Express the Cartesian coordinates ( - 5,5) in polar coordinates in at least two different ways. Write the point in polar coordinates with an angle in the range 0 < = theta < 2pi (Type an ordered pair. Type an exact answer, using pi as needed.) Write the point in polar coordinates with an angle in the range - 2pi < = theta < 0. [ ] (Type an ordered pair. Type an exact answer. using pi as needed.)

Answer: The mileage of a Chevy Cavalier weighing 1.1 thousand kg is 29.72 mpg.

Step-by-step explanation:

if there is a linear relationship between two variables x and y , then we represent this relation in the form of equation as :[tex]y= mx+c[/tex]   (*)

, where m = rate of change of y with respect to x

c= Constant or the value of y when x=0.

We assume there is a linear relationship between the curb weight of a car (in thousands of kilograms) and its combined mileage (in miles per gallon).

Let y= combined mileage (in miles per gallon)

x= curb weight of a car (in thousands of kilograms)

When x= 3 thousand kg  , y = 9 mpg

⇒ [tex]9= m(3)+c[/tex]                   [Put values in (*)]

⇒ [tex]9= 3m+c--------(1)[/tex]

When x= 1.9 thousand kg  , y = 21 mpg

⇒ [tex]21= m(1.9)+c[/tex]                   [Put values in (*)]

⇒ [tex]21= 1.9m+c--------(2)[/tex]

Eliminate the equation (1) from (2) , we get

[tex]1.9m-3m=21-9[/tex]

[tex]-1.1m=12\\\Rightarrow\ m=\dfrac{12}{-1.1}=\dfrac{-120}{11}[/tex]

Put value of m in (1) , we gte

[tex]9= 3(\dfrac{-120}{11})+c[/tex]

[tex]9= \dfrac{-360}{11}+c\\\Rightarrow\ c=9+\dfrac{360}{11}=\dfrac{459}{11}[/tex]

Substitute the value of m and c in (*) , we get

[tex]y= \dfrac{-120}{11}x+\dfrac{459}{11}[/tex]

When x= 1.1

[tex]y= \dfrac{-120}{11}(1.1)+\dfrac{459}{11}[/tex]

[tex]y= \dfrac{-120}{11}(\dfrac{11}{10})+\dfrac{459}{11}[/tex]

[tex]y=-12+\dfrac{459}{11}=\dfrac{327}{11}\approx29.72[/tex]

Hence, the mileage of a Chevy Cavalier weighing 1.1 thousand kg is 29.72 mpg.

Answer:

Explanation:

The function that can determine the distance from a point on the bottom edge of the banner to the floor is:

[tex]f(x)=0.25x^2-x+9.5[/tex]

That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.

So, you need to find the vertex of the parabola.

I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).

[tex]f(x)=0.25x^2-x+9.5\\ \\ 4(f(x))=4(0.25x^2-x+9.5)\\ \\ 4f(x)=x^2-4x+38\\ \\ 4f(x)-38=x^2-4x\\ \\ 4f(x)-38+4=x^2-4x+4\\ \\ 4f(x)-34=(x-2)^2\\ \\ 4f(x)=(x-2)^2+34\\ \\ f(x)=(1/4)(x-2)^2+8.5[/tex]

Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.

The lowest point on the bottom edge of the banner which results in a height of 8.5 feet above the floor.

To find the height above the floor of the lowest point on the bottom edge of the banner using the function f(x) = 0.25x^2 - x + 9.5, we need to determine the vertex of this quadratic function. The vertex form of a quadratic function f(x) = ax^2 + bx + c gives the minimum or maximum value of the function.

Here, the coefficient a is positive (0.25), indicating that the parabola opens upwards and thus has a minimum point. The x-coordinate of the vertex can be found using the formula x = -b / (2a).

Substitute x = 2 back into the function to find the minimum height:

f(2) = 0.25(2)^2 - 2 + 9.5 = 1 - 2 + 9.5 = 8.5 feet.

Therefore, the lowest point on the bottom edge of the banner is 8.5 feet above the floor.

sinФ = 1/6

sinФ = opposite/hypotenuse

cosФ = adjacent/hypotenuse

tanФ = opposite/adjacent

SOHCAHTOA

1^(2)+b^(2)=6^(2)

1+b^(2)=36

b^(2)=35

[tex]\sqrt{35}[/tex]

cosФ = [tex]\sqrt{35}[/tex]/6

tanФ = 1/[tex]\sqrt{35}[/tex] = [tex]\sqrt{35}[/tex]/35

Answer:

Cos ø = √35/6

Tan ø = √35/35

Step-by-step explanation:

Sin ø = opposite/hypothenus

Sin ø = 1/6

Pythagoras theorem says

Hyp² = Opp² + Adj²

6² = 1² + A²

A² = 35

A = √35

Hence, cos ø = √35/6

tan ø = 1/√35 = √35/35

Answer:

False

Step-by-step explanation:

Consider the equations with the same number of equations and variables as shown below,

Case 1

                        [tex]x_{1} + x_{2} = 0\\x_{1} + x_{2} = 1[/tex]

This equation has no solution because it is not possible to have two numbers that give a sum of 0 and 1 simultaneously.

Case 2

                       [tex]x_{1} + x_{2} = 1\\2x_{1} + 2x_{2} = 2[/tex]

This equation has infinitely many possible solutions.

Therefore it is FALSE to say a linear system with the same number of equations and variables, must have a unique solution.

The statement that a linear system with the same number of equations and variables must have a unique solution is false. Other considerations, such as whether the system is consistent or inconsistent and dependent or independent, can impact the amount of solutions a system has.

The statement is false. Even if a linear system has the same number of equations and variables, it does not necessarily mean that it will have a unique solution. Rather, whether a system has a unique solution, no solutions, or infinitely many solutions depends on whether the system is consistent or inconsistent and dependent or independent.

For instance, consider two linear equations: x + y = 5 and 2x + 2y = 10. Even though these two equations have the same number of variables and equations, they represent the same line and thus have infinitely many solutions. Similarly, consider the system x + y = 5 and x + y = 6. These two equations have also the same number of equations and variables but they are parallel lines and do not intersect, so this system does not have any solution.

So, the number of variables and equations is not always enough to determine the number of solutions to a linear system.

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Answer:

matrices can be simple added by ading the adjacent elements of the two matrices

The matrix multiplication is done by multiplying row of first matrix to columns of the other matrix.

each multiplication for each element of the resultant matrix.

Step-by-step explanation:

Answer:

1) Explanation and figure attached below.

2) For this case we see that most of the values are on the right part of the distribution so then we can conclude that the distribution is skewed to the left. The mean seems to be < Median< Mode for this case.

Step-by-step explanation:

Part 1

If we order the data from the smallest to the largest we got:

13.1 , 16.2  ,18.3 , 21.1 , 23.4 , 24.3 , 24.5

25.1 , 25.2 , 26.4 , 26.6 ,27.3  ,28 , 28.6 ,

28.7 , 29 , 29.4 , 29.4 , 29.5 , 30 , 30.7

31.2 , 32 , 32 , 33.5 , 33.6 , 33.7 , 33.9

34.2 , 34.4 , 34.5 , 34.5 , 34.8 , 34.8

34.8 , 34.9 , 35.3 , 35.3 , 35.6 , 35.7

35.9 , 36 , 36.6 , 36.8 , 37.7 , 37.9

38.1 , 38.8 , 39.2 , 39.9

For this case if we use 10 mpg as the lower limit and with a width of 5 mpg for the intervals we have the following table:

Interval   Frequency   Midpoint

[10-15)           1                 12.5

[15-20)          2                17.5

[20,25)         4                 22.5

[25-30)         12               27.5

[30-35)          17              32.5

[35-40)          14              37.5

Total             50

So the histogram is on the figure attached. The midpoint for the class interval with the largest number of observations is 32.5.

Part 2

For this case we see that most of the values are on the right part of the distribution so then we can conclude that the distribution is skewed to the left. The mean seems to be < Median< Mode for this case.

Final answer:

To construct the histogram, determine the class intervals and count the number of observations in each interval. The midpoint of the cell with the largest number of observations is approximately 37.45 mpg.

Explanation:

To construct a histogram with intervals of width 5 mpg, we start by determining the class intervals. Given that the lower limit of the first interval is 10 mpg, the class intervals can be calculated as follows: 10-14.9, 15-19.9, 20-24.9, 25-29.9, 30-34.9, 35-39.9. Next, we count the number of observations falling into each interval:

10-14.9: 3

15-19.9: 6

20-24.9: 5

25-29.9: 7

30-34.9: 9

35-39.9: 10

The cell with the largest number of observations is the one corresponding to the interval 35-39.9 mpg. To calculate the midpoint of this interval, we take the average of the lower and upper limits: (35 + 39.9) / 2 = 37.45. Therefore, the midpoint of the cell with the largest number of observations (the mode) is approximately 37.45 mpg.

Answer:

(a) 142 km trip requires 15.16 Liters of Gasoline

(b) The money spent is 69.34 euros or $87.37.

(c) The average speed of sprinter is 34.45 km/h.

(d) 4 lb of candy contains 0.559 kg of dietary fat.

Step-by-step explanation:

(a)

Given that;

Mileage = 22 mi/gal

Converting it to km/L

Mileage = (22 mi/gal)(1 gal/3.78 L)(1 km/0.6214 mi)

Mileage = 9.36 km/L

Now, the gasoline required for 142 km trip:

Gasoline Required = (Length of trip)/(Mileage)

Gasoline Required = (142 km)/(9.36 km/L)

Gasoline Required = 15.16 L

(b)

Given that;

Mileage = 30 mi/gal

Converting it to km/L

Mileage = (30 mi/gal)(1 gal/3.78 L)(1 km/0.6214 mi)

Mileage = 12.77 km/L

Now, the gasoline required for 142 km trip:

Gasoline Required = (Length of trip)/(Mileage)

Gasoline Required = (115 km/day)(7 days/week)/(12.77 km/L)

Gasoline Required = 63 L/week

Now, we find the cost:

Weekly Cost = (Gasoline Required)(Unit Cost)

Weekly Cost = (63 L/week)(1.1 euros/L)

Weekly Cost = 69.34 euros/week = $87.37

since, 1 euro = $1.26

(c)

Average Speed = (Distance Travelled)/(Time Taken)

Average Speed = 200 m/20.9 s

Average Speed = (9.57 m/s)(3600 s/1 h)(1  km/ 1000 m)

Average Speed = 34.45 km/h

(d)

22.7 g piece contains = 7 g dietary fat

(22.7 g)(1 lb/453.592 g) piece contains = (7 g)(1 kg/1000 g) dietary fat

0.05 lb piece contains = 0.007 kg dietary fat

1 lb piece contains = (0.007/0.05) kg dietary fat

4 lb piece contains = 4(0.007/0.05) kg dietary fat

4 lb piece contains = 0.559 kg dietary fat

Answer:

Since the equation was missing, I solved it with another equation and got an answer of T(0) = <3j / 5 + 4k / 5>.

Please see my explanation. I hope this helps

Step-by-step explanation:

The question asked us to find out unit tangent vector.

Recall unit vector = vector / magnitude of vector

Since the question is missing with an equation. I suppose an equation.

r(t)=Cost i, 3t j, 2Sin(2t) k at t=0

Lets take out differentiation

r'(t) = <(-Sint), 3, 2(Cos(2t)(2))>

r'(t)= <-Sint, 3, 4Cos(2t)>

Now substitute t=0 in the differentiate found above.

r'(0)= <-Sin(0), 3, 4Cos(2*0)>

r'(0)= <0, 3, 4(1)>

r'(0)= <0,3,4>

vector r'(0)=<0i, 3j, 4k>

Now lets find out magnitude of vector

|r'(0)| = [tex]\sqrt{0^{2}+3^{2}+4^{2} }[/tex]

|r'(0)| = [tex]\sqrt{0+9+16}[/tex]

|r'(0)| = [tex]\sqrt{25}[/tex]

|r'(0)| = 5

Unit Tangent Vector

T(0) = <0, 3, 4> / 5

T(0) = <3j / 5  +  4K / 5>

To find the unit tangent vector, we first need to find the velocity vector. Given that the position vector is r(t) = Acos(wt)i + Asin(wt)j, we can find the derivative of this vector to get the velocity vector. To find the unit tangent vector, we divide the velocity vector by its magnitude.

To find the unit tangent vector, we first need to find the velocity vector. Given that the position vector is r(t) = Acos(wt)i + Asin(wt)j, we can find the derivative of this vector to get the velocity vector:

v(t) = -Aw*sin(wt)i + Aw*cos(wt)j

To find the unit tangent vector, we divide the velocity vector by its magnitude:

T(t) = (v(t))/(|v(t)|) = (-Aw*sin(wt)i + Aw*cos(wt)j)/(sqrt((Aw*sin(wt))^2 + (Aw*cos(wt))^2))

So, the unit tangent vector at any point is T(t).

