Circle each number that is a solution of the given inequality.

Find the Area of the Circle.

Sergio [31]

200.96
(A=pi*r^2)
It’s right just trust me.

5 0

3 years ago

How many solutions are there to the equation below 6×+30+4×=10(×+3)

Elena-2011 [213]

Answer:

Infinite many solutions. Any x-value can satisfy the equation.

Step-by-step explanation:

Let's work on simplifying the equation a little to investigate which x-values satisfy it. Start by combining like terms on the left side (6x +4x=10x),

then distribute the factor "10" into the binomial (x+10), obtaining 10x +30.

Now we have the same expression on the left and the right of the equal sign:

10x +30=10x+30. We may subtract 30 from both sides, and obtain 10x=10x, and at this point divide by 10 both sides, and we obtain: x=x

The process is shown below.

$6x+30+4x=10(x+3)\\6x+4x+30=10x+30\\10x+30=10x+30\\10x=10x\\x=x$

x=x is an equation that is verified by absolutely ANY x value on the number line, and there are infinite x-values in the number line.

Therefore there are infinite many solutions to this equation (any x-value will satisfy it).

7 0

4 years ago

Suppose that the pH of soil samples taken from a certain geographic region is normally distributed with a mean pH of 7 and a sta

Otrada [13]

Answer:

a) P=0

b) P=1

c) P=0

d) X=7.1645

Step-by-step explanation:

We have the pH of soil for some region being normally distributed, with mean = 7 and standard deviation of 0.10.

a) What is the probability that the resulting pH is between 5.90 and 6.15?

We calculate the z-score for this 2 values, and then compute the probability.

$z_1=(X_1-\mu)/\sigma=(5.9-7.0)/0.1=-11\\\\z_2=(X_2-\mu)/\sigma=(6.15-7)/0.1=-8.5$

Then the probability is

$P(5.90$

b) What is the probability that the resulting pH exceeds 6.10?

We repeat the previous procedure.

$z=(6.10-7)/0.1=-9\\\\P(x>6.1)=P(z>-9)=1$

c) What is the probability that the resulting pH is at most 5.95?

$z=(5.95-7)/0.1=-10.5\\\\P(x$

d. What value will be exceeded by only 5% of all such pH values?

We have to calculate the value of pH for which only 5% is expected to be higher. This can be represented as P(X>x)=0.05.

In the standard normal distribution, it happens for a z=1.645.

$P(z>1.645)=0.05$

Then, we can calculate the pH as:

$x=\mu+z\sigma=7.0+1.645*0.1=7.0+0.1645=7.1645$

4 0

3 years ago

What is the best name of the solid that can be formed by this net?

mixer [17]

Answer:

Triangular prism.

Step-by-step explanation:

That would be a triangular prism.

The 3 sides are rectangles and the top and bottom are triangles.

4 0

3 years ago

Read 2 more answers

two marathon runners leave the starting gate, one running at 12mph and the other at 8 mph. if they maintain this pace, how long

CaHeK987 [17]

So let us set up the equations:

d = rt

d = 12t and plug in r = 12

so after t hours, the faster runner is 12t miles which is for the faster runner.

d = rt

d = 8t plug in r = 8

so after t hours, the slower runner has 8t miles.

Now if you want to get the distance, simply subtract:

12t – 8t = 4t

Since we need to get the distance of ¼ mile, meaning:

12t – 8t = ¼

= 4(12t – 8t) = 4 x 1/4 -> multiply both sides by the lcd to clear the fractions

= 48t – 32t = 1

=16t = 1

Get t by dividing both sides by 16 to isolate t.

So the answer is 1/16 which is about 0.0625.

8 0

3 years ago