A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true? As h increases, s approaches r so that rh approaches r². As r increases, h approaches r so that rh approaches r². As s increases, h approaches r so that rh approaches r². As n increases, h approaches r so that rh approaches r².

A Regular Polygon Inscribed In A Circle Can Be Used To Derive The Formula For The Area Of A Circle. The

Answers

Answer 1

Answer:

Option (D)

Step-by-step explanation:

Formula to get the area of a regular polygon in a circle will be,

Area = [tex]n[\frac{1}{2}\times (\text{Base})\times (\text{Height})][/tex]

        = [tex]n[\frac{1}{2}\times (\text{s})\times (\text{h})][/tex]

Here 'n' is the number of sides.

If n increases, h approaches r so that 'rh' approaches r².

In other words, if the number of sides of the polygon gets increased, area of the polygon approaches the area of the circle.

Therefore, Option (4) will be the answer.

Answer 2

In this exercise it is necessary to have knowledge about polygons, so we have to:

Letter D

Then using the formula for the area of ​​a regular polygon we find that:

[tex]A=n(1/2*B*H)\\=n(1/2*S*H)[/tex]

So from this way we were not able to identify the option that best corresponds to this alternative.

See more about polygons at  brainly.com/question/17756657


Related Questions

Hey market sales six cans of food for every seven boxes of food the market sold a total of 26 cans and boxes today how many of each kind did the market sale

Answers

Answer:

It sold 14 cans boxes of food and 12 cans of food.

Step-by-step explanation:

The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.

Let the no. of sets of food boxes be x.

According to the question,

6x+7x=26

13x=26

x=26/13

x=2

No. of food cans =6x=6×2=12 cans

No. of food boxes=7x=7×2=14 boxes

Please mark brainliest ,if it is truly the best ! Thank you!

How do you compress this?

Answers

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]

Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.

Answers

Answer: $2750

Step-by-step explanation:

Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.

Given:  I= $495

t= 3 years

r= 6% = 0.06

Then, according to the above formula:

[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]

Hence, the principal invested = $2750

Suppose that a sample mean is .29 with a lower bound of a confidence interval of .24. What is the upper bound of the confidence interval?

Answers

Answer:

The upper bound of the confidence interval is 0.34

Step-by-step explanation:

Here in this question, we want to calculate the upper bound of the confidence interval.

We start by calculating the margin of error.

Mathematically, the margin of error = 0.29 -0.24 = 0.05

So to get the upper bound of the confidence interval, we simply add this margin of error to the mean

That would be 0.05 + 0.29 = 0.34

10) How many possible outfit combinations come from six shirts, three
slacks, and five ties? *
A 15
B 18
C 30
D 90

Answers

Answer:

The answer is D)90

Hope I helped

Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?
A)Right
B)Obtuse
C)Can't be determined
D) Acute

Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?
A)0.33 feet
B)3.75 feet
C)3 feet
D)5 feet

Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?
A)Acute
B)Right
C)Can't be determined
D)Obtuse

Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?
A)21.34 ft.
B)21.93 ft.
C)27.73 ft.
D)19.21 ft.

Answers

Answer:

Question 1 = D) Acute

Question 2 = C)3 feet

Question 3 = D) Obtuse

Question 4 = C)27.73 ft.

Step-by-step explanation:

Question 1: A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse?

In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem

Where:

If a² + b² = c² = Right angle triangle

If a² +b² > c² = Acute triangle.

If a² +b² < c² = Obtuse triangle.

It is important to note that the length ‘‘c′′ is always the longest.

Therefore, for the above question, we have lengths

5 = a, 6 = b and c = 7

a² + b² = c²

5² + 6² = 7²

25 + 36 = 49

61 = 49

61 ≠ 49, Hence 61 > 49

Therefore, this is an Acute Triangle

Question 2: A 15-foot statue casts a 20-foot shadow. How tall is a person who casts a 4-foot-long shadow?

This is question that deals with proportion.

The formula to solve for this:

Height of the statue/ Length of the shadow of the person = Height of the person/ Length of the shadow of the person

Height of the statue = 15 feet

Length of the shadow of the person = 20 feet

Height of the person = unknown

Length of the shadow of the person = 4

15/ 20 = Height of the person/4

Cross Multiply

15 × 4 = 20 × Height of the person

Height of the person = 15 × 4/20

= 60/20

Height of the person = 3 feet

Therefore, the person is 3 feet tall.

Question 3: A triangle has sides with lengths 17, 12, and 9. Is the triangle right, acute, or obtuse?

