Karabo is training by running for the Comrades Marathon ; he starts his training by running 40km per week . Each week he increases the distance covered by 10km.

(a) Write down the formula to calculate the distance he runs in the n-th week .

(b) Use the formula to calculate the distance he runs in the 12 week of training.​

Answer:

mean=71

Step-by-step explanation:

Mean x¯¯¯x¯

71

Median x˜x~

72

Mode

64, 83, 79, 38, 81, 90, 59, 93, 70, 73, 71, 51

Range

55

Minimum

38

Maximum

93

Count n

12

Sum

852

Quartiles

Quartiles:

Q1 --> 61.5

Q2 --> 72

Q3 --> 82

Interquartile

Range IQR

20.5

Outliers

none

Answer:

84.861

Step-by-step explanation:

In the given figure, 1/4 part of Circle is missing

so, we have to find the area of 3/4 part of circle

Area of circle = πr²

Given, r = 6

Now, Area of 3/4 part of circle = (3/4)×πr²

= (3/4) × 3.143 × 6²

= 84.861

Step-by-step explanation:

Elisa made the greater number of withdrawals, because she made 9 withdrawals, while Frances only made 6 withdraws.

Answer:

c. {1/15,16,1/17,18}

Step-by-step explanation:

please follow me

Answer:

[tex]{ \sf{set \:A \: and \: B }}[/tex]

[tex]\frac{28}{9}[/tex]   liters do they drink in 4 days.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the question

John's family drinks 7/9 of milk a day.

Liters do they drink in 4 days: X

Using unitary method

X = [tex]\frac{7}{9} \times4[/tex]

X = [tex]\frac{28}{9}[/tex]

[tex]\frac{28}{9}[/tex]   liters do they drink in 4 days.

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cos(4x + π/5) - sin(2x) = 0

Since cos(x + π/2) = -sin(x), we can write

cos(4x + π/5) = cos(4x + π/2 - 3π/10) = -sin(4x - 3π/10)

Then we can absorb the negative signs into either sin expression, using the fact that sin(-x) = -sin(x):

-sin(4x - 3π/10) - sin(2x) = 0

sin(3π/10 - 4x) + sin(-2x) = 0

Recall that

• sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

• sin(a - b) = sin(a) cos(b) - cos(a) sin(b)

==>   • 2 sin(a) cos(b) = sin(a + b) + sin(a - b)

We can further condense the left side in our equation if there exists a solution to

{ 3π/10 - 4x = a + b

{ -2x = a - b

We have

(a + b) + (a - b) = (3π/10 - 4x) + (-2x)

==>   2a = 3π/10 - 6x

==>   a = 3π/20 - 3x

(a + b) - (a - b) = (3π/10 - 4x) - (-2x)

==>   2b = 3π/10 - 2x

==>   b = 3π/20 - x

So in our equation, we have

sin(3π/10 - 4x) + sin(-2x) = 0

2 sin(3π/20 - 3x) cos(3π/20 - x) = 0

sin(3π/20 - 3x) cos(3π/20 - x) = 0

Solve for x :

sin(3π/20 - 3x) = 0   or   cos(3π/20 - x) = 0

[3π/20 - 3x = arcsin(0) + nπ   or   3π/20 - 3x = π - arcsin(0) + nπ]

  or   [3π/20 - x = arccos(0) + nπ   or   3π/20 - x = -arccos(0) + nπ]

[3π/20 - 3x = nπ   or   3π/20 - 3x = π + nπ]

  or   [3π/20 - x = π/2 + nπ   or   3π/20 - x = -π/2 + nπ]

[3x = 3π/20 - nπ   or   3x = -17π/20 - nπ]

  or   [x = -7π/20 - nπ   or   x = 13π/20 - nπ]

[x = π/20 - nπ/3   or   x = -17π/60 - nπ/3]

  or   [x = -7π/20 - nπ   or   x = 13π/20 - nπ]

(where n is any integer)

Answer:

5.

Step-by-step explanation:

Distance = √(2-6)^2 + (-2-(-5)^2)

= √(16 + 9)

= √25

= 5.

Hello ;)

We can calculate the distance between two points by knowing their coordinates.

Here is the formula :

Let two points [tex]A(x_{A};y_{A})[/tex] and [tex]B(x_{B};y_{B})\\[/tex]

The distance between those two points is given by using this formula :

[tex]AB^{2} =(x_{B}-x_{A})^{2} +(y_{B}-y_{A})^{2}[/tex]

Now, we can use this formula in your exercice.

(2 - 6)² + (-2 - (-5))²

= (-4)² + 3²

= 16 + 9

= 25

Do not forget to do the square root of 25 ;)

So we obtain : [tex]\sqrt{25}=5[/tex]

The distance between points (6 ; -5) and (2 ; -2) is 5 units of lengh.

Answer:

Distance cannot be negative because no matter which direction you travel, you will never travel negative units.

Step-by-step explanation:

Distance cannot be negative in the same way that when you put a car in reverse, the odometer does not go backwards.

If you have a mailbox 30 feet east of your house and a park 30 feet west of your house, you can think of it like a number line: your house is 0, the park is -30 and the mailbox is 30. But, if you walk to your park, you have not walked -30 feet.

