The 1400-kg mass of a car includes four tires, each of mass (including wheels) 34 kg and diameter 0.80 m. Assume each tire and wheel combination acts as a solid cylinder. A. Determine the total kinetic energy of the car when traveling 92 km/h . B. Determine the fraction of the kinetic energy in the tires and wheels. C. If the car is initially at rest and is then pulled by a tow truck with a force of 1400 N , what is the acceleration of the car? Ignore frictional losses. D. What percent error would you make in part C if you ignored the rotational inertia of the tires and wheels?

The explanation about the graph is illustrated below.

The graph shows 0 to 30 on the x-axis at increments of 5 and 0 to 12 on the y-axis at increments of 1. The label on the x-axis is Temperature in degrees C, and the label on the y axis is the Number of Sweaters Sold.

If you will draw lines through, (12.5,6) and (15,4), it will best represent a line of best fit, because most of the points on the same and opposite sides of line are equidistant from each other.

Equation of line passing through (12.5,6) and (15,4) A line of best is the line that passes through all or some points or only through a single point, which describes the relationship between x and y values of data set

4x + 5y = 80

5y = -4x + 80.

y = -4x/5 + 16

Slope = -4/5 and y intercept is 16.

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The margin of error of this poll is

Given that 230 people were asked if they liked dogs, and 90% said they did.

In a random sample, a margin of error is a statistical measure that takes into account the discrepancy between actual and expected results.

Sample size (N)=230

Sample proportion  [tex](\hat{p})[/tex] = 90% = 0.90  and

confidence interval = 99%

The critical value at 99% confidence interval with α=0.01 is

[tex]\begin{aligned}Z_{c}&=Z_{1-\frac{\alpha}{2}}\\ &=Z_{1-\frac{0.01}{2}}\\ &=Z_{0.995}\\ &=2.576\end[/tex]

This value is taken from the Standard normal distribution table.

Now, we will calculate the margin of error (E) by using the formula

[tex]E=Z_{c}\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}[/tex]

Substituting the values in the formula, we get

[tex]\begin{aligned}E &=2.576\times \sqrt{\frac{0.90(1-0.90)}{230}}\\ &=2.576\times \sqrt{\frac{0.09}{230}}\\ &=2.576\times\sqrt{0.00039}\\ &=2.576\times 0.0197\\ &=0.0507\end[/tex]

Hence, the margin of error when 230 people were asked if they liked dogs, and 90% said they did is 0.0507.

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Answer:

math math math math math math math math math math

Using the Fundamental Counting Theorem, there are 15 ways to travel from Andy's house to Willie's house.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, the parameters are:

[tex]n_1 = 3, n_2 = 5[/tex].

Hence the number of ways is:

N = 3 x 5 = 15.

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I am the number 4052. It is rather confusing and i cannot promise that it is correct. Hope it helps : )

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

A worker at a shoe factory is required to box at least 8 pairs of shoes per minute, and not more than 12 pairs of shoes per minute.

For 168 pairs of shoe:

Maximum time = 168 pair / 8 pairs per minute = 21 minutes

Minimum time = 168 pair / 12 pairs per minute = 14 minutes

The possible amount of time, in minutes, that it could take the worker to box 168 pairs of shoes is between 14 minutes to 21 minutes.

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The expression for g in terms of other variables is g = Fd^2/m1m2

Given the expression below as shown

F=gm1*m2/d2

We are to make g the subject of the formula

F=gm1*m2/d2

Cross multiply

Fd2 = gm1m2

Divide both sides by m1m2

Fd^2/m1m2 = g

g = Fd^2/m1m2

Hence the expression for g in terms of other variables is g = Fd^2/m1m2

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The solution to the system of equations is one solution at (2, -2)

The system of equations is given as:

4x + 3y = 2

3x − 2y = 10

Multiply (1) by 2 and (2) by 3.

So, we have:

8x + 6y = 4

9x − 6y = 30

Add both equations

17x = 34

Divide by 17

x = 2

Substitute x = 2 in 3x − 2y = 10

3(2) − 2y = 10

Solve for y

y = -2

Hence, the solution to the system of equations is one solution at (2, -2)

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Answer:

8 minutes.

Step-by-step explanation:

We work in fractions of the wall they can paint in 1 minute, so

1/12 + 1/24 = 1/x  where x is the time it takes when working together.

Multiplying through by 24x:

2x + 1x = 24

3x = 24

x = 8 minutes.

The solution to the equation (x+21)=7 is x = -14

The equation is given as:

(x+21)=7

Remove the brackets

x + 21 = 7

Subtract 21 from both sides

x + 21 - 21 = 7 - 21

Evaluate the expression

x = -14

Hence, the solution to the equation (x+21)=7 is x = -14

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The correct answer is none of the above.

A line is defined as the shortest distance between two points and the point  where two lines meet is known as an angle.

