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Feliz [49]
3 years ago
7

The sum of two positive integers, x and y, is not more than 40. The difference of the two integers is at least 20. Chancee choos

es x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions. She determines that x must be between 0 and 10 and y must be between 20 and 40. Determine if Chancee found the correct solution. If not, state the correct solution.

Mathematics
1 answer:
kvasek [131]3 years ago
5 0

Answer:

No, Chancee mixed up the variables, the correct solution is that x must be between 20 and 40 and y must be between 0 and 10.

Step-by-step explanation:

Here, x and y are positive integers,

Such that, their sum is not more than 40,  

i.e. x + y ≤ 40 where x, y ≥ 0,

⇒ y ≤ 40 - x                 ...............(1),

Their difference is at least 20,

i.e. x - y ≥ 20

-y ≥ 20 - x

⇒ y ≤ x - 20   ............(2),

Graphing y ≤ 40 - x :

Related equation of inequality (1),

y = 40 - x

if x = 0, y = 40,

if y = 0, 0 = 40 - x ⇒ x = 40,

'≤' represents a solid line,

Join the points (0, 40) and (40, 0) by solid line.

Graphing y ≤ x - 20:

Related equation of inequality (1),

y = x - 20,

if x = 0, y = -20,

if y = 0, 0 = x - 20 ⇒ x = 20,

'≤' represents a solid line,

Join the points (0, -20) and (20, 0) by solid line.

By graphing we obtained a feasible region that is the solution of the system of inequalities (1) and (2) ( shown below ),

In which,

20 ≤ x ≤ 40 and 0 ≤ y ≤ 30

Hence, Chancee did not find the correct solution.

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What is the product of 2x - 5 and 3x2 + 5x - 7? Write your answer in standard form.
Orlov [11]

Answer:

(2x - 5 ) (3x^2 + 5x - 7) = 6x^3 - 5x^2 - 39x - 35

The product of 2x – 5 and 3x2 + 5x - 7equal to the product of 5x - 2 and 3x2 + 5x - 7 are not equal.

Step-by-step explanation:

Product means multiplication

Product of 2x - 5 and 3x^2 + 5x - 7

(2x - 5 ) (3x^2 + 5x - 7)

= 6x^3 + 10x^2 - 14x - 15x^2 - 25x - 35

Collect like terms

= 6x^3 + 10x^2 - 15x^2 - 14x - 25x - 35

= 6x^3 - 5x^2 - 39x - 35

Product of 5x - 2 and 3x^2 + 5x - 7

(5x - 2) (3x^2 + 5x - 7)

= 15x^3 + 25x^2 - 35x - 6x^2 - 10x + 14

Collect like terms

= 15x^3 + 25x^2 - 6x^2 - 35x - 10x + 14

= 15x^3 + 19x^2 - 45x + 14

The product of 2x – 5 and 3x^2 + 5x - 7equal to the product of 5x - 2 and 3x^2 + 5x - 7 are not equal.

They both consist of different variables in their multiplier

8 0
3 years ago
Suppose that E and F are two events and that P(E)=0.3 and P(F|E)=0.5. What is P(E and F)?
Sergio [31]

E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15


Bayes' theorem is transforming preceding probabilities into succeeding probabilities. It is based on the principle of conditional probability. Conditional probability is the possibility that an event will occur because it is dependent on another event.

P(F|E)=P(E and F)÷P(E)

It is given that P(E)=0.3,P(F|E)=0.5

Using Bayes' formula,

P(F|E)=P(E and F)÷P(E)

Rearranging the formula,

⇒P(E and F)=P(F|E)×P(E)

Substituting the given values in the formula, we get

⇒P(E and F)=0.5×0.3

⇒P(E and F)=0.15

∴The correct answer is 0.15.

If, E and F are two events and that P(E)=0.3 and P(F|E)=0.5. Thus, P(E and F)=0.15.

Learn more about Bayes' theorem on

brainly.com/question/17010130

#SPJ1

4 0
2 years ago
An online service charges $3 for each downloaded movie, plus a monthly fee of $6,50 Which function represents this
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Answer:

ANSWER

y = 3x + 6.50

EXPLANATION

The $3 for each downloaded movie is the unit rate of change.

This is represent the slope of the linear function that models this situation.

The monthly fee of monthly fee of $6.50 the constant rate.

It represents the y-intercept of the function.

The linear function is given by

y = mx + by=mx+b

The correct choice is y = 3x + 6.50

3 0
3 years ago
Read 2 more answers
Simplify the expression below, I really just need the steps I have the answer (also can someone tell me how to edit points on th
Sloan [31]

Answer:  3x^2y\sqrt[3]{y}\\\\

Work Shown:

\sqrt[3]{27x^{6}y^{4}}\\\\\sqrt[3]{3^3x^{3+3}y^{3+1}}\\\\\sqrt[3]{3^3x^{3}*x^{3}*y^{3}*y^{1}}\\\\\sqrt[3]{3^3x^{2*3}*y^{3}*y}\\\\\sqrt[3]{\left(3x^2y\right)^3*y}\\\\\sqrt[3]{\left(3x^2y\right)^3}*\sqrt[3]{y}\\\\3x^2y\sqrt[3]{y}\\\\

Explanation:

As the steps above show, the goal is to factor the expression under the root in terms of pulling out cubed terms. That way when we apply the cube root to them, the exponents cancel. We cannot factor the y term completely, so we have a bit of leftovers.

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How to show your work for the depth of a swimming pool that is 8.5 meters but has to be in Milli meter?
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1 meter equals 1000 millimeters

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