In order to be able to accurately classify that a triangle with 3 given sides is either a right , acute or obtuse angle, we use the Pythagoras Theorem

Where:

If a² + b² = c² = Right angle triangle

If a² +b² > c² = Acute triangle.

If a² +b² < c² = Obtuse triangle.

It is important to note that the length ‘‘c′′ is always the longest.

Therefore, for the above question, we have lengths 17, 12, 9

9 = a, 12 = b and c = 17

a² + b² = c²

9² + 12² = 17²

81 + 144 = 289

225 = 289

225 ≠ 289

225 < 289

Hence, This is an Obtuse Triangle.

Question 4: Two friends are standing at opposite corners of a rectangular courtyard. The dimensions of the courtyard are 12 ft. by 25 ft. How far apart are the friends?

To calculate how far apart the two friends are we use the formula

Distance = √ ( Length² + Breadth²)

We are given dimensions: 12ft by 25ft

Length = 12ft

Breadth = 25ft

Distance = √(12ft)² + (25ft)²

Distance = √144ft²+ 625ft²

Distance = √769ft²

Distance = 27.730849248ft

Approximately ≈27.73ft

Therefore, the friends are 27.73ft apart.

Which of the following represents "next integer after the integer n"? n + 1 n 2n

Answers

Answer:

n + 1

Step-by-step explanation:

Starting with the integer 'n,' we represent the "next integer" by n + 1.

Please help ! I’ll mark you as brainliest if correct.

Answers

Answer:

D = -87Dx = 174Dy = -435Dz = 0(x, y, z) = (-2, 5, 0)

Step-by-step explanation:

The determinant of the coefficient matrix is ...

  [tex]D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}[/tex]

The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.

Those determinants are ...

  [tex]D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174[/tex]

  [tex]D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435[/tex]

  [tex]D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0[/tex]

The solutions are ...

  x = 174/-87 = -2

  y = -435/-87 = 5

  z = 0

That is, (x, y, z) = (-2, 5, 0).

solve this equation 4log√x - log 3x =log x^2​

Answers

Answer:

[tex]x = \frac{1}{3} [/tex]

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒([tex]\frac{1}{3x}[/tex])

*rewrite to solve for x :

10⁰ = [tex]\frac{1}{3x}[/tex]

1 = [tex]\frac{1}{3x}[/tex]

1 · x = [tex]\frac{1}{3x}[/tex] · x

1x = [tex]\frac{1}{3}[/tex]

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = [tex]\frac{1}{3}[/tex]

Gail paid a total of $12,000 for stock that was $6 per share. If she sold all her shares for $18,000, how much profit on each share did she make?
A
$9
B
$3
С.
S2000
D
$6.000

Answers

Answer:

$3

Step-by-step explanation:

Given

Total Cost Price: $12,000

Unit Cost Price= $6

Total Selling Price = $18,000

Required

Determine the profit on each share

First, we need to determine the units of share bought;

Units = Total cost price / Unit Cost Price

[tex]Units = \frac{\$12000}{\$6}[/tex]

[tex]Units = 2000[/tex]

Next is to determine the selling price of each share; This is calculated as follows;

Unit Selling Price = Total Selling Price / Units Sold

[tex]Unit\ Selling\ Price = \frac{\$18000}{\$2000}[/tex]

[tex]Unit\ Selling\ Price = \$9[/tex]

The profit is the difference between the unit cost price and unit selling price

[tex]Profit = Unit\ Selling\ Price - Unit\ Cost\ Price[/tex]

[tex]Profit = \$9 - \$6[/tex]

[tex]Profit = \$3[/tex]

Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

Answers

Find the powers [tex]a=\sqrt{2}+\sqrt{3}[/tex]

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

Answer:

[tex]y^3 -6y-6[/tex]

(21x-3)+21=23x+6 solve​

Answers

Answer:

False

Step-by-step explanation:

You Cnat solve it

Answer:

you cannot solve it

Step-by-step explanation:

false

Use the two highlighted points to find the
equation of a trend line in slope-intercept
form.

Answers

Answer: y=(4/3)x+2/3

Step-by-step explanation:

Slope-intercept form is expressed as y=mx+b

First, find the slope (m):

m= rise/run or vertical/horizontal or y/x (found between the highlighted points)

m = 4/3

Second, find b:

Use one of the highlighted points for (x, y)

2=4/3(1)+b

6/3=4/3+b

2/3=b

b=2/3

Plug it into the equation:

You get y=(4/3)x+2/3 :)

Please help me solve for the median !!!

