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3 years ago

How do you rearrange the equation (2x) /(4pi) +((1-x) /2) =0 to solve for x?

1 answer:

3 0

$\frac{2x}{4 \pi } + \frac{1-x}{2} =0 \\ 
 \frac{x}{2 \pi } + \frac{1-x}{2} = 0$
Then we will multiply both sides of the equation by 2 π :
x + π ( 1 - x ) = 0
x + π - π x = 0
x ( 1 - π ) = - π / · ( - 1 )
x ( π - 1 ) = π
x = π / ( π - 1 )

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Mathematical Statistics with Applications Help Homework

Mars2501 [29]

7.43: Let $X$ denote the random variable for height and $\overline X$ for the sample mean. Then if $\mu$ is the mean of

So the probability that the difference between the sample and population means does not exceed 0.5 inch is

$P(|\overline X-\mu|\le0.5) = P\left(\left|\dfrac{\overline X-\mu}{0.25}\right|\le\dfrac{0.5}{0.25}\right) = P(|Z|\le 2) \approx \boxed{0.95}$

per the empirical or 68/95/99.7 rule.

7.44: For a sample of size n, the sample standard deviation would be $\frac{2.5}{\sqrt n}$ . We want to find n such that

$P(|\overline X-\mu| < 0.4) = 0.95$

Comparing to the equation from the previous part, this means we would need

$\dfrac{0.4}{\frac{2.5}{\sqrt{n}}} = 0.16\sqrt n = 2 \implies \sqrt n = 12.5 \implies n = 156.25$

so a sample of at least 157 men would be sufficient.

7 0

3 years ago

Jay had 6 times as much money as Kay. Then Jay gave Kay $33. Jay now has twice as much money as Kay. How much did they each star

timofeeve [1]

Answer:

Jay started with $148.5 and Kay with $24.75.

Step-by-step explanation:

With the information provided you know that Jay had 6 times as much money as Kay wich can be expressed as:

J=6K, where

J is the money Jay had

K is the money Kay had

Also, you know that Jay gave Kay $33 and Jay now has twice as much money as Kay, which would be:

J-33=2(K+33)

Now, you can replace J=6K in this equation and solve for K:

6K-33=2K+66

6K-2K=66+33

4K=66

K=24.75

Then, you can replace the value of K in J=6K:

J=6*24.75

J=148.5

According to this, the answer is that Jay started with $148.5 and Kay with $24.75.

7 0

2 years ago

Which equation could be solved using this application of the quadratic formula?

Alex_Xolod [135]

Answer:

C. x^2 + 2x - 1 = 3

Step-by-step explanation:

The standard form of a quadratic equation is

ax^2 + bx + c = 0

We need to use the quadratic formula and the given expression to find the values of a, b, and c.

The quadratic formula is

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Where the formula has -b, the problem has -2, so b = 2.

Now we have

ax^2 + 2x + c = 0

In the denominator, where the formula has 2a, the problem has 2(1), so a = 1.

Now we have

x^2 + 2x + c = 0

Inside the root, the quadratic formula has -4ac. the problem shows -4(1)(-4). Since we already know that a = 1, then c = -4.

Now we have

x^2 + 2x - 4 = 0

Let's look at choice A.

x^2 + 1 = 2x - 3

Subtract 2x from both sides. Add 3 to both sides.

x^2 - 2x + 4 = 0 This is not it!

Let's look at choice B.

x^2 - 2x - 1 = 3

Subtract 3 from both sides.

x^2 - 2x - 4 = 0 This is not it!

Let's look at choice C.

x^2 + 2x - 1 = 3

Subtract 3 from both sides.

x^2 + 2x - 4 = 0 This is it!

Answer: C. x^2 + 2x - 1 = 3

8 0

3 years ago

Reid will be driving through Spain this summer. He did some research and knows that the average price of gas in Spain is approxi

Molodets [167]

Answer:

(a)The amount of fuel in dollars = $1.62

(b)The rate equivalent to in U.S. dollars per gallon = $ 1.45

Step-by-step explanation:

Reid will be driving through Spain this summer. He did some research and knows that the average price of gas in Spain is approximately 1.12 euros per liter.

1 USD = 0.69 euros

We have to find the money that we should pay in order to get the same amount of fuel.

1 euro = $\frac{1}{0.69}$

1 euro = $1.45

So 1.12 euros = 1.12 $\times$ 1.45 = $1.62

(a)The amount of fuel in dollars = $1.62

(b)The rate equivalent to in U.S. dollars per gallon = $ 1.45

5 0

3 years ago

Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couple

yulyashka [42]

Answer:

the residual is 0.2032

Step-by-step explanation:

The regression line has been given as:

Y^ = 0.00753X-0.06759

The paired observation for X is (31, 0.369)

The value of X is the empathy score under subject 15 = 31

The value of the brain activity under subject 15 is 0.369

So we have y^ = 0.00753(31) - 0.06759

= 0.1658

Then the residual = y - y^

= 0.369 - 0.1658

= 0.2032

Therefore the residual is 0.2032

Please check the attachment for the table, it will aid you in understanding the solution

4 0

3 years ago