In AABC, which ratio equals cos C?

The area of the purple band is [tex]A = 4 - x^2[/tex]

Since both the shape contains the square so here the area square should be applied,

A  = Total purple area - Total green area

[tex]A = (2)^2 - (x)^2\\\\A = 4 - x^2[/tex]

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Final answer:

The area of the purple band around the green square is calculated by finding the difference between the area of the larger purple square and the green square. It is determined by subtracting the green square's area (x²) from the total area of the larger square ((x + 4)²), resulting in an area of 8x + 16 square inches for the purple band.

Explanation:

To calculate the area of the purple band on the rug, we must first determine the dimensions of both the inner green square and the larger purple square that includes the band. The side length of the green square is given as x inches, and we know the width of the purple band surrounding it is 2 inches. To find the side length of the larger purple square, we add twice the width of the purple band (2 inches on each side) to the side length of the green square, giving us x + 2 + 2 or x + 4 inches.

The area of the larger purple square is therefore (x + 4)² square inches. The area of the inner green square is x² square inches. To find the area of just the purple band, we subtract the area of the green square from the area of the larger purple square.

So, the area of the purple band is (x + 4)² - x² square inches. Expanding this expression, we get x² + 8x + 16 - x² which simplifies to 8x + 16 square inches. Therefore, the area of the purple band around the green square is 8x + 16 in²

Answer:

2/10 of her income will go to these items

Step-by-step explanation:

29 +15 = 41

41/1900  equal 2/10

Final answer:

Ena plans to spend 29% of her income on entertainment and 15% on groceries, which is a total of  [tex]\(\frac{44}{100}\)[/tex]of her income. Simplifying this to its lowest terms gives us [tex]\(\frac{11}{25}\)[/tex] of her income spent on these two items together.

Explanation:

To find the fraction of Ena's income that is spent on entertainment and groceries together, we need to sum the fractions of income allocated to each category. Ena plans to spend 29% of her income on entertainment and 15% on groceries. In fractional terms, 29% is the same as 29/100 and 15% is equivalent to 15/100. Adding these fractions together:

[tex]\(\frac{29}{100} + \frac{15}{100} = \frac{44}{100}\)[/tex]

Now, we simplify the fraction to its lowest terms:

[tex]\(\frac{44}{100} = \frac{44 \div 4}{100 \div 4} = \frac{11}{25}\)[/tex]

Thus, Ena plans to spend  [tex]\(\frac{11}{25}\)[/tex]of her income on entertainment and groceries together.

Answer:

Ans _ angle b = 79

Hope it helps

∠B4 = ∠A2

b° = 79°

hope this helps :)

Answer:

Step-by-step explanation:

The given system of simultaneous equations is expressed as

-5=x-3y

11=-3x+7y

Rearranging both equations, it becomes

x - 3y = - 5- - - - - - - - - - 1

- 3x + 7y = 11 - - - - - - - - - -2

Multiplying equation 1 by 3 and equation 2 by1, it becomes

3x - 9y = - 15 - - - - - - - - - - -3

- 3x + 7y = 11 - - - - - - - - - - - 4

Adding equation 3 to equation 4, it becomes

- 2y = - 4

Dividing the left hand side and the right hand side of the equation by

- 2, it becomes

- 2y/ - 2 = - 4y/- 2

y = 2

Substituting y = 2 into equation 1, it becomes

x - 3 × 2= - 5

x - 6 = - 5

Adding 6 to left hand side and the right hand side of the equation, it becomes

x - 6 + 6= - 5 + 6

x = 1

Final answer:

To find the year when the record became 19.68 seconds, substitute the value of R into the equation. Solve for t and add 1920 to get the year.

Explanation:

To find the year when the record became 19.68 seconds, we need to substitute the value of R into the equation:

R = -0.028t + 20.8

19.68 = -0.028t + 20.8

Solving for t:

Subtract 20.8 from both sides: -0.028t = -1.12

Divide both sides by -0.028: t = 40

Since t represents the number of years since 1920, we add 1920 to the result to get the year:

t + 1920 = 40 + 1920 = 1960

Therefore, the record became 19.68 seconds in the year 1960.