Answers

Answer:

50.93

Step-by-step explanation:

Add up the frequencies:

2 + 5 + 14 + 15 + 21 + 18 + 15 + 9 + 2 = 101

Divide by 2: 101/2 = 50.5

So the median is the 51st number, with 50 below and 50 above.

Add up the frequencies until you find the interval that contains the 51st number.

2 + 5 + 14 + 15 = 36

2 + 5 + 14 + 15 + 21 = 57

So the median is in the group 49.5 − 51.5.  To estimate the median, we use interpolation.  Find the slope of the line from (36, 49.5) to (57, 51.5).

m = (51.5 − 49.5) / (57 − 36)

m = 2/21

So at x = 51:

2/21 = (y − 49.5) / (51 − 36)

y = 50.93

Use Lagrange multipliers to minimize the function subject to the following two constraints. Assume that x, y, and z are nonnegative. Question 18 options: a) 192 b) 384 c) 576 d) 128 e) 64

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

Option C is the correct option

Step-by-step explanation:

From the question we are told that

   The equation is  [tex]f (x, y , z ) = x^2 +y^2 + z^2[/tex]

    The constraint is  [tex]P(x, y , z) = x + y + z - 24 = 0[/tex]

Now using Lagrange multipliers  we have that  

   [tex]\lambda = \frac{ \delta f }{ \delta x } = 2 x[/tex]  

   [tex]\lambda = \frac{ \delta f }{ \delta y } = y[/tex]  

   [tex]\lambda = \frac{ \delta f }{ \delta z } = 2 z[/tex]

=>       [tex]x = \frac{ \lambda }{2}[/tex]

          [tex]y = \frac{ \lambda }{2}[/tex]

         [tex]z = \frac{ \lambda }{2}[/tex]

From the constraint  we have

      [tex]\frac{\lambda }{2} + \frac{\lambda }{2} + \frac{\lambda }{2} = 24[/tex]

=>   [tex]\frac{3 \lambda }{2} = 24[/tex]

=>   [tex]\lambda = 16[/tex]

substituting for x, y, z

=>   x =  8

=>  y =  8

=>   z =  8        

Hence

    [tex]f (8, 8 , 8 ) = 8^2 +8^2 + 8^2[/tex]

    [tex]f (8, 8 , 8 ) = 192[/tex]

 

Transform the given parametric equations into rectangular form. Then identify the conic.

Answers

Answer:

Solution : Option B

Step-by-Step Explanation:

We have the following system of equations at hand here.

{ x = 5 cot(t), y = - 3csc(t) + 4 }

Now instead of isolating the t from either equation, let's isolate cot(t) and csc(t) --- Step #1,

x = 5 cot(t) ⇒ x - 5 = cot(t),

y = - 3csc(t) + 4 ⇒ y - 4 = - 3csc(t) ⇒ y - 4 / - 3 = csc(t)

Now let's square these two equations. We know that csc²θ - cot²θ = 1, so let's subtract the equations  as well. --- Step #2

 

( y - 4 / - 3 )² = (csc(t))²

- ( x - 5 / 1 )² = (cot(t))²  

___________________

(y - 4)² / 9 - x² / 25 = 1

And as we are subtracting the two expressions, this is an example of a hyperbola. Therefore your solution is option b.

A machine used to fill​ gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents. The sample mean of the cans is ounces. Does the machine need to be​ reset? Explain your reasoning. ▼ Yes No ​, it is ▼ very unlikely likely that you would have randomly sampled cans with a mean equal to ​ounces, because it ▼ lies does not lie within the range of a usual​ event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means.

Answers

Complete question is;

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be? reset? Explain your reasoning.

(yes/no)?, it is (very unlikely/ likely) that you would have randomly sampled 35 cans with a mean equal to 127.9 ?ounces, because it (lies/ does not lie) within the range of a usual? event, namely within (1 standard deviation, 2 standard deviations 3 standard deviations) of the mean of the sample means.

Answer:

Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.

Step-by-step explanation:

We are given;

Mean: μ = 128

Standard deviation; σ = 0.2

n = 35

Now, formula for standard error of mean is given as;

se = σ/√n

se = 0.2/√35

se = 0.0338

Normally, the range of values should be within 2 standard deviations of mean. In this case, normal range of values will be;

μ ± 2se = 128 ± 0.0338

This gives; 127.9662, 128.0338

So, Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.

Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente

Answers

De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL

O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.

