Answer:
20
Step-by-step explanation:
2L + 2W = P :))
Pls help
Cole is building a model rocket in science class. He selects the rocket parts from a set of solid cylinders and cones made from metal. Cole wants to build a rocket with the dimensions shown. For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. Will Cole's rocket meet the requirement for launch?
Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket.
Use 3.14 for r. Explain.
Part C
If Cole's rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
How to solveThe volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi* r^2 *h[/tex]
Part A
The total length of the assembled rocket will be the length of the cone and the cylinder.
The total length of the assembled rocket = 25 + 3 = 28cm
Part B
The volume of the rocket is the combined volume of the cone and cylinder.
= 4/3 × 3.14 × 16 × 28
= 1875.62 cubic cm
To convert cm into pounds
1875.62 cubic cm = 4.135 pound
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.
Then 1875.62 cubic cm × 0.006
= 11.253
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
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Pick the linear model for this equation: y=-2x-3
Answer:
y=2x3 - 3
Step-by-step explanation:
Here's the photo for the solution if needed.
The linear model for the given equation would be the model that has the points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).
How to find the linear model ?To find the linear model that has the given equation, come up with values of x and then use the equation to solve for y. The linear model that has the points that you solve for, would be the right one.
Assuming values of x of -1, 0, 1, 2, 3
The y values would be:
x = - 1 :
y = - 2 x ( - 1 ) - 3
y = - 1
x = 0
y = - 3
x = 1
y = - 5
x = 2
y = - 7
x = 3
y = - 9
The linear model has points (1, - 1 ) ( 0, - 3 ) ( 1, - 5 ) ( 2, - 7 ) and ( 3, - 9 ).
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2x^2+5x+10=0 Find the best method to solve this equation.
x = -5±-55i/5 is the solution and the best method to solve is by using the general formula.
Solving quadratic equation using the general formulaGiven the quadratic equation below;
2x^2+5x+10=0
The best method to solve the equation is by using the completing the square method as shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the equation;
a = 2
b = 5
c = 10
Substitute into the formula to have:
x = -5±√5²-4(2)(10)/2(2)
x = -5±√25-80/4
x = -5±√-55/5
x = -5±-55i/5
Hence the solution to the given system of equation is x = -5±-55i/5
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What is the probability that the throw of two dice yields a total of 5 or 8
Answer:
The probability of getting a sum of 5 or 8 when 2 dice are rolled once is 1/4.
Step-by-step explanation:
Your welcome ;)
What are the rectangular coordinates of the polar coordinates?
The rectangular coordinate from the given polar coordinate is (2.73, -0.73)
What are the rectangular coordinatesTo find the rectangular coordinate from the polar coordinates, we can rewrite this as;
x = r cosθ
y = r sinθ
r = The distance from the origin to the pointθ = The angle the line segment connects with the point and the origin makes along the positive axis.x = r cosθ
Let's substitute the values into it;
x = (2√2)* cos(-π/12)
x =(2√2)cos(-15)
x = √3 + 1
x = 2.73
y = r sin θ
y = (2√2)sin(-π/12)
y = (2√2) * sin (-15)
y = -√3 + 1
y = -0.73
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the difference of two numbers is 0.77 . if the greater number is increased 5 times the difference becomes 77
Step-by-step explanation:
x - y = 0.77
5x - y = 77
let's subtract the first from the second equation :
5x - y = 77
- x - y = 0.77
---------------------
4x 0 = 76.23
x = 76.23/4 = 19.0575
x - y = 0.77
y = x - 0.77 = 19.0575 - 0.77 = 18.2875
Complete the proof that angle UYV is congruent to angle WYX
The statement and reason that completes the proof that ∠UYV ≅ ∠WYX is:
Statement - Reason
∠UYV ≅ ∠WYX - Equivalent Substitution Postulate.
What is Equivalent Substitution Postulate?
Incorporating various postulates into math problems has been an essential aspect of mathematics education for decades.
One such idea is the Equivalent Substitution Postulate, which relates specifically to geometry. This postulate indicates that if two geometric figures have identical size and shape, they can effectively substitute each other in any mathematical equation or statement without changing its accuracy.
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Michel-Eugène Chevreul found that the greatest intensity came from placing ______ colors next to each other.
tertirary
analogous
complementary
arbitrary
Answer:
your answer
Step-by-step explanation:
analogous colors
a) A mechanical engineer conducted experiments to investigate the effect of four different types of boxes on compression strength (lb). The sample means from five experiments for each type of box were 650, 750, 700, 650 (unit: lb). Compute the SSTr.
b) In a single-factor ANOVA problem involving 5 populations, the total number of observations is 20, SSTr = 12 and SST = 20. What is the MSTr, MSE, and test statistic f.
a) To calculate SSTr, we need to first find the overall mean of the samples and then use it to calculate the sum of squares due to treatments (SSTr).
The overall mean of the samples can be found by adding up all the sample means and dividing by the number of samples:
Overall mean = (650 + 750 + 700 + 650) / 4 = 687.5
Next, we can calculate SSTr using the formula:
SSTr = n * (sample mean - overall mean)^2
where n is the number of observations in each sample. In this case, n = 5 for each sample.
So for the first sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
For the second sample, SSTr = 5 * (750 - 687.5)^2 = 14062.5
For the third sample, SSTr = 5 * (700 - 687.5)^2 = 3062.5
For the fourth sample, SSTr = 5 * (650 - 687.5)^2 = 5362.5
Therefore, the total SSTr is:
SSTr = 5362.5 + 14062.5 + 3062.5 + 5362.5 = 27750
b) The degrees of freedom (df) for SSTr is k-1 where k is the number of groups/populations, and df for SSE is N-k where N is the total number of observations.
df(SSTr) = k - 1 = 5 - 1 = 4
df(SSE) = N - k = 20 - 5 = 15
The mean square for treatments (MSTr) is calculated as:
MSTr = SSTr / df(SSTr) = 12 / 4 = 3
The mean square for error (MSE) is calculated as:
MSE = SSE / df(SSE) = (20 - 5) / 15 = 1
Finally, we can calculate the F-test statistic as:
F = MSTr / MSE = 3 / 1 = 3
Therefore, the MSTr is 3, the MSE is 1, and the F-test statistic is 3.
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Jevonte surveyed 400 of the students in his school about their favorite color. 95% said their favorite color was red. How many students' favorite color was red?
Answer: 380
Step-by-step explanation:
95% = 95/100
95/100 x 400
= 380
Answer: 380 students
Step-by-step explanation:
Johnson cut a round pizza into 12 equal pieces. He ate 4 adjacent pieces. What is the measure of the angle of the pizza that Johnson ate?
A) 48 deegrees
B) 90 deegrees
C)120 deegrees
D) 160 deegrees
Please help fast!
Johnson's pizza had a 120-degree angle when he ate it. The solution is choice C.
When a pizza is cut into 12 equal pieces, each piece has a central angle of:
360 degrees / 12 pieces = 30 degrees/piece
If Johnson ate 4 adjacent pieces, then he ate a total central angle of:
4 pieces * 30 degrees/piece = 120 degrees
Therefore, the measure of the angle of the pizza that Johnson ate is 120 degrees. The answer is option C).
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct equation is 45(x+3)=60x. Option A
How do you form an equation?We are told in the word problem that the contractor got 45 expensive wood and 60 cheap wood for the same total price and that the 45 expensive wood cost $3.00 more than the 60 cheap wood.
If x =price of the 60 cheap wood then we have that 45(x + 3) + 60x = total cost of the wood.
