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dem82 [27]
3 years ago
10

43.12(bar on 12) in p/q form.​

Mathematics
1 answer:
arsen [322]3 years ago
4 0

Answer:

1423/33

Step-by-step explanation:

Let x = 43.121212.........

Two digits are repeating after decimal point. So multiply both sides by 100

100x = 4312.1212       --------------(I)

   <u> x =      43.1212  </u>   -----------(II)   { subtract equation (II) form (I)}

99x =      4269

x= 4269/99   {reduce to simplest form by giving by 3rd table}

x = 1423/33

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Rename the number 9,200 hundreds
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Nine thousand, two hundred
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Answer:

2ft^{3}

Step-by-step explanation:

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2 years ago
The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard
PtichkaEL [24]

Answer:

a)X \sim N(63,18)  

Where \mu=63 and \sigma=18

b) P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)

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

P(Z>1.5)=1-P(Z

c) P(X

P(Z

d) P(60

P(-0.167

P(-0.167

e)  IQR = 75.13-50.87=24.26

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 amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

X \sim N(63,18)  

Where \mu=63 and \sigma=18

Part b

We are interested on this probability

P(X>90)

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>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)

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

P(Z>1.5)=1-P(Z

Part c

We are interested on this probability

P(X

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

And we can find this probability using the normal standard table or excel:

P(Z

Part d

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

P(60

And we can find this probability with this difference:

P(-0.167

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

P(-0.167

Part e

Q1

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

P(X>a)=0.75   (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 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

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=-0.674

And if we solve for a we got

a=63 -0.674*18=50.87

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.  

Q3

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

z=0.674

And if we solve for a we got

a=63 +0.674*18=75.13

And then the IQR = 75.13-50.87=24.26

3 0
2 years ago
Why does sin(15) always equal the same number, no matter how big or small you make the triangle.
Alona [7]

Sin is equal to the same number, no matter how big or small you make the triangle because the sine of the angle is equal to the opposite side divided by the hypotenuse.

4 0
3 years ago
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