A roller skating rink charges a skate rental fee and an hourly rate to skate.
The total cost to skate for 2 hours is $9.50 and for 5 hours is $18.50.
Assume the relationship is linear. Find and interpret the rate of change and
where x represents the number of hours and y represents the total cost.
initial value. Then write the equation of the function in the form y = mx + b

Answers

Answer 1

Answer:

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink

Step-by-step explanation:

From the question we have;

The charges of the roller skating rink = A skate rental fee + An hourly rate

The total cost to skate for 2 hours = $9.50

The total cost to skate for 5 hours = $18.50

The relationship between the total cost of skating and the duration in hours = Linear relationship

Let 'x' represent the number of hours skating and let 'y' represent the total cost, we have;

The form of the equation is y = m·x + b

Where;

m = The rate of change of the linear relationship

b = The initial value (y-intercept)

When x = 2, y = 9.50

Therefore, we can write;

9.50 = 2·m + b...(1)

When x = 5, y = 18.50

Therefore, we can write;

18.50 = 5·m + b...(2)

Subtracting equation (1) from equation (2) gives;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

The rate of change, m = 3.0

Similarly, we have;

From equation (1), we get;

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The initial value = 3.50

Therefore, the initial value, b = $3.50 is the skate rental fee while rate of change m = $3.0 is the hourly rate the rate.


Related Questions

Can you give me the answer to this

Answers

Answer:

C. a translation of 1 unit right and 2 units up, followed by a dilation by a factor of 3

Step-by-step explanation:

NO LINKS PLEASE JUST THE ANSWER TEHEHHE THANKSSSS :))))
A square and rectangle are shown below. The width of the rectangle is the same as the length of a side of the square, both represented by x. The length of the rectangle is one foot more than twice its width. The perimeter of the rectangle is 26 feet more than that of the square.

A). Write an expression for the length of the rectangle in terms of x. Label the drawing

B). Show that 5 could not be the value of x

C). Set up an equation and solve it to find the value of x

THANKS FOR THE HELP!!!

Answers

Answer:

Since this is a multi-part question, just look at the bolded parts under each letter. I hope this helps a bit ;)

Step-by-step explanation:

A)  

All sides of a square are congruent. "s" represents the square's perimeter:

s=4x.

"r" is the rectangle's perimeter:

r= 4x+26

since the perimeter = 2W + 2L:

2W + 2L= 4x+ 26

and W=x, so:

2x + 2L= 4x + 26

Subtract from both sides:

2L= 2x +26

Divide both sides:

the length of the rectangle "L"= x +13.

B) Plug 5 into the equations:

L= 5+ 13 or 18.

2(18) + 2(5)= r

36+ 10 = r or 46

s= s+ 26

s= 46-26 or 20.

20/4= 5...

It seems (at least to me, feel free to give constructive criticism) that the only logical conclusion is that 5 could be the value of x.

C) You would likely need to use substitution to solve, but unless I am much mistaken, this looks like an infinite-solutions equation.

L=w+13

It is 1/2 mile from the students home to a store and back. In a week, she walked to the store and back home 1 time. In the same week, she rode her bike to the store and back 3 times. How many miles did she walk and ride to the store and back in that week?

Answers

Answer:

2

Step-by-step explanation:

So you will get the 1/2 and see how many times she does go back and forth and she did it 4 times so you would multiply 1/2 x 4 and get a total of 2

Hope It Helps

Answer:

2

Step-by-step explanation:

she walked to the store and back 1 time=1/2 mile :

from her house to the store=1/4 mile

she rode her bike to the store and back 3 times

So in total that week she went to the store and back 4 times

so 4 times 1/2 is 2

An example of the classical approach to probability would be_____
A. in terms of the proportion of times an event is observed to occur B. in a very large number in terms of the degree to which one happens to believe that an event will happen C. in terms of the proportion of times that an event can be theoretically expected to occur D. in terms of the outcome of the sample space being equally probable

Answers

Option C is the correct example of the classical approach to probability.

An example of the classical approach to probability would be option C: in terms of the proportion of times that an event can be theoretically expected to occur.

