An object of mass 2 kg moves in a straight line and is acted upon by aforce of 12t-24 newtons, where t is the time in seconds. initially the opject is 5 meters to the right of the origin, and it comes to rest after 2 seconds.
Find the velocity after one second.
Find the distance traveled by the object in the first two second.

______________________________

 - When calculating powers, you take the base and multiply by the base however what the number of the exponent is. In this case the base is 2. So you do 2 × 2 × 2 × 2 × 2 = 32.

So your answer is \(\bold{96}\).

______________________________

The function is growing exponentially at a rate of 5.5% every year.

The exponential decay equation is given by:-

\(y = (1 \pm r)^n\)

Where r is the rate of decay and A is the initial amount and n is the time period.

The function is given in the question below as:

The function \(f(t) = 1500(1.055)^{60}\) ....(i)

This represents the change in quantity over t days.

As per the given exponential decay equation,

\(\implies f(t) = 1500(1.055)^{60}\)

We can above function rewrite as:

\(\implies f(t) = 1500(1 + 0.055)^{60}\)

\(\implies f(t) = 1500\huge \text(1 + \dfrac{5.5}{100}\huge \text)^{60}\)

\(\implies f(t) = 1500(1 + 5.5\%)^{60}\)

Compare to the standard exponential decay equation, and we get

\(\implies r= 5.5\%\)

Therefore, the function is growing exponentially at a rate of 5.5% every year.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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(a) At t = 1.11 s, the distance from the particle to the origin is 3.15 m. (b) The speed of the particle at t = 1.11 s is 1.86 m/s. (c) The magnitude of the acceleration at t = 1.11 s is 0.32 m/s². (a) At t = 3.4 s, the x-coordinate of the particle is 11.56 m. (b) The y-coordinate of the particle at t = 3.4 s is 17.14 m. (c) The speed of the particle at t = 3.4 s is 4.48 m/s.


(a) To find the distance from the particle to the origin, we use the formula for the magnitude of a vector: distance = √(x² + y²). Plugging in the given values at t = 1.11 s, we calculate the distance to be 3.15 m.
(b) The speed of the particle can be found by taking the magnitude of its velocity vector: speed = √(v_x² + v_y²). Plugging in the given values at t = 1.11 s, we calculate the speed to be 1.86 m/s.
(c) The magnitude of the acceleration can be found using the formula: magnitude of acceleration = √(a_x² + a_y²). Plugging in the given values at t = 1.11 s, we calculate the magnitude of the acceleration to be 0.32 m/s².
For the second scenario, the x-coordinate at t = 3.4 s can be found by plugging the given values into x(t) = a*t + b, which gives us 11.56 m. Similarly, the y-coordinate at t = 3.4 s can be found using y(t) = c*t² + d, which gives us 17.14 m. The speed of the particle at t = 3.4 s can be calculated using the same method as in (b), resulting in a speed of 4.48 m/s.

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The required whole number, is either -19/3 or 7 which satisfied the given conditions

let us consider the whole number be x .

we have given the following

the twice a certain whole number i.e x and subtracted it from 3 times the square of the number leaves 133. Mathematically ,

3x^2 - 2x = 133

=> 3x^2 - 2x - 133 = 0

Factorize the above formula we get

=> (3x + 19)(x - 7)= 0

=> 3x + 19 = 0

=> 3x = -19

=> x = -19/3

=> x - 7 = 0

=> x = 7

Hence, possible value of x a whole number is either equal -19/3 or 7.

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225 = 81 - a2

a2 =225 - 81 = 144

\( \sqrt{144} \)

Answer:

x=5

Step-by-step explanation:

18x+5+18x-5=180(because they are interior angles)

38x=180

=36x/36=180/36

=5degrees

Answer:

The given parameters of the study are;

The number of people in the sample, n = 200

The p-value = 0.013

The average increase between fall and spring semester = $0.35

Therefore, we have;

Given that the p-value is less than 0.05, we reject the null hypothesis, and that there is significant statistical evidence to suggest that there is a difference between the fall and spring semester tuition at universities across the U.S.

Step-by-step explanation:

The result of the test hypothesis is incorrect or should be rejected.

Researchers frequently use P-values to determine if a trend they've seen is statistically significant. The p-value of a statistical test is small enough to reject the null hypothesis of the test, which is referred to as statistical significance.

The likelihood that the null hypothesis is true is P > 0.05. The likelihood that the alternative hypothesis is correct is (1-P) the P-value. The test hypothesis is incorrect or should be rejected if the test result is statistically significant (P≤0.05). There was no effect if the P-value was bigger than 0.05.

We reject the null hypothesis since the p-value is less than 0.05, and there is strong statistical evidence to imply that there is a difference between autumn and spring semester tuition at institutions across the United States.

Hence, the result of the test hypothesis is incorrect or should be rejected.

