Answer:
C
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
Let P(x) be a predicate over the variable x. Rules from logic tell us that the negation of ∀xP(x) is ∃x(¬P(x)). That is, the negation operator ¬ satisfies ¬(∀xP(x))≡∃x(¬P(x)). Similarly, ¬(∃xP(x))≡∀x(¬P(x)).
Apply these rules to each statement to obtain:
a) ∃ a fish x, x does not have gills.
b) ∃ a computer c, c does not have a CPU.
c) ∀ movie m, m is not over 6 hours long. ⇔ ∀ movie m, m is under 6 hours long.
d) ∀ band b, b has not won at least 10 Grammy awards. ⇔ ∀ band b, b has won less than 9 Grammy awards.
Answer: Tom will pay $20.01 lesser than the original price.
Step-by-step explanation:
The original price of the phone is $137.99. It is now on sale for 1/10 off the original price. This means that the discount on the original price is 1/10 × 137.99 = 13.799. The new price will be the original price - the discount.
The new price is 137.99 - 13.799 = $124.191
Tom has a coupon for an extra 5% off the sale price. It means that Tom would pay 5% off $124.191. The amount that Tom would pay will be
124.191 - (5/100 × 124.191) = 124.191 - 6.20955 = $117.98
The difference between the original price and the price that Tom will pay is
137.99 - 117.98 = $20.01
You'll need to specify the accuracy to which you want your answer. For example: "Find the volume of this cone to 3 decimal place accuracy."
The formula for the volume of a cone is V = (1/3) (base) (height), where "base" represents the area of the base.
Here the diameter of the base is 24 feet, so the radius of the base is 12 feet.
Thus, the area of the base is (12 feet)^2 times pi: A = 144 pi ft^2.
Multiply this area by the height of the cone, which is 10 feet:
V = 1440 pi ft^3
By calculator, this volume is 4523.893421 cubic feet.
If you want this volume to the nearest cubic foot, it'd be 4524 cubic ft.
If you want this vol. to the nearest 100th cubic ft., it'd be 4523.89 cu. ft.
We have that
<span>sin (7π/12)=?
we know that
</span>7π/12=(π/4+π/3)
and
<span><span>sin<span>(A+B)</span>=sin<span>(A)</span>cos<span>(B)</span>+cos<span>(A)</span>sin<span>(B)
then
</span></span>sin(π/4+π/3)=sin(π/4)cos(π/3)+cos(π/4)sin(π/3)
sin(π/4+π/3)=(√2/2)(1/2)+(√2/2)(√3/2)-------> (√2/4)+(√6/4)---> (√2+√6)/4
the answer is (√2+√6)/4
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