Final answer:
It will take approximately 20.2 seconds for the water bottle rocket to return to the ground after being launched, determined by solving the given quadratic equation by completing the square.
Explanation:
The question asks how long it will take for a water bottle rocket launched from a rooftop to return to the ground, given the equation h = -16t2 + 320t + 32, where h is height in feet and t is time in seconds. To find when the rocket hits the ground, we need to solve for t when h equals zero by completing the square.
First, rearrange the equation: 0 = -16t2 + 320t + 32.
Factor out -16 to simplify: 0 = -16(t2 - 20t - 2).
To complete the square, take half of the -20, square it and add to both sides: 100 + 2 = -16(t2 - 20t + 100).
This simplifies to 0 = -16((t - 10)2 + 98) and then (t - 10)2 = -98/(-16).
Solve for t: t = 10 + sqrt(98/16), which gives approximately t = 20.2 seconds.
Therefore, it will take approximately 20.2 seconds for the water bottle rocket to return to the ground.
4 points: A,B,C and D are marked in order on a line such that AB:AC = 3:7 and BD:CD= 9:2. If CD is 100cm long, find the length of AB.
Owen settled on a price of $7,870 for a new car. The dealer had to add 4.5% sales tax to this price, but allowed a $1,200 trade-in for Owen's old car. Although not a universal practice, please add the sales tax to the price of the new car first and then deduct the trade- in value. If the dealer required a 15% down payment, calculate the amount of the purchase price that Owen financed.
To find the amount that Owen financed, we first calculate the sales tax, add it to the initial price, deduct the trade-in value, and then calculate the percent of the final price that Owen needs to finance.
Explanation:To solve the problem, we first need to calculate the total cost of the car by adding the sales tax to the original price. Sales tax is calculated as follows: $7,870 * 4.5/100 = $354.15. So, the total cost before the trade-in is $7,870 + $354.15 = $8,224.15.
Next, we deduct the trade-in value of the old car, which is $1,200. The price after trade-in is, therefore, $8,224.15 - $1,200 = $7,024.15.
Finally, the dealer requires a 15% down payment. The amount Owen needs to finance is therefore 85% of the final price (100% - 15% = 85%). The financed amount is: $7,024.15 * 85/100 = $5,970.53.
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11 + 5 + 22 × 12 − 10
Bill is shopping for folder, notebook, and pencils for the first day of school. a notebook costs 4 times as much as a folder. a notebook costs 2 times as much as a set of pencils. each folder costs $ 2 . determine the costs for 1 folder, 1 notebook, and 1 set of pencils.
Which of the sets of ordered data represents this box-and-whisker plot?
65, 65, 70, 75, 80, 80, 85, 90, 95, 100
65, 70, 75, 80, 80, 85, 90, 95, 100
65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
65, 70, 75, 80, 85, 90, 95, 100
the calculated five-number summaries with the given box-and-whisker plot, the set of ordered data that matches the plot is: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
To determine which set of ordered data represents a given box-and-whisker plot, we need to understand how a box-and-whisker plot is constructed.
A box-and-whisker plot shows the distribution of a dataset by displaying the five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Here's how these values are calculated:
1. Arrange the data in ascending order.
2. Find the median (Q2), which is the middle value of the dataset.
3. Find the first quartile (Q1), which is the median of the lower half of the dataset (excluding the median itself).
4. Find the third quartile (Q3), which is the median of the upper half of the dataset (excluding the median itself).
5. Determine the minimum and maximum values.
Let's calculate the five-number summary for each set of ordered data:
1. For the dataset: 65, 65, 70, 75, 80, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 70
- Median: 80
- Q3: 90
- Maximum: 100
2. For the dataset: 65, 70, 75, 80, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 75
- Median: 80
- Q3: 90
- Maximum: 100
3. For the dataset: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100
- Minimum: 65
- Q1: 70
- Median: 77.5 (average of 75 and 80)
- Q3: 85
- Maximum: 100
4. For the dataset: 65, 70, 75, 80, 85, 90, 95, 100
- Minimum: 65
- Q1: 72.5 (average of 70 and 75)
- Median: 82.5 (average of 80 and 85)
- Q3: 92.5 (average of 90 and 95)
- Maximum: 100
Comparing the calculated five-number summaries with the given box-and-whisker plot, the set of ordered data that matches the plot is: 65, 65, 72.5, 70, 75, 80, 80, 85, 90, 100.
