The LCM of 5 and 3 is 15.
The LCM of x and x^2 is x^2.
The LCM of y and y^3 is y^3.
Putting it all back together.
15x^2y^3
Answer:
0.089
Step-by-step explanation:
f(x) = -ln(x) and g(x) = x²
Start by graphing the region. The two curves intersect at about (0.653, 0.426), with g(x) on the left and f(x) on the right. The region is the triangular area between the curves and above the x-axis.
If we were to cut the region horizontally (perpendicular to the y-axis), the resulting line is the width of the square cross section. The thickness of this square is dy. So the volume of the square is:
dV = A dy
dV = s² dy
dV = (x₂ − x₁)² dy
dV = (e⁻ʸ − √y)² dy
The total volume is the sum of all the squares from y=0 to y=0.426.
V = ∫ dV
V = ∫₀⁰'⁴²⁶ (e⁻ʸ − √y)² dy
Evaluate with a calculator:
V ≈ 0.089
Answer:
Step-by-step explanation:
When the three cards are removed, the sample space becomes 49.
Probability of a heart = 13/49. No hearts were removed from the deck.
Probability of a king = 3/49. One king was removed from the deck.
Probability of the 10 of hearts = 1/49. There's only one 10 of hearts in the deck, and it was not removed.
Probability of a black face card = 3/49. Three of the black face cards were removed, so all that is left are the king, queen, and jack of clubs.
Probability of an ace OR a queen = 7/49 = 1/7. There are 3 queens and 4 aces remaining in the deck.
The correct answer is option B which is {x | x ≤ 4.5}
<h3>What is a number line?</h3>
A number line is a representation of a graduated straight line used to represent real numbers in introductory mathematics.
Because the arrow is pointing to the left, the answer to the solution set needs to be less than the number the dot is on.
A solid dot on a number means that that number is included in the solution set.
In the picture the solid dot is on 4.5, so the solution set needs to be equal to or less than 4.5.
Therefore the correct answer is option B which is {x | x ≤ 4.5}
To know more about number lines follow
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