Solve the following inequality. Graph the solution.
4b + 3 < 19

Step-by-step explanation:

(a)(i) The average rate of change is:

(895 − 455) / (250 − 150)

4.4

(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change.  Using point-slope form:

y − 455 = 4.4 (x − 150)

Simplifying to slope-intercept form:

y − 455 = 4.4x − 660

y = 4.4x − 205

(a)(iii) The break-even point is when the profit is 0.

0 = 4.4x − 205

4.4x = 205

x = 46.6

(b)(i) The "demand function" is the selling pice of the compasses:

p = 40 − 4q²

where p is the price in dollars and q is the quantity in millions of units.

Profit is revenue minus cost.

P = R − C

P = pq − 15q

P = (p − 15) q

P = (25 − 4q²) q

P = 25q − 4q³

where P is the profit in millions of dollars and q is the quantity in millions of units.

(b)(ii) Find values of q when P = 18.

18 = 25q − 4q³

4q³ − 25q + 18 = 0

We know that q=2 is a root of this equation.  Using grouping:

4q³ − 8q² + 8q² − 25q + 18 = 0

4q² (q − 2) + (q − 2) (8q − 9) = 0

(q − 2) (4q² + 8q − 9) = 0

4q² + 8q − 9 = 0

Solve with quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)

q = (-8 ± √208) / 8

q = (-8 ± 4√13) / 8

q = (-2 ± √13) / 2

Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.

Answer:

Two solutions.

hope that will help you

Answer:

A. zero

Step-by-step explanation:

3x + 13 = 3(x + 6) + 1

step 1. distribute 3 through the parantheses:

3x + 13 = 3(x + 6) + 1

step 2. cancel equal terms on both sides of the equation:

3x + 13 = 3x + 18 + 1

13 = 18 + 1

step 3. add the numbers:

13 = 18 + 1

13 = 19

13 ≠ 19, so there is no solution.

may i please have brainliest?

Answer:

A. 2

Step-by-step explanation:

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

Use any two points given in the table of values. Let's use (1, 5), (3, 9)

Let,

[tex] (1, 5) = (x_1, y_1) [/tex]

[tex] (3, 9) = (x_2, y_2) [/tex]

Plug these values into the slope formula:

[tex] slope (m) = \frac{9 - 5}{3 - 1} [/tex]

[tex] slope (m) = \frac{4}{2} [/tex]

[tex] slope (m) = 2 [/tex]

Answer:

convergent

Step-by-step explanation:

the function increases or decreases or as the number of terms of the series increases.

Answer:

Divergent

Step-by-step explanation:

The series can be written as:

∑ 1 / (4n − 1)

We can compare this to 1 / (5n).  1 / (5n) is smaller and diverges (p-series test).  Therefore, the larger function also diverges.

Answer:

Step-by-step explanation:

960/3. that's 320 a side. They said maximum, I'm guessing they just wanted you to use base times height as if it was a square, since I'm not seeing any other information. the maximum possible area would be, if the sides were 320 each would be 102,400 square feet. Maximum

Answer:

It can be a passing thought or a question that launches a full-on existential exploration. Having a sense of meaning and purpose in life is usually a positive motivator, at home and at work. But maybe the questioning itself is where life's true mission is found...

Step-by-step explanation:

Answer:

13 inches of snow

Step-by-step explanation:

Answer:

he has to get at least a score of 88

Step-by-step explanation:

Answer:

84.25%

Step-by-step explanation:

85+76+95+81 = 337

337/4= 84.25

so Jack needs to get at least 84.25% on his fifth test to have an average of at least 85%:)

Answer:

The cost of the dryer would be 425$

Step-by-step explanation:

796 - 54 = 742

742 ÷ 2 = 371

371 = washer cost

371 + 54 = 425

425 = dryer price

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

Explanation:

w = cost of washer

d = cost of dryer

costs are in dollars

w+d = 796 since the two costs combine to get a total cost of $796

w = d-54 because the washer is $54 cheaper

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

Let's start with the first equation and plug in the second equation

w+d = 796

(w) + d = 796

(d-54)+d = 796 ... replace w with d-54

d-54+d = 796

2d-54 = 796

2d = 796+54 ... adding 54 to both sides

2d = 850

d = 850/2 ... dividing both sides by 2

d = 425

The dryer costs $425

We can stop here.

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

If you want to find the cost of the washer, then,

w = d-54

w = 425-54 .... plug in d = 425

w = 371

The washer costs $371

Note that

w+d = 371+425 = 796

which matches with the total cost we were given. This confirms our answer.

Answer:

13/4*19/3=20.5833 or 20 and 7 over 12

You are correct. The answer is choice B.

The base angles of an isosceles triangle are congruent. The base angles are opposite the congruent sides as shown by the tickmarks.

Answer:

Step-by-step explanation:

Given expression is,

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

To prove this identity we will take the left hand side of the equation and will prove equal to the right side.

(2x - 1)² + 2(2x - 1) = (2x - 1)(2x + 1)

4x² - 4x + 1 + 4x - 2 = (2x - 1)(2x + 1)

4x² - 1 = (2x - 1)(2x + 1)

(2x - 1)(2x + 1) = (2x - 1)(2x + 1) [Since a² - b² = (a - b)(a + b)]

Answer:

Step-by-step explanation:

Multiply answer = - 106

Divide answer = 1.25

Answer:

15 uniforms.

