We want to find how far is the jogger from his house after he runs a total of 8 miles, we will see that the distance is equal to 7 miles.
So we need to define a coordinate axis, the point (0, 0) will be the jogger's house (where he/she starts). North is the positive y-axis and East is the positive x-axis.
Then the jogger starts at (0, 0).
Then he ran 3 miles due East, so the new position is:
(0, 0) + (3mi, 0) = (3mi, 0)
Then he ran 5 miles at 30° East of North (or 60° North of East).
The components are:
x-component = 5mi*cos(60°) = 2.5 miy-component = 5mi*sin(60°) = 4.33 miThen the new position is:
(3mi, 0) + (2.5mi, 4.33 mi) = (5.5mi, 4.33 mi)
The distance to the jogger's house is just the magnitude of that final vector, which is:
|| (5.5mi, 4.33 mi) || = √( (5.5mi)^2 + (4.33mi)^2) = 7mi
So the jogger is at 7 miles from his/her house.
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The jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast after running 8 miles.
Explanation:To find how far the jogger is from his house after running 8 miles, we need to calculate the resultant displacement. The jogger ran 3 miles due east, so his displacement in the east direction is 3 miles. Then, he ran 5 miles at a heading of 30° east of north (or 30° NE). We can split this displacement into the north and east components. The east component can be calculated as 5 miles * cos(30°) = 5 miles * 0.866 = 4.33 miles. The north component can be calculated as 5 miles * sin(30°) = 5 miles * 0.5 = 2.5 miles.
To calculate the resultant displacement, we can use the Pythagorean theorem. The east and north components form a right triangle, with the resultant displacement as the hypotenuse. The magnitude of the resultant displacement can be found as √(3^2 + 4.33^2 + 2.5^2) = √(9 + 18.7489 + 6.25) = √33.9989 = 5.83 miles. The direction of the resultant displacement can be found using trigonometry. tan(θ) = opposite/adjacent = (2.5 miles + 3 miles)/(4.33 miles) = 5.5/4.33. Taking the arctan of both sides, θ = arctan(5.5/4.33) = 51.83°. Therefore, the jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast.
Each voter in a county is given a number that uniquely identifies them. A computer is used to select 500 of these numbers at random. The 500 voters identified by the computer are interviewed for a study. Which type of sampling was used? convenience cluster systematic random
Answer:
Random sampling
Step-by-step explanation:
Given : . A computer is used to select 500 of these numbers at random. The 500 voters identified by the computer are interviewed for a study.
To Find : Which type of sampling was used?
1. convenience
2. cluster
3. systematic
4. random
Solution :
Definition of convenience sampling: A type of non-probability sampling method where the sample is taken from a group of people easy to contact
Definition of cluster sampling :In this sampling one divides the population into separate groups Then, a simple random group is selected from the population.
Definition of systematic sampling : A type of sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval. The interval is called sampling interval, is calculated by dividing the population size by the desired sample size.
Definition of random sampling :It is a type of sampling technique in which each sample has an equal probability of being chosen.
After considering all the definitions we can see that in the given case random sampling was used .
Hence random sampling was used .
helen didvided her colored pencils evenly among herself and three freinds. write an expression to represent the number of pencils each person received
The mathematical expression to represent the number of colored pencils each person received is [tex]\frac{P}{4}[/tex], where P represents the total number of pencils.
The question asks us to write an expression to represent the number of colored pencils each person received when Helen divided her pencils evenly among herself and three friends. To do so, we should first denote the total number of colored pencils Helen has as P. Since there are four people in total (Helen and her three friends), we need to divide the total number of pencils by four.
The expression to represent the number of colored pencils each person received is thus [tex]\frac{P}{4}[/tex]. This formula can be used to calculate how many pencils each person would get if you replace P with the actual number of pencils.
How do you write 331 in scientific notation?
PLEASE HELP 50 POINTS
Consider the following equation in chemical equilibrium. C2H4(g) + H2(g) mc009-1.jpg C2H6(g) + 137 kJ What happens to the amount of ethane (C2H6) when the temperature of the system is increased? The amount of ethane decreases. The amount of ethane increases initially and then decreases. The amount of ethane increases. The amount of ethane decreases initially and then increases.
A. The amount of ethane increases.
what am i supposed to do??
Caitlin has 4 and 3/4 lb of place use 1 1/10 pound to make a cup and another 2 pounds to make a jar how many pounds are left
All the answers to 6ft.12 in
During dance practice, Sasha drank 21⁄2 pints of water, and on the way home she drank 1⁄2 cup of water. How much water did she drink in total?
Cups and ounces
Sasha drank a total of 5.5 cups of water, considering that 1 pint equals 2 cups.
