what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]

Let the coordinates of point p be (x,y)

The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]

We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:

[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]

We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:

[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]

Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.

Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]

Learn more about coordinates of point here:

https://brainly.com/question/21950350

#SPJ4

Reduced matrix to its reduced echelon form Original Matrix:

[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,4)

Pivot Columns (Original): 1, 2, 4

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,4)

Pivot Columns (Reduced): 1, 2, 4

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column

4. Divide row 2 by 3 to get the coefficient 2/3 in the third column

5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column

6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column

Exercise 4:

Original Matrix:

[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]

Pivot Positions (Original): (1,1), (2,2), (3,3)

Pivot Columns (Original): 1, 2, 3

Reduced Echelon Form:

[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]

Pivot Positions (Reduced): (1,1), (2,2), (3,3)

Pivot Columns (Reduced): 1, 2, 3

To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:

1. Divide row 1 by 1 to get the leading 1 in the first column

2. Subtract two times row 1 from row 2 to get the leading 1 in the second column

3. Subtract row 1 from row 3 to get the leading 1 in the third column

4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column

5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column

6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively

7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column

8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ4

The denominator could be any real value

From the question, we have the following parameters that can be used in our computation:

Fraction = same denominator

Such that the numerators are 5 and 7

This means that the fractions can be represented as

Fractions = 5/x and 7/x

There is no restriction on the possible value of x

hence, the denominator is any value

Read more about fractions at

https://brainly.com/question/2929160

#SPJ1

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

The equation of a line passing through the terminal point of a vector a and in the direction of vector b is  r = a + λb.

In math the equation of a straight line is y = m x + c

where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.

Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.

Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,

=> r = a + λb.

Where λ refers the constant term.

To know more about equation here.

https://brainly.com/question/10413253

#SPJ4

The centroid of the given triangle is =(5.3 , 7.3)

The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.

The centroid formula of a given triangle can be expressed as,

C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)

where,

C denotes the centroid of a triangle

x1,x2,x3  are the x-coordinates of the 3 vertices.

y1,y2,y3  are the y-coordinates of the 3 vertices

To find: Centroid of a triangle.

We are taking the Cordinates of the traiangle XYZ

as x1,y1,x1,y2,x3,andy3

so,Given parameters are,

(x1,y1)=(-2,6)

(x2,y2)=(4,10)

(x3,y3)=(14,6)

Using centroid formula,

The centroid of a triangle = ,

 =-2+4+14/3  6+10+6/3

 =5.3 7.3

The centroid of a triangle is ==(5.3 and 7.3)

To know more about The centroid of a triangle,refer to:

brainly.com/question/7644338

#SPJ1

The height of the building that cast the shadow 98 feet will be 61.25 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.

Let 'h' be the height of the building. Then the equation is given as,

h / (90 + 8) = 5 / 8

h / 98 = 5 / 8

h = 98 x 5 / 8

h = 12.25 x 5

h = 61.25 feet

The height of the building that cast the shadow 98 feet will be 61.25 feet.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

The domain of each expression is given as follows:

1. All real values except y = 0 and y = 2.

2. All real values.

3. All real values except y = 0 and y = -7.

The domain of an expression is composed by the set of all the possible input values that the expression can assume.

For an expression that is a fraction, the denominator cannot be zero, hence:

For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.

More can be learned about the domain of a function at https://brainly.com/question/30348691

#SPJ1

The perimeter of a rectangle is 700 feet. A quadratic function for its area in terms of its width is A(w) = 350w - w²

The formula for the perimeter of a rectangle is given by:

p = 2w + 2l

While its area is:

A = w x l

Where:

w = width

l = length

Substitute p = 700 ft.,

700 = 2w + 2l

700 = 2(w + l)

w + l = 350

l = 350 - w

Substitute l = 350 - w into the formula of area:

A = w x l

A = w (350 - w)

A(w) = 350w - w²

Hence, the expression is: A(w) = 350w - w²

Learn more about rectangle here:

https://brainly.com/question/16239445

#SPJ4

Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.

Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.

Learn more about expression here

https://brainly.com/question/14083225

#SPJ4

Answer:

Step-by-step explanation:

You want the number of lines of symmetry of the 4-leaved rose shown in the figure.

The figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.

The petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)

The figure maps to itself when rotated 90° or 180°.

Answer: The answer is 3

Step-by-step explanation:

IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.

The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.

We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.

In another sentence, we were told that the size of the transistor today  is expressed as  1 × 10^-2

We can then know the difference in size will  which will be

= 1 × 10^4 / 1 × 10^-2

= 1 × 10^6

Learn more about size at:

https://brainly.com/question/14470673

#SPJ1

complete question:

Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?

