Answer:
a. 0.24094
b. 0.2494
c. 0.1473
Step-by-step explanation:
The total probability of choosing any 20 random balls out of 80 is . We use combination since the order of selection does not matter
a. P(all numbers are selected)
are our numbers,
is the selection of other ten numbers apart from our numbers.
b. P(none of them are selected)
Since none of our numbers are selected, we assume that all the numbers selected are from the other 70.
c. P (exactly four are selected)
Only four from our numbers are selected and the rest 16 from the other 70 numbers.
Answer:
On a coordinate plane, a triangle has points (negative 4, 3), (negative 4, negative 2), (1, negative 2).
Step-by-step explanation:
The points (-4,3), (1,2) and (-4, -2) would form a right triangle when graphed and connected by lines.
(-4,3), (1,2) and (1,3) would also work as well
Answer:
Line segment A B is longer than Line segment F D. This is the correct statement from the given statements.
Step-by-step explanation:
Given:
In ΔABC and ΔFDE
Segment AC≅Segment FE
Segment BC≅Segment DE
∠BCA = 72° and ∠DEF = 65°
Now by the property of a Triangle we know that
Side opposite to the greater angle is longer than the side opposite to the smaller angle.
So, Side opposite to the greater angle (∠BCA = 72°) is AB and
The side opposite to the smaller angle (∠DEF = 65°) is FD.
Therefore, side AB is Longer than side FD.
Answer:
see below
Step-by-step explanation:
The first equation is in slope-intercept form, so you can see that the boundary line has a slope of -2 and goes through the point (x, y) = (0, -4). Since the comparison is "<", the line is dashed and shading is below it.
The second equation is that of a vertical boundary line at x=-3. It is solid, because the comparison includes the "equal" case. Shading is to the right of it, where x values are greater than -3.
Answer:
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Explanation:
<u>Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m</u>
<u></u>
a) By definition:
b) Given:
c) By substitution:
<u>Question 2: Find the general solution of this equation. Use A as a constant of integration.</u>
a) <u>Separate variables</u>
b)<u> Integrate</u>
c) <u>Antilogarithm</u>
<u>Question 3. Which particular solution matches the additional information?</u>
<u></u>
Use the measured rate of 4 grams per hour after 3 hours
First, find the mass at t = 3 hours
Now substitute in the general solution of the differential equation, to find A:
Round A to 1 significant figure:
<u>Particular solution:</u>
<u>Question 4. What was the mass of the bacteria at time =0?</u>
Substitute t = 0 in the equation of the particular solution: