Two consecutive odd number have a product of 35. What are the numbers?

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

6 0

3 years ago

A survey was taken of students in math classes to find out how many hours per day students spend

Hoochie [10]

Answer:

1. Mean, because there are no outliers that affect the center

Step-by-step explanation:

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

6 0

3 years ago

4/7 - -3/5 step by step pls explain

lidiya [134]

Answer:

41/35

Step-by-step explanation:

Simplify the following:

4/7 + 3/5

Put 4/7 + 3/5 over the common denominator 35. 4/7 + 3/5 = (5×4)/35 + (7×3)/35:

(5×4)/35 + (7×3)/35

5×4 = 20:

20/35 + (7×3)/35

7×3 = 21:

20/35 + 21/35

20/35 + 21/35 = (20 + 21)/35:

(20 + 21)/35

| 2 | 1

+ | 2 | 0

| 4 | 1:

Answer: 41/35

5 0

4 years ago

Multiply: 5x(2x4 – x3 + 3)

Leno4ka [110]

Answer:

10

x

5

A

−

5

x

4

A

+

15

x

A

Step-by-step explanation:

6 0

3 years ago

67 times a number minus 58 is equal to 36 less than the number

marusya05 [52]

67n - 58 = n - 36

hope this helps, have a great day!

6 0

3 years ago