Your cafeteria line requires 8 minutes on the average for each customer to proceed through the line and pay the cashier. The average time space between each customer is 30 seconds. If the line is open for 1 1/2 hours for lunch, how many customers can you serve for lunch?​

Answer:

X= -3 or X=-9

Step-by-step explanation:

Answer: x = -3, x = -9

Step-by-step explanation: |x + 6| + 10 = 13

Firstly, subtract 10 from both sides:

|x + 6| = 3

Since it is an absolute value, separate it into two equations with either outcome:

x + 6 = 3

x + 6 = -3

Solve for x now.

x + 6 = 3

Subtract 6 from both sides:

x = -3

x + 6 = -3

Subtract 6 from both sides:

x = -9

Voila! Hope this helps.

Answer: 30 days.

Step-by-step explanation: Figure out the least common multiple for each number.

Answer:

-2

Step-by-step explanation:

-8 + 2 = -6; -6=3y; then -6 divided by 3 = -2

The positive solution of the quadratic equation [tex]\rm 0=-x^2+2x+1[/tex]  is x=2.41

It is given that the quadratic equation:

[tex]\rm 0=-x^2+2x+1[/tex]

It is required to find the solution to the above quadratic equation.

A quadratic equation is a second-degree algebraic equation represented by the:

[tex]\rm ax^2+bx+c=0[/tex]........(1)

Where a, b, and c are the constants and [tex]\rm a\neq 0[/tex]

We know that:

[tex]\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

We have:

[tex]\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0[/tex] ..........(2)

After comparing (1) and (2) we get:

[tex]\rm a=-1, b=2, and \ c=1[/tex]

Put these values in the above formula we get:

[tex]\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}[/tex]

[tex]\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41[/tex]

Thus, the positive solution of the quadratic equation is x=2.41

Learn more about quadratic equations here:

https://brainly.com/question/2263981

Answer:

x= 2.41

Step-by-step explanation:

Answer:

$173

Step-by-step explanation:

Given the following :

Amount spent on wedding cake = $200

Amount deposited = $500

Amount spent on new books = $127

Change in savings :

Amount deposited - total amount spent

Total amount spent = ($200 + $127).= $327

Hence,

Change in saving = $500 - $327

= $173

Answer:

5x + 6y

Hope it helps!

1)

[tex]m = \frac{y - y}{x - x} = \frac{55 - 59}{10 - 0} = \frac{ - 4}{10} = - \frac{2}{5} [/tex]

[tex]y = - \frac{2}{5} x + b[/tex]

Since the line passes through the point (0,59), the coordinates of this point satisfies the equation of y;

[tex]59 = - \frac{2}{5} (0) + b[/tex]

[tex]b = 59[/tex]

Final answer:

[tex]y = - \frac{2}{5} x + 59[/tex]

Answer:

0.5

Step-by-step explanation:

Considering we are given a mean and standard deviation, the distribution of the data is likely to be a normal or Gaussian distribution, i.e. a symmetrical, bell-shaped distribution of probability density, peaked at the mean;

Such a distribution has 0.5 probability each side of the mean;

So, if the mean is 200 then, the probability that the number of customers is greater than 200 (x > 200), according to this mean, is 0.5;

As a normal distribution is symmetrical, this is also the probability of a number of customers less than 200.

Answer:

The y-intercept is 2 because it is on the y-axis. The y-intercept is located on the y-axis.

Answer: 12.5 square centimeters

Step-by-step explanation:

Answer:

-12 < x  

or:

x > -12

Step-by-step explanation:

[tex]5 > -x-7[/tex]

[tex]5+7 > -x[/tex]

[tex]12 > -x[/tex]

[tex]12(-1) > -x(-1)[/tex]

[tex]-12 < x[/tex]

Hope this helps

Using coordinates, the field judge is exactly 5 yards in front of the ball.

These are values that show the position of an object, these values often include a number for the x-axis (horizontal axis) and one for the y-axis (vertical axis).

If we consider the ball as 0 or the starting point the coordinates are:

Learn more about coordinates in: https://brainly.com/question/13140132

d = rt

d/r  rt/r

d/r = t

While guessing and checking is one way to do this problem, I will show you how to do it algebraically.

Let one side be A

Let the other side be B

2(A+B)=16

A*B=15

First equation because the perimeter is 16 and the second because the area is 15. Now solve the system of equations

A+B=8

A=8-B

Substitute into equation two

B(8-B)=15

-B^2+8b-15=0

B^2-8b+15=0

(B+3)(B+5)=0

B=3,5

A=5,3 respectively

From this we can see that one side is 5 meters long while the other side is three meters long.

Step-by-step explanation

Since we're looking at a rectangle, let's consider its perimeter and area formulas.

Perimeter: 2x + 2y (A rectangle has four sides, with two equal sides, so this is x + x + y + y simplified)

Area: (x)(y) (length x breadth so, x times y)

So we have two equations: 2x + 2y = 16 and x*y = 15. Solve simultaneously. Refer to the attached image.

Answer:

-10xy

Step-by-step explanation:

Answer:

-10xy

Step-by-step explanation:

distributive property

5*-2=-10

-10xy

Answer:

The value of x is equal to 1, written as x = 1.

General Formulas and Concepts:
Algebra I

Equality Properties

Terms/Coefficients

Functions

Step-by-step explanation:

Step 1: Define

g(x) = 5x + 4

g(x) = 9

Step 2: Solve for x

∴ when the function g(x) equals 9, the value of x that makes the function true would be x = 1.

