Answer:
48 adult tickets were sold.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let's define:
x: the number of student tickets soldy: the number of adult tickets soldFrom the problem statement, we know:
x + y = 320 (the total number of tickets sold is 320)3x + 8y = 1200 (the total revenue from ticket sales is $1200)We can use the first equation to solve for x in terms of y:
x = 320 - y
Substituting this expression for x into the second equation, we get:
3(320 - y) + 8y = 1200
Expanding the left side, we get:
960 - 3y + 8y = 1200
Simplifying, we get:
5y = 240
Solving for y, we get:
y = 48
Therefore, 48 adult tickets were sold.
Additional:
To find the number of student tickets sold, we can substitute y=48 into the first equation:
x + 48 = 320
x = 272
Therefore, 272 student tickets were sold.
What is the simplest radical form of the expression?
The simplest radical form of the given expression (∛(8x⁴y⁵))² is 4x²y³∛(x²y). So, correct option is A.
To simplify the expression (∛(8x⁴y⁵))², we can first simplify the cube root of 8x⁴y⁵. Since 8 is equal to 2³, and we have three factors of x and five factors of y, we can simplify the cube root as 2[tex]x^{(4/3)}y^{(5/3)[/tex].
Substituting this into the original expression, we get:
(2[tex]x^{(4/3)}y^{(5/3)[/tex])²
Squaring each term inside the parentheses, we get:
4[tex]x^{(8/3)[/tex][tex]y^{(10/3)[/tex]
To express this in radical form, we can rewrite [tex]x^{(8/3)[/tex] and [tex]y^{(10/3)[/tex] as cube roots:
4∛(x²)⁴ ∛(y³)³
Simplifying the cube roots, we get:
4x²y³∛(x²y)
So, correct option is A.
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Hooke's Law says that the force exerted by the spring in a spring scale varies directly with the distance that the spring is stretched. If a 39 pound mass suspended on a spring scale stretches the spring 10 inches, how far will a 48 pound mass stretch the spring? Round your answer to one decimal place if necessary
48 pound mass will stretch the spring approximately 12.31 inches.
To solve this problemIf the spring's force is directly proportional to how far it is stretched, we can express this relationship mathematically as follows:
F = kx
Where
F is the force exerted by the springx is the distance that the spring is stretchedk is the proportionality constantWe can use the first value of the spring scale to determine k:
39 = k(10)
k = 3.9
Now, using this value of k, we can calculate how far the spring is stretched when a 48-pound mass is applied:
F = kx
48 = 3.9x
x = 48/3.9
x = 12.31
Therefore, a 48 pound mass will stretch the spring approximately 12.31 inches.
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Find the derivative of the given function.
y= (4x² – 9x) e⁻⁴
ˣy' = ... (Type an exact answer.)
The derivative of the given function is:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
Find the derivative?
To find the derivative of the given function y= (4x² – 9x) e⁻⁴, we need to use the product rule of differentiation. The formula for the product rule is:
(fg)' = f'g + fg'
Where f and g are two differentiable functions. Applying this formula, we get:
y' = (4x² – 9x)' e⁻⁴ + (4x² – 9x) (e⁻⁴)'
The first term on the right-hand side can be simplified using the power rule and the constant multiple rule of differentiation:
(4x² – 9x)' = 8x – 9
The second term on the right-hand side requires the chain rule of differentiation. Let u = -4x, then we have:
(e⁻⁴)' = (e^u)' = e^u (-4) = -4e⁻⁴x
Substituting these results back into the expression for y', we get:
y' = (8x – 9) e⁻⁴ + (4x² – 9x) (-4e⁻⁴x)
Simplifying this expression, we get:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
Therefore, the derivative of the given function is:
y' = (8x – 9) e⁻⁴ - 16x (4x - 9) e⁻⁴
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Hunter needs 12 ounces of a snack mix that is made up of seeds and dried fruit. The seeds cost $1.50 per ounce, and died fruit costs $2.50 per ounce. Hunter has $22 to spend and plans to spend it all.
Let x = the amount of seeds
Let y = the amount of dried fruit
Part 1: Create a system of eqution to represent the senario.
Part 2: Solve your system using any method (Desmos, Linear combination, or subsitution). Write your answer as an orderd pair.
