Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.
a(t) = 19ti + etj + e -tk, v(0) = k, r(0) = j + k

The height of the wall is 14 feet

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Therefore ;

TH/ JS = TV/VS

4/JS = 6/21

21× 4 = 6 JS

JS = 21× 4/6

JS = 84/6

JS = 14 feet

therefore the height of the wall is 14 feet

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Answer:

Step-by-step explanation:

24. Gravetter/Wallnau/Forzano, Essentials - Chapter 3 - End-of-chapter question 24

A sample yielded the following scores:

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

n= 10

Assume that the scores are measurements of a discrete variable and find the median.

Median =5Correct

Points:

1 / 1

Median = 5

To find the median for a set of numbers with an even quantity the two middle numbers are added together and divided by 2.

n=102+(n = 102+1)2

= 5th score + 6th score2

= 5 + 52

= 102=5

Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution. (Use two decimal places.)

Median = 4.83Correct

The median for the discrete variable is 5 and for continuous variable is 5.

Median in statistics is the middle value of a list of data when arranged in order. It is a measure of central tendency that separates the data into two halves: the upper half and the lower half.

Given that: scores = 2, 3, 4, 4, 5, 5, 5, 6, 6, 7

a) The scores are in ascending order; then the median which is the middle number will be:

median = (5th term + 6 term)/2

= (5+5)/2

= 10/2

= 5

b) Use the cumulative percentage table ;

X     frequency    cumulative frequency     cumulative percentage

2         1                     1                                           10%

3         1                     2                                          20%

4        2                     4                                          40%

5        3                     7                                           70%

6        2                     9                                           90%

7        1                      10                                          100%

Fraction = the no. required to reach 50%/ no. in that interval

= 1/3

Since we have a total of 4 boxes when we reach the value of 4.5

The median of the continuous variable = 4.5 + (1/3)

= 4.833

≈ 5

Hence, the median for the discrete variable is 5 and for continuous variable is 5.

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F ∩ H = [4, 9)

FUH= ∞

Generally, To find the intersection of F and H, denoted as F ∩ H, we need to identify the values that are in both sets F and H.

From the definitions of F and H, we have:

F = {v | v=4 or v>4}

H = {v | v<9}

The values that are in both F and H are those that satisfy both conditions, i.e., v=4 or v>4 and v<9. This is equivalent to just the condition v=4, since any value that satisfies v<−4 will also satisfy v>4 and v<9.

Therefore, F ∩ H = {v | 4}.

In interval notation, we can write this as:

F ∩ H = [4, 9)

To find the union of F and H, denoted as F ∪ H, we need to identify all the values that are in either set F or set H or both.

From the definitions of F and H, we have:

F = {v | v=4 or v>4}

H = {v | v<9}

this denotes

F=  {v | v=4> x > ∞}

H = {v |-∞ <v<9}

FUH= ∞

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The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

Given,

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

1) A Poisson distribution characterizes the random variable x that is provided.

2) Having 8 occurrences in 10 minutes is likely based on the following formula:

P(X = 8) = (e^(-5.3) * 5.3^8) / 8! = 0.0241 (rounded to four decimal places) (rounded to four decimal places)

Consequently,

(a) 0.0241 is the correct response.

3) The likelihood that there are fewer than 3 occurrences is as follows:

P(X 3) = P(X = 0), P(X = 1), and P(X = 2) = (e(-5.3) * 5.30), (e(-5.3) * 5.31), and (e(-5.3) * 5.32), respectively, / 0!, / 1/1, and / 2/ respectively, / 2! = 0.0659 (rounded to four decimal places)

Accordingly,

(a) 0.0659 is the correct response.

The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

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The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

Given,

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of equal length. It is known that the mean number of occurrences in ten minutes is 5.3.

1) A Poisson distribution characterizes the random variable x that is provided.

2) Having 8 occurrences in 10 minutes is likely based on the following formula:

P(X = 8) = ([tex]e^(-5.3)[/tex] * [tex]5.3^8[/tex]) / 8! = 0.0241 (rounded to four decimal places) (rounded to four decimal places)

Consequently,

(a) 0.0241 is the correct response.

3) The likelihood that there are fewer than 3 occurrences is as follows:

P(X 3) = P(X = 0), P(X = 1), and

P(X = 2) = ([tex]e(-5.3)[/tex]* 5.30), ([tex]e(-5.3)[/tex]* 5.31), and ([tex]e(-5.3)[/tex] * 5.32),

respectively, / 0!, / 1/1, and / 2/ respectively, / 2! = 0.0659 (rounded to four decimal places)

Accordingly,

(a) 0.0659 is the correct response.

The random number x satisfies Poisson distribution of probability and the probability that there are 8 occurrences in ten minutes is 0.0241 and The probability that there are less than 3 occurrences is 0.0659.

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Answer:

  4.5 mm

Step-by-step explanation:

You want the length of AB in similar triangles ACE and BCD, given BD is parallel to AE, and AC=36 mm, ED=9 mm, EC=72 mm.

Corresponding segments in the two triangles are proportional, so we have ...

  AB/ED = AC/EC

  AB/(9 mm) = (36 mm)/(72 mm) = 1/2

  AB = (9 mm)(1/2) = 4.5 mm . . . . . multiply by 9 mm

The length of segment AB is 4.5 mm.

The proportion of selling times in the sample that are greater than or equal to 10 days is 0.85.

As per the data given:

HOME Realty claims that it can sell a detached, residential house faster than any other realty company.

With the aim of examining HOME's claim, you sample 20 customers who sold a detached.

The data has been summarized in the histogram(attached at the end of solution)

Here we have to determine the proportion of selling times in the sample that are greater than or equal to 10 days.

Selling Time Frequency

0 - 10                    3

10 - 20                  4

20 - 30                 7

30 - 40                 3

40 - 50                 3

Frequencies for which selling times are 10 or greater

= 4 + 7 + 3 + 3

= 17

Total frequencies = 3 + 4 + 7 + 3 + 3

= 20

Proportion for which selling times are 10 or greater

= [tex]$\frac{17}{20}[/tex]

= 0.85

Therefore the proportion is 0.85.

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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized in the following histogram(attached at the end of solution):

Based on the histogram, find the proportion of selling times in the sample that are greater than or equal to 10 days. Write your answer as a decimal, and do not round your answer.

The probability the child arranges the blocks in such a way that block f is in either the first position or the last position is found to be 1/3.

The child under observation of the researcher is given 6 unequally labelled block that are number as, a, b, c, d, e and f.

Now, the total number ways in which the child can arrange these block is,

Total possible ways = 6 x 5 x 4 x 3 x 2 x 1

Total possible ways = 720

Now, if the position of the block labelled f is fixed at either 1st or the last position then, total such ways are,

= 2 x 5 x 4 x 3 x 2 x 1

= 240

So, the probability that the child arranges the blocks in such a way that block f is in either the 1st position or the last position,

P = 240/720

P = 1/3

So, the probability is found to be 1/3.

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The equation for the pony's path is -

(x - 8)² + (y - 8)² = 128.

The general equation for a circle is -

(x - h)² + (y - k)² = r²

where (h, k) is the center and (r) is the radius.

Given is that the pony is staked at the coordinate point (8, 8).

The general equation for a circle is -

(x - h)² + (y - k)² = r²

We can write the equation for the pony's path as -

(x - 8)² + (y - 8)² = 128

Therefore, the equation for the pony's path is -

(x - 8)² + (y - 8)² = 128.

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The equation for the surface with all points which are equidistant of (−1,0,0)and the plane x=1 is x² - 2x + y² + z² = 2.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=).

To start with, let's consider the given information. We have been given that all points on the surface are equidistant from (-1,0,0) and the plane x=1. This means that the distance between any point on the surface and (-1,0,0) is the same as the distance between that point and the plane x=1.

We can use the formula for the distance between a point and a plane to derive an equation for the surface. The formula for the distance between a point (x1, y1, z1) and a plane Ax + By + Cz + D = 0 is given by:

distance = |Ax1 + By1 + Cz1 + D| / √(A² + B² + C²)

In our case, the plane is x=1, which can be written as x - 1 = 0. So, A=1, B=0, C=0, and D=-1. The point (-1,0,0) can be substituted as x1=-1, y1=0, and z1=0.

