AP Macroeconomics students were given an exam on a particular topic. Each week, they were tested with a comparable exam on the same topic and the average
score for the class was measured the function M (1) = 75 - 10log(t + 3) models the average score for the class after tweeks. How many weeks will it take until the
average score of the class is 65?
A. 10 weeks
B. 9 weeks
C. 8 weeks
D. 7 weeks ✅

the correct answer is D

Answer: 1.54166666667 Hope that helped

Answer:

1/625

Step-by-step explanation:

Answer:

2) Add 21 to both sides

Step-by-step explanation:

When solving \(16x-21=52\) for \(x\), our goal to isolate \(x\) such that we have \(x\) set equal to something.

Therefore, we want to start by adding 21 to both sides. This leaves us with \(16x=73\) and we are one step closer to isolating \(x\).

The difference in rainfall between the wettest and driest months is the amount of precipitation.

Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.

The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.

The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.

The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.

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Answer:

2 games

Step-by-step explanation:

Sanjay = $1 + $4 x amount of games

Hunter = $3 + $3 x amount of games

$1 + $4 x 2 = $9

$3 + $3 x 2 = $9

Answer:

0.128rad/sec

Step-by-step explanation:

Let x represent the between the man and the point on the path

θ = the angle

dx/dt = 4 ft/s

dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight

tan θ = x/20 ft

Cross Multiply

20tan θ = x

dx/dt = 20sec² θ dθ/dt

dθ/dt = 1/20 × cos² θ dx/dt

dθ/dt= 1/20 × cos² θ × 4

dθ/dt = 1/5 × cos² θ

Note : cos θ = 4/5

dθ/dt = 1/5 × (4/5)²

dθ/dt = 16/125

dθ/dt = 0.128rad/sec

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

-9/0

Step-by-step explanation:

(x1, y1) and (x2, y1)

(-8, 3) and (-8,-6)

slope/m = y2 - y1 / x2 -x1

= -6 -3 / -8 -(-8)

= -6 -3 / -8 + 8

= -9 / 0

A salary slip for the month of March 2023 with information given below.

Salary Slip - March 2023

Employee Details:

Name: [Employee Name]

Employee ID: [Employee ID]

Designation: [Employee Designation]

Earnings:

Basic Salary: [Basic Salary]

House Rent Allowance (HRA): [HRA]

Dearness Allowance (DA): [DA]

Incentive: [Incentive]

Total Earnings: [Total Earnings]

Deductions:

Provident Fund (PF): [PF]

Insurance: [Insurance]

Loss of Pay (LOP): [LOP]

Total Deductions: [Total Deductions]

Net Pay: [Net Pay]

Breakdown:

Basic Salary: 50% of CTC (18L) = [Basic Salary]

HRA: 20% of Basic Salary = [HRA]

DA: 12% of Basic Salary = [DA]

Incentive: 75% of target completion = [Incentive]

Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]

PF: 12% of Basic Salary = [PF]

Insurance: Rs. 2500 = [Insurance]

LOP: [LOP]

Total Deductions = PF + Insurance + LOP = [Total Deductions]

Net Pay = Total Earnings - Total Deductions = [Net Pay]

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Answer:

Step-by-step explanation:

Based on the fact that the motorboat is 10km south of the lighthouse and is travelling on a bearing of 053°, the shortest distance between the motorboat and the lighthouse is 7.986 km.

The motorboat is 10km south of the lighthouse. As it is travelling on a bearing of 053°, we can model the situation as a right angled triangle where the shortest distance between the two is the hypotenuse of the triangle.

The shortest distance can then be found to be:

= 10 x Sin 53°

= 10 x 0.7986

= 7.986 km

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the set of vectors b over Rm so that Ax=b has (at least) a solution, where the rank is the dimension of a column space. False: The rank-nullity theorem states that the null space is 0 if m=n.

Principle of Linear Pairs Two angles are supplementary if they form a pair along a straight line. theorem addition Two angles are congruent if they are the same angle's supplements. The principle of congruent complements Two angles are congruent if they are the same angle's complements.

Theorem 7: To enquire about: the connection here between angle opposite the larger of two sides and also the degree opposite the smaller of two sides. both the side across from the smaller of the two aspects and the side across from the greater of the two angles.

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Answer:

10x=40

x=40/10

x=4

4 is the answers, not -4

Step-by-step explanation:

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Answer:

10 square inches

Step-by-step explanation:

cost of a plain t-shirt = $10

cost of 1 square inch of design addition = $1.50

let there be x square inches of design

then cost of x square inches of design = x*cost of 1 square inch of design

                                                                 = 1.50*x = 1.5x

Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design   = 10 + 1.5 x

It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only

Thus,

10 + 1.5 x = 25

=> 1.5x = 25-10 = 15

=> x = 15/1.5 = 10

Thus, Makeeya can  put 10 square inches of design on her T-shirt.

The Area of the shaded portion is: 72 square inches

The formula for the area of a triangle is given by the formula:

Area = ¹/₂ * base * height

Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.

