−p(51+z)=dz+84 solve for z

Answer:

7

Step-by-step explanation:

:)

Answer:

x = 45 degrees

Step-by-step explanation:

The measure of exterior angles is equal to the sum of non-adjacent interior angles

=> 2x = x+45

=> 2x-x = 45

=> x = 45 degrees

Answer:

45 degrees.

Step-by-step explanation:

The exterior angle = sum of the 2 opposite interior angles.

2x =  x + 45

2x - x = 45

x = 45.

Answer:

Well the best answer would be 1    0.75 cubic feet bag of dirt  

Step-by-step explanation:

Answer:

Textbooks: $506Course Materials and Electronics: $323

Step-by-step explanation:

First, we need to divide the amount into 2 equal parts:

$819/2 = $414.50

Now, because they spent $183 more on textbooks, we add half of that to $414.50.

$414.50 + $91.50 = $506

$414.50 - $91.50 = $323

To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.

$323 + $183 = $506 ✅

Textbooks: $506Course Materials and Electronics: $323I'm always happy to help

Answer:

Decimal: 5.66478

Step-by-step explanation:

√6 + √11 / √5 + √3

= √3 + 1/5 √55 + √6

--Answer--

I put the numbers in my calculator and got 1.453110364

[tex]\frac{\sqrt{6}+\sqrt{11} }{\sqrt{5} +\sqrt{3} }[/tex] is what I did.

Answer:

n = 600

Step-by-step explanation:

To solve this equation:

1. Simplify all like terms: 5400/9 = 600 = n

2. The n cannot be simplified.

3. The answer is n = 600 because 5400/9 is 600 which is equal to n

Answer:

Step-by-step explanation:

Cos θ = u*v    

             IuI *IvI

u * v = 7*(-1) + (-2)*2

       = -7 - 4

      = -11

IuI = [tex]\sqrt{7^{2}+(-2)^{2}}\\[/tex]

    = [tex]\sqrt{49+4}\\\\[/tex]

    = [tex]\sqrt{53}[/tex]

I vI = [tex]\sqrt{(-1)^{2}+2^{2}}\\[/tex]

     = [tex]\sqrt{1+4}\\\\[/tex]

      = [tex]\sqrt{5}\\[/tex]

Cos θ = [tex]\frac{-11}{\sqrt{53}*\sqrt{5} } \\\\[/tex]

          = [tex]\frac{-11}{16.28}\\\\[/tex]

   Cos θ = -0.68

θ = 132.5°

Answer:

Step 4

Step-by-step explanation:

Jose's Steps are:

Step 1: Declare the variable:

Let x = the number of student signatures still needed.

Step 2: Create a ratio equivalent to:

[tex]\dfrac{\text{Total number of signatures needed}}{\text{Total number of students in the school}} =\dfrac{x + 82}{426}.[/tex]

Step 3: Convert 25% to a decimal:

25% = 0.25.

Step 4: Write the inequality:

[tex]\dfrac{x + 82}{426}\leq 0.25[/tex]

Since they need at least 25% of the student population to sign a petition, In Step 4, the inequality should be:

[tex]\dfrac{x + 82}{426}\geq 0.25[/tex]

Answer:

(D).Step 4

Step-by-step explanation:

I got it right on edge

Answer:

all real number except 0

Step-by-step explanation:

Answer: 107.67°C

Step-by-step explanation:

I guess that we could do a Taylor expansion around the point (2, 1)

Remember that a Taylor expansion around the point (a, b) is:

[tex]T(x,y) = T(a, b) + \frac{dT(a,b)}{dx}(x - a) + \frac{dT(a,b)}{dy}(y - b) + .....[/tex]

Where the latter terms need higher orders of the derivates of T, so we can not find them, regardless of that, this expansion will be accurate near the point (a, b),

Then, using this, we can write our expanssion as:

T(x,y) = 107 + 9*(x - 2) - 8*(y - 1)

Now we evaluate this in x = 2.03 and y = 0.95

T(2.03, 0.95) =  107 + 9(2.03 - 2) - 8*(0.95 - 1) = 107.67

Then a good estimation of the temperature at the point (2.03,0.95) is 107.67°C

The estimate of the temperature of the unevenly heated metal plate at temperature at the point (2.03,0.95) is;

T(2.03, 0.95) = 107.67 °C

Formula for taylor expansion around a point (a, b) is given as;

T(x, y) = T(a,b) +  [tex]\frac{dT(a,b)}{dx}[/tex](x - a) +  [tex]\frac{dT(a,b)}{dy}[/tex](y - b) + ....

