Final answer:
To find the time it takes for a ball to fall from a 100 ft building, convert the height to meters and use the free fall motion formula. Solving s = (1/2)gt² for time, it takes approximately 2.5 seconds for the ball to hit the ground.
Explanation:
To determine how long it would take for a ball dropped from a 100 ft building to hit the ground, we can use the formula for the free fall motion under the influence of gravity, assuming air resistance is negligible. The formula is s = (1/2)gt², where s is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s², but we will need to convert it to feet per second squared for this problem), and t is the time in seconds.
First, convert 100 feet to meters because the standard unit of gravity is in meters per second squared. There are approximately 3.281 feet in a meter, so 100 feet is roughly 30.48 meters.
Now apply the formula and solve for t:
Convert acceleration due to gravity to feet: 9.8 m/s² is approximately 32.2 ft/s².
Use the formula: 100 = (1/2)(32.2)t².
Solve for t: t² = 100 / 16.1.
Find t: t = √(100 / 16.1).
Calculate t: t ≈ 2.49 seconds.
Therefore, it would take approximately 2.5 seconds for the ball to hit the ground.
Suppose the cpi was 110 last year and is 121 this year. instructions: in part a, enter your answer as a whole number. in part b, round your answer to 1 decimal place. if you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.
a. what is this year’s rate of inflation?
The rate of inflation from last year to this year is calculated by finding the 'change in CPI' which is then divided by the 'old CPI' and multiplied by 100 to convert it into percentage. The change in CPI is the new CPI minus the old CPI. By following the steps, we find that the rate of inflation is 10%.
Explanation:To calculate the rate of inflation, we first need to determine the 'change in CPI', which will then be divided by the 'old CPI'. The formula is:
(New CPI - Old CPI) / Old CPI x 100%
The 'change in CPI' is the new CPI (this year's CPI) minus the old CPI (last year's CPI). This will be:
121 (this year's CPI) - 110 (last year's CPI) = 11
Now, we'll divide 'change in CPI' by old CPI, which is:
11 (change in CPI) / 110 (old CPI) = 0.1
To convert the value into percentage, we should multiply it by 100:
0.1 x 100 = 10
So, this year's rate of inflation is 10%.
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what is a natural number
The set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.
Three examples of natural numbers are below.
642,000
440
81
In the citation, davis v. baugh industrial contractors, inc. 159 wash.2d 413, 150 p.3d 545 (2007) what does the "2d." represent
Chris has 5 1/2 cups of water in a pitcher. He pours 3/8 cup of water into a glass. How many cups of water is left in the pitcher? Enter your answer in the box as a mixed number in simplest form.
The Answer is 5 1/8
Answer:
The Answer is 5 1/8
Step-by-step explanation:
you have a secret that you to one person every hour each of the people that know the secret tells one person. The number of people who know when is N and T is the number of hours since you told the first person. Is an a linear function s of t?
the moon is 250,000 miles away. how many feet is it from earth
To convert the distance from the Earth to the Moon from miles to feet, multiply 250,000 miles by the number of feet in a mile, which is 5,280. This calculation yields a result of approximately 1.32 billion feet.
The distance from the Earth to the Moon is given as 250,000 miles. To convert this distance from miles to feet, we use the fact that there are 5,280 feet in a mile. Thus, we multiply the distance in miles by the number of feet per mile.
To find the distance in feet, perform the following calculation:
Multiply the distance in miles by the number of feet per mile: 250,000 miles × 5,280 feet/mile.
This equals 1,320,000,000 feet.
Therefore, the Moon is approximately 1.32 billion feet away from Earth.
The planet Mars has two moons – Phobos and Deimos. Phobos has a mass of 10.8 × 1015 kilograms, and Deimos has a mass of 2.0 × 1015 kilograms. How much greater is the mass of Phobos than the mass of Deimos?
Answer:
mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
Step-by-step explanation:
The planet Mars has two moons Phobos and Deimos.
