A store donated cases of crayons to a day care center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many crayons did the center receive?​

Answer:

35

Step-by-step explanation:

23,125/185= 125

125-90 = 35

$35 less amount  school district pay in salary by paying a substitute teacher instead of paying Mrs. Cook for that day

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Mrs. Cook is a teacher whose salary is $23,125 for a 185-day school year.

Mrs. Cook per day salary= 23125/ 185 = $125

Now,  substitute teachers are paid at a rate of $90 per day.

So, if  substitute teachers take class instead of Mrs. Cook, then school will pay

= 125-90

=$35 less amount.

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Starting with the 0th term the first 4 terms, would be 0, 1, 2, 3

Replace x with each term number and solve:

The answers are: 2, 10, 50, 250

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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Answer:

The degree of a polynomial is one more than the degree of its depressed polynomial.

Step-by-step explanation:

\(\\ \tt\longmapsto y=\sqrt{-x^2+px+q}\)

\(\\ \tt\longmapsto y^2=-x^2+px+q\)

\(\\ \tt\longmapsto 10^2=-(3^)2+3p+q\)

\(\\ \tt\longmapsto 100=-9+3p+q\)

\(\\ \tt\longmapsto 3p+q=109\)

Let p,q be (27,28)

Apply

\(\\ \tt\longmapsto 3(27)+28=81+28=109\)

Verified

Answer:

13.31 and - 3.31

Step-by-step explanation:

(x + y)^2 = x^2 + y^2 + 2xy ; x + y = 10; x^2 + y^2 = 56

This means ;

10^2 = 56 + xy;

100-56 = XY

44 = xy---------(3)

From x + y = 10

x = 10- y

Substitute that in eqn 3;

We have: 44 = (10-y) y

44 =10y - y^2

Y^2-10y -44 = 0;

From formula method of quadratic equation;

Y =[ - (-10) +_ √ (-10)^2 + 4 × 1 x (-44)] / 2 × 1

y = [ 10 +_√ (100 + 176) ]/ 2]

y = [ 10 +_ √ 276]/ 2

y = [ 10 + √ 276]/ 2 or [ 10 _ √ 276]/ 2

y = 13.31 or - 3.31

Similarly x = 10 - 13.31 or 10 - (-3.31)

x = - 3.31 or 13.31

The required ordered pairs are (5+√3, 5-√3) and  (5-√3, 5+√3).

Given equations are:

\(x+y=10\)......(1)

\(x^{2} +y^{2} =56\).......(2)

An equation is a statement that equates to two statements.

On squaring equation (1) we get

\(x^{2} +y^{2} +2xy=100\)

From equation(2) \(x^{2} +y^{2} =56\)

So, \(2xy=44\)

\(xy=22\)

\(y=\frac{22}{x}\)

Put \(y=\frac{22}{x}\) in equation (1)

We get \(x+\frac{22}{x} =10\)

\(x^{2} -10x+22=0\)

\(x=5+\sqrt{3}\)

\(x=5-\sqrt{3}\)

If  \(x=5+\sqrt{3}\),

\(y=10-x\)

\(y=5-\sqrt{3}\)

So the ordered pair is \((5+\sqrt{3}, 5-\sqrt{3} )\)

If  \(x=5-\sqrt{3}\),

\(y=10-x\)

\(y=5+\sqrt{3}\)

So the ordered pair is \((5-\sqrt{3}, 5+\sqrt{3} )\)

Hence, the required ordered pairs are \((5+\sqrt{3}, 5-\sqrt{3} )\) and \((5-\sqrt{3}, 5+\sqrt{3} )\).

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Answer:

120mph.

