What is the function value of f 4

What is the remainder when x^3 -1 is divided by (x+2)

Gnom [1K]

Answer:

Use m athway

Step-by-step explanation:

6 0

2 years ago

Which exponential function is graphed here?

jek_recluse [69]

Answer:

y = 5^x

Step-by-step explanation:

y= b*(a)^x + c

c could = 1 but then you would not have an exponential function. c = 0 because the graph follows the x axis up until x = -2. Suppose c = 1. The the graph would follow y = 1 up until x = - 2

When x = 0, y = 1 which means that b. If b is anything but 0 or 1 then the y intercept would be stretched to a different place. If be = 0 then y would = 0.

So the graph is of the form y = a^x

Now when x = 0 the graph, the y intercept is y = a^0 or y = 1 So the y intercept is (0,1)

Now the next point is thing to solve for is a.

When x = 1, y = 5 (read the graph)

y = a^x

5 = a^1

5 = a because a^1 is a.

Answer

y = 5^x.

5 = a^1

4 0

2 years ago

A new shopping mall is gaining in popularity every day since it open the number of shoppers is 20% more than the numbers of shop

erastovalidia [21]

Answer: the number of shoppers on the first day is 125

Step-by-step explanation:

The number of shoppers is 20% more than the numbers of shoppers the day before. It means that the number of shoppers is increasing in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1 + 20/100 = 1.2

n = 4(first 4 days)

S4 = 671

Therefore, the expression for the first 4 days is

671 = (a × 1.2^(4) - 1)/1.2 - 1

671 = (a × 1.2^(4) - 1)/0.2

671 = 1.0736a/0.2

671 = 5.368a

a = 671/5.368

a = 125

3 0

2 years ago

A computer system uses passwords that are six characters, and each character is one of the 26 letters (a–z) or 10 integers (0–9)

Blababa [14]

First of all, since we have 36 characters available per spot (26 letters and 10 digits), and we have 6 spots, we have a total of

$36^6$

possible passwords.

Event A happens if the password starts with either a, e, i, o or u. If we fix the first character, we're left with 36 characters available for each of the remaining 5 spots, leading to a total of

$5\cdot 36^5$

possible passwords.

So, the probability of event A, computed as the ratio between "good" cases and all possible cases, is

$\dfrac{5\cdot 36^5}{36^6}=\dfrac{5}{36}$

Event B works exactly the same, since we're fixing the last spot, leaving 36 characters available for each of the first 5 spots. So, we have

$P(A)=P(B)=\dfrac{5}{36}$

As for the intersection, we want the first character to be a vowel, and the last character to be an even digits. There are 25 passwords satisfying this request:

$axxxx0,\ axxxx2,\ axxxx4,\ axxxx6,\ axxxx8$

$exxxx0,\ exxxx2,\ exxxx4,\ exxxx6,\ exxxx8$

$ixxxx0,\ ixxxx2,\ ixxxx4,\ ixxxx6,\ ixxxx8$

$oaxxxx0,\ oxxxx2,\ oxxxx4,\ oxxxx6,\ oxxxx8$

$uxxxx0,\ uxxxx2,\ uxxxx4,\ uxxxx6,\ uxxxx8$

Where x can be any of the 36 characters.

So, we have 25 cases with 4 vacant slots, leading to a probability of

$P(A\cap B)=\dfrac{25\cdot 36^4}{36^6}=\dfrac{25}{1296}$

Finally, you can compute the probability of the union using the formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Since we already computed all these quantities.

7 0

2 years ago

A dartboard has a diameter of 18 inches.What are its radius and circumference?

allsm [11]

Diameter of the dartboard as given in the question = 18 inches
Then
Radius of the dartboard will be = 18/2 inches
      = 9 inches
We already know that
Circumference of a circle = <span>2π</span>r
We also know that the value of <span>π = 3.14159
Then
Circumference of the dartboard = 2 * 3.14159 * 9 inches
      = 56.548 inches
      = 56.55 inches
So the radius of the dartboard is 9 inches and the circumference of the dartboard is 56.55 inches. I hope the procedure is absolutely clear to you.
</span>

3 0

2 years ago