Answer:

12

Step-by-step explanation:

Given: Diagonal of square= [tex]3\sqrt{2}[/tex]

To find the perimeter of square, we need to find the length of sides of square.

∴ Using the formula of diagonal to find side of square.

Formula; [tex]Diagonal= s\sqrt{2}[/tex]

Where, s is side of square.

⇒ [tex]3\sqrt{2} = s\sqrt{2}[/tex]

Dividing both side by √2

⇒[tex]s= \frac{3\sqrt{2} }{\sqrt{2} }[/tex]

∴[tex]s= 3[/tex]

Hence, Length of side of square is 3.

Now, finding the perimeter of square.

Formula; [tex]Perimeter= 4s[/tex]

⇒[tex]Perimeter= 4\times 3[/tex]

∴ [tex]Perimeter= 12[/tex]

Hence, Perimeter of square is 12.

The perimeter of a square with a diagonal of 3 square root 2 units is 12 units.

To find the perimeter of a square with a diagonal of 3√2, we can use the fact that the diagonal of a square divides it into two congruent right triangles. The length of each leg of the triangle is equal to one side of the square. We can use the Pythagorean theorem to find the length of the side of the square. Let's assume that the length of the side of the square is s.

Using the Pythagorean theorem, we have s2 + s2 = (3√2)2. Simplifying, we get 2s2 = 18. Dividing by 2, we have s2 = 9. Taking the square root of both sides, we get s = 3.

The perimeter of the square is equal to 4 times the length of one side, so the perimeter is 4 * s = 4 * 3 = 12 units.

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Answer:

1. 1/2-2/5

2. 3/4-2/5

3. 1/2-3/4

Step-by-step explanation:

For you to be able to create such fractions you must make sure that the numerator is divisible by 20.

Clearly the number 2,4 and 5 can divide 20.so therefore any fraction formed with them will give the denominator 20

Answer:

[tex]a.\ 12[/tex]

Step-by-step explanation:

[tex]\frac{5}{6}y-8=2\\\\Add\ 8\ both\ sides\\\\\frac{5}{6}y-8+=2+8\\\\\frac{5}{6}y=10\\\\Multiply\ by\ 6\ both\ the\ sides\\\\\frac{5}{6}y\times 6=10\times 6\\\\5y=60\\\\divide\ by\ 5\ both\ the\ sides\\\\\frac{5y}{5}=\frac{60}{5}\\\\y=12[/tex]

Answer:

Step-by-step explanation:

x+x+(x+12)=180

3x=180-12=168

x=56

third angle=56+12=68

so angles are 56°,56°,68°

The larger angle is x + 12 i.e. 56 + 12 = 68⁰.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.

Let the first angle be x.

then second angle is equal to first i.e. x

and third angle = x + 12

we know that,

Sum of all angles of a triangle is 180⁰.

Now,

x + x + x + 12 = 180

3x = 180 -12

3x = 168

x = 168/3

x = 56

Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.

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Answer:

To find the x-intercept, substitute in  0  for  y  and solve for  x . To find the y-intercept, substitute in  0  for  x  and solve for  y -intercept(s):  ( − 1 + √ 6 , 0 ) , ( − 1 − √ 6 , 0 ) y-intercept(s):  ( 0 , − 5 )

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

C = 1.75M + 3.25

Step-by-step explanation:

Let E represent Economy

Let L represent Luxury

Let M be the number of miles driven

Let C be how much it cost to rent a luxury car than economy

E = -0.70M + 14.95

L = 1.05M + 18.20

C = L - M

C =(1.05M + 18.20) - (-0.70M + 14.95)

C = 1.05M + 18.20 + 0.70M - 14.95

collect like terms

C = 1.05M + 0.70M + 18.20 - 14.95

C = 1.75M + 3.25

The equation representing how much more it costs to rent a luxury car than an economy car, given the number of miles driven, is C = 1.75M + 3.25. This is derived by subtracting the equation for economy car costs from the equation for luxury car costs and simplifying.

The value of C, which is the cost difference between renting a luxury and an economy car, can be found by finding the difference between the charge equations for the two types of cars. To find C in terms of M, subtract the equation for the economy car (E) from the equation for the luxury car (L).

