10. f(3)=2x-5 Evaluate the function.
Answer should be written: f(3)=?
Type a response
2/1

For the given distributions, we have that:

a) The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

b) The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

The range of a distribution is given by the difference between the greatest value and the smallest value.

Hence, for the Traditional classroom, the range is given by:

86.4 - 56.6 = 29.8.

For the Flipped classroom, the range is given by:

92.6 - 64.4 = 28.2.

Hence:

The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.

Using a calculator, following the described procedure, the standard deviations are given as follows:

Hence:

The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.

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The speed of plane in still air is 715 MPH and the speed of the wind is 65 MPH

Distance travelled by airplane = 3900 miles

Time taken by the plane to travel the distance with the wind = 5 hours

Time taken by the plane to travel the distance against the wind = 6 hours

Let the speed of the plane in still air be x

Let the speed of the wind be y

Finding the speed of the air and airplane when distance is covered with the wind using the formula:

Speed of airplane + Speed of wind = Distance/Time

x + y= 3900/5

x + y = 780------(1)

Finding the speed of the air and airplane when distance is covered against the wind using the formula:

Speed of airplane - Speed of wind = Distance/Time

x - y = 3900/6

x - y = 650------(2)

Equating (1) and (2) we get:

2x = 1430

x = 715

Putting x = 715 in (1) we get:

y = 65

So, Speed of airplane in still air is 715 MPH and Speed of wind is 65 MPH  

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a) The total distance covered is 56 feet

b) The total displacement is 14 feet

c) The average speed  in the first, second, and third parts of the car’s motion are; 5 feet/sec,  0 feet/sec and  4.2 feet/sec

d) The average speed of the car is 3.5 feet/sec

e) The average velocity of the car is 0.875 feet/sec

We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.

Let us now carry pout the calculations;

a) Total distance = 35 feet +  21 feet = 56 feet

b) Total displacement =  35 feet -   21 feet = 14 feet

c) Average speed of the first, second, and third parts of the car’s motion;

i)  35 feet / 7 seconds = 5 feet/sec

ii) 0 feet/sec ( it sat still)

iii) 21 feet/5 seconds = 4.2 feet/sec

d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec

e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec

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When the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

The equation is given as

x = 1 - 1/(1 - (1/(1 - y)^2)))

The question implies that we change the subject and make x the subject

However, in the equation;

The subject of the equation is x

This means that when the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))

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Answer:

Step-by-step explanation:

E - 4,-2

F - 6, -3

G - 1, -4

The range measures the difference between the minimum value and the maximum value in a dataset. The interquartile range measures the difference between the first quartile (25th percentile) and third quartile (75th percentile) in a dataset. This represents the spread of the middle 50% of values

Answer:

x = 5.94

Step-by-step explanation:

The new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction.

When we dilate the points of a given figure, we simply multiply each x-coordinate and y-coordinate by the scale factor.

Here the points are Q (-3,0), R (-3,6), T (4,6), U (4,0) and the scale factor is

k = 1/3

Therefore,

⇒ Q (-3,0) → Q´ (-3 × 1/3,0 × 1/3) = (-1, 0)

⇒ R (-3,6) → R´  (-3 × 1/3, 6 × 1/3) = (-1, 2)

⇒ T (4,6) →  T´  (4 × 1/3, 6 × 1/3) = (4/3, 2)

⇒ U (4,0) → U´  (4 × 1/3, 0 × 1/3) = (4/3, 0)

Thus, the new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction

Dilation is the process of modifying the dimensions of an object or shape by varying some scale variables. For instance, a circle with a radius of 10 units gets shrunk to a circle with a radius of 5 units. This technique is applied in photography, fine art, logo design, and other fields.

Four fundamental categories of transformations exist in geometry.

These are:

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Answer:

16 meters is the answer of this question

We get the speed of the object as 5365 miles / day after rounding off.

We are given that an object is moving at a speed of 360 kilometers per hour.

We know that:

1 km = 0.621 miles.

So, 360 km will be:

360 km = 223.56 miles.

Also, we know that:

we have 24 hours in 1 day.

1 day = 24 hours.

1 hour = 1 / 24 day.

Re-writing the speed of the object, we get that:

223.56 miles in 1 / 24 day

That is:

5365.44 miles / day.

Rounding off:

= 5365 miles / day.

Therefore, we get the speed of the object as 5365 miles / day after rounding off.

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The cost of buying lemons to make two 9-inch lemon pies is $5.20.

The first step is to convert cup to tablespoons

1 cup = 16 tablespoons

one 9-inch lemon pie would require 8 tablespoons (16 /2)

two  9-inch lemon pie would require 16 tablespoons (8 x 2)

The second step is to determine how much lemons would be needed.

Lemons needed = table spoons needed / table spoon one lemon would yield

16 / 2 = 8 lemons

The total cost of lemons needs to make the pies = cost of one lemon x number of lemons needed

8 x 0.65 = $5.20

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Answer:

Step-by-step explanation:

7(4x-5) - 4(6x+5) = -91

28x - 35 - 24x -20 = -91

28x - 24x = -91 + 35 + 20

4x = -36

x = -36 : 4

x = -9

---------------

Answer:

57, 59 and 61

Step-by-step explanation:

Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)

We are given that the sum of the numbers is 177. So we have the following equation:

n + (n + 2) + (n +4) = 177

Simplifying gives

n + n + 2 + n + 4  = 177

Collect like terms:

n + n + n + 2 + 4 = 177
3n + 6 = 177

Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171

Divide by 3 both sides
3n/3 = 171/3

n = 57 and this is the first of the odd numbers

The next odd number is 57+ 2 = 59

and the next one after that is 59 + 2 = 61 (same as 57 + 4)

The linear system of equation has one solution as x = 16 and y = -12.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The given system of equation are :

y=-x+4..........(1)

x + 2y = -8......(2)

Now, solving the above using substitution of y in equation (2) :

x + 2y = -8

x+2(-x+4) = -8

x-2x+8 = -8

-x = -16

x = 16

Now, substituting back x value in equation (1) we get :

y = -x+4

y = -16 +4

y = -12

Therefore, The linear system of equation has one solution as x = 16 and y = -12.