Step-by-step explanation:

830-80=750/50=15  : )

Answer:

Supercalifragilisticexpialidocious is 34 letters long.

Step-by-step explanation:

I see you like Fortnite by your profile picture, I play as well. I'm an OG, I have Black Knight. That's why I think you should give it to me.

еthaȵ is my Epic if you ever want to play.

Answer:

9

Step-by-step explanation:

Answer:

x = 2.210526316

Step-by-step explanation:

Answer:

[tex]x = −1.9434851[/tex]

Step-by-step explanation:

[tex]0.11 +1 2.74(x + 3) = 0.08 + 13.49 \\ 0.11 + 12.74x + 38.22 = 0.08 + 13.49 \\ 12.74x + 38.33 = 13.57 \\ 12.74x = 13.57 - 38.33 \\ 12.74x = −24.76 \\ \frac{12.74x}{12.74} = \frac{ - 24.76}{12.74} \\ x = −1.9434851[/tex]

Answer: 8

Step-by-step explanation:

Using the probability concept, it is found that:

a) i) There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.

ii) There is a 0.849 = 84.9% probability that the first person selected is not in management.

b) The events are neither complementary nor mutually exclusive.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

In this problem, there is a total of 120 + 50 + 1460 + 302 + 68 = 2000 people.

[tex]p = \frac{118}{2000} = 0.059[/tex]

There is a 0.059 = 5.9% probability that the first person selected is either in maintenance or a secretary.

Item ii:

2000 - 302 = 1698 people are not in management, hence:

[tex]p = \frac{1698}{2000} = 0.849[/tex]

There is a 0.849 = 84.9% probability that the first person selected is not in management.

Item b:

If a person is either in maintenance or a secretary, they are also not in management, hence the events are neither complementary nor mutually exclusive.

To learn more about the probability concept, you can take a look at https://brainly.com/question/24437717

Following are the solution to the given points:

For point a:

i)

[tex]\to P(B \cup E) = P(B) + P(E) - P( B\cap E)[/tex]

Where [tex]P(B \cap E) = 0[/tex] because they are both separate occasions It is impossible to be a member of both departments.  

[tex]\to P(B\cup E) =\frac{50}{120 + 50 + 1460 + 302 + 68} +\frac{68}{120 + 50 + 1460+ 302 +68}\\\\[/tex]

                    [tex]=\frac{50}{2000} +\frac{68}{2000}\\\\=\frac{50+68}{2000} \\\\=\frac{118}{2000} \\\\=\frac{ 59}{1000} \\\\=0.059\\[/tex]

ii)

[tex]\to P(D^c) = 1 - P(D)[/tex]

               [tex]=1- (\frac{302}{120+50+1460+302+68})\\\\=1- (\frac{302}{2000})\\\\=1- (\frac{ 151}{1000})\\\\= 1- 0.151 \\\\= 0.849\\\\[/tex]

For point b:

Please find the attached file.

For point c:

Events in a. I are mutually incompatible since [tex]P(B \cap E) = 0[/tex]. One would be a part of the both departments.

Learn more:

brainly.com/question/20661176

Answer: 23

Step-by-step explanation: Plug in your values:

7(5) + 4(-3)

35 + (-12)

35 - 12

23

Hope this helps!

Answer:

50 degrees

Step-by-step explanation:

Angle ABE is the opposite of the angle given on two converging lines, making it the same degree :)

Answer:

Phillips brother is 11.

Step-by-step explanation:

11 + 15  = 26

Let x be age of Philip's brother.

4 + x +x = 26

2x = 26 -2

2x = 22

x = 22/2

x = 11

Philip's brother is 11 years old

Answer:

None

Step-by-step explanation:

First of all you have 12 balloonas, and you blow up 13 of them and your friend blows up 5 of them but you only have 12. So you can’t find the right amoun.

Answer:

The Awnser is 1/4

Step-by-step explanation:

Answer:

D. No

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

Answer:

(-12,2)

Step-by-step explanation:

2x + 4y = -16

2y - x = 16

Multiply the bottom part by 2.

2x + 4y = -16

4y - 2x = 32

Add the equations and the answers to the equations up, and they will equal each other.

(2x + 4y) + (4y - 2x) = -16 + 32

8y = 16

y = 2

Plug y = 2 to the 2nd equation.

2*2 - x = 16

4 - x = 16

Subtract 4 from both sides.

-x = 12

Multiply both sides by -1.

x = -12

Answer:

66 inches ;

95.44 ;

4

Step-by-step explanation:

Given that:

Normal distribution with;

Mean(m) = 66 inches

Standard deviation (s) = 3 inches

A.) If a horse is chosen at random, Expected height will be equal to the mean of the distribution = 66 inches

B.) percentage horses who are between 60 and 72 inches

Zscore = ( x - m) / s

x = 60

Zscore = (60 - 66) / 3

Zscore = - 6/3

= - 2

P(Z < - 2) = 0.0228

Zscore = ( x - m) / s

x = 72

Zscore = (72 - 66) / 3

Zscore = 6/3

= 2

P(Z < 2). = 0.9772

Between 60 and 72

0.9772 - 0.0228 = 95.44

c) In a particular year there are 25 horses running in the Melbourne Derby. How many of these would you expect to have a height of less than 63 inches?

Zscore = ( x - m) / s

x = 63

Zscore = (63 - 66) / 3

Zscore = - 3/3

= - 1

P(Z < - 1) = 0.1587

0.1587 * 25 = 3. 967 = 4