Answer:
The rocket is off the ground by 0 feet when it's launched, as ground level is defined as h = 0.To find the time at which the maximum height occurs, we can use the fact that the maximum or minimum point of a parabola given in the form y = ax^2 + bx + c occurs at x = -b/2a. In this case, we have h(t) = -16t^2 + 128, which has a = -16 and b = 0. Therefore, the maximum height occurs at t = -b/2a = -0/(-32) = 0 seconds.To find the maximum height reached by the rocket, we can substitute t = 0 into the equation h(t) = -16t^2 + 128, since the maximum height occurs at t = 0:[tex]h(0) = -16(0)^2 + 128[/tex]
[tex]= 128[/tex]
Therefore, the rocket goes to a maximum height of 128 feet.
4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of [tex]t^2[/tex] is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.
5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting [tex]h(t) = -16t^2 + 128[/tex], we get:
[tex]-16t^2 + 128 = 0[/tex]
Solving for t using the quadratic formula, we get:
t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))
= (±√8192) / (-32)
= ±8
Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.
6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:
h(2) = -16(2)^2 + 128
= -64 + 128
= 64 feet
Therefore, the rocket is at a height of 64 feet at 2 seconds.
7. To find when the rocket is at a height of 252 feet, we need to solve the equation [tex]-16t^2 + 128 = 252[/tex]. Rearranging and solving for t, we get:
[tex]-16t^2 + 128 = 252[/tex]
[tex]-16t^2 = 124[/tex]
[tex]t^2 = -124/-16[/tex]
t^2 = 7.75
t ≈ ±2.78 seconds
Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.
8. The graph coordinates of the rocket's path can be plotted using the function [tex]h(t) = -16t^2 + 128[/tex]. The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.
The radius of a circle is 5 in. Find its area in terms of pi
Answer:
Step-by-step explanation:
[tex]A=\pi r^2=\pi \times 5^2=25\pi[/tex]
Solution: [tex]A=25\pi[/tex] units²
Juniper Middle School serves students in 7th and 8th grades.
a. 55% of the students at Juniper are in the 8th grade. The remaining 117 students are in 7th grade. How many
students attend Juniper Middle School?
b. In September, there was an average of 4.8 daily unexcused absences. In October, this daily average was 6. By what
percent did the average daily unexcused absences change from September to October?
There are 260 students who attend Juniper Middle School. The average daily unexcused absences increased by 25% from September to October.
How to calculate . How many students attend Juniper Middle Schoola. Let's assume that the total number of students at Juniper Middle School is "x."
Given that 55% of the students are in the 8th grade, we can write:
0.55x = number of 8th grade students
And since the remaining 117 students are in 7th grade, we can write:
x - 0.55x = 117
0.45x = 117
x = 260
Therefore, there are 260 students who attend Juniper Middle School.
b. To find the percent change from September to October, we can use the formula:
percent change = ((new value - old value) / old value) x 100%
Substituting the given values, we get:
percent change = ((6 - 4.8) / 4.8) x 100%
percent change = (1.2 / 4.8) x 100%
percent change = 25%
Therefore, the average daily unexcused absences increased by 25% from September to October.
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please help me i need it
Answer:
75 degrees
Step-by-step explanation:
Since angle ABD = angle ABC + angle CBD, and we know each of those, we can add them to get the answer.
30+45=75 degrees.
For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evaluating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS.
The substitutions that would be most helpful in evaluating the integral are:
1. C (x = 8 secθ)
2. B (x = 8 sinθ)
3. A (x = 8 tanθ)
4. B (x = 8 sinθ)
5. A (x = 8 tanθ)
What are the substitutions that are most helpful?For problem 1, the substitution x = 8 secθ will be useful because it will transform the integral into a form that can be solved using the substitution u = tanθ.
For problem 2, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a trigonometric function that can be integrated using standard techniques.
For problem 3, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using integration by parts.
For problem 4, the substitution x = 8 sinθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = cosθ.