So, C = L - E

Substitute the given equations for L and E into the equation for C:

C = (1.05M + 18.20) - (-0.70M + 14.95)

Simplify the equation by distributing the negative sign on the right side of the equation:  

C = 1.05M + 18.20 + 0.70M - 14.95

Combine like terms:

C = 1.75M + 3.25

This equation represents how much more it costs to rent a luxury car than an economy car based on the number of miles driven.

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============================

Work Shown:

x = number of hours spent running

8x = distance he runs (since he runs at 8 mph)

y = number of hours spent walking

3y = distance he walks (he walks at a speed of 3 mph)

8x+3y = total distance = 16 miles

8x+3y = 16

This equation is in standard form Ax+By = C

--------

Extra Info

Solving for y will get

8x+3y = 16

3y = -8x+16

y = (-8x+16)/3

y = (-8x)/3+16/3

y = (-8/3)x+16/3

This is in slope intercept form y = mx+b

m = -8/3 is the slope

b = 16/3 is the y intercept

Step-by-step explanation:

a. 5/10 x 5/10 = 25%

b. 2/10 x 2/10 = 4%

c. 3/10 x 5/10 = 15% (Probability for getting black then green)

5/10 x 3/10 = 15% (Probability of getting green then black)

Thus, probability of getting green and black in any order is 30%

d. SIimilarly,

5/10 x 2/10 = 10% (Green then red)

2/10 x 5/10 = 10% (Red then green)

Green and red in any order 20%

Answer:

Depending on the remaining of the question.  C is the answer

Step-by-step explanation:

5/10 x 5/10 = 25%

2/10 x 2/10 = 4%

3/10 x 5/10 = 15%  Probability for getting black then green

5/10 x 3/10 = 15%  Probability of getting green then black

green and black in any order is 30% the changes are higher in this case.

5/10 x 2/10 = 10% (Green then red)

2/10 x 5/10 = 10% (Red then green)

Green and red in any order 20%

Yo sup??

The only way to solve this problem is by observing the graph closely and making some approximations.

We have to compare the value of x with the corresponding y value.

at x=4 you will find that the value of y is around 3.8-3.9

Therefore the answer is 3.8

Hope this helps.

Answer:

[tex]f(4) \approx 3.73[/tex]

Step-by-step explanation:

We can see that this function looks like a square root function but only shifted to the right by 1 and up by 2.

A square root function is:

[tex]f(x) = \sqrt{x}[/tex]

Shifting a function up means adding that value to the f(x):

[tex]f(x) = \sqrt{x}+2[/tex]

Shifting a function to the right means replacing a value x with the value (x-the value of shifting a function to the right):

[tex]f(x) = \sqrt{x-1}+2[/tex]

We can check that this really is a graph of a function [tex]f(x) = \sqrt{x-1}+2\\[/tex]:

[tex]f(1) = \sqrt{1-1}+2 = 0+2=2[/tex]

We can see on the graph that this really is the case : f(1)=2

Also,

[tex]f(2) = \sqrt{2-1}+2 = 1+2=3[/tex]

This is also the case if we check the graph.

So, now we have to estimate f(x) at x=4:

[tex]f(4) = \sqrt{4-1}+2 = \sqrt{3}+2[/tex]

where [tex]\sqrt{3} \approx 1.73[/tex] , hence:

[tex]f(4) \approx 1.73+2 = 3.73[/tex]

Answer:

A. The economy switches to producing less of one product without increasing the production of the other product

Step-by-step explanation:

PPC is the graphical representation of product combinations that an economy can produce, given resources & technology. It is downward sloping because given resources & technology, production of a good can be increased  by decreasing production of other good.

It is based on assumption that resources are efficiently utilised. Points on PPC show resources efficient utilisation, Points under PPC show under utilisation, Points outside PPC are beyond country's productive capacity.

If country produces less of a good without increasing production of other goods, implying wasted resources & production below PPC. This case doesn't satisfy productive efficiency

Other cases : Producing more of a good & less of other is just re allocative movement on the PPC itself. Production point at PPF intersection with either axis implies economy is producing only the good on that axis.

