A company manufacturing oil seals wants to establish and R control charts on the process. There are 25 preliminary samples of size 4 on the internal diameter of the seal. The summary data (in mm) are as follows:
∑ =1,253.75, ∑=14.08.
(1) Find the control limits that should be used on the and R control charts.
(2) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation.

Answers

Answer 1
(1) To find the control limits for the x-bar and R charts, we first need to calculate the center line and the standard deviation of the sample means and ranges.

The center line for the x-bar chart is:
CLx-bar = (∑x) / (n * k) = 1,253.75 / (4 * 25) = 7.92

The center line for the R chart is:
CL(R) = (∑R) / (n * k) = 14.08 / (4 * 25) = 0.14

The standard deviation of the sample means is:
σx-bar = R / d2 = 0.14 / 1.023 = 0.1366

The standard deviation of the sample ranges is:
σR = D4 * R-bar = 2.282 * 0.14 = 0.319

The upper and lower control limits for the x-bar chart are:
UCLx-bar = CLx-bar + A2 * σx-bar = 7.92 + 0.577 * 0.1366 = 7.999
LCLx-bar = CLx-bar - A2 * σx-bar = 7.92 - 0.577 * 0.1366 = 7.840

The upper and lower control limits for the R chart are:
UCLR = D3 * R = 0 * 0.14 = 0
LCLR = D3 * R = 0 * 0.14 = 0

(2) Assuming that the 25 preliminary samples plot in control on both charts, we can estimate the process mean and standard deviation using the x-bar chart. The center line of the x-bar chart is the estimate of the process mean, which is 7.92. The standard deviation of the sample means is the estimate of the process standard deviation, which is 0.1366.

Related Questions

which average is the most representative of the data​

Answers

The median is the average that is most representative of the data.

How to obtain the median of a data-set?

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.

As the data-set is not symmetric, it means that the median is the average that is most representative of the data.

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During 2022, Sam Reed purchased 350 shares of common stock issued by New Generation Electronics for $7800 including commission. Later in the same year, Sam sold the shares for $8400 after commission. Calculate the following. (Round all answers to two decimal places.)

1. Profit on this stock transaction: $
2. Percentage return on investment: %

Answers

This stock trade generated a profit of $600 and a 7.69% return on investment.

The total amount received from selling the shares, after commission.

The total cost of purchasing the shares = $7800

Total amount received from selling the shares = $8400

The commission paid for purchasing the shares and for selling the shares will cancel out since they will both be subtracted, so we do not need to consider them.

Profit on this stock transaction = Total amount received - Total cost of purchasing

= $8400 - $7800

= $600

To calculate the percentage return on investment, we need to divide the profit by the total cost of purchasing the shares, and then multiply by 100 to express it as a percentage.

Percentage return on investment = (Profit / Total cost of purchasing) x 100%

= ($600 / $7800) x 100%

= 7.69%

Therefore, the profit on this stock transaction was $600 and the percentage return on investment was 7.69%.

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It is possible to select 3 restraunts in how many different ways?

Answers

There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

In mathematics, what are a permutation and combination?

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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Suppose that you borrow $10,000 for four years at 8% toward the purchase of a car. Use PMT=
find the monthly payments and the total interest for the loan.
The monthly payment is
(Do not round until the final answer. Then round to the nearest cent as needed.)
ample
Get more help
Clear all
-|C
Check answer

Answers

Answer:

To find the monthly payments, we can use the PMT function in Excel or a financial calculator. The formula is:

PMT(rate, nper, pv)

where rate is the interest rate per period, nper is the total number of periods, and pv is the present value (i.e. loan amount).

For this problem, the interest rate is 8%/12 = 0.0066667 per month, the number of periods is 4 years * 12 months/year = 48 months, and the present value is $10,000. Therefore, the formula becomes:

PMT(0.0066667, 48, 10000)

Evaluating this formula gives a monthly payment of $242.42.

To find the total interest for the loan, we can multiply the monthly payment by the number of periods (i.e. 48) and subtract the loan amount. This gives:

total interest = monthly payment * number of periods - loan amount

total interest = $242.42 * 48 - $10,000

total interest = $2,678.16

Therefore, the monthly payments are $242.42 and the total interest for the loan is $2,678.16.

Step-by-step explanation:

Graph the equation y=-x^2+12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answers

Answer:

To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.