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Percentage is the way to represent the part of a whole in a fraction of 100.The greatest percent of the increase in the number of jobs from 2006 to 2016 is orthodontist which is 10.94 percent.

In the given table we have to find out the percent of the increase in the number of each job to find out the greatest one.

Percentage is the way to represent the part of a whole in a fraction of 100.

1-Orthodontist-

In 2006 the total number of orthodontists was 9206.

In 2016 the total number of orthodontists was 10214

Percent of increase in this job is,

\(p_{1} =\dfrac{10214-9206}{9206}\times100\)

\(p_{1} =10.94%\)

Hence, percent of the increase in this job is 10.94 present.

2-Sound engineer technician-

In 2006 the total number of Sound engineer technicians was 16125

In 2016 the total number of Sound engineer technicians was 17864

Percent of increase in this job is,

\(p_{2} =\dfrac{17864-16125}{16125}\times100\)

\(p_{2} =10.78%\)

Hence, percent of the increase in this job is 10.78 percent.

3-Police officer-

In 2006 the total number of Police officers was 648982

In 2016 the total number of Police officers was 719041

Percent of increase in this job is,

\(p_{3} =\dfrac{719041-648982}{648982}\times100\)

p_{3} =10.79%

Hence, percent of the increase in this job is 10.79 percent.

4- Editor-

In 2006 the total number of Editors was 122273

In 2016 the total number of Editors was 124135

Percent of increase in this job is,

\(p_{2} =\dfrac{124135-122273}{122273}\times100\)

\(p_{4} =1.52%\)

Hence, percent of the increase in this job is 1.52 percent.

Hence, the greatest percent of the increase in the number of jobs from 2006 to 2016 is orthodontist which is 10.94 percent.

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Answer:

Answer is A on edge

Step-by-step explanation: Took the test

Answer:

312

Step-by-step explanation:

1000x.078=78 interest per year

78 interest x4 years=312 interest after 4 years.

Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

Answer:

5/9

Step-by-step explanation:

0.813

Probability is the likelihood or chance that an event will occur. The probability that the student was male OR got a/an "C" is as shown:

P(male or a C) = Pr(male) + Pr(C) - Pr(male and C)

Pr(male U C) = Pr(male) + Pr(C) - Pr(male n C)

Given the following probabilities

Substitute the probability to have:

Hence the probability that the student was male OR got a/an "C" is 0.813

Answer:

-3 x^a y^(b + f) z^(c + g)

Step-by-step explanation:

Hope this will help

Answer:

A) Independent variable is "c"

Dependent variable is "p"

B) Yes, it's a function

C) p = 7c - 31

D)domain of the function: 0 ≤ c ≤ 40

Range of the function: 0 ≤ p ≤ 249

Step-by-step explanation:

A) c is the total number of cars washed and p is the profit. The profit depends on the total number of cars washed. Hence, profit(p) is the dependent variable while "c" is independent variable

B) Yes it's a function because for each number of cars washed, there is a distinct value of profit made.

C) We are told that the liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$.

$31 is cost to wash one car. Thus profit made per car is;

p = 7c - 31

D) The cost of $31 liquid soap is enough to only wash a maximum of 40 cars. This means the domain for the cars is from 0 cars to 40 cars

Thus;

domain of the function is 0 ≤ c ≤ 40

The profit function is given in answer C above as p = 7c - 31.

Now, if 0 cars are washed they will make zero profit but if 40 cars are washed then;

p = 7(40) - 31

p = 280 - 31

p = 249

Range of the function: 0 ≤ p ≤ 249

Answer:

25.6125

Step-by-step explanation:

since 25 is a whole number, it'd be 25.ˣˣˣˣ

now all you have to do it divide the fraction so 49 ÷ 80 =  0.6125

last step is to add ⇒ 25 + 0.6125 = 25.6125

Answer:

The correct answers are:

How much would your investment be worth at the end?

Answer: $550

What equation should you use to calculate this?

Answer: DA 500 (1+0.02*5)

Step-by-step explanation:

Answer:=−7

no problem!

Answer:

x= -7

Step-by-step explanation:

3x+15=-2x-20

Step 1 move the variable (x)  to the left hand and change its sign

3x+2x+15=-20

Move the constant (15) and change it's sign

3x+2x=-20-15

5x=-20-15

5x=-35

Divide both sides by 5

x= -7

The derivative of y = \(x^(p/q)\) with respect to x is y' =\((p/q)x^(p/q-1)\) and this is proved with the help of power rule using  implicit differentiation

To understand the proof of the power rule using implicit differentiation, let's start by considering the equation y = x^(p/q), where p and q are integers. We want to find the derivative of y with respect to x, denoted as y'.

Step 1: Take the qth power of both sides of the equation.