Answer:

The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.

Step-by-step explanation:

Given a function y, the average rate of change S of [tex]y=g(z)[/tex] in an interval  [tex](z_{s}, z_{f})[/tex] will be given by the following equation:

[tex]S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}}[/tex]

In this problem, we have that:

[tex]g(z) = 4z^{2} - 5[/tex]

Between the points( -2,11) and (2,11).

So [tex]z_{f} = 2, z_{s} = -2[/tex]

[tex]g(z_{f}) = g(2) = 4*(2)^{2} - 5 = 11[/tex]

[tex]g(z_{s}) = g(-2) = 4*(-2)^{2} - 5 = 11[/tex]

So

[tex]S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}} = \frac{11 - 11}{2 - (-2)} = \frac{0}{4} = 0[/tex]

The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.

Answer:

0.3667 or 36.67%

Step-by-step explanation:

The probability of getting at least 1 defective hard disk among the 5 (P(X>0)) is equal to 100% minus the probability of getting none defectives (1-P(X=0)).

If 23 out of 25 hard disks are non-defective, the probability is:

[tex]P(X>0) = 1 -P(X=0)\\P(X>0) = 1 -\frac{23}{25}*\frac{22}{24} *\frac{21}{23} *\frac{20}{22} *\frac{19}{21}\\ P(X>0) = 0.3667=36.67\%[/tex]

The probability that there is at least 1 defective hard disk is 0.3667 or 36.67%.

Answer:

a. The mean growth of plant is same for each type of soil.

Step-by-step explanation:

The analysis of variance is statistical procedure used to assess the equality of more than two means by computing two different estimate of variances. Basically when we have more than two means to compare, we can't use t-test or z-test because these procedure will be tedious and time taking. So, the null hypothesis will be the same. Hence the null hypothesis in the given scenario is that "the mean growth of plant is same for each type of soil".

Answer:

1920 k calories is the basal metabolism.

Step-by-step explanation:

Formula to get the total basal metabolism has been given by the formula

R(t) = [tex]80-0.18cos\frac{\pi t}{12}[/tex]

Where t = time

Now to calculate the total basal metabolism we will integrate the function with respect to time from 0 to 24 hours.

[tex]\int_{0}^{24}R(t)=\int_{0}^{24}(80-0.18cos\frac{\pi t}{12})dt[/tex]

= [tex][80t-{0.18}\times \frac{sin\frac{\pi t}{12}}{\frac{\pi}{12}}]_{0}^{24}[/tex]

= [tex][(80-0)24-\frac{0.18\times 12}{\pi}(sin2\pi - sin0)][/tex]

= [(80-0)24-(sin2\pi - sin0)]

= 80×24

= 1920 k calories

Therefore, 1920 k calories is the total basal metabolism of the young man.

Answer:

1. x = (199/130)e^(-2t) - (33/65)e^(-4t) - (18/65)cos3t - (1/65)sin3t

2. x = (191/128) - (63/128)e^(-4t) + (t³/12) - (t²/16) + (t/32)

Step-by-step explanation:

Steps are shown in the attachment.

Answer:

(0.185, 0.413)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

Z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 87, x = 26, p = \frac{x}{n} = \frac{26}{87} = 0.2989[/tex]

98% confidence interval

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.325[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2989 - 2.325\sqrt{\frac{0.2989*0.7011}{87}} = 0.185[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2989 + 2.325\sqrt{\frac{0.2989*0.7011}{87}} = 0.413[/tex]

So the correct answer is:

(0.185, 0.413)

The expression  [tex]Cosec\theta*Tan\theta[/tex] in terms of [tex]Sin\theta[/tex] and  [tex]Cos\theta[/tex] in simplified form is  [tex]Cosec\theta*Tan\theta = Sin\theta[/tex]

Given expression:

[tex]Cosec\theta*Tan\theta[/tex]

Express [tex]cosec\theta[/tex]  and  [tex]Tan\theta[/tex]  in terms of [tex]Sin\theta[/tex]  and [tex]Cos\theta[/tex]

Now,

[tex]Cosec\theta = \dfrac{1}{Sin\theta}[/tex]

