if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full

Answer:

Step-by-step explanation:

Hello!

Be the variable of interest:

X: Number of weeks it takes a worker aged 55 plus to find a job

Sample average X[bar]= 22 weeks

Sample standard deviation S= 11.89 weeks

Sample size n= 40

a)

The point estimate of the population mean is the sample mean

X[bar]= 22 weeks

It takes on average 22 weeks for a worker aged 55 plus to find a job.

b)

To estimate the population mean using a confidence interval, assuming the variable has a normal distribution is

X[bar] ± [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]

[tex]t_{n-1; 1-\alpha /2}= t_{39; 0.975}= 2.023[/tex]

The structure of the interval is "point estimate" ± "margin of error"

d= [tex]t_{n_1; 1-\alpha /2}[/tex] * [tex]\frac{S}{\sqrt{n} }[/tex]= 2.023*[tex](\frac{11.89}{\sqrt{40} })[/tex]= 3.803

c)

The interval can be calculated as:

[22  ±  3.803]

[18.197; 25.803]

Using s 95% confidence level, you'd expect the population mean of the time it takes a worker 55 plus to find a job will be within the interval [18.197; 25.803] weeks.

d)

Job Search Time (Weeks)

21 , 14, 51, 16, 17, 14, 16, 12, 48, 0, 27, 17, 32, 24, 12, 10, 52, 21, 26, 14, 13, 24, 19 , 28 , 26 , 26, 10, 21, 44, 36, 22, 39, 17, 17, 10, 19, 16, 22, 5, 22

To study the form of the distribution I've used the raw data to create a histogram of the distribution. See attachment.

As you can see in the histogram the distribution grows gradually and then it falls abruptly. The distribution is right skewed.

Answer:

Its right and scalene.

It has a right angle and all the sides are diferent.

Answer:

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Answer:

13. B

14. D

Step-by-step explanation:

13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.

14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.

Answer:

It would be 16!!!

The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (-1/2)⁻⁴

Simplify the equation, then we have

⇒ (-1/2)⁻⁴

⇒ (-2)⁴

⇒ -2⁴

⇒ 16

The value of the exponent numerical expression (-1/2)⁻⁴ will be 16. Then the correct option is D.

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Answer:

Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.

Step-by-step explanation:

Determine the time(s) at which the population was 600,000.

This is t for which P(t) = 600000. To do this, we solve a quadratic equation.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]P(t) = -1718t^{2} + 82000t + 10000[/tex]

We have to find t for which P(t) = 600000. Then

[tex]600000 = -1718t^{2} + 82000t + 10000[/tex]

[tex]-1718t^{2} + 82000t - 590000 = 0[/tex]

So [tex]a = -1718, b = 82000, c = -590000[/tex]

Then

[tex]\bigtriangleup = 82000^{2} - 4*(-1718)*(-590000) = 2669520000[/tex]

[tex]t_{1} = \frac{-82000 + \sqrt{2669520000}}{2*(-1718)} = 8.8[/tex]

[tex]t_{2} = \frac{-82000 - \sqrt{2669520000}}{2*(-1718)} = 38.9[/tex]

Rounding to the nearest hour, the times at which the population was 600,000 was at 9 hours and at 39 hours.

Answer:

Amount that Brian has after 2 years = £6932.53

Step-by-step explanation:

To find, the amount that Brian will have after 2 years:

Formula for amount where compound interest is applicable:

[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]

Where A is the amount after t years time

P is the principal.

R is the rate of interest.

In the question, we are given the following details:

Principal amount,P = £6300

Rate of interest,R = 4.9%

Time,t = 2 years

Putting the values in formula:

[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]

Hence, Amount that Brian has after 2 years = £6932.53

Answer:

THE ANSWER IS ABOVE

Step-by-step explanation:

hahahaha

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes

Answer: 4

Step-by-step explanation:

in order to divide one fraction by another, you must multiply by the reciprocal(the reverse of a certain fraction). the reciprocal of 1/6 is 6/1. so:

[tex]\frac{2}{3} / \frac{1}{6}[/tex] =           multiply by the reciprocal of 1/6

[tex]\frac{2}{3} * \frac{6}{1}[/tex] =         cross out

[tex]\frac{2}{1} * \frac{2}{1}[/tex] =         multiply

[tex]\frac{4}{1}[/tex] =               simplify

4

Answer:

4

Step-by-step explanation:

(2/3)/(1/6)

Eleminate the denominator by multiplying numerator and denominator with whatever is the reciprocal of the denominator. In this case the denominator is 1/6 so the reciprocal is 6/1 or "just" 6.

So, multiply numerator and denominator by 6. The next three (bold) steps, have been written down for explanatory purposes only, and normally are not nessasary.

(2/3)*6 / (1/6)*6

(2/3)*6 / (6/6)

(2/3)*6 / 1

(2/3)*6

12/3

4

Answer:

Step-by-step explanation:

If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by

bn=(n)^(5.6/n).

a)

[tex]L = \lim_{n \to \infty} b_n \\\\\\L= \lim_{n \to \infty} n^{\frac{5.6}{n} }[/tex]

Log on both sides

[tex]In (L) = \lim_{n \to \infty} In (n)^{\frac{5.6}{n} }\\\\= \lim_{n \to \infty} \frac{5.6}{n} In(n)[/tex]

[tex]=5.6 \lim_{n \to \infty} \frac{d}{dn} In(n)/\frac{d}{dn} (n)\\\\=5.6 \lim_{n \to \infty} \frac{1}{n} /1 \\\\=5.6 \lim_{n \to \infty} \frac{1}{n} \\\\=5.6 \times 0\\\\In(L) =0\\\\L=e^0\\\\L=1[/tex]

[tex]\therefore \lim_{n \to \infty} (n)^{\frac{5.6}{n} =1[/tex]

The limit value of given sequece is 1.

To understand more, check below explanation.

The given sequence is,

                   [tex]b_{n}=n^{5.6/n}[/tex]

We have to find limit of above sequence.

           [tex]L=\lim_{n \to \infty} b_n \\\\L=\lim_{n \to \infty}n^{5.6/n} \\\\ln(L)=\lim_{n \to \infty}\frac{5.6}{n}ln(n) \\\\ln(L)=5.6\lim_{n \to \infty}\frac{ln(n)}{n} \\\\ln(L)=5.6\lim_{n \to \infty}\frac{1/n}{1} \\\\ln(L)=5.6*0=0\\\\L=e^{0}=1[/tex]

Therefore, the limit value of given sequece is 1.

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Answer:

2 times some thing and plus 3 equals -7

Step-by-step explanation:

x = -5

Answer:

Step-by-step explanation:

From the news story, we are told that:

The odds are 1 in 150 that a piece of Skylab will hit someone.

However, 4 billion people live in the zone in which pieces could fall.

Therefore, any one person’s chances of being struck are:

[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]

Therefore, the odds are one in approximately 27 million.

The inaccuracy presented in this reasoning was that the odds are one in 600 billion.

Answer:

Step-by-step explanation:

Given that, we have 1851 bullets that we KNOW are NOT MATCHES of one another. One by one they examine two bullets at a time.

So, there are 1851 bullets but each time we choose 2.

We have, N choose K = N! / K! (N-k)!

Here, N = 1851 and K = 2

Therefore, 1851 choose 2 = 1851! / 2! (1851-2)!

                                         = 1851! / 2! * 1849!

                                         = 1712175 Possible Combinations

Out of these 653 are false positive.

The chance of getting false positive is = 658 / 1712175

                                                            = 0.000384

                                                           = 0.0384 %

Therefore, The correct option is

The chance of false positive is 0.0384% Because this probability is sufficiently small (< or = 1%) There is high confidence in the agency's forensic evidence.

