Final answer:
The jogger is approximately 7 miles from his house after running 3 miles east and then 5 miles at a 30° angle east of north, calculated using trigonometric functions and the Pythagorean theorem.
Explanation:
The question asks how far a jogger is from his house after running a total of 8 miles, initially 3 miles due east and then 5 miles at a 30° angle east of north. To solve this, we can use trigonometric functions to find the resultant displacement. The first leg of the journey is straightforward, 3 miles directly east. The second leg can be broken into its northward and eastward components using sine and cosine functions, with the length of the leg being the hypotenuse.
Northward component: 5 miles × cos(30°) = 4.33 miles
Eastward component: 3 miles (initial) + (5 miles × sin(30°)) = 3 + 2.5 = 5.5 miles
To find the total displacement, we calculate the straight-line distance from the starting point to the end point using the Pythagorean theorem.
Displacement = √(northward component² + eastward component²) = √(4.33² + 5.5²) = √(18.7489 + 30.25) = √(48.9989) = 7 miles approximately.
Therefore, the jogger is approximately 7 miles from his house.
To find the distance and direction from the starting point after the jogger's two separate runs, we apply vector addition by decomposing the second leg into its components with trigonometry and then use the Pythagorean theorem and arctangent function to find the resultant magnitude and direction.
Explanation:The question involves determining the distance from the starting point after a two-leg journey with given directions and distances. To solve this, we need to apply principles of vector addition to combine the two displacements into one resultant displacement. The first displacement is due east, and can be represented as a straight line on a horizontal axis. The second displacement, at a 30° angle east of north, requires us to decompose it into its northward and eastward components. These components are found using trigonometry: by multiplying the distance by the cosine (for the eastward part) and sine (for the northward part) of the angle.
After computing the respective components of the second displacement, we add both eastward displacements together and both northward displacements together to find the total displacement in the east and north directions. The final step is to use the Pythagorean theorem to determine the magnitude of the resultant vector, and trigonometry (specifically, the arctangent function) to find the direction of the resultant vector from the origin, which provides the required distance and direction from the jogger's house after running.
what are three ordered pair of y=2x+0.5
Arturo is customizing his next pair of basketball shoes. The following table shows the design components and how many options he has for each.
Design component Number of options
Primary color 8
Secondary color 8
Sole color 8
Lace color 5
How many different shoe combinations can Arturo create?
Answer:
2,560
Step-by-step explanation:
okay so im working on it right now on khan
so you have to do 8x8x8x5
8x8 = 64 then 64x8=512 then 512x5=
2,560
now im not just going to leave you guys with this explaination because i dont really like people just putting answers up when it's wrong just for the points thats why i try to show proff on MOST of my work
the screenshot is below for proff
please mark me brainlist
The local radio station played 9 hip-hop songs and 6 hard rock songs in one hour. What percent of the songs played during this hour was hip-hop?
Which relationship describes angles 1 and 2?
Select each correct answer.
supplementary angles
complementary angles
vertical angles
adjacent angles
A 6 mile walking trail has a distance marker every 1/3 mile.
Jordan is calculating the slope of the trend line in the scatterplot below.
How can Jordan use the plot to check the reasonableness of his answer?
His slope should be positive because the coordinates of all the plotted points are positive.
His slope should be positive because the trend line is slanted up to the right.
His slope should be negative because there are plotted points not on the line.
His slope should be negative because the x-coordinate of each plotted point is less than the y-coordinate.
Answer: B
His slope should be positive because the trend line is slanted up to the right.
Step-by-step explanation:
from left to right the line is increasing upward so it is positive so this means both of the bottom answers are wrong. answer A. is wrong because even slopes that are negative have all points positive sometimes so this is not a valid reason. therefore this leaves us with the answer B, which is correct.
His slope should be positive because the trend line is slanted up to the right. which is the correct answer would be an option (B).
What is the Scatter plot?The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis.
Jordan is calculating the slope of the trend line in the given scatterplot.
As per the given scatter plot, the required solution would be as:
Take two points (1,24) and (8,96)
So, slope = (96-24)/(8-1) = 72/7 = 10.28
The line is moving upward from left to right, hence it is positive, implying that both of the bottom solutions are incorrect. Answer A. is incorrect since even negative slopes can have all points positive at times, hence this is not a legitimate argument.
As a result, we are left with solution B, which is accurate.
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A recent survey reveals that of the 250 poodle owners interviewed, 93% of them regularly groom their dogs. If there are 50,000 registered poodle owners in the city, how many owners are expected to regularly groom their dogs?
A. 46,500
B. 93
C. 3,500
D. 7
Help as fast as possible
Graph the linear equation find three points that solve the equation then plot on the graph 2y=-x+2
Answer:
Step-by-step explanation:
A small business examines the income of 10 random households to determine if the community will be a good location for a store. Four of the households have an income between $30,000 - $55,000. Five of the households have an income between $70,000 - $100,000. One household has an income of over $700,000. Using the data obtained, which measure of central tendency will be greatly over-estimated?
A) mean
B) mode
C) median
D) None of the measures will be greatly over-estimated.
Answer:
mean trust me
Step-by-step explanation:
Which algebraic expressions are polynomials? Check all that apply. PLEASE HELP
Evie has scores of 72, 78, 80 And 84 On four Science quizzes. What score must she get on the next quiz to have an average of at least 80?
The tax rate on Jerome James 112000 vacation home is 25 Mills the property is assessed at full value how much will Jerome pay in taxes this year
Answer: $2,800
Step-by-step explanation:
Given: The assessment value of Jerome's home= [tex]$112,000[/tex]
We know that to calculate the property tax, we need to multiply the assessment value of the property by the mill rate and then divide by 1,000.
