Help me pls I need help ​

Answer:

a) k=2.08 1/hour

b) The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

c) 977,435,644 cells

d) 2.033 billions cells per hour.

e) 2.81 hours.

Step-by-step explanation:

We have a model of exponential growth.

We know that the population duplicates every 20 minutes (t=0.33).

The initial population is P(t=0)=58.

The exponential growth model can be written as:

[tex]P(t)=Ce^{kt}[/tex]

For t=0, we have:

[tex]P(0)=Ce^0=C=58[/tex]

If we use the duplication time, we have:

[tex]P(t+0.33)=2P(t)\\\\58e^{k(t+0.33)}=2\cdot58e^{kt}\\\\e^{0.33k}=2\\\\0.33k=ln(2)\\\\k=ln(2)/0.33=2.08[/tex]

Then, we have the model as:

[tex]P(t)=58e^{2.08t}[/tex]

The relative growth rate (RGR) is defined, if P is the population and t the time, as:

[tex]RGR=\dfrac{1}{P}\dfrac{dP}{dt}=k[/tex]

In this case, the RGR is k=2.08 1/h.

After 8 hours, we will have:

[tex]P(8)=58e^{2.08\cdot8}=58e^{16.64}=58\cdot 16,852,338= 977,435,644[/tex]

The rate of growth can be calculated as dP/dt and is:

[tex]dP/dt=58[2.08\cdot e^{2.08t}]=120.64e^2.08t=2.08P(t)[/tex]

For t=8, the rate of growth is:

[tex]dP/dt(8)=2.08P(8)=2.08\cdot 977,435,644 = 2,033,066,140[/tex]

(2.033 billions cells per hour).

We can calculate when the population will reach 20,000 cells as:

[tex]P(t)=20,000\\\\58e^{2.08t}=20,000\\\\e^{2.08t}=20,000/58\approx344.827\\\\2.08t=ln(344.827)\approx5.843\\\\t=5.843/2.08\approx2.81[/tex]

Answer:

d. The mean is 43.6°F, and the median is 43.5°F.

Step-by-step explanation:

Hello!

The data corresponds to the low temperatures in Phoenix recorded for April to November.

April: 32ºF

May: 40ºF

June: 50ºF

July: 61ºF

August: 60ºF

September: 47ºF

October: 34ºF

November: 25ºF

Sample size: n= 8 months

The mean or average temperature of the low temperatures in Phoenix can be calculated as:

[tex]\frac{}{X}[/tex]= ∑X/n= (32+40+50+61+60+47+34+25)/8= 43.625ºF (≅ 43.6ºF)

The Median (Me) is the value that separates the data set in two halves, first you have to calculate its position:

PosMe= (n+1)/2= (8+1)/2= 4.5

The value that separates the sample in halves is between the 4th and the 5th observations, so first you have to order the data from least to greatest:

25; 32; 34; 40; 47; 50; 60; 61

The Median is between 40 and 47 ºF, so you have to calculate the average between these two values:

[tex]Me= \frac{(40+47)}{2} = 43.5[/tex] ºF

The correct option is D.

I hope this helps!

Answer:

it is d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Surface Area of the rectangular box = 2(LW+LH+WH)

L is the length of the box

W is the width of the box

H is the height of the box

let dL, dW and dH be the possible error in the dimensions L, W and H respectively.

Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm

The surface Area of the rectangular box using the differentials is expressed as shown;

S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]

Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;

S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}

S = 2{19.2+11.6+19.2+9.6+11.6+9.6}

S = 2(80.8)

S = 161.6 cm²

Hence, the surface area of the box is 161.6 cm²

Answer:

40%

Step-by-step explanation:

We can find what percent 48 is of 120 by dividing:

48/120 = 0.4 or 40%

So, she saved 40% from the original price.