We are given;

T(2,1) = 107

T'x(2,1) = [tex]\frac{dT(a,b)}{dx}[/tex] = 9

T'y(2,1) = [tex]\frac{dT(a,b)}{dy}[/tex] = −8

Plugging in the relevant values into our taylor expansion above gives;

T(x, y) = 107 + 9(x - 2) - 8(y - 1)

Now, we want to estimate the temperature at the point (2.03, 0.95).

Thus, we will plug in x = 2.03 and y = 0.95 to get;

T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8(0.95 - 1)

T(2.03, 0.95) = 107 + 0.27 + 0.4

T(2.03, 0.95) = 107.67 °C

Read more at; https://brainly.com/question/9211177

Answer:

6

Step-by-step explanation:

nerd physics

Answer:

D

Step-by-step explanation:

It's decreasing then once it hits the origin, it starts to increase again. I hope this helps you:)

Answer:

D

Step-by-step explanation:

Answer:

9,000 inches^3

Step-by-step explanation:

The first part is 20 x 20 x 20, which equals 8,000

The second part is 10 x 10 x 10, which is 1,000

1,000 + 8,000 = 9,000

Answer:

Option B - 0.02

Step-by-step explanation:

In this question, the p-value is used to tell us the probability that a difference of (0.88 – 0.68) which is 0.2 or greater would occur in the distribution of simulated differences. This is created done with the assumption that there is no true difference in the two populations.

Due to the fact that the researchers found the difference in proportions to be statistically significant, hence these results would rarely occur due to just the sampling variability and thus the p-value must be small.

Looking at the options, the p-value in Option (B) will be the correct response,l as it indicates that a difference of 0.2 or more would only occur about 2% of the time by chance alone provided the proportion who text were the same in the population of seniors and the population of freshmen. This resonates well with the claim that the difference in proportions is statistically significant.

Thus, Option B is the correct answer.

Answer:

[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]

General Formulas and Concepts:

Pre-Calculus

Partial Fraction Decomposition

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy[/tex]

Step 2: Integrate Pt. 1

[Integral] Rewrite [Integration Property - Multiplied Constant]:                 [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{y^2 - 9y - 22}} \, dy[/tex][Integrand] Factor:                                                                                         [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{(y - 11)(y + 2)}} \, dy[/tex]

Step 3: integrate Pt. 2

[Integrand] Split [Partial Fraction Decomp]:                                                 [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{A}{y - 11} + \frac{B}{y + 2}[/tex][Decomp] Rewrite:                                                                                         [tex]\displaystyle y = A(y + 2) + B(y - 11)[/tex][Decomp] Substitute in y = -2:                                                                       [tex]\displaystyle -2 = A(-2 + 2) + B(-2 - 11)[/tex]Simplify:                                                                                                         [tex]\displaystyle -2 = -13B[/tex]Solve:                                                                                                             [tex]\displaystyle B = \frac{2}{13}[/tex][Decomp] Substitute in y = 11:                                                                       [tex]\displaystyle 11 = A(11 + 2) + B(11 - 11)[/tex]Simplify:                                                                                                         [tex]\displaystyle 11 = 13A[/tex]Solve:                                                                                                             [tex]\displaystyle A = \frac{11}{13}[/tex][Split Integrand] Substitute in variables:                                                     [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2}[/tex]

Step 4: Integrate Pt. 3

[Integral] Rewrite [Split Integrand]:                                                               [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\bigg( \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2} \bigg)} \, dy[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:              [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \int\limits^{10}_{-1} {\frac{\frac{11}{13}}{y - 11}} \, dy + \int\limits^{10}_{-1} {\frac{\frac{2}{13}}{y + 2}} \, dy \bigg][/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:               [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{10}_{-1} {\frac{1}{y - 11}} \, dy + \frac{2}{13}\int\limits^{10}_{-1} {\frac{1}{y + 2}} \, dy \bigg][/tex]

Step 5: Integrate Pt. 4

Identify variables for u-substitution.