Then, the property tax is given by :-
[tex]\text{Property tax}=\dfrac{\$112,000\times25}{100}\\\\\Rightarrow=\text{Property tax}=\$2,800[/tex]
Therefore, Jerome pay $2,800 as property tax in this year.
Answer:
[tex]Property tax=$2800[/tex]
Step-by-step explanation:
Given: The assessment value of Jerome's home is given as =[tex]112000[/tex]
Solution: Since we know that in order to calculate the property tax, we need to multiply the assessment value of the property by the mill rate and also divide by [tex]1000[/tex].
Then, the property tax is given as :-
[tex]Property tax=\frac{112000{\times}25}{100}[/tex]
[tex]Property tax=$2800[/tex]
Thus, Jerome pay $2,800 as property tax in this year.
In a triangle, the sum of two of the angles is equal to the third. If the lengths of the two longer sides are 12 and 13, what is the length of the shortest side?
Which of the following is the converse of the statement "if it is snowing, then it is my Birthday?
Estimate the length of a sheet of notebook paper.
A. 24 mm
B. 2.4 cm
C. 24 cm
D. 2.4 mm
The required standard length of the paper of the notebook sheet is 24 cm. Option C is correct.
Given that,
To estimate the length of a sheet of notebook paper.
All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
As per standard measurements, the length of the sheet of notebook paper for a standard notebook is 24 cm across the world.
This 24 cm is standardized as A4 size paper or A4 notebook.
Thus, The required standard length of the paper of the notebook sheet is 24 cm. Option C is correct.
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The tallest man ever recorded was Robert Wadlow, who was 272 cm tall. The tallest woman on record was Zeng Jinlian. Her height was 91% of wadlow’s height. How tall was Zeng Jinlian.
(Round to the nearest cm.)
247.52 centimeters.
To find this answer, you have to find 91% of Robert Wadlow's height. To do that, you multiply 272 by 0.91, which gives you the height of Zeng Jinlian.
Solve this problem - 35q = 5
how many rulers of 12-inches are needed to measure a door awnser
In the neighborhood park there is a circular grassy picnic area but half of the grass has died the city wants to replace the grass but needs to know the square footage of the damaged area if the circular picnic area is 150 feet across what is the square footage of the damaged area
In a division problem the ____ is the original number, which is being divided by the divisor, to get the quotient.
Can you show me how to do this?
A circular racetrack
has a diameter of 1/2 mile. How far does a car travel in one lap aroiund the track? Round to the nearest tenth.
How many different triangles can be drawn with one 60° angle and two sides measuring 2 inches each?
PLEASE HELP!!! NEED HELP ASAP!! EXTRA POINTS TO THE FIRST PERSON TO ANSWER!!
a school is constructing a new tennis courts. each rectangular court will, be enclosed by a 600 ft fence. the length of the rectangular region will be 60 ft longer than the width. what are the dimensions of the new courts? use an equation or a system of equations to explain how you determined your answer.
X^2 + 5x + c find the value of c that makes each trinomial a perfect square
To make the trinomial a perfect square, we can complete the square. The value of c that makes the trinomial a perfect square is c = 25/4.
Explanation:To make the trinomial a perfect square, we need to find the value of c. We can do this by completing the square. The trinomial can be written as x² + 5x + c = (x + a)², where a is a constant. Expanding the right side, we get x² + 2ax + a² which is equal to x² + 5x + c. Comparing the coefficients of x, we have 2a = 5. Solving for a, we get a = 5/2. Substituting this value back into the expression, we have x² + 5x + (5/2)² = (x + 5/2)². Therefore, the value of c that makes the trinomial a perfect square is c = (5/2)² or c = 25/4.
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A farm is to be built in the shape of Quadrilateral ABCD as shown belo all fou sides are equal A = 13.2 feet B= 15.5 feet
Bertha and Vernon are competing in a diving competition. Bertha's dive ended -32 m from the starting platform. Vernon's dive ended -4 m from the starting platform. How many times farther was the end of Bertha's dive than the end of Vernon's dive?
Solve for x.
4/5 = 7/x
A leaky pool loses 2 1/4 inches of water each day. Jermaine and Mildred are asked to determine the change in the amount of water in the pool over 5 days.
Jermaine’s Solution Mildred’s Solution
5(-2 1/4) 5(-2 1/4)
5(-2 -1/4) 5(-2 -1/4)
-10 -1/4 -10 -5/4
-10 1/4 -11 1/4
Which describes the reasoning used to determine whose solution is correct?
A. Jermaine is correct because -10 -1/4 equals -10 1/4.
B.Jermaine is correct because he distributed 5 correctly.
C.Mildred is correct because she multiplied 5 by –2 but not by -1/4.
D.Mildred is correct because she distributed 5 correctly.
Answer: D. Mildred is correct because she distributed 5 correctly.
Step-by-step explanation:
Since, the loss of water in one day = [tex]2\frac{1}{4}\text{ inches}[/tex]
⇒ The loss of water in 5 days = [tex]5(2\frac{1}{4})\text{ inches}[/tex]
⇒ The loss can be written with negative sign,
Thus, the expression that shows the changes in quantity of water in 5 days,
[tex]-5(2\frac{1}{4})[/tex]
[tex]=-5(2+\frac{1}{4})[/tex]
[tex]=5(-2-\frac{1}{4})[/tex]
[tex]=-10-\frac{5}{4}[/tex]
[tex]=-10-1\frac{1}{4}[/tex]
[tex]=-10-1-\frac{1}{4}[/tex]
[tex]=-11-\frac{1}{4}[/tex]
[tex]=-11\frac{1}{4}[/tex]
Since, the above steps are similar to that of Mildred's solution,
⇒ Mildred is correct.
Also, By the above explanation it is clear that jermaine incorrectly distribute 5 in his third steps.
⇒ Option D is correct.