What is the variable for which researchers elicit a change

The distance of the given coordinates (See attached image) are:

AB) 10

CD) 7
EF) 6

GH) 15

JK) 12

To solve the distance between the above coordinates, one must use the following formula:

d = √[(x2 - x1)² + (y2 - y1)²]

AB)
Distance (d) = √[(7 - -3)² + (5 - 5)²]

= √(10)² + (0)²

= √100

Distance = 10

CD) Distance (d) = √[(-6 - 1)² + (-3 - -3)²]

= √(-7)² + (0)²

= √49

Distance = 7

EF) Distance (d) = √[(2-2)² + (-3-(-9))²]
= 6

GH)
Distance (d) = √[(6-6)² + (16-1))²]

= 15

JK)
Distance (d) = √[(-3-(-3))² + (12-0))²]

= 12

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

Using the binomial distribution, it is found that the probabilities are given as follows:

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

Item 1:

The parameters are:

n = 15, p = 0.4, x = 4.

Hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228\)

Item 2:

The parameters are:

n = 12, p = 0.2, x = 2.

Hence:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835\)

Item 3:

The parameters are:

n = 20, p = 0.05.

The probability is:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

The formula is the same used in previous exercices, hence, using a calculator.

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841\)

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The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

The volume of the space between the balls and the rectangular box is \(4r^{3}(6 - \pi)\)

Step-by-step explanation:

The attachment below shows the description of the rectangular bow and the three spherical balls.

From the description,  

This means the balls are tightly fitted into the rectangular box.

Each of the balls has a radius r

Hence, The volume of one of the balls is given by the volume of a sphere

\(Volume of a sphere = \frac{4}{3} \pi r^{3} \\\)

The volume occupied by one of the balls is \(\frac{4}{3} \pi r^{3} \\\)

∴ The volume occupied by the three spherical balls will be

3 × \(\frac{4}{3} \pi r^{3} \\\)

= \(4\pi r^{3}\)

The volume occupied by the three spherical balls \(4\pi r^{3}\)

For the rectangular box,

The volume of a rectangular box = \(l w h\)

Where \(l\\\) is the length

\(w\) is the width and

\(h\) is the height

Since the balls are tightly packed,

The width of the rectangular box will be the diameter of the balls

diameter of the balls = 2r

∴ \(w\) = 2r

The height of the rectangular box will also be the diameter of the balls

∴ \(h\) = 2r

The length of the rectangular box will be 3 times the diameter of the balls

∴\(l\) = 3 × 2r = 6r

Hence,

The volume of a rectangular box = 6r × 2r × 2r

= 24r³

The volume of the space between the balls and the rectangular box is given by

Volume of the space between the balls and the rectangular box =

volume of the rectangular box -  volume occupied by the three spherical balls

Volume of the space between the balls and the rectangular box= 24r³ - 4πr³

=  24r³ - 4πr³

= 4r³(6 - π)

Answer:

Your answer would be

- 2/25 x^3a^3

Or vice versa with the variables

- 2/25 a^3x^3

TO solve it’s pretty simple if you do it correctly.

So with all the variables in the two multiples, you can find a way to combine them

So ignoring everything else you’d get

a^2x * x^2a

You we can see the difference,

theres a^2 and a

Whilst there is also x^2 and x

Now we can combine them

a^3 x^3

Now we can do the normal multipacation with the fraction

2/5 * - 1/5 which is -2/25

Now combine

ANd you got it :D

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Inverse of function f(x) = 7x + 6 is

Given,

f(x) = 7x + 6

Now,

Put y in place of f(x)

y = 7x + 6

Now interchange the variables,

x = 7y + 6

Solve for variable y,

y = x/7 - 6/7

Replace y with f-¹(x),

f-¹(x) = x/7 - 6/7

Thus the inverse of the function is obtained to be x/7 - 6/7 .

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Answer:

37 Degree celcius; is the correct answer...

The length of each part of the stick cut by Migual is obtained as 2/12 yd.

Miguel has a 2/3 yd long stick.

He cuts it into 4 equal pieces.

So, the length of each part is obtained as:

Each part length = total length / number of pieces.

Each part length = 2/3 / 4

Each part length = 2/(3*4)

Each part length = 2/12 yd.

Thus, the length of each part of the stick cut by Migual is obtained as 2/12 yd.

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The correct question is attached.

A: Find the length of each part.

\(3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\\)

Answer:

It is 50,000

Step-by-step explanation:

Because if you were to take the two 2 in front of it would leave you with 57,296, you would know it's 50,000.

Answer:

The difference of 15 and a number is 5 indeed 10 to be 15

Answer:

10

Step-by-step explanation:

Answer:

B 3360

Step-by-step explanation:

Area of Rectangle = Length X Width

120 X 28

= 3360 cm

Answered by Gauthmath

The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

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Answer:

x = 12, y = 42

Step-by-step explanation:

6 is multiplied by 6 to get 36 (lot of sixes lol)

So multiply everything else by 6

2 x 6 = 12

7 x 6 = 42

Answer:

d y/d x = y/x

Step-by-step explanation:

a/b The decay can be modeled by this equation, (1 - r), the r being the rate of decay. So it would be 1-0.115. (0.115 is your answer for a) You have to convert the percent into a decimal by moving the deicmal place two places to the left. 0.885 is your answer for b.

c. For function notation, that just means write an equation. So you want your decay times your inital.  V(t)=15000(0.885)^x. We get the V(t) from the directions that they want us to put it in; it's basically y.

d. Since it's two years, plug in 2 for x. This shows the decay after two years

V(t)=15000(0.885)^2

e. As with d, plug in 10 for x. V(t)=15000(0.885)^t

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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Answer:

I like looking and drawing a penguins

Step-by-step explanation:

And no 1-5 is not 3, it is -4

Answer: 162

Step-by-step explanation:

The second approximation x2 is 2.875

and the third approximation x3 is 2.806

The root of the equation = \(4x^7 + 5x^4 + 3 = 0\)

using Newton's method.