[tex]Tan\theta = \dfrac{Sin\theta}{Cos\theta}[/tex]

Substitute the expression of  [tex]Cosec\theta[/tex]  and  [tex]Tan\theta[/tex] in original expression:

[tex]Cosec\theta*Tan\theta = \dfrac{1}{Sin\theta} * \dfrac{Sin\theta}{Cos\theta}[/tex]

[tex]Sin\theta[/tex]  is cancel out in the right-hand side of the equation:

[tex]Cos\theta[/tex] can be written as:

[tex]\dfrac{1}{Cos\theta} = \dfrac{1}{\dfrac{1}{Sin\theta} }[/tex]

[tex]= Sin\theta[/tex]

For the given expression:

[tex]Cosec\theta*Tan\theta = Sin\theta[/tex]

The simplified expression is [tex]Cosec\theta*Tan\theta = Sin\theta[/tex]

Learn more about Trigonometric identities here:

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The expression csc θ tan θ simplifies to sec θ which further simplifies to [tex]\frac{1}{cos\theta}[/tex].

To express csc θ tan θ in terms of sin θ and cos θ, we start by rewriting each trigonometric function:

Answer:

a) 1/3

b) 0.0658436214  

Step-by-step explanation:

Part a

Ann wins first round = (P , R) + (S , P) + (R , S) = 3 possibilities of win

Total outcomes = Wins + Losses + Ties = 9 possibilities

Hence,

P (Ann wins first round) = 3/9 = 1/3

Part b

Ann losses or ties first 4 rounds and wins 5th round

P(Ann loosing or tie in any round) = 6/9 = 2/3

Hence,

P(Ann wins 5th round only) = (2/3)^4 * (1/3) = 0.0658436214  

Part c

Final answer:

In rock-paper-scissors, Ann has a 1/3 probability of winning the first round. The probability of Ann's first win in round #5 is (2/3)^4 × (1/3), and the probability of Ann's first win coming after round #5 is 1 - (2/3)^5.

Explanation:

To answer these questions, we will calculate the probabilities based on the uniform random choices made by Ann and Bill in the game of rock-paper-scissors.

Probability Ann wins the first round: Each player has 3 choices, resulting in 9 possible outcomes. There are 3 ways Ann can win (rock beats scissors, paper beats rock, scissors beats paper), so the probability is 3/9 or 1/3.

Probability Ann's first win happens in round #5: We need 4 consecutive non-wins (losses or ties) and a win in the 5th round. The probability of a non-win per round is 2/3, making the probability of four non-wins (2/3)^4. The probability Ann wins the 5th round is 1/3. Therefore, the probability of this scenario is (2/3)^4 × (1/3).

Probability that Ann's first win comes after round #5: This is the probability of Ann not winning in the first 5 rounds. As each round is independent, we raise the non-winning probability to the power of 5, (2/3)^5, and subtract from 1 to get the desired probability.

Final answer:

The probability of drawing a 7 followed by a king from a standard 52-card deck without replacing the first card is 4/663, which rounds to approximately 0.006 when rounded to the nearest thousandth.

Explanation:

The student is asking to find the probability of drawing a 7 for the first card and a king for the second card from a standard 52-card deck, without replacing the first card. To solve this, we need to calculate the probability of each event occurring consecutively.

First, the probability of drawing a 7 from a deck of 52 cards is 4/52 or 1/13, because there are 4 sevens in the deck. After drawing a seven, there are now 51 cards left in the deck. Next, the probability of drawing a king from the remaining 51 cards is 4/51, since there are still 4 kings in the deck.

To find the combined probability of both events happening, we multiply these probabilities together:

Probability of drawing a 7 and then a king = (1/13) × (4/51)

Which simplifies to:

Probability = 4/663

Rounded to the nearest thousandth, the probability is approximately 0.006.

Final answer:

To find the equation of a line perpendicular to 2x - 3y = 13 and passing through (-6, 5), first find the slope of the given line, then its negative reciprocal for the perpendicular line, and finally apply the point-slope formula with the new slope and given point.

Explanation:

To find the equation of a line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5), follow these steps:

Rewrite the given equation in slope-intercept form (y = mx + b) to find its slope.

Calculate the slope of the perpendicular line using the negative reciprocal of the given line's slope.

