Which equations are equivalent to his weekly addition of 0.5 km and would correctly determine how many weeks it will take Hector to reach 10 km if he starts at 2.5 km and adds 0.5 km every week? Select all that apply. 0.5x + 2.5 = 10 0.5 – 2.5 = 10x 10 = 2.5 + 0.5x 2.5x + 0.5 = 10 2.5x – 0.5 = 10

Answer:

A correlation coefficient shows where one variable changes in results to the other. A line of best fit is the best fit line that passes through or near the graphed data. It is used to describe data and predict where new data will appear on the graph. These two methods help to find correlation between variables as they are used to predict how and where variable are and will go in correlation to one another.

Step-by-step explanation:

Answer: [tex]24.02\ mph[/tex]

Step-by-step explanation:

Given

Boat is traveling due to north at [tex]v_{bf}=27\ mph[/tex]

The current is flowing [tex]60^{\circ}[/tex] west of south at [tex]v_f=8\ mph[/tex]

Suppose the actual velocity of boat is [tex]\vec{v_b}[/tex]

In vector notation we can write

[tex]\Rightarrow \vec{v_{bf}}=\vec{v_b}-\vec{v_f}\\\\\Rightarrow \vec{v_b}=\vec{v_{bf}}+\vec{v_f}[/tex]

Flow of current can be written as

[tex]\Rightarrow \vec{v_f}=-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}[/tex]

Insert the values of vectors

[tex]\Rightarrow \vec{v_b}=27\hat{j}-8\sin 60^{\circ}\hat{i}-8\cos 60^{\circ}\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+27\hat{j}-4\hat{j}\\\\\Rightarrow \vec{v_b}=-4\sqrt{3}\hat{i}+23\hat{j}[/tex]

Magnitude of the velocity is

[tex]=\sqrt{(4\sqrt{3})^2+(23)^2}\\=\sqrt{48+529}\\=24.02\ mph[/tex]

The actual direction and magnitude of the velocity of the boat is the sum of

the velocity of the boat and the velocity of the current both in vector form.

Reasons:

Direction of the boat = North

Speed of the both = 27 mph

Direction of the current = 60° west of south

Speed of the current = 8 mph

Required:

The actual speed and direction of the boat written in magnitude and

direction.

Solution:

The velocities given in vector form are;

Velocity of the boat, [tex]\vec {v}_{boat}[/tex] = 27·j

60° west of south = 30° south of west

Therefore;

Velocity of the current, [tex]\vec{v}_{current}[/tex] = -8 × cos(30°)·i - 8×sin(30°)·j

The actual velocity of the boat, [tex]\vec{v}_{actual}[/tex] = [tex]\mathbf{\vec {v}_{boat}}[/tex] + [tex]\mathbf{\vec{v}_{current}}[/tex]

Which gives;

[tex]\vec{v}_{actual}[/tex] = 27·j - 8 × cos(30°)·i - 8 × sin(30°)·j

[tex]\vec{v}_{actual}[/tex] = 23·j - (4·√3)·i

Therefore;

[tex]\vec{v} _{actual}[/tex] = -(4·√3)·i + 23·j

Which gives;

[tex]|v_{actual}|[/tex] = √((-4·√3)² + 23²) = √(577) ≈ 24.02

The actual direction of the boat, θ, is given by the arctangent of the ratio

of the vertical to the horizontal component of the velocity as follows;

[tex]\displaystyle \theta = arctan \left(\frac{23}{-4 \cdot \sqrt{3} } \right) \approx \mathbf{-73.24^{\circ}}[/tex]

Based on the horizontal and vertical component, the above angle θ is

approximately 73.24° relative to the negative x-axis, which is 90° - 73.24° =

16.76° west of north.

Therefore;

Learn more about vector quantities here:

https://brainly.com/question/1614684

Answer:

1

Step-by-step explanation:

the factors of 4 are 1, 2, 4

1 x 4 = 4

2 x 2 = 4

4 x 1 = 4

Answer:

its attatched

e

measure of center

as A measure that describes the typical value of a data set mean,median and mode.

0.07

EXPLANATION  

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

14

Step-by-step explanation:

Because it occurs the most frequently in the given data set

Answer:

14 and 77

Step-by-step explanation:

I just used a calculator

Answer:

your questions is not complete yet please send full questions and write your question ⁉️ so I will solve your problem

Answer:

Your solution is (-11/6, 7/6).

Step-by-step explanation:

-2x + 2y = 6

4x + 2y = -5

Right away I can see that our y-values are the same. We want to eliminate one variable at a time, so let's make one of the 2y's a positive by multiplying each term in the equation by -1.

4x + 2y = -5

-1(4x + 2y = -5)

-4x - 2y = 5

Now we have a new equation in our system.

-2x + 2y = 6

-4x - 2y = 5

Now eliminate by performing each action given by the terms.

-2x + 2y = 6

-4x - 2y = 5

_________

-6x = 11

Divide both sides by -6.

x = 11/-6

Now that we know x, plug it back into one of the original equations to find y.

-2x + 2y = 6

-2(11/-6) + 2y = 6

Multiply.

