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3 years ago

5a-2b=c solve for a

2 answers:

3 0

When trying to find value of variable, always try to get it alone.

5a-2b=c

Add 2b for both sides.

5a=2b+c

Divide by 5

Answer: 2b+c/5

adelina 88 [10]3 years ago

3 0

5a + -2b + 2b = 2b +c
-2b + 2b = 0
5a + 0 = 2b + c
5a = 2b + c
a = 0.4b = 0.2c
simplified
a = 0.4b + 0.2c

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Solve the equation x2-16x+54=0

kari74 [83]

Answer:

x1 = 8+√10, x2 = 8 -√10

Step-by-step explanation:

x² - 16x + 54 = 0

$x = \frac{-b +/-\sqrt{b^{2} -4ac} }{2a} \\x = \frac{-(-16)+/-\sqrt{(-16)^{2} -4*1*54} }{2*1} \\\\\\x = \frac{16+/-\sqrt{(40)} }{2*1} = 8+/-\sqrt{10} \\\\x_{1} = 8+\sqrt{10}\\\\x_{2} =8-\sqrt{10}$

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2 years ago

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Adam buys a car for £15060 which depreciates in value at a rate of 1.5 per year. Work out how much Adam's car will be worth in 9

Step2247 [10]

Answer: £13026.90

Step-by-step explanation:

1.5% of £15060 = 225.90

225.90 x 9 = 2033.10

15060 - 2033.10 = 13026.90

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4 0

2 years ago

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SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

$P(Z>1.25)=1-P(Z$

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

Step-by-step explanation:

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".

Part a

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

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

And we can find this probability using the complement rule and with the normal standard table or excel:

$P(Z>1.25)=1-P(Z$

Part b

We are interested on this probability

$P(400$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(400$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1$

Part c

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

$P(X>a)=0.8$ (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 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

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

$P(X$