What are the dimensions of the base of the pyramid?

Suppose you purchase a bundle of 18 bare-root broccoli plants. The sales clerk tells you that on average you can expect 8% of th

neonofarm [45]

Answer:

There is a 57.18% probability that you will lose at most 1 of the broccoli plants.

Step-by-step explanation:

For each plant, there are only two possible outcomes. Either they die, or they do not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we have that

There are 18 plants, so $n = 18$ .

8% of the plants die before producing any broccoli. So $p = 0.08$ .

Use the binomial formula to find the probability that you will lose at most 1 of the broccoli plants.

This is

$P = P(X = 0) + P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{18,0}.(0.08)^{0}.(0.92)^{18} = 0.2229$

$P(X = 1) = C_{18,1}.(0.08)^{1}.(0.92)^{17} = 0.3489$

$P = P(X = 0) + P(X = 1) = 0.2229 + 0.3489 = 0.5718$

There is a 57.18% probability that you will lose at most 1 of the broccoli plants.

7 0

3 years ago

Two mechanics worked on a car. The first mechanic to work for 5 Hours in the second mechanic work for 15 Hours. Together they ch

Butoxors [25]

<h2>Hello!</h2>

The answers is:

The first mechanic's rate is $70 per hour.

The second mechanic's rate is $110 per hour.

Let's write the given information in order to make the equations that will help us to solve this problem.

Let be "x" the first mechanic's rate and "y" the second mechanic's rate, so:

If the first mechanic worked for 5 hours and the second mechanic worked for 15 hours, and the together charged a total of $2000.

$5x+15y=2000$

Also, we know that the sum of the two rates was $170 per hour, so:

$x+y=180$

Then, isolating "x" and replacing it into the first equation, we have:

$x=180-y$

$5(180-y)+15y=2000$

$900-5y+15y=2000$

$10y=2000-900$

$10y=1100$

$y=\frac{1100}{10}=110$

So, the second mechanic's rate is $110 per hour.

Now, to calculate the first mechanic's rate we need to replace "y" into the second equation:

$x+y=180\\x+110=180\\x=180-110=70$

So, the first mechanic's rate is $70 per hour.

Have a nice day!

7 0

3 years ago

The quotient of-54 and 9, subtracted from 8 times a number, is-18

AysviL [449]

The number is: " -3 " .
_____________________________________
Explanation:
_____________________________________
Let "x" be the "unknown number" for which we are to solve.

8x − (-54/9) = -18 ; Solve for "x" ;

→ 8x − (-6) = - 18 ;

→ 8x + 6 = - 18 ;

Subtract "6" from each side of the equation:

→ 8x + 6 − 6 = - 18 <span>− 6 ;

to get: 8x = -24 ;

Divide EACH SIDE of the equation by "8" ; to isolate "x" on one side of the equation ; & to solve for "x" ;

8x / 8 = -24 / 8 ;

to get: x = -3 .
________________________________
The number is: " -3 " .
________________________________</span>

4 0

2 years ago

En la tienda de mascotas "Animalo-T", se desea elevar un elefante de 2,900 kg utilizando una elevadora hidráulica de plato grand

Korvikt [17]

Answer:

Se requiere una fuerza de 854.473 newtons sobre el émbolo pequeño.

Step-by-step explanation:

Por el Principio de Pascal se conoce que el esfuerzo experimentado por el elefante es igual a la presión ejercida por el plato pequeño. Es decir:

$\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$ (1)

Donde:

$F_{1}$ - Fuerza experimentada por el elefante, medida en newtons.

$F_{2}$ - Fuerza aplicada sobre el plato pequeño, medida en newtons.

$A_{1}$ - Área del plato grande, medida en metros cuadrados.

$A_{2}$ - Área del plato pequeño, medida en metros cuadrados.

La fuerza aplicada sobre el plato pequeño es:

$F_{2} = \left(\frac{A_{2}}{A_{1}} \right)\cdot F_{1}$

La fuerza experimentada por el elefante es su propio peso. Por otra parte, el área del plato es directamente proporcional al cuadrado de su diámetro. Es decir:

$F_{2} = \left(\frac{D_{2}}{D_{1}} \right)^{2}\cdot m\cdot g$ (2)

Donde:

$D_{1}$ - Diámetro del plato grande, medido en centímetros.

$D_{2}$ - Diámetro del plato pequeño, medido en centímetros.

$m$ - Masa del elefante, medida en kilogramos.

$g$ - Aceleración gravitacional, medida en metros por segundo cuadrado.

Si sabemos que $D_{1} = 0.75\,m$ , $D_{2} = 0.13\,m$ , $m = 2900\,kg$ y $g = 9.807\,\frac{m}{s^{2}}$ , entonces la fuerza a aplicar al émbolo pequeño es: