When a feasible region is bounded on all sides, where will the maximum and minimum values of the objective function occur?
at the center of the feasible region
at the top of the feasible region
anywhere within the feasible region
at the vertices of the feasible region

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:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.  

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

[tex]\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}[/tex]

Seperate the differential equation and solve for the constant C.

[tex]\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}[/tex]

You have 100 rodents when:

[tex]100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months[/tex]

You have 1000 rodents when:

[tex]1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months[/tex]

Answer:

the elevation of base camp is 35 ft

Step-by-step explanation:

Starting at 65 feet elevation, and the descending 30 feet to reach base camp, that means that base camp is at: 65 ft - 30 ft = 35 ft elevation

Answer:

35 feet

Step-by-step explanation:

65 feet- 30 feet= 35 feet is the elevation of the base

Answer:

A'(4,-6) , B'(0,1), C'(-2,-2)

Step-by-step explanation:

From the given graph the coordinates of ΔABC area A (2,-2), B(-2,5) and C(-4,2)

If a translation is applied on ΔABC two units to the right and four units down  to create ΔA'B'C'.

Then to find the coordinates of ΔA'B'C' will be we need to apply the translation rule

[tex](x,y)\rightarrow(x+2,y-4)[/tex]

Now, [tex]A(2,-2)\rightarrow A'(2+2,-2-4)=A'(4,-6)[/tex]

[tex]B(-2,5)\rightarrow B'(-2+2,5-4)=B'(0,1)[/tex]

and [tex]C(-4,2)\rightarrow C'(-4+2,2-4)=C'(-2,-2)[/tex]

Answer:

The box has sides of 11.07 cm and height of 3.69 cm.

The cost (minimum) is 147 cents per box.

Step-by-step explanation:

We have a box with open top, with a volume of 452 cm^3.

Let x: base side of the box, in cm, and y: height of the box, in cm.

Then, the volume can be expressed as:

[tex]V=x^2\cdot y=452\\\\y=452x^{-2}[/tex]

This box has 4 sides and 1 base. The material cost is 0.4 cents/cm^2 for the base and 0.6 cents/cm^2 for the sides.

Then, we can write the cost as:

[tex]C=0.4\cdot 1\cdot (x^2)+0.6\cdot 4\cdot (xy)\\\\\\xy=x\cdot(452x^{-2})=452x^{-1}\\\\\\C=0.4x^2+2.4(452x^{-1})\\\\\\C=0.4x^2+1084.8x^{-1}[/tex]

The value for x that gives a minimum cost can be found deriving the function C and equal to 0:

[tex]\dfrac{dC}{dx}=0.4(2x)+1084.8(-1\cdot x^{-2})=0\\\\\\0.8x-1084.8x^{-2}=0\\\\0.8x=1084.8x^{-2}\\\\0.8x^{1+2}=1084.8\\\\x^3=1084.8/0.8=1356\\\\x=\sqrt[3]{1356}\\\\x=11.07[/tex]

The height can be calculated with the equation:

[tex]y=452x^{-2}=452(11.07^{-2})=452\cdot 0.00816 =3.69[/tex]

The minimum cost can be calculated as:

[tex]C=0.4x^2+1084.8x^{-1}\\\\C(11.07)=0.4(11.07)^2+1084.8(11.07)^{-1}\\\\C(11.07)=0.4\cdot 122.51+1084.8\cdot0.09\\\\C(11.07)=49+98\\\\C(11.07)=147[/tex]

Answer:

5

Step-by-step explanation:

first you need to simplify this equation and put it in slope intercept form which is y = mx + b

after simplifying you will get y = 5x + 10

since the slope is m , the answer will be 5

Answer:

270

Step-by-step explanation:

For any arithmetic sequence

nth term is given by

nth term = a + (n-1)d

where a is first term,

d is common difference

d is given by nth term - (n-1)th term

sum of n terms given by

sum = n/2(2a + (n-1)d)

________________________________________________

Given arithmetic sequence

-2,0,2,4,6,8...

first term a = -2

lets take third term as nth term and second term as (n-1)th term to find common difference d.

d = 2 - 0 = 2

using a = -2 , d = 2, n = 18

thus, sum of first 18 terms = n/2(2a + (n-1)d)

                                           =18/2( 2*(-2) + (18-1) 2)

                                           =9 ( -4 + 34)

                                           =9 ( 30) = 270

Thus, sum of first 18 terms is 270.

Answer:

GH¢.37480.36

Step-by-step explanation:

Let the amount invested at 12% per annum =GH¢.x

He  invested 580.00 more than the first at 14%.

Therefore:

The amount invested at 14% =GH¢.(x+580)

For each investment option:

Amount Accrued =Principal + Simple Interest

Amount Accrued at 12%

[tex]=x+x*0.12\\=1.12x[/tex]

Amount Accrued at 14%

[tex]=(x+580)+0.14(x+580)\\=x+580+0.14x+81.2\\=1.14x+661.2[/tex]

Mr. Azu had total accumulated amount of  GH42,358.60

Therefore:

1.12x+1.14x+661.2=42,358.60

2.26x=42,358.60-661.2

2.26x=41697.4

x=GH¢.18450.18

Therefore:

The amount invested at 12% per annum= GH¢.18450.18

The amount invested at 14% per annum= GH¢.18450.18+580

=GH¢.19030.18

Mr Azu's Total Investment = 18450.18 +19030.18

=GH¢.37480.36

Answer:

[tex]\dfrac{1}{16}[/tex]

Step-by-step explanation:

Proportion of Heat Loss Between sundown and midnight[tex]=\dfrac{1}{3}[/tex]

Proportion of Heat Loss between midnight and 4 AM  [tex]=\dfrac{1}{2}[/tex]

Proportion of Total Heat Already Lost [tex]=\dfrac{1}{3}+\dfrac{1}{2} =\dfrac{5}{6}[/tex]

Proportion of Remaining Heat [tex]=1-\dfrac{5}{6}=\dfrac{1}{6}[/tex]

Between 4 AM and 5 AM, five-eighths of the remaining heat is lost.

Proportion of Heat Loss between 4 AM and 5 AM= [tex]\dfrac{5}{8}$ X \dfrac{1}{6} = \dfrac{5}{48}[/tex]

Therefore, Proportion of Remaining Heat Left [tex]=\dfrac{1}{6}- \dfrac{5}{48}=\dfrac{1}{16}[/tex]

We therefore say that:

[tex]\dfrac{1}{16}$ of the total heat loss occurs between 5 AM and sunrise.[/tex]

Answer: The answers are in the steps hopes it helps.

Step-by-step explanation:

40% * x = 23   convert 40% to a decimal

0.4 * x = 23     multiply 0.4 is by x

0.4x = 23    divide both sides by 0.4

x= 57.5  

Check:  

57.5 * 40% = ?

57.5 * 0.4 = 23

Answer:

A

Step-by-step explanation:

Answer:

The answer here is A.

A) A is congruent to D.

A=

Step-by-step explanation:

AP E

Answer:

Null hypothesis:[tex]\mu \leq 6[/tex]      

Alternative hypothesis:[tex]\mu > 6[/tex]      

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

Step-by-step explanation:

Information given

[tex]\bar X=370.69/60 =6.178[/tex] represent the sample mean

[tex]s=24.36/36=0.68[/tex] represent the standard deviation for the sample    

[tex]n=26[/tex] sample size      

[tex]\mu_o =6[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \leq 6[/tex]      

Alternative hypothesis:[tex]\mu > 6[/tex]      

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]      

The degrees of freedom are:

[tex]df=n-1=26-1=25[/tex]  

The p value would be given by:

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]  

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

Answer: 207^2 + 9km^2 = 216km^2

Step-by-step explanation:

(my explanation is wrong)

All you want to do is break this figure up into rectangles and triangles.