Answer:

0.11

Step-by-step explanation:

Let the random variable score, X = 26; mean, ∪ = 19.6; standard deviation, α = 5.2

By comparing P(0≤ Z ≤ 26)

P(Z ≤ X - ∪/α) = P(Z ≤ 26 - 19.6/5.2)

= P(Z ≤ 1.231)

Using Table: P(0 ≤ Z ≤ 1) = 0.39

P(Z > 1) = (0.5 - 0.39) = 0.11

∴ P(Z > 26) = 0.11

Answer:

The solution to the given Initial - Value - Problem is [tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]

Step-by-step explanation:

y' + 3y = f(t).................(1)

f(t) = t      when 0 ≤ t < 1

f(t) = 0     when t ≥ 1

Step 1: Take the Laplace transform of the LHS of equation (1)

That is L(y' + 3y) = sY(s) + 3Y(s) = Y(s)[s + 3]..............(*)

Step 2: Get an expression for f(t)

For f(t) = t      when 0 ≤ t < 1

f₁(t) = t (1 - u(t - 1)) ( there is a time shift of the unit step)

For f(t) = 0     when t ≥ 1

f₂(t) = 0(u(t-1))

f(t) = f₁(t) + f₂(t)

f(t) = t - t u(t-1)................(2)

Step 3: Taking the Laplace transform of equation (2)

[tex]F(s) = \frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s})[/tex]...............(**)

Step 4: Equating * and **

[tex]Y(s) [s + 3]=\frac{1}{s^2} - e^{-s} ( \frac{1}{s^2} + \frac{1}{s}) \\Y(s) = \frac{1}{s^2(s+3)} - e^{-s} ( \frac{1}{s^2(s+3)} + \frac{1}{s(s+3)})[/tex].......................(3)

Since y(t) is the solution we are looking for we need to find the Inverse Laplace Transform of equation (3) by first breaking every  fraction into partial fraction:

[tex]\frac{1}{s^2 (s+3)} = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)}[/tex]

[tex]\frac{1}{s (s+3)} = \frac{1}{3s} + \frac{1}{3(s+3)}[/tex]

We can rewrite equation (3) by representing the fractions by their partial fractions.

[tex]Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s} [\frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} + \frac{1}{3s} + \frac{1}{3(s+3)}]\\Y(s) = \frac{-1}{9s} + \frac{1}{3s^2} + \frac{1}{9(s+3)} - e^{-s}[\frac{2}{9s} + \frac{1}{3s^2} - \frac{2}{9(s+3)}][/tex]................(4)

step 5: Take the inverse Laplace transform of equation (4)

[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - u(t-1)[\frac{2}{9} + \frac{1}{3}(t-1) - \frac{2}{9}e^{-3(t-1)}][/tex]

Simplifying the above equation:

[tex]y(t) = \frac{-1}{9} + \frac{1}{3}t + \frac{1}{9}e^{-3t} - [\frac{-1}{9} + \frac{1}{3}t - \frac{2}{9}e^{-3(t-1)}]u(t-1)[/tex]

The Laplace transform is use to solve the differential equation problem.

The solution for the given initial-value problem is,

[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]

Given:

The given initial value problem is [tex]y' + 3y = f(t)[/tex].

Consider the left hand side of the given equation.

[tex]y'+3y[/tex]

Take the Laplace transform.

[tex]L(y' + 3y) = sY(s) + 3Y(s) \\L(y' + 3y) = Y(s)[s + 3][/tex]

Consider the right hand side and get the expression for [tex]f(t)[/tex].

[tex]f(t) = t[/tex]  when 0 ≤ t < 1

From time shift of the unit step

[tex]f_1(t) = t (1 - u(t - 1))[/tex]

For f(t) = 0     when t ≥ 1

Now,

[tex]f_2(t) = 0(u(t-1))f(t) = f_1(t) + f_2(t)f(t) = t - t u(t-1)[/tex]

Take the Laplace for above expression.

[tex]F(s)=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)[/tex]

Now, the equate the above two equation.

[tex]Y(s)\left[s+3\right ]=\dfrac{1}{s^2}-e^{-s}\left(\dfrac{1}{s^2}+\dfrac{1}{s}\right)\\Y(s)=\dfrac {1}{(s^2(s+3))}-e^{-s}\left(\dfrac{1}{(s^2(s+3))}+\dfrac{1}{s(s+3)\right)}[/tex]

Find the inverse Laplace for the above equation.

[tex]\dfrac{1}{(s^2(s+3))}=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}\\\dfrac{1}{(s(s+3))}=\dfrac{1}{3s}+\dfrac{1}{3(s+3)}[/tex]

Calculate the partial fraction of above equation.

