MATHEMATICS COLLEGE

Roy is 11 years old and his uncle is 59 years old. How many years ago was Roy’s uncle 7 times as old as Roy?

Answers

Answer 1

Answer:

Answer:

answer : 3 years ago

Step-by-step explanation:

Let x years ago.

59−x=7(11−x)

59−x=77−7x

6x=18

x=3

=3 years ago

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A Jewelry store makes necklaces and bracelets from gold and platinum. vThe store has 18 ounces of gold and 20 ounces of platinum. vEach necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. vThe demand for bracelets is no more than four. vA necklace earns $300 in profit and a bracelet $400. vThe store wants to determine the number of necklaces and bracelets to produce in order to maximize profit.a. Formulate a linear programming model for this problem.b. Solve this model using graphical analysis.

Answers

Answer:

maximum profit is$2400 when 4 necklace and 3 brackets are made.

Step-by-step explanation:

Total gold = 18 ounces

Total platinum = 20 ounces.

let X₁ represents the necklace and X₂ represents the bracelets.

A. Linear Programming Model

maximize:

$300x_(1) + 400x_(2)$

with constraints:

for gold:

$3x_(1) + 2x_(2) \leq 18$ ---(1)

for platinum:

$2x_(1) + 4x_(2) \leq 20$ ---(2)

The demand for bracelets is no more than four i.e.

$x_(2)\leq 4$ ---(3)

$x_(1),x_(2)\geq 0$

B. Graphical Analysis

Final answer:

To maximize profit, formulate a linear programming model with constraints for the number of necklaces and bracelets to produce. Solve the model using graphical analysis to find the optimal solution.

Explanation:

To formulate a linear programming model for this problem, let x be the number of necklaces to produce and y be the number of bracelets to produce. The objective is to maximize profit, which can be expressed as: Profit = 300x + 400y. The constraints are: 3x + 2y ≤ 18 (gold constraint), 2x + 4y ≤ 20 (platinum constraint), 0 ≤ x ≤ infinity (non-negativity constraint), and y ≤ 4 (demand constraint).

To solve this model using graphical analysis, graph the feasible region determined by the constraints. The feasible region is the region in which all constraints are satisfied. The optimal solution will be at one of the corner points of the feasible region. Calculate the objective function at each corner point and select the one that maximizes profit.

Learn more about Linear Programming here:

brainly.com/question/34674455

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When you roll a pair of dice, there are several outcomes, as shown below:When rolling the dice, the outcome is expressed as a sum of the two dice. For
example, if after you rolled the dice, and one die was a 3 and the other was a 4, you
will have rolled a 7.
Select all of the TRUE statements below. There may be more than one.
The probability of rolling the same digit with each die is 1/4.
The odds in favour of rolling a 10 is 1:13.
The odds against rolling a number less than 7 is 7:5.

Answers

Answer:

Step-by-step explanation:

Find the slope of the line that contains the following points ( -3 , 7) and (8, -2)

Answers

Answer:

-9/11

Step-by-step explanation:

The slope of a line given two points is

m = (y2-y1)/(x2-x1)

= (-2-7)/(8--3)

= (-9)/(8+3)

=-9/11

Hope this helped you. :)

Point C is the center of the circle. angle ACB measures 49. What is the of arc ADB

Answers

If arc ADB is that portion of the circle that is not arc AB, then its measure is ...

... 360° -49° = 311°

_____

The sum of the measures of the arcs of a circle is 360°.

Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A)=0.138, P(B)=0.261, and the probability that a household is both prosperous and educated is P(A and B)=0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?

Answers

Answer: 0.317

Step-by-step explanation:

Let A be the event that the selected household is prosperous and B the event that it is educated.

Given : P(A)=0.138, P(B)=0.261

P(A and B)=0.082

We know that for any events M and N ,

$\text{P(M or N)=P(M)+P(N)-P(M or N)}$

Thus , $\text{P(A or B)=P(A)+P(B)-P(A or B)}$

$\text{P(A or B)}=0.138+0.261-0.082\n\n\Rightarrow\text{ P(A or B)}=0.317$

Hence, the probability P(A or B) that the household selected is either prosperous or educated = 0.317

Find an equation of the line having the given slope and containing the given point.Slope is -2
Line through (5, -6)

Answers

Answer:

y = -2x + 4

Step-by-step explanation:

Pre-Solving

We are given that a line has a slope (m) of -2 and passes through (5, -6).

We want to write the equation of the line.

There are three ways to write the equation of the line:

Slope-intercept form, which is y=mx+b, where m is the slope and b the value of y at the y-intercept.
Standard form, which is ax+by=c, where a, b, and c are free integer coefficients.
Point-slope form, which is $y-y_1=m(x-x_1)$ , where m is the slope and $(x_1,y_1)$ is a point.