The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).

To find the roots, we need to set y=0 and solve for x:

0=-x^2+12x-35

x^2-12x+35=0

(x-5)(x-7)=0

x=5 or x=7

So the roots are (5,0) and (7,0).

The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.

Tickets numbered 1−10 are drawn at random and placed back in the pile. Find the probability that at least one ticket numbered with a 6 is drawn if there are 4 drawings that occur. Round your answer to two decimal places.

Answers

Answer:

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

(1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.

Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?

A. d= 163 + t

B. d= 163/2 × t/2

C. d= 163t

D. d= 81.50t

Answers

Answer:

b but I'm not exactly sureb

A square fence has a perimeter of (24x + 36) units. What is the length of one side of the fence?

Answers

The perimeter of a square fence is given by 4s, where s is the length of one side of the square. We can set up the equation 4s = 24x + 36 and solve for s.

Dividing both sides by 4, we get s = 6x + 9.

Therefore, the length of one side of the fence is 6x + 9 units.

Answer:

The perimeter of a square is four times the length of one side, so we can write:

4s = 24x + 36

Dividing both sides by 4, we get:

s = 6x + 9

Therefore, the length of one side of the fence is 6x + 9 units.

Step-by-step explanation:

PLEASE HELP - A triangle with side lengths a, b, and c is shown below. Which statement about the side lengths must be true?

Answers

Answer:

  A

Step-by-step explanation:

You want to know which inequality must be true regarding the side lengths of a triangle.

Triangle inequality

The triangle inequality requires the sum of any two side lengths be greater than the length of the third side:

  a + b > c . . . . . choice A

__

Additional comment

This means it must also be true that ...

  a + c > b

  b + c > a

Of course, this means the sum of the two shortest sides must be more than the longest side. It also means any side length must lie between the sum and difference of the other two side lengths:

  |a - b| < c < a + b

The version of this inequality most often seen uses the > or < symbol. Some authors use the ≥ or ≤ symbol instead. This allows triangles that look like a line segment and have zero area.

an aquarium is 3 feet wide, 1.5 feet tall, and 5 feet long. The bottom is covered with gravel to a height of 3 inches. the tank will be filled with water to 3 inches below the top. what is the volume of the tank that will be filled with water in ft cubed

Answers

The volume of the tank that will be filled with water through which the given relation is satisfied is [tex]22.5ft^{3}[/tex]

What about volume of cuboid?

The volume of a cuboid is the amount of space occupied by the three-dimensional solid figure known as a cuboid. A cuboid is a box-shaped object with six rectangular faces, where each face has a pair of parallel sides, and opposite faces are equal in size and shape.

The formula for calculating the volume of a cuboid is:

Volume = length x width x height

where length, width, and height are the three dimensions of the cuboid.

The unit of measurement for the volume of a cuboid will depend on the unit of measurement used for each dimension. For example, if the length, width, and height are measured in centimeters, then the volume of the cuboid will be expressed in cubic centimeters (cm³). Similarly, if the dimensions are measured in meters, the volume will be expressed in cubic meters (m³).

According to the given information:

As, we know that volume of cuboid is = length x breath x height

Here, length = 5 feet, breath = 3 feet and height = 1.5 feet

Volume of the aquarium = 5 x 3 x 1.5 =  [tex]22.5ft^{3}[/tex]

So, the given result is  [tex]22.5ft^{3}[/tex]

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For what values of x and y are the triangles to the right congruent by​ HL?

Answers

The values  of x and y that make the triangles congruent by HL are:

x = 3 and y = 1

Congruent triangles: Calculating the values of x and y

From the question, we are to determine the values of x and y that make the triangles congruent by HL.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Thus,

For the triangles to be right congruent by HL

x = y + 2

and

x + 1 = 4y

Solve the equations simultaneously

Substitute x = y + 2 in the second equation

x + 1 = 4y

y + 2 + 1 = 4y

y + 3 = 4y

3 = 4y - y

3 = 3y

Divide both sides by 3

3/3 = 3y/3

1 = y

Therefore,

y = 1

Substitute the value of y into the first equation

x = y + 2

x = 1 + 2

x = 3

Hence,

The values are:

x = 3 and y = 1

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According to the association of public and land grant universities (aplu) graduate students represents only 15% of post secondary students, but account for approximately 40% of the current student loan balances if the nations current studen loan balance is at 1.5 trillion estimate the amount of student debt held by graduate students by converting 1.5 trillion and 40% (0.4 as a decimal) to scientific notation then multiplying, give your answer in scientific notation.

