4. In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 12 hours. Write a function showing the number of bacteria after t hours, where the hourly growth rate can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per hour, to the nearest hundredth of a percent.

Answers

Answer 1

The function representing the number of bacteria after t hours is N(t) = 5300 * (1 + 0.0592)^t, and the growth rate per hour is approximately 5.92%.

To represent the number of bacteria after t hours, we can use the exponential growth formula:

N(t) = N₀ * (1 + r)^t,

where N(t) is the number of bacteria after t hours, N₀ is the initial number of bacteria, r is the hourly growth rate, and t is the time in hours.

In this case, the initial number of bacteria is 5300, and the hourly growth rate can be determined from the doubling time of 12 hours. The growth rate can be calculated using the formula:

r = 2^(1/t_double) - 1,

where t_double is the doubling time in hours.

Substituting the given values, we have:

r = 2^(1/12) - 1 ≈ 0.0592.

Now we can write the function for the number of bacteria after t hours:

N(t) = 5300 * (1 + 0.0592)^t.

To determine the percentage of growth per hour, we can calculate the relative growth rate as a percentage:

percentage_growth = r * 100 ≈ 5.92%.

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Related Questions

What means killogram?

Answers

Answer:

1,000 grams

noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.

Best way to solve this type of equation Ax+by=c

Answers

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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The graph of � = ∣ � ∣ y=∣x∣y, equals, vertical bar, x, vertical bar is shifted down by 9 99 units and to the right by 4 44 units. What is the equation of the new graph? Choose 1 answer: Choose 1 answer: (Choice A) � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 A � = ∣ � − 9 ∣ − 4 y=∣x−9∣−4y, equals, vertical bar, x, minus, 9, vertical bar, minus, 4 (Choice B) � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 B � = ∣ � − 4 ∣ − 9 y=∣x−4∣−9y, equals, vertical bar, x, minus, 4, vertical bar, minus, 9 (Choice C) � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 C � = ∣ � − 4 ∣ + 9 y=∣x−4∣+9y, equals, vertical bar, x, minus, 4, vertical bar, plus, 9 (Choice D) � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4y, equals, vertical bar, x, minus, 9, vertical bar, plus, 4 D � = ∣ � − 9 ∣ + 4 y=∣x−9∣+4

Answers

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

What is a translation?

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

What is the circumference of the circle if the radius is 10 cm?

Answers

C≈62.83c

Answer for this question

The circumference of the circle is 62.8cm.

The Circumference of the circle is given by the formula,

Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1

Given, r = 10cm

On substituting the radius value in equation 1

Circumference = 2*[tex]\pi[/tex]*10

Circumference = 62.8 cm

Therefore, the circumference of the circle is 62.8cm.

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Linear equations linear equations

Answers

A graph of the linear equation y = 2x - 1 in slope-intercept form is shown in the image attached below.

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.

Based on the information provided above, we have the linear equation:

y = 2x - 1

Lastly, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.

In conclusion, the slope of this linear equation is equal to 2 and it does not represent a proportional relationship.

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Complete Question:

Plot the linear equation on the coordinate axis shown on the right.

URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
PLEASE ANSWER!!

Answers

Answer:

Step-by-step explanation:

a. 2r + 5 = b because you have you have 5 more blue marbles than double the red *r= red and b=blue

b. to do the substitution you know that the red marbles plus the blue marbles add up to 77 so

b + r=77

now we can isolate for b and then substitute that value into the first equation

b=77-r and then this goes to 2r+5=77-r

c. now you just have to get like terms to their side of the equal sign

add r to both sides: 2r+r+5=77-r+r=  3r+5=77

and then you subtract 5 from both sides which makes 3r=72

to find r, divide both sides by 3

r=24

there are 24 red marbles

Please Help
8x + 1
115⁰

Answers

(8x+1) + (115°) = 180°

180-115=65
8x+1=65
(remove the +1 by -1 from both sides)
8x=64
(remove the 8• by dividing by 8 on each side)
64/8
x=8


ANSWER: x=8

in long division what is the working and answer for 348 divided by 4?​

Answers

4 will divide the 348 is 8 and 2 left, so you will write the two and move the 8 down, which is now 28, then divide the 28 by 4. It will be 7.

the bus comes at 8:05. It takes me 31 minutes to get to the bus stop. What time should I leave to catch the bus?

Answers

You should leave at 7:34 to catch the bus that comes at 8:05.

We have,

To catch the bus that arrives at 8:05, you should leave with enough time to reach the bus stop 31 minutes before the bus's arrival time.

