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Diano4ka-milaya [45]
3 years ago
10

Solve for each unknown

Mathematics
1 answer:
ehidna [41]3 years ago
5 0
<span>6=2+u then u = 6 - 2 = 4
(-16)=(-9)-w then w = 16 - 9 = 7
8=r+4 then r = 8 - 4 = 4
v+(-3)=(-10) then v = -10 + 3 = -7
9=j+7 then j = 9-7 = 2
(-14)=r-6 then r = -14 +6 = -8
(-2)-k=4 then k = -2 -4 = -6
(-10)=n-8 then n = -10 + 8 = -2
(-9)=s+(-4) then s = -9 + 4 = -5
(-4)-s=0 then s = -4</span>
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Which expression gives the distance between the points (2,3) and 4,-3)?
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Answer:

C

Step-by-step explanation:

The formula for finding the distance between 2 points (x1, y1) and (x2, y2) is

d = √[(x2 - x1)² + (y2 - y1)²]

Here (x2, y2) = (2, 3)  and (x1, y1) = (4, -3)

Plugging them gives us

d = √[(2 - 4)² + (3 - (-3))²]

   d = √[(2 - 4)² + (3 + 3)²]

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What is the final amount if 1920 is increased by 5% followed by a further 15% increase? Give your answer rounded to 2 DP.
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2318.4 is the correct wander

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Step-by-step explanation:

7 0
3 years ago
A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was record
makkiz [27]

Answer:

E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49  

Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899  

Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943  

Step-by-step explanation:

For this case we have the following data given:

X      1    2    3    4    5

F     74   10  11    3    2

The total number of values are 100, so then we can find the empirical probability dividing the frequency by 100 and we got the followin distribution:

X          1          2        3         4          5

P(X)     0.74   0.10   0.11    0.03    0.02

Previous concepts

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".  

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).  

And the standard deviation of a random variable X is just the square root of the variance.  

Solution to the problem

In order to calculate the expected value we can use the following formula:  

E(X)=\sum_{i=1}^n X_i P(X_i)  

And if we use the values obtained we got:  

E(X)=1*0.74 +2*0.1 +3*0.11+ 4*0.03 +5*0.02=1.49  

In order to find the standard deviation we need to find first the second moment, given by :  

E(X^2)=\sum_{i=1}^n X^2_i P(X_i)  

And using the formula we got:  

E(X^2)=1^2 *0.74 +2^2 *0.1 +3^2 *0.11 +4^2 0.03 +5^2 *0.02=3.11  

Then we can find the variance with the following formula:  

Var(X)=E(X^2)-[E(X)]^2 =3.11-(1.49)^2 =0.8899  

And then the standard deviation would be given by:  

Sd(X)=\sqrt{Var(X)}=\sqrt{0.8899}=0.943  

7 0
3 years ago
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