Step-by-step explanation:

let s = the speed of the private plane

then

(2s+60) = the speed of the commercial airliner

:

Write a time equation; time = dist/speed

300%2Fs = 750%2F%28%282s%2B60%29%29

cross multiply

750s = 300(2s+60)

750s = 600s + 18000

750s - 600s = 18000

150s = 18000

s = 18000/150

s = 120 mph is the speed of the private plane

then

2(120) + 60 = 300 mph is speed of the commercial airliner

:

:

Check this find the actual time for each

300/120 = 2.5 hrs

750/300 = 2.5 hrs, confirms our solutions

Find the speed of each aircraft

The ratio of the distances flown is 750:300 = 5:2. Since the times are the same, the ratio of the speeds is 5:2. So let the two speeds be 5x and 2x.

The speed of the airliner in mph is 60 more than twice the speed of the private plane:

5x+=+2%282x%29%2B60

5x+=+4x%2B60

x+=+60

The speeds of the two aircraft are 5x = 300mph and 2x = 120mph.

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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Answer:

The answer is C. 80%

Step-by-step explanation:

Hope this helped:)

a. Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b.   the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

To estimate the probability that a randomly selected house  has a value less than $500,000:

P( x < 500,000)=P(x=0)+P(x=500)

=0.34+0.37+

=0.71

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume a normal distribution.

-The probability can therefore be calculated as:

P(x')=P( z < (x' -u)/σ.sqrt(n)))

P(z< (500-403)/(578sqrt(40)))

=P(z<2.2068)

=0.986336

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

The complete question is -

a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

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Answer:

domain - -9 <x < 7

range - -6 < y < 4

Step-by-step explanation:

The relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

3/20.

A relative frequency is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of at bats in this problem is given as follows:

80.

In 12 of them, the pitcher threw exactly four pitches, hence the relative frequency of the pitcher throwing exactly 4 pitches in an at-bat is given as follows:

12/80 = 3/20.

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Step-by-step explanation:

i think you just have to subtract 460-187 equals 273 so he can put 273 or something lower then that

Answer:

12.64

To the nearest 10th it would be 12.6

Step-by-step explanation:

If the last number of a number is 5 or above it would up but if the last number is under 5 then it would round down.

As 12.64's last number is under 5 this means that it would round down, so the answer would be 12.6

Hope this helps :)

Answer:

Step-by-step explanation:

This number is in between 12.6 and 12.7 as shown on the number line.

This means that the number must be 12.60, 12.61, 12.62, 12.63, 12.64, 12.65, 12.67, 12.68, 12.69, or 12.70 (note that 12.6 and 12.60 are the same thing)

Now to find the exact decimal we see that the red dot is 4 jumps to the right of 12.6, meaning that it is 12.64. This is because the first line to the right is 12.61, the second line is 12.62, the third line is 12.63, the fourth line is 12.64.

To round to the nearest tenth, we need to look at the hundredths place. If the hundredths place is from 0-4, you round down, in this case to 12.6. If the hundredths place is from 5-9, you round up, in this case to 12.7.

Hope this helps!

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer:

364 miles

Step-by-step explanation:

                               Rate        Time         Distance

Flight #1                 260             x               260x

Flight #2                 140           4-x           140(4-x)

Because each flight was to or from the same airports the distance traveled by flight #1 and flight #2 must be the same. This means that you can set the two calculated distances equal to each other.

260x = 140(4-x)

260x = 560 - 140x

400x = 560

      x = 1.4 hours      This is the amount of time flight 1 spent in the air.

now we can use this and plug it into the distance formula (260x) to find the distance

260(1.4) = 364

so the distance between the two airports is 364 miles

The statement that is false on Jose drawing cards from the deck is B. For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.

Jose only recorded the number of aces he selected, not the number of diamonds. Therefore, we cannot use his graph to find the number of diamonds he picked.

However, if we were to use the graph to find the number of aces that Jose has picked so far, then we would be successful. The other statements are true as Jose recorded the cards he took and the cards were replaced after each pick.

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The full question is:

Jose draws a card from a deck replaces it and draws again he records a number of times he draws an ace. He decides to record the total number of aces that he selects and calculates the proportion of aces that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?