Use the point-slope formula with the slope from step 2 and the given point to find the equation of the perpendicular line.

Rewriting the given equation: 2x - 3y = 13 → -3y = -2x + 13 → y = (2/3)x - 13/3. The slope (m1) is 2/3. The slope of the perpendicular line (m2) is -3/2 (the negative reciprocal of m1). Using the point-slope formula with the perpendicular slope and the point (-6, 5), we get: y - 5 = (-3/2)(x + 6), which simplifies to y = (-3/2)x - 4. This is the equation of the line perpendicular to 2x - 3y = 13 that passes through (-6, 5).

Answer:

a) 10.6; 48.7; within

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 29.6

Standard deviation = 6.35

"According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years.

Nearly all(99.7%) will be within 3 standard deviations from the mean.

So from 29.6 - 3*6.35 = 10.6 years to 29.6 + 3*6.35 = 48.7 years.

Anna was 11-years old, so she was within this range.

So the correct answer is

a) 10.6; 48.7; within

The ages of nearly all lead actresses will be between 16.9 and 42.3 years according to the Empirical Rule. Anna Paquin's age falls within this range when she won the academy award.

According to the Empirical Rule, for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. Since the mean age is 29.6 years and the standard deviation is 6.35 years, we can calculate the range as follows:

One standard deviation: 29.6 ± 6.35 = 23.25 to 35.95

Two standard deviations: 29.6 ± (2 × 6.35) = 16.9 to 42.3

Three standard deviations: 29.6 ± (3 × 6.35) = 10.55 to 48.65

Since Anna Paquin was 11 years old when she won the academy award, her age falls within the range of two standard deviations, which is 16.9 to 42.3 years. Therefore, the correct answer is option c) 16.9: 42.3; not within.

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The number of ounces that can be bought for $4.60 will be 9.2 ounces.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Conversion means to convert the same thing into different units.

If a pound of almonds costs $8.

We know that in one pound, there are 16 ounces. Then the cost of each ounce will be

⇒ 8 / 16

⇒ $0.5 per ounce

Then the number of ounces that can be bought for $4.60 will be

⇒ 4.6 / 0.5

⇒ 9.2 ounces

The number of ounces that can be bought for $4.60 will be 9.2 ounces.

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Individual:  A single country.

Variable:   The mean density of people per square kilometer of all countries.

Population:  Set of all countries.

Sample:  Set of the 56 countries on which data is collected.

Parameter: The mean density of people per square kilometer calculated from the population.

Statistic:  The mean density of people per square kilometer calculated from the sample.

Individual: Individuals are the objects described by a set of data.

Variable: Variables are characteristics of individuals.

Population: Population is all individuals of interest.

Sample: Sample is a subset of the population.

Parameter: Parameter is a characteristic of a population.

Statistics: Statistic is a characteristic of a sample.

The individual is the country, the variable is the density of people per square kilometer, the population is all the countries in the world, the sample is the 56 countries, the parameter is the true mean density of all countries, and the statistic is the estimated mean density from the 56 sampled countries.

In the example given, the individual is each of the 56 countries from which the World Health Organization collects data. The variable is the density of people per square kilometer in each of these countries. The population consists of all the countries in the world. The sample includes the 56 countries for which data was collected. The parameter is the true mean density of people per square kilometer for all countries. Finally, the statistic is the estimated mean density of people per square kilometer based on the data from the sample of 56 countries.

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Answer:

The answer is "False."

Explanation:

An area is considered the amount of space that an object occupies. A filled-area subjects the object to be made  up of lines. These lines connect with each other to form an "edge."

The connection of the lines in order to define the object's shape or area are considered "snap points." Remember that "polygons" are made of line segments, where their endpoints meet with each other in order to define its closed shaped. Thus, it needs to conform to "snap points."

This explains the answer.

The given statement "Like the edges of a filled-in area, the endpoints of a polygon do not need to conform to snap points" is false.

The edge of a filled-in area is the boundary of the surface. Area is a two-dimensional space covered by any surface. The boundary of the surface is generally the edges of the area. The edges or the boundary should connect in order to make a closed area or surface.

Similarly, snap points are the end points of the sides of a polygon. These endpoints need to connect with each other in order to make a closed figure. Polygon is a closed figure with n number of sides.

Therefore, the given statement "Like the edges of a filled-in area, the endpoints of a polygon do not need to conform to snap points" is false.

