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love history [14]

3 years ago

13

Is the z score corresponding to a number or score below the mean always negative?

1 answer:

rusak2 [61]3 years ago

7 0

Answer:

Yes

Step-by-step explanation:

The z-score corresponding to a number or score can be calculated using:

$z = \frac{x - \mu}{ \sigma}$

Where x stands for the individual scores, and

$\mu$

stands for the mean.

Since

$x \: \: < \: \mu$

for all numbers or scores below the mean, the difference will always be negative these values below the mean.

This will always result in a negative z-score for all numbers below the mean.

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In trip 1 you drove 104 miles in 4 gallons; in trip 2 you drove 78 miles how many gallons did you use in trip 2

BlackZzzverrR [31]

First do 104/4 which equals which equals 26
so you can drive 26miles on one gallon

then do 78/26 which equals 3

so you used 3 gallons of gas on trip 2

4 0

3 years ago

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A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

The equation P= 21 + 2w models the perimeter, P, of a rectangle with a length of / units and a width of w units.

natima [27]

Answer:

width = 10 units and length = 20 units

Step-by-step explanation:

Let the width be w

so Length will be 2w

using the rectangle formula:

$\sf Perimeter \ of \ rectangle= 2L + 2W$

$\sf 60= 2(2w) + 2w$

$\sf 60= 4w + 2w$

$\sf 60= 6w$

$\sf w = 10 \ units$

Find length:

$\sf length = 2w$

$\sf length = 2(10)$

$\sf length = 20 \ units$

5 0

2 years ago

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ASAP PLEASE‼️‼️<br><br><br> What is the area rounded to the nearest 10th

Igoryamba

Answer:

379.56 ft

Step-by-step explanation:

25 squared = 625

diameter of the half circle is 25

Diameter divided by 2 is radius

pi r squared is the formula for area of circle

r=12.5

pi * 12.5 squared

4 0

3 years ago

ASAP<br> -will mark brianist

Amiraneli [1.4K]

Answer:

20-12

35-21

40-24

Step-by-step explanation:

You times both numbers by the same value

5 0

3 years ago

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