Fazendo a classica regra de 3, podemos chegar no volume desejado:

(atentar que 500mg = 0,5g)

     g               mL

     1    ---------   2

    0,5  ---------  X    

1 . X = 0,5 . 2

X = 1mL

find the perimeter of a square of sides 10.5cm​

Answers

Answer:

Perimeter = 42 cm

Step-by-step explanation:

A square has all equal sides so you would just add 10.5 + 10.5 + 10.5 + 10.5 to get 42 cm.

Answer:

42 cm

Step-by-step explanation:

Side of square = 10.5 cm (given)

Perimeter of square = Side X 4

                                  = 10.5 X 4

                                  = 42 cm

HOPE THIS HELPED YOU !

:)

Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?

Answers

Answer:

eddfdgdccggģdffcdrrfxddxcvgfx

The cost, C, in United States Dollars ($), of cleaning up x percent of an oil spill along the Gulf Coast of the United States increases tremendously as x approaches 100. One equation for determining the cost (in millions $) is:

Answers

Complete Question

On the uploaded image is a similar question that will explain the given question

Answer:

The value of k is  [tex]k = 214285.7[/tex]

The percentage  of the oil that will be cleaned is [tex]x = 80.77\%[/tex]

Step-by-step explanation:

From the question we are told that

   The  cost of cleaning up the spillage is  [tex]C = \frac{ k x }{100 - x }[/tex]  [tex]x \le x \le 100[/tex]

     The  cost of cleaning x =  70% of the oil is  [tex]C = \$500,000[/tex]

   

Now at  [tex]C = \$500,000[/tex] we have  

       [tex]\$ 500000 = \frac{ k * 70 }{100 - 70 }[/tex]

       [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]k = 214285.7[/tex]

Now  When  [tex]C = \$900,000[/tex]

       [tex]x = 80.77\%[/tex]

       

 

You are studying for your final exam of the semester up to this point you received 3 exam scores of 61% 62% and 86% to receive a grade of c and the class you must have an average exam score between 70% and 79% for all four exams including the final find the widest range of scores that you can get on the final exam in order to receive a grade of C for the class 63 to 100% 71 to 100% 68 to 97

Answers

There will be a total of 4 test scores including the final exam. To get a 70, the 4 tests need to equal 4 x 70 = 280 points , to be 79, they have to equal 4 x 79 = 316 points.

The 3 already done = 61 + 62 + 86 = 209 points.

The final exam needs to be between :

280 -209 = 71

316 -209 = 107. The answer would be between 71 and 100%

The cost of a daily rental car is as follows: The initial fee is $39.99 for the car, and it costs $0.20 per mile. If Julie's final bill was $100.00 before taxes, how many miles did she drive?

Answers

Answer:

300.05 miles

Step-by-step explanation:

initial fee= $39.99

final bill = $ 100

cost =$ 0.20 per mile

remaining amount = $ 60.01

solution,

she drive = remaining amount / cost

=60.01/0.20

=300.05 miles

Answer:

500 miles

Step-by-step explanation:

Let us use cross multiplication to find the unknown amount.

Given:

1) Cost for 1 mile=$0.20

2)Cost for x miles=$100

Solution:

No of miles                             Cost

1) 1                                             $0.20

2)x                                             $100

By cross multiplying,

100 x 1= 0.20x

x=100/0.20

x=500 miles

Thank you!

5x+4(-x-2)=-5x+2(x-1)+12

Answers

Answer:

x=9/2

Step-by-step explanation:

Let's solve your equation step-by-step.

5x+4(−x−2)=−5x+2(x−1)+12

Step 1: Simplify both sides of the equation.

5x+4(−x−2)=−5x+2(x−1)+12

5x+(4)(−x)+(4)(−2)=−5x+(2)(x)+(2)(−1)+12 (Distribute)

5x+−4x+−8=−5x+2x+−2+12

(5x+−4x)+(−8)=(−5x+2x)+(−2+12) (Combine Like Terms)

x+−8=−3x+10

x−8=−3x+10

Step 2: Add 3x to both sides.

x−8+3x=−3x+10+3x

4x−8=10

Step 3: Add 8 to both sides.

4x−8+8=10+8

4x=18

Step 4: Divide both sides by 4.

