rate of change. 80-60/20-10 which equals 2. The slope would be 2.

8 0

3 years ago