From the given figure, the measure of angle a and b are supplementary since the sum of the angles is not 180 degrees.

They are not vertical angles since they do not meet at a point of intersection

The measure of angle a and b are complementary since the sum of the angles is not 90 degrees. Hence the correct answer is none of the above.

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Solving the given equation, the value of v that makes the statement true is:

A. v = 8.

The equation is:

[tex]12 = 12 + \frac{v - 8}{2}[/tex]

Hence:

[tex]\frac{v - 8}{2} = 0[/tex]

Applying cross multiplication:

v - 8 = 0

v = 8.

Hence option A is correct.

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Answer:

900

Step-by-step explanation:

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR   (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.

1.(a) The number of marigolds used in a day is 42.

 (b) The total number of flowers used by using suitable property of whole numbers is 98.

 (c) She earned Rs. 3570

2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.

 (b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.

3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.

4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.

 (b) The multiplicative identity of whole numbers is 1.

5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.

1. (a) The number of marigolds used in a day is 42.

Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.

  (b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.

What is distributive property of whole numbers?

The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.

Distributive property = a×(b+c) = a×b+a×c

Total number of flowers = 7×(8+6) = 7×14 = 98.

(c) If she sold 42 bouquets in a whole week, find the amount she earned is  rs.3570.

Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.

2. (a)  By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.

Rearrangement of the given numbers = (819+181)+(364+436)

                                                               = 1000+800

                                                               = 1800    

   (b)  By suitable rearrangement, the value of 20 x 348 x 50 is 348000.

Rearrangement of the given numbers = 348×(50×20)

                                                               = 348×1000

                                                               = 348000  

3.  Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.

By using distributive property = 492 x 13 + 492 x 37

                                                   = 492×(13+37)

                                                  = 492×50

                                                  = 24600

4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.

What is commutative property?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

By using commutative property,  a+b = b+a

   86 + 65 = 65 + 86

          151 = 151                            

   (b)  The multiplicative identity of whole numbers is 1.

Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.

5.  The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.

Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0

1+0=1

1+1=2

2+1=3

3+2=5

5+3=8

8+5=13

Hence, The next two numbers for the given series are 13 and 21.

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Answer:

|-1| + |3|

Step-by-step explanation:

We can use absolute values to find the distance between positive and negative numbers on a number line.

|-1| + |3| =

Keep in mind that

- the absolute value of a positive number is positive and

- the absolute value of a negative number is positive

1 + 3 =

4 units

Answer:

The unit of measuring volume of the sphere is cubic meters.

The probability of choosing cards either Q or R when a card is drawn from a deck of 8 cards is 0.25.

Given that a card is randomly chosen from 8 cards shown in figure.

We have to calculate the probability of choosing either Q or R when a card is drawn from those 8 cards.

Probability means calculating the likeliness of happening an event among all the events possible. It lies between 0 and 1. It cannot be negative.

Number of cards=8

Number of repeated cards=0

Number of cards showing Q and R =1 each.

Probability of getting Q or R is P(X=Q)+P(X=R)

= 1/8+1/8

=2/8

=1/4

=0.25

Hence the probability of getting either P or Q when a card is drawn from 8 cards is 0.25.

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Depending on the number of teams, the possible numbers of students per team are in the set:

{2, 3, 4, 6, 9, 12, 18}

We know that there are 36 students divided equally into N teams.

Such that the number of teams is larger than 1 and smaller than 20.

Then we could have 2 teams, such that the number of students in each team is given by the quotient between the total number of students and the number of teams.

36/2 = 18

There are 18 students in each team.

Notice that the numbers of teams can only be factors of 36, where:

36 = 6*6 = 2*2*3*3

So the factors are:

2, 3, 2*3, 3*3, etc...

If there are 3 teams we have:

36/3 = 12 students per team.

If there are 6 teams we have:

36/6 = 6 students per team.

if there are 9 teams:

36/9 = 4 students per team.

If there are 12 teams:

36/12 = 3 students per team.

If there are 18 teams:

36/18 = 2 students per team.

These are all the possibilities.

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The area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

The curve is given as:

y = √(x + 3)

The area bounded by the curve, x-axis and y-axis is when x = 0 and y = 0

When y = 0, we have:

0 = √(x + 3)

This gives

x = -3

So, we set up the following integral

A = ∫ f(x) d(x) (Interval a to b)

This gives

A = ∫ √(x + 3) d(x) (Interval -3 to 0)

When the above is integrated, we have:

A = 1/3 * [2(x + 3)^(3/2)] (Interval -3 to 0)

Expand

A = 1/3 * [2(0 + 3)^3/2 - 2(-3 + 3)^3/2]

This gives

A = 1/3 * 2(3)^3/2

Apply the law of indices

A = 2(3)^1/2

Rewrite as:

A = 2√3 or 3.46

Hence, the area bounded by the curve, x-axis and y-axis of the function y = √(x + 3) is 2√3

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The  kind of statistical study the zoologist conducted was D. observational study.