Mass of Phobos = 10.8 × 10¹⁵ Kilograms
Mass of Deimos = 2 × 10¹⁵ Kilograms
So the difference in the masses of the moons
= 10.8 × 10¹⁵ - 2 × 10¹⁵
= (10.8 - 2) × 10¹⁵
= 8.8 × 10¹⁵ Kilograms
Therefore, mass of Phobos is 8.8 × 10¹⁵ Kilograms greater than mass of Deimos.
A stack of one hundred fifty cards is placed next to a ruler, and the height of the stack is measured to be
3/4 inches.
How thick is one card?
Answer: One card is 0.005 inches thick.
Step-by-step explanation:
Since we have given that
Number of cards in a stack = 150
Thickness of the stack = [tex]\dfrac{3}{4}\ inches[/tex]
So, Thickness of each card is calculated by "Unitary method":
Thickness of 150 cards = [tex]\dfrac{3}{4}\ inches[/tex]
Thickness of 1 card is given by
[tex]\dfrac{3}{4\times 150}\\\\=\dfrac{1}{4\times 50}\\\\=\dfrac{1}{200}\\\\=0.005\ inches[/tex]
Hence, One card is 0.005 inches thick.
if i need 5 tomatoes to feed 7 people, how many tomatoes do i need to feed 100 leople
Lee King Earns $5 per hour. Lee's brother, Nosmo, starts working three hours after Lee and earns $7 per hour. Write an equation that says each earned the same amount. Solve to find out how long each brother worked.
Which is the fraction 14/5 written as mixed number?
Answer: 2 and 4/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{14}[/tex] = 2 with a remainder of 4
Therefore, 14/5 can be written as the mixed number 2 and 4/5.
The fraction 14/5 written as a mixed fraction is equivalent to 2 4/5
Writing improper fraction as mixed fractionGiven the expression below:
14/5
Since 5 can go in 14 twice, the whole number of the mixed fraction will be 2.
Given the remainder as 4, the numerator will be 4 and the denominator will be the same that is 5 as shown below:
14/5 = 2 4/5
Hence the fraction 14/5 written as a mixed fraction is equivalent to 2 4/5
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If A=4-3i, M=-4+i, S=i, and$P=2, find A-M+S-P.
Please help!
The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
As per the given values,
A=4-3i, M= -4+i, S=i, and P=2
Put the above values into A - M + S - P as
4 - 3i - (-4 + i) + i - 2
⇒ 4 - 3i + 4 - i + i - 2
⇒ 4 - 2 + 4 - 3i
⇒ 6 + 3i
Hence "The value of the A - M + S - P by using an arithmetic operation will be 6 + 3i".
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Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Round 915 to the nearest ten
A PS4 uses 8.8 watts when on stand-by mode. How much carbon dioxide is emitted into the atmosphere by using this electricity?
Tiffany Baldwin earns $800 every week. Her federal income tax is $25. Her state tax is $11. Her FICA is 7.65% of his gross salary. She contributes 2% of her gross earnings to a 401K. She has $20 per paycheck deducted post-tax to pay for her gym membership. What are her pre-tax deductions?
rearrange w=3(2a+b)-4 to make A the subject
To make A the subject in the equation w = 3(2a + b) - 4, the rearranged equation is: a = (w + 4 - 3b) / 6.
To rearrange the equation w = 3(2a + b) - 4 to make A the subject, we need to isolate A on one side of the equation. Here's how we can do it step by step:
Step 1: Distribute the 3 to the terms inside the parentheses:
w = 6a + 3b - 4.
Step 2: Move the 3b and -4 terms to the other side of the equation:
w + 4 = 6a + 3b.
Step 3: Rearrange the terms to isolate a:
6a = w + 4 - 3b.
Step 4: Divide both sides of the equation by 6 to solve for a:
a = (w + 4 - 3b) / 6.
Now, a is the subject of the equation. We have successfully rearranged the equation to express a in terms of w and b.