Answer:

There are no solutions.

The left side of the equation will always be three less than the right side of the equation since both sides have the same variable.

Answer:

thanks for points

Step-by-step explanation:

too easy boi

Hi! I'm happy to help!

For this, you just simply follow the directions, and alter as you go. First, we need to place E between F and G, so we can put F and G on opposite sides of E.

F   E   G

From here, we put H between F and E

F   H   E   G

I hope this was helpful, keep learning! :D

Answer:

G. 105.

Step-by-step explanation:

Percentage of cars with  3 or more people

= 15 + 7 + 3

= 25%,

25% of 420

= 0.25 * 420

= 105.

Answer:

(x + 5) (x^2 -3)

Step-by-step explanation:

[tex]x^{3} +5x^{2} - 3x - 15[/tex]

Do the grouping:

[tex]x^{3} +5x^{2} - 3x - 15 = (x^{3} +5x^{2}) + (-3x - 15)[/tex]

Then factor out [tex]x^{2}[/tex] in the first and −3 in the second group.

[tex]x^{2}(x+5) - 3(x+5)[/tex]

Factor out the common term x + 5 by using the distributive property.

Polynomial [tex]x^{2}-3[/tex] is not factored in since it does not have any rational roots, thus getting the following:

[tex](x+5)(x^{2} -3)[/tex]

Answer:

the fourth option (x+5)(x²-3)

Step-by-step explanation:

the "-15" tells us we need a 3 and a 5 with different signs.

that eliminates the first and the second options.

and the "5x²" tells us it has to be +5, as there is only one part in the whole multiplication that delivers a x² term (5×x²).

it is also confirmed for the same reasons by "-3x" that the other number has to be -3.

Answer:

1: 5 2: 13 3: sqr root of 15 4: 1 5: 1 6: 3

Step-by-step explanation:

Follow the formula a squared plus b squared equals c squared. C is always the longest side of the equation. So figure out your variables to fill in and in the end, square root your remaining answer.

Answer:

about 15.08

Step-by-step explanation:

Angle BAC + Angle CAH = 180 (they are supplenmentary angles), which means (12x+4)+(x-20)=180

solve:

13x-16=180

13x=196

x≈15.08

Answer:

12x+4 + x-20 = 180

13x = 196

x = 15.08

Step-by-step explanation:

Answer:

31.1011905%

Step-by-step explanation:

Take the new price and subtract the original price

8.81 - 6.72

2.09

Divide by the original price

2.09/6.72

.311011905

Change to percent form

31.1011905%

Percent of increase in average movie theatre ticket price will be 31.1%

    Given prices of the ticket in two different years are,

To calculate the percent increase in the price of an object expression to be used,

Percent increase = [tex]\frac{\text{Final price - Initial price}}{\text{Initial price}}\times 100[/tex]

                             = [tex]\frac{8.81-6.72}{6.72}\times 100[/tex]

                             = [tex]0.311\times 100[/tex]

                             = [tex]31.10[/tex]%

          Therefore, percent of increase in the price of the ticket will be 31.1%

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Answer:

33 miles did the car travel on each gallon of gas

Answer:

A

Step-by-step explanation:

p^-8q^-20 * p^8q^-10

=q^-30

=1/q^30

Answer:

-15

Step-by-step explanation:

17+2a=-13

2a=-30

a=-15

Therefore, a linear equation in two variables has infinitely many solutions. Thus, y = 3x + 5 has infinitely many solutions. Hence (iii) is the correct answer.

Answer:

f(5) = 22

Step-by-step explanation:

Substitute x = 5 into f(x) for image , that is

f(5) = 3(5) + 7 = 15 + 7 = 22

Answer:

x = 3+y/2

Step-by-step explanation:

Answer:

About 76.5 ft.

Step-by-step explanation:

Draw a diagram of a right triangle.  The shorter leg represents the height of the main entrance of the library, which is 8 ft.  The longer leg won't matter in this case.  The hypotenuse is what we're trying to find, so mark it as x.  We know there's a 6° angle of elevation, so the 30° angle of the triangle will be 6° in this case.  Now we have to use trig.  Think of Soh Cah Toa.  The 6° is opposite from 8 and the hypotenuse is x.  So, the equation to find x would be:

sin (6°) = 8/x

Multiply both sides by x

sin (6°) * x = 8

Divide both sides by sin (6°)

x = 8/sin (6°)

When putting it into a calculator, your answer should be 76.534, which rounds to 76.5 ft.

Answer:

22.5 degrees and 67.5 degrees

Step-by-step explanation:

complementary angles add up to 90°

x + 3x = 90°

4x = 90

90/4 = x

x = 22.5

The first angle is 22.5

The second angle is 3 times as much

22.5 x 3 = 67.5

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Median- is the middle value whereby the values are place in order (ascending)

$9.25 is the median of these prices

Answer:

(4,3)

Step-by-step explanation:

If the triangle ABC is moved 5 units to the right, the coordinates of A will be (4,3). We can find this by using the values already given for A. We are given (-1,3) which is A's current position. Since we are moving it to the right we are only looking at the first number. If we add 5 to -1 we get 4 which we put in the place of the -1 in the coordinates to get our answer.