Calculate the distance between the points J=(-4, 0) and E = (4, 7) In the coordinate plane.
Round your answer to the nearest hundredth.
E
Distance: I

Step-by-step explanation:

Using the modified picture attached to this answer;

Parameters

x = Angle X

8 = x

19 = y

14 = z

Therefore,

Using Cosine rule

x² = y² + z² - 2·y·z·cos X

Masking Cos X the subject of the formula,

Cos X = (y² + z² - x²) / (2·y·z)

Cos X = (19² + 14² - 8²) / (2·19·14)

Cos X = (361 + 196 - 64) / 532

Cos X = (557 -64) / 532

Cos X = 493 / 532

Cos X = 0.92669

But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;

X = Cos-¹ [0.92669]

Since 1 / Cos = Cos-¹

Therefore,

X = 22.075

And since x, our unknown, is equal to angle X, then,

x = 22.1 (to the nearest tenth)

If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)

Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.

Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.

The former describes condition which cannot both (or all) obtain. and so exclude one another.

i.e., "not - (both A and not - A)"

The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"

I presume you intend to refer to the latter.

Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.

It is thus certain, not merely probable, that one or the other will obtain.

Learn more about Probability at:

https://brainly.com/question/11234923

#SPJ4

Answer:

The original price is $ 149.95

Operationalization of variables in research involves defining a concept in a way that it can be measured or observed.

It is the process of taking abstract concepts, such as attitudes, beliefs, or behaviors, and defining them in a way that they can be measured using empirical methods. This is done by creating a set of specific and concrete indicators or measures that represent the concept being studied. The operationalization of variables is a critical step in the research process, as it ensures that the data collected is both reliable and valid, and can be used to draw meaningful conclusions and make predictions.

Learn more about variables here: brainly.com/question/29583350

#SPJ4

(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

The box plot that represents the data-set is given as follows:

Option B.

From left to right, the five features of the box and whisker plot are listed as follows

The data-set in this problem has 11 elements, hence:

The quartiles are the mean of each half, hence:

Meaning that the second plot is correct.

More can be learned about box and whisker plots at brainly.com/question/30464750

#SPJ1

Answer:

Step-by-step explanation:

1. The Louisiana Purchase

2. The War of 1812

3. The Missouri Compromise

4. Trail of Tears

Hope this helped!

Answer:

Step-by-step explanation:

The minimum interior angle possible for a regular polygon is given by the formula:

interior angle = (180° * (n-2)) / n

where n is the number of sides in the polygon. The formula is based on the fact that the sum of the interior angles of a polygon with n sides is equal to (n-2) * 180°.

As n increases, the value of the interior angle decreases and approaches the minimum value of 180°. However, for a regular polygon, all interior angles must be equal, so the minimum possible value is given by the formula above.

For example, consider a regular hexagon (n=6). The minimum interior angle is given by:

interior angle = (180° * (6-2)) / 6 = 120°

So, the minimum interior angle possible for a regular polygon is 120°.

The graph of equation y = 6 - x - x² is shown in figure.

And, The value of gradient at x = 2 is, - 5.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ y = 6 - x - x²

Now, The graph of equation y = 6 - x - x² is shown in figure.

Which represent the graph of parabola.

And, The value of gradient at x = 2 is,

⇒ y = 6 - x - x²

⇒ y' (x) = 0 - 1 - 2x

⇒ y' (x) = - 1 - 2x

At x = 2;

⇒ y' (2) = - 1 - 2 × 2

⇒ y ' (2) = - 1 - 4

⇒ y' (2) = - 5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ9

Answer:

A = 80ft^2

Step-by-step explanation:

Area of trapezoid = (a + b/2) x h

A = ((6 + 10)/2) x 10

A = (16/2) x 10

A = 8 x 10

A = 80ft^2

Answer:

Area is 80 square feet

Step-by-step explanation:

The shape of the bedroom is a trapezoid

h = perpendicular height of trapezoid

Area of a trapezoid:

                      [tex]\frac{1}{2}[/tex]×(Sum of parallel sides)× h

                 = [tex]\frac{1}{2}[/tex] × [(10 + 6) feet] × (10 feet)

                 = [tex]\frac{1}{2}[/tex] × (16 feet) × (10 feet)

∴ Area of Skylar’s Bedroom    = 80 square feet

                                                   = [tex]80 ft^{2}[/tex]

The equations of the functions are C(x) = 2.5x + 60, R(x) = 10x and P(x) = 7.5x - 60

