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3 years ago

Solve: 5x – (7x + 4) = 3(x + 5) + 4(5 – 2x)

Mathematics

2 answers:

defon3 years ago

8 0

Answer:

x=13

Step-by-step explanation:

I hope this helps with your question :)

ki77a [65]3 years ago

4 0

Answer:

Step 1. Remove parenthesis.

$5x-7x-4=3(x+5)+4(5-2x)$

Step 2: Simplify the left side.

$-2x-4=3(x+5)+4(5-2x)\\-2x-4=3(x+5)+4(5-2x)$

Step 3: Expand.

$-2x-4=3x+15+20-8x$

Step 4: Simplify the right side.

$-2x-4=-5x+35$

Step 5: Add 4 to both sides.

$-2x=-5x+35+4$

Step 6: Simplify.

$-2x=-5x+39$

Step 7: Add 5x to both sides.

$-2x+5x=39$

Step 8: Simplify.

$3x=39$

Step 9: Divide both sides by 3

$x=13$

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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

Solve each equation. Round your answers to the nearest ten-thousandth. Please show work. Part 3A

Butoxors [25]

Answer:

19.

log9(5x^2 + 10) - log9(10) = 1

<=> log9((5x^2 + 10)/10) = log9(9)

<=> (5x^2 + 10)/10 = 9

<=> 5x^2 + 10 = 90

<=> 5x^2 = 80

<=> x^2 = 16

<=> x = +/- (4)

20.

log5(2x^2 + 4) + log5(3) = 2

<=> log5((2x^2 + 4) x 3) = log3(9)

<=> 6x^2 + 12 = 9

<=> 6x^2 = -3

=> No real x satisfies. ( x^2 always larger or equal to 0)

21.

log6(8) + log6(7 - 2x^2) = 2

<=> log6(8 x (7 - 2x^2)) = log6(36)

<=> 56 - 16x^2 = 36

<=> 16x^2 = 20

<=> x^2 = 5/4

<=> x = +/- sqrt(5/4)

Hope this helps!

5 0

4 years ago

Use a model to divide 2÷1/3

frutty [35]

.....

........

....ncncj

8 0

3 years ago

There are 30 businesses with 4 executives each for the new office building. each business needs one office for each of its execu

rodikova [14]

Answer:

1 executive for every 12 offices

7 0

3 years ago

Can anybody help me on this assignment I've been working on it for weeks and I can't get the slope

mr Goodwill [35]

Answer:

Y=7/3x+3

Step-by-step explanation:

you start at the y intercept which is b. you would then do a rise over run, starting with the lowest value ont the grid. you will count 7 up, and then you do run, which is counting across. you will get 3. your answer is y=7/3x+3

6 0

3 years ago