An observational study  serves as a study  whereby the researcher simply observes the subjects without interfering with it.

This is different from carrying out experiment on them or just a theoretical approach.

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CHECK THE COMPLETE QUESTION BELOW:

A zoologist researched the feeding habits of lemurs. She collected data by studying the lemurs in a zoo exhibit for a one-month period and drew conclusions based on her data. What kind of statistical study did the zoologist conduct? A. survey B. theoretical study C. experiment D. observational study

The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

Given that the area of rectangle is 169 [tex]inches^{2}[/tex].

We have to find the smallest perimeter and dimensions of the rectangle.

let the length of rectangle be x inches and breadth be y  inches.

We know that area of rectangle is the product of its length and breadth. So,

Area=xy

169=xy

y=169/x

Perimeter of rectangle =2(x+y)

Put the value of y=169/x in the perimeter.

P=2(x+169/x)

P=2x+338/x

Differentiate both sides with respect to x.

dP/dx=2-338/[tex]x^{2}[/tex]

Again differentiate it with respect to x.

[tex]d^{2} P/dP^{2}[/tex]=676/[tex]x^{3}[/tex]

Because the second derivative is greater than 0 so the perimeter is minimum.

Put dP/dx=0 to get the value of x.

dP/dx=0

2-338/[tex]x^{2}[/tex]=0

2=338/[tex]x^{2}[/tex]

[tex]x^{2}[/tex]=169

x=[tex]\sqrt{169}[/tex]

x=13

Put the value of x in y=169/x

y=169/13

=13

To calculate the perimeter, put the values of x and y in P=2(x+y)

P=2(13+13)

=2*26

=52 inches.

Hence The smallest perimeter and dimensions of rectangle having area of 169 [tex]inches^{2}[/tex] is 52 inches , length 16 inches and breadth also 16 inches.

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Question:

A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:

Draw normal curve to help - split into 8 section ( i can't draw it here)

a) 34.13% of cans will be between 480g and 486g.

b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.

Look at the Stand Dev Graph where the give you the number

Step-by-step explanation:

Let me give you a different question and i will answer it, which you help you answer your question.

Step-by-step explanation:

well, as you can witness both of the equations are equal to y, so you're free to reckon that they are equal as well

[tex]6x - 3 = 2x + 17 = = = > \\ 4x = 20 = = = > x = 5 \: and \: \\ y = 6(5) - 3= = = > y = 27[/tex]

Answer:

<3

Step-by-step explanation:

5, 27 is right on acellus

x=5

y=27

The number of weeks it will take for the budget money to run out is; 2 weeks.

The number of weeks it would take for the budget money to decrease till it runs out as required in the task can be interpreted as the x-value which corresponds to a Y-value of zero.

Hence, by setting y=0; we have;

-2x -0 = -4

-2x = -4

Divide both sides of the equation by; -2.

x = 2

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Answer:

V=  (pi) (r squared) (h)

Step-by-step explanation:

The term used to describe a customer who sees a pair of boots online but then decides to buy the same pair at Macy's after trying them on would be best classified as a cross-channel shopper.

A cross-channel shopper is a consumer who uses various combination of both several channels for the same purchase.

The customer has checked the pair of boots online but rather purchased the same boots at Macy's instead of purchasing online.

Therefore, a cross-channel shopper uses different purchasing channel to purchase a product.

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At office 826 they will meet if they leave at the same time.

It is given that,

Agent J has recently been relocated from office 2013 to office 1. But his former office neighbor, Agent K is still in office 2014.

So, there are  (2014 - 1) - 1 = 2012 offices in between them.

It is given that,

Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute.

So,

Per minute they cross

= 25 + 36

= 61 offices.  

Thus, the time required for crossing all the 2012 offices is,

= 2012/61

= 32.9 ≅ 33 minutes

Then,

They will meet at

1 + 25(33) = 826 office (or)

2014 - 36(33) = 826 office (Negative since opposite direction)

Therefore, both of them meet at office 826.

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Answer:

Step-by-step explanation:

We are given two sides and one angle opposite to one of the known sides.

In order to find the missing side we need to use the law of sines.

Find the angle opposite to the second known side, let it be x.

Find the missing third angle y, using angle sum theorem:

Find the required side length z, the distance from the plane to the observer tower, using the law of sines again.

Note. At this point you can use the law of cosines as we have found the angle between the known sides.

So the required distance is 7.7 km

The conversion factor of the chicken recipe used at the banquet is 4.5.

An equation is an expression that shows the relationship between two or more variables and numbers.

Conversion factor = (new amount * portion size) / (old amount * portion size)

Hence:

Conversion factor = (60 * 3) / (10 * 4) = 4.5

The conversion factor of the chicken recipe used at the banquet is 4.5.

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