What is the equation of the line that passes through the point (8,-8 and has a slope of -1/4

Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Answer:

V=216cm³

Step-by-step explanation:

V=216cm³

The correct answer is Option 'B'.

We are drawing cards without replacement,

So first card is a diamond  is 13/52 and

Second not a diamond is 39/51

51 because we have picked 1 card in the first draw.

so final answer is

(13/52) *(39/51) = 0.1912.

Therefore, the probability that the first card drawn is a diamond and the second card drawn is not a diamond is 0.1912.

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain occurrences. The degree to which something is likely to happen is essentially what probability means.

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Answer:

Hope this helps!!

Step-by-step explanation:

Answer:

168cmsqured

Step-by-step explanation:

as for me,15 acts as the lower part of the trapezium while 13 acts as the upper part of the trapezium .so since I know the measurements of the both sides I can easily calculate the area use using the formula indicated in the image.hope it helps

Lower Quartile Explanation: Arrange the terms in ascending order

20, 22, 25, 28, 29, 30, 32, 33, 34

Take the lower half of the ascending set: 20, 22, 25, 28

Find the median of 20, 22, 25, 28: 23.5

Upper Quartile Explanation: Arrange the terms in ascending order

20, 22, 25, 28, 29, 30, 32, 33, 34

Take the upper half of the ascending set: 30, 32, 33, 34

Find the median of 30, 32, 33, 34: 32.5

Interquartile Explanation:

Compute the first quartile of the list: 23.5

Compute the third quartile of the list: 32.5

Compute the difference between 32.5 and 23.5: 9

Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

The independent variable that has no effect on the dependent variable, the effect size statistic will  have a value of 0.00.

The independent variable is known to be one type of an experimenter controls.

Note that the dependent variable is seen as the variable that alters the response done to the independent variable.

The two variables may be linked by  the term cause and effect and when the independent variable is altered, so the dependent variable is affected.

Hence, The independent variable that has no effect on the dependent variable, the effect size statistic will  have a value of 0.00.

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Answer:

50%

Step-by-step explanation:

Answer:

your answer would be 50%

Step-by-step explanation:

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The correlation coefficient between the student's height and the distance they were able to jump is 0.86.

The correlation coefficient is a number that ranges from -1 to 1. It shows the strength of the relationship between two variables. It also shows the direction of the relationship.

Positive correlation is when the two variables move in the same direction. If one variable increases, the other variable also increases. Negative correlation is when two variables move in different direction. If one variable increases, the other variable decreases. Zero correlation is when there is no relationship between the variables.

The correlation coefficient is calculated using a financial calculator.

Here is the complete question:

A group of students want to determine if a person's height is linearly related to the distance they are able to jump.

To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.

Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.

Enter the correlation coefficient. Round your answer to the nearest hundredth.

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Answer:

It's 0.92

Step-by-step explanation:

I took the test already

Answer:

Step-by-step explanation:

3x + y = 9    and  y = -4x + 10

so:

3x + (-4x + 10) = 9

3x - 4x + 10 = 9

 - x = - 1

   x = 1

Answer:

x=1 y=6

Step-by-step explanation:

To declare a variable named apple of the class named "apple" and initialize it to a new object, we can use the following statement in most programming languages:

apple apple = new apple();

Here, the first "apple" is the class name, and the second "apple" is the name of the variable we are declaring. The "new" keyword is used to create a new object of the class, and the parentheses indicate that no parameters are being passed to the constructor.

This statement creates a new instance of the class named "apple" and assigns it to the variable also named "apple". The variable can now be used to access the properties and methods of the object, allowing us to manipulate and work with the data stored within it.
```java
Apple apple = new Apple();
```

This statement creates a new instance of the "Apple" class and assigns it to the variable "apple." The "new" keyword is used to create a new object, and "Apple()" calls the constructor for the class.

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The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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The average user spends approximately $3.65 per year on toothpaste.

To determine whether US retail toothpaste demand looks like a D, we need to understand what a D-shaped demand curve represents. A D-shaped demand curve is characterized by a small number of consumers who are willing to pay a high price for a product, while the majority of consumers are only willing to pay a low price. This type of demand curve is often seen in luxury goods or products with high status value.

In the case of toothpaste, it is unlikely that the demand curve would be D-shaped. This is because toothpaste is a necessity item that is used by the vast majority of Americans on a daily basis.

According to the given information, 90% of Americans use an average of 0.5 grams per day, indicating that there is a large and consistent demand for toothpaste.

To estimate how much the average user spends on toothpaste per year, we can use the following formula:

Annual toothpaste expenditure = (Daily usage in grams) x (Price per gram) x (Days in a year)

Assuming an average price of $0.02 per gram of toothpaste, the annual expenditure for an individual who uses 0.5 grams per day would be:

Annual toothpaste expenditure = (0.5 g/day) x ($0.02/g) x (365 days/year) = $3.65

Therefore, the average user spends approximately $3.65 per year on toothpaste.

