A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
after 2s : cm2/s
after 5s : cm2/s
after 6s : cm2/s

Answers

Answer 1

9514 1404 393

Answer:

2s: 45,239 cm²/s5s: 113,097 cm²/s6s: 135,717 cm²/s

Step-by-step explanation:

The radius is a function of time:

  r(t) = 60t . . . . . radius in cm; time in s

Then the area of the circle is ...

  A = πr² = π(60t)² = 3600πt²

The rate of change of area is the derivative of this:

  A' = 2·3600πt = 7200πt

The rates of change of interest are ...

  after 2s: 45,239 cm²/s

  after 5s: 113,097 cm²/s

  after 6s: 135,717 cm²/s


Related Questions

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)

Answers

Answer:

a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

b) the probability that the defective board was produced during the  last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

c) the required probability is 0.2000

Step-by-step explanation:

Given the data in the question;

During a specific ten-hour period, one defective circuit board was found.

Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.

Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.

f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex];   ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]

= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex];   ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]

f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex];   ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]

Now,

a) the probability that it was produced during the first hour of operation during that period;

P( Y < 1 )   =   [tex]\int\limits^1_0 {f(y)} \, dy[/tex]

we substitute

=    [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]

= [tex]\frac{1}{10} [y]^1_0[/tex]

= [tex]\frac{1}{10} [ 1 - 0 ][/tex]

= [tex]\frac{1}{10}[/tex] or 0.1000

Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

b) The probability that it was produced during the last hour of operation during that period.

P( Y > 9 ) =    [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]

we substitute

=    [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]

= [tex]\frac{1}{10} [y]^{10}_9[/tex]

= [tex]\frac{1}{10} [ 10 - 9 ][/tex]

= [tex]\frac{1}{10}[/tex] or 0.1000

Therefore, the probability that the defective board was produced during the  last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

c)

no defective circuit boards were produced during the first five hours of operation.

probability that the defective board was manufactured during the sixth hour will be;

P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )

= P( 5 < Y < 6 ) / P( Y > 5 )

we substitute

 [tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]

[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]

= ( 6-5 ) / ( 10 - 5 )

= 0.2000

Therefore, the required probability is 0.2000

if x¹=xcosA+ysinA and y¹=xsinA-ycosA, show that (x¹)²+(y¹)²=x²+y²​

Answers

Expanding each square on the left side, you have

(x cos(A) + y sin(A))² = x² cos²(A) + 2xy cos(A) sin(A) + y² sin²(A)

(x sin(A) - y cos(A))² = x² sin²(A) - 2xy sin(A) cos(A) + y² cos²(A)

so that adding them together eliminates the identical middle terms and reduces to the sum to

x² cos²(A) + y² sin²(A) + x² sin²(A) + y² cos²(A)

Collecting terms to factorize gives us

(y² + x²) sin²(A) + (x² + y²) cos²(A)

(x² + y²) (sin²(A) + cos²(A))

and sin²(A) + cos²(A) = 1 for any A, so we end up with

x² + y²

as required.

the area of a triangular garden is 200 square feet. If the base is 30 feet more than its height, what is the base of the garden?

Answers

The base of the triangular garden is calculated as 40 ft

The given parameters include:

the area of the triangular garden, A₁ = 200 ft²let the height of the triangular garden = hthe base of the triangular garden, b = 30 ft + h

The area of a triangle is given as;

[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]

Now solve for 'b' = 30 ft + 10 ft  =  40 ft

Therefore, the base of the garden is 40 ft

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Given the triangle below, what is the length of the third side, rounded to the nearest whole number?

Answers

Answer:

Step-by-step explanation:

You need the Law of Cosines for this, namely:

[tex]x^2=21^2+14^2-2(21)(14)cos58[/tex] where x is the missing side.

[tex]x^2=441+196-311.5925[/tex] and

[tex]x^2=325.4075[/tex] so

x = 18.0 or just 18

Write an equation that represents the line.
Use exact numbers.

Answers

Answer: y=2/3X- 4/3

Step-by-step explanation:

Slope = (4-2)/(4-1)=2/3

Y-2=2/3(x-1)

Y-2=2/3x-2/3

Y=2/3X-2/3+2

Y=2/3X-4/3

What is the probability that z equals 1.5

Answers

Answer:

0.1

Step-by-step explanation:

The probability value corresponding to z = 1.5 is 0.9332.