I see 3 rectangles and 1 triangle.

Three Rectangles:

The bottom one has the dimension of 5 and 20. 5 x 20 = 100 km^2

The middle one has the dimensions of 5+4 and 7. 9 x 7 = 63 km^2

The top one has the dimensions of 4 and 11. 4 x 11 = 44 km^2

Add them all up to get 207km^2

One Triangle:

We can see at the bottom rectangle that the left side is 5 and the right side is 3 + x. X being our missing height of the triangle. The height equals 2.

The triangle now has the dimensions of 2 and 6. 2 x 6 = 12. Then divide by 2 to get 6 km^2

Answer:

216 km²

Step-by-step explanation:

To solve this, you have to divide the figure into different parts.  I divided the parts up into four sections.  I will work on the parts in numerical order.

1.  At the top of the rectangle, it is marked 4 km. On the left side, it is marked 11 km.  This is the length and width.

A = lw

A = 11 × 4

A = 44 km²

2.  On the left side of this rectangle, it is marked 7 km.  At the top it is marked 5 km, but there is a portion that does not have a measurement (the part with a different color than the rest.  Because this line is also part of rectangle 1, we know that the line is 4 km.  Adding up the two numbers gives you 9 km.  

4 + 5 = 9

A = lw

A = 7 × 9

A = 63 km²

3.  On the left side, it is marked 5 km.  On the bottom, it is marked 20 km.

A = lw

A = 20 × 5

A = 100 km²

4.  This is one is a bit more tricky.  This is a triangle, so we have to find the base and the height.  The base is 6 km.  You have to figure the height.  Look at the picture with the red lines.  

The red line on the right side has a length of 17 + 3 + x = 20 + x.  The length is 20 + x because there is a portion of the line that is missing.

The red lines on the left side have a length of 5 + 7 + 11 = 23.  The two side should be equal so

23 = 20 + x

x = 3

Now, you have the height.  Use the equation for area of a triangle to solve.

A = 1/2bh

A = 1/2(3)(6)

A = 1/2(18)

A = 9 km²

Now you have to add up all the areas to find the total area.

44 km² + 63 km² + 100 km² + 9 km² = 216 km²

Answer:

120

Step-by-step explanation:

3480/29=120

           120

Simplify   ———

            1

final result is  120

Answer:

D.

Step-by-step explanation:

In the attached file

Answer: 1-20=2  and 60-80=4

Step-by-step explanation:

the first is 2 number of building

and the third one is 4 number of buldings

Hope this helps :)

Answer:

2 real solutions

Step-by-step explanation:

Answer:

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex]  to [tex]40^o[/tex]

Step-by-step explanation:

The temperature range is the difference between the maximum and the minimum temperature:

[tex]40^o-(-45^o)=40^o+45^o=95^o[/tex]

The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex]  to [tex]40^o[/tex]

Answer:

work is shown and pictured

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:

[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ4

Answer:

There are 60 marbles in the bag

Step-by-step explanation:

The total number of marbles  times the probability of red marbles = number of red marbles

total * 7/10 = 42

Multiply each side by 10/7

total * 7/10 * 10/7 = 42*10/7

total

60

There are 60 marbles in the bag

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

Answer:

[tex]\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

[tex]R_{in}[/tex] =(concentration of salt in inflow)(input rate of solution)

[tex]=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}[/tex]

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, [tex]C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}[/tex]

[tex]R_{out}[/tex] =(concentration of salt in outflow)(output rate of solution)

[tex]=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}[/tex]

Therefore, the differential equation for the amount of Salt in the Tank  at any time t:

[tex]\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg[/tex]

Answer:

q

Step-by-step explanation:

Since AB is a transversal of the two parallel lines, the angle with measure 135 degrees and angle q are vertical angles. Therefore, their measure must be equal.

Hope this helps!

