9. Nydia Soto's total cost to rent a car was $400. The number of miles she drove was 1,000. What was the
cost per mile to rent the vehicle?

If two rows of a 3×3 matrix A are the same, then detA = 0.

True, consider a 3 × 3 matrix A with two identical rows.

The determinant of a matrix is a scalar value that encodes various properties of the matrix.

One property of the determinant is that it changes sign if two rows (or two columns) of the matrix are interchanged.

Another property is that if two rows (or two columns) of the matrix are the same, then the determinant is zero.

Without loss of generality, assume that the first and second rows of A are the same.

Interchange the first and third rows of A using an elementary row operation without changing the value of the determinant, since this operation changes the sign of the determinant.

Then, we obtain a matrix B of the form:

[ a11 a12 a13 ]

[ a11 a12 a13 ]

[ a31 a32 a33 ]

Now, we can expand the determinant of B along the first column to get:

det(B) = a11 × det(B11) - a31 × det(B31)

B11 and B31 are the 2x2 matrices obtained by deleting the first row and the first column, and the third row and the first column of B, respectively.

Since the first and second rows of B are identical, we have det(B11) = 0. Hence, we obtain:

det(B) = a11 × det(B11) - a31 × det(B31) = -a31 × det(B31)

Now, we can expand the determinant of B31 along its first column to get:

det(B31) = a12 × a33 - a32 × a13

Substituting this into the previous expression, we obtain:

det(B) = -a31 × det(B31) = -a31 × (a12 × a33 - a32 × a13)

This shows that the determinant of A is zero, since det(A) = det(B) by elementary row operations.

If two rows of a 3 × 3 matrix A are the same, then detA = 0.

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Answer: solving for x is not meant for this type of problem.

Step-by-step explanation:

(a) The sum of everyone's utilities is highest when 2,000 people go After and the rest go Before is not a Nash Equilibrium beacuse it doesn’t meet the criteria for Nash Equilibrium.

(b) The Nash equilibrium number of After 7am drivers is 4000.

(c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

a) No, it is not a Nash Equilibrium.

Nash Equilibrium is a set of strategies that make sure that no player can improve their own utility by unilaterally changing their strategy.

Therefore, let’s say that all players choose to follow the strategy of entering After 7 am, given that N>4000 people want to drive into Central London. In this scenario, everyone’s utility would be as follows:

u(After) = 50 – 0.01N

However, if a single person changes his strategy and chooses to enter Before 7 am instead, his utility would be 10 instead of the previous 0 (as he is still affected by the congestion even if he enters after).

Thus, the new utility for the person who switched would be greater than what they would have gotten before.

Therefore, this scenario doesn’t meet the criteria for Nash Equilibrium.

b) The Nash equilibrium number of drivers entering after 7 am can be found by the following formula:

50-0.01N=10

40=0.01N

N=4000

which means 4000 people should choose to go Before 7 am, and the rest should go After 7 am.

c) A congestion charge of 20 for drivers going after can solve the discrepancy between a and b.

Let’s say the congestion charge is C. In this case, the utility of entering After 7 am would be

u(After)

=30-0.01(N-A)+20

= 50-0.01N+20-0.01A-20 50-0.01N-0.01A-20 30-0.01N-0.01A

Thus, the Nash Equilibrium number of drivers entering after 7 am would be as follows:

30-0.01N-0.01A=10

20=0.01A

A=2000

N = 4000+2000

N = 6000

Therefore, a congestion charge of 20 for drivers going after can solve the discrepancy between a and b, as the Nash equilibrium is now met with the 2000 drivers entering after 7 am, and 4000 entering before 7 am.

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Answer:

The option which is:

On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).

Step-by-step explanation:

At first we should know the rules of translation

1) {f(x) + a} is f(x) shifted up (a) units

2) {f(x) – a} is f(x) shifted down (a) units

3) {f(x + a)} is f(x) shifted left (a) units.

4) {f(x – a)} is f(x) shifted right (a) units.

Given:

f(x) = x²

g(x) = (x-5)² + 1

By comparing [ the translation from f(x) to g(x) ] with the rules of translation

We can deduce that g(x) is the image of f(x) by translation 5 units right and 1 unit up ( rules 1 and 4)

See the attached figure which represent the graph of f(x) and g(x)

As shown g(x) goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10)

The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:

(P/A, i%, n) = (1 - (1 + i)^(-n)) / i

Substituting the values given:

i = 8%

n = 145

(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08

Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:

(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)

Therefore, the correct choice for the value of (P/A,8%,145) is:

C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)

Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:

(F/P, i%, n) = (1 + i)^n

We want the investment to double, so we have:

(1 + i)^9 = 2

Taking the ninth root of both sides:

1 + i = 2^(1/9)

Solving for i:

i ≈ 0.0809 or 8.09% (rounded to two decimal places)

Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.

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Answer:

D) when one angle is acute and the other is obtuse.

Step-by-step explanation:

A linear pair of angles are formed when two adjacent angles are supplementary, meaning their measures add up to 180 degrees. In this case, if one angle is acute (less than 90 degrees) and the other angle is obtuse (greater than 90 degrees), their measures can add up to 180 degrees and form a linear pair.

For example, let's consider angle A as 60 degrees (acute) and angle B as 120 degrees (obtuse). The sum of these angles is 60 + 120 = 180 degrees, fulfilling the requirement for a linear pair.

Answer: Hope this helps :)

Step-by-step explanation:

a) =Let the boys be x

girls = x-10

so

x + x - 10 = 50

or, 2x = 60

so, x = 30

boys = 30

girls = 30-10 = 20

Therefore, 30 boys participated in the activity.

b) = Let the zilong's stamp be x and miya's stamp be y

so

first

x+y = 40

y = 40-x

now

x - 10 = 2y

x-10 = 2(40-x)

x-10 = 80-2x

or, 3x = 90

so, x = 30

then y = 40-x

        y = 40-30 = 10

Therefore, Zilong had 30 stamps and Miya had 10 stamps before.

Answer:

answer is 1

Step-by-step explanation:

Answer:

(-4)-(-2)-{(-5)-[(-7)+(-3)-(-8)]}

=-4+2-{-5-[-7-3+8]

=2-{-5-[-2]}

=2-{-5+2}

=2+3

=5

Step-by-step explanation:

Answer:

The percentage of change is an increase of 12% from the original

Step-by-step explanation:

The percentage of change is a percentage of increase because the new value is greater than the original.

To find the percentage of change, we can divide the new value by the old which will give us the amount it increased by in decimal form, which we can simply multiply by 100 to find percentage:

84/75=1.12

1.12x100 = 112

The new value is 112% of the original, this means that the percentage of change is an increase of 12% from the original.

Hope this helped!

Answer:

increase and 12%

Step-by-step explanation:

84 -75 = 9

9 ÷ original # (75) = 0.12

0.12 x 100 = 12%

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

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The best statistical measure to represent the entire spread of the data set when a data set is symmetrical is the standard deviation.

The standard deviation is a measure of how much the individual data points vary from the mean of the data set.

It is calculated by taking the square root of the variance.

It is the average of the squared differences of each data point from the mean.

In a symmetrical data set, the mean, median, and mode are all equal and located at the center of the data set.

This represents that the data points are evenly distributed around the center.

The standard deviation can provide a good measure of the spread of the data points from this center.

Other measures of spread representing the range or interquartile range, may not be as useful in a symmetrical data set .

As they are more affected by outliers and skewness in the data.

Therefore, the symmetrical data set in best way represented by statistical measure known as standard deviation.

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Answer:

It's B, because thats where the two points cross

Step-by-step explanation:

Answer:

3003

Step-by-step explanation:

This is just basically choosing 5 players out of 15 people.

15 choose 5 is \(\frac{15!}{10!*5!}\)

\(\frac{15*14*13*12*11}{5*4*3*2}\)

3*7*13*11=1001*3=3003

Feel free to tell me if I did anything wrong! :)

The basketball team has 3,003,600 possible starting lineups. Given that there are 15 players on the roster and 5 players on the basketball court, this calculation involves determining the number of ways to select 5 players out of the total 15.

To calculate the number of possible starting lineups, we can use the concept of combinations. We have 15 players on the roster, and we need to select 5 players to form a starting lineup.

The number of ways to choose 5 players out of 15 can be calculated using the combination formula:

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

In this case, n represents the total number of players (15) and r represents the number of players needed for the lineup (5).

Plugging these values into the formula, we get:

C(15, 5) = 15! / (5! * (15 - 5)!)

= (15 * 14 * 13 * 12 * 11 * 10!) / (5! * 10!)

= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)

= 3,003,600

Therefore, there are 3,003,600 possible starting lineups for the basketball team. This means that the team has a vast number of combinations to choose from when selecting the starting lineup from the 15 players on its roster.

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Answer:

b; [5]

Step-by-step explanation:

i took the quiz

Answer:

35175

Step-by-step explanation:

The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).

Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.

The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.

As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;

ess = 1/Kp = 153/5.

Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.

Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;

ess = 1/Ka = ∞.

Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.

By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.

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Answer:

51 degrees

Step-by-step explanation:

angle 1 is 104 and angle 3 is 25

add those and u get 129

it has to all equal 180 so...

180-129 is 51

Answer:

An included angle is the angle between two sides of a triangle. It can be any angle of the triangle, depending on its purpose.

Step-by-step explanation:

In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.

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Answer:

for the first one I got y=-2x-2 the second part i got y=-x-1 or -1x-y-1=0  Correct me if I am wrong

Step-by-step explanation:

Use the slope formula

-4-4 =-8

  /               =-2

1 - -3=4

2. The second part use this formula y-y1=m(x-x1)

     y--4=-1(x-3)

y+4=-x+3

  -4      -4

y+0=-x-1

 y=-x-1      or -1x-y-1=0    I am not sure  

Answer:

57in

Step-by-step explanation:

20 + 37 = 57in

Answer:

5

Step-by-step explanation:

let the number be a.

5a=25

divide both sides by 5

5a=25

5divide by 5a is a.

5divided by 25 is 5

therefore,a=5.

the number is 5

The level of measurement that is most appropriate for position of persons in a line is given as follows:

D.) Ordinal.

There are four levels of measurement for the data, given as follows:

The measures of central tendency for each level are given as follows:

For the position of the people in the line, we use the median, which is the midpoint of the line, hence the level of measurement is ordinal.

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Answer:

c is it

Step-by-step explanation:

a p e x

The correct option is D. y=60x + 200.To find the equation of the line that passes through the given points (4, 440) and (6, 560) on a coordinate grid, we use the point-slope formula.The point-slope formula is an equation used to find the straight line's slope and y-intercept with respect to an individual point, as well as the x and y-axis coordinates.

The point-slope formula for any line through two points (x1, y1) and (x2, y2) is given by:y − y1 = m(x − x1) where m is the slope of the line.Using the point-slope formula, we find the slope of the line that passes through the points (4, 440) and (6, 560) on a coordinate grid as follows:Slope, m = (y2 - y1) / (x2 - x1)

Putting the values of x1 = 4, y1 = 440, x2 = 6, y2 = 560.Slope, m = (560 - 440) / (6 - 4) = 120 / 2 = 60

Therefore, the slope of the line is 60.Using the point-slope formula,y − y1 = m(x − x1 ),where m = 60, x1 = 4, and y1 = 440.Substituting the values, we get:y - 440 = 60(x - 4).Simplifying the equation,y - 440 = 60x - 240y = 60x + 200.

Hence, the equation of the line is y = 60x + 200. Therefore, the correct option is D. y=60x + 200.

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The equation will be written as (42/2) = 21.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quotient of a number, 2, and 21 is 42. The equation of the quotient will be written as,

42 / 2 = 21

Here the value 42 when divided by 2 will give 21.

Therefore, the equation will be written as (42/2) = 21.

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An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The table that represents an arithmetic sequence is the third table.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

aₓ = a₁ + (x-1)d

where d is the difference and a₁ is the first term of the sequence.

For the table to be in an arithmetic sequence, the difference between any two consecutive terms must be equal.

Hence, the table that represents an arithmetic sequence is the third table.

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Answer:

y-9 = -1/12(x-8)

Step-by-step explanation:

To write an equation of a line perpendicular to the graph of y = 12x-3 and passing through the point, we will follow the following steps.