Defining the variables, we have

For the equation of the money they spend:

So, the equation for the total money spent can be written as:

C(x) = 2.5x + 60

For the equation of the money they collect:

So, the equation for the total money collected can be written as:

R(x) = 10x

To calculate the profit from selling, we subtract the cost from the revenue

So, we have

P(x) = 10x - 2.5x - 60

Simplifying this equation, we get:

P(x) = 7.5x - 60

Hence, the profit equation is P(x) = 7.5x - 60

Read more about profit function at

https://brainly.com/question/12983911

#SPJ1

Answer: $546.60 (*this was the actual number but I rounded it $546.644444444)

Step-by-step explanation:

Divide: $245.99/0.45 = 546.644444444

You can double check your answer by multiplying 546.644444444 by 0.45 and you will get $245.99

If you multiply by $546.60 you will get $245.97 since you rounded

Answer:

x=-2

Step-by-step explanation:

if we find sum of same variables ,

3x-2x+y-y=-8+6

x=-2

Note that the probability that a combined sample tests positive is 0.67232 or 67.232%.

Let P(pos) be the probability that an individual sample tests positive.

We know P(pos) = 0.2,

so the probability that an individual sample tests negative is:

P(neg) = 1 - P(pos) = 0.8.

Let P(combined_neg) be the probability that a combined sample tests negative (i.e., all five component samples are negative).

Since the component samples are independent, we can calculate

P(combined_neg) as the product of their individual probabilities:

P(combined_neg) = P(neg) x P(neg) x P(neg) x P(neg) x P(neg)

= 0.8⁵
= 0.32768

Therefore, the probability that a combined sample tests positive (i.e., at least one of the five component samples tests positive) is:

P(combined_pos) = 1 - P(combined_neg)

= 1 - 0.32768

P(combined_pos) = 0.67232

Thus, the probability that a combined sample tests positive is 0.67232 or 67.232%.

Learn more about probability:
https://brainly.com/question/11234923
#SPJ1

The algorithms are a problem solving tool in Python because it  provides a wide range of built-in algorithms that can be used to solve many common problems.

The Algorithms are a fundamental problem solving tool in Python . An algorithm is a set of instructions that are executed in a specific order to solve a particular problem. In Python, algorithms can be implemented in the form of functions or methods.

So , In addition to the built in algorithms, Python also provides a rich collection of third party libraries that contain various algorithms that can be used to solve complex problems.

Learn more about Algorithm here

https://brainly.com/question/27278644

#SPJ4

The given question is incomplete , the complete question is

How are algorithms a problem solving tool in Python ?

Answer:

2√21

Step-by-step explanation:

let the sides of bigger triangle be a, b and d.

then,

a²= b² + d² [ by Pythagoras theorem]

13² = 9² + d²

d² = 13² - 9²

d²= 169 - 81

d² = 88

d = √88

Now, the sides of smaller triangle are c, x, and d

by Pythagoras theorem,

d² = c²+x²

(√88)² = 2² + x²

88 - 4 = x²

x² = 84

x = √84

x= 2x2x3x7

x = 2√21

Therefore, the value of x is 2√21

Hope it's helpful..

Answer:

  (c)  A line graph, because it would show the association or relationship between two variables

Step-by-step explanation:

You want to know if scatter plot or a line graph more appropriate to construct for seeing the relationship between a manatee's weight and height.

The variables involved are "weight" and "height". Notice that "time" is not involved. (This eliminates choices B and D.)

A line graph is useful for showing how one variable relates to another as the value of one variable changes. It would be useful for plotting the weight and height of one animal as it changes during the animal's lifetime.

When multiple animals are involved, a scatter plot might be more helpful for showing the relationship.

The context is given as "a manatee's weight and height", not "manatees' weight and height." Hence it seems we can assume that we're looking at data for only one animal.

The appropriate graph would be ...

  A line graph, because it would show the association or relationship between two variables — choice C.

<95141404393>

Answer:

0.36

Step-by-step explanation:

and I got this answer by using calculator

AB and CD are not parallel lines.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

If the slope of AB and CD are equal then the lines are parallel.

A(-3, 5), B(1, 13), C(4, 2), and D(10, 5)

AB=13-5/1+3

=8/4=2

CD=5-2/10-4

=3/6=1/2

As the slope of lines are different, the lines are not parallel.

Hence, AB and CD are not parallel lines.