The classical approach to probability is based on the assumption of equally likely outcomes. In this approach, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

For example, consider a fair six-sided die. The classical approach would state that since there are six equally likely outcomes (the numbers 1 to 6), the probability of rolling a specific number, say 3, would be 1 out of 6, or 1/6. This is because there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling any number from 1 to 6).

Similarly, if we have a bag containing 10 red balls and 20 blue balls, the classical approach would state that the probability of drawing a red ball would be 10 out of 30, or 1/3. This is because there are 10 favorable outcomes (drawing a red ball) out of 30 possible outcomes (drawing any ball from the bag).

In both cases, the classical approach to probability relies on the concept of equally likely outcomes and uses the proportion of favorable outcomes to calculate the probability.

Therefore, option C is the correct example of the classical approach to probability.

For more questions on probability

https://brainly.com/question/251701

#SPJ8

median for 15,17,15,16,14,18,5

Answers

Answer:

the median is 15

Explanation:

you can find the median by arranging the numbers from smallest to largest and finding the number in the middle.

5 14 15 15 16 17 18

in this case, the number in the middle is 15 so the median for this data set is 15.

i hope this helps! :D




√3 • TV TV² (4) Let's evaluate x² + y² - 1 dy dr by converting it to polar coordinates.

Answers

To evaluate the expression x² + y² - 1 in polar coordinates, we need to convert the Cartesian coordinates (x, y) to polar coordinates (r, θ).

In polar coordinates, x = rcos(θ) and y = rsin(θ). Substituting these values into the expression, we obtain r²cos²(θ) + r²sin²(θ) - 1. This expression can be simplified using trigonometric identities to obtain r²(cos²(θ) + sin²(θ)) - 1, which simplifies further to r² - 1.

When converting Cartesian coordinates (x, y) to polar coordinates (r, θ), we use the equations x = rcos(θ) and y = rsin(θ). Substituting these values into the expression x² + y² - 1, we have (rcos(θ))² + (rsin(θ))² - 1. Applying the trigonometric identity cos²(θ) + sin²(θ) = 1, we can simplify the expression to r²cos²(θ) + r²sin²(θ) - 1.

Since cos²(θ) + sin²(θ) = 1, the expression simplifies further to r²(1) - 1, which becomes r² - 1. Therefore, in polar coordinates, the expression x² + y² - 1 is equivalent to r² - 1. This means that when evaluating the expression in terms of polar coordinates, we only need to consider the square of the radial distance, r², and subtract 1.

Learn more about Cartesian coordinates here:

https://brainly.com/question/31327924

#SPJ11


How deep is the water 31.5 feet from the shore? 05
(10 Points)

Answers

Answer:

This is impossible to answer, unless there is a picture that is not there.

Step-by-step explanation:

please help ASAP!!!!!!!

Answers

Answer: the length of the base is 50 cm

Step-by-step explanation:

what is the scale factor of figure b to a

Answers

Answer:

C. 2:5

Step-by-step explanation:

Find perimeter of each...

a. 10+25+21.5=56.5

b. 4+10+8.6=22.6

b:a

22.6:56.6

simplify

11.3 will go into both for..

2:5

A new sensor was developed by ABY Inc. that is to be used for their obstacle detection system. During tests involving 250 runs, the following data were acquired:

The alarm went off 33 times even if there is no obstacle.
There are 63 times when the alarm didn't activate even if an obstacle is present.
The alarm went off correctly 62 times.
For the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.

For answers that have decimal places, use four-decimal places.

1. How many times that the alarm didn't activate correctly?

2. How many runs have actual obstacles in place?

3. How often is the sensor correct?

4. How often is the sensor incorrect?

5. What is the hit rate of the sensor?

6. How often does the sensor predict a NO even if it is supposed to be a YES?

7. What is the CSI of the sensor?

8. What is the overall accuracy of the sensor?

9. What is the F-score?

10. Yes or No. Did the sensor pass the expectations?

Answers

A new sensor was developed by ABY Inc. that is to be used for their obstacle detection system. However, the sensor to be commercially produced, it must have an error rate that is lower than 40% and an F-Score that is more than or equal to 70%.

1. The alarm didn't activate correctly 63 times during the tests.

During the tests, it was observed that the alarm failed to activate in the presence of an obstacle 63 times. This means that the sensor missed detecting obstacles in those instances.