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Answer:

[tex]A)\,\,det(A)=1[/tex]

[tex]B)\,\,A^{-1}=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right] [/tex]

Step-by-step explanation:

[tex]det(A) = \left\Bigg|\begin{array}{ccc}1&1&1\\3&4&3\\3&3&4\end{array}\right\Bigg|[/tex]

Expanding with first row

[tex]det(A) = \left\Bigg|\begin{array}{ccc}1&1&1\\3&4&3\\3&3&4\end{array}\right\Bigg|\\\\\\det(A)= (1)\left\Big|\begin{array}{cc}4&3\\3&4\end{array}\right\Big|-(1)\left\Big|\begin{array}{cc}3&3\\3&4\end{array}\right\Big|+(1)\left\Big|\begin{array}{cc}3&4\\3&3\end{array}\right\Big|\\\\det(A)=1[16-9]-1[12-9]+1[9-12]\\\\det(A)=7-3-3\\\\det(A)=1[/tex]

To find inverse we first find cofactor matrix

[tex]C_{1,1}=(-1)^{1+1}\left\Big|\begin{array}{cc}4&3\\3&4\end{array}\right\Big|=7\\\\C_{1,2}=(-1)^{1+2}\left\Big|\begin{array}{cc}3&3\\3&4\end{array}\right\Big|=-3\\\\C_{1,3}=(-1)^{1+3}\left\Big|\begin{array}{cc}3&4\\3&3\end{array}\right\Big|=-3\\\\C_{2,1}=(-1)^{2+1}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=-1\\\\C_{2,2}=(-1)^{2+2}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=1\\\\C_{2,3}=(-1)^{2+3}\left\Big|\begin{array}{cc}1&1\\3&3\end{array}\right\Big|=0\\\\[/tex]

[tex]C_{3,1}=(-1)^{3+1}\left\Big|\begin{array}{cc}1&1\\4&3\end{array}\right\Big|=-1\\\\C_{3,2}=(-1)^{3+2}\left\Big|\begin{array}{cc}1&1\\3&3\end{array}\right\Big|=0\\\\\\C_{3,3}=(-1)^{3+3}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=1\\\\[/tex]

Cofactor matrix is

[tex]C=\left[\begin{array}{ccc}7&-3&3\\-1&1&0\\-1&0&1\end{array}\right] \\\\Adj(A)=C^{T}\\\\Adj(A)=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right] \\\\\\A^{-1}=\frac{adj(A)}{det(A)}\\\\A^{-1}=\frac{\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right] }{1}\\\\A^{-1}=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right][/tex]

Answer:

T = 72/4 = 18years

T = 20years (to the nearest tenth)

Step-by-step explanation:

Using the rule of 72, which is used to estimate the number of years for a given investment to double at a given interest rate.

Doubling time = 72/interest rate

T = 72/r

Rate r (in percentage) = 4%

Time T (in years)

T = 72/4 = 18years

T = 20years (to the nearest tenth)

Answer:

[tex](0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401[/tex]  

[tex](0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380[/tex]  

We are confident at 95% that the difference between the two proportions is between [tex]-0.4401 \leq p_B -p_A \leq -0.1380[/tex]

1.  -.4401 ≤ p1 - p2 ≤ -.1380

4.  The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

Step-by-step explanation:

In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a sample of 80 mail carriers, 56 had received animal bites. Is there a significant difference in the proportions? Use a 0.05. Find the 95% confidence interval for the difference of the two proportions. Sellect all correct statements below based on the data given in this problem.

1.  -.4401 ≤ p1 - p2 ≤ -.1380

2.  -.4401 ≤ p1 - p2 ≤ .1380

3.  The rate of mail carriers being bitten in San Jose is statistically greater than the rate San Francisco at α = 5%

4.  The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

5.  The rate of mail carriers being bitten in San Jose and San Francisco are statistically equal at α = 5%

Solution to the problem

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p_1[/tex] represent the real population proportion for San Jose

[tex]\hat p_1 =\frac{30}{73}=0.411[/tex] represent the estimated proportion for San Jos

[tex]n_1=73[/tex] is the sample size required for San Jose

[tex]p_2[/tex] represent the real population proportion for San Francisco

[tex]\hat p_2 =\frac{56}{80}=0.7[/tex] represent the estimated proportion for San Francisco

[tex]n_2=80[/tex] is the sample size required for San Francisco

[tex]z[/tex] represent the critical value for the margin of error  

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]  

The confidence interval for the difference of two proportions would be given by this formula  

[tex](\hat p_1 -\hat p_1) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]  

For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.  