The initial approximation x1 = 3.

Calculate the function value and derivative at x1:

\(f(x1) = 4(3)^7 + 5(3)^4 + 3 = 4083\\f'(x1) = 4(7)(3)^6 + 5(4)(3)^3 = 32640\)

We then apply Newton's method formula to find x2:

\(x_2 = x_1 - f(x_1)/f'(x1)\\x_2 = 3 - 4083/32640 = 2.875\)

\(f(x2) = 4(2.875)^7 + 5(2.875)^4 + 3 \\f(x2) = 46.48\\f'(x2) = 4(7)(2.875)^6 + 5(4)(2.875)^3 \\f'(x2) = 603.75\)

x3 = x2 - f(x2)/f'(x2)

x3 = 2.875 - 46.48/603.75

= 2.806

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There were 14 players on the soccer team.

In the given problem, the members of a soccer team raised $1210.50 to go to a tournament. They rented a bus for $769.50 and budgeted $31.50 per player for meals. We need to find how many players were on the team.To solve this problem, we can start by subtracting the cost of the bus rental from the total amount raised by the team:$1210.50 - $769.50 = $441Now, we can divide this remaining amount by the amount budgeted per player for meals:$441 ÷ $31.50 = 14Therefore, there were 14 players on the soccer team. We can check our answer by multiplying the number of players by the amount budgeted per player for meals:14 x $31.50 = $441This is equal to the remaining amount after the bus rental was paid, which confirms that our answer is correct.

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The customer will pay $6.30 for the 60 local calls that all lasted 3 minutes.

To find out how much the customer will pay, we need to calculate the total cost for all the local calls.
Step 1: Calculate the total number of minutes for all the calls
Since the customer made 60 local calls and each call lasted 3 minutes, we can multiply 60 by 3 to get the total number of minutes.
60 calls * 3 minutes/call = 180 minutes
Step 2: Calculate the total cost for all the minutes
The customer pays $0.035 per minute for local calls. To find the total cost, we can multiply the total number of minutes by the cost per minute.
180 minutes * $0.035/minute = $6.30

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The equation of the line is : y = -1x + 3

What is Equation of line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

Given,

3x + 3y = 2

3y = -3x + 2

y = -x + 2/3

Comparing it with

y = mx + c

we get,

m = -1

Now, let the equation of line be

y = mx + c

where, m = -1

Now we have to check for point (0,0) that it satisfies

0 = -1(0) + c

c = 0

So, the equation of line will be y = -1x

Now, let y = mx + c be the equation of line of point (-3, 6) should satisfy]

6 = -1(-3) + c

6 = 3 + c

c = 6 - 3

c = 3

So the equation of line is y = -1x + 3

Hence, The equation of the line is  y = -1x + 3

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The perimeter of the triangle will be 56 inches.

The triangle in which one angle is at 90 degrees and the two sides of the triangle are at 90 degrees is called a right-angled triangle. A triangle is a two-dimensional shape having three sides the angle suspended by the triangle is 180 degrees.

Given that the longer leg of a right triangle is three inches more than three times the length of the shorter leg. The area of the triangle is 84 square inches.

The perimeter of the triangle is calculated by knowing the length of all three sides of the triangle;-

Three sides are:-

Shorter side = s

Longer side = 3s + 3

Hypotenuse =?

H = √ ( s² + ( 3s + 3 )²

H = √ ( s² + 9s² +18s + 9 )

H = √ ( 10s² + 18s + 9 )

Form the area the value of s will be calculated as below:-

Area = ( 1 / 2 ) x s x (3s + 3 )

168 = 3s² + 3s

3s² + 3s - 168 = 0

s² + s -56 = 0

s² + 8s - 7s -56 =0

s ( s + 8 ) -7( s+ 8 ) = 0

s = 7 and -8 ignore negative

Three sides are:-

Shorter = s = 7 inches

Longer = 3s + s = 3 x 7 + 3 = 24 inches

Hypotenuse = √ ( 10( 7)² + 18 x (7 )  + 9 )

Hypotenuse = √ ( 490 + 126 + 9 0

Hypotenuse =  25 inches

Perimeter =  7 + 25 + 24 = 56 inches

Therefore, the perimeter of the triangle will be 56 inches.

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Answer:

-3 < z < 3

Step-by-step explanation:

×4

10 < 2z + 16 < 22. -16

-6 < 2z < 6. ÷2

-3 < z < 3

Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = \(\frac{27512 + 32019}{2}\)

= \(\frac{59531}{2}\)

= $29765.50

Answer:

$29,765.50 is the median salary

Step-by-step explanation:

To find the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

The steps to do this is:

Doing the steps:

This means take the average of $27,512 and $32,019

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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