Points on the coordinate plane
Point N is graphed on the coordinate plane.
-5-2
is
OF
Write the coordinates of point N.

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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Answer:

212000

Step-by-step explanation:

120000 - 5% = 190000

hence 5% is 10000

120000+ 30000= 212000

For the given equation of function, the production is equal when x = 1/3 and x = 3.

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function. y = f is how functions are typically represented (x).

The equation of the functions are:

A(x) = 3x²

B(x) = 8x + 3

The production when the functions are equal is given by:

3x² = 8x + 3

3x² - 8x - 3 = 0

3x² - 9x + x - 3 = 0

3x (x - 3) + 1 (x - 3) = 0

(3x + 1) (x - 3) = 0

x = 1/3 and x = 3

Thus, the production is equal when x = 1/3 and x = 3.

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In a scatter plot, if all data points were aligned along a 44º angle, the correlation would be 0. The correct answer is D.

In a scatter plot, the correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

When all data points are aligned along a 44º angle, it means that the points are distributed randomly and do not follow a clear linear pattern. There is no consistent increase or decrease in one variable as the other variable changes. Therefore, the correlation between the variables is 0, indicating no linear relationship or strength of association.

In other words, the angle of 44º suggests that the variables are unrelated and have no linear dependency on each other.

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Answer:

70 square inches

Step-by-step explanation:

We have to find the area of the rectangle and this would help us determine how much paint he would need to paint his rectangle

Area of a rectangle = Length × Width

Length = 10 inches

Height = 7 inches

Area of the rectangle = 10inches × 7 inches

= 70 square inches

Therefore, he would be needing 70 square inches of paint in order to paint his rectangel

Answer:
For this sin(x)=0  or  (2cos(x)-1)=0  , "x" should have one of these values:

For sin(x)=0,   X= π or X=2π or X=π*2πn ("n" can be any integer)

For (2cos(x)-1)=0,  X=  π/3 or  X=5π/3 , or X= π/3 *2n or X=5π/3 *2πn (n can be any integer)

Step-by-step explanation:

Sin(x)*(2cos(x) -1) = 0

As any amount multiplied by 0 results in 0. Then given the expression    Sin(x)*(2cos(x) -1) = 0,  

Then Sin(x)= 0 or  (2cos(x) -1) = 0
- For Sin(x)= 0  the funtion Sin(x) = 0 when X= π/2  or when X= 3π/2.

- For 2cos(x) -1 = 0:
2cos(x) -1 = 0

2cos(x) -1 +1 = 0+1

2cos(x) /2 =  1 /2

cos(x)       = 1/2 for cos(x) = 1/2,  by the properties of cosine X=π/3 or X=5π/3.

Finally as 2π*n is the same as 2π then the solutions are:
For sin(x)=0,   X= π or X=2π or X=π*2πn ("n" can be any integer) .

For (2cos(x)-1)=0,  X=  π/3 or  X=5π/3 , or X= π/3 *2n or X=5π/3 *2πn (n can be any integer).

The general solution for the function sin(x)(2cos(x) - 1) = 0:

x = nπ, π/3 + 2nπ, or 5π/3 + 2nπ, where n is an integer.

We have,

To find the general solution for the function sin(x)(2cos(x) - 1) = 0, we can set each factor equal to zero and solve for x separately.

Setting sin(x) = 0:

sin(x) = 0

x = nπ, where n is an integer.

Setting 2cos(x) - 1 = 0:

2cos(x) = 1

cos(x) = 1/2

x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.

Combining the solutions from both cases, we have the general solution for the equation sin(x)(2cos(x) - 1) = 0:

x = nπ, π/3 + 2nπ, or 5π/3 + 2nπ, where n is an integer.

Thus,

The general solution for the function sin(x)(2cos(x) - 1) = 0:

x = nπ, π/3 + 2nπ, or 5π/3 + 2nπ, where n is an integer.

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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Answer:

$37.5

Step-by-step explanation:

50× 25% = 12.5

50-12.5 = 37.5

The  ratio of goldfish to perch to sticklebacks in this pond in its simplest form is 11 : 6 : 3.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

55% of the fish in a pond are goldfish.

Fraction of fish that are goldfish = 55/100

                                                     = 11/20

That is, 11 fishes out of 20 fishes are goldfish.

Fraction of fish that are perch = 3/10 = (3 × 2) / (10 × 2) = 6/20

6 out of 20 fishes are perch.

Rest of the fishes = 20 - (11 + 6) = 3

Fraction of fish that are sticklebacks = 3/20

Ratio of goldfish to perch to sticklebacks = 11 : 6 : 3

Hence the required ratio is 11 : 6 : 3.

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Your question is confusing. The complete question is given below.

55% of the fish in a pond are goldfish. 3/10 of the fish are perch and the rest of the fish are sticklebacks.

Write the ratio of goldfish to perch to sticklebacks in this pond in its simplest form.

40,000 in scientific notation can be represented by the expression

4 × 10⁴ .