2. There were 126 runs with actual obstacles in place.

Out of the 250 runs, the alarm correctly activated 62 times and didn't activate correctly 63 times. Since the alarm failed to activate in the presence of an obstacle 63 times, we can infer that there were 126 runs with actual obstacles.

3. The sensor was correct 156 times out of 250 runs.

To calculate how often the sensor was correct, we need to sum up the number of times the alarm went off correctly (62 times) and the number of times the alarm didn't activate correctly (63 times).

This gives us a total of 125 correct activations. However, we also need to account for the 63 times when the alarm didn't activate even if an obstacle was present. So the sensor was correct 125 + 63 = 188 times out of 250 runs.

4. The sensor was incorrect 62 times out of 250 runs.

The sensor was incorrect when it failed to activate the alarm in the presence of an obstacle (63 times) and when the alarm went off even if there was no obstacle (33 times). Therefore, the sensor was incorrect 63 + 33 = 96 times out of 250 runs.

5. The hit rate of the sensor is 0.4960 or 49.60%.

The hit rate, also known as the True Positive Rate or Sensitivity, measures the proportion of actual positive cases that were correctly identified by the sensor.

It is calculated by dividing the number of correct activations (62) by the total number of runs with actual obstacles (126). Therefore, the hit rate is 62/126 = 0.4960 or 49.60%.

6. The sensor predicted a NO even when it was supposed to be a YES 33 times.

Out of the 250 runs, there were 33 instances where the alarm went off even if there was no obstacle present. This means that the sensor predicted a NO (no obstacle) incorrectly in those cases.

7. The CSI (Critical Success Index) of the sensor is 0.4032 or 40.32%.

The CSI, also known as the Threat Score or True Skill Statistic, measures the effectiveness of the sensor in detecting obstacles while avoiding false alarms.

It is calculated by dividing the number of correct activations (62) by the sum of correct activations, missed detections, and false alarms. So the CSI is 62 / (62 + 63 + 33) = 0.4032 or 40.32%.

8. The overall accuracy of the sensor is 62.80%.

The overall accuracy is calculated by dividing the number of correct activations (62) and correct non-activations (187) by the total number of runs (250). So the overall accuracy is (62 + 187) / 250 = 0.6280 or 62.80%.

9. The F-score is 0.5238 or 52.38%.

The F-score, also known as the F1-score, combines the precision and recall of the sensor's performance. It is calculated using the formula: F-score = 2 * (precision * recall) / (precision + recall).

Precision is the ratio of true positives (62) to the sum of true positives and false positives (33), while recall is the ratio of true positives to the sum of true positives and false negatives (63). Plugging in the values, we get F-score = 2 * (62)

To know more about F-score refer here:

https://brainly.com/question/31106364#

#SPJ11




(a) A vector equation of the plane P1 in R3 which passes through the points A = (2, 1, –4), B= = (3, 4, –4), and C = (3, -9,8) is 2 1 1 X = HOHE ) -4 12 Correct answer, well done. Correct answer,

Answers

The vector equation of the plane P1 in R3 which passes through the given points is:  `(-36, -12, -9).(X - (2, 1, -4)) = 0`.

We have three points `A (2, 1, -4), B (3, 4, -4)` and `C (3, -9, 8)` that lie on plane P1. To find the vector equation of the plane P1 in R3, we need to find the normal vector of the plane P1. The normal vector is perpendicular to the plane P1. We can find the normal vector by taking the cross product of any two nonparallel vectors that lie on the plane P1.

Let's choose two vectors `AB` and `AC`.

`AB = B - A = (3, 4, -4) - (2, 1, -4) = (1, 3, 0)`

`AC = C - A = (3, -9, 8) - (2, 1, -4) = (1, -10, 12)`

Now, we take the cross product of `AB` and `AC` to get the normal vector `n`.

`n = AB × AC = (-36, -12, -9)`

The equation of the plane P1 with normal vector `n` and passing through the point A can be written as:

`(n . (X - A)) = 0` where `.` is the dot product.

