Which of the following properties did he use? Check all that apply

(a) Find the remainder when 15! is divided by 17. (b) Find the remainder when 2(26!) is divided by 29, Thatermine whether 17 is

dlinn [17]

Answer:

Step-by-step explanation:

a) We have 15! as the product of 1 to 15 natural numbers. Since 17 is prime there will be no factor common to these

By actual division we find

15! (mod 17) =16

From this we deduce

even 16! mod 17 = 16 = -1

According to Wilson theorem

(17-1)! = -1 mod 17

Thus verified 17 is prime

Hence 15! (mod 17) =-1=16

-----------------------

b) 2(26!) is divided by 29

Since 29 is prime

(29-1)! = -1 mod 29

28! = -1 mod 29 = 28

When divided this gives 25 as remainder

4 0

3 years ago

What is the volume of a cube with a side length of 5?

larisa [96]

Answer:

125

Step-by-step explanation:

L x W x H

All are equal sides so 5 are all the lengths of each side of the cube.

6 0

3 years ago

If the measure of angle 4 is 11x and angle 3 is 4x , what is the measure of angle 3 in degrees?

fgiga [73]

Answer:
Let x = degree measure of the angle
So, the complement of the angle has degree measure 90-x
4/11 = x/(90-x)
4(90-x) = 11x
360 - 4x = 11x
15x = 360
x = 24°
Supplement = 180 - x = 156° x/(180-x) = 24/156 = 2/13

5 0

3 years ago

The weights of a certain dog breed are approximately normally distributed with a mean of μ = 55 pounds, and a standard deviation

weqwewe [10]

Answer:

(a)z=-1

(b)48.5 pounds

(c)61.5 pounds

Step-by-step explanation:

$z-score=\dfrac{x-\mu}{\sigma}$

Given:

Mean, μ = 55 pounds

Standard deviation,σ = 6 pounds.

(a)For a dog that weighs 49 pounds.

x=49 pounds

The z-score

$=\dfrac{49-55}{6}\\=\dfrac{-6}{6}\\\\=-1$

(b)When a dog has a z-score of -1.09

$-1.09=\dfrac{x-55}{6}\\x-55=-6.54\\x=55-6.54\\x=48.46 \approx 48.5$ pounds (to the nearest tenth)$

The weight of a dog with a z-score of -1.09 is 48.5 pounds.

(c)When a dog has a z-score of 1.09

$1.09=\dfrac{x-55}{6}\\x-55=6.54\\x=55+6.54\\x=61.54 \approx 61.5$ pounds (to the nearest tenth)$

The weight of a dog with a z-score of 1.09 is 61.5 pounds.

3 0

3 years ago

(10.05 LC)

loris [4]

Answer:

Cos x = $\frac{base}{hypotenuse}=\frac{\sqrt{3} }{2}$

Tan x = $\frac{perpendicular}{base} = \frac{1}{\sqrt{3} }$

Step-by-step explanation:

Sin x = $\frac{perpendicular}{hypotenuse} = \frac{1}{2}$

So, Perp = 1 and hyp = 2

Putting this in Pythagorean theorem to get the base

$c^2 = a^2+b^2$

$a^2 = c^2-b^2$

base ² = 4-1

base² = 3

Taking square root on both sides

Base = $\sqrt{3}$

Now

Cos x = $\frac{base}{hypotenuse}=\frac{\sqrt{3} }{2}$

Tan x = $\frac{perpendicular}{base} = \frac{1}{\sqrt{3} }$

5 0

3 years ago