Final answer:
Using the formula for the distance fallen under gravity, the height of the building is found to be approximately 70.856 meters, given a drop time of 3.8 seconds.
Explanation:
The question asks, "What is the height of a building in meters if it takes a rock 3.8 seconds to drop from its roof?" To solve this, we'll use the physics formula for the distance (height) fallen by an object under gravity, which is given by d = ½ gt², where d is the distance in meters, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds.
Substituting the given values into the equation, we have:
d = ½ × 9.8 m/s² × (3.8 s)²
= ½ × 9.8 × 14.44
= 70.856 meters
Therefore, the height of the building is approximately 70.856 meters.
The dimensions of a room measure 12ft by 9ft. In a scale drawing of a room, 1 inch= 3ft. What are the dimensions of the room in the drawing?
Final answer:
To calculate the scale drawing dimensions of a room that measures 12ft by 9ft with a scale of 1 inch=3ft, divide each dimension by the scale factor. The room would be 4 inches by 3 inches on the scale drawing.
Explanation:
To find the dimensions of the room in the drawing when given that 1 inch=3 feet, we need to set up a conversion based on the scale provided. The room measures 12 feet by 9 feet, so we must divide each dimension by the scale factor to convert feet to inches in the drawing.
First, calculating the length:
12 feet ÷ 3 feet/inch = 4 inches
Next, calculating the width:
9 feet ÷ 3 feet/inch = 3 inches
Therefore, the dimensions of the room on the scale drawing would be 4 inches by 3 inches.
1/1+sin theta + 1/1-sin theta
a rectangular porch has dimentions of (x+12) and (x+5) feet. If thr aria of the porch floor is 120 square feet, what is its length and width?
To find the length and width of the rectangular porch, solve the equation (x+12)(x+5) = 120 for x. The length is x+12 feet, and the width is x+5 feet. Substitute the value of x to find the length and width.
Explanation:To find the length and width of the rectangular porch, we need to solve the equation (x+12)(x+5) = 120 for x. Expanding the equation, we get x^2 + 17x + 60 = 120. Rearranging the terms and solving for x, we find x = 5. So the length of the porch is x+12 = 5+12 = 17 feet, and the width is x+5 = 5+5 = 10 feet. Therefore, the porch has a length of 17 feet and a width of 10 feet.
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CAN SOMEONE PLEASE HELP ME I WILL GIVE BRAINLEST
Jake wants to compare the mean height of the players on his favorite badminton and basketball teams. He creates the dot plots shown below:
First dot plot is labeled Height of Badminton Players and shows 1 cross on 66, 1 cross on 69, 2 crosses on 70, 2 crosses on 71, 4 crosses on 72, 6 crosses on 73, 4 crosses on 74, 1 cross on 76, and 1 cross on 78. Second dot plot is labeled Height of Basketball Players and shows 3 crosses on 72, 2 crosses on 75, 2 crosses on 76, 2 crosses on 78, 2 crosses on 79, 2 crosses on 80, 2 crosses on 81, 2 crosses on 82, and 1 cross on 84
The mean absolute deviation is 1.74 inches for the badminton team and 3.02 inches for the basketball team. Which of the following conclusions can be drawn from the data?
The badminton players are all taller than the basketball players.
The basketball players are all taller than the badminton players.
There is more variability in the badminton team member heights.
There is more variability in the basketball team member heights.
There is more variability in the basketball team member heights.
Mean Absolute Deviation, or MAD, describes the variability of a model. The greater the MAD, the more variability there is in the data. Since the MAD of the basketball players is higher than that of the badminton players, the basketball team members' heights vary more.
the equation y equals 1/5x represents a proportional relationship. explain how you can tell the relationship is proportional from the graph of the equation, and how can you find the constant of proportionality
Answer:
Sample answer: When you graph the equation, you get a straight line that passes through the origin, which means the relationship is proportional. The constant of proportionality is the y-value when x = 1, which is 1/5.
Step-by-step explanation:
This is just a simpler version of what the other person said :)
What does this equation equal to? 2010=0.507x+5.543
Calculate the force on an object that has a mass of 12 kg and an acceleration of 4 m/s2.
Answer:
3 kg/s
Step-by-step explanation:
could rectangle a be a scale drawing of rectangle b? explain.
Math Help PLEASE! ASAP
Jim’s dog weighs 18 pounds 10 ounces. His cat weighs 6 pounds 3 ounces. How many more ounces does Jim’s dog weigh than his cat? PLEASE HELP HARD!
what are the factors of 2n^2 -5n- 42
The factors of the quadratic expression 2n^2 - 5n - 42 are found by looking for two numbers that multiply to -84n^2 and add up to -5n. The correct pair is 7n and -12n, leading to the factors (2n + 7) and (n - 6).
Explanation:The factors of 2n^2 - 5n - 42 need to be determined by finding two numbers that multiply to 2n^2 times -42 (which is -84n^2) and add up to -5n. To factor this quadratic expression, we should look for a pair of numbers that meet these criteria.