To catch the bus that arrives at 8:05, you need to be at the bus stop before the bus arrives. Since it takes you 31 minutes to get to the bus stop, you should leave your starting point early enough to allow for that travel time.

By subtracting 31 minutes from the bus's arrival time of 8:05, you determine the time at which you should depart.

In this case, subtracting 31 minutes gives you 7:34, meaning you should leave at 7:34.

To calculate the departure time, subtract 31 minutes from the bus's arrival time:

= 8:05 - 31 minutes

= 7:34

Thus,

You should leave at 7:34 to catch the bus that comes at 8:05.

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What is (fg)(x)?
f(x)=2x
g(x)=2x2+3x
Write your answer as a polynomial or a rational function in simplest form

Answers

Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.

f(x) = 2x

g(x) = [tex]2x^2[/tex] + 3x

To find (fg)(x), we substitute g(x) into f(x):

(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)

Now we substitute f(x) = 2x into the expression above:

(fg)(x) = 2([tex]2x^2[/tex] + 3x)

Distribute the 2:

(fg)(x) = [tex]4x^2[/tex] + 6x

So, (fg)(x) = [tex]4x^2[/tex] + 6x.

Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

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Decide whether pairs of angles <1 and <2​, <6 and<1 ​, and <5 and <6 are alternate interior​ angles, same-side interior​ angles, corresponding​ angles, or alternate exterior angles. Question content area bottom Part 1 Choose the statement that correctly describes angles 1 and 2.

*PLEASE ANSWER EACH QUESTION. IN ALL 3 PICS. THANKS

Answers

<1 and <2 are same-side interior angles. Option D

<1 and <5 are same-side interior angles. Option B

<6 and <8 are corresponding angles. Option C

How to determine the angles

To determine the angles, we need to know the following;

Corresponding angles are  angles formed in matching corners  with the transversal when two parallel lines are intersected by any other lineSame side interior angles are two angles that are found on the interior of  two lines and exactly on the same side of the transversal. Adjacent angles are equal

Now, from the information given, we have that;

1. <1 and <2 are same-side interior angles because they are found on the same side of the transversal

2. We can see that < 1 and <5 are also same-side interior angles because they are two angles found on the exact same side of the transversal

3. Since corresponding angles are angles on matching corners of a transversal, < 6 and < 8 are corresponding angles

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Find the number that belongs
in the green box.
[?]
37°
64°
21.1
30
Round your answer to the nearest tenth.

Answers

The number that belongs in the green box is 32.8

How to find the number that belongs in the green box

From the question, we have the following parameters that can be used in our computation:

The triangle

The third angle in the triangle is calculated as

Third angle = 180 - 37 - 64

Evaluate

Third angle = 79

If the number that belongs in the green box is x, then we have

x/sin(79) = 30/sin(64)

This gives

x = sin(79) * 30/sin(64)

Evaluate

x = 32.8

Hence, the number that belongs in the green box is 32.8

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These shapes are similar.
Find X.
5
X
5
30
24
30

Answers

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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En uno de los corrales de la granja de mi abuela hay gallinas y conejos. Aún cuando todos se mueven, logré contar 40 cabezas y 106 patas.
a) Explica cuáles son las incógnitas del problema.
b) Escribe una ecuación que represente el número de animales que hay en el corral.
c) Escribe una ecuación que represente el número total de patas.
d) ¿cuántos conejos y cuántas gallinas hay en el corral?

Answers

There are 27 chickens and 13 Rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.

a) The unknowns in the problem are the number of chickens and rabbits in the pen. We don't know the exact quantities of each animal, which is what we need to determine.

b) Let's denote the number of chickens as "C" and the number of rabbits as "R." To represent the total number of animals in the pen, we can write the equation: C + R = total number of animals.

c) The total number of legs can be represented by the equation: 2C + 4R = total number of legs. This equation accounts for the fact that chickens have two legs, while rabbits have four.

d) To find the solution, we can use the given information: 40 heads and 106 legs. Since each animal has one head, the total number of animals is equal to the total number of heads, which is 40.

Using the equation C + R = 40, we can solve for one variable in terms of the other. For example, if we solve for C, we get C = 40 - R.

Substituting this value of C into the equation 2C + 4R = 106, we can solve for R:

2(40 - R) + 4R = 106

80 - 2R + 4R = 106

2R = 26

R = 13

Therefore, there are 13 rabbits in the pen.

To find the number of chickens, we can substitute the value of R into the equation C = 40 - R:

C = 40 - 13

C = 27

Hence, there are 27 chickens in the pen.

In conclusion, there are 27 chickens and 13 rabbits in the pen on your grandmother's farm, based on the given information of 40 heads and 106 legs.