Answer: (18, 4)
Part 1:
The cost of seeds and dried fruit together is $22:
1.5x + 2.5y = 22
Hunter plans to spend all of his money on seeds and dried fruit:
x + y = 22
Part 2:
We can use substitution method to solve the system of equations:
x = 22 - y (from the second equation)
1.5(22 - y) + 2.5y = 22 (substitute x into the first equation)
33 - 1.5y + 2.5y = 22
y = 4
Substituting y = 4 into x + y = 22, we get x = 18.
Therefore, the ordered pair representing the number of seeds and dried fruit that Hunter bought is (18, 4).
help pls rlly fast i will give good points
Answer: less than
Step-by-step explanation:
Can you explain to me how to solve this?????
√19x^5
The final step when solving the given math problem is:
Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5)[/tex]
How to solveTo solve √19x^5 for x, follow these steps:
Isolate the square root term: [tex]\sqrt{19x^5}[/tex] = y (Let y be the other side of the equation)
Square both sides: [tex](y^2) = 19x^5[/tex]
Divide both sides by 19: [tex](y^2)/19 = x^5[/tex]
Take the fifth root of both sides: x = [tex]((y^2)/19)^(^1^/^5^)[/tex]
The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √ and can be found using mathematical operations.
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Suppose 45% of all students at aiden's school brought a can of food to contribute to a canned food drive. aiden picks a representative sample of 25 students and determines the samples percentage he expects the percentage for this sample will be 45% do you agree? explain your reasoning
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, after using sampling distribution we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
Based on the given information, we can assume that the population proportion of students who brought a can of food to contribute to the canned food drive is 0.45. Aiden picks a representative sample of 25 students, and he expects the percentage for this sample will be 45%.
We can use the sampling distribution formula to calculate the expected sample proportion:
SE = sqrt[p(1-p) / n]
where p is the population proportion, n is the sample size, and SE is the standard error.
Plugging in the values, we get:
SE = sqrt[0.45(1-0.45) / 25] = 0.0984
Next, we can use the normal distribution to find the z-score corresponding to a sample proportion of 0.45:
z = (0.45 - 0.45) / 0.0984 = 0
A z-score of 0 means that the sample proportion is equal to the population proportion. Therefore, we can conclude that we agree with Aiden's expectation that the percentage for this sample will be 45%.
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Choosing only among rectangle,rhoumbos,square, name all parallelograms that have the following property
Among rectangles, rhombuses, and squares, all three of these shapes are parallelograms that have specific properties.
A rectangle is a parallelogram with four right angles. Its opposite sides are equal and parallel, and it has diagonals that are equal in length and bisect each other.
A rhombus, on the other hand, is a parallelogram with all four sides being equal in length. Like a rectangle, its opposite sides are parallel, but it does not necessarily have right angles. The diagonals of a rhombus are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other into two equal parts.
Finally, a square is a special type of parallelogram that combines the properties of both rectangles and rhombuses. It has four equal sides and four right angles, making it a unique shape. The diagonals of a square are equal in length, bisect each other, and are also perpendicular bisectors.
In conclusion, rectangles, rhombuses, and squares are all parallelograms with distinct properties. Rectangles have right angles and equal opposite sides, rhombuses have equal sides and diagonals that are perpendicular bisectors, and squares possess all the properties of both rectangles and rhombuses.
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BRAIN-COMPATIBLE
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
Write your answer in your activity notebook.
1. If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
Problem
Solution
2. I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
Problem:
Solution:
3 What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a. M. And arrived station Y ay 9:30 a. M.
The correct arrangement of problem is explained below and their solution are as follows:
(1) Zaira will arrive at her grandmother's house at 9:00 am.
(2) The total distance covered by bus is 207.5 km.
(3) The average-speed of the train was 28 km/h.
Part (1) : The Problem is : Zaira goes to her grandmother's house. If she leaves home at 6:00 in the morning, she cycles 30 km at a steady speed of 10 km. What time will she arrive?
Solution:
Zaira cycles at a steady speed of 10 km, she will cover the distance of 30 km in 30/10 = 3 hours.
So, she will arrive at her grandmother's house at 6:00 + 3:00 = 9:00 am.
Part (2) : Problem : A bus had an average speed of 65 kph for 1.5 hours in the morning. It had average speed of 55 kph for 2 hours in afternoon. What was total distance covered by bus?
Solution:
The distance covered by the bus in the morning can be calculated as:
Distance = Speed × Time = 65 kph × 1.5 hours = 97.5 km,
The distance covered in the afternoon can be calculated as:
Distance = Speed × Time = 55 kph × 2 hours = 110 km
So, total-distance covered by bus is = 97.5 km + 110 km = 207.5 km.
Part (3) : Problem : A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m. The distance between the two stations is 14 km. What was average speed of train?
Solution:
The time taken by the train to cover the distance of 14 km can be calculated as:
Time = Arrival Time - Departure Time = 9:30 am - 9:00 am = 0.5 hours
The average speed of the train = Distance/Time = 14 km/0.5 hours = 28 km/h;
Therefore, the average speed of the train was 28 km/h.
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The given question is incomplete, the complete question is
Directions: Arrange the sentences in the box to form a problem. Then solve each problem.
(1) If she leaves home at 6:00 in the morning
What time will she arrive?
Zaira goes to her grandmother's house
She cycles 30 km at a steady speed of 10 km
(2) I had an average speed of 55 kph for 2 hours in the afternoon
What was the total distance covered by the bus
A bus had an average speed of 65 kph for 1. 5 hours in the morning.
(3) What was the average speed of the train?
The distance between the two stations is 14 km
A train left Station X at 9:00 a.m. and arrived station Y at 9:30 a.m.
A ship headed due east is moving through the water at a constant speed of 8 miles per hour. However, the true course of the ship is 60°. If the currents are a constant 4 miles per hour, what is the ground speed of the ship? (Round your answer to the nearest whole number. )
The ground speed of the ship is approximately 10 miles per hour.
To calculate the ground speed, we need to use vector addition. The ship's velocity can be broken down into two components: its speed in the easterly direction and its speed in the northerly direction. The easterly component is 8 miles per hour (since the ship is moving due east), and the northerly component can be found using trigonometry: northerly component = 8 * sin(60°) ≈ 6.93 miles per hour
Now, we need to take into account the effect of the currents, which are moving in a southerly direction. Again using vector addition, we can find the resultant velocity (i.e., the velocity of the ship relative to the ground) by adding the ship's velocity vector to the current's velocity vector. Since the current is moving due south, its velocity vector has no easterly component, but its southerly component is 4 miles per hour. resultant velocity = (8, 6.93) + (0, -4) = (8, 2.93)
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity: |resultant velocity| = [tex]\sqrt{} (8^2 + 2.93^2)[/tex]≈ 8.6 miles per hour. Rounding to the nearest whole number, the ground speed of the ship is approximately 10 miles per hour.
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A tailor charges set amounts for alterations on dresses and suits.
One customer has
2
dresses and
1
suit altered for a total of
$
80
.
Another customer has
1
dress and
3
suits altered for a total of
$
115
The cost to alter each dress is $25 and each suit is $30 based on the given set of relations.
Let us represent the dresses as x and suit as y. Forming the equation for both customers.
Cost of one dress × number of dress +
Cost of one suit × number of suit = total cost
2x + y = 80 : equation 1
x + 3y = 115 : equation 2
Multiply equation with 1
6x + 3y = 240 : equation 3
Subtract equation 2 from equation 3
6x + 3y = 240
- x + 3y = 115
5x = 125
x = 125/5
x = $25
Keep the value of x in equation 2 to find the value of y
25 + 3y = 115
3y = 115 - 25
3y = 90
y = 90/3
y = $30
Hence, the altering cost of each is $25 and $30.
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The complete question is -
A tailor charges set amounts for alterations on dresses and suits. One customer has 2 dresses and 1 suit altered for a total of $80. Another customer has 1 dress and 3 suits altered for a total of $115. How much does it cost to alter each dress?
A fractal is a geometric figure that has similar characteristics at all levels of
magnification. One example of a fractal is Koch's (sounds like "Cokes")
snowflake. To build this fractal, start with an equilateral triangle whose sides
each have length 1. Then on the middle of each side, create a triangular
"bump" to make a new figure having 12 sides. On the middle of each of
these 12 sides, create a smaller bump, and so on. The upper part of the
illustration shows the first four stages in the construction of a Koch's
snowflake. The "real" snowflake is the result of carrying on this process
forever!
