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Brums [2.3K]
3 years ago
12

A college is currently accepting students that are both in-state and out-of-state. They plan to accept three times as many in-st

ate students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
Mathematics
2 answers:
densk [106]3 years ago
7 0

Answer:

\[y < = 300\]

Step-by-step explanation:

Let x = number of out-of-state students at the college

Let y = number of in-state students at the college

As per the given problem, the constraints are as follows:

\[x < = 100\]    --------- (1)

\[y = 3 * x\]      --------- (2)

From the given equations (2), \[ x = y/3 \]

Substituting in (1):

\[y/3 < = 100\]

Or, \[y < = 300\] which is the constraint representing the incoming students.

Lina20 [59]3 years ago
5 0

Answer:

Constraint that represents the incoming students at the college is

y ≤ 300

Step-by-step explanation:

It is given in this question that a college is currently accepting both in-state and out of state students where,

y = Number of in-state students

x = Number of out-of-state students

Their plan is to accept three times as many in students as out of state

Which is represented by he equation y = 3x

x = \frac{y}{3}

College has space for 100 out-of-state students only, so the inequality which represents this situation will be

x ≤ 100

Now the constraint to represent the incoming students in the college will be

\frac{y}{3}\leq  100

y ≤ 300

Therefore, constraint that represents the incoming students at the college is y ≤ 300

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. A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and six 75-W bulbs. Suppose that three bulbs ar
yaroslaw [1]

Answer:

a) 59.34%

b) 44.82%

c) 26.37%

d) 4.19%

Step-by-step explanation:

(a)

There are in total <em>4+5+6 = 15 bulbs</em>. If we want to select 3 randomly there are  K ways of doing this, where K is the<em> combination of 15 elements taken 3 at a time </em>

K=\binom{15}{3}=\frac{15!}{3!(15-3)!}=\frac{15!}{3!12!}=\frac{15.14.13}{6}=455

As there are 9 non 75-W bulbs, by the fundamental rule of counting, there are 6*5*9 = 270 ways of selecting 3 bulbs with exactly two 75-W bulbs.

So, the probability of selecting exactly 2 bulbs of 75 W is

\frac{270}{455}=0.5934=59.34\%

(b)

The probability of selecting three 40-W bulbs is

\frac{4*3*2}{455}=0.0527=5.27\%

The probability of selecting three 60-W bulbs is

\frac{5*4*3}{455}=0.1318=13.18\%

The probability of selecting three 75-W bulbs is

\frac{6*5*4}{455}=0.2637=26.37\%

Since <em>the events are disjoint</em>, the probability of taking 3 bulbs of the same kind is the sum 0.0527+0.1318+0.2637 = 0.4482 = 44.82%

(c)

There are 6*5*4 ways of selecting one bulb of each type, so the probability of selecting 3 bulbs of each type is

\frac{6*5*4}{455}=0.2637=26.37\%

(d)

The probability that it is necessary to examine at least six bulbs until a 75-W bulb is found, <em>supposing there is no replacement</em>, is the same as the probability of taking 5 bulbs one after another without replacement and none of them is 75-W.

As there are 15 bulbs and 9 of them are not 75-W, the probability a non 75-W bulb is \frac{9}{15}=0.6

Since there are no replacement, the probability of taking a second non 75-W bulb is now \frac{8}{14}=0.5714

Following this procedure 5 times, we find the probabilities

\frac{9}{15},\frac{8}{14},\frac{7}{13},\frac{6}{12},\frac{5}{11}

which are

0.6, 0.5714, 0.5384, 0.5, 0.4545

As the events are independent, the probability of choosing 5 non 75-W bulbs is the product

0.6*0.5714*0.5384*0.5*0.4545 = 0.0419 = 4.19%

3 0
3 years ago
Q
Tema [17]

Answer:

y = \frac{1}{2} x+7

Step-by-step explanation:

Slope-intercept form: y = mx + b

Slope formula: \frac{y2-y1}{x2-x1}

Given points: (-6, 4), (6, 10)

(-6, 4) = (x1, y1)

(6, 10) = (x2, y2)

To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.

First, let's find the slope. To do this, input the given points into the slope formula:

\frac{10-4}{6-(-6)}

Simplify:

10 - 4 = 6

6 - (-6) = 6 + 6 = 12

\frac{6}{12}=\frac{1}{2}

The slope is \frac{1}{2}.

To find the y-intercept, input the slope and one of the given points(in this example I'll use point (6, 10)) into the equation and solve for b:

10 = \frac{1}{2}(6)+b

10 = 3 + b

7 = b

The y-intercept is 7.

Now that we know the slope and the y-intercept, we can write the equation:

y = \frac{1}{2} x+7

4 0
3 years ago
Find the minimum value of
Lana71 [14]

Answer:

14

Step-by-step explanation:

2x + y = 20                                                                                     (1)

2x + 3y = 36                                                                                  (2)

(2) - (1) ⇔ (2x - 3y) - (2x + y) = 36 - 20

          ⇔ 2y = 16

          ⇔ y = 8                                                                               (3)

From (3) and (1), we have:

    2x + y = 2x + 8 = 20

⇔ 2x = 12

⇔ x = 6

So: C = x + y = 6 + 8 = 14

Conclusion : C = 14

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4 0
3 years ago
Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of
Temka [501]

Answer:

2/5

Step-by-step explanation:

i took test and i got 100

4 0
3 years ago
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Igoryamba

Answer:

30) =

36) >

Explanation:

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2 years ago
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