45x + 135 + 60x = total cost of the wood
105x + 135 = total cost of the wood
45(x + 3) + 60x = 105x + 135
Simplifying;
45(x + 3) = 60x
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The high tide at midnight in Key West was 15.42 feet. A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM. What was the height of the low tide at 7 AM? 45.06 feet 18.2 feet 2.65 feet 47.4 feet
Answer:45.06
Step-by-step explanation:
no explanation
The height of the low tide at 7 AM was 45.06 feet.
Given that, the high tide at midnight was 15.42 feet.
A nearing hurricane tripled the tide height. At low tide it went down by 1.2 feet at 7 AM.
We need to find the height of the low tide at 7 AM,
So,
When the hurricane is near the height of the tide is triples so the height is 15.42 × 3 = 46.26 feet
Now, at low tide it went down by 1.2 feet at 7 AM.
so, the height will be = 45.26 feet - 1.2 feet = 45.06 feet
Hence, the height of the low tide at 7 AM was 45.06 feet.
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A 1300-seat theater sells two types of tickets for a concert. Premium seats sell for $30 each and regular seats sell for $20 each. At one event $32,240 was collected in ticket sales with 10 seats left unsold. How many of each type of ticket was sold
The required, there were 644 premium seats and 646 regular seats sold.
Let x be the number of premium seats sold and y be the number of regular seats sold. Then we have two equations:
x + y = 1290 (total seats sold)
30x + 20y = 32240 (total revenue)
We can use the first equation to solve for y in terms of x:
y = 1290 - x
Substituting this into the second equation, we get:
30x + 20(1290 - x) = 32240
Simplifying and solving for x, we get:
x=644
So 644 premium seats were sold. Substituting this into the first equation, we get:
644+ y = 1290
y = 646
So 646 regular seats were sold.
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It takes 4 minutes to complete an administrative task. There are 60 seconds in 1 minute. How many seconds does it take to complete the same task?
There are 60 seconds in 1 minute, so 4 minutes would be:
4 minutes * 60 seconds/minute = 240 seconds
Therefore, it takes 240 seconds to complete the administrative task.
The volume of this rectangular prism is 199.68 cubic yards. What is the value of z?
Answer:
z=199.68
Step-by-step explanation:
Oki and Stephen are making bags of trail mix to sell. Oki’s trail-mix recipe requires 3 cups of nuts and 3 cups of dried fruit per bag. Stephen’s trail-mix recipe requires 4 cup of nuts and 2 cups of dried fruit per bag. Together, they want to make as many bags of trail mix as possible. They have exactly 120 cups of nuts and 90 cups of dried fruit. Find the maximum number of bags of trail mix Oki and Stephen can make together.
A. write a system of inequalities
B. Graph and find coordinates of the vertices of the feasible region.
C. Find the maximum number of bags of trail mix oki and stehpen can make. How many of each type of recipe should they make to maximize the total number of bags
Answer: Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.
For vertex (15,15):
3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15
3x + 2y = 90 --> 3(15) + 2y = 90 -->
Step-by-step explanation: A. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we can use a system of inequalities to represent the constraints:
Let "x" be the number of bags of trail mix that Oki makes and "y" be the number of bags that Stephen makes. Then we have:
3x + 4y ≤ 120 (constraint on the number of cups of nuts)
3x + 2y ≤ 90 (constraint on the number of cups of dried fruit)
x ≥ 0 (non-negative constraint for Oki's bags)
y ≥ 0 (non-negative constraint for Stephen's bags)
B. To graph the feasible region, we can start by graphing the two constraint equations as lines:
3x + 4y = 120 (line A)
3x + 2y = 90 (line B)
We can find the x and y intercepts for each line:
For line A:
When x = 0, 4y = 120, y = 30 (y-intercept)
When y = 0, 3x = 120, x = 40 (x-intercept)
For line B:
When x = 0, 2y = 90, y = 45 (y-intercept)
When y = 0, 3x = 90, x = 30 (x-intercept)
Next, we can shade the region that satisfies all of the constraints. This region is below line A and to the left of line B, and is bounded by the x and y axes.
We can find the vertices of the feasible region by finding the intersection points of the two lines and the axes. These vertices are (0,0), (0,30), (15,15), and (30,0).
C. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we need to evaluate the objective function at each vertex of the feasible region, and choose the vertex that maximizes the objective function.
The objective function is the total number of bags of trail mix:
z = x + y
Evaluating at the vertices:
Vertex (0,0): z = 0 + 0 = 0
Vertex (0,30): z = 0 + 30 = 30
Vertex (15,15): z = 15 + 15 = 30
Vertex (30,0): z = 30 + 0 = 30
The maximum value of the objective function occurs at vertices (0,30) and (15,15), where z = 30 bags of trail mix.
To determine how many of each type of recipe to make, we can substitute each vertex into the two constraint equations to find the corresponding values of x and y.
For vertex (0,30):
3x + 4y = 120 --> 3x + 4(30) = 120 --> 3x = -90 --> x = -30
3x + 2y = 90 --> 3(-30) + 2(30) = 90 --> y = 15
Therefore, Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.
For vertex (15,15):
3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15
3x + 2y = 90 --> 3(15) + 2y = 90 -->
Here is a Venn Diagram with sets B, D, and the universal set U . Shade (BUD)’ on the Venn diagram.
The Venn diagram is attached in the solution.
Given that, a Venn Diagram with sets B, D, and the universal set U, we need to Shade (BUD)’ on the Venn diagram,
We know that, the complement of a set is the set that includes all the elements of the universal set that are not present in the given set.
Therefore, (BUD)’ = U - (BUD)
therefore, we will shade all the portion except (BUD),
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One owl hoots every 3 hours, and a second owl hoots every 8 hours, and a third owl hoots every 12 hours. If they all hoot together at midnight of the first day, how many times on the hour in 3 days will at least two owls not give a hoot.
The number of times on the hour in 3 days at least two owls will not hoot obtained using number theory are 69 times.
What is number theory?Number theory is the study of integers and functions of arithmetic.
The number of hours in 3 days = 72 hours
Number theory indicates that the multiples of the periods of hooting are;
The multiples of 8 are; 8, 16, 24, 32, 40, 48, 56, 64, 72
The multiples of 3 are; 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72
The multiples of 12 are; 12, 24, 36, 48, 60, 72
The common multiples of 3 and 8 are 24, 48, 72
The common multiples of 8 and 12 are 24, 48, 72
The number of times in 72 hours when at least 2 owls are hooting are therefore;
The times when only one owl is hooting are
8, 16, 32, 40, 56, 64, = 6 times only the second owl is hooting
3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36, 39, 42, 45, 51, 54, 57, 60, 63, 66, 69 = 21 times when only the first owl hoots
The times when non of the owls hoot are;
72 - 24 - 6 = 42 times
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Samuel runs around a 100 meter track.He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps. Which of the following best describes the slope of the linear equation?
Samuel runs 5 meters per second best describes the slope of the linear equation
Given that Samuel runs around a 100 meter track.
He uses the linear equation y=200+5x to describe how far he runs after he has already jogged two laps.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
y=200+5x
y=5x+200
Slope is 5
Hence, Samuel runs 5 meters per second best describes the slope of the linear equation
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Which is a function and what is not a function?
Alan owes the bank $11750. To repay his debt, he paid a fixed amount back to the bank each month. After 0.5 year(s), Alan's remaining debt was $6650. How much did Alan pay each month?
Alan paid an amount $850 to the bank each month to repay his debt.
The total amount that Alan paid back to the bank is equal to the initial amount that he owed minus the remaining amount after 0.5 year(s):
Total amount paid = Initial amount - Remaining amount
= $11750 - $6650
= $5100
We know that Alan paid this amount back over a period of 0.5 year(s), which is equivalent to 6 months.
Let x be the fixed amount that Alan paid back to the bank each month. Therefore, we can set up the following equation:
Total amount paid = Monthly payment × Number of months
$5100 = x × 6
x = $5100 / 6
= $850
Therefore, Alan paid an amount $850 to the bank each month to repay his debt.