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Find the number that belongs
in the green box.
[?]
37°
64°
21.1
30
Round your answer to the nearest tenth.

Answers

The value of x is 33.4

How to determine the value

To determine the value in the green box, we need to know that there are six different trigonometric identities.

These identities are enumerated as;

sinecosinetangentcotangentsecantcosecant

Using the sine identity, we have;

sin θ = opposite/hypotenuse

We have that;

θ = 64 degrees

Opposite = 30

Hypotenuse  = x

Substitute the values, we have;

sin 64 = 30/x

cross multiply

x = 30/0. 8987 = 33. 4

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The sum of 18 and a number, x, equals negative 40. Part A Which equation represents this situation? x-18=-40. x-18-40 18+x=-40. 18 + x = 40​

Answers

Answer:

18+x = -40

Step-by-step explanation:

The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40

log base 4 of 9
HELPPPPPPPP

Answers

Answer:

1.58 ish

Step-by-step explanation:

For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007

a new social media sit is increasing its user base by approximately 4% per month. If the site currently has 35.930 users, what will the approximate user base be 10 months from now?

Answers

Answer:

The approximate user base of the social media site 10 months from now would be approximately 52,374.

Step-by-step explanation:

To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:

1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04

2. Apply the growth factor to the current user base for each month:

  Month 1: 35,930 * 1.04 = 37,387.2 (approx.)

  Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)

  ...

  Month 10: Previous Month * 1.04

By repeating this calculation for each month, we can determine the approximate user base 10 months from now.

Month 1: 37,387.2

Month 2: 38,868.49

Month 3: 40,391.33

Month 4: 41,957.61

Month 5: 43,569.34

Month 6: 45,228.24

Month 7: 46,936.32

Month 8: 48,695.44

Month 9: 50,507.45

Month 10: 52,374.40 (approx.)

Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.

A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)

Answers

The equation that represents this situation is:

⇒ 60t = 0.0284091

where t is the time in minutes.

We have to given that,

The speed of the cheetah is 60 miles per hour

The distance timed was 50 yards

Now, We have to convert the distance to miles, because the speed is in miles per hour.

Since, 1 yard = 0.000568182 miles

Hence, 50 yards = 50 x 0.000568182 miles

50 yards = 0.0284091 miles

Now we can use the formula:

distance = speed x time

We know that,

The distance is 0.0284091 miles, and the speed is 60 miles per hour.

Hence, the time it took the cheetah to run the 50-yard distance.

So, the speed from miles per hour to miles per minute, since we want the time in minutes:

60 miles per hour = 1 mile per minute

Now we can plug in the values we know:

0.0284091 miles = (1 mile per minute) x time

Solving for time:

time = 0.0284091 / 1

time = 0.0284091 minutes

time = 0.0284091 minutes x 60 seconds per minute

time = 1.704546 seconds

Thus, the equation that represents this situation is:

⇒ 60t = 0.0284091

where t is the time in minutes.

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A merchant has 1500 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is

Answers

Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

De los 12 jugadores del equipo 2/8 son delanteros

Answers

There are a total of 3 forwards on the team.

How many forwards are there on the team?

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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What is the sum of 104, 25, -11 to come of it

Answers

Answer:

118

Step-by-step explanation:

104+25+(-11)

129-11

118

Therefore, our answer is 118

Find the equation of a parabola with focus (3, 4) and directrix y = 1.

Answers

The equation of the parabola with focus (3, 4) and directrix y = 1 is [tex]x^2 - 6x - 12y + 57 = 0.[/tex]

To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:  

[tex]4p(y - k) = (x - h)^2[/tex]  

where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.

In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).

The directrix is given as y = 1.

First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.

Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.

Now that we have the value of p, we can substitute it into the equation:

[tex]4p(y - k) = (x - h)^2[/tex]

Plugging in the values (h, k) = (3, 4) and p = 3, we get:

[tex]4(3)(y - 4) = (x - 3)^2[/tex]

Simplifying further:

[tex]12(y - 4) = (x - 3)^2[/tex]

Expanding the equation:

[tex]12y - 48 = x^2 - 6x + 9[/tex]

Bringing all terms to one side:

[tex]x^2 - 6x - 12y + 57 = 0[/tex]

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Graph the image of this quadrilateral after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the quadrilateral.

Answers

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

We have,

To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.

Given the original coordinates of the quadrilateral ABCD:

A = (-3, 3)

B = (-4, -2)

C = (2, -4)

D = (0, 0)

To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:

A' = 2 x (-3, 3) = (-6, 6)

B' = 2 x (-4, -2) = (-8, -4)

C' = 2 x (2, -4) = (4, -8)

D' = 2 x (0, 0) = (0, 0)

Thus,

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

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what is an example of "an extension of a function f"?