[tex]Y(s)=\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{-1}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}+\dfrac{1}{3s}+\dfrac{1}{3(s+3)}\right]\\Y(s)=\dfrac{2}{9s}+\dfrac{1}{3s^2}+\dfrac{1}{9(s+3)}-e^{-s}\left[\dfrac{2}{9s}+\dfrac{1}{3s^2}-\dfrac{2}{9(s+3)}\right][/tex]

Take the inverse Laplace of the above equation.

[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]

Thus, the solution for the given initial-value problem is,

[tex]y(t)=\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{1}{9}e^-3t-\left[\dfrac{-1}{9}+\dfrac{-1}{3}t+\dfrac{2}{9}e^{-3(t-1)}\right]u(t-1)[/tex]

Learn more about what Laplace transformation is here:

https://brainly.com/question/14487937

Answer:

width = 4.5 m

length = 14 m

Step-by-step explanation:

okay so first you right down that L = 5 + 2w

then as you know that Area = length * width so you replace the length with 5 + 2w

so it's A = (5 +2w) * w = 63

then 2 w^2 + 5w - 63 =0

so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14

Step-by-step explanation:

it can be simply done by using remainder theorem.

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

1/256

Step-by-step explanation:

The table shows a chain of fractions for f(x), x1 is 1/4, x2 is 1/16 and x3 is 1/64. All you need to do is multiply the denominator by 4 and put 1 over it. 64*4 = 256, adding the 1 as the numerator gives us the answer of 1/256 as x4.

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6

Answer:

SAS

Step-by-step explanation:

ΔABD ~ ΔECD is similar through:

S - because ED = CD (Given)

A - same angle ∠D (Statement 2)

S - because AD = BD (Given)

Cheers!

Answer:

SAS

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Equation of the given quadratic function is,

y = 2x² + 8x + 3

y = 2(x² + 4x) + 3

  = 2(x² + 4x + 4 - 4) + 3

  = 2(x + 2)² - 8 + 3

  = 2(x + 2)² - 5

By comparing this equation with the equation of a quadratic function in vertex form,

y = a(x - h)² + k

Here (h, k) is the vertex of the parabola

Vertex of the given equation will be (-2, -5) and coefficient 'a' is positive (a > 0)

Therefore, vertex will lie in the 3rd quadrant and the parabola will open upwards.

Option (A). Graph A will be the answer.

Answer:

d.  a = 39

Step-by-step explanation:

Question:

for which value of "a" will the trinomial be factorizable.

x^2+ax-40

For the expression to have integer factors, a = sum of the pairs of factors of -40.

-40 has following pairs of factors

{(1,-40), (2,-20, (4,-10), (5,-8), (8, -5), (10,-4), (20,-2), (40,-1) }

meaning that the possible values of a are

+/- 39, +/- 18, +/- 6, +/- 3

out of which only +39 appears on answer d.  a=39

Answer:

OD. 45,45,90

Step-by-step explanation:

Answer:

The probability plot of this distribution shows that it is approximately normally distributed..

Check explanation for the reasons.

Step-by-step explanation:

The complete question is attached to this solution provided.

From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).

The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.

Also, the p-value for the plot was obtained to be 0.541.

For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.

The interpretation of p-valies is that

When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).

For this distribution,

p-value = 0.541

Significance level = 0.05 (Evident from the plot)

Hence,

p-value > significance level

So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.

Hope this Helps!!!

Answer:

[tex]3\frac{4}{5}[/tex]

Step-by-step explanation:

You first need to make the denominators the same and the LCM (least Common Multiple of this equation is 10.

10/10-->1

1/2--> 5/10

2--> 20/10

3/10, the denominator is already 10, so don't need to change.