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ9

Answer:

[tex]\huge\boxed{\sf f(5) = 11}[/tex]

Step-by-step explanation:

f(x) = 2x + 1

Put x = 5

So,

f(5) = 2(5) + 1

f(5) = 10 + 1

[tex]\rule[225]{225}{2}[/tex]

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

In Math's, an intercept is a point on the y-axis, through which the slope of the line passes. It is y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept. There are basically two intercepts, x-intercept and y-intercept.

Rewrite the function as an equation:

→ y = 2x + 1

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is y = mx + b where m is the slope of b is the y-intercept:

→ y = mx + b

Find the values of m and b using the form y = mx + b:

→ m = 2

→ b = 1

Therefore, A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

Learn more about intercept here: https://brainly.com/question/14180189

#SPJ3

Answer:

the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Step-by-step explanation:

The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.

However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.

In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Answer:

B. 1/12

Step-by-step explanation:

1/8 × 5/6 = 5/48 × 4/5 = 1/12

To validate a min-heap, you can follow these steps: Start at the root, Check each subtree, Repeat the process recursively, If any node violates the min-heap property, then the heap is not valid.

Start at the root: Verify that the value at the root node is the minimum value in the heap. This is the defining property of a min-heap. Check each subtree: For each subtree, check that the value at the root of the subtree is less than or equal to the values of its child nodes. If this property holds true for all subtrees, the heap is a valid min-heap. Repeat the process recursively: Continue the above steps for each subtree until all nodes have been checked. If any node violates the min-heap property, then the heap is not valid. In that case, you can either rebuild the heap or identify the specific node or subtree that violates the property and fix it. In summary, to validate a min-heap, you need to check that the root node contains the minimum value, and each subtree obeys the min-heap property. You can check the property recursively until all nodes have been verified, and identify any nodes that violate the property for correction.

To learn more about  minimum value click here

brainly.com/question/14316282

#SPJ4

Answer:An ordered pair contains the coordinates of one point in the coordinate system. A point is named by its ordered pair of the form of (x, y). The first number corresponds to the x-coordinate and the second to the y-coordinate. To graph a point, you draw a dot at the coordinates that corresponds to the ordered pair.

Step-by-step explanation:

Answer: 124950

Step-by-step explanation:

So, let’s look at this logically. For first place, you can any one of the 51 runners finish there. For 2nd place, you can have any one of the remaining 50 runners finish there. For 3rd place, you can have any one of the 49 runners who haven’t finished finish there. runners who haven’t finished finish doesn’t matter .So, you take all of the possibilities, and times them together, 51*50*40 different possibilities.Now, if you want a generic equation, you can run it through this equation, x being the number of possibilities, and n being the number of ones your choosing:

(51!)/(51-3)!

Answer:

If the Esteban's car continues to decrease 20%, by five years the car will be worthless.

20 x 5 is 100. This means that 100%  of the car will have lost its value and will be worthless.

I hope this helps & Good luck <3 !!!

Answer:

y=12-5x

Step-by-step explanation:

We know that 12 is our original number so we put that first. X represents the number of hours. And 5 is how much its dropping per hour. Y would be our final answer. If you sub in for x the amount of hours outside and multiply it by 5, that's how many degrees it dropped.

Answer:

x=1,y=4

Step-by-step explanation:

5x+y=9

5x=9-y

x=(9-y)/5

put it in 10x-7y=-18

10x((9-y)/5)-7y=-18

18-2y-7y=-18

-9y=-36

y=4

x=(9-4)/5=1

Answer:

x = 1

y = 4

Step-by-step explanation:

5x + y = 9

10x - 7y = -18

Time the first equation by -2

-10x - 2y = -18

10x - 7y = -18

-9y = -36

y = 4

Now put 4 in for y and solve for x

5x + y = 9

5x + 4 = 9

5x = 5

x = 1

Let's check

5(1) + 4 = 9

5 + 4 = 9

9 = 9

So, x = 1 and y = 4 is the correct answer.

The approximate area of the remaining cardboard would be = 246 cm². That is option B.

To calculate the area of the remaining cardboard = (area of rectangle) - 2(area of circle)

The formula that is used to calculate the area of rectangle = length×width

where length = 14 cm

width = 18cm

area = 14×18 = 252 cm²

The area of the 2 circle formula;

= 2(πr²)

where π = 3.14

r = 2/2 = 1

area = 2(3.14) = 6.28

Area of the remaining cardboard

= 252 cm²- 6.28

= 245.72

= 246 cm²

Learn more about rectangle here:

https://brainly.com/question/28497588

#SPJ1