For problem 5, the substitution x = 8 tanθ will be useful because it will transform the expression inside the integral into a form that can be solved using the substitution u = secθ.
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1. bmi calculator: design a program in raptor that prompts user to enter a person's weight in number of pounds and height in number of inches, then calculate that person's body mass index (bmi) using the formula below, and finally display the person's weight, height, and bmi. bmi
The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.
To design a program in Raptor that prompts the user to enter a person's weight in pounds and height in inches, and then calculates and displays their body mass index (BMI), we can follow these steps:
Start by opening Raptor and creating a new program.
Add three input symbols to prompt the user for their weight, height, and a constant value for BMI. Label each input symbol accordingly.
Add three assignment statements to assign the input values to variables. We can use the labels we assigned to the input symbols as variable names to make the code more readable.
Add two calculation statements to calculate the person's BMI using the formula [tex]BMI = (weight in pounds * 703) / (height in inches)^2.[/tex]Assign the result to the BMI variable.
Add three output symbols to display the person's weight, height, and BMI. We can concatenate strings with the variable values to make the output more informative.
Finally, save the program and run it to test it with different input values.
Here's what the program would look like:
Start
// Prompt the user for weight, height, and BMI
Input "Enter weight in pounds:", weight
Input "Enter height in inches:", height
Input "BMI:", bmi_constant
// Calculate BMI
Set weight_in_kg = weight / 2.205 // Convert weight to kilograms
Set height_in_m = height / 39.37 // Convert height to meters
[tex]Set bmi = weight_in_kg / (height_in_m ^ 2)[/tex] // Calculate BMI
// Display results
Output "Weight: " + weight + " lbs"
Output "Height: " + height + " in"
Output "BMI: " + bmi
Stop
When the program is run, it will prompt the user to enter their weight, height, and a constant value for BMI. It will then calculate the person's BMI using the formula, convert the weight to kilograms and the height to meters, and display the results along with the original weight and height values. The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.
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Find the surface area of the rectangular prism below:
3m
2m
2.4 m
- 2.4 m
3 m
The surface area of the rectangular prism is 72 square meters.
Describe Rectangular Prism?A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional figure that consists of six rectangular faces. It is a polyhedron with two identical and parallel bases, which are rectangles, and four rectangular lateral faces. The height of the prism is the perpendicular distance between the two bases. The volume of a rectangular prism is given by the formula V = l × w × h, where l, w, and h are the length, width, and height of the prism, respectively. The surface area of a rectangular prism is given by the formula SA = 2lw + 2lh + 2wh, where l, w, and h have the same meanings as in the volume formula. Rectangular prisms are commonly encountered in everyday life, such as in the shape of boxes, rooms, and buildings.
The surface area of a rectangular prism can be found by adding up the area of all its faces.
Area of blue rectangles:
= 2 x (length x width)
= 2 x (2.4m x 2m)
= 9.6m²
Area of green rectangles:
= 2 x (length x width)
= 2 x (2.4m x 3m)
= 14.4m²
Area of yellow rectangles:
= 2 x (length x width)
= 2 x (2m x 3m)
= 12m²
Total surface area = sum of all face areas
= (2 x blue rectangles) + (2 x green rectangles) + (2 x yellow rectangles)
= 2(9.6m²) + 2(14.4m²) + 2(12m²)
= 19.2m² + 28.8m² + 24m²
= 72m²
Therefore, the surface area of the rectangular prism is 72 square meters.
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Graham wants to take snowboarding lessons at a nearby ski resort that charges $40 per week. The resort also charges a one-time equipment-rental fee of $99 for uninterrupted enrollment in classes. The resort requires that learners pay for three weeks of classes at a time
Answer:
$40+99=136 For 1 week
For 3 weeks it would be $120
Betsy is working on draining her pool for the winter. Her pool has 1,200 gallons of water and can drain 100 gallons an hour. After 5 hours, how much water will still be in the pool?
After 5 hours, there will be 700 gallons of water still in the pool.
After 5 hours, how much water will still be in the pool?Given that, the pool has 1,200 gallons of water and can drain 100 gallons an hour.
After 5 hours, the total amount of water drained from the pool will be 100 gallons per hour times 5 hours, or 500 gallons.
= 100 gallons × 5
= 500 gallons
To find out how much water will still be in the pool, we need to subtract the amount of water drained from the original amount "y":
This forms an equation.
Amount of water still in the pool = original amount - water drained from the pool.
y = 1,200 gallons - 500 gallons
y = 700 gallons
Therefore, 700 gallons of water is still in the pool.
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Solve for x. Round to the nearest tenth, if necessary
Answer: 1.0
Step-by-step explanation:
sohcahtoa means you use sine.
sin(37) = 0.6/x
xsin(37) = 0.6
x = 0.6/sin(37)
x = 0.996
x = 1.0
Ruby wants to find the height of the tallest building in her city. She stands 190 feet away from the building. There is a tree 31 feet in front of her, which she knows is 20 feet tall. How tall is the building? (Round to the nearest foot.)
To solve this problem, we can use similar triangles. Let's call the height of the building "h". Then, we have two similar triangles: one formed by Ruby, the tree, and the top of the tree; and the other formed by Ruby, the building, and the top of the building.
We know that the height of the tree is 20 feet, and the distance from the tree to Ruby is 31 feet. We also know that the distance from Ruby to the building is 190 feet.
Using these values, we can set up a proportion:
h / (190 + 31) = 20 / 31
Simplifying the proportion, we get:
h / 221 = 20 / 31
Multiplying both sides by 221, we get:
h = (20 / 31) * 221
h ≈ 143.23
Therefore, the height of the building is approximately 143 feet. Rounded to the nearest foot, the height of the building is 143 feet.
At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.
a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent
How many gold and bronze medals were won?
50
70
105
120
Answer:
70 gold and bronze
Step-by-step explanation:
Add gold at 20 percent and bronze at 50 percent to get 70 percent gold and bronze.
Can someone pls help me its delta really annoying
The cost per boxed lunch is $9.46.
what equation can be used to represent the relation shown in the table ?
Question Below.
Answers: 250|253|254|255|307|433|434|435|507|.
First to answer this question the quickest is rewarded branliest + 100 points
Answer:
Minimum--> 250
Q1--> 255
Q2--> (Median): 307
Q3--> 433
Maximum-->507
Step-by-step explanation:
To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.
First, we need to sort the data set in ascending order:
{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }
Minimum: 250
Maximum: 507
To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.
Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.
Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.
Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.
Find the volume of the composite. The solid below is a square prism with a cylinder
cut out of it. Round to the nearest whole centimeter.
Answer:
17,242 cm³
Step-by-step explanation:
Step 1:
Volume of square prism = (area of base) * height
Volume of square prism = (25 * 30) * 25
Volume of square prism = 750 * 25
Volume of square prism = 18,750 cm³
Step 2:
Volume of cylinder = (area of base) * height
Volume of cylinder = (π * (8/2)²) * 30
Volume of cylinder = 16π * 30
Volume of cylinder = 480π
Volume of cylinder ≈ 1,508 cm³
Step 3:
Volume of composite = (Volume of square prism) − (Volume of cylinder)
Volume of composite = 18,750 cm³ − 1,508 cm³
Volume of composite = 17,242 cm³
A kettle is sold at a profit equal to one-fourth of its cost price. Find the profit percentage.
Answer:
25%
Step-by-step explanation:
If the cost price could be 100
Then there's A/Q
One-fourth is always 100/4 = 25%
Your local hardware store is having a 35% off everything sale. But Wait!!!! For the next 3 days they
are offering a coupon to save an additional 30%. If the store applies the sale price then applies the
coupon, find each of the following. Let a represent the price of any item. Round all decimals to 4
decimal places.
Write an function that will directly calculate the final price on an item.
What percentage is actually being saved by the costumer?