Answers

An example of an extension of a function f is adding additional input-output pairs beyond the original domain and range of f.

What is an example of "an extension of a function f"?

The extension of a function f means new function that preserves the properties and behavior of the original function on its domain while adding new values or expanding its domain.

For example, we will consider the function f(x) = x^2 defined on the interval [0, 1]. An extension of this function could be g(x) = x^2 for x in [0, 1] and g(x) = 0 for x outside [0, 1].

This extension maintains the quadratic behavior of f on [0, 1] while assigning a constant value of 0 to points outside that interval.

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a number cube is tossed 60 times Determine the experimental probability of landing on a number less than two

Answers

Answer:

1.67% approx

Step-by-step explanation:

To determine the experimental probability of landing on a number less than two when a number cube is tossed 60 times, we need to count the number of times the number on the cube is less than two and divide it by the total number of tosses.

Let's denote the event of landing on a number less than two as "A." We'll count the number of successful outcomes, where the number on the cube is less than two.

Assuming the number cube is fair and unbiased, it has six sides numbered from 1 to 6. Out of these, only one side has a number less than two, which is one.

Now, we can calculate the experimental probability using the formula:

Experimental Probability (P(A)) = Number of successful outcomes / Total number of tosses

In this case, the number of successful outcomes is the number of times the cube lands on a number less than two, which is one. The total number of tosses is given as 60.

Therefore, the experimental probability of landing on a number less than two is:

P(A) = 1 (successful outcomes) / 60 (total number of tosses)

= 1/60

≈ 0.0167 or 1.67%

So, the experimental probability of landing on a number less than two is approximately 0.0167 or 1.67%.

obove answer is correct i think

Answer Question 11 please

Answers

Answer:

increasing exponential function.

Step-by-step explanation:

We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.

It  must be exponential.

It is increasing at it increases in x, so it is an increasing exponential function.

what is a Pythagoras theorem

Answers

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

What is mathematical representation of Pythagoras theorem?

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.

'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.

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Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1

Answers

The radius of the cylinder is 2.25 feet.

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.

400 = 3.14 r² x 25

Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:

r² = 400 / (3.14 x 25)

r² ≈ 5.08

Taking the square root of both sides to solve for r, we get:

r ≈ √5.08

r ≈ 2.25

Therefore, the radius of the cylinder is 2.25 feet.

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Which of the following shows a 90° counterclockwise rotation of the blue figure