Integral 1

Set u:                                                                                                             [tex]\displaystyle u = y - 11[/tex][u] Differentiation [Basic Power Rule, Derivative Properties]:                   [tex]\displaystyle du = dy[/tex][Bounds] Switch:                                                                                           [tex]\displaystyle \left \{ {{y = 10 ,\ u = 10 - 11 = -1} \atop {y = -1 ,\ u = -1 - 11 = -12}} \right.[/tex]

Integral 2

Set v:                                                                                                               [tex]\displaystyle v = y + 2[/tex][v] Differentiate [Basic Power Rule, Derivative Properties]:                       [tex]\displaystyle dv = dy[/tex][Bounds] Switch:                                                                                           [tex]\displaystyle \left \{ {{y = 10 ,\ v = 10 + 2 = 12} \atop {y = -1 ,\ v = -1 + 2 = 1}} \right.[/tex]

Step 6: Integrate Pt. 5

[Integrals] U-Substitution:                                                                             [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{-1}_{-12} {\frac{1}{u}} \, du + \frac{2}{13}\int\limits^{12}_{1} {\frac{1}{v}} \, dv \bigg][/tex][Integrals] Logarithmic Integration:                                                              [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}(\ln |u|) \bigg| \limits^{-1}_{-12} + \frac{2}{13}(\ln |v|) \bigg| \limits^{12}_{1} \bigg][/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}[-\ln (12)] + \frac{2}{13}[\ln (12)] \bigg][/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 11[-\ln (12)] + 2[\ln (12)][/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -11\ln (12)] + 2\ln (12)[/tex]Simplify:                                                                                                         [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer: B) y = 1/2x

Step-by-step explanation:

In a perpendicular line, the slope is the opposite reciprocal.  Thus, the equation can be simplified into y = 1/2x+b.  Then, to get b, simply plug in 4 for x and 2 for y

2=1/2(4)+b

2=2+b

0=b

Thus, the equation of the line is y = 1/2x + 0, or y = 1/2x

Hope it helps <3

Answer:

4/5 or 0.8

Step-by-step explanation:

3*3*4/45

3*3=9

9*4=32

32/45=4/5

Hope it helps ;)

━━━━━━━☆☆━━━━━━━

▹ Answer

0.8 (4/5 or 8 × 10⁻¹)

▹ Step-by-Step Explanation

3 × 3 × 4 ÷ 45

3² × 4 ÷ 45

9 × 4 ÷ 45

36 ÷ 45

= 0.8 (4/5 or 8 × 10⁻¹)

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22

Step-by-step explanation:

Unit price of any product is given by

unit price = weight of product/ price of product

Given sizes

A

13.5 ounces bottle cost $2.98

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

 cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22

Unit price for this size is $.022

B

9.2 ounce bottle cost $6.12

cost of 1 ounce of shampoo for this size = cost price/weight of shampoo

 cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66

Unit price for this size is $0.66

As $0.22 is less than $0.66 thus,

9.2 ounce bottle cost $6.12 is better buy.

Answer:

5, 6 and 9 , 10 so E and F.

Step-by-step explanation:

Answer:

1.23?

Step-by-step explanation:

Answer:

b. 9

Just use PEMDAS

Answer: I had the same assingment and came here looking for answers myself. When I saw the only anwser was 20 (Which is wrong) I decided I would try my best and If I got it right come back here and share the correct answers for future students.

Just look at the PDF attached below, I somehow got a 50/50.

Step-by-step explanation:

Statements                                                   Reasons

1. △EGC ≅ △EGB                                     1. Given

2. EB ≅ EC                                              Supposition

3. <EGC ≅ <EGB                                       Given

4. Equilateral  Triangle                       EB ≅ EC ≅ BC

5. Equilateral  Triangle                      m∠BEC = 60°

Statements                                                 Reasons

1. △BEC is equilateral                      AAS≅AAS postulate (angle angle side)

2. m∠ GCE = 60°                                   m∠ BEC = 60°  Equilateral Triangles

3. FG ⊥ BC &  FG ⊥ AD                                   ABCD is a square

4.  m∠ECD +  m∠ BEC = 30°+60°                           Substitution (right angles)

m∠DCG = 90°                                                  right angles of a square

m∠BED=   135°

Statements                                                   Reasons

1. △ECG ≅ △EBG                                             Given

2.  ABCD is a square                                       Given

3. BC ≅ BE                                                     Given

4. AB ≅ DC                                                   ABCD is a square

5.  m∠ABE ≅  m∠DCE                           Outside angles of congruent  

                                                               triangles △EGB≅      △EGC    

5.  △AEB≅ △DEC                         S.S.A ≅ S.S.A. ( side side angle) Postulate

△BEC is equilateral                                m∠BEC = 60°

△ECD is isosceles                                 m CD= mCE

∠ECD = 30°                                          m∠BEC = 60°

As m∠BEC +∠ECD = 30°+ 60°          right angle of the square ABCD

The equal sides of the isosceles triangles are called the legs and the unequal third side is called the base.

