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3 years ago

In algeb, what is 4^x=64?

1 answer:

4 0

Hi

Here are the steps

4^x = 64
First, we need to solve for the exponent
log(4^x) = log(64)
Now we need to take log of
x * (log(4)) = log(64)
x = log(64)/(log(4)
x= 3

Here you go guys :)

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Estimate 3/8 + 3/4 + 7/8 =

goldfiish [28.3K]

Answer:

Step-by-step explanation:

3/8+3/4+7/8

=3/8+6/8+7/8

=16/8

8 0

2 years ago

a fair coin is flipped 10 times. what is the probability of getting the same number of heads and tails

Dafna11 [192]

If you flip a coin one time, the probability to get a Head is

p = 1/2

The probability of not getting a head in a single toss is :

q = 1 - 1/2 = 1/2

Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.

Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :

P(X = 5) = $\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}$ ≈ 0.246

So the probability of that is 24,6 %

Good Luck

3 0

2 years ago

a ferry is traveling at a constant speed back to the dock, as shown in the graph. which function represents the relationship bet

horsena [70]

Answer: y = -35x + 105

Step-by-step explanation:

The graph represents a function that is between hours and miles and to determine the equation which belong to this graph, we need to find the slope first by using two points from the graph which are (0, 105) and (3, 0).

The definition of slope is

m = (y2 - y1)/(x2 - x1)

= (0-105)/3-0

= -105/3

= -35

The slope is -35 and remember that the slope is the coefficient of the variable x. Therefore, the answer is:

y = -35x + 105

6 0

3 years ago

Find the missing side lengths leave your answer as a racials simplest form

Aleksandr-060686 [28]

Answer:

m= $7\sqrt3$

n=7

Step-by-step explanation:

Hi there!

We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14

We need to find the lengths of m and n

Firstly, let's find the measure of the other acute angle

The acute angles in a right triangle are complementary, meaning they add up to 90 degrees

Let's make the measure of the unknown acute angle x

So x+60°=90°

Subtract 60 from both sides

x=30°

So the measure of the other acute angle is 30 degrees

This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle

In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is $\frac{a}{2}$ , and the leg opposite from the 60 degree angle is $\frac{a\sqrt3}{2}$