Express the confidence interval 0.333 less than p less than 0.999 in the form Modifying Above p with caret + or - E. Modifying Above p with caret + or - E = + or -.

===================================================

Work Shown:

y = (3/2)x + 4

2y = 3x + 8 .... multiply both sides by 2

0 = 3x + 8 - 2y

3x-2y+8 = 0

The original equation transforms to 3x-2y+8 = 0. It is in the form Ax+By+C = 0. We see that A = 3, B = -2, C = 8. This form is very useful to help find the distance from a point to this line.

The formula we will use is

[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\[/tex]

where A,B,C were the values mentioned earlier. The p,q are the x and y coordinates of the point given. So p = 9 and q = -2

Plugging all that in gives...

[tex]d = \frac{|A*p+B*q+C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|3*9+(-2)*(-2)+8|}{\sqrt{3^2+(-2)^2}}\\\\d = \frac{|27+4+8|}{\sqrt{9+4}}\\\\d = \frac{|39|}{\sqrt{13}}\\\\d = \frac{39}{\sqrt{13}}\\\\d = \frac{39\sqrt{13}}{\sqrt{13}\sqrt{13}} \ \text{ rationalizing denominator}\\\\d = \frac{39\sqrt{13}}{13}\\\\d = 3\sqrt{13}\\\\d = \sqrt{9}*\sqrt{13}\\\\d = \sqrt{9*13}\\\\d = \sqrt{117}\\\\[/tex]

Answer:

k = -10/9 and k = 10/9

Step-by-step explanation:

given y = cos(kt) and the differential equation 81y'' = -100y

y' = -ksin(kt)

y'' = -k²cos(kt)

Substituting the value of y and y'' in the differential equation we have;

81 (-k²cos(kt))= -100 (cos(kt))

-81k²cos(kt)) = -100cos(kt))

-81k² = -100

k² = 100/81

k = ±[tex]\sqrt{\frac{100}{81} }[/tex]

k = ±10/9

k = -10/9 and k = 10/9

Answer:

4+10-284-4819+2948929

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

use photomath and it will solve ur problem

Answer:

vol = 62 in³

Step-by-step explanation:

First determine r (see attached image) by using pythagorean theorem.

a² = b² + c²

a = 3 in

b = 3/2 = 1.5 in

c = r

3² = 1.5² + r²

r = [tex]\sqrt{3^{2}-1.5^{2} }[/tex]

r = 2.598 in

Get the area = n/2 * a * r

n = number of sides = 6

r = 2.598 in

Area = 6/2 * 3 * 2.598

Area = 23.38 in²

get the volume = 1/3 * Area * h

Area = 23.38 in²

h = 8 in (as given)

vol = 1/3 * 23.38 * 8

vol = 62 in³

Answer:  y-intercepts: 250,000 & 3,000

Step-by-step explanation:

The first equation represents the trees cleared. The starting/original amount cleared was 250,000.

The second equation represents the trees planted. The starting/original amount planted was 3,000.

Answer:

Volume = π [ 2/3 - 12/2].

Step-by-step explanation:

So, in this question we are asked to find or Calculate for or determine the value of volume v of the solid obtained by rotating the region bonded by the given curves about the specified lines = ? (Unknown). In addition, we are given that y = x, y = x , so, about x = 3.

Volume = π ∫ [ (3 - y)^2 - (3 - y)^2 ] dy.

(Taking 0 and 1 as the lower and upper limit).

Volume = π ∫ 9 - 6y + y^2 - 9 - 6y + y^2 dy.

(Taking 0 and 1 as the lower and upper limit).

Volume = π ∫ 2y^2 - 12y dy.

(Taking 0 and 1 as the lower and upper limit).

(Solving the quadratic equation above, we have; Roots: -6, 0

Root Pair: -3 ± 3

Factored: f(x) = 2(x + 6)x)

Also,

Volume = π [ 2y^3 / 3 - 12y2/2]

Volume = π [ 2/3 - 12/2] cubic units.