Thus:

Area of larger triangle = ¹/₂ *  17 * 13 = 110.5 square inches

Area of smaller triangle =  ¹/₂ * 11 * 7 = 38.5 square inches

Thus:

Area of shaded portion = 110.5 square inches - 38.5 square inches

Area of shaded portion = 72 square inches

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Step-by-step explanation:

c= 105

a = 180 - 105 = 75

105 + 105 + 75= 285

360 - 285 = 75 = b

Answer:

(-2,-3)

Step-by-step explanation:

Answer: The two numbers that multiply to -65 and add to -8 are -13 and 5.

Steps: Here are the steps to find two numbers that multiply to -65 and add to -8:

Write down the equation x * y = -65 where x and y are the two numbers you’re looking for.

Write down the equation x + y = -8.

Solve for one of the variables in one of the equations. For example, solving for x in the second equation gives us x = -8 - y.

Substitute this expression for x into the first equation: (-8 - y) * y = -65.

Solve this quadratic equation for y: -y^2 - 8y + 65 = 0.

Use the quadratic formula to find the values of y: y = (-(-8) +/- sqrt((-8)^2 - 4 * (-1) * 65)) / (2 * (-1)).

This gives us two possible values for y: -13 and 5.

Substitute these values back into one of the original equations to find the corresponding values of x. For example, when y = -13, we have x = -8 - (-13) = 5. When y = 5, we have x = -8 - 5 = -13.

So, the two numbers that multiply to -65 and add to -8 are -13 and 5.

The simplified expression of -7(3z + 5t - 3g) is  -21z - 35t + 21g.

An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication etc.

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's simplify the expression as follows:

-7(3z + 5t - 3g)

Hence, open the brackets

-7(3z + 5t - 3g) = -21z - 35t + 21g

Therefore, the simplified expression is -21z - 35t + 21g.

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Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Multiplication has the associative property, this means that you can compute 14 x 2 x 3, computing first 14 x 2 = 28, and then 28 x 3 = 84; or you can compute first 2 x 3 = 6, and then 14 x 6 = 84 (second option)

Answer: 72 square units

Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.

Answer: Just the first one

Step-by-step explanation:

Both coordinates need to be negative

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

The answer is the garbage truck had 6 wheels

Step-by-step explanation:

Since the semitruck has 18 wheels and the semitruck had 3 times more wheels than a garbage truck all you would have to do is divide 18 by 3 and you will get 6 as your answer.

Hope this helps, its my first time answering.

Answer:

a

\(P(X \ge 1) = 0.509 \)

b

\(P(X  \ge 1) = 0.6807 \)

Step-by-step explanation:

From the question we are told that

   The number of students in the class is  N  =  20  (This is the population )

   The number of student that will cheat is  k =  3

   The number of students that he is focused on is  n  =  4

Generally the probability distribution that defines this question is the  Hyper geometrically distributed because four students are focused on without replacing them in the class (i.e in the generally population) and population contains exactly three student that will cheat.

Generally  probability mass function is mathematically represented as

      \(P(X = x) =  \frac{^{k}C_x * ^{N-k}C_{n-x}}{^{N}C_n}\)

Here C stands for combination , hence we will be making use of the combination functionality in our calculators  

Generally the that  he finds at least one of the students cheating when he focus his attention on four randomly chosen students during the exam is mathematically represented as

      \(P(X \ge 1) =  1 - P(X \le 0)\)

Here  

   \(P(X \le 0) =  \frac{ ^{3} C_0 *  ^{20 - 3} C_{4- 0}}{ ^{20}C_4}\)

   \(P(X \le 0) =  \frac{ ^{3} C_0 *  ^{17} C_{4}}{ ^{20}C_4}\)

   \(P(X \le 0) =  \frac{ 1 *  2380}{ 4845}\)

    \(P(X \le 0) =  0.491\)

Hence

    \(P(X \ge 1) =  1 - 0.491\)

     \(P(X \ge 1) = 0.509 \)

Generally the that  he finds at least one of the students cheating when he focus his attention on six randomly chosen students during the exam is mathematically represented as

    \(P(X \ge 1) =  1 - P(X \le 0)\)

   \(P(X  \ge 1) =1- [  \frac{^{k}C_x * ^{N-k}C_{n-x}}{^{N}C_n}] \)

Here n =  6

So

    \(P(X  \ge 1) =1- [  \frac{^{3}C_0 * ^{20 -3}C_{6-0}}{^{20}C_6}] \)

    \(P(X  \ge 1) =1- [  \frac{^{3}C_0 * ^{17}C_{6}}{^{20}C_6}] \)

    \(P(X  \ge 1) =1- [  \frac{1  *  12376}{38760}] \)

    \(P(X  \ge 1) =1- 0.3193 \)

    \(P(X  \ge 1) = 0.6807 \)

Answer:

No multiplying both quantities in the ratio 60 : 36 by 1  would not give the answer .

But multiplying both quantities in the ratio 60 : 36 by 1/6  would solve it.

Step-by-step explanation:

Multiplying any number or ratio by 1 gives the same answer no matter what the expression or how much bigger the number is.This will not give the solution .

If it is multiplied with a fraction like 1/6  that would give the correct answer.

Multiplying it with 1/6 reduces the ratio and gives a better estimate.

A:B

60:36

60*1/6: 36*1/6

10: 6

Meaning that for a total of 16 there are 10 of category A and 6 of category B.

But if we do the same procedure with the answer is same which does not solve the question.

A:B

60:36

60*1: 36*1

60: 36