4x/4=18/4

x=9/2

The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 2. You wish to test H0: μ = 100 versus H1: μ ≠ 100 with a sample of n = 9 specimens.
A. If the acceptance region is defined as 98.5 le x- 101.5, find the type I error probability alpha.
B. Find beta for the case where the true mean heat evolved is 103.
C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

Answers

Answer:

A.the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. β  = 0.0122

C. β  = 0.0000

Step-by-step explanation:

Given that:

Mean = 100

standard deviation = 2

sample size = 9

The null and the alternative hypothesis can be computed as follows:

[tex]\mathtt{H_o: \mu = 100}[/tex]

[tex]\mathtt{H_1: \mu \neq 100}[/tex]

A. If the acceptance region is defined as [tex]98.5 < \overline x > 101.5[/tex] , find the type I error probability [tex]\alpha[/tex] .

Assuming the critical region lies within [tex]\overline x < 98.5[/tex] or [tex]\overline x > 101.5[/tex], for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is [tex]\mu = 100[/tex]

[tex]\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}[/tex]

[tex]\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}[/tex]

when  [tex]\mu = 100[/tex]

[tex]\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }[/tex]

[tex]\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) + P(Z > 2.25) }[/tex]

[tex]\mathtt{\alpha = P ( Z <-2.25 ) +( 1- P(Z < 2.25) })[/tex]

From the standard normal distribution tables

[tex]\mathtt{\alpha = 0.0122+( 1- 0.9878) })[/tex]

[tex]\mathtt{\alpha = 0.0122+( 0.0122) })[/tex]

[tex]\mathbf{\alpha = 0.0244 }[/tex]

Thus, the type 1 error probability is [tex]\mathbf{\alpha = 0.0244 }[/tex]

B. Find beta for the case where the true mean heat evolved is 103.

The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis [tex]\mathtt{H_o}[/tex]

Thus;

β = P( type II error) - P( fail to reject [tex]\mathtt{H_o}[/tex] )

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 103[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }[/tex]

[tex]\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}[/tex]

From standard normal distribution table

β  = 0.0122 - 0.0000

β  = 0.0122

C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

[tex]\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }[/tex]

Given that [tex]\mu = 105[/tex]

[tex]\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }[/tex]

[tex]\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }[/tex]

[tex]\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }[/tex]

[tex]\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}[/tex]

From standard normal distribution table

β  = 0.0000 - 0.0000

β  = 0.0000

The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.

Findℒ{f(t)}by first using a trigonometric identity. (Write your answer as a function of s.)f(t) = 12 cost −π6

Answers

Answer:

[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]

Step-by-step explanation:

Given that:

[tex]f(t) = 12 cos (t- \dfrac{\pi}{6})[/tex]

recall that:

cos (A-B) = cos AcosB + sin A sin B

[tex]f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}][/tex]

[tex]f(t) = 12 [cos \ t \ \dfrac{3}{2}+ sin \ t \ sin \dfrac{1}{2}][/tex]

[tex]f(t) = 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t)[/tex]

[tex]L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ][/tex]

[tex]L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ][/tex]

[tex]L(f(t)) = 6 \sqrt{3} \dfrac{S}{S^2 + 1^2}+ 6 \dfrac{1}{S^2 +1^2}[/tex]

[tex]L(f(t)) = \dfrac{6 \sqrt{3} +6 }{S^2+1}[/tex]

[tex]L(f(t)) = \dfrac{6( \sqrt{3} \ S +1 }{S^2+1}[/tex]

[tex]L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ][/tex]

Find usubscript10 in the sequence -23, -18, -13, -8, -3, ...

Answers

Step-by-step explanation:

utilise the formula a+(n-1)d

a is the first number while d is common difference

Answer:

22

Step-by-step explanation:

Using the formular, Un = a + (n - 1)d

Where n = 10; a = -23; d = 5

U10 = -23 + (9)* 5

U10 = -23 + 45 = 22

one third multiplied by the sum of a and b

Answers

Answer:

1/3(a+b)

hope it helps :>

a+b/3
This is the answer of ur question

logx-log(x-l)^2=2log(x-1)​

Answers

Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

Time

(minutes)

Water

(gallons)

1

16.50

1.5

24.75

2

33

find the constant of proportionality for the second and third row

Answers

Answer:

16.50

Step-by-step explanation:

Constant of proportionality = no of gallons of water per 1 minute.

In the first row, we have 16.50 gallons of water per 1 minute.

In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons

In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.

We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.

Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]

This means the constant of proportionality, 16.50, is same for all rows.