The standard form of point-slope form of the equation of a line is  given as

y − y1 = m(x − x1),

m is the slope of the unknown line

(x1, y1) is a point on the line.

Step 1: We need to calculate the slope of the known line first,

Given y = 12x-3

from the equation, m = 12 on comparison.

Step 2: get the slope of the unknown line. since the line given is perpendicular to the line y = 12x - 3, the product of their slope will be -1 i.e Mm = -1

M = -1/m

M is the slope of the unknown line

M = -1/12

Step 3: We will substitute M = -1/12 and the point (8, 9) into the point-slope form of the equation of a line i.e y − y1 = M(x − x1),

M = -1/12, x1 = 8 and y1 = 9

y-9 = -1/12(x-8)

Using linear functions, it is found that the sales price in Port Townsend is never double the Seattle price.

A linear function has the following format:

\(y = mx + b\)

In which:

For Seattle:

\(m = \frac{137000}{20} = 6850\)

Thus, the sales prince in n years after 1970 for Seattle is:

\(S(n) = 38000 + 6850n\)

For Port Townsend:

\(m = \frac{160000}{20} = 8000\)

Thus, the sales prince in n years after 1970 for Port Townsend is:

\(P(n) = 8400 + 8000n\)

Port Townsend is double Seattle in n years after 1970, for which:

\(P(n) = 2S(n)\)

Then

\(8400 + 8000n = 2(38000 + 6850n)\)

\(8400 + 8000n = 76000 + 13700n\)

\(7500n = -67600\)

Negative number, and we are working only with positive, thus, it is found that the sales price in Port Townsend is never double the Seattle price.

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Answer:

0, 1/18, and 1/36

Step-by-step explanation:

For i = 2, the probability it lands on 6 is 0, because you cannot sum to 2 with a 6. The same applies to i = 3 thru i = 6.

For the probability that at least one of a pair of fair dice lands on 6 for i = 7, there are only two possible ways, the first roll is a 6 and the second roll is a 7, and the first roll is a 1 and the second roll is a 6. The total amount of ways is 6 * 6 = 36, so the total probability is 1/18. This also applies to i = 8 thru i = 11.

For i = 12, there is only one way to get 12, the first dice lands on 6 and the second dice lands on 6. Assuming the dice are indistinguishable, the probability is 1/36.

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

We have,

The complementary probability of "at least one die lands on 6" is "neither of the dice lands on 6."

Therefore, you need to find the probability that neither of the dice lands on 6 for each possible sum i, and then subtract that probability from 1 to get the desired probability.

Let's go through the cases:

i = 2 (only possible sum with two dice):

In this case, both dice must show a 1.

The probability of this happening on a fair 6-sided die is

(1/6) * (1/6) = 1/36.

i = 3: The combinations are (1, 2) and (2, 1).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 4:

The combinations are (1, 3), (2, 2), and (3, 1).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 5:

The combinations are (1, 4), (2, 3), (3, 2), and (4, 1).

The probability of any of these happening is 4 * (1/6) * (1/6) = 1/9.

i = 6:

The combinations are (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 7:

The combinations are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of any of these happening is 6 * (1/6) * (1/6) = 1/6.

i = 8:

The combinations are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

The probability of any of these happening is 5 * (1/6) * (1/6) = 5/36.

i = 9:

The combinations are (3, 6), (4, 5), and (5, 4).

The probability of any of these happening is 3 * (1/6) * (1/6) = 1/12.

i = 10:

The combinations are (4, 6) and (6, 4).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 11:

The combinations are (5, 6) and (6, 5).

The probability of either happening is 2 * (1/6) * (1/6) = 1/18.

i = 12:

The combination is (6, 6).

The probability of this happening is (1/6) * (1/6) = 1/36.

Now, sum up the probabilities for each case:

(1/36) + (1/18) + (1/12) + (1/9) + (5/36) + (1/6) + (5/36) + (1/12) + (1/18) + (1/18) + (1/36)

This simplifies to:

69/36 = 23/12

Thus,

The probability that at least one of a pair of fair dice lands on 6, given that the sum of the dice is i, where i ranges from 2 to 12, is 23/12.

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