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2 years ago

Find the value of x in 4:x::x:16

Mathematics

1 answer:

AnnyKZ [126]2 years ago

4 0

Given:

4:x::x:16

To find:

The value of x.

Solution:

We have,

4:x::x:16

It means, we have

4:x = x:16

It can be rewritten as

$\dfrac{4}{x}=\dfrac{x}{16}$

On cross multiplication, we get

$4\times 16=x\times x$

$64=x^2$

Taking square root on both sides.

$\pm \sqrt{64}=x$

$\pm 8=x$

Since ratio can be negative or positive, therefore, the value of x is either -8 or 8.

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1 year ago

Find an equation for the line perpendicular to 2x+ 6y = 30 and goes through the point (6,2)

Mashutka [201]

Answer:

y = 3x - 16

Step-by-step explanation:

We are asked to find the equation of the line perpendicular to 2x + 6y = 30

We can use two formulas for this question, either

y = mx + c. Or

y - y_1 = m(x - x_1)

Step 1: calculate the slope

From the equation given

2x + 6y = 30

Make y the subject of the formula

6y = 30 - 2x

6y = -2x + 30

Divide both sides by 6, to get y

6y/6 = ( -2x + 30)/6

y = (-2x + 30)/6

Separate them in order to get the slope

y = -2x/6 + 30/6

y = -1x/3 + 5

y = -x/3 + 5

Slope = -1/3

Step 2:

Note: if two lines are perpendicular to the other, both are negative reciprocal of each other

Perpendicular slope = 3/1

Substitute the slope into the equation

y = mx + c

y = 3x + c

Step 3: substitute the point into the equation

( 6,2)

x = 6

y = 2

2 = 3(6) + c

2 = 18 + c

Make the c the subject

2 - 18 =c

c = 2 - 18

c = -16

Step 4: sub the value of c into the equation

y = 3x + c

y = 3x - 16

The equation of the line is

y = 3x - 16

If you try out the other formula, u will get the same answer

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3 years ago

7b divided by 12 = 4.2 what does b equal

iogann1982 [59]

It is 0.35 That is the answer.

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2 years ago

Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampl

galben [10]

The missing part of the question is highlighted in bold format

The Wall Street Journal reported that the age at first startup for 90% of entrepreneurs was 29 years of age or less and the age at first startup for 10% of entrepreneurs was 30 years of age or more.

Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p is the sample proportion of entrepreneurs whose first startup was at 29 years of age or less. If required, round your answers to four decimal places. np = n(1-p) = E(p) = σ(p) = (b) Suppose a sample of 200 entrepreneurs will be taken to learn about the most important qualities of entrepreneurs. Show the sampling distribution of p where p is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more. If required, round your answers to four decimal places.

Answer:

(a)

np = 180

n(1-p) = 20

E(p) = p = 0.9

σ(p) = 0.0212

(b)

np = 20

n(1 - p) = 180

E(p) = p = 0.1

σ(p) = 0.0212

Step-by-step explanation:

From the given information:

Let consider p to be the sample proportion of entrepreneurs whose first startup was at 29 years of age or less

So;

Given that :

p = 90% i.e p = 0.9

sample size n = 200

Then;

np = 200 × 0.9 = 180

n(1-p) = 200 ( 1 - 0.9)

= 200 (0.1)

= 20

Since np and n(1-p) are > 5 ; let assume that the data follows a normal distribution ;

Then:

The expected value of the sampling distribution of p = E(p) = p = 0.9

Variance $\sigma^2=\dfrac{p(1-p)}{n}$

$=\dfrac{0.9(1-0.9)}{200}$

$=\dfrac{0.9(0.1)}{200}$

$\mathbf{=4.5*10^{-4}}$

The standard error of σ(p) = $\sqrt{\sigma ^2}$

$\mathbf{= \sqrt{4.5*10^{-4}}}$

= 0.0212

(b)

Here ;

p is now the sample proportion of entrepreneurs whose first startup was at 30 years of age or more

p = 10% i.e p = 0.1

sample size n = 200

Then;

np = 200 × 0.1 = 20

n(1 - p) = 200 (1 - 0.1 ) = 180

Since np and n(1-p) are > 5 ; let assume that the data follows a normal distribution ;

Then:

The Expected value of the sampling distribution of p = E(p) = p = 0.1

Variance $\sigma^2=\dfrac{p(1-p)}{n}$

$=\dfrac{0.1(1-0.1)}{200}$

$=\dfrac{0.1(0.9)}{200}$

$\mathbf{=4.5*10^{-4}}$

The standard error of σ(p) = $\sqrt{\sigma ^2}$

$\mathbf{= \sqrt{4.5*10^{-4}}}$

= 0.0212

4 0

3 years ago