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Answer:

120

Step-by-step explanation:

We note that 2, 4 is the least common multiple of 6,8 and 12

We have to find the smallest 3 -digit multiple of 24.

Also 24 × 4 = 96 and 24 ×5 = 120.

The smallest 3-digit number which is exactly divisible by 6,8 and 12 is 120.

Answer:

120

Step-by-step explanation:

Answer:

w = 3, x = -35/2, y = 8, z = -1

Step-by-step explanation:

Solve the following system:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

In the fourth equation, look to solve for w:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

Divide both sides by -4:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{w = 3

Substitute w = 3 into the first, second, and third equations:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

In the third equation, look to solve for z:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

Subtract 12 from both sides:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z = -4

{w = 3

Divide both sides by 4:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{z = -1

{w = 3

Substitute z = -1 into the first and second equations:

{-4 y - 2 x - 8 = -5

{y = 8

{z = -1

{w = 3

Substitute y = 8 into the first equation:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

In the first equation, look to solve for x:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

Add 40 to both sides:

{-2 x = 35

{y = 8

{z = -1

{w = 3

Divide both sides by -2:

{x = -35/2

{y = 8

{z = -1

{w = 3

Collect results in alphabetical order:

Answer: {w = 3, x = -35/2, y = 8, z = -1

Answer: 31 sides

Step-by-step explanation: 4 sides per quadrilateral so 16 sides and 5 sides per pentagon so 15 sides. 16 + 15 = 31.

Answer: 14 1/7

Step-by-step explanation:

Answer:

y = 4x + 7

or y - 4x = 7

Step-by-step explanation:

x + 4y = 2

4y = -x + 2

y = -1/4x + 2

The slopes of two perpendicular lines are negative reciprocals of each other. So the slope of the perpendicular line should be negative reciprocal of -1/4, then it is 4

Given m = 4, y = 3, x = -1

y = mx + b

3 = 4(-1) + b

3 = -4 + b

b = 7

y = 4x + 7

Answer: m=2

Step-by-step explanation:

Highlighted points: (0, 4) and (-4, -4)

m=(y2-y1)/(x2-x1)

m=(-4-4))/(-4-0)

m=(-8)/(-4)

m=2

Using the concepts of asymptotes and inverse function, we have that:

a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.

b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

For this problem, the function is given by:

[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]

The zero of the denominator is:

6x + 4 = 0

6x = -4

x = -4/6 = -2/3.

Hence the vertical asymptote is x = -2/3.

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]

To find the inverse function of a function y = f(x), we exchange x and y then isolate y.

Exchanging x and y, we have that:

[tex]x = \frac{y + 10}{6y + 4}[/tex]

Applying cross multiplication:

x(6y + 4) = y + 10

6xy - y = 10 - 4x

y - 6xy = 4x - 10

y(1 - 6x) = 4x - 10

[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

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Answer: the better option would be to fill your tank up 15 gallons for $53.08

If you were to multiply 3.60 by 15, you would get 54.

53.08 < 54, therefore 53.08 is the better option.

Hope this helps!

Answer: l=32/3 meters

w=16/3 meters

Step-by-step explanation:

P=perimeter, l=length, w=width

P=2l+2w

32=2(2w)+2w

32=4w+2w

6w=32

w=32/6

w=16/3 meters

32=2l+2(16/3)

32=2l+32/3

(32=2l+32/3)*3

96=6l+32

6l=64

l=64/6

l=32/3 meters

Answer:

Step-by-step explanation:

If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.

We can only see one sequence with all negative terms and common ratio of 5, this is REID's.

Answer:

$235

Step-by-step explanation:

‎‎‎‎‎‎‎‎‎‎.....................

The organization’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder is 13%

What is the number of employees who are regarded as remainder?

The number of employees out of the total workforce left after having deducted the number of employees making up the sales team, the customer support team the software development and HR departments is computed as shown below:

remainder of workforce=80,000-16,000-24,000-14,000

remainder of workforce=26,000

finance team=2/5*26000

finance team=10,400

finance team as % of total workforce=10,400/80,000

finance team as % of total workforce=13.00%

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The amount Logan should charge for each cupcake is $1.60 based on the markup of 35%

What is equivalent inputs for 60 cupcakes?

The equivalent inputs for 60 cupcakes, means the number of cupcakes that the materials used would have yielded in cupcakes if there was no wastage, hence, the cost per unit needs to be expressed to include 20% wastage

equivalent cost per unit=$0.95/(1-20%)=$1.1875

The 35% markup needs to be added to the equivalent cost per unit since markup is the profit as a percentage of cost

selling price=$1.1875*(1+35%)

selling price=$1.60

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Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, you know:

Substituting the value of the slope m:

y= 1/3x +b

Substituting the point to calculate the value of b:

-1= 1/3×(-1) + b

-1= -1/3 + b

-1 + 1/3= b

-2/3= b

Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

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nwm życzę powodzenia kolego drogi