Angles opposite to the equal sides of the isosceles triangle must also be equal.

As the third angle is 30° so the other two angles must be 75° each to make a total of 180°.

m∠BED=  m∠BEC +  m∠CED

             = 60° + 75°= 135°

https://brainly.com/question/22140109

Answer:

A) Option B is correct.

H₀: μ₁ = μ₂

Hₐ: μ₁ - μ₂ < 0

B) t = -2.502

p-value = 0.0112

C) Option A is correct.

Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.

D) Option A is correct.

The distributions of compression strengths are approximately normal.

Step-by-step explanation:

The complete Question is presented in the two attached images to this answer.

A) To perform this test we first define the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, we want to test if the extra carbonation of cola results in a higher average compression strength. That is, that cola has a higher average compression strength than the strawberry drink.

Hence, the null hypothesis would be that there isn't significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

The alternative hypothesis is that there is significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

Mathematically, if the average compression strength of strawberry drink is μ₁, the average compression strength of cola is μ₂ and the difference in compression strengths is μ = μ₁ - μ₂

The null hypothesis is represented as

H₀: μ = 0 or μ₁ = μ₂

The alternative hypothesis is represented as

Hₐ: μ < 0 or μ₁ - μ₂ < 0

B) So, to perform this test, we need to compute the test statistic

Test statistic for 2 sample mean data is given as

Test statistic = (μ₁ - μ₂))/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = average compression strength of strawberry drink = 537

n₁ = sample size of the sample of strawberry drink in cans surveyed = 10

s₁ = standard deviation of the compression strength of strawberry drink in cans surveyed= 22

μ₂ = average compression strength of cola = 559

n₂ = sample size of the sample of cola in cans surveyed = 10

s₂ = standard deviation of the compression strength of strawberry drink in cans surveyed = 17

σ = [(17²/10) + (22²/10)] = 77.5903160379 = 8.792

We will use the t-distribution as no information on population standard deviation is provided

t = (537 - 559) ÷ 8.792

= -2.502 = -2.50

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n₁ + n₂ - 2 = 10 + 10- 2 = 18

Significance level = 0.05

The hypothesis test uses a one-tailed condition because we're testing in only one direction (whether compression strength of cola in can is greater).

p-value (for t = -2.50, at 0.05 significance level, df = 18, with a one tailed condition) = 0.011154 = 0.0112 to 4 d.p.

C) The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.0112

0.0112 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis accept the alternative hypothesis & say that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.

D) The necessary conditions required before a t-test is deemed valid include.

- The samples used must be a random sample of the population distribution with each variable in the sample independent of other one.

- The distribution of the population where the samples were extracted from must be normal or approximately normal to ensure some degree of normality for the samples.

Hence, the necessary assumption for this t-test among the options is that the distributions of compression strengths are approximately normal.

Hope this Helps!!!

Answer: (10 - 3) x 25 = 175

Step-by-step explanation:

10 - 3 = 7

            7 x 25 = 175

Answer:

$52.96

Step-by-step explanation:

To find the total cost of his clothing, add up the prices of everything he bought.

Jeans: $23.00

Shirt: $14

Ties: 2 ties for $7.98 each.

Each tie costs $7.98, and the man bought two ties. Therefore, multiply 2 and $7.98

2*$7.98 = $15.96

Add all the prices together.

jeans + shirt + ties

$23 + $14 + $15.96

$37 + $15.96

$52.96

The total cost of his clothing is $52.96

Answer:

total cost=52.96

Step-by-step explanation:

Things he bought:

jeans for $23.00

a shirt for $14.00

two ties for $7.98 each

the total const would be the sum of all his clothes

which is

jeans for $23.00

+shirt for $14.00

+one tie for $7.98

+one tie for $7.98

_______________

total cost=52.96

HOPE IT HELPS :0

PLEASE MARK IT THE BRAINLIEST!

