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3 years ago

If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq

1 answer:

6 0

By way of example, suppose A = {1, 2, 3} and B = {a, b, c}. Then the Cartesian product of A and B is

A × B = {{1, a}, {1, b}, {1, c}, {2, a}, {2, b}, {2, c}, {3, a}, {3, b}, {3, c}}

That is, each element in A gets a pairing with each element in B, and for each pairing you have n(A) choices for the first element and n(B) choices for the second element.

So if n(A) = p and n(B) = q, then n(A × B) = pq.

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John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John

kirza4 [7]

Answer:

2 times as large

Step-by-step explanation:

For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128

For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus

V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256

To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in

π * 256 / (π *128) = 2

8 0

3 years ago

A car is traveling at a steady speed. It travels 1 3/4 miles in 2 1/3 minutes. How far will it travel in 47 minutes? In 1 hour?

aleksandrvk [35]

Answer:

Distance in 47 minutes = 0.75 × 47 = 35.25 miles

Distance in 1 hour or (60 minutes) = 0.75 × 60 = 45 miles

Step-by-step explanation:

Given that the car is traveling at a steady speed.

Distance traveled in 2 1/3 or 7/3 or (2.33) minutes = 1 3/4 miles

= 7/4 or 1.75 miles

Thus,

distance in 1 minute: 1.75/2.33 = 0.75 miles per minute

Thus,

Distance in 47 minutes = 0.75 × 47 = 35.25 miles

Distance in 1 hour or (60 minutes) = 0.75 × 60 = 45 miles

7 0

3 years ago

How much must be deposited today into the following account in order to have $35,000 in 7 years for a down payment on a house?

Rom4ik [11]

Answer:

The amount that must be deposited is $ 19973.87.

Step-by-step explanation:

We have a relation between future value present value as:

F= P $(1 +\frac{r}{n} )^{nt}$

F=future value

P=present value

r=rate (as a decimal)

n=number of compounding periods per year

t=number of years

Now,

assume rate as 8%

35000= P $(1+\frac{0.08}{12} )^{12*7}$

or, 35000= P × $1.0067^{84}$

or, P = $\frac{35000}{1.7522}$

or, P = $ 19973.87

So you must deposit $ 19973.87 today.

7 0

3 years ago

Need help on attached problem

Shkiper50 [21]

2,3,5
.................

6 0

3 years ago

Consider the following numbers: 7000, 700, 70, 0.7, 0.07, 0.007

masya89 [10]

Answer:

7000= 7 x 10^{3}, 700= 7 x 10^{2}, 70= 7 x 10^{1}, 0.7= 7 x 10^{-1}, 0.07= 7 x 10^{-2}, 0.007= 7 x 10^{-3}

Step-by-step explanation:

YES

6 0

3 years ago

If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq​

If n(A) = P and n(B)=q then n(AxB) is (a ) p (b ) q ( c ) p+q ( d ) pq