Answers

I’m not sure I’m so sorry :(

The solids are similar.
Find the surface area of
solid B to the nearest
hundredth.
Cylinder A
24 mm
S = 594 mm²
Cylinder B
16 mm
The surface area of solid B is
square millimeters.

Answers

Answer:

264π

Step-by-step explanation:

Horatio has $230 to be used only on his car. He
wishes to save $160 of this money and spend $24.95 on
an oil change. Horatio knows that gas costs $3.81 per
gallon. Which of the following show how many gallons
of gas (g) he could buy? Select all that apply.
A g≤11.82
B g≤60.37
C 3.81g ≤45.05
D 3.81g ≤ 230 +160+24.95
E 160 + 24.95 +3.81g ≤ 230
184.95 +3.81g ≤ 45.05
F 184.95 + 3.81g < 45.05

Answers

The statement that shows the quantity of gallons of gas that he can buy would be =g≤11.82. That is option A.

How to calculate the quantity of gallons Horatio is able to buy?

The total number of money he has to spend on his vehicle = $230

The amount of money he wishes to save = $160

The remaining amount he can spend = 230+160 = $70

The amount he wishes to spend on oil change = $24.95

The remaining amount = 70-24.95

= $40.05

The cost per gallon of gas = $3.81 per gallon.

The quantity of gallons of gas he can purchase = 40.05/3.81 = 10.51 gallons.

Therefore the quantity of gallons of gas he can purchase would be g≤11.82

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Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function f (x) = 10\x. Suppose the width of the rectangle increases 1 unit, while the area remains constant. Which graph models the length of the new rectangle?

please explain the answer step by step and explain why you chose the option you chose.​

Answers

In linear equation, The graph in option 3 models the length of the new rectangle.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

According to the problem,

width of the rectangle is  x units

Area of the rectangle is 10 square units

Length of the rectangle is given by f(x) = 10/x

Now if width becomes (x+1) units

∴ Length will be represented as 10/(x+1)

Now from the given options we need to find the exact graph of              f(x) = 10/(x +1)

Here if x = 4 , y =2

So the point (4 , 2) is satisfied which is only happening in the graph of option 3

Option 3 represents the correct graph.

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What is the midpoint of the line segment graphed below?

Answers

The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).

Given that:

Endpoints, (-1, 5) and (-8, -4)

The coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]

(x, y) = (-9 / 2, 1 / 2)

(x, y) = (-4.5, 0.5)

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Need Help fast please

Answers

A graph of the transformed function [tex]y=\frac{1}{(x+2)^2} +5[/tex] is shown in the image attached below.

What is a translation?

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function is [tex]y = \frac{1}{x^{2} }[/tex], it ultimately implies that the transformed function would be created by translating the parent function to the left by 1 units and 5 units upward as shown below.

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​,Kofi, Adoma and Esenam are three siblings, Kofi is x years older than Adoma and Adoma is y years older than Esenam. a. How much older than Esenam is Kofi ? b. If Esenam is 5 years old, how old is (i) Adoma (ii)Kofi​

Answers

a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.

b. (i) Adoma = (5 + y) years

   (ii) Kofi = (5 + (x+y)) years

What is a word problem?

Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.

In the given question, we have;

Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;

K = A + x ...... i

A = E + y........ ii

substitute i into ii

K = (E + y) + x

  = E + (x + y)

K = E + (x + y) ........ iii

Thus,

a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.

b. The age of Adoma = 5 + y years

ii. The age of Kofi = 5 + (x + y) years

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The number of bacteria in a certain population is predicted to increase according to a continuous exponential growth model, at a relative rate of 12% per hour. Suppose that a sample culture has an initial population of 535 bacteria. Find the population predicted after two hours, according to the model.
Do not round any intermediate computations, and round your answer to the nearest tenth.

Answers

The population predicted after two hours is approximately 666.5 bacteria as they have exponential growth.

The continuous exponential growth model is given by the formula:

P(t) = P0 * [tex]e^{(rt)[/tex]

where P0 is the initial population, r is the relative growth rate (expressed as a decimal), t is the time in hours, and P(t) is the predicted population after t hours.

