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2 years ago

Which number below is a prime number? O A. 61 OB. 102 O C. 75 O D. 64

Mathematics

1 answer:

d1i1m1o1n [39]2 years ago

3 0

Answer:

Step-by-step explanation:

61 is divisible by itself and 1. It's prime.

102 ends in a 2. Therefore it is not prime because it can be divided by 2,

75 = 3*5*5 not prime.

64 = 2 * 2 * 2 *2 * 2*2 Not prime.

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How many terms are there in the sequence 1, 8, 28, 56, ..., 1 ?

BabaBlast [244]

Answer:

9 terms

Step-by-step explanation:

Given:

1, 8, 28, 56, ..., 1

Required

Determine the number of sequence

To determine the number of sequence, we need to understand how the sequence are generated

The sequence are generated using

$\left[\begin{array}{c}n&&r\end{array}\right] = \frac{n!}{(n-r)!r!}$

Where n = 8 and r = 0,1....8

When r = 0

$\left[\begin{array}{c}8&&0\end{array}\right] = \frac{8!}{(8-0)!0!} = \frac{8!}{8!0!} = 1$

When r = 1

$\left[\begin{array}{c}8&&1\end{array}\right] = \frac{8!}{(8-1)!1!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 2

$\left[\begin{array}{c}8&&2\end{array}\right] = \frac{8!}{(8-2)!2!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} =2 8$

When r = 3

$\left[\begin{array}{c}8&&3\end{array}\right] = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 4

$\left[\begin{array}{c}8&&4\end{array}\right] = \frac{8!}{(8-4)!4!} = \frac{8!}{4!3!} = \frac{8 * 7 * 6 * 5 * 4!}{4! *4*3* 2 *1} = \frac{8 * 7 * 6*5}{4*3 *2 *1} = 70$

When r = 5

$\left[\begin{array}{c}8&&5\end{array}\right] = \frac{8!}{(8-5)!5!} = \frac{8!}{5!3!} = \frac{8 * 7 * 6 * 5!}{5! *3* 2 *1} = \frac{8 * 7 * 6}{3 *2 *1} = 56$

When r = 6

$\left[\begin{array}{c}8&&6\end{array}\right] = \frac{8!}{(8-6)!6!} = \frac{8!}{6!2!} = \frac{8 * 7 * 6!}{6! * 2 *1} = \frac{8 * 7}{2 *1} = 28$

When r = 7

$\left[\begin{array}{c}8&&7\end{array}\right] = \frac{8!}{(8-7)!7!} = \frac{8!}{7!1!} = \frac{8 * 7!}{7! * 1} = \frac{8}{1} = 8$

When r = 8

$\left[\begin{array}{c}8&&8\end{array}\right] = \frac{8!}{(8-8)!8!} = \frac{8!}{8!0!} = 1$

The full sequence is: 1,8,28,56,70,56,28,8,1

And the number of terms is 9

3 0

3 years ago

One side of a square has a value of 3x+2, find the perimeter of the square

alexira [117]

Answer:

P = 12x +8

Step-by-step explanation:

The perimeter of a square is given by

P = 4s where s is the side length

P = 4(3x+2)

Distribute

P = 12x +8

6 0

3 years ago

Read 2 more answers

What's 4+ -1 1/3 as a fraction in simplest form

Ivenika [448]

4 + -1 1/3

Turn 4 into an improper fraction.

4/4 is equal to 12/3. We want both 4 and 1 1/3 to have the same denominator so that they could be subtracted from each other.

New question :

12/3 + - 1 1/3

Turn {-1 1/3} into an improper fraction.

(3 × 1) + 1 = 4/3

So, -1 1/3 = -4/3

Our new question :

12/3 + - 4/3

Simplify.

12/3 - 4/3 = 8/3

Turn into a mixed number.

2 2/3

~Hope I helped!~

7 0

2 years ago

I've been struggling a bit with Composite Figures. This is 2 ones I've really struggled with though so, could I have some help?

Natali5045456 [20]

You are right with : Which shapes could a pentagon be decomposed into to find its area? Chose all that apply.
C. five triangles
D. one triangle and one trapezoid
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3 years ago

The Vega family has a 3-year cell phone contact. Javier Vega says that the family gets a total of 3x10 (4) (4 as an exponent) mi

pashok25 [27]

What I think: Use this, please excuse my dear aunt Sally, e= exponent my=multiplication. 4 to the tenth power (10,000) times 3 is equal to 30,000 which means they all get 10,000 minutes (I Think)

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2 years ago

Read 2 more answers

Which number below is a prime number? O A. 61 OB. 102 O C. 75 O D. 64​

Which number below is a prime number? O A. 61 OB. 102 O C. 75 O D. 64