In all the cases except A. satisfy the 'productive efficiency'

Answer: the mixture contained 15 pounds of white chocolate and 5 pounds of dark chocolate.

Step-by-step explanation:

Let x represent the number of pounds of white chocolate in the candy shack mixture.

Let y represent the number of pounds of dark chocolate in the candy shack mixture.

The candy shack has 20 lb of mixed white and dark chocolate. This means that

x + y = 20

The 20lb mixture is worth $7.50 per pound. This means that the total cost of the mixture is

20 × 7.50 = $150

White chocolate alone sells for $8.00 per pound and dark chocolate sells for 6.00 per pound. This means that

8x + 6y = 150 - - - - - - - - - - - - - -1

Substituting x = 20 - y into equation 1, it becomes

8(20 - y) + 6y = 150

160 - 8y + 6y = 150

- 8y + 6y = 150 - 160

- 2y = - 10

y = - 10/ - 2

y = 5

x = 20 - y = 20 - 5

x = 15

Answer:

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle,

DE represents the hypotenuse of the right angle triangle.

With m∠E as the reference angle,

EF represents the adjacent side of the right angle triangle.

DF represents the opposite side of the right angle triangle.

To determine m∠E, we would apply

the Tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan E = 8/5 = 1.6

E = Tan^-1(1.6)

W = 58.0° to the nearest tenth.

Model A's optimal price is $5, with a $3 increase, and Model B's optimal price is $6, with a $4 increase.

Let's walk through the step-by-step calculations for both Model A and Model B.

Model A:

Given Function:

f(x) = -12.5x^2 + 75x + 200

Completing the Square to Find Vertex:

f(x) = -12.5(x^2 - 6x - 16)

f(x)/(-12.5) = (x^2 - 6x - 16)

f(x)/(-12.5) + 16 + 9 = (x-3)^2

f(x)/(-12.5) + 25 = (x-3)^2 - 25

f(x) = (-12.5)[(x-3)^2 + 312.5]

Vertex Form:

f(x) = (-12.5)(x-3)^2 + 312.5

The vertex is at (3, 312.5).

Optimal Price Calculation:

The x-coordinate of the vertex indicates the optimal increase, which is $3. So, the optimal price is 3 + 2 = $5.

Y-intercept:

f(x) = -12.5(9) + 312.5 = 200

The y-intercept is $200.

X-intercepts:

Factorizing the original equation, we get x = 8 and x = -2.

Model B:

Symmetry Axis Calculation:

Midpoint between x-intercepts x = (-2 + 10)/2 = 4.

Optimal Price Calculation:

The optimal increase is $4, resulting in a price of 4 + 2 = $6.

Y-intercept:

The y-intercept is graphically determined to be between $180 and $210.

In summary, Model A's optimal price is $5, achieved with a $3 increase, while Model B's optimal price is $6, attained with a $4 increase.

The sum of -4 and -8 is -12, so the numerical expression for the given phrase is 36 / (-12) and the simplified expression is -3.

To write a numerical expression for the phrase 'The quotient of 36 and the sum of -4 and -8,' we need to divide 36 by the sum of -4 and -8. The sum of -4 and -8 is -12, so the numerical expression is 36 / (-12).

Simplifying this expression, we get -3. Therefore, the simplified expression is -3.

Answer:

Third option: Definition of Congruent angles.

Step-by-step explanation:

For this exercise it is important to know the definition Congruent angles.

Congruent angles are defined as those angles that have equal measure.

The symbol used for Congruent angles is the following:

≅

Keep the explanation above on mind.

In this case, you know that [tex]\angle ABC[/tex] measures 90 degrees (This is also known as "Rigth angle"):

[tex]\angle ABC=90\°[/tex]

And you can observe in the table attached that the measure of [tex]\angle ABD[/tex] is also 90 degrres:

[tex]\angle ABD=90\°[/tex]

Therefore, since they have exactly the same measure, these angles are congruent. Then:

[tex]\angle ABC[/tex] ≅ [tex]\angle ABD[/tex]

Based on this, you can identify that the missing reason number 8 is: Definition of Congruent angles.

