Final answer:
A real-world problem involving the calculation of a triangle's area could include finding the area of a triangular plot of land to determine how much grass seed is needed for landscaping. By using the formula for the area of a right-angled triangle, we can calculate the area in square meters and subsequently determine the required quantity of grass seed.
Explanation:
Real World Triangle Area Problem
Calculating the area of a triangle is a common problem in real-world applications. For instance, consider a scenario where you need to find the area of a triangular plot of land to determine how much grass seed to purchase for landscaping. If the plot is a right-angled triangle with one leg measuring 50 meters and the other leg measuring 40 meters, you can use the formula for the area of a right-angled triangle, which is ½ × base × height.
In this case, the base would be one leg of the triangle (50 meters), and the height would be the other leg (40 meters). Therefore, the area would be:
Area = ½ × 50 m × 40 m
Area = 25 m × 40 m
Area = 1000 square meters
Knowing the area of the triangular plot, you can then calculate the amount of grass seed needed, based on the recommended seeding rate per square meter. This practical example demonstrates how mathematics, specifically triangular area calculation, is applied in landscaping projects.
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 is the inverse of y = 9x^2 - 4?
The inverse of
[tex]y = 9x^2 - 4[/tex]can be mathematically given by y = +/- sqrt((x + 4) / 9), yet it is not considered a function because it does not pass the horizontal line test.
Explanation:The inverse of a function flips the x and y values such that each x becomes a y and vice versa. However, it's important to mention that not all functions have an inverse that is also a function. Your provided function,
[tex]y = 9x^2 - 4[/tex], is a quadratic function (a type of polynomial function), and it does not have an inverse that can also be called a function because it does not pass the horizontal line test.
Yet, mathematically it can be found by swapping x and y and solving for y. If we do that, we have:
Switch the roles of y and x, we get: x = [tex]9y^2 - 4[/tex].Solving for y, we have: y = +/- sqrt((x + 4) / 9), where "sqrt" denotes the square root.Again, this is not a function due to the presence of the plus/minus symbol.
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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?
1.304 times 10 ^7 in standard form
In preparation for the Senior Prom, 8 seniors got together and decided to travel in style and rent a limousine. They investigated and found a company that would rent the limousine for a minimum charge of $180 for the first 3 hours and $30 per hour thereafter. They estimated that they needed to be picked up at 8:00 p.m. and be back by 1:00 a.m. How much money would each student have to pay if they planned to leave the limousine driver a $20.00 tip?
Each student would have to pay__________.
can someone help!!!plz
(-3+v+3u)(-7)y
Use the distributive property to remove the parentheses.
what is the value of x enter your answer in the Box
HELPPPPPPPPPPPPPPPPPPPPP
Write an equation of the line that passes through the points.
(2, 5), (0, 5)
Use the distance formula to find the length of the line with endpoints at (1,3) and (3,1)?
√8
8
√32
32
Louie has 20 more than twice as many baseball cards as Gerarardo does. Together they have at least 350 cards.At least how many baseball cards does Gerardo have?
show steps in solving ax^2+bx+c=0
a chef makes 1 1/2 os soup in a large pot.How many 1 cup servings can the chef get
Manny has a credit card with a line of credit at $4,000. He made the following purchases: $425.36, $358.33, $377.11, and $90.20. What is Manny's available credit?
Manny's available credit is $2,749.00.
Explanation:To find Manny's available credit, we need to subtract the total of his purchases from his line of credit. Manny's purchases total $425.36 + $358.33 + $377.11 + $90.20 = $1,251.00. So, to find his available credit, we subtract $1,251.00 from his line of credit of $4,000.00. The available credit is $4,000.00 - $1,251.00 = $2,749.00.
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ami would like to withdraw $10,364.10 at the end of each year, for 10 years, from an account paying 2.3% compounded annually. Determine the amount needed in the account for Tami to do this. Round to the nearest cent.
Answer:
The amount needed in the account is $ 91,651.91 .
Step-by-step explanation:
This can be solved applying the annuity formula for a present value.
The annual withdraw is P=$10,364.10.
The interest rate is r=2.3%, compounded anually.
The period for the withdrawals is n=10 years.