Other Questions
Combine like terms to simplify the expression: -5.55-8.55c+4.35c How do I solve 3(x+1)=5(x2)+7? according to Petrocelli , what is this crime about Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system. At four hundred miles they stopped to eat, at a thousand miles they pitched their camp. They had traveled for just three days and nights, a six weeks' journey for ordinary men. When the sun was setting, they dug a well, they filled their waterskins with fresh water, Gilgamesh climbed to the mountaintop Which statement best describes the epic feature used in this excerpt and its effect on the plot? The interference of the gods creates more tension and suspense in the plot. The use of poetic verse causes the narrative to become confusing. The long and difficult journey reflects how strong and enduring Gilgamesh is. The presence of a brave hero indicates that the challenge ahead will be simple. A circle has center D and passes through the points F and G. Which of the following is the name of this circle? Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $22.31 and a 95% confidence interval of [$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval. A) 95% of all taxi fares are between $20.51 and $24.21. B) We are 95% confident that a randomly selected taxi fare will be between $20.51 and $24.21. C) The mean amount of a taxi fare is $22.31, 95% of the time. D) We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21. A reaction mechanism has the following proposed elementary steps:Step 1: A B + CStep 2: A + B DStep 3: 2 A + D C + EIf Step 2 is the rate-limiting step, what would the proposed rate law for this mechanism be? The Camp David Accords Group of answer choices was Jimmy Carter's notoriously flawed attempt to stave off the Russian invasion of Afghanistan. was the first peace treaty between an Arab nation and the Jewish state of Israel. were between Iraq and the U.S., which led to the Iran-Iraq War. were an agreement between the U.S. and Israel to reinforce American commitment to the defense of Israel. Next What is the role of religion in Lincoln's understanding of the war? What role does religion play in his understanding of the United States more broadly Which kind of research is most likely to improve the health of theenvironment? A student ran the following reaction in the laboratory at 242 K: 2NOBr(g) 2NO(g) Br2(g) When she introduced 0.143 moles of NOBr(g) into a 1.00 liter container, she found the equilibrium concentration of NOBr(g) to be 0.108 M. Calculate the equilibrium constant, Kc, she obtained for this reaction. Kc COME ON!! Whats the answer 53 points! (05.03 LC) Read the text and question. Then, choose the correct option that answers the question. My name is Tatiana, and I live in Managua, Nicaragua. My dads side of the family is Mexican and African, while my moms side of the family is Colombian. My friend Dominic lives in Texas, United States, and his dads family is Mexican and Puerto Rican, while his moms side of the family is Guatemalan. What is similar about Tatiana and Dominics heritage? A. They both have Cuban ancestry. B. They both have French ancestry. C. They both have Italian ancestry. D. They both have Mexican ancestry. WILL GIVE BRAINLIEST!!! Statement of retained earnings.Use the data from the following financial statements in the popup window,LOADING...Partial Income Statement Year Ending 2014Sales revenue$350,200Cost of goods sold$141,800Fixed costs$42,900Selling, general, and administrative expenses$28,000Depreciation$46,200Partial Balance Sheet 12/31/2013ASSETSLIABILITIESCash$16,000Notes payable$14,000Accounts receivable$27,800Accounts payable$19,100Inventories$48,000Long-term debt$189,900Fixed assets$368,000OWNERS' EQUITYAccumulated depreciation (-)$140,200Retained earningsIntangible assets$82,000Common stock$131,900Partial Balance Sheet 12/31/2014ASSETSLIABILITIESCash$26,200Notes payable$11,900Accounts receivable$18,800Accounts payable$24,100Inventories$53,200Long-term debt$161,800Fixed assets$447,800OWNERS' EQUITYAccumulated depreciation (-)Retained earningsIntangible assets$82,200Common stock$181,900. The company paid interest expense of$ 18 comma 700$18,700for 2014 and had an overall tax rate of40 %40%for 2014. Complete the statement of retained earnings for2014, and determine the dividends paid last year.The distributed earnings is$nothing.(Round to the nearest dollar.)Complete the statement of retained earnings:(Round to the nearest dollar.)Statement of Retained EarningsYear Ending December 31, 2014Beginning balance$Add net income$Subtract dividends$Ending balance$ why did alexander hamilton believe the brittish constitution was the best model the world has ever produced Hi i need help asap my parent taught me how to do this equation (x^2-4x)^2+7x^2-28x+12=0 but i still dont understand I really need help understanding this i know the answer i just need an explanation please help me Please answer this correctly without making mistakes Stephen Battista argues that public relations should help Under Armour convince customers that the company has a new kind of sports apparel. One way that public relations differs from other kinds of marketing communications is that it substitutes the term ________ for target market. Multiple Choice target audience consumer referent group public market segment