Upon inspecting possible pairs, we find that 7n and -12n are the numbers that work since (7n) * (-12n) = -84n^2 and 7n + (-12n) = -5n. The quadratic trinomial can be expressed as:
2n^2 - 5n - 42 = (2n + 7)(n - 6)
By factoring this way, we have broken down the expression into its factors, which are (2n + 7) and (n - 6).
The factors of the quadratic expression [tex]\(2n^2 - 5n - 42\)[/tex] are [tex]\(2n + 7\)[/tex] and [tex]\(n - 6\)[/tex].
To find the factors of the quadratic expression \(2n^2 - 5n - 42\), we can use the factoring method. This involves finding two numbers that multiply to give the product of the coefficient of \(n^2\) (which is 2) and the constant term (which is -42), and also add up to the coefficient of \(n\) (which is -5).
The product of the coefficient of [tex]\(n^2\)[/tex] and the constant term is:
[tex]\(2 \times -42 = -84\)[/tex]
Now we need two numbers that multiply to -84 and add up to -5. These numbers are -12 and 7 because:
[tex]\(-12 \times 7 = -84\)[/tex]
[tex]\(-12 + 7 = -5\)[/tex]
Now we can rewrite the middle term of the quadratic expression using -12 and 7:
[tex]\(2n^2 - 12n + 7n - 42\)[/tex]
Next, we can factor by grouping. Group the first two terms and the last two terms:
[tex]\(2n(n - 6) + 7(n - 6)\)[/tex]
Notice that [tex]\(n - 6\)[/tex] is a common factor. We can factor this out:
[tex]\((2n + 7)(n - 6)\)[/tex].
one month charlie rented 2 movies 3 video games for a total of $21. The next month he rented 4 movies and 8 video games for a total of $53. Find the rental cost of each movies and each video game.
The cost to rent a movie is $2.25 and to rent a video game is $5.50, which was determined by solving a system of linear equations derived from the problem statement.
Explanation:This problem is a classic example of a system of linear equations, and we can solve it using either substitution or elimination method. Let's denote the cost of renting a movie as 'm' and the cost of a video game as 'v'. From the problem statement, we know:
2m + 3v = $214m + 8v = $53We can multiply the first equation by 2, giving us 4m + 6v = $42. Now if we subtract the second equation from this, we can solve for 'v':
(4m + 6v) - (4m + 8v) = $42 - $532v = $11v = $5.50Substitute 'v' back into the first equation to solve for 'm':
2m + 3($5.50) = $212m + $16.50 = $212m = $4.50m = $2.25Therefore, the cost to rent a movie is $2.25 and to rent a video game is $5.50.
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Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best shows Tina's age? x − 4 4x − 3 3x − 4 4 − 3x
Answer:
3x-4
Step-by-step explanation:
which one is equivalent?
Algerbra One Question
48.078 to the nearest tenth
What is the difference between a uniform and non-uniform probability model. Please help
A. A uniform probability model has outcomes that are all equally likely.
B. A uniform probability model has an even number of outcomes in the sample space. Whereas, a non-uniform probability model has an odd number of outcomes
C. A uniform probability model has an odd number of outcomes in the sample space
D. A uniform probability model has outcomes that are equally likely.
David took a survey of 12 people to find out what their favorite animal is.mOf those, 1/3 of the people said they like dogs best. How can you find out how many people liked dogs the best?
Serena bought 4 pounds of dough to make pizza the recipes gives the amount of dough needed for a pizza in ounces how many ounces of dough did she buy
64 ounces
Step-by-step explanation:
On a spinner: P(3) = ⅜ and the p(4) = ⅓ What is the probability of getting 3 or 4
The probability of obtaining 3 or 4 in the scenario described is 17/24.
The probability of getting A or B defined as P(A) or P(B) is :
P(A or B) = P(A) + P(B)Given that :
P(3) = 3/8P(4) = 1/3P(3 or 4) = 3/8 + 1/3 = (9 + 8)/24 = 17/24
Therefore, the probability of 3 or 4 is 17/24.
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Write the fact family for 7 and 49
Puzzle time what do you say when you get off A Boat?
Traveling on a boat, you were on it for 3 hours as you got off at Point B which is 15 kilometers away from Point A, with a boat speed of 5 kilometers per hour.
The time and distance formula is:
Distance = Speed × Time
Given that,
Traveling on a boat
Got off at Point B
Point B is 15 kilometers away from Point A
The boat traveled at a speed of 5 kilometers per hour
Substituting the values into the formula,
Distance = Speed × Time
We get:
15 = 5 × Time
To find dividing both sides of the equation by 5:
Time = 15/5
Time = 3 hours
Hence,
The required time is 3 hours.
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The complete question is:
If you were traveling on a boat and you got off at Point B, which is 15 kilometers away from Point A, and the boat traveled at a speed of 5 kilometers per hour, how long were you on the boat?