Substituting the values, we get:

`(-36, -12, -9) . (X - (2, 1, -4)) = 0`

`(-36, -12, -9) . (X - 2, X - 1, X + 4) = 0`

`-36(X - 2) - 12(X - 1) - 9(X + 4) = 0`

`-36X + 72 - 12X + 12 - 9X - 36 = 0`

`-57X + 48 = 0`

`57X = 48`

`X = 48/57 = 16/19`

Therefore, the vector equation of the plane P1 in R3 which passes through the points A = (2, 1, –4), B= = (3, 4, –4), and C = (3, -9,8) is:

`(-36, -12, -9) . (X - 2, X - 1, X + 4) = 0`

`-36(X - 2) - 12(X - 1) - 9(X + 4) = 0`

`-36X + 72 - 12X + 12 - 9X - 36 = 0`

`-57X + 48 = 0`

`57X = 48`

`X = 16/19`

The answer is, `(-36, -12, -9).(X - (2, 1, -4)) = 0`.

To know more about vector equation refer here:

https://brainly.com/question/31044363

#SPJ11

I need help!!!
Find∠KML

Answers

Answer:

62

Step-by-step explanation:

180 - 56 = 124

124/2 = 62

Determine if Q[x]/(x2 - 4x + 3) is a field. Explain your answer.

Answers

The quotient ring  [tex]Q[x]/(x^2 - 4x + 3)[/tex]  is not a field because the polynomial x²- 4x + 3 can be factored into linear factors in Q[x], indicating the presence of zero divisors in the quotient ring.

To determine if the quotient ring [tex]Q[x]/(x^2 - 4x + 3)[/tex] is a field, we need to check if the polynomial x² - 4x + 3 is irreducible in Q[x], which means it cannot be factored into non-constant polynomials of lower degree in Q[x].

The polynomial x² - 4x + 3 can be factored as (x - 1)(x - 3) in Q[x], so it is not irreducible. This means that Q[x]/(x² - 4x + 3) is not a field.

In fact, Q[x]/(x² - 4x + 3) is an example of a quotient ring that is not a field. It can be shown that this quotient ring is isomorphic to Q[x]/(x - 1) x Q[x]/(x - 3), which is a direct product of two fields.

Since a field cannot have nontrivial zero divisors, and in this case, both (x - 1) and (x - 3) are zero divisors, the quotient ring is not a field.

To know more about quotient ring refer here:

https://brainly.com/question/32556645#

#SPJ11

WILL GIVE BRAINLIST!!!

MAD (Mean absolute deviation) is always a negative number

True or False

Answers

False, regardless of whether data values are zero, positive, or negative, the MAD can never be negative. This is because the MAD is calculated by finding absolute values of the deviations (or differences) from the mean, and then taking the average (or mean) of these absolute values.

what is 10x32 I will give brainliest and thanks

Answers

Answer:

320

Step-by-step explanation:

Convert 5.7×108 to its expanded form. sorry guys im not good with math so i need halp ^_^

Answers

The answer is 615.6.If you have more problems like this go to math-way calculator

HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

Answer: D

Step-by-step explanation:

maybe

Answer:

the answer for your question is d


no link just put the answerrrrr

Answers

Answer:

4in

Step-by-step explanation:

Can you help me pleaseeeeeeeeeee

Answers

This is so wasy n u dk how to do it u just add 3 my god

Answer:

Pounds of candy      Cost ($)       Cost/pound

1                                  $3                $3/1                                                  

3                                 $9                $3/1                                      

7                                 $21               $3/1                                                          

10                               $30              $3/1                                                      

Use the formula to find the simple interest:
$34,100 at 4% for 3 years

Answers

Answer:

$4092

Step-by-step explanation:

Find all the values of p for which the series is convergent.
[infinity]
∑ 3 / (n[ln(n)]p
ₙ ₌ ₂

Answers

The series ∑ 3 / (n[ln(n)]^p is convergent for all values of p greater than 1.

To determine the values of p for which the series is convergent, we can use the integral test. According to the integral test, if the integral of the series converges, then the series itself converges.
Considering the series ∑ 3 / (n[ln(n)]^p, we can evaluate its convergence by integrating the series function. Integrating 3 / (n[ln(n)]^p with respect to n gives us ∫ (3 / (n[ln(n)]^p)) dn.By performing the integration, we obtain ∫ (3 / (n[ln(n)]^p)) dn = 3 ∫ (1 / (n[ln(n)]^p)) dn.
Simplifying further, we have 3 ∫ (1 / (n^1 * [ln(n)]^p)) dn = 3 ∫ (1 / (n^1 * n^p * [ln(n)]^p)) dn.
Now, we can observe that the integral is dependent on the value of p. For the integral to converge, the exponent of n^p must be greater than 1.
Therefore, we conclude that the series is convergent for all values of p greater than 1.

