The annual profits for a company are given in the following table, where x represents the number of years since 2014, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the profits would reach 144 thousand dollars.

Answers

Answer 1

The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.

How to write the linear regression equation?

First of all, we would determine the slope of the given data set by using this formula:

[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]

For the sample mean (years), we have:

∑x = 0 + 1 + 2 + 3

∑x = 6.

∑x² = 0² + 1² + 2² + 3²

∑x² = 14.

For the sample mean (profits), we have:

∑y = 46 + 57 + 84 + 76

∑y = 263.

∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)

∑xy = 453.

Now, we can determine the slope:

[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]

Slope, m = 11.7.

For the intercept, we have:

[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]

Intercept, c = 48.2.

Therefore, the linear regression equation is given by:

y = 11.7x + 48.2.

Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:

144 = 11.7x + 48.2

11.7x = 144 - 48.2

11.7x = 95.8

x = 95.8/11.7

x = 8.2.

For the calendar year, we have:

Year = 2014 + 8.2

Year = 2022.2 2022.

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Related Questions

In which triangle is the value of x equal to cos−1(StartFraction 4.3 Over 6.7 EndFraction)?

(Images may not be drawn to scale.)

A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.
A right triangle is shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle opposite to side with length 4.3 is x.
A right triangle is shown. The length of the hypotenuse is 4.3 and the length of another side is 6.7. The angle between 2 sides is x.
A right triangle is shown. The length of the 2 sides are 6.7 and 4.3. The angle opposite to side with length 4.3 is x.

Answers

The correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.

The complete figure is attached with the answer below.

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

In the given figure of option A, we can see that the hypotenuse is 6.7 and the base is 4.3 and the angle between both the sides is x. Now we will calculate the angle of cosine x.

Cos(x)= Base / Hypotenuse

Cos(x) = ( 4.3 / 6.7 )

(x) = Cos⁻¹ ( 4.3 / 6.7)

Therefore the correct answer is option A. which is the right triangle shown. The length of the hypotenuse is 6.7 and the length of another side is 4.3. The angle between the 2 sides is x.

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Answer:

The answer is A

Step-by-step explanation:

Just took the test

Test Scores Find the percentile rank for each test score in the data set. Round to the nearest whole percentile.

10, 15, 19, 23, 30

Part 1 of 6

The percentile rank for the value 10 is

Answers

The percentile rank for 10 will be 10th.

What is percentile rank?

The percentile rank of a particular score in statistics refers to the percentage of scores in the frequency distribution that are smaller than that score.

Percentile rank = [(Number of values below x) + 0.5]/ total number of values * 100

For 10,

Percentile rank = {[0 + 0.5]/5} x 100 = 10th

For 15,

Percentile rank = ([1 + 0.5]/5) x 100 = 30st

For 19,

Percentile rank = [2 + 0.5]/5 x  100 = 50th

For 23,

Percentile rank = [3 + 0.5]/5  x  100 = 70th

For 30,

Percentile rank = [4 + 0.5]/ 5  x 100 = 90th

The percentile rank for 10 will be 10th.

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Question 2 On the line that passes through point C, mark a point D that is distinct from point C. Use the slope formula along with coordinates of points to find the slopes of and . Show your work.

Answers

The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].

What is the slope of a straight line?

A slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.

The slope of a line that passes through points ( p,q) and (x,y)

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

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After sales tax, a $600 antique clock costs $642. What is the sales tax percentage?

Answers

well, clearly the tax is the added 42 bucks, so hmmm if we take 600 to be the 100%, how much is 42 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 600 & 100\\ 42& x \end{array} \implies \cfrac{600}{42}=\cfrac{100}{x}\implies \cfrac{100}{7}=\cfrac{100}{x} \\\\\\ 100x=700\implies x=\cfrac{700}{100}\implies x=7[/tex]

Answer:

Answer is 7% sales Tax

Step-by-step explanation:

I first like to take one percent of the original value, in this case 1% of 600 is 6 dollars. I then multiply 6 by the number needed to get to 642, which is 107- you will always then subtract 100 from this number and you get 7%. This should work for other problems as well. This is probably not the best explanation btw

You can buy a car for $5995.67 cash or pay $759.00 as a down payment and $129.95 a month for 4 years.
How much more does the installment plan cost than paying cash?
A. $1000.93
B. $241.93
C. $507.43
D. $2475.27
E. $99.27

Answers

well, if you had the cash right now, you can put it down cold for 5995.67 bucks

OR

put as a downpayment now 759 and then over 48 months pay 129.95 each month, well, 129.95  48 times is 129.95 * 48 = 6237.6, now let's add the 759 down and that's 6237.6 + 759 = 6996.6.

well, heck if you had the cash it'd be 5995.67, if you don't is 6996.6, their difference is 6996.6 - 5995.67 = 1000.93.