What is probability?

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The standard normal curve is a special case of a normal curve with a mean of 0 and a standard deviation of 1. Since it is symmetric around the mean, 50% of the observations lie under the mean while the other 50% of the observations lie above the mean.

Thus the probability value corresponding to z = 1.5 is 0.9332.

Since the total probability value under the curve is 1, we subtract 0.9332 from 1 to calculate the area to the right.

P(Z>1.5)

=P(Z≤1.5)

=1−0.9332

=0.0668

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Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.

Answers

Answer:

Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:

W = int_a^b kx dx

W = k * int_a^b x dx

Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)

W = k * x^(1+1)/(1+1)|_a^b

W = k * x^2/2|_a^b

 

From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches.   To be consistent, apply the conversion factor: 12 inches = 1 foot then:

 

2 inches = 1/6 ft

 

1/2 or 0.5 inches =1/24 ft

To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring  2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.

Applying  W = k * x^2/2|_a^b , we get:

7.5= k * x^2/2|_0^(1/6)

Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .

7.5 =k [(1/6)^2/2-(0)^2/2]

7.5 = k * [(1/36)/2 -0]

7.5= k *[1/72]

 

k =7.5*72

k =540

 

To solve for the work needed to compress the spring with additional 1/24 ft, we  plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .

Note that compressing "additional one-half inches" from its 2 inches compression is the same as to  compress a spring 2.5 inches or 5/24 ft from its natural length.

W= 540 * x^2/2|_((1/6))^((5/24))

W = 540 [ (5/24)^2/2-(1/6)^2/2 ]

W =540 [25/1152- 1/72 ]

W =540[1/128]

W=135/32 or 4.21875 ft-lbs

Step-by-step explanation:

Parallel Lines:
If the two lines are parallel and cut by a transversal line, what is the value of x?

Answers

Step-by-step explanation:

The corresponding angles theorem tells us that angles that correspond with each other are equal. In this case, B and C are corresponding angles.

(2x+8) = 60

2x = 60 - 8

2x = 52

x = 26



The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.

Answers

Answer:

280.8997

Step-by-step explanation:

cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15

= 280.8997

Total surface area of prism is 280.890cm²

What is surface area?

A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.

The term "surface area" is sometimes used to refer to "total surface area".

Find the sector angle in radians

α = 25× (π/180)

α = (25π)/(180) rad

Find the area of the prism:

A = 2×15×5 + 15×15×α + 5×15×α

A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)

A = 280.890cm²

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juan compra 12 dulces por 30 pesos, si al dia siguien el precio del dulce se incremento a 3.5 pesos cuanto se ahorro juan por cada dulce al comprarlos con el precio anterior

Answers

Djdjsjjsjsjzjnzn hJsbw susn i jendi je i jendi jend


HURRY! HELP PLS
Janelle is conducting an experiment to determine whether a new medication is effective in reducing sneezing she finds 1000 volunteers with sneezing issues and divides them into two groups the control group does not receive any medication the treatment group received the medication the patients in the treatment group show reduced signs of sneezing what can genetic include from this experiment?

Answers

Answer: You can conclude that the medication is effective and decreases sneezing

Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing.

What is a control experiment?

A control experiment can be defined as a type of experiment in which a condition assumed to be a probable cause of an effect is compared with the same situation without involving or using the suspected condition.

What is a treatment group?

A treatment group refers to a group of participants in an experiment that are exposed to some manipulation in the independent variable such as an administration of medication to a particular group.

Thus, Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing because the treatment group show reduced signs of sneezing.

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I need to know the answer ASAP

Answers

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The numerical coefficient is sqrt(8/3), so all you have eliminated is D.

Now you have to consider the literal all by itself.

sqrt(x^2)/sqrt(x) can be written as (sqrt(x^2/x)) = sqrt(x)

x^2 when divided by x leaves x

another way of looking at it is sqrt(x)*sqrt(x) / sqrt(x) = sqrt(x)

So the answer is sqrt(8/3 * x)

PLEASE HELP ME !!!!
How many solutions does the system of equations below have?
y = x - 3
3y-3x = -9
A. Exactly 1 solution
B. At least 1 solution
C. More than 1 solution
D. No solution

Answers

9514 1404 393

Answer:

  C. More than 1 solution

Step-by-step explanation:

Divide the second equation by 3.

  y -x = -3

Add x.

  y = x -3

This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."