The lower part of the illustration shows how, when a bump is added to any
side, the ležgth you have is multiplied by If a bump is added to every side
of a snowflake figure, then the entire perimeter is multiplied by
The perimeter of Koch's snowflake fractal will be infinite.
Find out how Koch's snowflake fractal is created by adding triangular bumps to the side of an equilateral triangle?Koch's snowflake fractal is created by adding triangular bumps to the sides of an equilateral triangle at progressively smaller scales. At each stage, the number of sides of the resulting figure increases by a factor of 4, and the perimeter of the figure increases as well.
To see how the perimeter changes as bumps are added to all sides of the figure, we can use the fact that each bump adds a segment of length 1/3 to the original side. So if we start with a triangle of side length 1 and add a bump to each side, the new perimeter is:
P = 3(1 + 1/3) = 4
Now we have a figure with 12 sides. If we add a bump to each of these sides, the new perimeter is:
P = 12(1 + 1/3 + 1/9) = 16/3
In the next stage, we have 48 sides, and each side has a length of 1/3^2, so the new perimeter is:
P = 48(1 + 1/3 + 1/9 + 1/27) = 64/3
At each stage, we can see that the perimeter is multiplied by a factor of 4/3. So if we carry on this process forever, the perimeter of Koch's snowflake fractal will be infinite.
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Simplify. Show Work Please.
If BC = 12 and CE = 15, then BE =
Answer:
BE = 17
Step-by-step explanation:
We Know
BC = 12 and CE = 15
Find BE.
We Take
12 + 15 = 27
So, BE = 17
I NEED HELP PLEASE!
1. 3 statements about limiting frictional force between two surfaces are given below.
A - Nature of surfaces in contact affects to limiting frictional force.
B - Normal reaction between them affects to limiting frictional force.
C - Area of surfaces in contact affects to limiting frictional force.
Correct statement / statements from above A, B, C is/ are,
(1) A
(2) B
(3) A and C
(4) A, B and C
The limiting frictional force depends only on:
A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right optionSuppose the horses in a large stable have a mean weight of 807lbs, and a variance of 5776. what is the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the stable?
The probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
Suppose the horses in a large stable have a mean weight of 807lbs and a variance of 5776. We want to find the probability that the mean weight of a sample of 41 horses would differ from the population mean by greater than 18lbs.
Step 1: Calculate the standard deviation of the population.
Standard deviation (σ) = √variance = √5776 = 76lbs.
Step 2: Calculate the standard error of the mean.
Standard error (SE) = σ / √n = 76 / √41 ≈ 11.88lbs, where n is the sample size (41 horses).
Step 3: Calculate the z-score for the difference of 18lbs.
z = (difference - 0) / SE = (18 - 0) / 11.88 ≈ 1.51
Step 4: Find the probability corresponding to the z-score.
Using a z-table, we find that the probability corresponding to a z-score of 1.51 is approximately 0.9345.
Step 5: Calculate the probability of the mean weight differing by more than 18lbs.
Since we are looking for the probability of the mean weight differing by more than 18lbs (in either direction), we need to consider both tails of the distribution.
P(z > 1.51) = 1 - 0.9345 = 0.0655
P(z < -1.51) = 0.0655 (since the distribution is symmetric)
Total probability = P(z > 1.51) + P(z < -1.51) = 0.0655 + 0.0655 = 0.1310
So, the probability that the mean weight of the sample of horses would differ from the population mean by greater than 18lbs if 41 horses are sampled at random from the large stable is approximately 0.131 or 13.1%.
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Binary operations
if a * b = a - 2b, evaluate
5 * 2
can someone help ?
In the given binary operation, a and b are two numbers, and the operation is defined as a * b = a - 2b.
How to perform binary operation?
Binary operations are mathematical operations that take two operands and produce a single result. In this problem, we are given a binary operation "*". The operation is defined such that for any two numbers a and b, a * b = a - 2b.