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Please help!!!!!!!!!!!!
Answer:
48
Step-by-step explanation:
total cost will be the answer
✔️z-=4z-2. Solve this problem. It should be the square root of z.
The equation is solved to give 16z² - z - 4 = 0
How to determine the valueNote that algebraic expressions are defined as expressions that are composed of terms, variables, coefficients, constants and also factors.
The expressions are also identified with mathematical operations, such as;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
√z= -4z - 2
Find the square of both sides, we get;
z = 16z² - 4
collect the like terms
16z² - z - 4
Equate to zero
16z² - z - 4 = 0
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1) Ellen works as a train conductor. On her last route, she counted the number of riders who got on at each stop. 11 16 3 0 2 4 0 ) which box plot represents the data? 8 0 New riders 2 New riders CO New riders 12 6 0 16 16 14 4 8 20 20
The box plot that represents the data is the second box plot.
How to find the correct box plot ?To find the box plot, look for the measure that is different in both box plots and you will find it to be the value of Q1.
Therefore find the value of Q1 in the data by Ellen by first arranging the riders in order :
0, 0, 2, 2, 3, 4, 6, 8, 8, 9, 11, 14, 16
Q1 would be at the 25 th percentile :
= 25 / 100 x 13
= 3.25 position
Q1 is therefore 2 which makes the correct box plot the second one which shows the Q1 value as 2.
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math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
Answer:
Here's an interesting project idea for mathematics that can relate three different topics:
Topic 1: Fractals
Topic 2: Chaos Theory
Topic 3: Differential Equations
Research Question: Can fractals be used to model chaotic systems described by differential equations?
In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.
Your research paper can cover the following areas:
Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.
Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.
Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.
Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.
Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.
Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.
Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.
Step-by-step explanation:
Find the measure of ∠GJK. (I need the answer as fast as possible)
Answer:
∠ GJK = 102°
Step-by-step explanation:
(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so
2x + 92 + 3x + 63 = 180
5x + 155 = 180 ( subtract 155 from both sides )
5x = 25 ( divide both sides by 5 )
x = 5
Then
∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°
Given the table of values below from a quadratic function, write an equation of that function.
X | 0 | 1 | 2 | 3 | 4 |
———————————
Y | 4 | 10 | 12 | 10 | 4 |
this is a answer, thanks
Answer:
Step-by-step explanation:
Brooke has money in an account that earns 10% interest compounded annually.
She earns $1.47 in 2 years, how much money did Brooke initially invest?
The money Brooke initially invest is $1.21.
How to calculate how much money did Brooke initially investUsing the formula for compound interest formula:
A = P(1 + r/n)^(nt)
where:
A = final amount after t years
P = initial investment
r = annual interest rate
n = number of times interest is compounded per year
t = number of years
Substituting the given values:
1.47 = P(1 + 0.10/1)^(1*2)
1.47 = P(1.10)^2
1.47 = P(1.21)
P = 1.47/1.21
P = 1.2148...
Rounding to the nearest cent, Brooke initially invested $1.21.
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Help as soon as possible!
Find the height of each figure.
(Triangle)
The area of the triangle is 6,460 inches squared.
The base is 136 inches and 196 inches. Find the missing height of the figure which is X inches.
The missing height of the triangle is h = 66 inches
Given data ,
Let's denote the missing height of the triangle as "h" inches.
The formula for the area of a triangle is given by:
Area = (1/2) * base * height
Given that the area of the triangle is 6,460 inches squared and the base is either 136 inches or 196 inches, we can set up two equations to solve for "h".
For the base of 136 inches:
Area = (1/2) * 136 * h
6460 = 68h
h = 6460 / 68
h ≈ 95 inches
For the base of 196 inches:
Area = (1/2) * 196 * h
6460 = 98h
h = 6460 / 98
h ≈ 66 inches
Hence , the height of the triangle is h = 66 inches or 95 inches
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