Learn more about convergent here
https://brainly.com/question/29258536



#SPJ11

Martin drew a triangle. Its sides were

3

cm

3 cm3, start text, space, c, m, end text,

4

cm

4 cm4, start text, space, c, m, end text, and

5

cm

5 cm5, start text, space, c, m, end text.

It has one right angle and two acute angles.

Answers

Answer:

It is a right triangle

Step-by-step explanation:

Complete question

Martin drew a triangle. Its sides were 3\text{ cm}3 cm3, start text, space, c, m, end text, 4\text{ cm}4 cm4, start text, space, c, m, end text, and 5\text{ cm}5 cm5, start text, space, c, m, end text. It has one right angle and two acute angles. Complete the sentence to describe the triangle Martin drew. Martin's triangle is ----- and ------ .

First you must know that for a triangle to be right angled, the square of the largest side must be equal to the sum of the square of the other two sides

Given

Largest side c = 5

Other sides a = 3 and b=4

Square of largest side c² =5²=25

Sun of the squares of other two sides = a²+b²

Sum of the squares of other two sides =3²+4²

Sum of the squares of other two sides = 9+16 =25

Since c² =a²+b² according to pythagoras theorem, hence the triangle is right angled

Khan khan khan khan

Answers

Answer:

11

Step-by-step explanation:

it says motor cycles combined with garbage so add both of them then subtract that from the bull dosers

motor =18

garbage=4

18+4=22

bulldosers=11

22-11= 11 more

Answer:

11

Step-by-step explanation:

On the last 4 math assignments, Andrew scored the following:
88, 92, 100, 75

What is the median?

Answers

Answer:

median is 90

Step-by-step explanation:

75, 88, 92, 100

(88+92)/2 = 90

The correct answer would be 90. Im very good with finding medians.

Chester plays football at East Washington
Junior High School. In one quarter of
Friday's game, Chester ran +15 yards,
-23 yards, +34 yards, +17 yards, and
-28 yards. How many yards is Chester
from his starting point?

Answers

Answer:

15 yards

Step-by-step explanation:

hope this helps ❤️

Tammy needs at least an 85% in order to pass
her chemistry class.

Answers

17/20 or 0.85 is the answer

Give an example of a single polygon that has at least 5 sides and has exactly 2 lines of symmetry,

Answers

One example of a single polygon that has at least 5 sides and has exactly 2 lines of symmetry is a regular pentagon.

A regular pentagon is a five-sided polygon in which all five sides are equal in length and all five angles are congruent, i.e., the same measure. A regular pentagon also has five lines of symmetry, which cut through its center point and the midpoint of each side.

However, we need a polygon with exactly 2 lines of symmetry. Therefore, we can take a regular pentagon and remove two opposite edges and vertices. This leaves us with a polygon that still has 5 sides but has exactly 2 lines of symmetry: the red lines represent the two lines of symmetry of the polygon.

To know more about pentagon refer to:

https://brainly.com/question/30242660

#SPJ11

solve for x round to your nearest tenth

Answers

The answer is x = 8.1

math a man made pond has the sape of a reverse truncate square pyramid as shown below. the top side length is 20 meters

Answers

The man-made pond has the shape of a reverse truncated square pyramid with a top side length of 20 meters.

A reverse truncated square pyramid is a three-dimensional shape that resembles an inverted pyramid. It has a square base and four triangular faces that taper toward a smaller square top. In the case of the man-made pond, the top side length is given as 20 meters.

The specific dimensions and characteristics of the pond, such as the height, the length of the slanted sides, and the volume, are not provided in the question.

However, based on the given information, we can understand the general shape and structure of the pond. It is a geometric figure resembling a reverse truncated square pyramid, with a square base and sloping sides that converge toward a smaller square top.

Learn more about square pyramid here:

https://brainly.com/question/31200424

#SPJ11

Can y’all help me with this one?