In this case, P0 = 535, r = 0.12 (12% per hour), and t = 2. Plugging in these values, we get:

P(2) = 535 * [tex]e^{(0.12*2)[/tex] ≈ 666.5

Therefore, the population predicted after two hours is approximately 666.5 bacteria (rounded to the nearest tenth).

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A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the perimeter and the area

Answers

Answer:

Parameter= 98ft

Area=180ft^2

Step-by-step explanation:

Parameter= Length times 2 plus width times 2 or

L2+W2=P 4(2)+45(2)=8+90=98

Area= LxW=A^2

4x45=180^2

Perimeter = 2(length + width)
Perimeter = 2(45 + 4)
Perimeter = 2(49)
Perimeter = 98 feet

Area = length x width
Area = 45 x 4
Area = 180 square feet

The one-to-one functions g and h are defined as follows.

Answers

Fro the one to one functions g and h defined, the value of :

g⁻¹(6) = 2

h⁻¹(x) = 7x + 8

(h⁻¹ o h)(1) = 1

Given one to one functions h and g.

We have that,

g(2) = 6

So, g⁻¹(6) = 2

We have,

y = (x - 8) / 7

Switch x and y.

x = (y - 8) / 7

7x = y - 8

y = 7x + 8

So, h⁻¹(x) = 7x + 8

(h⁻¹ o h) (x) = h⁻¹ (h(x))

                  = h⁻¹ ((x - 8) / 7)

                  = 7 ((x - 8) / 7)) + 8

                  = x - 8 + 8

                  = x

(h⁻¹ o h) (1) = 1

Hence the functions are found.

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Write an equation in the form y = mx +b of the line that is described.
The line rises from left to right. It passes through the origin and a second point with equal x and y
coordinates.
The equation of the line is y Write your response here...

Answers

Answer:

I have my answer in the picture i will upload

please check the below pictures.

PLEASE HELP ME!!! Unit 10 Circles Homework Inscribed Angles questions 15 and 17

Answers

Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127°         16. m(PL) = 62°

How to Apply the Inscribed Angle Theorem?

15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:

m<DEF = 1/2(m(FGD)

Plug in the values:

6x + 37 = 1/2(19x - 31)

2(6x + 37) = 19x - 31

12x + 74 = 19x - 31

12x - 19x = -74 - 31

-7x = -105

x = 15

m<DEF = 6x + 37 = 6(15) + 37 = 127°

16. m<LMP = m<LNP

Plug in the values:

5x - 19 = 2x + 11

5x - 2x = 19 + 11

3x = 30

x = 10

m(PL) = 2(LMP) [based on the inscribed angle theorem]

Plug in the values:

m(PL) = 2(5x - 19)

Plug in the value of x:

m(PL) = 2(5(10) - 19)

m(PL) = 62°

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Richard is saving money for a down payment on a car. He opens a savings account at his local bank and deposits $500. He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate. What does the y-intercept of linear model represent?

Question 8 options:

The date the savings account was started.


The starting amount in his savings account.


The date when he will have enough money.


The largest amount that he can save.

Answers

In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate  y-intercept of linear model represent B. The starting amount in his savings account.

How can the linear model be interpreted?

It should be noted that in a  linear equation the y intercept  can be seen as one that is starting point  whereby x is zero, which implkies that starting balance he had is 1000 in the bank.

Therefore, from the  equation y = 200x + 500, the  y-intercept of linear model serves as the starting amount in his savings account.

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What is the value of cos(15°)?

StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 2 EndFraction
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction

Answers

Appropriate Question:-

What is the value of cos(15°)?

SolutioN:-

we know that,

[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]

Therefore,

[tex] \sf \leadsto \: cos \: 15 \degree[/tex]

[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]

[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]

[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]

[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]

Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.
a(t) = 2t + 2, v(0) = −15, 0 ≤ t ≤ 5
Find the distance traveled during the given time interval.
I keep getting 25/3 but that is not correct :(

Answers

Answer:

[tex]\dfrac{137}{3}\approx 45.7\; \sf m[/tex]

Step-by-step explanation:

To find the velocity function, integrate the acceleration function (and add a constant of integration).

