If the ropes are pulled taunt,how many knots do you get?

The product of 3 consecutive odd numbers is 2,145. Enter a simplified expression for finding the numbers. Let n be the first odd

Arlecino [84]

Answer:

11, 13 and 15.

Step-by-step explanation:

Let's say that the odd number is "x". If x is for example 15, then the next ODD number would be 15+2=17 and the one after that would be 15+2+2=15+4=19.

Applying that here, we get:

Odd number* the next odd number*the next odd number=2145

x*(x+2)*(x+4)=2145

x*(x^2+4x+2x+8)=2145

x^3+6x^2+8x=2145

By solving the polynomial, you get x=11.

Which makes our three numbers: 11, 13 and 15.

11*13*15=2145. The answer checks.

6 0

4 years ago

The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d

aksik [14]

Answer:

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

$f(t)=\left \{ {{0 ,\-t$

Consider the second function:

$f(t)=\frac{e^{-t/\mu}}{\mu}\\$

Where Average waiting time = μ = 2.5

The function f(t) becomes

$f(t)=0.4e^{-0.4t}$

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

$\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt$

which is equal to 0.01

Solve the equation for x

$\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01$

Take natural log on both sides

$ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53$

<h3>Results</h3>

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

3 0

3 years ago

Indicate the equation of the given line in standard form.The line containing the median of the trapezoid whose vertices are R(-1

maxonik [38]

RS => y - 5 = (8 - 5)/(1 - (-1)) (x - (-1))
y - 5 = 3/2 (x + 1) => slope = 3/2
ST => y - 8 = (-2 - 8)/(7 - 1) (x - 1)
y - 8 = -10/6 (x - 1) = -5/3 (x - 1) => slope = -5/3
TU => y - (-2) = (0 - (-2))/(2 - 7) (x - 7)
y + 2 = 2/5(x - 7) => slope = 2/5
UR => y = 5/(-1 - 2) (x - 2)
y = -5/3 (x - 2) => slope = -5/3

The median is the line joining the midpoints of the non-parallel sides.
Midpoint of RS = ((-1 + 1)/2, (5 + 8)/2) = (0, 13/2)
Midpoint of TU = ((7 + 2)/2, -2/2) = (9/2, -1)

Equation of the line joining (0, 13/2) and (9/2, -1) is given by y - 13/2 = (-1 - 13/2)/(9/2) x
y - 13/2 = (-15/2)/(9/2) x
y - 13/2 = -15/9x
18y - 117 = -30x
30x + 18y = 117

7 0

3 years ago

It said i need to simplify. how do i

horrorfan [7]

Answer:

The equation relating the volume of water, y to the volume of flour, x is therefore;

y = 1/3×x

The quantity of water per liter of flour = 1/3 liters

The quantity of flour per liter of water = 3 liters

Step-by-step explanation:

The given information from the graph are;

At 0 liters of water, the volume of flour = 0 liters of flour

At 1 liter of water, the volume of flour = 3 liters of flour

The relationship between the volume of water and flour is linear given s follows;

The equation for a linear relationship is y = m·x + c

m = The gradient or slope of the line, c = the y-intercept

In the graph the y-intercept = 0 therefore, c = 0

The slope, m is (change in y-coordinate)/(Change in x-coordinate)

∴ m = (1 - 0)/(3 - 0) = 1/3

The equation relating the volume of water, y to the volume of flour, x is therefore;

y = 1/3×x

Such that when the question asks, how many liter of water is used per liter of flour, we get;

y = 1/3× 1 = 1/3 liters

Similarly when the question asks, how many liter of flour is used per liter of water, we get;

1 = 1/3×x

x = 3 × 1 = 3 liters.

4 0

3 years ago

Which properties justify the steps taken to solve the system? {3x−2y=10 4x−3y=14

Alexeev081 [22]

The answer is: Substitution property of equality.

The explanation is shown below:

1. To solve this problem you must apply the proccedure shown below:

2. When you clear the variable x from the first equation, and subtitute it into the second equation, you obtain:

<span>3x−2y=10
x=(10+2y)/3

4x−3y=14
</span>4[(10+2y)/]−3y=14
<span> y=-2

3. When you subsitute y=-2 into the first equation and clear the x, you have:

x=2
</span>

7 0

3 years ago

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