In conclusion, based on the fact that toothpaste is a necessity item with consistent and widespread usage among Americans, it is unlikely that US retail toothpaste demand looks like a D.

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Answer:

M<DEG + m<GEF = m<DEF

Step-by-step explanation:

Given: Figure

To find: Choose correct option

Solution: In the figure, using angle addition postulate, M<DEG + m<GEF = 180 (sum of < on straight line)

M<DEG + m<GEF = m<DEF

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

The point-slope form of an equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line

m is the slope of the line.

We can use the given point (−5,−2) as (x1,y1)

Choose any value for the slope m to write the equation of the line in point-slope form.

For example:

Option 1:

Let's choose the slope m to be 2.

Then the equation of the line becomes:

y - (-2) = 2(x - (-5))

Simplifying the equation:

y + 2 = 2(x + 5)

Option 2:

Let's choose the slope m to be -3.

Then the equation of the line becomes:

y - (-2) = -3(x - (-5))

Simplifying the equation:

y + 2 = -3(x + 5)

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

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The integers x and y that satisfy 17x + 101y = 1 are x = -4 and y = 12.

The question asks us to find integers x and y such that 17x + 101y = 1.

We can use the Extended Euclidean Algorithm to solve this problem. This algorithm is used to find the greatest common divisor (GCD) of two integers.


Let A = 17 and B = 101


1. A = B * q + r

17 = 101 * q + r


2. A = A * s + t

17 = 17 * s + t


3. B = r * s + t

101 = r * s + t


4. The GCD(A,B) = GCD(17,101) = t


5. If t = 1 then A * x + B * y = 1, so x and y are the integers we are looking for.


We can calculate the values of x and y as follows:


x = s = -4

y = r = 12

Hence the value of x and y can be found using Extended Euclidean Algorithm.

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The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

From the above given data, the following solution is given below:

Given:

Let f(x,y,z) = x³z - yz²

To find the partial derivatives of f

Here the directional derivative of a function f(x,y,z) is given by:

(df/dx , df/dy, df/dz)

df/dx = 3x²

df/dy = -z²

df/dz = x³ - 2yz

at points(1,3,2)

(df/dx)₍₁,₃,₂₎ = 3(1)² = 3

| (df/dx)₍₁,₃,₂₎ | = 3

(df/dy)₍₁,₃,₂₎ = -2² = 4

| (df/dy)₍₁,₃,₂₎ | = 4

(df/dz)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11

| (df/dz)₍₁,₃,₂₎  | = 11

As we got the maximum modulus of derivative in direction of x. Since, therefore we should move into z direction to maximize the directional derivative.

(df/dz)₍₁,₃,₂₎  = -11

Hence, the instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

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The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point | (∂f/∂z)₍₁,₃,₂₎  | = 11.

What is instantaneous rate of change?

The derivative value change at a particular point is the same as the instantaneous rate of change, which is the change in rate at a specific instant. The tangent line slope and the instantaneous rate of change at a given point on a graph are the same. That is, the slope is curved.

From the given data, the solution is given below:
Given:
Let f(x, y, z) = x³z - yz²
To find the partial derivatives of f
Here the directional derivative of a function f(x, y, z) is given by:
(∂f/∂x , ∂f/∂y, ∂f/∂z)

∂f/∂x = 3x²

∂f/∂y = -z²

∂f/∂z = x³ - 2yz

at points(1,3,2)

(∂f/∂x)₍₁,₃,₂₎ = 3(1)² = 3

| (∂f/∂x)₍₁,₃,₂₎ | = 3

(∂f/∂y)₍₁,₃,₂₎ = -2² = 4

| (∂f/∂y)₍₁,₃,₂₎ | = 4

(∂f/∂z)₍₁,₃,₂₎ = 1³ - 2*3*2 = 1-12 = -11

| (∂f/∂z)₍₁,₃,₂₎  | = 11

As we got the maximum modulus of derivative in direction of z. Since, therefore we should move into z direction to maximize the directional derivative.
(∂f/∂z)₍₁,₃,₂₎  = -11
Hence, The instantaneous rate of change is the change in the rate at a particular instant and it is same as the change in derivative value at a specific point.

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Complete question:

Complete question is attached below.

Very nice question! Have a good day!

The completed table showing the radius, angle at the center, arc length, and area of the sector of the circle are as follows;

\({}\)       Radius             Angle at center            Arc Length           Area

(a)    4 cm      \({}\)         1.25 rad                          5 cm                   22.5 cm²

(b) \({}\)  6 cm                1.5 rad                            9 cm                   22.5 cm²

(c) \({}\)  12 cm               0.8 rad                           9.6 m                  57.6 m²

(d)  \({}\) 10 m                 1.2 rad                            12 m                   60 m²

(e) \({}\)  8 mm               2 rad                               16 mm               64 mm²

(f)  \({}\)  9 mm              (2/3) rad                          6 mm                 27 mm²

A sector of a circle is a part of a circle that is pie shaped, with parts including, two radii of the circle and part of the circumference of the circle.