By raising both sides of the equation y = \(x^(p/q)\) to the power of q, we obtain \(y^q = (x^(p/q))^q = x^p.\)

Step 2: Differentiate both sides of the equation implicitly.

To find the derivative of y with respect to x, we differentiate both sides of the equation \(y^q = x^p\) with respect to x using the rules of differentiation.

On the left-hand side, we have a composition of functions: \(y^q\). By applying the chain rule, we differentiate the outer function \(y^q\) and multiply it by the derivative of the inner function y with respect to x.

On the right-hand side, we have\(x^p\), which we can differentiate directly using the power rule.

Differentiating \(y^q\):

\(d/dx\)\((y^q)\) = \(q(y^(q-1)) * (dy/dx).\)

Differentiating \(x^p\):

\(d/dx (x^p) = px^(p-1).\)

Step 3: Solve for y'.

Setting the derivatives equal, we have \(q(y^(q-1)) * (dy/dx) = px^(p-1).\) Now, we solve for dy/dx (which is y').

Dividing both sides of the equation by \(q(y^(q-1))\), we get:

\((dy/dx) = (px^(p-1))/(q(y^(q-1))).\)

Simplifying further, we can write y' as:

\(y' = (p/q)x^(p-1).\)

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The connection string for SQL Server using Windows Authentication is as follows:

Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;

Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.

Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.

Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.

Use semicolons (;) to separate the different parts of the connection string.

Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.

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In the first iteration, we obtained approximate values of x1(1) ≈ 1.67 and x2(1) = 8. In the second iteration, we updated the values to x1(2) ≈ -3.67 and x2(2) ≈ 26.35. In the third iteration, the values were further updated to x1(3) ≈ -38.77 and x2(3) ≈ 198.85.

To solve the set of linear algebraic equations using the Gauss-Seidel method with the given initial values and accuracy requirement, we can follow these steps:

Step 1: Rearrange the equations in terms of x1 and x2:

Equation 1: 3x1 + 2x2 = 5

Equation 2: 5x1 + x2 = 8

Step 2: Write the equations in iterative form:

Equation 1: x1(k+1) = (5 - 2x2(k)) / 3

Equation 2: x2(k+1) = (8 - 5x1(k)) / 1

where x1(k) and x2(k) represent the initial values and x1(k+1) and x2(k+1) represent the updated values in the kth iteration.

Step 3: Initialize the values and set the desired accuracy:

Let x1(0) = 0 and x2(0) = 0 (given initial values)

Set the desired accuracy as ε = 0.03

Step 4: Perform iterations until the desired accuracy is reached:

Iterate the following steps until the condition |x1(k+1) - x1(k)| < ε and |x2(k+1) - x2(k)| < ε are satisfied:

- Calculate the updated values using the iterative equations:

 x1(k+1) = (5 - 2x2(k)) / 3

 x2(k+1) = (8 - 5x1(k)) / 1

- Calculate the differences:

 Δx1 = |x1(k+1) - x1(k)|

 Δx2 = |x2(k+1) - x2(k)|

- Check if the differences are less than ε:

 If Δx1 < ε and Δx2 < ε, exit the iteration.

Step 5: Output the solution:

The solution will be the values of x1 and x2 obtained in the final iteration.

Let's perform the iterations:

Iteration 1:

x1(1) = (5 - 2x2(0)) / 3 = (5 - 2(0)) / 3 ≈ 1.67

x2(1) = (8 - 5x1(0)) / 1 = (8 - 5(0)) / 1 = 8

Iteration 2:

x1(2) = (5 - 2x2(1)) / 3 = (5 - 2(8)) / 3 ≈ -3.67

x2(2) = (8 - 5x1(1)) / 1 = (8 - 5(-3.67)) / 1 ≈ 26.35

Iteration 3:

x1(3) = (5 - 2x2(2)) / 3 = (5 - 2(26.35)) / 3 ≈ -38.77

x2(3) = (8 - 5x1(2)) / 1 = (8 - 5(-38.77)) / 1 ≈ 198.85

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Hence the answer is 480ml

Step-by-step explanation:

Given Elena wonders how much water it will take to fill her cup. She drops her pencil in the cup and notice it just fit diagonally. The pencil is 17cm long (hypotenes) and the cup is 15cm tall.

To find how much water it can hold

SOLUTION

s

\( \sqrt{x {} ^{ 2} + x {}^{2} + 15 {}^{2} = 17 } \)

\(2x {}^{2} = 64\)

\(x {}^{2} = 32\)

\(x = 5.66\)

therefore volume of the cup

\(5.66 \times 5.66 \times 15cm| \)

480cm³= 480ml

Answer:

Step-by-step explanation:

plug the equations into Desmos

as attached

y = -3x-6

x + 3y = 6

3y = -x +6

y = -1/3x +2

-3x-6 = -1/3x +2

-8/3x = 8

x = - 3

y=-3(-3)-6

y = 9-6

y = 3

Espero que te sirva de ayuda.