Answer:

Step-by-step explanation:

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown;

[tex]\int\limits {0.5 + \frac{6}{(t+4)^{3} } } \, dt \\= \int\limits {0.5} \, dt + \int\limits\frac{6}{(t+4)^{3} } } \, dx } \, \\= 0.5t +\int\limits {6u^{-3} } \, du \ where \ u = t+4 \ and\ du = dt\\= 0.5t + 6*\frac{u^{-2} }{-2} + C\\= 0.5t-3u^{-2} +C\\= 0.5t-3(t+4)^{-2} + C[/tex]

a)  The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from  t =1 to t = 2

[tex]\int\limits^2_1 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_1\\= [0.5(2)-3(2+4)^{-2}] - [0.5(1)-3(1+4)^{-2}]\\= [1-3(6)^{-2}] - [0.5-3(5)^{-2}]\\ = [1-\frac{1}{12}] - [0.5-\frac{3}{25} ]\\= \frac{11}{12}-\frac{1}{2}+\frac{3}{25}\\ = 0.9167 - 0.5 + 0.12\\= 0.5367feet[/tex]

b)  The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from  t =2 to t = 3

[tex]\int\limits^3_2 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^3_2\\= [0.5(3)-3(3+4)^{-2}] - [0.5(2)-3(2+4)^{-2}]\\= [1.5-3(7)^{-2}] - [1-3(6)^{-2}]\\ = [1.5-\frac{3}{49}] - [1-\frac{1}{12} ]\\ = 1.439 - 0.9167\\= 0.5223feet[/tex]

c) The total number of feet grown during the second year can be gotten by substituting the value of limit from t = 0 to t = 2 into the equation as shown

[tex]\int\limits^2_0 {0.5 + \frac{6}{(t+4)^{3} } } \, dt = [0.5t-3(t+4)^{-2}]^2_0\\= [0.5(2)-3(2+4)^{-2}] - [0.5(0)-3(0+4)^{-2}]\\= [1-3(6)^{-2}] - [0-3(4)^{-2}]\\ = [1-\frac{1}{12}] - [-\frac{3}{16} ]\\= \frac{11}{12}+\frac{3}{16}\\ = 0.9167 - 0.1875\\= 0.7292feet[/tex]

Answer:

  19.8 cm

Step-by-step explanation:

Angle B is the complement of angle A, so we have this relation for the angles:

  B/A = 3/2 = (90°-A)/A

  2(90° -A) = 3A . . . . . cross multiply

  180° = 5A . . . . . . . . . eliminate parentheses, add 2A

  36° = A . . . . . . . . . . . divide by 5

The relations expressed by the mnemonic SOH CAH TOA remind you that ...

  Cos = Adjacent/Hypotenuse

  cos(A) = AC/AB

  AB = AC/cos(A) = (16 cm)/cos(36°)

  AB ≈ 19.8 cm

Answer:

4 ft

Step-by-step explanation:

288=16 * 18

12+4=16

14+4=18

The dimensions increased by 4 feet.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given;

Dimensions of rectangle = 12 + x and 14 + x

The area of the rectangle= (12 + x) (14 + x) = 288

x² + 26x + 168 = 288

x² + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x =4

Hence, The dimensions increased by 4 feet.

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Answer:

so halve the deck is black and halve the deck is red so you have 26 black cards then divide by 5 and you get 5 with 1 card leftover

Answer:

The probability that all four received a raised when they asked for one is 0.370.

Step-by-step explanation:

Let the random variable X represent the number of business executives who received a pay raise when they asked for one.

The probability that a business executives received a pay raise when they asked for one is, p = 0.78.

A random sample of n = 4 executives was selected.

The events of any executive receiving a pay raise when they asked for one is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 4 and p = 0.78.

The probability mass function of X is:

[tex]P(X=x)={4\choose x}\ (0.78)^{x}\ (1-0.78)^{4-x};\ x=0,1,2,3...[/tex]

Compute the probability that all four received a raised when they asked for one as follows:

[tex]P(X=4)={4\choose 4}\ (0.78)^{4}\ (1-0.78)^{4-4}[/tex]

                [tex]=1\times 0.37015056\times 1\\\\=0.37015056\\\\\apporx 0.370[/tex]

Thus, the probability that all four received a raised when they asked for one is 0.370.

Answer:

The value of X would be 4.

