Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation?

Answer:

Explanation:

In order to calculate the variance and standard deviation of a set of data, you first must calculate the mean.

Mean = average = μ = ∑ values / (number of data)

Hence, the mean of our data set is:

Now you can calcuate the variance using the formula.

For a data set (which is all your population and not a sample) the formula is:

That is:

The standard deviation, S.D., is the square root of the variance:

Answer:

Variance = 8732.24 and standard deviation = 93.45

Step-by-step explanation:

We have to calculate the variance and standard deviation of the data set

3,832, 3,779, 3,655, 3,642, 3,579

First we calculate the mean of the data

Mean = [tex]\frac{(3,832+3,779+3,655+3,642+3,579)}{5}[/tex]

         = [tex]\frac{18487}{5}[/tex]

         = 3697.4

Now we calculate the variance by subtracting the mean from value of data set and square it.

3832 - 3697.4 = 134.6² =  18,117.16

3779 - 3697.4 = 81.6² = 6,658.56

3655 - 3697.4 = -42.4² = 1,797.76

3642 - 3697.4 = -55.4 = 3069.16

3579 - 3697.4 = -118.4 = 14,018.56

Add up the squared result and take the mean

=  [tex]\frac{(18117.16+6658.56+1797.76+3069.16+14018.56)}{5}[/tex]

=  [tex]\frac{43661.2}{5}[/tex]

Variance = 8732.24

To calculate standard deviation, we take the square root of the variance = [tex]\sqrt{8732.24}[/tex]

Standard deviation = 93.44645526 ≈ 93.45

Variance = 8732.24 and standard deviation = 93.45

Answer:

97.79

Step-by-step explanation:

1062.98 * 0.092 = 97.79416

To the nearest hundredth would be to the second 9. Since 4 is less than 5 just drop the 4 and anything after it.

Answer:

The value of x=6 and y=4.

Answer:

(6, 4 )

Step-by-step explanation:

Given the 2 equations

4x - 3y = 12 → (1)

x + 2y = 14 → (2)

Multiplying (2) by - 4 and adding to (1) will eliminate the y- term

- 4x - 8y = - 56 → (3)

Add (1) and (3) term by term

(4x - 4x) + (- 3y - 8y) = (12 - 56) ← simplify

- 11y = - 44 ( divide both sides by - 11 )

y = 4

Substitute y = 4 into either (1) or (2)

(2 ) : x + 8 = 14 ( subtract 8 from both sides )

x = 6

Solution is (6, 4 )

Answer: It is!!!!!!!!

Answer:

The correct option is C.

Step-by-step explanation:

The standard form of a parabola is

[tex]y=ax^2+bx+c[/tex]

The table of values represents the coordinate pairs of the parabola. It means the graph of the parabola must be passes through these coordinate pairs.

From the given table it is clear that the parabola passes through the points (0.5,21), (1,34) and (1.5,39).

[tex]21=a(0.5)^2+b(0.5)+c[/tex]

[tex]21=0.25a+0.5b+c[/tex]             .... (1)

[tex]34=a(1)^2+b(1)+c[/tex]

[tex]34=a+b+c[/tex]                      .... (2)

[tex]39=x(1.5)^2+y(1.5)+z[/tex]

[tex]39=2.15a+1.5b+c[/tex]            .... (3)

On solving (1), (2) and (3), we get

[tex]a=-16, b=50,c=0[/tex]

The equation of parabola is

[tex]y=-16x^2+50x+0[/tex]

[tex]y=-16x^2+50x[/tex]

The graph of parabola is shown below. It is same as graph in option C.

Therefore the correct option is C.

Answer:

13. 23/4

14. 13/2

15. 6 and 1/2

16. 2 and 7/12

Answer:

13. 23/4

14. 13/2

15. [tex]6\frac{1}{2}[/tex]

16. [tex]2 \frac{7}{12}[/tex]

Step-by-step explanation:

13) 5×4=20

    20+3=23

    [tex]\frac{23}{4}[/tex]

14) 2×6=12

     12+1=13

     [tex]\frac{13}{2}[/tex]

15 an 16 divide

Answer: I believe nine

Step-by-step explanation: If one and 11 stay in the same place then it would start as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. then it would be 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, 11. then 1, 9, 10, 2, 3, 4, 5, 6, 7, 8,11 and so one.

Answer:

sin(arccos(-4/√25)) = 0.6

Step-by-step explanation:

The expression you want to evaluate is

sin(arccos(-4/√25))

= sin(arccos(-4/5))

We place this expression into a calculator and get the result

arccos(-4/5) = 2.498 rads = 143.1°

then

sin(143.1°) = 3/5

sin(143.1°) = 0.6

sin(arccos(-4/√25)) = 0.6

Answer:

The correct answer is last option  

10

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here  (x1, y1) = R(0, 0)  and (x2, y2)  = S(6, 8)

Distance, RS = √[(x2 - x1)² + (y2 - y1)²]

 = √[(6 - 0)² + (8 - 0)²]

 = √[6² + 8²]

 = √[36 + 64]

 = √100

 = 10

Therefore the correct answer is last option  10

Answer:

The answers to your three problem question are shown

1) the value of p is

p = -1

2) The coordinates of the focus are

Focus =  (-1,0)

3) The equation of the directrix is

Directrix

x = 1

Step-by-step explanation:

The general equation for this parabola is

y^2 = 4px

Problem 1

Find the value of p.