Answer:

5 y 5

Step-by-step explanation:

Answer:

0.119

Step-by-step explanation:

Based on the concept of conditional probability, the probability that the first iPod is defective and the others are not defective is approximately 0.1842

Conditional Probability is a term that is used to describe the chances that some outcome occurs given that another event has also occurred.

Generally, the functional probability is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening

In this case, to find the answer we break down the problem step by step:

Step 1: Find the probability that the first iPod is defective.

Since there are 3 defective iPods out of 20 total the probability of selecting a defective iPod on the first draw is 3/20.

Step 2: Find the probability that the second and third iPods are not defective.

After selecting a defective iPod there are 19 remaining iPods in the box out of which 17 are not defective.

Hence, the probability of selecting a non-defective iPod on the second draw is 17/19.

Also, given that the probability of selecting a non-defective iPod on the third draw (assuming the previous two iPods were not defective) is 16/18.

Step 3: Finding the overall probability.

The overall probability of the first iPod being defective and the second and third iPods being non-defective can be computed by multiplying the probabilities of each step:

Probability = (3/20) * (17/19) * (16/18)

= (51/380) * (16/18)

= 0.1842105

Therefore, in this case, it is concluded that the correct answer is approximately 0.1842 or 18.42%.

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The mean of this sample of car prices can be calculated by adding all the prices and dividing by the total number of dealers:

($35,700 x 2) + ($35,900 x 1) + ($36,200 x 3) + ($37,400 x 2) + ($37,900 x 2) = $326,500

$326,500 / 10 dealers = $32,650 (mean price)

To calculate the standard deviation, we first need to find the variance:

1. Subtract the mean from each individual price:

($35,700 - $32,650) = $3,050
($35,700 - $32,650) = $3,050
($35,900 - $32,650) = $3,250
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($36,200 - $32,650) = $3,550
($37,400 - $32,650) = $4,750
($37,400 - $32,650) = $4,750
($37,900 - $32,650) = $5,250
($37,900 - $32,650) = $5,250

2. Square each of these differences:

$3,050^2 = $9,302,500
$3,050^2 = $9,302,500
$3,250^2 = $10,562,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$3,550^2 = $12,602,500
$4,750^2 = $22,562,500
$4,750^2 = $22,562,500
$5,250^2 = $27,562,500
$5,250^2 = $27,562,500

3. Add up all of these squared differences:

$9,302,500 + $9,302,500 + $10,562,500 + $12,602,500 + $12,602,500 + $12,602,500 + $22,562,500 + $22,562,500 + $27,562,500 + $27,562,500 = $167,052,500

4. Divide the total by the number of dealers minus 1 (this is called the sample variance):

$167,052,500 / 9 = $18,561,388.89

5. Take the square root of the sample variance to get the standard deviation:

√$18,561,388.89 = $4,307.17 (standard deviation)

So the mean price of this sample of car prices is $32,650 and the standard deviation is $4,307.17.

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The circumference of circle is 132 centimeter.

What is circumference of circle?

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.

The Circumference (or) perimeter of circle = 2πR

given, radius of the circle is 21 centimeter

circumference = 2*22/7*21

= 2*22*3

=44 *3

=132

Therefore, the circumference is 132 centimeter.

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The correct answer is C. A family may own both a minivan and an SUV. The events are not disjoint, so the addition rule does not apply.

The addition rule of probability states that if two events are disjoint (or mutually exclusive), meaning they cannot occur simultaneously, then the probability of either event occurring is equal to the sum of their individual probabilities. However, in this case, owning a minivan and owning an SUV are not mutually exclusive events. It is possible for a family to own both a minivan and an SUV at the same time.

When using the addition rule, we assume that the events being considered are mutually exclusive, meaning they cannot happen together. Since owning a minivan and owning an SUV can occur together, adding their individual probabilities will result in double-counting the families who own both types of vehicles. This means that simply adding the percentages of families who own a minivan (53%) and those who own an SUV (24%) will overestimate the total percentage of families who own either a minivan or an SUV.

To calculate the correct percentage of families who own either a minivan or an SUV, we need to take into account the overlap between the two groups. This can be done by subtracting the percentage of families who own both from the sum of the individual percentages. Without information about the percentage of families who own both a minivan and an SUV, we cannot determine the exact percentage of families who own either vehicle.

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Answer

Probability that the next time Bella chooses a Lego, it will be a white or blue

= (9/20)

= 0.45

Explanation

The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.

Number of white or blue legos = 10 + 8 = 18

Total number of legos = 4 + 10 + 8 + 18 = 40

Probability that the next time Bella chooses a Lego, it will be a white or blue

= (18/40)

= (9/20)

= 0.45

Hope this Helps!!!