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4 years ago

25 POINTS for this question. Find all the integer solutions to each system of the inequalities:

Mathematics

2 answers:

goblinko [34]4 years ago

7 0

Answer:

The integer solutions are 4,5,6 and 7.

Step-by-step explanation:

12a - 37 > 0

12a > 37

a > 37/12

a > 3 .083.

6a ≤ 42

a ≤ 7.

sineoko [7]4 years ago

5 0

Answer:

Step-by-step explanation:

12a-37 > 0 ...(1)

6a ≤ 42....(2)

by (1) : a ≤ 7 but a is the integer number so : a =1 ; a =2 : a =3 : a=4 ; a = 5

a = 6 and a = 7

1) cas : a = 1 by (2) : 12(1) -37 > 0 -25 > 0 ...... false

2) cas : a = 2 by (2) : 12(2) -37 > 0 -13 > 0 ...... false

3) cas : a = 3 by (2) : 12(3) -37 > 0 -1 > 0 ...... false

4) cas : a = 4 by (2) : 12(4) -37 > 0 11 > 0 ...... true

5) cas : a = 5 by (2) : 12(5) -37 > 0 23> 0 ...... true

6) cas : a =6 by (2) : 12(6) -37 > 0 35 > 0 ...... true

7) cas : a = 7 by (2) : 12(7) -37 > 0 47 > 0 ...... true

all the integer solutions to each system of the inequalities: 4 ; 5; 6: 7 .

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What percent of 120 is 90

Alex777 [14]

Answer:

75%

Step-by-step explanation:

90/ 120 is the same as 75 or 3/4 so 75% of 120 is 90

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3 years ago

What is the value of x and y?

Pavel [41]

Answer:

$x=\boxed{2}$

$y=\boxed{4}$

Step-by-step explanation:

$\begin{cases} y= 6x-8... (1)\\\\y=-3x+10...(2)\end{cases}$

From equations (1) & (2), we find:

6x - 8 = - 3x +10

$\therefore 6x+3x = 8+10$

$\therefore 9x = 18$

$\therefore x =\frac{18}{9}$

$\therefore x = 2$

Plug x = 2 in equation (1)

y = 6(2)-8 = 12-8 =4

So,

$x=\boxed{2}$

$y=\boxed{4}$

6 0

3 years ago

Read 2 more answers

(6) Give the equation of the line passing through the points (1,5) and (-2, 6) in

Bas_tet [7]

Answer:

⅓x + y = 5⅓

⅓x + y = 5.3333333

⅓x + y = 16/3

Step-by-step explanation:

Solve for slope using rise/run

Y2 - Y1 / X2 - X1

(6) - (5) / (-2) - (1)

1 / -3

Slope: -⅓

y = -⅓x + b

solve for b using one of the points

I'll be using (1,5)

Substitute the point into the equation

5 = -⅓(1) + b

5 = -⅓ + b (add ⅓ to both sides)

+⅓ +⅓

5⅓ = b

5⅓ can also be written as 16/3 or 5.333333

The equation is now:

y = -⅓x + 5⅓

Convert to standard form by adding ⅓x to both sides

y = -⅓x + 5⅓

+⅓x +⅓x

Solution: ⅓x + y = 5⅓

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3 years ago

Calculate the length of the circumference of a circle with radius of 7cm

Natasha2012 [34]

Hey there,
Length (diameter)= 7 + 7
= 14 cm
Circumference = 2 x pi x r
= 2 x pi x 7
= 14 pi

Hope this helps ^_^

~Top

5 0

3 years ago

Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 60% can be repaired

nignag [31]

Answer:

0.0052 = 0.52% probability that exactly four will end up being replaced under warranty.

Step-by-step explanation:

For each telephone, there are only two possible outcomes. Either they are replaced under warranty, or they are not. The probability of a telephone being replaced under warranty is independent of any other telephone, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Twenty percent of all telephones of a certain type are submitted for service while under warranty. Of those, 40% are replaced.

This means that $p = 0.2*0.4 = 0.08$

Company purchases ten of these telephones.

This means that $n = 10$

What is the probability that exactly four will end up being replaced under warranty?

This is P(X = 4). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{10,4}.(0.08)^{4}.(0.92)^{6} = 0.0052$

0.0052 = 0.52% probability that exactly four will end up being replaced under warranty.

4 0

3 years ago