If 0 lies in the quadrant IV. What can be the value of cos 0 ?​

Answers

Answer:

the value of cos 0 is 7

Step-by-step explanation:

because you have to times it twice

Answer:

Between 0 and 1

Step-by-step explanation:

Cos Θ is the x coordinate of the unit circle. The points of that circle in quadrant IV have an x coordinate of 0≤x≤1.

4 The angle of elevation of point P from point Q is 40°. PQ = 45 km. How high is point P above the level of point Q?​

Answers

Answer: [tex]45\sin 40^{\circ} \approx 28.925[/tex] km

Step-by-step explanation:

[tex]\sin 40^{\circ}=\frac{x}{45} \\ \\ x=45 \sin 40^{\circ} \approx 28.925[/tex]

The height of point P above the level of point Q is given by trigonometric relations h = 34.7 km

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let's call the height of point P above the level of point Q as h.

We know that the angle of elevation of point P from point Q is 40°, which means that the angle between the horizontal line passing through Q and the line segment connecting Q and P is 40°.

We also know that PQ = 45 km, which represents the distance between Q and P.

Using trigonometry, we can set up the following equation:

tan(40°) = h / 45

Solving for h, we get:

h = 45 x tan(40°) ≈ 34.7 km

Therefore, point P is approximately 34.7 km above the level of point Q

Hence , the height is h = 34.7 km

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where do banks get the money to lend to consumers

Answers

Answer:

Depositors

Step-by-step explanation:

Answer:

Banks get the money from the people that deposit their money at the bank for a low interest rate and lend to the customers with a high interest rate.

The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7The 7 in which number represents a value of 0.7
*903038393JKLSi933003

9=28
when 834 nine=365 and 7

Answers

Answer:

The answer is C

Step-by-step explanation:

good job on quiz i got a 15/15 but keep up 3´5

Answer:

i got a 0/15 i didnt do it

Step-by-step explanation:

0000.7 C

Question 1 of 10
Evaluate the following expression. Round your answer to two decimal places.
log79
A. 0.89

Answers

Step-by-step explanation:

log(79) = 1.897627091... ≈ 1.90

Solve the inequality |a + 3| > 14

Answers

Answer:

a∈(-∝;-17)∩(11;+∝).

Step-by-step explanation:

|a+3|>14; ⇔ 14<a+3<-14; ⇔ 11<a<-17;

The following diagram shows a 4-step process that begins with Operation 1 and ends with Operation 4.

Answers

Based on the operations and their times, the capacity of this process is 10 per hour and the action that would yield the greatest increase would be 2. increase operation 2 by 14%.

What is the capacity of the process?

The capacity of the process is the least operation time in the process which is 10/ hr.

How can we get the greatest increase in process capacity?

Check all the alternatives given. The alternative with the lowest capacity is best.

Increase operation 1 by 12%:

= 11 x (1 + 12%)

= 12.32 per hour

Increase operation 2 by 14%:

= 10 x (1 + 14%)

= 11.4 per hour

Increase operation 3 by 10%:

= 12 x (1 + 10%)

= 13.2 per hour

The best alternative is therefore to increase operation 2 by 14%.

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Elaina Kicks A Soccer Ball With An Initial Velocity Of

Answers

By using the motion equations, we conclude that she will make the goal.

Will she make the goal?

First, we know that the goal is 20ft away, and the position in x is given by:

[tex]x = 28*cos(58)*t[/tex]

Let's find the time in which the ball will travel these 20 ft.

[tex]20 = 28*cos(58)*t[/tex]

[tex](20)/(28*cos(58)) = t = 1.35[/tex]

So the horizontal distance is covered in 1.35 seconds, now let's see which is the height of the ball at that time.

The height equation is:

[tex]y = -16*t^2 +28*sin(58)*t[/tex]

Evaluating in t = 1.35 we get:

[tex]y = -16*(1.35)^2 +28*sin(58)*1.35\\\\y = 2.9[/tex]

And the goal is 5ft tall, so we can conclude that she will make the goal.

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can someone help me with this worksheet please!!!!

Answers

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

Missing term of the sequence

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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Cooper just started a running plan where he runs 8 miles the first week and then
increases the number of miles he runs by 5% each week. If he keeps up this plan for
21 weeks, how many total miles would Cooper have run, to the nearest whole
number?