---

Topic: Algebra I

Answer:

Step-by-step explanation:

Converse of alternate interior angles theorem:

This theorem states that if two lines are intersected by a transversal and the alternate interior angles are congruent, lines will be parallel.

Therefore, p║n.

Perpendicular transversal theorem:

By this theorem,

In a plane, if a line is perpendicular to one of two parallel lines, then it will be perpendicular to the other line.

Therefore, l ⊥ p.

Options selected in the blank spaces are correct.

Answer:3/2

Step-by-step explanation:

Answer:

2

lb

,

0.05

a

,

2

,

0.1

lb

,

0.99

lb

2

,

4.18

lb

2

,

4.2

lb

2

,

2.1

lb

Step-by-step explanation:

We are given that :

Using Formulas:

Area of rectangle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak {length\times breadth }}}[/tex]

Area of semicircle:

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak{ \dfrac{\pi r^2 }{2}}}}[/tex]

Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;

[tex] \quad\dashrightarrow\quad \sf {Area_{\tiny { total}} = Area_{\tiny {rectangle}}+ Area_{\tiny {semicircle}}}[/tex]

[tex] \quad\dashrightarrow\quad \sf {A = ( l \times b ) + \dfrac{\pi r^2 }{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf {41.4 = ( l \times 4 ) +\dfrac{3.14\times 2^2}{2} }[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= ( l \times 4 )+ \dfrac{ 3.14\times 4}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4=( l \times 4 )+ \dfrac{12.56}{2}}[/tex]

[tex] \quad\dashrightarrow\quad \sf { 41.4= (l \times 4 )+ 6.28}[/tex]

[tex] \quad\dashrightarrow\quad \sf {l \times 4 = 41.4-6.28 }[/tex]

[tex] \quad\dashrightarrow\quad \sf { l\times 4 = 35.12}[/tex]

[tex] \quad\dashrightarrow\quad \sf { l =\dfrac{35.12}{4}}[/tex]

[tex] \quad\dashrightarrow\quad \underline{\underline{\pmb{\sf {l = 8.78\:cm}}} }[/tex]

The length of the longer side of the rectangle will be 8.78 cm.

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

On one of a rectangle's shorter sides, a semicircle is drawn. The rectangle's shorter side is 4 cm long. The figure has a surface area of 41.4 square centimeters.

Then the length of the rectangle is calculated as,

A = πr² / 2 + l × b

41.4 = (3.14 / 2) × (4/2)² + 4l

41.4 = 6.28 + 4

l = 8.78 cm

The length of the longer side of the rectangle will be 8.78 cm.

More about the area link is given below.

https://brainly.com/question/27683633

#SPJ3

Answer:

Y= -1.5x+3

Step-by-step explanation:

(Y-Y1)=m(x-x1)

0-3=m(2-0)

m= -1.5

Y= -1.5x+B

when y=3 and x=0 b=3

Answer:

See below.

Step-by-step explanation:

a) Complementary angles (= 90°)

b) ∠FMG, ∠GMC, and ∠DMC

Answer:

2×2×13 = 52

or 2² × 13 = 52

it depends on how you want to present your answer

Answer:

you forgot to distribute 2 into the -3

I'm going to assume you ment 8

Step-by-step explanation:

2(x-3)=5

2x-6=5

+6 to both sides

2x=11

÷2 both sides

x = 5.5

Step-by-step explanation:

Equation for the volume of a cone is

V = (pi(r^2)h)/2

Plug in the known values to get

350 = (pi(6^2)h)/2

To find h, just isolate it by first dividing both sides by 2 and squaring 6 to get

175 = pi(36)h

Then, divide both sides by pi36 to get

h = 175/pi(36)

Answer:

The answer is below

Step-by-step explanation:

Given the cost as C(x) = x² + 4x - 40

a) Since the bracelets sell for $8 each, the revenue from x bracelets is given as:

Revenue = price for each bracelet × number of bracelet

Revenue = 8 × x = 8x

b) Profit (P) = Revenue - Cost

P(x) = 8x - [x² + 4x - 40]

P(x) = 8x - x² - 4x + 40

P(x) = -x² + 4x + 40

c) To maximize profit, the derivative of profit is equal to 0

Hence P'(x) = 0

-2x + 4 =0

2x = 4

x = 2

To maximize profit, the company should produce 2 bracelets

d) The maximum profit is:

P(2) = -(2²) + 4(2) + 40 = -4 + 8 + 40

P(2) = $44

The maximum profit is $44

Answer:

[tex]\sf 35 \%[/tex]

explanation:

[tex]\hookrightarrow \sf \dfrac{orange \ juice \ intake}{recommended \ mg} * 100[/tex]

[tex]\hookrightarrow \sf \dfrac{7*100}{2000} *100[/tex]

[tex]\hookrightarrow \sf 35 \%[/tex]

Answer:

Step-by-step explanation:

100x7=700

So you ate 700mg of Vitamin C by eating oranges 7 times in that day.

Now, lets figure out the percent part

700 n/100x2000

=35%

We didn't even have to round.

So hence, your answer is B.35%

Thanks!

Mark me brainliest!

Hey there!

1/5 + 3/10
= 2/10 + 3/10

= 2 + 3/10 - 0

= 5/10

= 5 ÷ 5 / 10 ÷ 5

= 1 / 2

Therefore, your answer is: 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)