-22/-6 + 2y = 6

22/6 + 2y = 6

Subtract 22/6 from both sides.

2y = 6 - 22/6

2y = 36/6 - 22/6

2y = 14/6

2y = 7/3

Divide both sides by 2.

y = (7/3)/2

y = 7/6

Your solution is (-11/6, 7/6).

Check your answer by plugging both values into one of the original equations.

4x + 2y = -5

4(-11/6) + 2(7/6) = -5

Multiply.

-44/6 + 14/6 = -5

Add.

-30/6 = -5

Divide.

-5 = -5

Your answer is correct.

Hope this helps!

Answer:

C

Step-by-step explanation:

if the two lines were parallel, then the alternate, on opposite side of the trasversal, exterior, or not inside the lines, angles would be congruent. sicne they are, the line are parallel

Answer:

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2} \\6^{2} +7^{2} =x^{2} \\\sqrt{85} = x[/tex]

Answer:

sqrt(85) =x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the hypotenuse

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2 + 7^2 = x^2

36+49 = x^2

85 = x^2

Take the square root of each side

sqrt(85) = sqrt(x^2)

sqrt(85) =x

Answer:

$3.42

Step-by-step explanation:

the cost = 11.4 × 0.30 = $ 3.42

Answer:

y = - 0.181x + 24157.2

Step-by-step explanation:

Equation of the regression line is given from. The table by the Coefficient of the predictor, x variable and the intercept value :

The predictor here is mileage, which has a Coefficient of - 0.181

The constant value = intercept 24157.2

The regression equation is written in the form :

y = mx + c ; m = slope = Coefficient of predictor, ; x = predictor,

Hence, we have :

y = - 0.181x + 24157.2

Answer:

A.

Step-by-step explanation:

on edge2022

Answer:

7 / 30

Step-by-step explanation:

This is a selection without replacement probability :

Total boxes = 16

With money = 3

With traveling prices = 5

Empty = 8

P(choosing 2 empty boxes) :

P(empty) * P(empty)

P(empty) = Number of empty boxes / total number of boxes

First pick = empty

P(empty) = 8 / 16 = 1/2

Without replacement :

Second pick = empty

P(empty) = 7 / 15

P(choosing 2 empty boxes) = 1/2 * 7/15 = 7 /30

Answer:21 students

Step-by-step explanation: 3x7=21 students.

57 = 30 × t

t = 57/30

t = 19 × 3 / 10 × 3

t = 19/10

t = 1.9

Answer:

t = 1.9

Step-by-step explanation:

Given

d = rt

Substitute d = 57 and r = 30 into the equation

57 = 30t ( divide both sides by 30 )

[tex]\frac{57}{30}[/tex] = t , that is

t = 1.9

Answer:

3 and -2

Step-by-step explanation:

xy = -6

x + y = 1

let 'x' = y-1

y(y-1) = -6

y² - y + 6 = 0

(y-3)(y+2) = 0

y = 3 and -2

Answer:

You will pay $13.50 in interest and end up paying $238.50 total after the eight years

Step-by-step explanation:

225 x 0.06 = 13.5

225 + 13.5 = 238.5

Answer:

you pay 108 dollars after 8 years

Answer:

15 apples

Step-by-step explanation:

Answer:

2/729

Step-by-step explanation:

2/3÷3 = 2/9

2/9÷3=2/27

2/27÷3=2/81

2/81÷3=2/243

2/243÷3=2/729

Answer:

The speed of the train is 40 km/h.

Step-by-step explanation:

Since a train travels a distance of 120 km at a constant speed of V km / h, and if the speed is reduced by 10km / h, then the time taken to the journey is increased by one hour, to find the constant speed V of the train, the following calculations must be performed:

20 x 6 = 120

10 x 7 = 140

30 x 4 = 120

20 x 5 = 100

40 x 3 = 120

30 x 4 = 120

Therefore, the speed of the train is 40 km/h.

Answer:

1/10

Step-by-step explanation:

P heads,even,heads = P heads * P even *P heads =

1/2 * 2/5* 1/2 = 1*2*1/2*5*2= 1/10

Answer:

2.25

Step-by-step explanation:

divide

Answer:

9/4 or 2.25 Hope this helps

Step-by-step explanation:

Answer:

10(6) + 5x = 180

60 + 5x = 180

- 60 - 60

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

5x = 120

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

5 5

x = 24

Step-by-step explanation:

The shipment contains a total of 180 pounds of potatoes. There are two types of bags of potatoes. One weighing 10 pounds and the other weighing 5 pounds. There are 6 bags of potatoes weighing 10 pounds each and x bags of potatoes weighing 5 pounds each. Two numbers can be added up to bring a total of 180 so we can write this equation as 10(6) + 5x = 180. This problem speaks of pounds in particular so that is why 10 and five go in front of the secondary numbers. After that, just solve. The steps are shown above. ^^^ If I am wrong, please let me know. I hope this helps! :D

Answer:

correct answers

15 m=1,500

117 mm=0.117 m

79 m=0.079 km

hope it helps

Answer:

8  ;)

Thanks for the easy points