Answer:

D 7/27

Step-by-step explanation:

If Maria ate 2/9 of the pizza, that means she DIDN'T eat 7/9 of the pizza. So far so good? Ok, then you just need to find out what is 1/3 of 7/9, because the three brothers are dividing the leftover pizza equally, right? Hint - "of" usually means multiply. And remember multiplying fractions is lovely - you simply multiply the numerators together, then multiply the denominators together (no common denominator mumbo jumbo). So...

1/3 * 7/9 = 7/27.

Maria's brothers will each receive option D. 7/27 of the pizza.

To determine the fraction of the whole pizza each of Maria's brothers will receive, if they share the remaining pizza equally, follow these steps:

Therefore, each of Maria's brothers will receive option D. 7/27 of the whole pizza.

Answer:

  a.  see below

  b.  Rita: 300; John: 900; Rodell: 925

  c.  Rita: L; John: 3L; Rodell: 3L+25

  d.  L +3L +(3L+25) = 2125

  e.  Rita: $600; John: $1800; Rodell: $1850

Step-by-step explanation:

Since John's number of laps is expressed in terms of Rita's number of laps, it makes a certain amount of sense to use Rita's laps as a unit of measure. We don't yet know what that unit of measure is, but we can use it to describe both John's laps and Rodell's laps. Rodell will have 25 additional laps added to the 3 units that match John's laps.

Altogether, these 7 units +25 laps will match the total of 2100 +25 laps. It is pretty clear that 1 unit will be 2100/7 = 300 laps. This is shown in the attachment.

__

a) The attachment matches the above description.

__

b) 1 unit of 300 laps is the number of laps Rita swam. Then John's 3 units correspond to 3×300 = 900 laps, and Rodell's laps will be 25 more than John's, so 925.

__

c) In this part, we define 1 unit as L, so the three contributors are ...

__

d) The equation shows that the sum of the parts is equal to the whole:

  L + 3L + (3L+25) = 2125

__

e) The numbers of part (b) get multiplied by $2, so are ...

Answer:

a) Positively skewed

b) Median

Step-by-step explanation:

We are given the following in the question:

For a particular data, mean levels of attraction are much higher than the median and the mode for these data.

[tex]\text{Mean} > \text{Median}\\\text{Mean} > \text{Mode}[/tex]

a) Shape of data

Since the mean of data is greater than the median and mode of the data, thus, is a skewed data.

For a positively skewed data:

[tex]\text{Mean} > \text{Median} > \text{Mode}[/tex]

Thus, the given data is positively skewed data.

b) Measure of central tendency

Since it is a positively skewed data, median is a better measurement of central of tendency.

Advantage of median:

Final answer:

The data likely has a right-skewed distribution, making the median the most suitable measure of central tendency due to the impact of outliers.

Explanation:

a. What is the shape of the distribution for the data in this study?
The data distribution is likely skewed to the right, as the mean is much higher than the median and mode, indicating a long tail to the right.

b. What measure of central tendency is most appropriate for describing these data? Why?
In this case, the median is the most appropriate measure of central tendency because it is less affected by extreme values compared to the mean. Since the mean is much higher than the median and mode, it suggests outliers are pulling the mean upwards.

Final answer:

To find the three numbers, we determine 'a' and 'r' using a system of equations derived from the conditions that they form a geometric progression with 12 and an arithmetic progression with 9. By solving these equations, we obtain the three numbers in sequence.

Explanation:

The question requires us to find three numbers that form a geometric progression with the third being 12, and when the third number is changed to 9, the numbers form an arithmetic progression.

Let's denote the first number as 'a' and the common ratio of the geometric progression as 'r'. The three numbers in the geometric progression can be represented as 'a', 'ar', and 'ar^2'. Given that the third number is equal to 12, we have 'ar^2 = 12'.

When 12 is replaced with 9 to form an arithmetic progression, the common difference 'd' can be found by subtracting the first term from the second term. The three numbers in this sequence are 'a', 'a + d', and 'a + 2d'. Given that the third number is now 9, we have 'a + 2d = 9'.