Answers

-44+18=-26degrees

negative 26 degrees is your answer

please mark brainliest and have a nice day

Negative 26 degrees will be your answer
Other Questions
Which of the following best characterizes the source of European immigrants during the age of mass migration?a. By the turn of the 20th century, Eastern and Southern Europeans had replaced Northern Europeans as the dominant immigrant groups.b. Throughout the period Northern Europeans were the dominant immigrant group.c. Throughout the period Southern Europeans were the dominant immigrant group.d. By the turn of the 20th century, Northern Europeans had replaced Eastern and Southern Europeans as the dominant immigrant group. When describing a thermodynamic system, which is a good description of "internal energy"? 21. Your local grocery store stocks rolls of bathroom tissue in single packages and in more economical 12-packs. You are trying to decide which to buy. The single package costs 45 cents and the 12-pack costs $5. You consume bathroom tissue at a fairly steady rate of one roll every three months. Your opportunity cost of money is computed assuming an interest rate of 25 percent and a fixed cost of $1 for the additional time it takes you to buy bathroom tissue when you go shopping. (We are assuming that you shop often enough so that you don't require a special trip when you run out.) a. How many single rolls should you be buying in order to minimize the annual holding and setup costs of purchasing bathroom tissue? b. Determine if it is more economical to purchase the bathroom tissue in 12-packs. Verify the identity.sin x/1-cos x = csc x + cot x Define the linear transformation T: RR by T(v) Av. Find the dimensions of R" and Rm. A = [-2-22] 12 dimension of R" dimension of R The groups that comprised the majority ofimmigrants to the United States between 1890 and1920 were called "new immigrants" because they1 were the last immigrants to enter the UnitedStates before World War2 settled in frontier areas of the country3 stayed only for a short time before returning totheir homelands.4 came from different regions of the world thanmost of the groups who came before 1890 HELP ASAP PLEASE Wernicke's area is responsible fora. comprehensionb. articulationc. pronunciationd. fluency What Supreme Court decision emphasized the "one person, one vote" idea in relation to the House of Representatives? In your opinion, what was the most significant change to gender roles in the early 19th century?Must be 4 to 6 sentences long! I give Brainliest! Please answer quickly!!Which set of data is represented by the box plot? Find the area of the circle. Round your answer to the nearest hundredth. diameter 3in Jennifer ran 2 miles at the track on Tuesday. If one lap around the track is 1/4 of a mile, how many laps did she run? Help me answer the question for me please! Complete the paragraph about legal conflicts between the Cherokees and white Americans_______ was a Supreme Court case that decided Cherokees lacked the rights to sue in a federal court.A. Cherokee Nation v. South CarolinaB. Cherokee Nation v. GeorgiaC. Worcester v. Georgia_______ was a Supreme Court case that supported the Cherokees and ruled Georgia did not have the right to enforce laws in Cherokee territory.A. Worcester v. GeorgiaB. Cherokee Nation v. GeorgiaC. Choctaws v. Georgia if matter cannot be created nor destroyed where did the matter in the univerce com from ???????BIG BRAIN How does Sales Order Processing is connectedwith Purchase Requisition Processing? Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.29 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12. 19 and 12.25 ounces. The central bank targets the real policy rate, i.e., r = Tt, by setting the nominal interest rate it accordingly, with rt = it - and = Tt-1. The approximate Phillips curve is given - with expectations formation as stated - by: t = t-1 + (m+z) - ax ut, with the specific values of the markup m = 0.025, the catch-all variable z = 0.015 and a = 0.5 in this exercise. The labor force is given by L = 5,000. For the time being, the government follows a balanced budget policy, i. e., G = Tt. The risk premium equals t = 0.03 and the central bank sets the nominal interest rate at Tt = 0.01. (b) Calculate the natural rate of unemployment un, natural output Y, and transform - using the specified values - the Phillips curve from the format given above into the format given in Chapter 9 of the slides and the book, i.e., t Tt-1 = (Yt - Yn). Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. The monthly rents for studio apartments in a certain city have a mean of $900 and a standard deviation of $180. If random samples of size 30 are drawn from the population, identify the mean, wx, and standard deviation, 7, of the sampling distribution of sample means with sample size n how does oxygen and carbon dioxide levels change over time?