An arithmetic sequence has the first term Ina and a common difference In 3. The 13th term in the sequence is 8 ln9. Find the value of a.​

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:

\(X^{2}_{0.95}\) = 8.672

\(X^{2}_{0.05}\) = 27.587

90% Confidence interval estimate of the population variance

The boundaries of CI are computed using formula:

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

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

                       = (17) 0.36 / 27.587

                       =  6.12 / 27.587

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

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

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

                          = √((17) 0.36 / 27.587)

                          =  √(6.12 / 27.587)

                          = √0.2218

                          = 0.4709

                          = 0.4710

√(n−1) s² / \(X^{2}_{1-\alpha/2}\) = √((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.

Answer: \(\sqrt[3]{a}\)

Step-by-step explanation:

Just as the square root is \(\sqrt[2]{a}\), the cube root is \(\sqrt[3]{a}\)

Hope it helps <3

Answer:

\(\sqrt[3]{a}\)

Step-by-step explanation:

a cube root of a number x is a number a such that a³ = x.

Answer:

--------------------------------

Answer:

4 butter dishes

Step-by-step explanation:

To determine how many butter dishes the restaurant filled, calculate how many eighths go into a half.

To do this, divide one half by an eighth:

\(\implies \dfrac{1}{2} \div \dfrac{1}{8}\)

When dividing fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

\(\implies \dfrac{1}{2} \times \dfrac{8}{1}\)

\(\implies \dfrac{1 \times 8}{2 \times1}\)

\(\implies \dfrac{8}{2}\)

\(\implies 4\)

Therefore, the restaurant filled 4 butter dishes.

Answer:

x = 150 miles

Cost = $100

Step-by-step explanation:

Company A = 50 + 20 + 0.20x

= 70 + 0.20x

Company B = 55 + 0.30x

Where,

x =number of miles

find the number of miles for which the companies charge will be the same

Equate the charges of both companies

70 + 0.20x = 55 + 0.30x

70 - 55 = 0.30x - 0.20x

15 = 0.10x

Divide both sides by 0.10

x = 15 / 0.10

= 150

x = 150 miles

The number of miles for which the companies charge will be the same is 150 miles

Substitute 150 miles into any of the companies charges to find the charge

Company B = 55 + 0.30x

= 55 + 0.30(150)

= 55 + 45

= $100

We want to find the number of miles for which both companies charge the same amount.

We will see that the number of miles such that the costs are equal is 150 miles, and both companies charge $100 for that number of miles.

Adobe charges $50 for rental, $20 for gas and $0.20 per mile drive, so if you drive for x miles, the cost is:

A(x) = $50 + $20 + $0.20*x = $70 + $0.20*x

While we know that Vamos card charges $55 for rental and gas (together) and $0.30 per mile, so if you drive for x miles the cost is:

V(x) = $55 + $0.30*x

We want to find the value of x such that the cost equations are equal, so we must solve:

A(x) = V(x)

$70 + $0.20*x = $55 + $0.30*x

$70 - $55 = $0.30*x - $0.20*x

$15 = $0.10*x

$15/$0.10 = x = 150

So for 150 miles, both companies charge the same amount.

The cost is:

V(150) = A(150) = $70 + $0.20*150 = $100

If you want to learn more, you can read:

https://brainly.com/question/21835898

The slope of the line is 7/9

It is important to note that the equation of a line is represented as;

y = mx + c

Where;

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, let's substitute the values into the formula from the points given we have;

Slope, m =1 -(-6)/ -3 - (-6)

expand the bracket

Slope, m = 1 + 6/ 3 + 6

add the values

Slope, m = 7/9

Hence, the value is 7/9

Learn more about slope here:

https://brainly.com/question/3493733

#SPJ1

The balance based on the.data given in the table is shown below.

Balance from day 1 to 10 = 11000

Balance from day 11 to 21= 8000

Balance from day 21 to 30- 5500

Balance on day 31 7500

Balance from day 1 to 10= 11000

Balance from day 11 to 21= 8000 Balance from day 21 to 30 5500

Balance on day 31- 7500

The average daily balance of the credit card for the month of december is:

Average daily balance The ratio of total balance from each day in cycle to the total number of days in cycle.

Total balance from each day in cycle=

(11000 x 10)+(8000 × 10)+(5500 x 10) + (7500 x 1) = 104000

Average daily balance=104000 / 31

= 8145

Learn more about balance on

https://brainly.com/question/24914390

#SPJ1

Answer:

We are given the fractions.

As we know the denominator of a fraction can't be zero.

So the values of x that are not allowed are:

The value of length DE in the triangle is determined as 19.43 cm.

The value of length DE is calculated by applying sine rule of determining length and angle of a triangle.

angle CDE = angle BAC (alternate angles are equal)

sin D/CE = sin E/CD

sin 64 / 19 = sin E / 16

sin E = 16 x (sin 64 / 19)

sin E = 0.7569

E = sin⁻¹ (0.7569)

E = 49.2⁰

The value of length DE is calculated as follows;

angle C = 180 - (64⁰ + 49.2⁰) = 66.8⁰

sin C /DE = sin D/CE

sin (66.8) / DE = sin (64) / (19)

DE = 19 x sin(66.8) / sin (64)

DE = 19.43 cm

Learn more about sine rule here:

https://brainly.com/question/20839703

#SPJ1

Answer:

--------------------------------------

Vertex form of a quadratic function:

Given (h, k) = (-2, -13) and a point (0, - 5).