10/10+5/10+20/10+3/10=38/10=[tex]3\frac{8}{10}[/tex]=[tex]3\frac{4}{5}[/tex]

Answer:

3 4/5

Step-by-step explanation:

hopefully this helped :3

Answer:

Step-by-step explanation:

Given the confidence interval of the heights of american heights given as (65.3,73.7);

Lower confidence interval L = 65.3 and Upper confidence interval U = 73.7

Sample mean will be the average of both confidence interval . This is expressed mathematically as [tex]\overline x = \frac{L+U}{2}[/tex]

[tex]\overline x = \frac{65.3+73.7}{2}\\\overline x = \frac{139}{2}\\\overline x = 69.5[/tex]

Hence, the sample mean is 69.5

Answer:

3/20

Step-by-step explanation:

15%

15/100

/5  /5

3/20

Answer:

x = -2 , -1

Step-by-step explanation:

Set the equation equal to 0. Add 2 to both sides:

x² + 3x = -2

x² + 3x (+2) = - 2 (+2)

x² + 3x + 2 = 0

Simplify. Find factors of x²  and 2 that will give 3x when combined:

x²  + 3x + 2 = 0

x               2

x               1

(x + 2)(x + 1) = 0

Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.

(x + 2) = 0

x + 2 (-2) = 0 (-2)

x = 0 - 2

x = -2

(x + 1) = 0

x + 1 (-1) = 0 (-1)

x = 0 - 1

x = -1

x = -2 , -1

~

Answer:

x = -2       OR      x = -1

Step-by-step explanation:

=> [tex]x^2+3x = -2[/tex]

Adding 2 to both sides

=> [tex]x^2+3x+2 = 0[/tex]

Using mid-term break formula

=> [tex]x^2+x+2x+2 = 0[/tex]

=> x(x+1)+2(x+1) = 0

=> (x+2)(x+1) = 0

Either:

x+2 = 0    OR     x+1 = 0

x = -2       OR      x = -1

P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!

Answer:

C

Step-by-step explanation:

write an equation for the costs:

if x is the number of sodas

and y is the number of waters

2.75x + 2y <= 15

(<= is less than or equal to)

if we substitute 3 for y

we get 2.75x + 2(3) <= 15

2.75x + 6 <= 15

2.75x <= 9

9 / 2.75 = 3.2727

however, you cannot buy part of a soda

so, round to 3

you also cannot buy negative sodas

so, the answer is C

Answer:

No. At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the bags are underfilled (population mean significantly less than 418 g.)

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=418\\\\H_a:\mu< 418[/tex]

The significance level is 0.1.

The sample has a size n=9.

The sample mean is M=413.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{9}}=6.6667[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{413-418}{6.6667}=\dfrac{-5}{6.6667}=-0.75[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=9-1=8[/tex]

This test is a left-tailed test, with 8 degrees of freedom and t=-0.75, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-0.75)=0.237[/tex]

As the P-value (0.237) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.1, there is not enough evidence to support the claim that the bags are underfilled (population mean significantly less than 418 g.)

Answer:

The answer is below

Step-by-step explanation:

We have the following information:

Number of songs you like = 2

Total number of songs = 12

a) P(you like both of them) = 2/12 x 1/11 = 0.015

This is unusual because the probability of the event is less than 0.05

b) P(you like neither of them) = 10/12 x 9/11  = 0.68

c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30

d) If  a song can be replayed before all 12,

P(you like both of them) = 2/12 x 2/12  =0.027

This is unusual because the probability of the event is less than 0.05

P(you like neither of them) = 9/12 x 9/12  = 0.5625

P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25

Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Learn more about probability in https://brainly.com/question/14393430

Answer:

14.  C   41

15. k = 72

Step-by-step explanation:

14.

For parallel lines, alternate exterior angles must be congruent.

3x - 43 = 80

3x = 123

x = 41

15.

The sum of the measures of the angles of a triangle is 180 deg.

k + 33 + 75 = 180

k + 108 = 180

k = 72

Answer:

1. 32

2. 41

3. 72

Step-by-step explanation:

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Answer:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]

Step-by-step explanation:

First, notice that since the graph of the function is a line, we have a linear function.

To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

We are given the point (0,3) which is the y-intercept. Thus, b = 3.

To find the slope, we can use the slope formula:

[tex]\displaystyle m=\frac{\Delta y}{\Delta x} =\frac{2-3}{3-0}=-1/3[/tex]

Therefore, our equation is:

[tex]\displaystyle y=-\frac{1}{3}x+3[/tex]