[tex]z_{\alpha/2}=1.96[/tex]  

And replacing into the confidence interval formula we got:  

[tex](0.411-0.7) - 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.4401[/tex]  

[tex](0.411-0.7) + 1.96 \sqrt{\frac{0.411(1-0.411)}{73} +\frac{0.7(1-0.7)}{80}}=-0.1380[/tex]  

We are confident at 95% that the difference between the two proportions is between [tex]-0.4401 \leq p_B -p_A \leq -0.1380[/tex]

Since the confidence interval contains all negative values we can conclude that the proportion for San Jose is significantly lower than the proportion for San Francisco at 5% level.

Based on this the correct options are:

1.  -.4401 ≤ p1 - p2 ≤ -.1380

4.  The rate of mail carriers being bitten in San Jose is statistically less than the rate San Francisco at α = 5%

The student's question relates to analyzing trends in car safety award data and understanding supply curve dynamics in the context of business or economics at the college level. It requires statistical analysis and economic reasoning.

The student's question involves analyzing data to determine if there has been a change in the distribution of cars that earned top safety picks between the years 2009 and 2013. This question lies within the field of Business or specifically within the area of business statistics, focusing on the analysis of trends over time.

Furthermore, considering the supply of cars and how it changes with price is another key aspect of this question. Using the supplied figures and tables, which is common in business studies, the student is asked to interpret how the quantity supplied of cars changes as the price increases from $20,000 to $22,000—a concept known in economics as the law of supply.

In summary, the question requires the application of statistical analysis to evaluate changes in car safety awards over time and the understanding of basic supply curve dynamics.

Your complete question is: High demand cars that are also in low supply tend to retain their value better than other cars. The data in the table below is for a car that won a resale value award. a. Write a function to represent the change in the percentage of the car's value over time. Suppose that the function is linear for the first 5 years. b. Based on your model, by what percent did the car's value drop the day it was bought and driven off the lot? c. Do you think the linear model would still be useful after 10 years? Why or why not? d. Assume you used months instead of years to write a function. How would your model change?

Answer:

A. Statistic

Step-by-step explanation:

Usually whole population is difficult to cover so the part of population is considered to assess the aspects of population. The statistic is the quantity which summarizes the sample. The problem illustrate that summary measure is calculated from sample to describe a population. As the summary measure is computed from sample then it is a statistic.

Answer:

140·80=11200

Step-by-step explanation:

From exercise we have example for how we find  half the sum of 246 and 388, we can enter "(246+388)/2".  

Based on this example, we will calculate what is required in the task using a calculator. So we use a calculator to find the product of the following numbers, 140 and 80.

We calculate, and we get

140·80=11200

Answer:

True

Step-by-step explanation:

A linear system of equations will have a unique solution if and only if the number of variables equal the number of independent equations.

By independent equations we mean the same equation not repeated by multiplying by any constant.

Suppose number of variables are n, we must have the determinant formed by the coefficients non zero to have a unique solutions.

Here the no of equations are less than the number of variables.  So we cannot have a unique solution but can have a parametric solution using the number of parameters as n-m where n = number of variables and m = the number of independent equations given.

So the given statement is true.

Answer:

a) [tex]H_{0}: p = 0.66\\H_A: p > 0.66[/tex]

b) P-value = 0.2650

c) No, this programme will not be recommended as there is no real improvement over the national average.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 240

p = 66% = 0.66

Alpha, α = 0.05

Number of students admitted to law school , x = 163

a) First, we design the null and the alternate hypothesis  

[tex]H_{0}: p = 0.66\\H_A: p > 0.66[/tex]

This is a one-tailed(right) test.  

Formula:

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{163}{240} = 0.6792[/tex]

[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]

Putting the values, we get,

[tex]z = \displaystyle\frac{0.6792-0.66}{\sqrt{\frac{0.66(1-0.66)}{240}}} = 0.6279[/tex]

b) Now, we calculate the p-value from the table.

P-value = 0.2650

c) Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is no real improvement over the national average.

No, this programme will not be recommended as there is no real improvement over the national average.