Substitute all into equation and solve for a:

The parabola is:

Convert it to the standard form:

Answer:

\(f(x)=2x^2+8x-5\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given:

Substitute the given vertex and point into the Vertex formula and solve for a:

\(\implies -5=a(0-(-2))^2+(-13)\)

\(\implies -5=a(0+2)^2-13\)

\(\implies -5=4a-13\)

\(\implies 4a=8\)

\(\implies a=2\)

Substitute the given vertex and found value of a into the Vertex formula:

\(y=2(x+2)^2-13\)

The standard form of a quadratic function is  f(x) = ax² + bx + c

Expand the function in vertex form to standard form:

\(\implies y=2(x^2+4x+4)-13\)

\(\implies y=2x^2+8x+8-13\)

\(\implies y=2x^2+8x-5\)

Answer:

\(\frac{8}{x}\)

Step-by-step explanation:

what is the sum 3/x+9+5/x-9

\(\frac{3}{x} + 9 + \frac{5}{x} - 9 =\)     (add \(\frac{3}{x}\) and \(\frac{5}{x}\))

\(\frac{8}{x} + 9 - 9 =\)            (solve 9 - 9 = 0)

\(\frac{8}{x}\)                           ( your answer)

82% of the candidates did not have a chance for an interview.

We have,

To find the percentage of candidates who did not have a chance for an interview, we need to subtract the percentage of candidates who scored above 85% from 100%.

Number of candidates who scored above 85%: 45

Total number of candidates: 250

Percentage of candidates who scored above 85%:

= (45/250) x 100%

= 18%

Percentage of candidates who did not have a chance for an interview:

= 100% - 18%

= 82%

Therefore,

82% of the candidates did not have a chance for an interview.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

To know more about the inscribed angle theorem visit:

brainly.com/question/16120801

#SPJ1

Answer:

0.25

Step-by-step explanation:

0.52 is like 2 quarters

0.25 is 1 quarter

So, 1 < 2

Have a nice day! :)

Answer:

111m²

Step-by-step explanation:

area = (12*3) + (15*3) +´(5*6)

        = 36 + 45 + 30

         = 111m²

Answer: 111 m²

Ok done. Thank to me :>

Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

The slope is -8

Step-by-step explanation:

To find the slope, we can do a very easy equation. We can do the formula

y1 - y2 / x1 - x2

We fit in all of the respective numbers to get the equation as this.

-51-(-75) / 7-10

Then, we get

24/ -3

Simple division gives us -8.

Answer:

I think the A is the best answer

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

PLEASE please please please please please please I need it Badly

The area of the sector is 37.68ft²

The region inside the portion of the circle formed by two radii and an arc is known as the area of a sector. It just covers a small portion of the circle's total area.

Area of a sector

The area of a sector can be gotten using the expression (θ/360º) × π r ² where

Using the expression we will get,(270/360) x 3.14 x 4²

From the solution, we will find the area to be 37.68ft²

To learn more on area of a sector, visit https://brainly.com/question/14647523

#SPJ1

Answer:

=19-(-3);22

Step-by-step explanation:

19-(-3)=19+3

         =22

Answer: The expected number of bulbs that would last longer than 22,250 hours is approximately 2,857.

Step-by-step explanation:

To solve this problem, we can start by finding the z-score for 22,250 using the formula:z = (x - mean) / standard deviationz = (22,250 - 20,000) / 2,250 = 1Next, we need to find the proportion of bulbs lasting longer than 22,250. We can look up this proportion in a standard normal distribution table or use a calculator, which gives us a probability of 0.1587.Finally, we can use this probability to find the expected number of bulbs that will last longer than 22,250:Expected number of bulbs = probability * total number of bulbs sold Expected number of bulbs = 0.1587 * 18,000 = 2,857Therefore, we can expect that approximately 2,857 of the 18,000 bulbs sold will last longer than 22,250 running hours.

Answer:

the afternoon is the right one

Answer:

I believe the answer is n/3 + 15n.

Answer:

Your answer would be 15 and 3

Step-by-step explanation:

correct on edge

Step-by-step explanation:

If cos(x) = 0.28, then we know that cos(-x) = cos(x) because cosine is an even function. Therefore, cos(-x) = cos(x) = 0.28.

Answer:

2x - 12

Step-by-step explanation:

Given:

-3(6x+4)+20x

Distribute:

-18x-12+20x

Combine like terms:

2x-12

Hope this helps, have a nice day :))

Answer:

3 8 + 1 2

i searched it

Answer:

x=25

Step-by-step explanation:

2x-14=36

2x=50

x=25

Answer:

20.68976

Step-by-step explanation:

Convert the percentage into decimal :

58% = 0.58

0.58 × x = 12

Divide both sides by 0.58 :

x = 12÷0.58

x = 20.689655...

x = 20.68976

So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .

Hope you understood and have a good day

Ahab's total change to funds is -$175, which means he spent more than he gained.

Ahab spent 3 tires at $50 each, which is a total of 3 x $50 = $150.

Later, he returned one tire, so he gets $50 back.

He also found a $5 bill, so he has an extra $5.

He then bought 2 jackets at $40 each, which is a total of 2 x $40 = $80.

The total amount Ahab spent is $150 + $80 = $230.

However, he also received $50 back and found $5, so his total change to funds is $50 + $5 - $230 = -$175.

Therefore, Ahab's total change to funds is -$175, which means he spent more than he gained.

Learn  more about fund here:

https://brainly.com/question/14705214

#SPJ1