1. The function that will directly calculate the final price on an item is " a * 0.455".
2. The percentage that is actually being saved by the custumer is 54.5%.
Function which will calculate the final price on an item:The final price of an item after the discount and coupon can be calculated using the following function:
Final price = a * (1 - 0.35) * (1 - 0.30)
Final price = a * 0.455
This function first applies the 35% discount, which reduces the original price (a) to 65% of its value. Then, it applies the 30% coupon to the discounted price, which reduces it to 70% of its value.
What percentage is actually being saved by the custumer?Original price = $100
Sale price (35% off) = $100 * (1 - 0.35)
Sale price (35% off) = $65
Final price = $65 * (1 - 0.30)
Final price = $45.50
Savings = $100 - $45.50
Savings = $54.50
Percentage saved:
= (Savings / Original price) * 100%
= ($54.50 / $100) * 100%
= 54.5%
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Trey purchases 200 shares of Turner stock for per share. Trey pays in cash to complete the purchase. One year later, Trey sells the stock for per share. Part 2 Calculate the return that Trey earned on his investment of .
Answer: Formula
Step-by-step explanation:
Stocks x per share = return
Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.
We have,
Purchase price per share: $50
Number of shares purchased: 200
Total purchase cost (excluding loan interest):
Purchase price per share * Number of shares purchased
= $50 * 200
= $10,000
Loan amount: $5,000
Loan interest rate: 10%
Interest paid on the loan:
Loan amount * Interest rate
= $5,000 * 10%
= $500
Total purchase cost (including loan interest):
Total purchase cost + Loan interest
= $10,000 + $500
= $10,500
Selling price per share: $60
Total revenue from selling the stock:
Selling price per share * Number of shares sold
= $60 * 200
= $12,000
Return on investment (ROI):
(Total revenue - Total purchase cost) / Total purchase cost
ROI = ($12,000 - $10,500) / $10,500
Simplifying the expression:
ROI = $1,500 / $10,500
ROI = 0.1429 (approximately)
To express the ROI as a percentage:
ROI as a percentage = 0.1429 * 100 = 14.29%
Therefore,
Trey's return on investment, if the stock paid no dividends during the year, is 14.29%.
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The complete question:
Trey purchases 200 shares of Turner stock for $50 per share.
Trey pays $5,000 in cash and borrows $5,000 from his broker at 10 percent interest to complete the purchase.
One year later, Trey sells the stock for $60 per share.
Trey's return, if the stock paid no dividends during the year, is?
two sets of the sum of a number and eight are added to five times the same nunmber
Answer:
2 (x + 8) + 5x.
Step-by-step explanation:
This question is to find the algebraic expression given by words. Call the unknown number x. Then the sum of it and eight is x + 8. Two sets of it means 2 (x + 8). Now that added to five times the number is 2 (x + 8) + 5x. Then, the answer is: 2 (x + 8) + 5x.
Can someone help me with this please,thanksss
Answer:
gradient= rise \ run
and cuz line is coming downward
it will be negative
so your answer is
- 5\6
A new water park, Tony’s Tidal Takeover, just opened. You have not heard anything specific about how much it costs to go to this park, but some of your friends have told you what they spent. The information is organized in the table below.
If I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50
How to calculate the word problemA word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, if I had $14 to spend, the park that I will choose based on the information will be park D where 6 rides cost $16.50. This is because it's the cheapest.
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Is (2+8), 3y a constant?
Step-by-step explanation:
3y is not a constant for it has a variable.
However, (2+8) = (10) is a constant
a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds
per hour does the machine makes nails?
Answer:
a machine in a factory makes 2 1/4 pounds of nails in 1 1/2 hours. At what rate in pounds
per hour does the machine makes nails?
(CO 3) A bottle of water is supposed to have 20 ounces. The bottling company has determined that 96% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?
Group of answer choices
a. n=0, p=36, x=98
b. n=20, p=0.98, x=36
c. n=36, p=0.96, x=36
d. n=36, p=0.98, x=1
The parameter to describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled is x = 36, p = 0.96 and n = 36. So, the right choice for answer is option (c).