In one year, a government collected $6770 per person in taxes. If the population was 220,000,000, how much did the government collect in taxes that year?

Answers

Answer:

$1,489,400,000,000

Step-by-step explanation:

Multiply to get the solution.

220,000,000 × 6770 = 1,489,400,000

6 times the sum of 5 and K​

Answers

Answer:

6(5+k)

Step-by-step explanation:

The sum of 5  and k

5+k

6 times the sum

6(5+k)

Factorise: x^3 + x^2 + x^2y + xy + y

Plz also show me the process.

Answers

Factor out the greatest common factor from each group.
x^2 (x-1y)-y^2(x-y)

Factor the polynomial by factoring out the greatest common factor, x-1y
(x-1y)(x^2-y^2)

rewrite -1y as -y.
(x-y) (x^2-y^2)

Factor.
(x-y)(x+y)(x-y)

Combine exponents.
(x-y)^2 (x+y) (your answer)

really hoped this helped. :)




rose says the quantity of four dollars is a terminating decimal. Sharon says it is an integer.Do you agree witheither of them

Answers

Answer:

Agree with Sharon

Step-by-step explanation:

A terminating decimal includes numbers beyond the decimal point.

An integer is a whole number.

4 is a whole number so it's an integer which is what Sharon said.

The graph shows the distribution of lengths of songs (in seconds). The distribution is approximately Normal, with a mean of 227 seconds and a standard deviation of 31 seconds.

A graph titled Song length has length (seconds) on the x-axis, going from 103 to 351 in increments of 31. The highest point of the curve is at 227.

What percentage of songs have lengths that are within 31 seconds of the mean?

34%
68%
95%
99.7%

Answers

its everything between 196 and 258 seconds (at max 31secs away from the mean). imagine straight upward lines separating this area from the rest.

34% would be way too low, 95 and above way too much.

only 68% is remotely plausible.

Elijah invested $ 830 in an account paying an interest rate of 4.9% compounded quarterly. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 13 years?

Answers

Answer:

$9986

Step-by-step explanation:

You got 13*4=52 quarters in 13 years.

Amount = 830*(1+0.049)^52

Amount = 9986.27

Help please:)) 2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,

a. What would be the optimal dimensions (radius and height) to minimize surface area?

b. What would the surface area be?

C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

Answers

Answer:

a. The radius r = 5.42 cm and the height h = 10.84 cm

b. 553.73 cm²

c. i. Beauty ii. Design

Step-by-step explanation:

a. What would be the optimal dimensions (radius and height) to minimize surface area?

The volume of the standard container is a cylinder and its volume is V = πr²h where r = radius of container and h = height of container.

Since V = 1000 cm³,

1000 cm³ = πr²h  (1)

Now, the surface area of a cylinder is A = 2πr² + 2πrh where r and h are the radius and height of the cylinder.

From (1), h = 1000/πr².

Substituting h into A, we have

A = 2πr² + 2πrh

A = 2πr² + 2πr(1000/πr²)

A = 2πr² + 2000/r

To maximize A, we differentiate A with respect to r and equate to zero to find the value of r at which A is maximum.

So, dA/dr = d[2πr² + 2000/r]/dr

dA/dr = d[2πr²]/dr + d[2000/r]/dr

dA/dr = 4πr - 2000/r²

Equating the equation to zero, we have

4πr - 2000/r² = 0

4πr = 2000/r²

r³ = 2000/4π

r = ∛(1000/2π)

r = 10(1/∛(2π))

r = 10(1/∛(6.283))

r = 10/1.8453

r = 5.42 cm

To determine if this value of r gives a minimum for A, we differentiate dA/dr with respect to r.

So, d(dA/dr)/dr = d²A/dr²

= d[4πr - 2000/r²]/dr

= d[4πr]/dr - d[2000/r²]/dr

= 4π  + 4000/r³

Substituting r³ = 2000/4π into the equation, we have

d²A/dr² = 4π  + 4000/r³ = 4π  + 4000/(2000/4π) = 4π  + 2 × 4π = 4π + 8π = 12π > 0

Since d²A/dr² = 12π > 0, then r = 5.42 cm gives a minimum for A.