We can simplify the distance formula to:

distance = |x-1|

Now, since all points on the surface are equidistant from (-1,0,0) and x=1, we can set up the following equation:

|x-1| = √( (x+1)² + y² + z² )

Squaring both sides and simplifying, we get:

(x-1)² = x² + 2x + 1 + y² + z²

Rearranging and simplifying, we get the final equation for the surface:

x² - 2x + y² + z² = 2

This is the equation of the surface that contains all points that are equidistant from (-1,0,0) and x=1.

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If Mr. Phil T. Rich had a boat load of money. The original value of his estate is $152,000.

Let's call the original value of Mr. Phil T. Rich's estate "x".

After he gave 1/2 of the estate to his wife, he was left with x/2.

After he gave 30,000 to his daughter, he was left with x/2 - 30,000.

After he gave half of what was left to his butler Niles, he was left with (x/2 - 30,000)/2.

After he gave half of what was left to Bubbles, he was left with (x/2 - 30,000)/4.

Finally, after he donated the 8,000 to charity, he was left with (x/2 - 30,000)/4 - 8,000.

We know that the final amount after all these transactions was $0, so we can set up an equation to solve for x:

0 = (x/2 - 30,000$)/4 - 8,000

Multiplying both sides by 4 to isolate x/2:

0 * 4 = (x/2 - 30,000) - 8,000 * 4

Expanding the right side:

0 = (x/2 - 30,000) - 32,000

Adding 30,000 and 32,000 to both sides:

30,000+ 32,000 = (x/2)

Dividing both sides by 1/2:

62,000 * 2 = x

Multiplying both sides by 2:

62,000* 2 * 2 = x * 2

Expanding the left side:

62,000* 4 = x

Dividing both sides by 4:

62,000 * 4 / 4 = x / 4

Expanding the left side:

$62,000 = x

Therefore the original value of Mr. Phil T. Rich's estate was $62,000.

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Answer:17x25 i think

Step-by-step explanation:

Both items have different rate of change, m₁ = -2, m₂ = -1/2, Item 1 is steeper.

Correct option is C.

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

m = Δy/Δx

where,m is the slope

Slope of line denotes rate of change and steepness.

Given,

A) a line with y-intercept (0,0) and passes through point (-2 , 4).

slope of the line

= (y₂ - y₁)/(x₂ - x₁)

= (4 - 0)/(-2 - 0)

= 4/-2

m₁ = -2

B) In the graph, line passes through (2, -1) and (-2 , 1 )

slope of the line

= (y₂ - y₁)/(x₂ - x₁)

= (1 - -1)/(-2 - 2)

= 2/-4

m₂ = -1/2

Hence, by the calculation

Items have different rate of change, Item 1 is steeper.

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The error which Jake made is likely to be a result of confusion or oversight in identifying the variable y as having a coefficient of 1.

The coefficients of an expression are the numerical factors that multiply the variables, while the constants are the numerical values that do not contain any variables.

In the expression 9m + 4 + y, the coefficients are 9 and 1 (which is the implied coefficient for y since there is no visible numerical factor), and the constant is 4.

So Jake correctly identified 9 as a coefficient and 4 as a constant, but missed the implied coefficient of 1 for the variable y. The error that Jake made is likely to be a result of confusion or oversight in identifying the variable y as having a coefficient of 1, rather than assuming it is a constant or neglecting it entirely.

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Step-by-step explanation:

reflect the shape, will give you:

A = (-1,0)

B= (3, -5)

C= (-6, -7)

D= (-4, -1)

If a point A(x, y) is dilated by a factor P, the new point would be at

A'(Px, Py).

A = -1/2.5 = -0.4             0/2.5= 0

= ( - 0.4, 0)

B = 3/2.5 =  1.2              -5/2.5 = -2

= (1.2, -2)

C = -6/2.5= -2.4       -7/2.5 = -2.8

= ( -2,4, -2.8)

D = -4/2.5 = -1.6.     -1/2.5 = -0.4

= ( -1.6, -0.4)

You're Welcome!

Answer:

Step-by-step explanation:

( -1.6, -0.4)

Answer: The equation of a line in the form of y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the slope, you can use the two points on the line: (1, 2) and (3, 5). The slope is found by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

m = (5 - 2) / (3 - 1) = 3 / 2 = 1.5

The y-intercept can be found by plugging in one of the points and the slope into the equation and solving for b. Let's use the point (1, 2).