A binomial experiment is an experiment using a fixed number of independent trials with only two outcomes. These experiments'outcomes are defined as either success or failure. The following requirements for experiment are :
Each fixed trial performed in the experiment had only two possible outcomes. One result will be marked as a success and the other as a failure.The probability of success in each trial must remain the same for each trial conducted. It is represented by p.Each trial in the experiment must be independent of the other trials.Water Quantity in a bottle = 20 ounces
According to bottling company, the percentage of bottle with correct amount = 96% = 0.96
so, probability of success, p = 0.96
Probability for 36 bottles has all bottles properly filled, that is x = 36. Now, looking the all choice, we conclude option(c) is correct choice.
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Chase decided he was going to start selling cups of lemonade this weekend too. He calculated his profit using the given table
number of cups sold (c) 15 20 25 30 35
total profit earned S(c) $5.05 $9.05 $13.05 $17.05 $21.05
$5.05 15
+ $9.05 20
+ $13.05 25
+ $17.05 30
+ $21.05 + 35
$65.25 125
NUMBER OF CUPS SOLD :-125
TOTAL PROFIT:- $65.25
What is the difference between the points (8, 10) and (8, 4) on coordinate plane
Answer:
6 units
Step-by-step explanation:
(8, 10 ) → (8, 4 )
since the x- coordinates of each point are the same, both 8
then this is a vertical straight line
the difference is then the absolute value of the difference in the y- coordinates, that is
| 10 - 4 | = | 6 | = 6
or
| 4 - 10 | = | - 6 | = | 6 | = 6
Evaluate the function when x = 3, x = 0, and x = -2.
10. g(x) = 3x
12. h(x) = 1.2x
13. f(x)=1.5x-2
14. h(x)=-4x+1/2
15. f(x)=1/3x + 2/3
Answer: The answer is -10 :)
Step-by-step explanation:
12)f(x)=2x-6
=》f(3)=2(3)-6
=》6-6=0
f(×)=2x-6
f(0)=-6
=》f(-2)=2(-2)-6
=》-4-6
=-10
13)h(3)=6(3)+2
=》18+2
=20
h(0)=0+2
h=2
(-2)=6(-2)+2
=》-12+2
=-10
What is the least common denominator of the fractions in the sum 1/8 + 1/9?
This means that the lowest goal (LCD) is 72 and that the total of 1/8 and 1/9 stated with one common denominator = 72 is 17/72.
What or who is a denominator?The denominator of a fraction, which represents many spaced evenly out parts are utilized to split an object, is the smallest amount inside the fraction. The fraction is divided by it. The denominator in this situation is 4, suggesting there are four parts altogether.
The fractions mentioned have 8 and 9 as their denominators. Multiples of 8 include 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80, while multiples of 9 include 9, 18, 27, 36, 45, 54, 63, 72, and 81.
It is evident that 72 will be the first common number of 8 and 9. Hence, for 1/8 and 1/9, its least common factor (LCD) is 72.
We must express every fraction with denominator 72 in order to sum the fraction with a common denominator:
1/8 Equals 9/72 (with multiplying both the numerator and the denominator by 9)
1/9 Equals 8/72 (with multiplying both the denominator and the numerator by 8)
We can now combine the fractions:
1/8 plus 1/9 = 9/72 plus 8/72
= 17/72
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a movie streaming service offers 12 children movies this is 15% of the total number of movies offerd
Answer: the movie streaming service offers 80 children's movies
Step-by-step explanation:
A grain silo has a cylindrical shape. Its radius is 8ft, and its height is 38ft. What is the volume of the silo?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
13487 ft³
Step-by-step explanation:
Volume of a Cylinder: 2πr²*h
π = 3.14
r = 9 ft
h = 53 ft
Volume = 2(3.14)(9)²*53 = 13486.86 ft³
Rounded to nearest whole number
Volume of the Cylindrical Water tank is 13487 ft³