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Verizon [17]
3 years ago
10

Prove that 16^4–2^13–4^5 is divisible by 11

Mathematics
2 answers:
vazorg [7]3 years ago
6 0
<h3>Explanation:</h3>

(16^4 -2^13 -4^5) mod 11 = ((2^4)^4 -2^13 -(2^2)^5) mod 11

= (2^16 -2^13 -2^10) mod 11

= (2^10 mod 11)·((2^6 -2^3 -1) mod 11)

= (1024 mod 11)·(55 mod 11)

= 1 · 0 = 0

When the sum shown above is divided by 11, its remainder is zero. Hence the sum is divisible by 11.

Alex777 [14]3 years ago
6 0

16^4-2^{13}-4^5=2^{16}-2^{13}-2^{10}=2^{10}(2^6-2^3-1)=2^{10}(64-8-1)=\\=2^{10}\cdot55=2^{10}\cdot5\cdot11

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There are 7 gallons of black paint available to motorola. If 5/9 gallons is used each run, How many runs can we paint?
nadya68 [22]

There are 7 gallons of black paint available to motorola. If 5/9 gallons is used each run. To find the amount of runs you can paint, you have to divide the total by the amount for each run.

7 \div \frac{5}{9}

When dividing fractions, you have to keep, change, and flip.

Keep\ 7 \\ Change\ \div\ to\ \times \\ Flip \frac{5}{9} = \frac{9}{5}

Your new equation is:

7 \times \frac{9}{5}

Multiply:

7 \times \frac{9}{5} = \frac{63}{5} = 12 \frac{3}{5}

You can paint 12 \frac{3}{5} or 12.6 runs.

4 0
3 years ago
Find the volume in cubic millimeters.
forsale [732]

Answer:

Option B is correct.

volume in cubic millimeters is, 8000 cubic mm

Step-by-step explanation:

Volume of a cube is found by multiplying the length of any edge by itself twice.

It is given by:

V = a^3 cubic units,......[1] where V represents the volume of a cube and a represents the side of a length.

From the given figure;

Length of a side(a) = 2 cm

Use conversion, to convert cm into mm;

1 cm = 10 mm

then;

2cm  =20 mm

⇒length of a side(a) = 20 mm

Substitute the value of a = 20 mm in [1];

V = (20)^3 cubic mm

Simplify:

V = 8000 mm^3

Therefore, the volume in cubic millimeters is, 8000 cubic mm


8 0
4 years ago
Read 2 more answers
Which of the following statements are always true for any two sets A and B?
Ivanshal [37]

Answer:

If A ⊆ B, then A ⊂ B.

If A = B, then A ⊆ B.

If A = B, then A ⊂ B.

Step-by-step explanation:

In set theory '⊂' is the symbol of proper subset and '⊆' is the symbol of subset of a set.

In option (a),

If A ⊆ B

⇒ A ⊂ B or A = B

Thus, If A ⊆ B, then A ⊂ B.

Option a is true.

(b) If A ⊂ B

⇒ A is the subset of B

That is, all elements of A are also the element of B,

But we can not say A = B

Thus, option b is not true.

(c) If A = B

⇒ A ⊂ B and A ⊃ B or A ⊆ B and B ⊆ A ( Because every set is the subset of itself )

⇒  A ⊆ B.

Option c is true.

(d) If A = B,

⇒ A ⊂ B

Option d is true.

(e) If A ⊂ B,

Then we can not say that,

A = B or A ≠ B

Thus, option e is not correct.

4 0
4 years ago
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Amanda rented a bike from Ted's Bikes.
Reptile [31]

Answer:

≈ 5.51 hours

Equation: 4.25h + 10

8 0
3 years ago
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You are creating identical picnic basket using 30 sandwiches and 42 apples. What is the greatest number of basket that you can f
UNO [17]

Answer:

Step-by-step explanation:

30: 1, 2, 3, 5, 6, 10, 15, 30

42: 1, 2, 3, 6, 7, 14, 21, 42

greatest number of fill using all of the food is 6

6 0
4 years ago
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