2 = 1.5 * 1 + b

b = 2 - 1.5 = 0.5

So the equation of the regression line is:

y = 1.5x + 0.5

Therefore, the correct answer is: yˆ = 1.5x + 0.5

Step-by-step explanation:

Answer:

Step-by-step explanation:16/17

Answer:

16/17 is the simplest form

Answer:

The answer is:-

Step-by-step explanation:

x^3+y^3+z^3=k

xyz^9=k

xyz/9=k

xyz=9k

Hence, k=9 and, x, y and z are 1.

The first derivative of the composite function r(x) = √[x + √(x + √x)] is equal to r' (x) = [1 / [2 · √[x + √(x + √x)]]] · [1 + [1 / [2 · √(x + √x)]] · [1 + 1 / (2 · √x)]].

In this problem we find the case of a composite function of the form:

f ° g ° h (x) = f [g [h (x)]]

Whose first derivative must be found by means of the following differentiation rules:

Chain rule

d [f [u (x)]] / dx = (df / du) · (du / dx)

Derivative of a square root

d (√x) / dx = 1 / (2√x)

And the first order derivative of the function r(x) = √[x + √(x + √x)] is:

r' (x) = [1 / [2 · √[x + √(x + √x)]]] · [1 + [1 / [2 · √(x + √x)]] · [1 + 1 / (2 · √x)]]

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The probability of carrying the AIDS virus in B1 is 0.5%

Probability is a fundamental concept in understanding the ELISA test results for AIDS diagnosis.

The probability of carrying the AIDS virus (B1) can be calculated by dividing the number of people who carry the virus by the total number of people who were tested.

From the contingency table, we can see that the number of people who carry the virus is 5000. Therefore, the probability of carrying the virus can be expressed as:

=> P(B1) = Number of people who carry the virus / Total number of people tested

=> 5000 / 1000000

=> 0.005 or 0.5%

This means that out of 1 million people who were tested, only 0.5% were found to be carrying the AIDS virus.

In this context, probability helps us understand the likelihood of carrying the virus and the accuracy of the test results. It also allows us to estimate the prevalence of the virus in a population and make informed decisions about public health policies and interventions.

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Complete Question:

A common test for AIDS is called the ELISA(enzyme-linked immunosorbent assay) test. Among 1 million peoplewho are given the ELISA test. we can expect results similar tothose given in the following table:

                     B1: Carry AIDS Virus       B2: Do not Carry AIDS Virus  Totals

A1: Test          4885                                73630                                       78515

Positive

A2: Test         115                                    921370                                   921485

Negative

Totals           5000                                995000                               1000000

If one of these 1 million people is selected randomly, find the value of P(B1).

The total duration of the phone call was 33 minutes.

Given that, by using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 33 cents per minute. If the total cost of the call is $11.84 and we have to calculate the time how long was the phone call.

Let the number of minutes a phone call held be x.

Now, we will be representing the above given information in terms of linear equation and then solve for the value of x which will give us the number of minutes the phone call held.

[tex]Total[/tex] [tex]cost=[/tex] $[tex]0.95[/tex] [tex]+[/tex] $[tex]0.33x[/tex]

$[tex]11.84=[/tex] $[tex]0.95[/tex] [tex]+[/tex] $[tex]0.33x[/tex]

[tex]11.84=0.95+0.33x[/tex]

[tex]11.84-0.95=0.33x[/tex]

[tex]0.3=0.33x[/tex]

[tex]\frac{0.3}{0.33}=x[/tex]

[tex]33=x[/tex]

Therefore, the call will go 33 minutes long.

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The adjusting entry for deferred revenue at its year-end of December 31 is $1,150

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

We are given that;

The amount of payment=$3,450
Now,

The adjusting entry for deferred revenue at its year-end of December 31

Debit: Deferred Revenue $1,150 (which is one-third of the total payment received)

Credit: Revenue $1,150 (which represents the portion of the service that has been provided in December)

Therefore, by the given interest answer will be $1,150

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1. Two lines are MT and UW. 2. Two segments are SX and SY. 3. A pair of congruent angles is ∠QNT and ∠QNM. 4. Four right angles are ∠QNT and ∠QNM. ∠TNY and ∠MNY.

