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Paladinen [302]
2 years ago
15

-3=12y-5(2y-7). Solve for y

Mathematics
2 answers:
Yuliya22 [10]2 years ago
4 0
1. distribute the parentheses.
-3=12y-10y+35

2. Move the constants to the other side
-3-35=12y-10y

3. Subtract the terms
-38=2y

4. Divide by 2 to get y by itself
y=-19
Rasek [7]2 years ago
3 0

Answer:

y = -19

Step-by-step explanation:

-3 = 12y -5(2y - 7)

distribute -5 to (2y -7)

-3 = 12y - 10y + 35

subtract 35 from both sides and simplify

-38 = 2y

divide both sides by 2 to isolate y

-19 = y

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Find two numbers if their difference is 16 and their ratio is 5:7.
myrzilka [38]

Let us say that the numbers are x and y. The given clues are:

1. x – y = 16         (so x is the larger number)

2. y / x = 5 / 7

 

rewriting eqtn 2 in terms of y:

y = (5/7) x

 

combining 1 and 2:

x – (5/7) x = 16

(2/7) x = 16

x = 56

 

y = (5/7) x = 40

 

So the two numbers are 56 and 40.

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The scores on the LSAT are approximately normal with mean of 150.7 and standard deviation of 10.2. (Source: www.lsat.org.) Queen
faltersainse [42]

Answer:

a=150.7 -0.385*10.2=146.773

So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the  scores on the LSAT of a population, and for this case we know the distribution for X is given by:

X \sim N(150.7,10.2)  

Where \mu=150.7 and \sigma=10.2

We want to find a value a, such that we satisfy this condition:

P(X>a)=0.65   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.35 of the area on the left and 0.65 of the area on the right it's z=-0.385. On this case P(Z<-0.385)=0.35 and P(Z>-0.385)=0.65

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

Z=-0.385

And if we solve for a we got

a=150.7 -0.385*10.2=146.773

So the value of height that separates the bottom 35% of data from the top 65% (Or the 35 percentile) is 146.7.  

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3 years ago
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