The amount needed in the account is equal to the present value ot the withdrawals:
[tex]PV=\sum_{k=1}^{10} \dfrac{P}{(1+r)^k}=\dfrac{P}{r}\left[1-(1+r})^{-10}\right]\\\\\\ PV=\dfrac{10,364.10}{0.023}\left[1-(1.023})^{-10}\right]\\\\\\PV=450,613.04\left[1-0.80\right]\\\\\\PV=450,613.04*0.20\\\\\\PV= 91,651.91[/tex]
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:
The mass in a pendulum clock completes one complete swing in 1.00 s . what is the length of the rod?
The length of the pendulum or rod in a pendulum clock that completes one swing in 1.00 seconds is approximately 0.25 meters, or 25 centimeters.
Explanation:The time taken by the pendulum to complete one full swing is also known as its period, denoted by T. You indicated that in this case the pendulum completes one swing in 1.00 seconds. To determine the length of the pendulum, or rod, we use the formula for the period of a simple pendulum, T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).
Setting T to 1.00 seconds and g to 9.8 m/s², we can solve this equation for L:
L = (T² * g) / 4π²
Substituting the given values:
L = (1.00² * 9.80) / 4π²
This gives us a pendulum length of approximately 0.25 meters, or 25 centimeters.
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There are 108 flights from an airport, 20 of which are longer than 3 hours. The flight from this airport will be randomly chosen. What is the probability it is longer than 3 hours? Enter your answer as a fraction, in simplest form, in the box.
The required solution of the probability it is longer than 3 hours is 5/27.
What is probability?
probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
There are 108 flights from an airport, 20 of which are longer than 3 hours.
According to given question we have
By the use of probability we get,
the probability it is longer than 3 hours
=20/108
By simplifying we get
=5/27
Therefore, the required solution of the probability it is longer than 3 hours is 5/27.
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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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Mr. Nelson’s Shoes Mr. Nelson manages a shoe store. One day a man came into the store right after it opened and before Mr. Nelson had a lot of change in the register. The man purchased a pair of shoes that cost $80 and gave Mr. Nelson a $100 bill. Mr. Nelson did not have change, so he went next door and exchanged the $100 for five $20 bills. He gave the customer his shoes and $20 in change. Later, the cashier next door heard there were some counterfeit bills being passed, so she asked Mr. Nelson for five $20 bills, which Mr. Nelson now had, in trade for the $100 bill. Shortly after that the police arrived and determined that the $100 bill was counterfeit and confiscated it. Who lost money? How much money?
what am i supposed to do??
which is bigger 3.3 or 0.8
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 .
apply the distribution property to produce an equivalent expression 2(7g + 7)
Please help with number 10
Answer:
see below for a drawingthe area of one of the trapezoids is 20 units²Step-by-step explanation:
No direction or other information about the desired parallelogram is given here, so we drew one arbitrarily. Likewise for the segment cutting it in half. It is convenient to have the bases of the trapezoids be the sides of the parallelogram that are 5 units apart.
The area of one trapezoid is ...
A = (1/2)(b1 +b2)h = (1/2)(3+5)·5 = 20 . . . . square units
The sum of the trapezoid base lengths is necessarily the length of the base of the parallelogram, so the area of the trapezoid is necessarily 1/2 the area of the parallelogram. (The area is necessarily half the area of the parallelogram also because the problem has us divide the parallelogram into two identical parts.)
A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 6 feet from the base of the building. How high up the wall does the ladder reach?
Round to the nearest hundredth
The ladder reaches a height on the wall of approximately 24.29 feet.
Explanation:To find the height on the wall that the ladder reaches, we can use the Pythagorean theorem. The ladder, the wall, and the ground form a right triangle. The ladder is the hypotenuse, the distance from the base of the building to the ladder is one leg, and the height on the wall that the ladder reaches is the other leg. Using the Pythagorean theorem, we have:
a² + b² = c²
where a is the distance from the base of the building to the ladder (6 feet), b is the height on the wall, and c is the length of the ladder (25 feet).
Solving for b, we have:
b = √(c² - a²)
Substituting the given values, we get:
b = √(25² - 6²) = √(625 - 36) = √589 ≈ 24.29 feet
Therefore, the ladder reaches a height on the wall of approximately 24.29 feet.
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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.
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.
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
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