Since h = 1000/πr²

h = 1000/π(5.42)²

h = 1000/92.288

h = 10.84 cm

So, the radius r = 5.42 cm and the height h = 10.84 cm

b. What would the surface area be?

Since the surface area, A = 2πr² + 2πrh

Substituting the values of r and h into A, we have

A = 2πr² + 2πrh

A = 2πr(r + h)

A = 2π5.42(5.42 + 10.84)

A = 10.84π(16.26)

A = 176.2584π

A = 553.73 cm²

c. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.​

i. Beauty

ii. Design

A diameter perpendicular to a chord
that chord
Select one:
a. is parallel to
b. bisects
c. is equal to

Answers

The correct answer is a)

Find the area of the figure. (Sides meet at right angles.)

Answers

Answer:

[tex]9 \times 2 = 18 \: \: \\ 4 \times 5 = 20 \\ 20 + 18 = 38 \\ 38 {in}^{2} [/tex]

hi please give brainly

Find the missing side length in the image below

Answers

Answer:

? = 5

Step-by-step explanation:

Recall: when 2 transversal lines cuts across 3 parallel lines, the parallel lines are divided proportionally by the transversals.

Therefore:

?/10 = 3/6

Cross multiply

?*6 = 3*10

?*6 = 30

Divide both sides by 6

? = 30/6

? = 5

A triangle. A ABC, has angle measures of 82*, 75, and 23' and no sides equal (congruent) in length. How would this triangle be
classified?
Equilateral right
Isosceles obtuse
O Scalene acute
Isosceles acute

Answers

The triangle given is a scalene acute triangle

Classification of Triangle

A triangle can be classified based on the measures of its angles and the lengths of its sides.

In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.

The triangle is not an equilateral triangle because all the sides are not of equal length.

The triangle also doesn't have one right angle so it can't be right triangle.

Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.

So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.

As the triangle has no sides of equal length, it is also a Scalene triangle.

Therefore, the triangle would be classified as a Scalene acute triangle (c).

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If an angle of a right angle triangle is 81 find the remaining angle in grades​

Answers

Answer:

9

Step-by-step explanation:

90+81+mising angle=180, missing angle is 9

What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3

Answers

9514 1404 393

Answer:

  C.  1

Step-by-step explanation:

The only rotation that maps the figure to itself is rotation by 360°. The rotational order is 1.

11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next

Answers

Answer:

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]:                                                                     [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]:                                                                         [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(\frac{2e}{x})[/tex]

Step 2: Simplify

Expand [Logarithmic Property - Dividing]:                                                      [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]:                                                  [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify:                                                                                                             [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite:                                                                                                             [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]

Factor this polynomial expression.
3x^2 - 12x+ 12

A. (3x - 2)(x-6)
B. 3(x-2)(x + 2)
C. 3(x-2)(x-2)
D. 3(x + 2)(x + 2)

Answers

The answer is C. I tried factoring the equation itself, and I got the correct answer but I noticed that it isn’t one of the options. Therefore, the options are partly factored but not completely. I decided to just eliminate each of the multiple choice options. I got C after expanding it. Firstly, we need to distribute the 3 to (x-2). This gives us (3x-6)(x-2). After that, we can use the FOIL method. 3x^2 - 6x -6x + 12 is the same as 3x^2 - 12x + 12.

In case you want to see the fully factored polynomial, I won’t explain the steps since you don’t need it here, but it’s 3(x-2)^2. This is equivalent to 3(x-2)(x-2). That’s the same as C.