Answer:

Dear Laura Ramirez

Answer to your query is provided below

1) option A is correct

2) option B is correct

Step-by-step explanation:

Explanation for the first question attached in image

Also note - The converse of the hinge theorem states that if two triangles have two congruent sides, then the triangle with the longer third side will have a larger angle opposite that third side.

Answer:

1) option A is correct2) option B is correct

Step-by-step explanation:

Answer:

$5,882

Step-by-step explanation:

To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:

PV=FV/(1+i)^n

PV= present value

FV= future value= $8,000

i= interest rate= 8%

n= number of periods= 4

PV= 8,000/(1+0.08)^4

PV=8,000/1.08^4

PV=8,000/1.36

PV= 5,882

According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.

Answer:

a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

c)

Step-by-step explanation:

a) Let p be  the probability of winning each ticket be = 0.1

Then q which is the probability of failing each ticket  = 1 - p = 1  - 0.1 = 0.9

Assume X represents the  number of failure preceding the 5th success in x + 5 trials.

The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:

[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

Then, the probability distribution of random variable X is

[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

where;

X represents the  negative binomial random variable.

K= X + 5 = number of ticket buy up to and including fifth winning ticket.

Since K =X+5 this signifies that  X = K-5

as X takes value 0, 1 ,2,...

K takes value 5, 6 ,...

Therefore:

The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

Let p represent the probability of getting a tail on a flip of the coin

Thus p = 0.5 since it is a fair coin

where L = number of flips of the coin including 33rd occurrence of  tails

Thus; the negative binomial distribution of L can be illustrated as:

[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]

where

X= L

r = 33  &

p = 0.5

Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...

Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]

c)  

Given that:

Let  M be the random variable which represents  the number of tickets need to be bought to get the first success,

also success probability is 0.01.

Therefore, M ~ Geo(0.01).

Thus, the PMF of M is given by:

[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]

[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]

Answer:

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

P-value = 0.003.

Step-by-step explanation:

If we perform a regression analysis relating x and y, we get the best fitting line with equation:

[tex]y=15.82x+92.9[/tex]

and a correlation coefficient r:

[tex]r=0.693[/tex]

We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).

This can be written as:

[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]

where ρ is the population correlation coefficient for x and y.

The significance level is assumed to be 0.05.

The sample size is n=16.

The degrees of freedom are df=14.

[tex]df=n-2=16-2=14[/tex]

The test statistic can be calculated as:

[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]

For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:

[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]

The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.

Answer:

24 square units

Step-by-step explanation:

The formula for computing the area of a trapezoid is shown below:

As we know that

Area of a trapezium is

[tex]= \frac{1}{2} \times h(a+b)[/tex]

where

h = perpendicular height

The a and b =  length of the parallel sides.

Now,

h = 2 - -2 = 4 units

a = 5 - -3 = 8 units

b = 3 - -1 = 4 units

Now placing these values to the above formula

So, the area of a trapezoid is

[tex]= \dfrac{1}{2} \times 4(8+4)[/tex]

[tex]= 2 \times 12[/tex]

= 24 square units.

Hence we applied the above formula so that the area of trapezoid could come

Answer:

The table that illustrates this equation is table A:

1   -6   0   up   (0,0)

Step-by-step explanation:

The values of the parameters a, b, and c have to agree with the values for the general quadratic equation in standard form:

[tex]y = a\,x^2+b\,x+c[/tex]

compared to:

[tex]y=x^2-6\,x[/tex]

So the coefficient "a" of the quadratic term in our case is: "1"

the coefficient "b" of the linear term is : "-6"

the coefficient "c" for the constant term s : "0" (zero)

since the coefficient "a" is a positive number, we know that the parabola's branches must be opening "UP".

The y intercept can be found by evaluating the expression for x = 0:

[tex]y=x^2-6x\\y=(0)^2-6\,(0)\\y=0[/tex]

Therefore the y-intercept is at (0, 0)

These results agree with those of Table "A"

Answer:

Table A.)

Step-by-step explanation:

a 1, b -6, c 0, up, (0, 0), Table A.