[tex]\begin{aligned}\displaystyle v(t)=\int a(t) &= \int (2t + 2)\; \text{d}t\\\\&=\int 2t \; \text{d}t+\int 2\; \text{d}t\\\\&=\dfrac{1}{2} \cdot 2t^{(1+1)}+2t+\text{C}\\\\&=t^2+2t+\text{C}\end{aligned}[/tex]

To find the constant of integration, C, substitute v(0) = -15 into the velocity function and solve for C:

[tex]\begin{aligned}v(0)=(0)^2+2(0)+\text{C}&=-15\\0+0+\text{C}&=-15\\\text{C}&=-15\end{aligned}[/tex]

Therefore, the velocity function (in m/s) is:

[tex]v(t)=t^2+2t-15[/tex]

As we want to find the distance travelled during the given time interval 0 ≤ t ≤ 5, we first need to determine if the particle momentarily stops at any point in the given interval (and therefore changes direction). The particle will stop when its velocity is zero, so when v(t) = 0:

[tex]\begin{aligned}v(t)&=0\\\implies t^2+2t-15&=0\\t^2+5t-3t-15&=0\\t(t+5)-3(t+5)&=0\\(t-3)(t+5)&=0\\\\\implies t&=3, -5\end{aligned}[/tex]

As time is positive only, the velocity is zero at t = 3 seconds.

Therefore, at t = 3, the particle changes direction and begins to move in the opposite direction. Therefore, the displacement between 0 ≤ t ≤ 5 consists of two parts: 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5.

To find the distance travelled, first find the displacement function by integrating the velocity function:

[tex]\begin{aligned}\displaystyle s(t)=\int v(t) &= \int (t^2+2t-15)\; \text{d}t\\\\&= \int t^2\; \text{d}t+\int 2t\; \text{d}t-\int 15\; \text{d}t\\\\&=\dfrac{1}{3}t^3+t^2-15t\left(+\text{C}\right) \end{aligned}[/tex]

Distance is the absolute value of displacement.

As we want to find the distance travelled for the intervals 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5, we need to add the absolute values of displacement for these intervals. So, the absolute values of the definite integrals for these intervals:

[tex]\begin{aligned}\textsf{Distance}&=\left|\int^3_0 v(t)\right|+\left|\int^5_3 v(t)\right|\\\\&=\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^3_0\right|+\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^5_3\right|\\\\&=\left|\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)-\left(\dfrac{1}{3}(0)^3+(0)^2-15(0)\right)\right|+\\&\left|\left(\dfrac{1}{3}(5)^3+(5)^2-15(5)\right)-\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)\right|\\\\&=\left|(-27-0)\right|+\left|\left(-\dfrac{25}{3}-(-27)\right)\right|\end{aligned}[/tex]

             [tex]\begin{aligned}&=27+\dfrac{56}{3}\\\\&=\dfrac{137}{3}\end{aligned}[/tex]

Therefore, the total distance travelled during the given time interval is 137/3 ≈ 45.7 meters.

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BRAINLIEST! AND 100 POINTS

Answers

Answer:

The y-intercept represents Adam's base salary

Step-by-step explanation:

Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.

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During one week an overnight delivery company found that the weight of its parcels were normally distributed with a mean of 32 ounces and a standard deviation of 8 ounces.
What percent of the parcels weighed between 16 ounces and 40 ounces? Round your answer to one decimal place.

Answers

The percent of the parcels weighed between 16 ounces and 40 ounces is 81.9%.

What is z-score?

To solve this problem, first, find the z-scores for the weights of 16 ounces and 40 ounces using the given mean and standard deviation:

z1 = (16 - 32) / 8 = -2

z2 = (40 - 32) / 8 = 1

Next, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we get:

P(-2 < Z < 1) = 0.8186

So, approximately 81.9% of the parcels weighed between 16 ounces and 40 ounces.

Learn more about percent, here:

https://brainly.com/question/29090174

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HELP PLEASE
Solve by graphing g(x)=lx-4l+3

Answers

Please refer to the attachment

A class plants 20 seeds. Only 60% of the seeds grow into plants. How many plants does the class have?​

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Answer:

If only 60% of the seeds planted by the class grow into plants, we can find the number of plants by multiplying the total number of seeds planted by the percentage of seeds that grow, expressed as a decimal.

To do this, we can start with the total number of seeds planted, which is 20, and multiply by 0.6:

20 x 0.6 = 12

Therefore, the class has 12 plants.

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