4(a) The specified dimensions of the sectors of the circles are;

Radius = 4 cm

Angle at the center = 1.25 radians

The arc length is therefore;

The area of the sector is therefore;

(b) Radius = 6 cm

Arc length = 9 cm

The angle at the center, θ, is therefore;

Arc length = 2×π×6 × θ/(2·π) = 9

6 × θ = 9

θ = 9/6 = 1.5

(c) Angle at center = 0.8 rad

Arc length = 9.6 m

Arc length = 2×π× Radius × 0.8 rad/(2·π rad) = 9.6

Radius = 9.6 m/0.8 = 12 m

(d) Angle at the center = 1.2 radians

Area = 60 m²

The area = π × (Radius)² × 1.2/(2·π) = 60 m²

(Radius)² × 0.6 = 60 m²

(Radius)² = 60 m²/(0.6) = 100 m²

The arc length = 2 × π × 10 mm × 1.2/(2·π) = 12 mm

(e) The radius of the circle = 8 mm

The area of the sector = 64 mm²

The angle at the center, θ, can therefore, be found as follows;

Area = π × (8 mm)² × θ/(2·π) = 64 mm²

θ = 2 × 64 mm²/((8 mm)²) rad = 2 rad

(f) Arc length = 6 mm

Area = 27 mm²

The radius and angle at the are found as follows

Let r represent the radius, we get;

Arc length = 2 × π × r × θ/(2·π) = 6

Therefore; θ = 6/r

Area of the sector = π × r² × θ/(2·π) = 27 mm²

Therefore; π × r² × (1 mm²) × (6/(r × 1 mm))/(2·π) = 27 mm²

r × (1 mm) × 3 = 27 mm²

r = 27 mm²/(3 × 1 mm) = 9 mm

Please find the completed table for the sectors of a circle above

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The probability distribution of the random variable X, which represents the number of spots that turn up when a balanced die is rolled, is a discrete uniform distribution.

This means that each possible outcome has an equal probability of occurring, and the probabilities are evenly distributed across the different values of X.

In a balanced die, there are six possible outcomes, corresponding to the numbers 1 through 6. Since each outcome is equally likely, the probability of each individual outcome is 1/6. Therefore, the probability distribution of X can be represented as follows:

P(X = 1) = 1/6

P(X = 2) = 1/6

P(X = 3) = 1/6

P(X = 4) = 1/6

P(X = 5) = 1/6

P(X = 6) = 1/6

In summary, the probability distribution of the random variable X, representing the number of spots that turn up when rolling a balanced die, follows a discrete uniform distribution, where each possible outcome has an equal probability of occurring, with a probability of 1/6 for each value from 1 to 6.

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Answer: $115,000

Step-by-step explanation:

The common stock is 9000 times 5 = $45000

To Paid-in Capital in Excess of Par = 160,000 - 45,000 = $115,000

To determine the values of m, n, and p in the table, we can use the given relationship between x and y:

x + 1 = m * y + n

We can substitute the values from the table into this equation to find the values of m, n, and p:

For the first row:

2 + 1 = m * 4 + n

3 = 4m + n

For the second row:

3 + 1 = m * 26 + n

4 = 26m + n

For the third row:

4 + 1 = m * 100 + n

5 = 100m + n

Now, we have a system of three equations with three unknowns (m, n, and p):

3 = 4m + n -- (Equation 1)

4 = 26m + n -- (Equation 2)

5 = 100m + n -- (Equation 3)

By solving this system of equations, we can find the values of m, n, and p.

Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

Answer:

6 4/5

Step-by-step explanation:

2 4/5 x 2 3/7 = 6 4/5

Hope this helped you

648 pounds of topsoil in total.

( for this question it's asking how many bags she bought in total, which I dont understand cuz it already says she bought 18 bags.)

(It really should have asked, how much topsoil in total did she buy)

but what I did to find my ans is that I multiplied.

36×18, cuz it says each bag contains 36 pounds.

The value of x from the given equation is 4.

The given equation is 24x - 19=16x + 13.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 24x - 19=16x + 13

⇒ 24x-16x=13+19

⇒ 8x=32

⇒ x=4

Therefore, the value of x from the given equation is 4.

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Answer:

this is the answer

Step-by-step explanation: pretty easy tbh

Answer:

A

Step-by-step explanation:

30:18 /6 =5/3

15:9 /3 =5/3

20:12 /2 =5/3

Answer:

free points

Step-by-step explanation:

thanks sis

Answer: It is not possible

Step-by-step explanation:

to have a triangle with sides 5 cm, 3 cm and 2 cm. Sum of any two sides of a triangle must be greater than the third side.

3 cm + 2 cm = 5 cm