All categories

3 years ago

The function f is defined by the following rule. Find f(x) for each x-value in the table.

Mathematics

1 answer:

ddd [48]3 years ago

7 0

Answer:

x y

-2 36

-1 6

0 1

1 1/6

2 1/36

Step-by-step explanation:

Given

$f(x) = (\frac{1}{6})^x$

Required

Complete the table

When x = -2.

Substitute -2 for

$f(-2) = (\frac{1}{6})^{-2$

$f(-2) = 1/\frac{1}{36}$

$f(-2) = 36$

When x = -1

$f(-1) = (\frac{1}{6})^{-1$

$f(-1) = 1/\frac{1}{6}$

$f(-1) = 6$

When x = 0

$f(0) = \frac{1}{6}^0$

$f(0) = 1$

When x = 1

$f(1) = \frac{1}{6}^1$

$f(1) = \frac{1}{6}$

When x = 2

$f(2) = \frac{1}{6}^2$

$f(2) = \frac{1}{36}$

You might be interested in

Matt paid $450 in interest on a 15 month note for<br> $5600. Find the rate of interest paid.

Olin [163]

Answer:

The rate is 6.43%

Step-by-step explanation:

Given

$I = 450$ --Interest

$P = 5600$ -- Principal

$T= 15\ months$ --Time

Required

Determine the rate

Using simple interest formula:

$I = PRT$

Make R the subject

$R = \frac{I}{PT}$

Convert time to years

$T= 15\ months$

$T =\frac{15}{12}\ years$

$T =1.25\ years$

Substitute values for I, P and T

$R = \frac{450}{5600*1.25}$

$R = \frac{450}{7000}$

$R = 0.0643$

Convert to percentage

$R = 0.0643*100\%$

$R = 6.43\%$

7 0

3 years ago

A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If

victus00 [196]

Answer:

The expected profit is $10,600.

Step-by-step explanation:

The expected profit can be calculated as the sum of the possible outcomes weighted by their probability of occurrence.

In this case, there are four possible outcomes:

1) The horse win both races. The value of the horse will be $100k-$20k=$80k.

The probability of this outcome is:

$P(ww)=P(w1)*P(w2)=0.2*0.3=0.06$

2) The horse win the first race, but lose the second one. The value will be $50k-$20k=$30k.

The probability is:

$P(wl)=P(w1)*(1-P(w2))=0.2*(1-0.3)=0.2*0.7=0.14$

3) The horse lose the first race, but win the second one. The value will be $50k-$20k=$30k.

The probability is:

$P(lw)=(1-P(w1))*P(w2)=(1-0.2)*0.3=0.8*0.3=0.24$

4) The horse lose both races. The value will be $10k-$20k=-$10k.

The probability is:

$P(lw)=(1-P(w1))*(1-P(w2))=(1-0.2)*(1-0.3)=0.8*0.7=0.56$

Then, the expected profit can be calculated as:

$E(x)=\sum\limits^4_{i=1} {p_ix_i}\\\\E(x)=0.06*80,000+0.14*30,000+0.24*30,000+0.56*(-10,000)\\\\E(x)=4,800+4.200+7,200-5,600=10,600$

6 0

3 years ago

Pleaseeeeee helpppppppppp

uysha [10]

Answer:

19.2 Cubed Cm.

Step-by-step explanation:

I think this would be the asnwer bceause the formula is volume = base times the height which is 3 times 6.4 in yoru case which is 19.2 cubed cm.

4 0

3 years ago

Identify the equation in point slope form

Yanka [14]

The answer is D.............

8 0

4 years ago

Find the graph of the inequality y<3/4x+2

kumpel [21]

The first thing that we need to do when solving a linear inequality, is drawing the line:

That is, we must draw the line y=(3/4)x+2.

We know that two points are enough: For example, for x=0, we immediately get y=2.

While, for y=0, we have (3/4)x=-2, that is 3x=-8, which yields x=-8/3.

Thus, we got (0, 2) and (-8/3, 0), which are the x-intercept and the y-intercept, respectively.

We draw the line through these lines, but it must be dashed since the points on this line are solutions of the equation y=(3/4)x+0, NOT solutions of the inequality.

Now, we can check which side to color, by picking a point not on the line, for example (0, 5), as follows:

for x=0, y=5, substituting into the inequality we have 5<2, which is not true. So, the part of the plane above the line is not a solution, but rather, the lower part is.

4 0

3 years ago