Answers

He would’ve ran 286 miles in total.

Cooper ran 286 miles in 21 weeks.

what's the answer to this

Answers

Step-by-step explanation:

the angle CDB is the supplementary angle to 9x+10 (angle ADC).

that means they stand together for 180°. as all angles around a single point on one side of a line are together always 180°.

and then, the sum of all angles in a triangle is always 180°.

so,

CDB + (4x + 10) + 50 = 180

CDB = 180 - (9x + 10) = 180 - 9x - 19 = 170 - 9x

therefore,

(170 - 9x) + (4x + 10) + 50 = 180

170 - 9x + 4x + 10 + 50 = 180

-5x = -50

5x = 50

x = 10

angle CDB = 170 - 9x = 170 - 90 = 80°

#18 please I’m not good at math at all

Answers

Answer:

The answer is in the picture.

Step-by-step explanation:

By hand, you can factor it. I did it on a website called Cymath.

Answer:

3x(y - 3)(y + 1)

Step-by-step explanation:

Factor 3x out of 3xy^2

Factor 3x out of -6xy

Factor 3x out of -9x

Factor 3x out of 3x(y^2)+3x(-2y)

Factor 3x out of 3x(y^2-2y) + 3x(-3)

follow the steps to construct a diagram:
1:create points A, B, and C in order on a horizontal line with a distance of four units between successive points.
2:draw Circle with center that passes through b, and two tangents to the circle passing through C.
3:locate the points of intersection of the tangents with the circle, and labeled them D and E.
4: draw the radii AD and AE to create central angel EAD.
Take a screenshot of your construction, and paste it below.

Answers

Answer:

a=3=8

Step-by-step explanation:

there is none

The construction forms a diagram consisting of a circle, two tangents, and a central angle EAD as shown in the attached figure.

Construction is a topic that requires drawing a required shape, line, and figure with constructing tools. The appropriate steps should be taken so as to complete the required figure.

In the given question, the circumference of the required circle passes through points A and C. And the radius of the circle with center B is 4 units so its diameter is 8 units. Then joining the points D and E to A, creates a central angle EAD.

Following the appropriate steps, the required diagram for the construction is as given in the attachment to this question.

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Write the prime factorization of 10

Answers

Answer:

2|10

5|5

1

Prime factors of 10 are 2*5

is there anyone who understands this?

Answers

Answer:

The question was most likely asking for exponential form.(The list shows questions 16 through 20, not 1 through 5.)

b 1/6X Z/49 3/2m p/nj 2 + x/2

To best show a possible linear trend in a scatter plot, draw a _________________.
A. regressive line
B. line of best fit
C. vertical line
D. horizontal line\

Answers

Answer:

b. line of best fit

A freight elevator has a weight limit of 2 tons. Each crate that is loaded weighs 80 pounds. What is the greatest number of crates that can be loaded onto the elevator

Answers

Hope this helps! Let me know if you need anything.

3t-2/4 - 2t-3/3 = 2/3 - t

Answers

The value of the variable t will be 13 / 12.

What is Algebra?

The analysis of mathematical representation is algebra, and the handling of those symbols is logic.

The equation is given below.

3t - 2/4 - 2t - 3/3 = 2/3 - t

Then the value of t will be

t - 3/2 = 2/3 - t

      2t = 2/3 + 3/2

      2t = 13 / 6

         t = 13/12

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Una camioneta transportaba 3/4 de tonelada de arena para entregar a diferentes clientes. Si al primer cliente le dejo 1/3 de la carga que fracción de toneladas quedo en la camioneta

Answers

Si, it should be number 8

what is two significant digit for 59.3506494?

Answers

Answer:

59

Step-by-step explanation:

Round 59.3506494 to the first 2 sig figs which is 59 since the number next to the decimal isnt over or 5, so it stays as 59 instead of 60.

Let f(x)=20/5+6e^−0.1x What is (5)? Round your answer to 4 decimal places.

Answers

We can conclude that the function evaluated in x = 5 is equal to 2.3150

How to evaluate the function?

Here we have the function:

[tex]f(x) = \frac{20}{5 + 6e^{-0.1x}}[/tex]

And we want to evaluate in x = 5, this just means to replace the x by a 5 in the given function:

We can evaluate this with a calculator (as doing it by hand is kinda hard), we will get:

[tex]f(5) = \frac{20}{5 + 6e^{-0.1*5}} = 2.3150[/tex]

So we can conclude that the function evaluated in x = 5 is equal to 2.3150.