The probable question maybe:
rearrange w=3(2a+b)-4 to make A the subject in the equation.
The rearranged equation solving for [tex]\( a \)[/tex] is : [tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]
This equation expresses [tex]\( a \)[/tex] as a function of [tex]\( w \)[/tex] and [tex]\( b \)[/tex], where [tex]\( w \)[/tex] is multiplied by [tex]\( \frac{1}{6} \) and \( b \)[/tex] is subtracted and then divided by [tex]\( 2 \)[/tex]. This equation can be used to calculate the value of [tex]\( a \)[/tex] given [tex]\( w \) and \( b \).[/tex]
To rearrange the equation [tex]\( w = 3(2a + b) - 4 \)[/tex] to solve for [tex]\( a \)[/tex], the first step is to isolate the term containing [tex]\( a \)[/tex] on one side of the equation.
1. Start by distributing the [tex]\( 3 \)[/tex] on the right side:
[tex]\[ w = 6a + 3b - 4 \][/tex]
2. Next, move the constants to the other side of the equation by adding [tex]\( 4 \)[/tex] to both sides:
[tex]\[ w + 4 = 6a + 3b \][/tex]
3. Now, to isolate [tex]\( a \)[/tex], divide both sides by [tex]\( 6 \):[/tex]
[tex]\[ \frac{{w + 4}}{6} = a + \frac{{3b}}{6} \][/tex]
4. Simplify:
[tex]\[ \frac{{w + 4}}{6} = a + \frac{{b}}{2} \][/tex]
5. To solve for [tex]\( a \)[/tex], subtract [tex]\( \frac{{b}}{2} \)[/tex] from both sides:
[tex]\[ \frac{{w + 4}}{6} - \frac{{b}}{2} = a \][/tex]
So, the rearranged equation solving for [tex]\( a \)[/tex] is:
[tex]\[ a = \frac{{w + 4}}{6} - \frac{{b}}{2} \][/tex]
The formula d = rt gives the distance traveled in time t at rate r. A bicyclist rides for 1.5 hours and travels 25 miles.
What was her average speed?
Answer:
16 2/3
Step-by-step explanation:
The bicyclist's average speed was 16.67 miles per hour
The student asks about the average speed of a bicyclist who traveled for 1.5 hours and covered 25 miles. The average speed can be found using the formula v = d/t, which suggests speed (v) equals distance (d) divided by time (t). To solve for the bicyclist's average speed, we'll insert the given values into the formula.
Here's the step-by-step calculation:
Identify the given variables: d = 25 miles and t = 1.5 hours.
Substitute the values into the formula: v = 25 miles / 1.5 hours.
Calculate the quotient to find the average speed: v = 16.67 miles per hour (rounded to two decimal places).
Therefore, to find the bicyclist's average speed, divide the distance traveled, 25 miles, by the time spent, 1.5 hours, which yields an average speed of 16.67 miles per hour.
The Long family spent $38.62 for school supplies and $215.78 for new school clothes. They paid % sales tax on their
Final answer:
The Long family spent $38.62 for school supplies and $215.78 for new school clothes. To find the total amount spent, add the cost of school supplies and new school clothes. To calculate the sales tax, multiply the total amount spent by the sales tax rate.
Explanation:
To find the total amount spent, we need to add the cost of school supplies and new school clothes. The Long family spent $38.62 on school supplies and $215.78 on new school clothes, so the total amount spent is $38.62 + $215.78 = $254.40. Now, to calculate the sales tax, we need to find the percentage of the total amount spent. Let's assume the sales tax rate is 8%. To find the sales tax amount, we multiply the total amount spent by the sales tax rate as a decimal: $254.40 x 0.08 = $20.35.
wire the place of the underlined digit. then write it's value. 5,342 the 3 is underlines
41>6m-7 help please
Frederick is working on a number puzzle and discovers that the product of the two base numbers is exactly twice as large as the sum of those same base numbers.
