The graph Y= F(x), what is f (-4)

1. Solve the shape equation puzzle:<br> = 8<br> =<br> = 15

Vesnalui [34]

Star = 5
square =3
or the other way around

6 0

3 years ago

1. Which function represents exponential decay?

MatroZZZ [7]

Answer:

y= 7^-t

Step-by-step explanation:

Equation for exponential decay:

An equation represents exponential decay if a term between 0 and 1 is elevated to the independent variable.

In this question:

First option 4 is elevated, so not exponential decay.

Second option:

$7^{-t} = \frac{1}{7^t} = (\frac{1}{7})^{t}$

$0 < \frac{1}{7} < 1$ , thus, the second option represents exponential decay.

7 0

3 years ago

Six different colored dice are rolled. Of interest is the number of dice that show a one. In words, define the random variable X

olga nikolaevna [1]

Answer:

Step-by-step explanation:

Six dice (each of a different color) are rolled. Since the number of times the 6 dice were rolled isn't stated, take it to be 1.

Hence, 6 dice are rolled at once for this experiment.

Of interest is the number of dice that show a "one". In other words, the variable in question (X) is:

The number of dots that show on the upward face of the rolled dice.

The values that X may take on are:

1 2 3 4 5 6

On average, how many dice would you expect to show a one?

One die.

How is this gotten? By finding the probability that a one or one dot appears when the 6 dice are rolled at once. Since there are 6 dice in number, and each die has the same 6 faces containing dots, the probability of getting a one is 1/6. In this case, one out of 6 dice is expected to show one dot.

Find the probability that all six dice show a dot in just one toss.

Logically, this probability is going to be very small! It is almost impossible for all 6 dice to land on the same face in just a single toss. In other words, expect many decimal places in the probability figure.

1/6 divided by 6 = 0.167/6 = 0.028 approximated to three decimal places.

This would also represent the probability that 2 dots, 3 dots, or any other number of dots appears on all dice in one toss!

Is it more likely (in this experiment) that 3 or 4 dice will show a one (a single dot)?

The answer is yes! It is more likely that 3 or 4 dice (instead of all 6) will show a one or will show the same number of dots.

Kudos!

7 0

3 years ago

Find the longer leg of the triangle.

Paha777 [63]

Answer:

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

$\displaystyle \begin{aligned}\text{Adjacent} &= \text{Hypotenuse} \times \cos{30^{\circ}}\\ &=2\sqrt{3}\times \frac{\sqrt{3}}{2} \\&= 3\end{aligned}$ .

The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.