Answer:

Dy/Dx=-4x/(1+x²)²

Step-by-step explanation:

The differential of 1_x² over 1+x²​

First of all

1_x² over 1+x²​ = (1_x²) / (1+x²​)

Let (1_x²) = u

Let (1+x²​) = v

Differential = Dy/Dx

Dy/Dx of (1_x²) / (1+x²​)

= (VDu/Dx -UDv/Dx)V²

u = (1-x²)

Du/Dx = -2x

(VDu/Dx) =(1+x²)(-2x)

V = 1+x²

Dv/Dx = 2x

UDv/Dx= (1-x²)(2x)

v² = (1+x²)²

Dy/Dx = ((1+x²)(-2x) - (1-x²)(2x))/(1+x²)²

Dy/Dx= ((-2x -2x³)-(2x-2x³))/(1+x²)²

Dy/Dx=( -2x -2x - 2x³ +2x³)/(1+x²)²

Dy/Dx=-4x/(1+x²)²

Answer:

A. (0, 4)

Step-by-step explanation:

y=mx+b

y=7x+4

7x<-- mx

4<-- b

b=y intercept

The value of the y-intercept of the line described by the equation is,

⇒ (0, 4)

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The equation of line is,

y = 7x + 4

Now, We know that;

The equation of line is,

y = mx + c

Where, c is y - intercept.

Hence, We get;

The value of the y-intercept of the line described by the equation is,

⇒ y = 4

⇒ (0, 4)

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Answer:

13/20<--->65%

21/25<--->84%

3/4<--->75%

2/5<--->40%

3/5<--->60%

To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.

Ex:  1/2=   .50->5.0->50.->50%

The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%

Fractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given  by 100.

For the fraction 13/20

13/20 * 100 = 13 * 5

13/20 = 65%

For the fraction 21/25

21/25 * 100 = 21 * 4

21/25 = 84%

For the fraction 3/4

3/4 * 100 = 3 * 25

3/4 = 75%

For the fraction 2/5

2/5 * 100 = 2 * 20

2/5 = 40%

For the fraction 3/5

3/5 * 100 = 3* 20

3/5 = 60%

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%
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Answer: 95 degrees.

Step-by-step explanation:

A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.

Answer:

Option C is the correct option

Solution,

The sum of the angles in the quadrilateral is 360°

Let the forth angle be X

X + 80° + 110° + 75° = 360°

Calculate the sum:

X + 265° = 360°

Subtract 265° on both sides

X + 265° - 265° = 360° - 265°

Calculate the difference

X = 95°

Hope this helps...

Good luck on your assignment...

Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310

Answer:

Solution,

[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]

[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

CL = LD

Step-by-step explanation:

In a circle, diameter AB is perpendicular to chord CD at point L. Which statement will always be true about this circle?

1) (CL)(LD)=AB

2) AL > LB

3) CL = LD

4) BL > AB

Answer: The chord is CD and the diameter AD of the circle are perpendicular to each other at point L. According to the perpendicular bisector theorem, if the diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc. This means that chord CD is bisected by the diameter of the circle at point L.

Since CD is bisected at point L, CL = LD

Also CD = 2CL = 2LD

Answer:

The height increase by

20/49π when pile is 14ft high

Step by step Explanation

Given:

rate of 20 ft3/min

To asolve this quest we will be using the volume of a cone then find the partial derivative

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Obtain the next iterate by plugging the previous iterate into the function.

First iterate:

[tex]z_0=2+i\implies z_1=f(z_0)=(2+i)^2-2-2i=1+2i[/tex]

Second iterate:

[tex]z_2=f(z_1)=(1+2i)^2-2-2i=-5+2i[/tex]

Third iterate:

[tex]z_3=f(z_2)=(-5+2i)^2-2-2i=19-22i[/tex]

Fourth iterate:

[tex]z_4=f(z_3)=(19-22i)^2-2-2i=-125-838i[/tex]

Answer:

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 29.5

Standard deviation r = 5.2

Number of samples n = 59

Confidence interval = 90%

z-value (at 90% confidence) = 1.645

Substituting the values we have;

29.5+/-1.645(5.2/√59)

29.5+/-1.645(0.676982337100)

29.5+/-1.113635944529

29.5+/-1.11

= ( 28.39, 30.61)

Therefore, the 90% confidence interval (a,b) =( 28.39, 30.61)

Answer:

Length=29.8 inches

Width=11.8 inches

Height=4.6 inches

Volume=1,617.54 cubic inches

Step-by-step explanation:

Let the side of congruent square cut =x inches

So the length of the rectangular box=(39-2x)

width = (21-2x)

height = x

The volume V=Length*Width*Height

= (39-2x)*(21-2x)*x

dV/dx= (39-2x)(21-4x)-2x(17-2x)=0

Simplify the equation above

819-156x-42x+8x^2-34x+4x^2=0

We have,

12x^2 -232 +819=0

Solve the quadratic equation using formula

a=12

b= -232

c=819

x= -b +or- √b^2-4ac/2a

= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)

= 232 +or- √53824 - 39312 / 24

= 232 +or- √14512 / 24

= 232 +or- 4√907 / 24

x= 232 / 24 + 4√907 / 24

=14.6861

Or

x=232 / 24 - 4√907 / 24

=4.64726

x=4.6 inches

Length=(39-2x)

={39-2(4.6)}

= 29.8 inches

Width=(21-2x)

={21-2(4.6)}

= 11.8 inches

Height=x= 4.6 inches

Volume=(39-2x)*(21-2x)*x

={39-2(4.6)}*{21-2(4.6)*4.6

=(39-9.2)*(21-9.2)*4.6

=29.8*11.8*4.6

=1,617.544

Approximately 1,617.54

Volume=1,617.54 cubic inches

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

sin(B) = sin(A)

sin(B) = cos(90 – B)

cos(B) = sin(180 – B)

cos(B) = cos(A)

Assuming the angles are in degrees, the second relation is always true.

By definition of sine,

sin(B) = AC/AB

cos(90-B) = cos (A) = AC/AB

therefore the second relation is true, for arbitrary values of B.

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true?

Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

6 x (10+ 6) = 8 x (8 +x)

Simplify:

96 = 64 + 8x

Subtract 64 from both sides:

32 = 8x

Divide both sides by 8

X = 4

Answer:

The provement is below

Step-by-step explanation:

z^(1/2)=x^(1/2)+y^(1/2)  =>  (z^(1/2))^2=  (x^(1/2)+y^(1/2))^2

=> z=x+y+2*x^(1/2)*y^(1/2) => z-x-y= 2*x^(1/2)*y^(1/2)

=> (z-x-y)^2= (2*x^(1/2)*y^(1/2) )^2 => (z-x-y)^2=4*x*y           (1)

Pls note that (z-x-y)^2= ((-1)*(-1)*(z-x-y))^2= ((-1)*(x+y-z))^2= (-1)^2*(x+y-z)^2=

=(x+y-z)^2

So  (z-x-y)^2= (x+y-z)^2 !!! Substitute in (1) (z-x-y)^2 by (x+y-z)^2   and will get

the required equality  (x+y-z)^2=4*x*y

Answer:

900

Step-by-step explanation:

A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

Given that are two events P(A) = 1/3, P(B) = 1/3, and P(A ∩ B) = 2/9.

We need to determine if the events are independent or not.

The chance of occurrences A and B intersecting (P(A B)) must be compared to the sum of both events' individual probabilities (P(A) × P(B)) in order to assess if events A and B are independent.

Two events A and B are independent if and only if:

P(A ∩ B) = P(A) × P(B)

Let's check if this condition holds for the given probabilities:

P(A) = 1/3

P(B) = 1/3

P(A ∩ B) = 2/9

Next, add up the odds of each separately:

P(A) × P(B) = (1/3) × (1/3) = 1/9

We can infer that A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

In other words, the likelihood that one event (A) occurs influences the likelihood that another event (B) occurs, and vice versa.

The probability of both events happening at once (P(A B)) would be equal to the product of their individual probabilities (P(A) × P(B)) if A and B were independent, but this is not the case in this situation.

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Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Answer:

9x^4

Step-by-step explanation:

(3x)^2 * x^2

9x^2 * x^2

Add the exponents

9x^(2+2)

9x^4

Answer:

x = 15

Step-by-step explanation:

You want to remove the opposites which will leave you with x = 15

Hope this helped! :)

Hey there!

ORIGINAL PROBLEM/EQUATION:

x + x - x = 15

CONVERSION/NEW EQUATION:

1x + 1x - 1x = 15

COMBINE the LIKE TERMS:

2x - 1x = 15

1x = 15

DIVIDE 1 to BOTH SIDES

1x/1 = 15/1

SIMPLIFY AFTER CANCELING OUT 1/1 BECAUSE IT GAVE YOU 1 & KEEPING 15/1 BECAUSE IT HELP/GIVE YOU THE x-value

NEW EQUATION: x = 15

Therefore, your answer is: x = 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)