Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?
To maximize his income, Dr. Lum should teach_______classes for Hilltop College and __________classes for Serra College. His maximum income would be________.

Answer:

[tex]y> 3x + 2[/tex]

Step-by-step explanation:

Hope it is helpful....

The linear inequality that represents the given graph is y > 3x + 2.

The solutions to the graph of the inequalities is given as;

(x, y) = (0, 2)

(x, y) = (-3, -7)

To determine the inequality represented in the graph;

Thus, the linear inequality that represents the given graph is y > 3x + 2.

Learn more about graphs of linear inequality here: https://brainly.com/question/371134

Answer:

2

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

0.016

Step-by-step explanation:

Answer:

0.016

Step-by-step explanation:

Answer:

Ask your Teacher if you are missing any work and if you are do it and do some things for extra credit

Step-by-step explanation:

Answer: yes,it depends on the points

if you have 65% and you score a 80 on a 45 point assingment it can go up to a c

+ep explanation:

Answer:

C. (4, -6)

Hope it helps :)

Answer:

7 hours

Step-by-step explanation:

9 : 30 to 17:00 = 7 hours 30 minutes

Minus 30 minutes = 7 hours

Answer:

a) Yes

b) Yes

c) Yes

d) 0.6

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A large population has skewed data with a mean of 70 and a standard deviation of 6.

This means that [tex]\mu = 70, \sigma = 6[/tex]

Samples of size 100

This means that [tex]n = 100[/tex]

a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?

According to the Central Limit Theorem, yes.

b) Will the mean of the means of the samples remain close to 70?

According to the Central Limit Theorem, yes.

c) Will the distribution of the means have a smaller standard deviation?

According to the Central Limit Theorem, the standard deviation of the population is divided by the sample size, so yes.

d) What is that standard deviation?

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{100}} = \frac{6}{10} = 0.6[/tex]

So 0.6.

Answer:

10. Where was the medical mission held? A. At Barangay Tatalon Marikina B. At Barangay Almanza Las Piñas City C. At Barangay Pamplona Las Piñas City D. At Barangay CAA BF INT'L Las Piñas City

Answer:

B) $85,167

Step-by-step explanation:

u got discount 45% so u just have to pay 55% of it

cost = 55% x $154,85 = $85,1675

9514 1404 393

Answer:

 C.  45

Step-by-step explanation:

Apparently, your recursive definition is ...

  [tex]a_1=5\\a_n=a_{n-1}\cdot3[/tex]

Each term is 3 times the previous one, so the sequence starts ...

  5, 15, 45, 135, 405, ...

The 3rd term is 45.

Answer:

2025 is not a perfect cube

Answer:

64km/h

Step-by-step explanation:

Average speed= 48km÷45 minutes

= 48km÷0.75h

= 64km/h

Answer:

a) correct

b) 70 degrees

Step-by-step explanation:

since in the triangle BXC the sides BX and XC have the same length, they must also have the same angles with the baseline BC.

so, we know, XBC = 55 degrees.

and therefore BCX = 55 degrees.

the sum of all angles in a triangle is always 180 degrees.

so,

BXC = 180 - 55 - 55 = 70 degrees

Answer:

(a) Tree (see diagram)

(b)   (i) 9/64   (ii) 3/8

Step-by-step explanation:

3 black, 5 white, picks two at random with replacement.

SEE DIAGRAM FOR EXPLANATIONS

(a) Tree (see diagram)

(b)

(i) 9/64

(ii) 3/8

In the given problem we have 3 black ball and 5 white ball, the probability tree be constructed as per ball picks from bag.

(a) Refer the attached figure for the probability tree.

(b)

(i) The probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii) The probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Given:

The bag contain 3 black and 5 white balls.

(a)

Refer the attached figure for the construction of probability tree.

(b)

(i)

Since the getting two black ball are independent event so multiply the branch B ( refer attached figure)

[tex]P(\rm two\: black)=\dfrac{3}{8}\times\dfrac {3}{8}\\P(\rm two\: black)=\dfrac{9}{24}[/tex]

Thus, the probability that Paul picks two black balls is [tex]\dfrac{9}{64}[/tex].

(ii)

There should be two outcomes either (B,B) or (W, B).

From the attached figure,

[tex]P(\rm B,B)=\dfrac{9}{64}[/tex]

[tex]P(\rm W, B)=\dfrac{15}{64}[/tex]

Calculate the probability of second ball black.

[tex]P(\rm second\: ball\: black)=P(B, B) + P(W, B)\\P(\rm second\: ball\: black)=\dfrac{9}{64}+\dfrac{15}{64}\\P(\rm second\: ball\: black)=\dfrac{3}{8}[/tex]

Thus, the probability that Paul picks a black ball in his second draw is [tex]\dfrac{3}{8}[/tex].

Learn more about probability here:

https://brainly.com/question/11234923

Answer:

the answer is (4)

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Answer:

6

Step-by-step explanation:

The product of three consecutive numbers is divisible by ​6

Let us say the numbers are x, x+1 , x+2

if x = 1,

Product of the three consecutive numbers,

(1)(2)(3)

=> 6, which is divisible by 6

if x = 2,

Product of the three consecutive numbers,

(2)(3)(4)

=> 24, which is divisible by 6

Similarly if we take any 3 consecutive numbers their product will be divisible by 6.