100.331 divide 99.355​

Answers

Answer:

1.009823361

Step-by-step explanation:

Just divide like this:

[tex] \frac{100.331}{99.355} = 1.009853361[/tex]

Find the average rate of change from x=1 to x=2 f(x) = -18/x^2

Answers

Answer:

13.5

Step-by-step explanation:

Average rate of change=(f(2)-f(1))/1=-18/2^2-(-18))=13.5

Other Questions
6). One unique element of the Irish migration was...A. the unwillingness of the Irish to work as manual laborers. B. the number of single women who made the journey. C. the lack of a cohesive ethnic identity. D. None of the answers provided are true. Fill in the blanks with suitable preposition:1. It suddenly became so dark as the train went ________ the tunnel. 2. The restaurant is ________ the bank and the post office. 3. What language do you speak ________ English? 4. You are not going out ________ you finish your homework 5. The book was written ________ Mark Twain. 6. I will show you the picture ________ the palace. 7. The TV is ________ the corner of the room. 8. Many of us eat ________ fork and spoon. 9. There is a good restaurant ________ the end of the street. 10. He is fond ________ TV. 11. The cat jumped ________ the fence. 12. He has a positive attitude ________ his work. 13. The artist dipped his brush ________ the bright colours. 14. What do you think ________ the concert? On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 3 kg weighs 30 N. Find the weight of an object whose mass is 5 kg To prepare a standard (calibration) curve for a spectroscopy experiment, start by preparing ___________ with ______________ Then, measure the ______________ of each solution at _____________ and create a plot of ____________ for the measured values. Finally, find the best-fit line of the data set. On a plant, stomates are small openings that regulate the passage of air and water vapor to and from the plant. Generally, the stomates open during sunlight and exchange gases with the atmosphere. The stomates of a few specialized desert plants can open only at night. The best explanation for the pattern of stomate opening and closing is that the desert plants are adapted to protect against (1) harmful insects (2) dust particles (3) destructive plant disease (4) excess water loss (5) total energy lossPlease help me somebody answer this. Which function is the inverse of h(x) = 18x+7/3 ?Question 10 options thank you scholarship thank you letters I don't need a language ABC Read the passage, and answer the question that follows:Yvonne sighed as she stood on the sidewalk. She wanted to cross the street but was stuck because of the traffic. She felt stuck in real life, too. Her career was going nowhere. She adjusted her glasses and looked left when a gust of wind blew a stack of papers from her hand. She ran quickly to gather them, wondering where they might lead.What object in the paragraph symbolizes change? Select all correct answers What are the solution to this equation -7+(x^2-19)^3/4=20 For some parents, their offspring have larger beak depths; for others it's smaller. How does the concept of variation of traits help to explain this? Antimicrobial susceptibility testing was performed to screen a novel compound. The MIC was found to be 10ng/mL. Use the following data to determine the percent recovery for each treatment group. What is the MBC and would you describe the antimicrobial tested as static or cidal?Novel compound concentration CFU/mL Present Recovery0ng mL 3.4 x 10^5 10ng/mL 2.4 x 10^5 20ng/mL 6.4 x 10^4 40ng/mL 1.4 x 10^4 80n mL 4.4 x 10^3 160n mL 0 ASAPIdentify the error in the following statement: Photosynthesis is a chemical reaction that takes place in the chloroplasts of green plant cells, where light energy is used to convert glucose and water into carbon dioxide and oxygen.A. glucose and carbon dioxide should be switchedB. No errorsC. water and oxygen should be switchedD. chloroplasts should be mitochondria Nazrul was a poet and a novelist; but (a).............., he was a patriot Last year, you purchased a stock at a price of $64.00 a share. Over the course of the year, you received $2.20 per share in dividends and inflation averaged 2.7 percent. Today, you sold your shares for $69.00 a share. What is your approximate real rate of return on this investment using trig to solve for missing angles Find the smallest possible value of x+y so that x^2 y^2 is divisible by 74, where x and y are positive integers. A researcher would like to investigate whether or not there is a difference in IQ between Psychology and History majors. She gathers 16 students (8 whose major is Psychology, and 8 whose major is history) and has them all take an IQ test to test this hypothesis using an alpha level of .01. Below are the data: Psych History 110 90 120 98 100 100 90110 124 100 102 120 110 110 123 120 a. What is the appropriate test? b. State the null hypothesis: c. State the alternative hypothesis: d. Find the critical value: e. Calculate the obtained statistic: f. Make a decision: g. What does your decision mean? A car accelerates from rest at 1.0 m/s2 for 20.0 seconds along a straight road. It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car. HELP The story told in Around the World in Eighty Days is set the year 1873. It is about a man who makes a bet that he can travel around the world in eighty days.How does the historical time period influence the events in the passage? Use evidence from the text ("around the world in 80 days", Jules Verne) to support your response. Your response should be at least two complete paragraphs.