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2 years ago

If a normal distribution has a mean of 62 and a standard deviation of 12 what is the z-score for a value of 80

Mathematics

1 answer:

kap26 [50]2 years ago

3 0

Answer with explanation:

$\text{Mean}=\mu = 62\\\\ \text{standard deviation}=\sigma=12\\\\ \bar X=80\\\\Z_{score}=\frac{\bar X -\mu}{\sigma}\\\\Z_{score}=\frac{80-62}{12}\\\\Z_{score}=\frac{18}{12}\\\\Z_{score}=1.5$

Option B:→ 1.5

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Initially a tank contains 10 liters of pure water. Brine of unknown (but constant) concentration of salt is flowing in at 1 lite

zhenek [66]

Answer:

Therefore the concentration of salt in the incoming brine is 1.73 g/L.

Step-by-step explanation:

Here the amount of incoming and outgoing of water are equal. Then the amount of water in the tank remain same = 10 liters.

Let the concentration of salt be a gram/L

Let the amount salt in the tank at any time t be Q(t).

$\frac{dQ}{dt} =\textrm {incoming rate - outgoing rate}$

Incoming rate = (a g/L)×(1 L/min)

=a g/min

The concentration of salt in the tank at any time t is = $\frac{Q(t)}{10}$ g/L

Outgoing rate = $(\frac{Q(t)}{10} g/L)(1 L/ min)$ $\frac{Q(t)}{10} g/min$

$\frac{dQ}{dt} = a- \frac{Q(t)}{10}$

$\Rightarrow \frac{dQ}{10a-Q(t)} =\frac{1}{10} dt$

Integrating both sides

$\Rightarrow \int \frac{dQ}{10a-Q(t)} =\int\frac{1}{10} dt$

$\Rightarrow -log|10a-Q(t)|=\frac{1}{10} t +c$ [ where c arbitrary constant]

Initial condition when t= 20 , Q(t)= 15 gram

$\Rightarrow -log|10a-15|=\frac{1}{10}\times 20 +c$

$\Rightarrow -log|10a-15|-2=c$

Therefore ,

$-log|10a-Q(t)|=\frac{1}{10} t -log|10a-15|-2$ .......(1)

In the starting time t=0 and Q(t)=0

Putting t=0 and Q(t)=0 in equation (1) we get

$- log|10a|= -log|10a-15| -2$

$\Rightarrow- log|10a|+log|10a-15|= -2$

$\Rightarrow log|\frac{10a-15}{10a}|= -2$

$\Rightarrow |\frac{10a-15}{10a}|=e ^{-2}$

$\Rightarrow 1-\frac{15}{10a} =e^{-2}$

$\Rightarrow \frac{15}{10a} =1-e^{-2}$

$\Rightarrow \frac{3}{2a} =1-e^{-2}$

$\Rightarrow2a= \frac{3}{1-e^{-2}}$

$\Rightarrow a = 1.73$

Therefore the concentration of salt in the incoming brine is 1.73 g/L

8 0

3 years ago

−9x (5x+4 ) +10 (x+3) can someone please solve his for me thank u step by step please i really need to find out how to do it

Ivahew [28]

Answer:

-45 $x^{2}$ -26x+30

Step-by-step explanation:

So first you let's divide this equation into three parts.

Part one -9x(5x+4)

Step one: you have to distribute the -9x to the numbers in the parentheses. That would leave us with a -9x*5x = -45 $x^{2}$ and -9x*4 = -36x
Step two: Put the answers together. That would leave us with -45 $x^{2}$ -36x.

Part two 10(x+3)

Step one: you have to distribute the 10 to the numbers in the parentheses. That would leave us with a 10*x = 10x and 10*3 = 30
Step two: Put the answers together. That would leave us with 10x+30

Part three solve

Step one: combine and put together what you have solved for. That would leave us with a -45 $x^{2}$ -36x+ 10x+30
Step two: combine like terms. The like terms here are -36x and 10x. When you combine them you would get -26x.
Step three: Write the equation in standard form. Therefore the answer is -45 $x^{2}$ -26x+30.

Let me know if anything is confusing!

5 0

2 years ago

Let mZA = 40°. If zB is a complement of ZA, and ZC is a supplement of ZB, find these measures.

seraphim [82]

Angle b= 50

Angle c= 130

Complementary angles are two angles that add to equal 90

Supplementary angles are two angles that add to equal 180

To find the measurement of angle b, subtract 40 from 90 (50)

To find the measurement of angle c, subtract 50 from 180 (130)

7 0

3 years ago

Jed Sites

g100num [7]

Answer:

Option B: 3x + 3y - 3

Step-by-step explanation:

In an isosceles triangle, the two congruent sides are equal.

We are told the base is; x - y - 2 units

Now let each of the congruent sides be represented as A.

Thus the perimeter equation will be;

P = 2A + x - y - 2

Now, we are told that the perimeter is; 7x + 5y - 8 units

Thus;

7x + 5y - 8 = 2A + x - y - 2

Rearranging gives;

7x - x + 5y + y - 8 + 2 = 2A

2A = 6x + 6y - 6

Divide through by 2 to give;

A = 3x + 3y - 3 units

6 0

2 years ago

Transformations questions! thank you :)

denis-greek [22]

Answer:

Either B or D is the answer

4 0

3 years ago