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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?

Mathematics
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
Read 2 more answers
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

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\sf 60= 4w + 2w

\sf 60= 6w

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\sf length = 2w

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\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:

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Step-by-step explanation:

25 squared = 625

diameter of the half circle is 25

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r=12.5

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4 0
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Amiraneli [1.4K]

Answer:

20-12

35-21

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Step-by-step explanation:

You times both numbers by the same value

5 0
3 years ago
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