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If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be ______ that when the population is not highly skewed a. different from b. the same as c. larger than d. smaller than​

Answers

Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

What is the central limit theorem?

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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IK
rying the Distributive Property
Try it
Which statement is an example of the distributive property?
O3+ (2)(15)= 3(2) + 3(15)
O3(2+15) = 3 + 2(3) + 15
O3(2+15)= 3(2) + 3(15)
O 3(2+15)= 3(2) + 15

Answers

The statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)

How to determine the example?

The distributive property states that:

a(b + c) = a(b) + a(c)

Using the above property, we have:

3(2+15)= 3(2) + 3(15)

Hence, the statement that is an example of the distributive property is (c) 3(2+15)= 3(2) + 3(15)

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how many prime number are between 2 and 22​

Answers

Answer:

8

Step-by-step explanation:

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 easily get rid of all the even numbers except 2 and then look at the numbers to see if they can be divisible by anything but 1 and its self. then you will get the answers 2, 3, 5, 7, 11, 13, 17, and 19

if x+7y=16 and 3x-7y=4 what is the value of x​

Answers

Answer:

[tex]x=5\\[/tex]

Step-by-step explanation:

First, put your equations into a system.

[tex]\left \{ {{x+7y=16} \atop {3x-7y=4}} \right.[/tex]

Next, use the method of elimination to solve the system. Elimination is when either x or y has an opposite coefficient (so in this case y has a coefficient of 7 or -7 depending on the equation). You can then add the equations, and y is eliminated as a variable. Now you can solve for x.

[tex]4x=20[/tex]

Lastly, divide by 4 on both sides to get x by itself.

[tex]x=5\\[/tex]

Other Questions
Find the slope please What did women accomplish in western states that they were unable to do in other parts of the nation?O They worked in factories.O They gained voting rights.O They held conventions for women's rights.O They received an education. Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.The quotient of is . In this figure, a || b | c and m/1 = 50What is m/3 ?O 40O 50O 130O I don't know. PLEASE HELPP! ILL GIVE BRAINLIEST!Which graph represents a quadratic function that has exactly one real zero? Select all the correct answers.What do scientists use to communicate extremely small measurements?scientific notationunit prefixesgraduated cylindersphysical modelsbase units Help pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeePROBLEMS1) Add the following: 30 mg, 2.5 kg and 7.0 g. Express the answer in g.2) Express the amount of 1.243 g as:mg ________kg ________mcg _______3) How many grams of the active ingredient "aspirin" would be needed to make 500 aspirin tablets if each tablet must contain 325 mg? Sam runs 9 kilometers in 2.5 hours. what is his speed? Why are elements classified? Under President George Washington, the U.S. federal governmentbecame more powerful by:A. letting rebel groups weaken by state governments.B. taking more control over the U.S. economy.C. forming alliances with powerful foreign countries.D. encouraging immigrants to serve in the federal government 5. What is the measurement of each angle? A descriptive technique for obtaining the self-reported attitudes or behaviors of a representative sample of a population is known as. Milo Millworks Incorporated has maintained a sustainable competitive advantage for its framing style. In order to accomplish this, the framing style must be in History of re-naming of slaves , where does Abraham's name come from? We are faced, according to Dr. Elton, with a life-and-death need not just to find new technological means of suppressing this plant or that animal; instead we need the basic knowledge of animal populations and their relations to their surroundings that will promote an even balance and damp down the explosive power of outbreaks and new invasions. Much of the necessary knowledge is now available but we do not use it. . . . We allow the chemical death rain to fall as though there were no alternative, whereas in fact there are many, and our ingenuity could soon discover many more if given opportunity. Silent Spring, Rachel Carson Use the drop-down menus to analyze the writers use of persuasive strategies. In the first paragraph, the writer quotes an expert to . After presenting a possible solution, the writer then claims we do not use the knowledge we have, making the assumption that people . Read the excerpt from Katies personal narrative how does the dialogue develop the characters in this paragraph select two options 1. Swimming pool manufacturers recommend maintaining thepool chlorine concentration at 3.0 ppm. What is the mass ofchlorine in a pool containing 3.4 x 106 L of water? 5x 2x + 7 x = ?x + ?I need the answer for "no solution" and "infinite solutions".(preferably with an explanation)thanks to anyone who helps the average of 5 girls is 6 yrs. the average of 4 of them is 16. what is d age of d fifth gal What is the difference between speaking the truth and speaking your truth? Explain your thoughts.