Answer:

-9

Step-by-step explanation:

3 time 7

minus

4 times 8

21 - 32

-11+2= -9

Answer:

3/20s

Step-by-step explanation:

Answer:

12 m

Step-by-step explanation:

Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.

Thus, we are given the ratio, CD:GH = 2:3.

This means, any of the corresponding lengths of both figures would be in that same ratio.

Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.

The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔

[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]

[tex] \frac{8}{EH} = \frac{2}{3} [/tex]

Cross multiply

[tex] 3*8 = 2*EH [/tex]

[tex] 24 = 2*EH [/tex]

Divide both sides by 2 to make EH the subject of formula

[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]

[tex] 12 = EH [/tex]

The length of side EH = 12 m

Answer:

{ 0.58, 0.89, 0.98, 1.26, 1.42 }

Step-by-step explanation:

We are given the data set { 1.26, 0.98, 1.07, 0.97, 1.28, 0.89, 1.14, 0.58, 1.42, 0.59, 0.96 }, consisting of 11 elements, each the radiation of 11 cell phones.

To construct the " 5 - number summary " the first thing we want to do is arrange the numbers from least to greatest, to find the median of the data set,

{ 0.58, 0.59, 0.89, 0.96, 0.97, 0.98, 1.07, 1.14, 1.26, 1.28, 1.42 }

The median of this data set is thus 0.98 W / kg. Mind you the units are not required here!

____

Now that we have the median, we can determine the first and third quartile, which are simply medians of the data set to the left and right of the median,

{ 0.58, 0.59, 0.89, 0.96, 0.97, 0.98, 1.07, 1.14, 1.26, 1.28, 1.42 }

[tex]Q_1[/tex] = 0.89, [tex]Q_3[/tex] = 1.26

And of course the minimum and maximum of the data set are given to be 0.58, and 1.42

____

We have our 5 - number summary now! This includes the minimum, first quartile, median / second quartile, third quartile, and maximum values, in that order -

The 5 - number summary is { 0.58, 0.89, 0.98, 1.26, 1.42 }

And, your box and whisker plot is shown in the attachment below!

Answer:

a) 0.2218 to 0.7057

b) 0.4710 to 0.8401

Step-by-step explanation:

Given:

sample = n = 18

sample variance = s² = 0.36

To find:

a) 90% confidence interval estimate of the population variance.

b) 90% confidence interval estimate of the population standard deviation.

a)

Compute degree of freedom

degree of freedom = df = n - 1 = 18 - 1 = 17

Compute value of α for a 90% confidence interval  

The confidence level for 90% is:

c = 0.90

So

α = 1 - c = 1 - 0.90 = 0.1

α = 0.1

Now use the table of critical values of the chi-square distribution in order to find critical values. Search for the 17th row of table using df = 17 and find the column corresponding to 1 - α/2 i.e. 0.95 of table for upper tail critical values and column corresponding to α /2 i.e. 0.05 of table for lower tail critical values.

Using the table:

[tex]X^{2}_{0.95}[/tex] = 8.672

[tex]X^{2}_{0.05}[/tex] = 27.587

90% Confidence interval estimate of the population variance

The boundaries of CI are computed using formula:

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  ≤ σ² ≤ (n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = (18-1) 0.36 / 27.587

                       = (17) 0.36 / 27.587

                       =  6.12 / 27.587

(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = 0.2218

(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = (18-1) 0.36 / 8.672

                          = (17) 0.36 / 8.672

                          =  6.12 / 8.672

                          = 0.7057

This results in inequalities 0.2218 ≤ σ² ≤ 0.7057 for the variance

b)

90% Confidence interval estimate of the population standard deviation

The boundaries of CI are computed using formula:

√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  ≤ σ ≤ √(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]

√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex]  = √((18-1) 0.36 / 27.587)

                          = √((17) 0.36 / 27.587)

                          =  √(6.12 / 27.587)

                          = √0.2218

                          = 0.4709

                          = 0.4710

√(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = √((18-1) 0.36 / 8.672)

                            = √((17) 0.36 / 8.672)

                            = √ (6.12 / 8.672)

                            = √0.7057

                            = 0.8401

0.4710 ≤ σ ≤ 0.8401 for the standard deviation.