A rectangular field is 0.45 kilometers long and 0.4 kilometers wide. What is the area of the field in square meters? Do not round your answer. Be sure to include the correct unit in your answer.
area of rectangle = l * w
here l=0.45 km
w=0.4 km
area = 0.45 * 0.4 = 0.18 sq. km
Answer : Area = 0.18 km²
If a piece of cardboard is 6 in long and I line up a hundred and ten of them what would be the length of my row and feet
I need help for 2, 4,7 and 9 !! SOLVE FOR X !!! Thank you
A family reunion of 27 decided to go to Six Flags Magic Mountain. Adult tickets cost $40 each and child tickets cost $30 each. The total cost of all tickets was $930. Use the SUBSTITUTION METHOD to determine how many adults and how many child tickets were purchased?
To solve the problem, set up a system of equations with 'a' representing the number of adult tickets and 'c' representing the number of child tickets. Use the substitution method to solve for the variables. The solution is 12 adult tickets and 15 child tickets.
Explanation:To solve this problem using the substitution method, we need to set up a system of equations. Let's use the variables 'a' to represent the number of adult tickets and 'c' to represent the number of child tickets.
The cost equation can be expressed as: 40a + 30c = 930. This equation represents the total cost of all the tickets.
The quantity equation can be expressed as: a + c = 27. This equation represents the total number of people attending the reunion.
We can solve this system of equations using the substitution method. Multiply the second equation by 30 to get 30a + 30c = 810. Now subtract this equation from the first equation: 40a + 30c - (30a + 30c) = 930 - 810. Simplifying, we get: 10a = 120. Divide both sides by 10 to get a = 12.
Now that we know the number of adult tickets, we can substitute this value back into one of the original equations to solve for the number of child tickets. Using the second equation, we have: 12 + c = 27. Subtracting 12 from both sides, we get c = 15.
Therefore, 12 adult tickets and 15 child tickets were purchased.
Ryan made 65 ounces if apple jelly. He put the same amount of jelly into 6 jars. How much jelly is in each jar?
The cost of 3 pounds of grapes is $6.57 what is the constant of proportionality that relates that cost in dollars,y,to the number of pounds of grapes,x?
Lorenzo plans to purchase three identical shirts. The shirts are on sale for 20% off. Let c represent the cost of each shirt. Which expressions can Lorenzo use to calculate his total cost for the three shirts after the discount?
Select each correct answer.
A. 0.80(3c)
B. 3c−0.20(3c)
C. 3(c−0.20c)
D. 1.20(3c)
please help
Answer:
Options A, B and C are correct choices.
Step-by-step explanation:
Let c represent the cost of each shirt.
As Lorenzo bought 3 shirts, so the cost of 3 shirts will be 3c.
We have been given that the shirts are on sale for 20% off, so the total cost of three shirts after discount will be 3c minus 20% of 3c.
We can represent this information in an equation as:
[tex]\text{Total cost for the three shirts after the discount}=3c-(\frac{20}{100}\times 3c)[/tex]
[tex]\text{Total cost for the three shirts after the discount}=3c-(0.20\times 3c)[/tex]
[tex]\text{Total cost for the three shirts after the discount}=3c-0.60c[/tex]
[tex]\text{Total cost for the three shirts after the discount}=2.40c[/tex]
Let us see our given choices one by one.
A. 0.80(3c)
Upon simplifying our given expression we will get,
[tex]0.80(3c)=2.40c[/tex]
Therefore, option A is a correct choice.