We are told that the equation of the problem is

y^2 = -4x

And the general formula is

y^2 = 4px

From there, we can deduce that

p = -1, because

y^2 = 4(-1)x = -4x

This means that p = -1

Problem 2

Find the focus

To find the focus we can see the equations attached below for the focus, vertex and directrix.

In these case, the equations still apply, even though the variable is inverted, we just need to adjust it

y^2 = -4x =>

x = (-1/4)*y^2

x = a*y^2 + b*y +c

Focus

((4ac -b^2  + 1)/4a, -b/2a)

But, b = 0 and c = 0

=>

(1/4a,0) = (1/4(-1/4),0) = (-1,0)

Focus =  (-1,0)

Problem 3

Find the directrix

The equation is

x = c - (b^2 + 1).4a

But, b = 0 and c = 0

x = -4*a

x = -4* (-1/4) = 1

x = 1

Directrix

x = 1

Answer: P is -1

Focus is (-1,0)

Directrix is X= 1

Answer:

a)  [tex]240\degree[/tex]

b) [tex]\frac{15\pi}{4}[/tex]

Step-by-step explanation:

Coterminal angles have the same terminal sides in standard position.

a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range.

 [tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].

In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.

b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.

We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.

[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]

Answer: y= -2x+2

Step-by-step explanation: y-y₁=m(x-x₁)

y-(-6)= -2(x-4)

y+6=-2x+8

y=-2x+8-6

y= -2x+2

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope m = -2 and the point (4, -6). Substitute:

[tex]y-(-6)=-2(x-4)\\\\y+6=-2(x-4)[/tex]

Plug in values.

xy=

6(3) =

18 = Answer

Answer:

f(4) = 4

Step-by-step explanation:

F(x)=1/4•2^x

Let x = 4

F(4)=1/4•2^4

      = 1/4 * 2^4

      = 1/4 *16

      = 4

Answer: f(4) = 4

Step-by-step explanation:

f(x) = 1/4 . 2^x

To find f(4) we simply replace x by 4 in the above equation;

f(4) =1/4 . 2^4

f(4) = 1/4 . 16

f(4) = 16/4

f(4) = 4

Therefore f(4) is equal to 4

Answer:D

Step-by-step explanation: 4y-3x=4    -2x-8y=8

                                        4(-.5)-3(-2)=4    -2(-2)-8(-.5)=8

Work this problem from here

4*-.5= -2

-3*-2=6

6+-2=4

so this is a true statement

-2*-2=4

-8*-.5=4

4+4= 8

so this statement is also true

Answer:

Option B: [tex]\frac{5+a}{a-1}[/tex]

Step-by-step explanation:

Given function is:

[tex]f(x) = \frac{3+x}{x-3}[/tex]

In order to find f(a+2), we have to put a=2 in place of x in the function

So,

[tex]f(a+2) = \frac{3 + (a+2)}{(a+2)-3}\\ =\frac{3+a+2}{a+2-3}\\ = \frac{5+a}{a-1}[/tex]

Hence, we can see that option b is correct ..

Answer:

Remember, 1 is the multiplicative identity.  That means that we can multiply a value by 1 and not change the value, only change the units.

For example:  If we have 3 dozen eggs, how many eggs do we have?

             3 dozen

          (3 dozen)*(12 eggs / 1 dozen) = 36 eggs    (dozen cancels out, leaving only eggs)

In this problem:

   (16 miles / 1 week)

   (16 miles / 1 week)*(52 weeks / 1 year)       (weeks cancel out, leaving miles/year)

   832 miles/year

Note: with either 365 (or 366) days in a year, there are 365/7 = 52.14 weeks in a year, but we'll use 52 because the problem gave miles/week.

Step-by-step explanation:

Answer:

[tex]<CGF = 130[/tex]

Step-by-step explanation:

A triangle adds up to 180.

180 - 50 = 130

Since both of the missing angles are congruent each of the missing angles is 65 degrees.

130/2 = 65

As per the exterior angle theorem, the measure of the exterior angle is determined by the sum of the opposite interior angles.

65 + 65 = 130

So, the measure of [tex]<CGF = 130[/tex]

To simplify an expression you need to combine like terms.

In  the given equation, there are two like terms, 5r and 9r.

There is a plus sing in front of each one, so add those together: 5r + 9r = 14r

There are no ther like terms so the simplified expresssion becomes:

8w + 14r - t

Answer:

58%

Step-by-step explanation:

The change between 12 to 19 is 7

The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%

7/12*100

=58.3333333%

=58%(rounded to nearest percent)

58% increase

Percent change = 19 - 1212 × 100 = 58.333333333333 % (increase) Where: 12 and 19 is the new value. In this case we have % of increase because the new value is greater than the old value.