The number 40000 can be written in the scientific notation as 4 × 10⁴ .

Scientific notation must be used when a number is either too large or too little to be stated in decimal form, which typically yields a long string of digits. It's also known as standard index form or scientific form.

460000000 = 4.6×10⁸

6230000000 = 6.23×10⁹

60500000 = 6.05 x 10⁷

Since it may make a number of mathematical operations simpler, this base ten notation is frequently employed by scientists, mathematicians, and engineers. A digit that improves a number's correctness is referred to as an essential figure. This includes all non-zero values, significant zeroes, and zeros in significant intervals between significant digits.

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Answer:

That is one big M

Step-by-step explanation:

Other than that I cannot help with this question because of the picture that was taken was enlarged too much!

Answer:

I can't see the numbers        

Step-by-step explanation:

I can't see the numbers for me to find the area can you pull back the camera back then take another picture .

The roots of the equation are;

a. (n +2)(n -8)

b. (x-5)(x-3)

From the information given, we have the expressions as;

f(x) = n² - 6n - 16

Using the factorization method, we have to find the pair factors of the product of the constant and x square, we have;

a. n² -8n + 2n - 16

Group in pairs, we have;

n(n -8) + 2(n -8)

Then, we get;

(n +2)(n -8)

b. y = x² - 8x + 15

Using the factorization method, we have;

x² - 5x - 3x + 15

group in pairs, we have;

x(x -5) - 3(x - 5)

(x-5)(x-3)

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Answer:

6 and -2

Step-by-step explanation:

Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

The value of x shown in the right angled triangle is 15.9 units

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Pythagoras theorem shows the relationship for the sides of a right angled triangle. It is given by:

Hypotenuse² = Adjacent² + Opposite²

From the diagram, substituting:

17² = x² + 6²

x² = 17² - 6²

x² = 253

x = 15.9 units

The value of x is 15.9 units

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The radius of convergence, R = 11 is found for the given function using the power series.

The given function is F(X) = ln(11 - X).

Find the power series representation for the function F(X).

We have:

F(X) = ln(11 - X)

F(X) = ln 11 + ln(1 - X/11)

Using the formula for ln(1 + x), we get:

F(X) = ln 11 - Σn=1∞ (-1)n-1 * (x/11)n/n

We can write the series using the sigma notation as:

∑n=1∞ (-1)n-1 * (x/11)n/n + ln 11

Thus, the power series representation of

F(x) is Σn=1∞ (-1)n-1 * (x/11)n/n + ln 11.

Determine the radius of convergence, R.

The power series converges absolutely whenever:

|x/11| < 1|x| < 11

Thus, the radius of convergence is 11.

In other words, the series converges absolutely for all values of x within a distance of 11 from the center x = 0.

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Answer:

\(\boxed{x = 251.4 cm}\)

Step-by-step explanation:

Part 1: Sketching the triangle

We are given the angle of elevation, 70°, and the distance along the ground, 86 centimeters. Our unknown is a ladder leaning against the building. Buildings are erected vertically, so the unknown side length is the hypotenuse of the triangle.

We can then sketch this triangle out to visualize it (attachment).

Part 2: Determining what trigonometric ratio can solve the problem

Now, we need to refer to our three trigonometric ratios:

\(sin = \frac{opposite}{hypotenuse}\)

\(cos = \frac{adjacent}{hypotenuse}\)

\(tan = \frac{opposite}{adjacent}\)

Visualizing the sketched triangle, we can assign the three sides their terms in correspondence to the known angle -- this angle cannot be the right angle because the hypotenuse is opposite of it.

Therefore, we know our unknown side length is the hypotenuse of the triangle and because the other side is bordering the 70° angle, it is the adjacent side.

By assigning the sides, we can see that we need to use the trigonometric function that utilizes both the hypotenuse and the adjacent side to find the angle. This is the cosine function.

Part 3: Solving for the unknown variable

Now that we have determined what side we need to solve for and what trigonometric function we are going to use to do so, we just need to plug it all into the equation.

The cosine function is provided: \(cos( \alpha) = \frac{adjacent}{hypotenuse}\), where \(\alpha\) is the angle. We just need to plug in our values and solve for our unknown side; the hypotenuse.

\(cos (70) = \frac{86 cm}{x}\), where x is the unknown side/the hypotenuse.

\(x * cos (70) = \frac{86 cm}{x} * x\) Multiply by x on both sides of the equation to eliminate the denominator and make the unknown easier to solve for.

\(\frac{xcos (70)}{cos(70)} = \frac{86 cm}{cos(70)}\), Evaluate the second fraction because the first one cancels down to just the unknown, x.

\(\frac{86}{cos(70)} = 251.4\), round to one decimal place.

Your final answer is \(\boxed{x=251.4cm}\).

Answer: I think that the answer of the question would be actually a athlete and a tool, because versatile is something that is able to adapt or be adapted to many different functions or activities. You can be a tennis athlete or soccer athlete or a athlete of any sport. A tool is also versatile since you can use it to do different things/fix different things.

