Coopers & Lybrand surveyed 210 chief executives of fast-growing small companies. Only 51% of these executives had a management succession plan in place. A spokesperson for Cooper & Lybrand said that many companies do not worry about management succession unless it is an immediate problem. However, the unexpected exit of a corporate leader can disrupt and unfocus a company for long enough to cause it to lose its momentum. Use the data given to compute a 92% confidence interval to estimate the proportion of all fast-growing small companies that have a management succession plan.

Answers

Answer 1

Answer:

Answer:

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

(0.46154 , 0.558)

Step-by-step explanation:

Given sample size 'n' = 210

The sample proportion 'p' = 51% = 0.51

Confidence intervals are determined by

$(p^(-) - z_(\alpha ) \sqrt{(p^(-) (1-p^(-) )/(n) } , p^(-) +Z_(\alpha ) \sqrt{(p^(-) (1-p^(-) ))/(n ) } )$

The 92% of z-score value

$Z_{(\alpha )/(2) } = Z_{(0.08)/(2) } = Z_(0.04) = 1.405$

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

$(0.51 - 1.405 \sqrt{(0.51 (1-0.51 )/(210) } , 0.51 +1.405 \sqrt{(0.51 (1-0.51))/(210 ) } )$

on calculation , we get

(0.51-0.048 , 0.51 + 0.048)

(0.46154 , 0.558)

Final answer:-

92% Of confidence intervals to estimate the proportion of all fast-growing small companies that have a management succession plan.

(0.46154 , 0.558)

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Solve for x: 4x/5= -20

We must use substitution to do this second integral. We can use the substitution t = 7x, which will give dx = Correct: Your answer is correct. dt. Ignoring the constant of integration, we have sin(7x) dx =

Answers

Answer:

Therefore, the solution is:

$\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}$

Step-by-step explanation:

We calculate the given integral. We use the substitution t = 7x.

$\int \sin 7x\, dx=\begin{vmatrix} 7x=t\n 7\, dx=dt\n dx=(dt)/(7) \end{vmatrix}\n\n=\int \sin t \cdot (1)/(7)\, dt\n\n=(1)/(7)\cdot (-\cos t)\n\n=-(\cos 7x)/(7)$

Therefore, the solution is:

$\boxed{\int \sin 7x\, dx=-(\cos 7x)/(7)}$

On 1st September 2014 there were 5400 trees planted in a wood.On 1st September 2015, only 5184 of these trees were still alive.
It is assumed that the number of trees still alive is given by N = art
where / is the number of trees still alive t years after 1st September 2014.
a) Write down the value

c) Show that on 1st September 2040
the number of trees still alive is predicted
o have decreased by over 65% compared
with September 2014.

b) Show that r = 0.96

Answers

Answer:

1. a = 5400

2. r = 0.96

3. Percentage decrement = 65.4%

Step-by-step explanation:

Given

N = ar^t

Solving (a): Write down the value of a

a implies the first term

And from the question, we understand that the initial number of trees is 5400.

Hence,

a = 5400

Solving (b): Show that r = 0.96

Using

N = ar^t

When a = 5400, t = 1 i.e. the first year and N = 5184

Substitute these values in the above expression

5184 = 5400 * r¹

5184 = 5400 * r

5184 = 5400r

Solve for r

r = 5184/5400

r = 0.96

Solving (c): Show that the trees has decreased by over 65% in 2040

First, we need to calculate number of years (t) in 2040

t = 2040 - 2014

t = 26

Substitute 26 for t, 5400 for a and 0.96 for r in N = ar^t to get the number of trees left

N = 5400 * 0.96^26

N = 1868.29658019

N = 1868 (approximated)

Next, we calculate the percentage change as thus:

%Change = (Final - Initial)/Initial * 100%

Where the initial number of trees =5400 and final = 1868

%Change = (1868 - 5400)/5400 * 100%

%Change = -3532/5400 * 100%

%Change = -3532%/54

%Change = -65.4%

The negative sign indicates a decrements or reduction.

Hence, percentage decrement = 65.4% and this is over 65%

-13 = n/9 - 14

it's due in a couple of minutes, pls help me :(

Answers

-9. first, add 14 on both sides = “-1=n/9
-9/9=-1

Answer:

$n = 9$

Step-by-step explanation:

1) Add 14 to both sides.

$- 13 + 14 = (n)/(9)$

2) Simplify-13 + 14 to 1

$1 = (n)/(9)$

3) Multiply both sides by 9.

$1 * 9 = n$

4) Simplify 1 × 9 to 9.

$9 = n$

5) Switch sides.

$n = 9$

Therefor,theanswerisn=9.

Lola used 2 1/2 ink cartridges while her friends used 1 3/4 ink cartridges. How many more ink cartridges did Lola use than her friends

Answers

Answer:

Lola used 3/4 more ink cartridges than her friends

Step-by-step explanation:

What is the equation of the line through the origin and (-5, 6)?O A. y = -5x
O B. y = -6/5 x
O C. y = -6x
0 D. y = -5/6 x

Answers

Answer:

answer is option b

Step-by-step explanation:

B. y=-6/5x

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1:x=9+6t,y=12-3t,z=3+9t L2:x=4+16s, y=12-8s, z=16+20s parallel skew intersecting If they intersect, find the point of intersection. (If an answer does not exist, enter DNE.)

Answers

Answer:

L1 and L2 are skew

Step-by-step explanation:

Since the equation of the line is

L1:x=9+6t,y=12-3t,z=3+9t

L2:x=4+16s, y=12-8s, z=16+20s

then if they intersect each other , they will have both in that point P=(xp , yp ,zp) then

1)9+6t = 4+16s

2) 12-3t =2-8s

3) 3+9t = 16+20s

adding 2*2) to 1)

9+6*t + 24-6t = 4+16*s + 4-16*s

33 = 8

since this is not possible , the error comes from our assumption that the lines intersect each other

then they are skew or parallel. They are parallel if their corresponding vectors are parallel , that is

L1 (x,y,z) = (9,12,3) + (6,-3,9)*t

L1 (x,y,z) = (4,2,16) + (16,-8,20)*t

then if they are parallel

(16,-8,20)= k*(6,-3,9)

16=6*k

-8 = -3*k

20= 9*k

since there is no k that satisfy for x , y and z simultaneously then L1 and L2 are not parallel

therefore L1 and L2 are skew

Final answer:

The lines L1 and L2 are neither parallel nor intersecting. Upon comparing their direction vectors and attempting to find a common solution, it is determined that they are skew.

Explanation:

In order to determine whether two lines in three dimensions are parallel, skew, or intersecting, we compare their direction vectors. The given lines L1 and L2 are in the form of parametric equations. The direction vectors for the lines are d1 = <6, -3, 9> for L1 and d2 = <16, -8, 20> for L2. To determine if they are parallel, we check if there is a constant ratio between the corresponding terms. This isn't the case here, so the lines are not parallel.

For skew lines, they neither intersect or are parallel. Since we have already confirmed the lines are not parallel, to confirm if they are skew we must try to find a common solution (point of intersection). If we cannot, then they are skew. However, solving the equations does not give a common solution, so they do not intersect either. Hence, the lines are skew.

Learn more about Analysis of Lines in 3D here:

brainly.com/question/33134474

#SPJ3

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