Percent change differs by the percent increase or percent decrease of the sense that we could see both directions of the change. For example, the percent increase calculator calculates amount of increase, in which we shall say, "x percent increase".

The change between 12 to 19 is 7

The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%

7/12*100

=58.3333333%

=58%(rounded to nearest percent)

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Answer: 7 boxes of carrots, 9 boxes of potatoes, 18 boxes total

Step-by-step explanation:

75 -68=7 boxes of carrots

80-71=9 boxes of potatoes

For this case we have:

x: Represents the number of carrot boxes

y: Represents the number of boxes of potatoes

Initially we have:

[tex]x = 75\\y = 80[/tex]

If you sold 68 boxes of carrot we have:

[tex]x = 75-68 = 7[/tex]

If you sold 71 boxes of potatoes, we have:

[tex]y = 80-71 = 9[/tex]

The number of boxes I take home is given by:[tex]x + y = 7 + 9 = 16[/tex]

ANswer:

7 boxes of carrots left

There are 9 boxes of potatoes left

A total of 16 boxes remain

Answer:

D

Step-by-step explanation:

A difference of squares is represented in general as

a² - b²

Both variables have an even power (2) → a

There are only two terms → b

Answer:

[tex]2\frac{2}{9} hrs[/tex]

Step-by-step explanation:

At a speed of 50m/h time taken is 2hours

At a speed of 45m/h time take is 2.5 hours

You can find the distance between A and B

Distance=speed × time

[tex]D=50*2=100\\[/tex]

But time y varies inversely with speed x , hence

[tex]y=\frac{k}{x}[/tex]

where k is a constant of proportionality and D is distance.

To find k

[tex]2=\frac{k}{50} \\\\2*50=k\\\\100=k\\\\y=\frac{100}{x}[/tex]

where y is time and x is speed

Given

x=45m/h  you should find time y. Apply the expression above

[tex]y=\frac{100}{x} \\\\\\y=\frac{100}{45} =\frac{20}{9} =2\frac{2}{9} hrs[/tex]

Answer:

3*5=15

15 is your answer

ANSWER

15 square units.

EXPLANATION

Each box is 1 square units.

When we count the number of boxes we obtain 15 boxes.

This implies that the area of the rectangle is 15 square units.

Alternatively, we can observe that:

The rectangle is a 3 by 5 rectangle.

So the area is

[tex]3 \times 5 = 15 \: units \: square[/tex]

The rectangle is 15 units square.

Answer:

See attached images

Step-by-step explanation:

The expression of your question is

f(x) = 2x^2+8x-7

A full analysis of the function is shown in the images below

Answer:

[tex](x-5)(x+4)[/tex]

Step-by-step explanation:

We have the following quadratic equation

[tex]a^2-a-20[/tex]

The factored expression will have the following form

[tex](x+b)(x+c)[/tex]

Where b and c are two real numbers which when added together result in -1, and multiplying them results in -20

[tex]b*c=-20\\b+c=-1[/tex]

You can verify that the numbers that meet this condition are:

-5 and 4

Then the factors are:

[tex](x-5)(x+4)[/tex]

Answer:

15+25d=t

Step-by-step explanation:

the initial value is 15 it increases(+) by 25 to each kilometer(distance=d) of depth.

The equation that models the relationship between distance d in kilometers and temperature t in degrees Celsius is t = 25d + 15. This means that for each kilometer increase in depth, the temperature increases by 25 degrees Celsius in addition to the initial 15 degrees Celsius surface temperature.

The relationship between the variables, distance (d) and temperature (t), is described as a linear function. Given that the surface temperature is 15 degrees Celsius and it increases by 25 degrees Celsius with every kilometer, the mathematical model is expressed as:

t = 25d + 15

In this equation, t represents the temperature and d is the distance from the surface in kilometers. This implies that for every kilometer increase in depth, the temperature increases by 25 degrees Celsius on top of the initial 15 degrees Celsius surface temperature.

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Answer:

False

Step-by-step explanation:

Vertical angles are a pair of opposite angles created by intersecting lines. The Vertical Angles Theorem states that if two angles are vertical, then they are congruent.

Answer:

False.

Step-by-step explanation:

Supplementary angles always equal up to 180 degrees.

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2.  Thus, f(-2.2) = 1.

Answer:

f(-2.2) = 1

Step-by-step explanation:

There is a horizontal blue line with equation y = 1 between x = -3 and x = -2. Thus, f(-2.2) = 1.

Answer:

The correct answer will be "588 square centimeters"

Step-by-step explanation:

The answer would be 588 squared cm because the area of a triangle is 1/2(base*height).

and The base is 42 cm and the height is 28 cm.

588 square centimeters is the correct answer !

Answer:

C) 588

Step-by-step explanation:

A= 1/2 b*h

First you need to find the base and height

Which is 42 and 28

42*28=1176

1176/2= 588

Answer:

4(x-7)^2 - 19

Step-by-step explanation:

Shifting 7 units to the right:  4(x-7)^2 - 16.

3 units down:                         4(x-7)^2 - 16 - 3, or    4(x-7)^2 - 19