Help on this, please?
The two base numbers can be represented as x and y. Setting them equal in the equation x * y = 2(x + y) allows you to solve for them. One solution is x = 2 and y = 2.
Explanation:This problem can be solved using basic algebra. Let's assume the two base numbers be x and y. Since the product of the two base numbers (x * y) is twice as large as the sum of those numbers (x + y), we can create the following equation: x * y = 2(x + y).
To solve for x and y, you may set x and y to different numbers and check if they satisfy the equation. One solution is x = 2 and y = 2, since 2*2 = 2(2+2). Similarly, other pairs of numbers may also satisfy this equation based on the specific constraints of Frederick's number puzzle.
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To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. By rearranging the terms and factoring, we can find the base numbers that satisfy the equation. An example solution is provided with a = 3 and b = 6.
Explanation:To solve the number puzzle, we need to find two base numbers whose product is exactly twice as large as their sum. Let's represent the base numbers as 'a' and 'b'. According to the information given, we have the equation:
ab = 2(a + b).
We can simplify the equation by rearranging the terms and factoring: ab - 2a - 2b = 0. Using a technique called 'completing the square', we can rewrite the equation as (a - 2)(b - 2) = 4.
From here, we can choose different values for 'a' and 'b' that satisfy the equation, such as a = 3 and b = 6. Therefore, the base numbers for the number puzzle are 3 and 6.
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Rewrite the equation so that y is a function of x 5y-2x=15
An equation that is not true for any values of the variable is called a(n
Answer:
I am pretty sure this is either a Linear Equation or called a Contradiction
An equation that is not true for any values of the variable is called a false or inconsistent equation.
Explanation:An equation that is not true for any values of the variable is called a false equation or an inconsistent equation. This means that the equation has no solution that satisfies the given equation. For example, if we have the equation x + 3 = x + 5, subtracting x from both sides gives us 3 = 5, which is not true for any value of x.
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How to solve 5 x 198 with the distributive property that includes multiplication and subtraction
Answer:
Value of 5×198 is:
990
Step-by-step explanation:
We have to find the value of 5 x 198 with the help of distributive property that includes multiplication and subtraction
Distributive property says that if a,band c are three numbers
then, a(b-c)= ab-ac
5 x 198= 5(200-2)
= 5×200 - 5×2
= 1000-10
= 990
Hence, Value of 5×198 is:
990
What is the common ratio for this geometric sequence?
Answer: The correct option is (C) [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: We are given to find the common ratio for the following geometric sequence :
64, 16, 4, 1, . . .
We know that
if a(n) represents the n-th term of a geometric series, then the common ratio is given by
[tex]r=\dfrac{a(n+1)}{a(n)},~~~n=0,~1,~2,~~.~~.~~.[/tex]
For the given geometric sequence, we have
a(1) = 64, a(2) = 16, a(3) = 4, a(4) = 1, . . .
So, the common ratio r will be given by
[tex]r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.[/tex]
We have
[tex]\dfrac{a(2)}{a(1)}=\dfrac{16}{64}=\dfrac{1}{4},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{4}{16}=\dfrac{1}{4},\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{1}{4},~~\cdots[/tex]
Thus, the required common ratio for the given geometric sequence is [tex]\dfrac{1}{4}.[/tex]
Option (C) is CORRECT.
Sean lives about 15.5 miles from the airport. Which number rounds to 15.5 when rounded to the nearest tenth?
You are given n = 5 measurements: 5, 3, 3, 8, 8. (a) calculate the sample mean, x. (enter your answer to one decimal place.)
A rectangular box has length 14 inches, width 11 inches, and a height of 16 inches. find the angle between the diagonal of the box and the diagonal of its base. the angle should be measured in radians.
Nissan Appliances bought two dozen camcorders at a total cost of $3,864. The markup on the camcorders is 30% of the selling price. What was the original selling price of each camcorder?