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3 years ago

Y varies inversely as x and y=5 when x=3

Mathematics

2 answers:

cluponka [151]3 years ago

6 0

Xy=k

3*5=k

k=15

xy=15 or y=15/x

Veronika [31]3 years ago

3 0

So if somthing varies inversely then when one value goes up, the other value goes down so xy=z and z has to be the same so lets say that z=16
when x=2 y=8
when x=4 y=4
when x=8 y=2
when x=16 y=1
so xy=z
subtitute
(3)(5)=15
so if x=5 y=3
x=1 y=15
x=15 y=1

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Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation:

Vikentia [17]

Answer:

$\= x = 18.5$ , $\sigma = 5.15$

$15.505 < \mu < 21.495$

$14.93 < \mu < 22.069$

Step-by-step explanation:

From the question we are are told that

The sample data is 21, 14, 13, 24, 17, 22, 25, 12

The sample size is n = 8

Generally the ample mean is evaluated as

$\= x = \frac{\sum x }{n}$

$\= x = \frac{ 21 + 14 + 13 + 24 + 17 + 22+ 25 + 12 }{8}$

$\= x = 18.5$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x- \=x )^2}{n}}$

$\sigma = \sqrt{\frac{\sum ((21 - 18.5)^2 + (14-18.5)^2+ (13-18.5)^2+ (24-18.5)^2+ (17-18.5)^2+ (22-18.5)^2+ (25-18.5)^2+ (12 -18.5)^2 )}{8}}$

$\sigma = 5.15$

considering part b

Given that the confidence level is 90% then the significance level is evaluated as

$\alpha = 100-90$

$\alpha = 10\%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.645$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.645 * \frac{5.15 }{\sqrt{8} }$

=> $E = 2.995$

The 90% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 2.995 < \mu < 18.5 + 2.995$

$15.505 < \mu < 21.495$

considering part c

Given that the confidence level is 95% then the significance level is evaluated as

$\alpha = 100-95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table the value is

$Z_{\frac{ \alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E =1.96 * \frac{5.15 }{\sqrt{8} }$

=> $E = 3.569$

The 95% confidence interval is evaluated as

$\= x - E < \mu < \= x + E$

substituting values

$18.5 - 3.569 < \mu < 18.5 + 3.569$

$14.93 < \mu < 22.069$

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Kasey and Jordan are counting calories while eating lunch in the school cafeteria. In one week, Kasey had

malfutka [58]

Answer:

Jordan got 222 calories from pizza

Step-by-step explanation:

Given:

slices of pizza ate by Kasey =10

cups of fruit salad by Kasey= 5

slices of pizza ate by Jordan = 6

cups of fruit salad by Jordan= 7

Kasey's calorie count = 3070

Jordan calorie count = 2522

To Find:

calories Jordan got from pizza =?

Solution:

Let the calorie of one slice of pizza be x

and the calorie of one cup of fruit salad be y

According to the question, the equation that represents the Kasey's Scenario is

10x + 5y = 3070-------------------------------------(1)

Similarly the equation that represents the Jordan Scenario is

6x + 7y = 2522--------------------------------------(2)

multiply eq(1) by 6 we get

60x + 30y = 18420---------------------------------(3)

multiply eq(2) by 10 we get,

60x + 70y = 25220----------------------------------(4)

Subtracting eq (3) from (4) we get

60x + 70y = 25220

60x + 30y = 18420

(-) (-) (-)

-----------------------------------

0x + 40y = 6800

---------------------------------

=>40 y = 6800

=>y = $\frac{6800}{40}$

=> y = 170

So calorie of one cup fruit salad is = 170 calories

substituting the y values in eq 1 we get

10x + 5(170) = 3070

10x + 850 = 3070

10x = 3070 - 850

10x = 2220

x = $\frac{2220}{10}$

x= 222

So calorie of one pizza slice = 222 calories

Now we know that Jordan ate 6 slices of pizza

calories Jordan get from pizza = number of pizza he ate X calore per pizza slice

=> 6 x 222

=>1332 calories

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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3 years ago