Need help on 4.9.2 project: performance task: the subway stop

Answer:

Her age is 40 years

Step-by-step explanation:

Let Jerry's age be represented as j

Let Marjorie's age be denoted as m

The first part of the question states:

j = 4 + m/2

For the second equation:

m = 3j - 32

Multiply the first equation by 2 to get:

2j = 8 + m

Leading to m = 2j - 8

Set both equations for m equal to each other:

2j - 8 = 3j - 32

By simplifying, we get:

3j - 2j = 32 - 8

Therefore, j = 24

Now substituting back:

m = 2j - 8

m = 2(24) - 8

Thus, m = 48 - 8

Final result: m = 40

A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)

b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells

d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour

e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours

Answer:

The option is D: Absolute value function

Step-by-step explanation:

The absolute value indicates how far a number is from 0 on the number line, in either direction.

We have the function;

f(x) = |2x³ - 3x| + 5

This function holds an absolute value operator which is |2x³ - 3x|.

Consequently, this function is characterized as an absolute value function since it includes algebraic terms enclosed in absolute value notation.

Respuesta:

El salario mensual de Koffi: $3500 ($42000 anuales)

Salario mensual de Pete: $4416.7 ($53000 anuales)

Salario mensual de Pat: $8750 ($105000 anuales)

Explicación paso a paso:

Sea x el salario anual de Pat

Sea y el salario anual de Pete

Sea z el salario anual de Koffi

Según el enunciado, sus salarios anuales suman $200000 es decir, x + y + z= $200000

Pete gana $11000 más que Koffi anualmente, lo que significa que y = $11000 + z

Pat gana $1000 menos que el doble (×2) del salario anual de Pete, es decir, x = 2y - $1000

Así, tenemos 3 ecuaciones:

(1)..... x + y + z= $200000

(2).... y = $11000 + z

(3).... x = 2y - $1000

Primero, sustituimos y en la ecuación (3), es decir,

x = 2(11000 + z) - 1000

x = 22000 + 2z - 1000

x = 21000 + 2z............ (4)

Luego incorporamos las ecuaciones (4) y (2) en la ecuación (1) para encontrar z:

x + y + z = 200000

21000 + 2z + 11000 + z + z = 200000

4z + 32000 = 200000

4z = 200000 - 32000

4z = 168000

z = 42000

Así que z (salario anual de Koffi) es de $42000.

Para conocer y, sustituimos z en la ecuación (2).

y = 11000 + z

y = 11000 + 42000

y = 53000

Por lo tanto, y (salario anual de Pete) es de $53000

Para hallar x, sumamos $42000 y $53000, y restamos de $200000 es decir, 42000 + 53000 = 95000

200000 - 95000 = 105000

Por lo tanto, x (salario anual de Pat) es de $105000.

Para obtener el salario mensual de cada individuo, dividimos su salario anual entre 12:

Koffi (z) = 42000/12 = $3500

Pete (y) = 53000/12 = $4416.7

Pat (x) = 105000/12 = $8750

To tackle this question, we will apply the z statistic to discover the probability. The formula used for z score is:

z = (x – u) / s

Where,

u = sample mean = 68

s = standard deviation of the samples = 12

x = sample value = 70

In this instance, we want the probability that the sample mean exceeds 70, so we will look at the right side of z on the normal distribution graph.

Calculating z:

z = (70 – 68) / 12

z = 2 / 12

z = 0.17

Next, we will find P at z ≥ 0.17 using standard distribution tables:

P (z = 0.17) = 0.5675

However, this value is not our desired answer as it pertains to the left of z. Therefore, we need to compute:

P (z ≥ 0.17) = 1 - 0.5675

P (z ≥ 0.17) = 0.4325, which translates to 43.25%

 

<span>The probability that the sample mean surpasses 70 is 43.25%</span>