Answer:

x=4

Step-by-step explanation:

f(2)=3*2-1=5

g(x)=2x-3=5

2x=8

x=4

Answer:

x>−6 and x<7

Step-by-step explanation:

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

|−2x+1|<13

Solve Absolute Value.

|−2x+1|<13

We know−2x+1<13and−2x+1>−13

−2x+1<13(Condition 1)

−2x+1−1<13−1(Subtract 1 from both sides)

−2x<12

−2x

−2

<

12

−2

(Divide both sides by -2)

x>−6

−2x+1>−13(Condition 2)

−2x+1−1>−13−1(Subtract 1 from both sides)

−2x>−14

−2x

−2

>

−14

−2

(Divide both sides by -2)

x<7

Answer:

x>−6 and x<7

Answer:

33.2

Step-by-step explanation:

70−30+2−9+0.3−0.1

=40+2−9+0.3−0.1

=40+−7+0.3−0.1

=33+0.3−0.1

=33+0.2

=33.2

Answer:

33.2

Step-by-step explanation

If we start from the left and work our way right:

70+(-30) is the same as 70-30 which would give 40

2+(-9) is the same as 2-9 which would give -7

0.3(-0.1) is the same as 0.3-0.1 which would give 0.2

now if you put them together

40-7+.2 gives 33.2

Answer:

Step-by-step explanation:

[tex]100 (0.96)^{25} =[/tex] around 36.04

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Step-by-step explanation:

make brainiest please

Answer:

Step-by-step explanation:

F(x) results in a parabola with vertex (0,0) wich mean there is only one x-int at that point. g(x) has been shifted the grapgh of f(x) to the right by to units and down by three unites. Now our vertex lies in the point (2,-3) and since the graph was move dow i=of the x-axis we now have two different x-intercepts.

Answer:

100 muffins

Step-by-step explanation:

We can use a ratio to solve

6 cups          15 cups

-------------   = -----------

40 muffins     x muffins

Using cross products

6x = 40*15

Divide each side by 6

6x/6 = 40*15/6

x =100

100 muffins

Answer:

100 muffins

Step-by-step explanation:

If she could bake 40 muffins with 6 cups, then she could bake 80 muffins with 12 cups. Then, we have 3 cups left over, which is half of 6, meaning she can only bake half of her regular amount with 3 cups, which would be 20. 80+20=100

40+40+20=100

Answer:

Yes additive inverse is two complete opposite numbers if added = 0

Answer:

additive

Step-by-step explanation:

Because the point is not past the postive live or below the negative.

There is a missing content in the question.

After the statements and before the the options given; there is an omitted content which says:

Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?

Answer:

C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).

Step-by-step explanation:

From the given question:

The resulting regression equation can be represented as:

[tex]\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3[/tex]

where;

the estimated number of contracts in a quarter X is the coded quarterly value with X = 0

the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise

Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise

Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise

Our null and alternative hypothesis can be stated as;

Null hypothesis :

[tex]H_0 :[/tex]  The quarterly growth rate in the number of contracts is not  significantly different from 0% (? = 0.05)

[tex]H_a:[/tex]  The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From the missing omitted part we added above; we can see that the   t-statistics value = 9.08 and the p-value = 0.000 .

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

Answer:

Step-by-step explanation:

a) sum of 100 can be achieved from following set of score

10,40,50. This score can be achieved in 3! ways

20,30,50. This score can be achieved in 3! ways

20,40,40. This score can be achieved in 4 ways

30,30,40. This score can be achieved in 4 ways

So,

P(score of 100)=

Answer:

x= -3    x=8

Step-by-step explanation:

(x+3)(x-8)=0

We can use the zero product property to solve

x+3 =0   x-8 =0

x= -3    x=8

Answer:

x=8

Step-by-step explanation:

Answer:

The number of weeks it will take for the  beetle population to reach 236 is 28.75.

Step-by-step explanation:

If a quantity starts at size P₀ and grows by d every time period, then the

quantity after n time periods can be determined using explicit form:

[tex]P_{n} = P_{0} + d \cdot n[/tex]

Here,

d = the common difference, i.e. the amount  that the population changes each time n is increased by 1.

In this case it is provided that the original population of beetle was:

P₀ = 6; (week 0)

And the population after 8 weeks was,

P₈ = 86

Compute the value of d as follows:

[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]

Thus, the explicit formula for the beetle population after n weeks is:

[tex]P_{n}=P_{0}+8n[/tex]

Compute the number of weeks it will take for the  beetle population to reach 236 as follows:

[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]

Thus, the number of weeks it will take for the  beetle population to reach 236 is 28.75.