A. The theoretical probability for selecting an in each pick is 1 / 13.

B. For a given number of selections, we can use Jose's graph to find the number of diamonds that he has picked so far.

C. This is an example of the law of large numbers.

D. The relative frequency of selecting an ace changes with the increase in number of selections.

Therefore , the solution of the given problem of triangle comes out to be the triangle can have side lengths AB = 7, AC = 7, and BC = 2√2,

AC = 4.

A polygon is a hexagon if it has two maybe more additional components. It is shaped like a simple rectangle. A and B are the only two clearly defined edges of a form that can set it apart from a regular triangle. While the limits remain perfectly collinear, Euclidean geometry produces one section rather than a full cube. Three sides plus three angles make up a triangle.

Here,

With the aid of this knowledge, we can determine if each set of side lengths conforms to the Pythagorean theorem:

This pair of side lengths, AB = 7 and AC = 7, is conceivable because the triangle is an isosceles right triangle with 7-length legs.

BC = 2√2, AC = 4: This set of side lengths is feasible because

=> BC²+ AC² = (2√2)² + 4² = 8 + 16 = 24, and

=> AB = BC√2 = 2√2√2 = 4√2.

=> AB = 4, AC = 4√2:  

This set of side lengths is feasible because

=> AB²+ AC² = 4² + (4√2)²= 16 + 32 = 48, and

=>  BC = AB/√2 = 4/√2√2 = 2√2.

If AB = 6 and BC = 6, then this pair of side lengths cannot exist.

If BC = 4 and AC = 43, then this pair of side lengths cannot exist.

This set of side lengths has AB = 4, BC = 3 is not conceivable

As a result, the triangle can have side lengths AB = 7, AC = 7, and BC = 2√2, AC = 4.

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

Explained below.

Step-by-step explanation:

(a)

In this case we need to determine if the proportion of customer complaints has decreased by more than 10% under the new packaging design.

The hypothesis can be defined as follows:  

H₀: The proportion of customer complaints has not decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ ≤ 0.10.  

Hₐ: The proportion of customer complaints has decreased by more than 10% under the new packaging design, i.e. p₁ - p₂ > 0.10.  

(b)

The information provided is:

n₁ = 220

n₂ = 220

X₁ = 86

X₂ = 41

Compute the sample proportions and total proportions as follows:

\(\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{86}{220}=0.3909\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{41}{220}=0.1864\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{86+41}{220+220}=0.2886\)

Compute the test statistic value as follows:

 \(z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.3909-0.1864}{\sqrt{0.2886(1-0.2886)\times[\frac{1}{220}+\frac{1}{220}]}}\\\\=\frac{0.2045}{\sqrt{0.0018665}}\\\\=4.733524\\\\\approx 4.73\)

The test statistic value is 4.73.

Compute the p-value as follows:

\(p-value=P(Z>4.73)\)

               \(=1-P(Z<4.73)\\=1-(\approx 1)\\=0\)

The p-value of the test is 0.

(c)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0 < α = 0.01.

The null hypothesis will be rejected at 1%significance level.

Thus, there is enough evidence at 1% significance level to support the engineers' claim.

(d)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

p-value = 0 < α = 0.10.

The null hypothesis will be rejected at 10%significance level.

Thus, there is enough evidence at 10% significance level to support the engineers' claim.

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer:

1/x

Step-by-step explanation:

Answer:

71/100

Step-by-step explanation:

71 and 100 do not have a common number to simplify/ reduce by. There for 71/100 is the simplest as a fraction for for .71

Answer:

answer is 3/4

Step-by-step explanation:

0.75 ×4=3/4

Answer:

The answer is sector. B.

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Step-by-step explanation:

a=17+3b, a=Number of points by A, b=Number of points by B

All the best!!

The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)

\(= (t^2, 2t, 2)\)

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

For more such questions on displacement , Visit:

https://brainly.com/question/1581502

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