Explanation:The question is asking us to determine the total amount of water Sasha drank in pints and cups. First, it is important to note that 1 pint equals 2 cups. Sasha drank 21⁄2 pints of water during dance practice, which is equivalent to 5 cups of water (2.5 pints * 2). On the way home, she drank an additional 1⁄2 cup of water. Therefore, in total, Sasha drank 5.5 cups of water.
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What is the value of x when 3/x+6=6/8x-12
which is bigger 3.3 or 0.8
can someone help!!!plz
if Trigg spends 23.50 on gas, what is the total distance the boys could travel
To determine the total distance Trigg could travel with $23.50, you divide this amount by the cost per gallon of gas and then multiply by the car's MPG. Using an MPG of 27 and a gas price of $2.86 per gallon as example figures, Trigg could travel approximately 221.859 miles.
To calculate the total distance Trigg could travel with $23.50 spent on gas, we need to know the car's fuel efficiency (miles per gallon) and the current gas price per gallon. Since this information isn't provided directly in your question, let's use the example information provided. Assuming a car gets 27 miles per gallon and gas costs $2.86 per gallon, we first calculate how many gallons Trigg can buy with $23.50:
Divide $23.50 by the cost of a gallon of gas ($2.86) to find out how many gallons he can purchase:Therefore, with $23.50 and the given fuel efficiency and gas price, Trigg could travel approximately 221.859 miles.
The denominator of a fraction is three more than twice the numerator. If both numerator and denominator are decreased by one, the simplified result is 7/16. Find the original fraction.
Jenny live 6 1/4 miles from school. Raymond lives 5 1/2 miles from school. How much farther from school does Jenny live then Raymond? Write an equation and solve it
To find out how much farther Jenny lives from school than Raymond, we subtract Raymond's distance from Jenny's, converting both to improper fractions to subtract easily, resulting in Jenny living 3/4 of a mile farther than Raymond.
Explanation:The question asks how much farther from school Jenny lives compared to Raymond. Jenny lives 6 1/4 miles from school, and Raymond lives 5 1/2 miles from school. To find out how much farther Jenny lives from the school than Raymond, we can write an equation and solve it.
Let ‘d’ represent the difference in distance between how far Jenny lives from the school and how far Raymond lives from the school. The equation can be written as:
d = 6 1/4 miles - 5 1/2 miles
To solve this, we first convert the mixed numbers to improper fractions. Therefore, 6 1/4 miles becomes 25/4 miles, and 5 1/2 miles becomes 11/2 miles. Our equation now looks like this:
d = 25/4 miles - 11/2 miles
We need a common denominator to subtract these fractions, which is 4 in this case. So we convert 11/2 miles into 22/4 miles. The revised equation is:
d = 25/4 miles - 22/4 miles
When we subtract 22/4 from 25/4, we find d = 3/4 miles. Therefore, Jenny lives 3/4 of a mile farther from school than Raymond.
find the slope pf the line on the grap (-2,2),(4,0) reduce all fractional answers to the lowest term.
1). -3
2 ). -1/3
3). -1
Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 333 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 333 choices for her trip home. If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
Answer:
4/9
Step-by-step explanation:
a chef makes 1 1/2 os soup in a large pot.How many 1 cup servings can the chef get
Checking account A charges a monthly fee of $7 and a per-check fee of $0.20, and checking account B charges a monthly fee of $8 and a per-check fee of $0.15. How many checks would a person have to write for the two accounts to cost the same?
Answer:
ummmmmmmmmmm the answer is 20
Step-by-step explanation:
on apex
(-3+v+3u)(-7)y
Use the distributive property to remove the parentheses.
Tom can whitewash a fence at a rate of six square feet per minute. Huck can whitewash a fence at a rate of ten square feet per minute. Tom starts painting her fence, and five minutes later, Huck starts to help Tom. When they finish painting the fence, each person has painted half of the fence. How many square feet is the fence?
Which equation represents an inverse variation function that passes through the point (4,5) and (10,2)
Answer:
[tex]y*x=20[/tex] or [tex]y=20/x[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
so
Find the value of k
For [tex](4,5)[/tex]
[tex]y*x=k[/tex] -----> [tex]5*4=k[/tex] ----> [tex]k=20[/tex]
For [tex](10,2)[/tex]
[tex]y*x=k[/tex] -----> [tex]2*10=k[/tex] ----> [tex]k=20[/tex]
The equation that represent an inverse variation is equal to
[tex]y*x=20[/tex] or [tex]y=20/x[/tex]
PLZ HELP FOR BRAINLESS AND POINTS
Write a real-world problem that could be represented by the inequality. 2x + 5 > 23
Answer:
you have 2x oranges and you add 5 more but you still have 23 apples more than oranges
A compact disc costs $17.97. The sales tax rate is 5%. How much will the total cost be for this compact disc?