Angles that are both vertical and obtuse are known as obtuse vertical angles. In order to comprehend what obtuse vertical angles are, we must first learn the definitions of each of these kinds of angles.

Angles that cross one other at the junction of two lines are known as vertical angles. There is always an equal amount of vertical angles.

With these definitions, we get that obtuse vertical angles are angles that are in front of one another at the intersection between two lines, and both of which share a comparable measure that is between 90° and 180°.

From the given figure we observe that:

1. Two lines are MT and UW.

2. Two segments are SX and SY.

3. A pair of congruent angles is ∠QNT and ∠QNM.

4. Four right angles are ∠QNT and ∠QNM. ∠TNY and ∠MNY.

5. Two pairs of obtuse vertical angles ∠MSW and ∠UST. ∠VNT and ∠PNM.

6. Two pairs of adjacent supplementary angles are ∠MSW and ∠WST. ∠WNM and WNT.

7. Two pair of complementary angles are ∠TNP and ∠PNY. ∠QNW and ∠WNM.

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Answer: The passion fruit will run out first and 420 ounces left.

Step-by-step explanation: If you put the same amount of cranberry and passion fruit in each juice than they will be using an equal amount each time. We know that there are more ounces of cranberry than passion fruit which already tells us that there will be more cranberry when the passion fruit runs out. In order to find how much is left we can simply subtract the amount of cranberry and passion fruit.

1100-680=420

1) The  model is R = 1820 - 19t

2) After six years R = 1706 barrels

3) There would be non more oil in 96 years.

We know that an equation can be used as a model. This implies that we can be able to use an equation to show how a variable is changing over time and that is what the problem that we have here is all about.

If at the current time we have 1820 billion barrels Then they decrease by 19 barrels per year and t is the number of years then the model is;

R = 1820 - 19t

After six years we would have;

R = 1820 - (19 * 6)

R = 1706 barrels

When there are no further barrels;

0 = 1820 - 19t

1820 = 19t

t = 1820/19

t = 96 years.

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a) Probability, P(y = 2) = P(AA) is equals to the 0.81.

b) Probability, P(y = 3), is equals to the 0.162.

c) For P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y= 5 , probability is equals to the 0.00324.

d) General formula for p(y) is P(y)= (y-1)(0.1)⁽ʸ⁻²⁾(0.9)².

A new battery’s voltage may be acceptable (A) or unacceptable (U). Assume that 90% of all batteries have acceptable voltages. So, probability of acceptance = 0.90 and

probability of unacceptance = 1 - 0.9 = 0.1

Let the number of batteries that must be tested be "Y". A particular flashlight requires two batteries, that is batteries will be independently selected.

a) For P(y = 2), both the batteries must be acceptable. Hence probability, P(y = 2)

= P(AA) = 0.90× 0.90 = 0.81

b)For P(y = 3 ) = P(AUA) + P(UAA)

=0.9× 0.1×0.9 + 0.1× 0.9× 0.9 = 0.162

C) For any(Y = n), nᵗʰ batterry should be acceptable, as search for two acceptable batteries will complete once second acceptable battery gets selected. Hence for P(y=5), 5ᵗʰ battery must be an A. four outcome for which Y

= 5 are (AUUUA) ,(UAUUA),(UUAUA),(UUUAA)

P(y=5) = P(AUUUA) + P(UAUUA) + P(UUAUA) + P(UUUAA)

= 4× 0.9² × 0.1³

= 0.00324

d) From above probabilities we conclude, the general formula for p(y) is p(y) =(y- 1)(0.1)⁽ʸ⁻²⁾(0.9)².

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The steps regarded essential for a successful simulation study are:

a. Problem formulation

b. Model validation

c. Model verification

d. Experimental design

e. Output analysis

To give any solution to the problem the very first step necessary is to understand the problem . Now through the observations of the process the problem is defined and formulated .

Keeping in mind the real life solutions and necessities a model is developed . Now the further process of verification and validation is carried out . In verification we make sure that the model works as we thought through animation whereas validation makes sure that the model reflects reality .

Experimental design multiple similar models are compared with minute changes and the performance are compared to find the best suited model.

Finally the results of the study are discussed in output analysis through written reports , documents or presentation and the best product is chosen .

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