A historical event is not versatile, because you can't have one history event that has adapted and a report card is also not versatile, since the report card serves mainly for only purpose.

I am only trying to help the person that asked the question, so sorry if I hurt anyone's feelings or offend any one that has a different answer.

Answer:

0.603

Step-by-step explanation:

Given the data:

X 57 58 59 59 60 61 62 64

Y 77 78 75 78 82 82 79 81

The Correlation Coefficient, R value gives a measure of the degree of correlation between two variables, the dependent and independent variable. The correlation Coefficient value ranges from - 1 to 1. With negative values depicting a negative relationship and positive values meaning a positive relationship. The closer the R value is to + or - 1, the higher the strength of the relationship. With a value of 0 meaning 'no correlation'.

The correlation Coefficient value of the data above is 0.603, this gives a fairly strong positive correlation

Answer:

GIVE ME MY RAMEN

Step-by-step explanation:

3.

add like terms

30 + 7k = 100

100-30 = 70

70 divided by 7k = 10

k = 10

4. add the z's together

2z - 6 -2 = -10

+ 6 + 2

-10 will be -2 now since we dragged the -6 and -2 to the other side

2z = -2

z = -1

5. 3.2x - 1.7x = 1.5x

1.5x + 5.5 = 10

10 would be 4.5 since we dragged 5.5 to the other side so it would be 10 - 5.5

3.2x = 5.5

x = 1.71875

6.

3/4x - 1/4x = 2/4x

14 - 3 = 11

2/4x = 11

x = 22

The returns when 30 tickets were sold would be $ 70 .

To calculate the total earnings from 30 sold tickets using the formula a ( n ) = 3 n - 20 , we must input n as 30 and assess the outcome .

Therefore, the returns raised when there were 30 tickets sold would be :
= 3 n - 20

= 3 ( 30 ) - 20

= 3 x 30 - 20

= 90 - 20

= 90 - 20

= $ 70

Therefore, with 30 tickets sold, the amount of money raised is $70.

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Question is:

How much was raised when 30 tickets were sold?

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

-30x 6 = -9 -3x=

x = 3/13

Answer:

a) 2.5 x 10^5

b) 8.1 x 10^4

c) 9.06 x 10^8

d) 1.034 x 10^10

The angle between the two planes is 113.75°.

Firstly, we find the normal vectors of each plane. The normal vector of a plane is the vector perpendicular to the plane.

The first equation can be rewritten as:

6x - 8y + 10z = 12

Note that the coefficients of x, y, and z represent the components of the normal vector.

So the normal vector of the first plane is:

N₁ = <6, -8, 10>

For the second equation, the plane can be extracted:

x + y - z = 2

N₂ = <1, 1, -1>

The angle between the two planes can be found using the dot product of the normal vectors and the formula:

cosθ = (N₁ . N₂) / (|N₁| |N₂|)

where |N| represents the magnitude of vector N.

The dot product of the normal vectors is:

N1 . N2 = (6)(1) + (-8)(1) + (10)(-1) = -12

The magnitudes of the normal vectors are:

|N1| = sqrt(6² + (-8)² + 10²) = sqrt(296) = 17.205

|N2| = sqrt(1² + 1² + (-1)²) = sqrt(3) = 1.732

Substituting these values into the formula gives:

cosθ = (N1 . N2) / (|N1| |N2|)

cosθ = -12 / (17.205 * 1.732)

cosθ = -12/29.799

cosθ = -0.4027

The angle θ can be found using the inverse cosine function:

θ = cos⁻¹(0.4027)

θ ≈ 113.75°

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The line segment between 0 and 48 represents the possible heights for the ride.

A number line is a visual representation of numbers that is used to illustrate numerical values and their relationships to one another. It is a straight line that is usually horizontal, with numbers placed at equal intervals along its length. Positive numbers are represented on the right-hand side of zero, and negative numbers are represented on the left-hand side of zero. The number line can be extended infinitely in both directions, allowing for the representation of any number, including decimals and fractions. It is a useful tool in many areas of mathematics, including arithmetic, algebra, and geometry.

Here,

Here's the graph on the number line to represent the possible heights for the ride:

0   12  24  36  48  60

|---|---|---|---|---|---|

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ANSWER:

1/2

EXPLANATION:

Plug this into calculator -->

(1/64) ^ (1/6) and you will get exactly

0.5 which is equal to 1/2

*Note = this can also be done by changing it to...

⁶√[1/64]

If you know this root (2⁶ = 64) then it is 2, and 1 over 2 is equal to one half

The numbers of passengers that need to be booked to ensure the cruise line makes a profit, using a compound inequality is x ≥ 2,052 and x ≤ 2,462.

From the information given, we are told that the cruise ship needs to book at least 2,052 passengers to be profitable, but the most passengers the ship can accommodate is 2,462.

Learn x be the number of people that can be accommodated. Therefore, the model is x ≥ 2,052 and x ≤ 2,462.

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Answer:

Step-by-step explanation:

12