Answer:

0.750

Step-by-step explanation:

Yellow sections: section 2 and section 3

Number of yellow sections: 2

Number of non yellow sections: 6

Total sections: 8

p(not yellow) = 6/8 = 0.75

Answer:

0.750

Step-by-step explanation:

you take a quarter and then you divide and think  

Answer: Maybe if you post the question

Step-by-step explanation:

answer

no

steps

February ends on the 28th this year 2023

leap year February ends on the 29th

The altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

In order to find the altitude of the second beetle, let x be the altitude of the second beetle above the first beetle.

The horizontal distance between the two beetles is 72 cm.

The first beetle moves twice as fast as the second beetle, so the vertical distance between them is 2x.

Therefore, the equation for the problem is:

3x + 2x = 72

5x = 72

x = 14.4 cm

Therefore, the altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

learn more about altitude: https://brainly.com/question/1159693

#SPJ1

The exponent form that represents the side length of the square is √x

From the question, we have the following parameters that can be used in our computation:

Area = x in.²

The area of a square is calculated as

Area = Side length²

substitute the known values in the above equation, so, we have the following representation

Side length² = x

Take the square root of both sides

Side length = √x

Hence, the expression is √x

Read more about area at

https://brainly.com/question/22972014

#SPJ1

Answer:

The area of a circle is pi multiplied by the radius squared (A = π r²)

The radius (r) is the distance from the center of the circle, to the edge of the circle.

Example:

if you have a circle with radius 2, the area would be:

r = 2

A = π (2)²

A = π(4)

A = 4π

Answer:

Area can be calculated by the formula = [tex]\pi r^{2}[/tex]

Step-by-step explanation:

We can calculate the area of a circle with the formula,

Area of Circle = [tex]\pi r^{2}[/tex]

Where r replicates the radius of the circle

The product of the binomial factors is x² + 16x + 64

from the question, we have the following parameters that can be used in our computation:

(x+8)2

Express properly

So, we have

(x+8)²

Using the square of a binomial sum, we have

(x+8)² = x² + 2 * x * 8 + 8²

Evaluate

(x+8)² = x² + 16x + 64

Hence, the solution is x² + 16x + 64

Read more about expression at

https://brainly.com/question/4344214

#SPJ1

By adding (81.7-23.456)+(78.44+2.72), we get 139.404

Use the three rules below to calculate the number of significant figures in a number:

Non-zero digits are always meaningful.

Any zero between the first and second significant digits is significant.

Only the last zero or trailing zeros in the decimal section are important.

Numbers Have Rules INCLUDING a Decimal Point

START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.

STOP COUNTING FOR SIGNIFICANT FIGURES.

Non-zero numbers are ALWAYS meaningful.

After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.

To learn more about significant figures, visit

brainly.com/question/29153641

#SPJ1

No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.

To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.

Learn more about sample mean here:

https://brainly.com/question/30023845

#SPJ4

The image that gives the translation of the polygon six units to the left and two units upward is given as follows:

The fourth graph.

(which is the third graph if we consider that the first is the original image).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

For the translation 5 units left, we have that:

The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.

For the translation 2 units up, we have that:

The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.

More can be learned about translations at brainly.com/question/28174785

#SPJ1

Answer: 22 vaccines

Step-by-step explanation:

first, reduce the amount that doctors leave out from the total amount of a vial

6 - 0.5 = 5.5

next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give

5.5/ 0.25 = 22 vaccines

The eastbound airplane has traveled 16 miles.

This can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance the northbound airplane has traveled (12 miles) is one side of the triangle, the distance the eastbound airplane has traveled is the other side, and the distance between the two airplanes (20 miles) is the hypotenuse.

So, we can set up the equation as:

(distance eastbound airplane)^2 + 12^2 = 20^2

Solving for the distance eastbound airplane, we get:

distance eastbound airplane = sqrt(20^2 - 12^2) = sqrt(256 - 144) = sqrt(112) = 16 miles

Given that IJ = 2, we know that IJ is the radius of the circle.

The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:

(x/360) * pi * 2^2 =

Solving for x:

x = (180/pi)*

We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.

Answer:

1

Step-by-step explanation:

We have g(f(2))

Working from the inside out, we start with f(2)

So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2

Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)

Now we can go to the other graph, g(x) and find where X is -2.

That's where we find the point (-2,1)

Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1

Now we can conclude g(f(2)) = 1

Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

What is the graph?

A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.

To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).

Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.

To learn more about Graph, Visit

https://brainly.com/question/19040584

#SPJ1

A perimeter longer than 50 for any point, C satisfies the area requirement.

Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.

The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.

Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.

Know more about perimeter

https://brainly.com/question/397857

#SPJ4

The full question

In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?