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2 years ago

Translate the following phase into an inequality -3 times r is at least 57

Mathematics

1 answer:

artcher [175]2 years ago

3 0

Answer:

Step-by-step explanation:

at least means it can be 57 or higher

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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

2 years ago

if the domain of a coordinate transformation that is reflected over the y-axis is (-1,3),(2,1),(5,-1)and(-1,-2) what is the rang

AURORKA [14]

Answer:

Range remains the same.

Step-by-step explanation:

(1,3),(-2,1),(-5,-1) and (1,-2)

7 0

3 years ago

Read 2 more answers

A local school has was evaluated the the Education Department and received the

Angelina_Jolie [31]

Answer: 79

Step-by-step explanation:

Given the following :

Graduation Rates:

Grade:82

Weight: 50%

Passing Rates:

Grade: 75

Weight: 30%

Enrollment Numbers:

Grade: 60

Weight: 10%

Career readiness:

Grade: 95

Weight: 10%

Overall score : Σ(grade × weight)

(82 × 50%) + (75 × 30%) + (60 × 10%) + (95 × 10%)

= (41 + 22.5 + 6 + 9.5)

= 79

Hence, overall score is 79

5 0

2 years ago

To investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample o

OLga [1]

Answer:

0.15401

Step-by-step explanation:

Given that test statistic = 3.7408

From the question, we could deduce that, this is scenario could be analysed A ONE - WAY analysis of Variance method as it has one independent variable, Age subdivided into 3 levels

The test statistic value obtained is the Chisquare (χ²) value, which equals 3.7408

To Obtain the requested Pvalue, we need the degree of freedom, which is :

(Number of columns - 1) * (number of rows - 1)

Number of candidates = 2

Number of levels = 3

Hence,

Degree of freedom = (3 - 1) * (2 - 1) = 2 * 1 = 2

Using the Chisquare Pvalue calculator or distribution table :

χ²;3.7408, 2 = 0.154062

Pvalue = 0.1541

3 0

2 years ago

Expand<br> (2x - 3)4 <br><br> Can you help me expand this by using the binomial theorem?

saw5 [17]

The value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

<h3>How to expand the expression?</h3>

The expression is given as:

(2x -3)^4

Using the binomial expansion, we have:

$(2x -3)^4 = ^4C_0 * (2x)^4 * (-3)^0 +^4C_1 * (2x)^3 * (-3)^1 + ^4C_2 * (2x)^2 * (-3)^2 + ^4C_3 * (2x)^1 * (-3)^3 + ^4C_4 * (2x)^0 * (-3)^4$

Evaluate the combination factors.

So, we have:

$(2x -3)^4 = 1 * (2x)^4 * (-3)^0 + 4 * (2x)^3 * (-3)^1 + 6 * (2x)^2 * (-3)^2 + 4 * (2x)^1 * (-3)^3 + 1 * (2x)^0 * (-3)^4$

Evaluate the exponents and the products

$(2x -3)^4 = 16x^4 + 96x^3 +216x^2 -216x + 81$

Hence, the value of expanding (2x -3)^4 is 16x^4 + 96x^3 +216x^2 -216x + 81

Read more about binomial expansions at:

brainly.com/question/13602562

#SPJ1

8 0

1 year ago