B. 3c−0.20(3c)
We have already seen that total cost of 3 shirts after discount will be 3c minus 20% of 3c and after simplifying our expression we will get,
[tex]3c-0.20(3c)=3c-0.60c=2.40c[/tex]
Therefore, option B is a correct choice as well.
C. 3(c−0.20c)
Upon simplifying our given expression we will get,
[tex]3(c-0.20c)=3c-0.60c=2.40c[/tex]
Therefore, option C is a correct choice as well.
D. 1.20(3c)
Upon simplifying our given expression we will get,
[tex]1.20(3c)=3.60c[/tex]
Since total cost of 3 shirts after discount is 2.40c, therefore, option D is not a correct choice.
HELP
How many pieces 3/7 of a foot each can I make out of 7/2 feet of rope?
Using the given points, determine the slope. (5,-6)and(2,15)
A right circular cylinder has a height of 19 3/4 ft and a diameter 1 2/5 times its height.
What is the volume of the cylinder?
Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Height of cylinder = [tex] 19\frac{3}{4} =19.75 [/tex]ft
Diameter of cylinder = [tex] 1\frac{2}{5} [/tex]times its height = [tex] 1.4 * 19.75=27.65 [/tex]ft
Now Radius = half of diameter = [tex] \frac{27.65}{2} =13.825 [/tex]ft
Now we have to find the Volume of cylinder
formula for Volume of cylinder is
Volume of cylinder = [tex] \pi r^2 h [/tex]
let's plug the values
Volume of cylinder = [tex] (3.14)*(13.825)^2 *(19.75) [/tex]
Plug the values in calculator
= 11852.9657 cubic feet
Round off the answer to two decimal places(i.e. hundredth)
= 11852.97 cubic feet
how many minutes are in the time interval from 7:09 a.m. to 10:36 a.m.
how to find the height of a cylinder knowing the volume
The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?
A piece of wood is 3/4 meter long is being cut into smaller pieces that are each 1/10 meter long. Which expression is one of the steps in determining how many pieces can be cut?
A. 3/4 • 1/10
B. 3/4 • 10/1
C. 10/1 • 4/3
D. 1/10 • 3/4
112=7x+7(-4x-17)
So i need help with this and a worksheet that relates to these types of problems i got a 10% on it please helpppp
Find the missing value to the nearest hundredth of a degree. Help!!
Answer:
The answer above for question 7 is also correct its B. 30 degrees. Because that anser is hard to find on here.
Step-by-step explanation:
how do you compare y intercepts and rates of change
What is the area of this circle
7in*7in=49square in
than multiply by pi
hope this helps
87.5% of what number is 49?
Lee baked 50 cookies. He gave some to a friend and ate 50% of the remaining cookies. He had 15 cookies left. What percentage of the cookies did he give to his friend?
what is the length of line segment ab
Answer:
The length of line segment is 13 units
Step-by-step explanation:
Given the line segment AB.
we have to find the length of line segment.
The coordinates of A and B are (0, 12) and (5, 0) respectively.
By distance formula,
[tex]\text{The distance between the points }A(x_1,y_1)\text{ and } B(x_2, y_2)[/tex]
[tex]AB=\sqrt{(x_2-x_1)^2+y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(5-0)^2+(0-12)^2}[/tex]
[tex]AB=\sqrt{25+144}=\sqrt{169}=13 units[/tex]
Hence, the length of line segment is 13 units.
ax+z=aw-y solve for a
At the library you find nine books on a certain topic the librarian tells you that 55% of the books on this topic have been signed out how many books does the library have available on the topic
Which trinomials are perfect square trinomials? Select each correct answer.
A) m^2+10m+100
B) m^2+10m+25
C) m^2+24m+144
D) m^2+36m+60
Kim and her two brothers each use 1 1/2 cups of milk for breakfast how many fluid ounces of milk do they use in 4 days?