The width and length of the bulletin board are whole numbers what is the width of the bulletin board if the length is 4 feet
The width of the bulletin board cannot be determined with the given information, as any whole number could be the width if only the length is known to be 4 feet.
Explanation:The question asks for the width of the bulletin board given that the length is 4 feet, and we are told that both measurements are in whole numbers. Without additional information about the actual measurement of the width or the relation between the length and the width, we cannot determine the width exactly. Since the length is 4 feet, which is a whole number, the width could be any whole number. The width could be the same as the length if the bulletin board is square, or it could be different if the board is rectangular.
Since we know that 1 yard is equivalent to 3 feet, it's relevant when converting between these units of measure, but this information is not directly helpful for determining the width without further details. If we had a ratio, scale factor, or additional information regarding the relationship between the length and width, then we could proceed with a mathematical calculation to find the width. For example, if the bulletin board were to have a given aspect ratio or if the problem stated that the width is a certain multiple of the length, then we could use that information to calculate the width.
The width of the bulletin board is 4 feet.
Explanation:To find the width of the bulletin board, we need to know the scale factor between the length and width. Since the length is given as 4 feet, we can assume that the width is also in feet. Therefore, the width of the bulletin board is also 4 feet.
Find the greatest common factor of the terms in the following expression: 6ab + 24a.
Which table represents the increasing linear function with the greatest unit rate?
A. x y 2 16 5 10
B. x y 2 14 6 12
C. x y 2 -24 5 -15
D. x y 2 -12 6 -16
E. x y 2 -19 6 -17
For any two given points [tex](x_{1} ,y_{1} ) and(x_{2},y_{2})[/tex]
Rate of change =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }.[/tex]
To find linear function with the greatest unit rate we find the rate of change of each points.
A) The given points are(2, 16) and (5, 10 )
Rate of change =[tex]\frac{10-16}{5-2}=\frac{-6}{2}=-3.[/tex]
B) The given points are :(2,14) and (6,12)
Rate of change=[tex]\frac{12-14}{6-2}=\frac{-2}{4}=\frac{-1}{2}.[/tex]
C) Points are (2,-24) and (5,-15)
Rate of change = [tex]\frac{-15+24}{5-2}=\frac{9}{3}= 3.[/tex]
D) Points are :(2,-12) and (6,-16)
Rate of change =[tex]\frac{-16+12}{6-2}=\frac{-4}{4}=-1.[/tex]
E) Points are (2, -19 ) and (6, -17)
Rate of change =[tex]\frac{-17+19}{6-2}=\frac{-2}{4}=\frac{-1}{2}.[/tex]
Option C has the greatest rate of change.
The increasing linear function with the greatest unit rate is represented by the table in option B. The unit rate is 0.5.
Explanation:The table that represents the increasing linear function with the greatest unit rate is option B (x y 2 14 6 12). In this table, as the value of x increases by 4, the value of y increases by 2. This gives us a unit rate of 2/4 or 0.5.
For the other options:
A. The unit rate is (-6)/3 = -2
C. The unit rate is 9/3 = 3
D. The unit rate is -4/4 = -1
E. The unit rate is (-17-(-19))/(6-2) = -2
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A health food store has launched a new pack of vitamins for children. The store records the number of packs ordered by a random sample of 100 online customers and the number of packs ordered by a random sample of 100 walk-in customers.
(PICTURE IS BELOW)
Which of the following inferences can be drawn about the buying pattern of the online customers versus that of the walk-in customers?
A.Online customers buy an average of four packs compared with walk-in customers, who buy an average of one pack.
B.Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
C.Online customers buy an average of four packs compared with walk-in customers, who buy an average of two packs.
D.Online customers buy an average of five packs compared with walk-in customers, who buy an average of one pack.
The random Sample can be drawn the buying pattern on the online customers versus that of the walk in interview, the correct option is B.
What is sample?Sample is "a small and manageable version of a larger group".
According to the question,
The number of packs ordered by random samples through the online customers = 100
The number of packs ordered by random samples through the walk-in-interview =100
To find the inferences,
Online customers buy an average of five packs compared with walk-in customers, who buy an average of two packs.
Hence, the Option B.
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7th grade math! Proportionality and similar shapes
PLEASE answer all or as much as you can, thank you!
what is 15% of "x"
PLEASE HELP
Answer:
0.15x
Step-by-step explanation:
15% of anything is 15/100 or 0.15 of it. You find that value by multiplying the "anything" by 0.15.
Since we don't know the value of x, the best we can do is show that the number of interest is x multiplied by 0.15.
Please help choose the best answer x/-4 >6
A: x <-24
B: x >-24
C: x < 10
D: x > 2
d=1/2at^2 ; for a
solve for a
Answer:
a = 2d/t²
Step-by-step explanation:
1- Divide by 1/2 on both sides:
(d ÷ 1/2 = d × 2/1 = 2d)
2d = at²
2- Divide by t² on both sides:
2d/t² = a
a = 2d/t²
You can do those two steps in one but I made it in two so it's easier to understand.