To find 'a' and 'r', we can set up a system of equations using the fact that the second number in both progressions is the same. So 'ar = a + d'. We have the following system:

ar^2 = 12 (1)

a + 2d = 9 (2)

ar = a + d (3)

From equation (3), we can solve for 'd' in terms of 'a' and 'r': 'd = ar - a = a(r - 1)'. Substituting 'd' in equation (2), we get 'a + 2(a(r - 1)) = 9', which simplifies to 'a(2r + 1) = 9'.

Using this new equation along with equation (1), we solve for 'a' and 'r' to find the three numbers:

a(2r + 1) = 9 (4)

ar^2 = 12 (1)

From equation (1), 'a = 12/r^2'. Substituting this into equation (4) gives us a single equation: '12/r^2(2r + 1) = 9', which we can solve to find 'r', and subsequently, 'a'. After solving these, we find the three numbers that form both the geometric and arithmetic progressions.

Answer:

Step-by-step explanation:

[tex]tan K=\frac{2}{3} \\m \angle K=tan^{-1} (\frac{2}{3} ) \approx 33.7 ^\circ[/tex]

Answer:

Y doesn't vary directly with x

Answer:28

Step-by-step explanation:

X varies inversely as y

X©1/y

X=k/y

4=k/7

Cross product

We get 4×7=k×1

28=k

Therefore constant (k)=28

Answer:

  1 1/3 gallons per day

Step-by-step explanation:

To find gallons per day, divide gallons by days. ("per" means "divided by")

  (4 gal)/(3 day) = (4/3) gal/day

Demont used 4/3 = 1 1/3 gallon each day.

To find out how many gallons of gasoline Demonte used each day, divide the total amount used (4 gallons) by the number of days (3), yielding approximately 1.33 gallons per day.

Demonte used 4 gallons of gasoline in three days driving to work and used the same amount of gasoline each day. To calculate the amount of gasoline he used each day, you divide the total gallons of gasoline by the number of days. This can be represented by the following equation:

Gallons per day = Total gallons used ÷ Number of days

Gallons per day = 4 gallons ÷ 3 days

Gallons per day = 1.33 gallons per day (approximately)

Therefore, Demonte used approximately 1.33 gallons of gasoline each day.

The average net force on the man as he is brought to rest is: F = -1143.9N

Therefore, P.E = K.E

When the man comes to rest, the final velocity becomes, 0.

As, such, acceleration which is the rate of change of velocity becomes;

The force on the man; F = mass × acceleration.

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The average net force on the diver as he is brought to rest is approximately 689.56 N.

First, we can find the velocity of the man just before he reaches the water using the kinematic equation:

d = vt + 1/2at²

Now, let's calculate the velocity of the man just before he reaches the water using the equation:

vf​=0+(−9.8m/s2)×0.782s≈−7.664m/s

Since the velocity is negative, it means the man is moving downward.

After entering the water, the man comes to rest in 0.55 seconds. During this time, he decelerates due to the force of gravity, but this time in the opposite direction to his motion. We can use the equation:

Finally, we can determine the average net force using Newton's second law:

Given that the mass m of the man is 82 kg, we find:

F net = 82 kg × 14.025 m/s 2 ≈ 1147.35 N

Therefore, the average net force on the diver as he is brought to rest is approximately 1147.35 N.

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Answer:

Option C) z = 3                                  

Step-by-step explanation:

We are given the following in the question:

IQ scores are normally distributed.

An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,

[tex]x = \mu + 3\sigma[/tex]

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]

Thus, the z-score is 3.

Thus, the correct answer is

Option C) z = 3

The z-score for a student with an IQ three standard deviations above the mean would be z = 3.

If a very bright student is described as having an IQ that is three standard deviations above the mean, and if this student's IQ is reported as a z-score, the z-score would be z = 3. This is because a z-score is a measure of how many standard deviations an observation is above or below the mean. When we say an observation is three standard deviations above the mean, we are describing a z-score of 3. Thus, the correct answer is c. z = 3.

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Final answer:

To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.

Explanation:

To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.

The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.

The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.

To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.

Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.

Now we can subtract the fractions: 25/40 - 16/40 = 9/40.

Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.