Answer:

x = 1/2

hope it helps

have a nice day

Answer:

maybe  x=3.5

Step-by-step explanation:

6x= 1/2 (2x+5)

we take the 1/2 and distribute it into (2x+5) so we end up with

6x= 1x (or just x) + 2.5

We subtract 2.5 from both sides of the equation and we end up with

3.5x= 1x

we then need to isolate the x, so we divide both sides of the equation by x

and then we end up with

3.5= x/x, which ends up just being

3.5=x

Answer:

[tex]R = \frac{x(x+1)}{2x+1}[/tex] --- total resistance

Step-by-step explanation:

Given

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Required

Find R when

[tex]R_1 = x[/tex]

[tex]R_2 = x+1[/tex]

So, we have:

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Substitute values for both R's

[tex]\frac{1}{R} = \frac{1}{x} + \frac{1}{x+1}[/tex]

Take LCM

[tex]\frac{1}{R} = \frac{x+1+x}{x(x+1)}[/tex]

Collect like terms

[tex]\frac{1}{R} = \frac{x+x+1}{x(x+1)}[/tex]

[tex]\frac{1}{R} = \frac{2x+1}{x(x+1)}[/tex]

Inverse both sides

[tex]R = \frac{x(x+1)}{2x+1}[/tex]

Answer:

x = 20

Step-by-step explanation:

We can use a ratio to solve

10         14

------ = ----------

x          28

Using cross products

10 * 28 = 14*x

280 = 14x

Divide by 14

280/14 = 14x/14

20 =x

Answer:

20 cm

Step-by-step explanation:

It says that both of these shapes are similar. If we divide 28/14=2.

Then we can also multiply 10 cm by 2 cm to get 20 cm .

x= 20 cm

Hope this helps!

Given:

The two sets are:

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

To find:

The [tex]A\times B[/tex] and the number of relations from A to B.

Solution:

If A and B are two sets, then

[tex]A\times B=\{(x,y)|x\in A, y\in B\}[/tex]

We have,

[tex]A=\{1,4\}[/tex]

[tex]B=\{2,3,5\}[/tex]

Then,

[tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex]

If number of elements in set A is m and the number of element in set B is n, then the number of relations from A to B is [tex]2^{m\times n}[/tex].

From the given sets, it is clear that,

The number of elements in set A = 2

The number of elements in set B = 3

Now, the number of relations from A to B is:

[tex]2^{m\times n}=2^{2\times 3}[/tex]

[tex]2^{m\times n}=2^{6}[/tex]

[tex]2^{m\times n}=64[/tex]

Therefore, the required relation is [tex]A\times B=\{(1,2),(1,3),(1,5),(4,2),(4,3),(4,5)\}[/tex] and the number of relations from A to B is 64.

Answer:

0.4069 ; 1.843

Step-by-step explanation:

Given:

Base of parallelogram, b = (2x - 1)

Height = (4x - 7)

Area = 1

Area of parallelogram = Base * height

Area of parallelogram = (2x - 1) * (4x - 7)

(2x - 1) * (4x - 7) = 1

8x² - 14x - 4x + 7 = 1

8x² - 18x + 7 - 1 = 0

8x² - 18x + 6 = 0

Divide through by 2

4x² - 9x + 3 = 0

Solving the quadratic equation :

Using the formula

-b ± √(b² - 4ac) / 2a

a = 4 ; b = - 9 ; c = 3

Plugging in the values :

-(-9) ± √((-9)² - 4(4)(3)) / 2(4)

9 ± √(81 - 48) / 8

9 ± √33 / 8

(9 ± 5.7445626) / 8

(9 - 5.7445626) / 8) = 0.4069

(9 + 5.7445626) / 8 = 1.843

Answer:

2, 3, 4, 7, 8, 10 I hope

Answers

=================================================

Explanations:

---------------

Acronyms

SSS = side side side

SAS = side angle side

ASA = angle side angle

AAS = angle angle side

Answer: 180 degrees rotation, center (1.5, -0.5)

=====================================================

Explanation:

Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)

Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2

--------------

Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11

--------------

We have this system of equations

[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]

Equate the right hand sides and solve for x

7x-11 = x-2

7x-x = -2+11

6x = 9

x = 9/6

x = 3/2

x = 1.5

which leads to

y = x-2 = 1.5-2 = -0.5

or

y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5

Either way, x = 1.5 leads to y = -0.5

We get the ordered pair (x,y) = (1.5, -0.5)

This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)

Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that

AD = A''D

BD = B''D

CD = C''D

Answer:

x=-1

Step-by-step explanation:

the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1

Answer:

12. if 3/5 of them like chocolate ice cream 2/5 don't and 2/5 of 20 is 8.

A=8

13. 296 divided by 8 is 37

A=37

14. 123 divided by 7 is 17.5714285714 so each child will get 17 sweets and there will be 4 left over.

A=17 remainder of 4

15. umm i don't know just multiple 4.50 by the amount of soccer balls

A=?

16. srry i don't realy know there not enough of the pattern

Brainlest please

Your Welcome

BIFFY OUT!!!

Answer:

y = 6/5x -7

Step-by-step explanation:

the answer for this question is A

Answer:

x = 12 , y = 7

Step-by-step explanation:

Let the numbers be x and y

Sum of the numbers,         x + y = 19 -------- ( 1 )

Difference of the number , x - y = 5 -------- ( 2)

( 1 ) + ( 2 ) => 2x = 24  

                    x = 12

Substitute : x in ( 2 ) => 12 - y = 5

                               => 12 - 5 = y

                              => 7 = y