What is the value of the expression shown below?
3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 (4 points)
4 and 1 over 32
4 and 9 over 16
6 and 1 over 8
6 and 1 over 32
Answer:
4 and 9 over 16
Step-by-step explanation:
The expression is 3 + (2 + 8)^2 ÷ 4 × 1 over 2 to the power of 4 . it can be represented mathematically as
3 + (2 + 8)^2 ÷ 4 × (1/2)^4
using PEMDAS
parenthesis come first
3 + 10^2 ÷ 4 × (1/2)^4
exponential comes next
3 + 100 ÷ 4 × 1/16
3 + 25 × 1/16
3 + 25/16
(48 + 25)/16
73/16
4 9/16
Answer:
I think the answer is B which is 4 9/16.
Step-by-step explanation:
The volume of a cylinder is 24(pi) ft3. What is the volume of a cone that has the same base and height?
A week before the election, 1,500 people were asked who they planned to vote for. 45% said they planned to vote for Candidate X. 38% said they planned to vote for Candidate Y. The rest said they had not decided yet. How many of the people who were asked have not yet decided for whom they plan to vote?
A week before the election, [tex]1,500[/tex] people were asked who they planned to vote for. [tex]45[/tex]% said they planned to vote for Candidate [tex]X[/tex]. [tex]38[/tex]% said they planned to vote for Candidate [tex]Y[/tex]. So, the answer is A. [tex]255[/tex] people.
To find out how many people have not yet decided who they plan to vote for, let's first calculate the total number of people asked.
[tex]Total[/tex] [tex]people[/tex] [tex]asked[/tex] [tex]= 1,500[/tex]
Now, let's find out how many people have already decided:
[tex]For candidate X: 45% of 1,500\\\\= 0.45 * 1,500 = 675 people\\For candidate Y: 38% of 1,500\\= 0.38 * 1,500 = 570 people[/tex]
Now, let's subtract the people who have already decided from the total number of people asked:
[tex]Total people who have not decided = Total people asked - (People for candidate X + People for candidate Y)[/tex]
[tex]= 1,500 - (675 + 570)\\= 1,500 - 1,245\\= 255[/tex]
So, the answer is A. [tex]255[/tex] people.
COMPLETE QUESTION:
A week before the election, [tex]1,500[/tex] people were asked who they planned to vote for. [tex]45[/tex]% said they planned to vote for Candidate [tex]X[/tex]. [tex]38[/tex]% said they planned to vote for Candidate [tex]Y[/tex]. The rest said they had not decided yet. How many of the people who were asked have not yet decided for whom they plan to vote?
collins cafeteria offers a selection of 5 meats,six vegetables and 8 deserts.in how many ways can you select a meal of 2 different meats,3 different vegetables and 2 different deserts
if slope =2;goes through(-1,4) y =
Insurance that pays for damages to houses or businesses is called _____.
A.property/homeowners insurance
B.renters insurance
C.building insurance
D.liability insurance
Option A is correct answer.
Step-by-step explanation:
Insurance that pays for damages to houses or businesses is called - property/homeowners insurance.
The homeowners insurance protects ones personal property. This insurance deals with the insurance covers for repairing or replacing ones home and belongings, if they are damaged by fire or theft.
It also covers for the damage to others property inflicted by you or when any visitor damages your property.
Final answer:
Insurance that pays for damages to houses or businesses is called property/homeowners insurance, which covers a range of risks and includes liability coverage. The policy generally provides cash value or replacement value for the insured property and possessions.
Explanation:
The insurance that pays for damages to houses or businesses is called property/homeowners insurance. This type of insurance is crucial as it provides a safety net against various risks such as fire, wind damage, theft, and falling trees. Besides covering damages to the physical structure of a home, homeowners insurance often includes liability coverage, which protects the homeowner up to a certain amount if someone is injured on their property, except in cases where the law is being broken.
Furthermore, it is worth noting that an insurance policy generally has a cash value. If a house is destroyed, the policy will pay out the current value of the house. A replacement value policy is recommended, as it will adjust the payout based on inflation and cover the cost to replace the home, including other structures like garages and pools as well as personal property within the house.
solve the equation what is -12=3x+3
1.-5
2.-2
3.0
4.3
In this problem, you are tasked to find the value of x.
-12 = 3x + 3
This is the same as:
3x + 3 = -12
You have to transpose the 3 to the other side to solve the equation.
3x = -12 – 3
3x = -15
x = -5