Answers

The answer is letter B
Other Questions
Should there be regulations in place to safeguard email information from being used for content extraction? Why or why not? Question 1 (6 points) Let { r, s, t, u, s, p, q, w, z} B = {y, c, z} C = {y, s.r, d, t, z} a) Find all the subsets of B b) Find Anc c) Find n ( A UBU) a coin sold at auction in 2019 for $4,573,500. the coin had a face value of $2 when it was issued in 1789 and had been previously sold for $285,000 in 1968. The following is the actual sales for Manama Company for a particular good: t Sales 15 20 22 27 5 30 The company wants to determine how accurate their forecasting model, so they asked their modeling expert to build a trend model. He found the model to forecast sales can be expressed by the following model: Ft-5-24 Calculate the amount of error occurred by applying the model is: Hint: Use MSE if load is 10 kn, cross sectionl area is 2 square mm, contact area = 5 square mm. what will be bearing stress? which concept describes the process in which the nurse collects information related to a patient problem by speaking with the patient? focused assessment objective data collection subjective data collection comprehensive assessment C151 Activity: Related rates-Challenge Purpose: of this activity is for you to explore, strategize and learn to solve physical problems involving derivatives-related rates Task: work together, set up and solve Criteria: grade is determined by your strategy, correct solution and group inclusion [a] A 15 foot ladder is resting against the wall. The bottom is initially 10 feet away from the wall and is being pushed towards the wall at a rate of % fUsec. How fast is the top of the ladder moving up the wall 12 seconds after we start pushing? [B] Two people are 50 feet apart. One of them starts walking north at a rate so that the angle shown in the diagram below is changing at a constant rate of .01 rad/min. At what rate is distance between the two people changing when 0.5 radians [C] A light is on the top of a 12 ft tall pole and a 5'6" tall person is walking away from the pole at a rate of 2 ft/sec a) At what rate is the tip of the shadow moving away from the pole when the person is 25 ft from the pole? b) At what rate is the tip of the shadow moving away from the person when the person is 25 ft from the pole? if the spot exchange rate is equal to the break-even price of an option, then the option must be: 6. (10 points) You randomly select 20 cars of the same model that were sold at a car dealership and determine the number of days each car sat on the dealership's lot before it was sold. The sample mean is 9.75 days, with a sample standard deviation of 2.39 days. Construct a 99% confidence interval for the population mean number of days the car model sits on the dealership's lot. Giant acquired all of Small's common stock on January 1, 2017, in exchange for cash of $770,000. On that day, Small reported common stock of $170,000 and retained earnings of $400,000. At the acquisition date, $90,000 of the fair-value price was attributed to undervalued land while $50,000 was assigned to undervalued equipment having a 10-year remaining life. The $60,000 unallocated portion of the acquisition-date excess fair value over book value was viewed as goodwill. Over the next few years, Giant applied the equity method to the recording of this investment. The following are individual financial statements for the year ending December 31, 2021. On that date, Small owes Giant $10,000. Small declared and paid dividends in the same period. Credits are indicated by parentheses. a. How was the $135,000 Equity in Income of Small balance computed? b. Without preparing a worksheet or consolidation entries, determine and explain the totals to be reported by this business combination for the year ending December 31, 2021. c. Verify the amounts determined in part (b) by producing a consolidation worksheet for Giant and Small for the year ending December 31, 2021. Page 144 d. If Giant determined that the entire amount of goodwill from its investment in Small was impaired in 2021, how would the parent's accounts reflect the impairment loss? How would the worksheet process change? What impact does an impairment loss have on consolidated financial statements? Giant Small $ (360,000) Revenues $(1,175,000) Cost of goods sold 550,000 90,000 Depreciation expense 172,000 130,000 Equity in income of Small (135,000) -0- Net income $ (588,000) $(140,000) Retained earnings, 1/1/21 $(1,417,000) $ (620,000) Net income (above) (588,000) 310,000 (140,000) 110,000 Dividends declared $(1.695.000) $ (650,000) $ 398,000 $ 318,000 995,000 440,000 -0- 165,000 419,000 304,000 648,000 286,000 -0- -0- $2.785,000 $1.188,000 $ (368,000) $ (840,000) (250,000) (170,000) (1.695.000) (650,000) $(2.785,000) $(1,188,000) Retained earnings, 12/31/21 Current assets Investment in Small Land Buildings (net) Equipment (net) Goodwill Total assets Liabilities. Common stock Retained earnings (above). Total liabilities and equity For the process X(t) = Acos(wt + 0) where and w are constants and A~ U(0, 2) . Check whether the process is wide-sense stationary or not? what would be the ph at the half-equivalent point in titration of a monoprotic acid with naoh solution if the acid has Ka = 5.2 x 10-6? a 30-year-old active duty man presents for mmr vaccine. in medical readiness review, serology testing showed he is non-immune to measles. his wife is 3 months pregnant. can he safely receive mmr vaccine today? Solve the polynomial inequality and graph the solun set on a real number line Express the solution set in 12x+10 Use the quality in the time to write the intervals detained by the boundary points as t the ability of a corporation to shift from one dominant strategy to another is called At the beginning of 2021, Ehrlich Co. purchased an asset for $1,800,000 with an estimated useful life of 5 years and an estimated salvage value of $150,000. For financial reporting purposes the asset is being depreciated using the straight-line method; for tax purposes the double-declining-balance method is being used. Ehrlich Co.s tax rate is 20% for 2021 and all future years. Pretax financial statement income is $1,000,000. Instructions: What is the taxable income? Show your calculations. Prepare a journal entry showing the deferred tax liability, income tax expense, and income tax payable. Show all calculations. Prepare the income tax expense section of the balance sheet, beginning with the line "income before income taxes". Terry transfers two assets to a partnership on the day its created for a 60% partnership interest worth $120,000. She contributed cash = $80,000 and equipment worth $40,000 with an adjusted basis = $16,000. What result?a.Terry realizes and recognizes a $24,000 gainc.Terry realizes but does not recognize a $24,000 gainb.Terry neither realizes nor recognizes any gaind.Terry does not realize but may elect to recognize a $24,000 gain Using only a simple calculator, find the values of k such that det (M) . -1 k 0such that det (M)=0, where M= 1 1 k1 1 9As your answer, enter the SUM of the value(s) of k that satisfy this condition. Which of the following is not an example of state spending? a. the building and maintenance of the highway system b.state water quality inspections c.the state campground where your family vacations dthe public library where you find sources for a research paper a. Net income was $466,000. b. Issued common stock for $79,000 cash. c. Paid cash dividend of $13,000. d. Paid $110,000 cash to settle a long-term notes payable at its $110,000 maturity value. e. Paid