We are then asked to evaluate 5 * 2 using this operation. To do so, we substitute a = 5 and b = 2 into the expression a * b = a - 2b:
5 * 2 = 5 - 2(2)
Simplifying the right-hand side of the equation, we get:
5 * 2 = 5 - 4
5 * 2 = 1
Therefore, 5 * 2 equals 1 when the binary operation is defined as a * b = a - 2b.
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not all summer blockbusters are cinematic breakthroughs. subject term: summer blockbusters predicate term: cinematic breakthroughs which of the following statements is true of this categorical proposition? it is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p. it is a standard-form categorical proposition because it is a substitution instance of this form: no s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: some s are p. it is a standard-form categorical proposition because it is a substitution instance of this form: all s are p. it is not a standard-form categorical proposition.
The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.
A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."
Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.
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The spinner has 8 congurent sections it is spun 24 times what is a reasonable prediction for the number of times the spinner will land on the number 3.
A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.
1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.
2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24
3. Simplify the expression:
Expected number of times = 3
So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
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Evaluate the integral (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) 3 V x2 +8514 dx = Shule) 32+2). 10/8+) 6 + + *(x+8) corec
To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:
∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C
Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.
Consider the integral:
∫(3√(x² + 8514) dx)
To solve this integral, let's perform a substitution:
u = x² + 8514
du = 2x dx
Now, we can rewrite the integral as:
(3/2) ∫(√u du)
Now, we can integrate:
(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C
Now, substitute u back with the original expression:
(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C
So, the evaluated integral is:
(x^2 + 8514)^(3/2) + C
Where C is the arbitrary constant.
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Allison is cleaning the windows on her house. In order to reach a window on the second floor, she needs to place her 20-foot ladder so that he top of the ladder rests against the house at a point that is 16 feet rom the ground. How far from the house should she place the base of her ladder?
The base of her ladder should be 12 feet from the house.
Pythagorean theorem.A Pythagorean theorem is a useful theorem which can be applied so as to determine the length of the missing side of a right angled triangle. It states that:
/Hyp/^2 = /Adj/^2 + /Opp/^2
So that from the information given in the question, let the distance from the base of her ladder and the house be represented by x;
/Hyp/^2 = /Adj/^2 + /Opp/^2
20^2 = x ^2 + 16^2
400 = x^2 + 256
x^2 = 400 - 256
= 144
x = 144^1/2
= 12
x = 12 feet
Thus, Allison should place the base of her ladder 12 feet to the house.
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Dinah is driving on the highway. She must drive at a speed of at least
60 miles per hour and at most70 miles per hour. Based on this information, what is a possible amount of time, in hours, that it could take Dinah to drive 420 miles?
The possible amount of time for Dinah to drive 420 miles on the highway is between 6 & 7 hours.
What time can Dinah use to drive 420 miles?To get the possible time, we need to consider the range of speeds she can drive at.
Because she must drive at least 60 miles per hour and at most 70 miles per hour, we can calculate the possible time ranges using "Time = Distance / Speed"
At 60 miles per hour:
= 420 miles / 60 miles per hour
= 7 hours
At 70 miles per hour:
= 420 miles / 70 miles per hour
= 6 hours.
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Show that the two straight lines through the origin which make an angle 45° with the line px + qy + r = 0 are given by the equation (p²-q)(x² - y²) + 4pqxy = 0.
The equation of the two straight lines through the origin making an angle of 45° with the line px + qy + r = 0 is (p²-q)(x² - y²) + 4pqxy = 0.
How to show the equation for the two straight lines passing through the origin and making a 45° angle with the line px + qy + r = 0?To prove that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0, we can use the concept of slopes and trigonometric identities.
Let's consider the line px + qy + r = 0. The slope of this line is given by -p/q.
Now, the lines making an angle of 45° with this line will have slopes equal to tan(45°), which is 1.
Using the formula for the tangent of the sum of angles, we have:
tan(45°) = (m - (-p/q))/(1 + m(-p/q)), where m represents the slope of one of the lines.
Simplifying the equation, we get:
1 = (mq + p)/(q - mp)
Cross-multiplying and rearranging the terms, we obtain:
(p² - q)(m² - 1) + 2pqm = 0
Since these lines pass through the origin (0,0), we can replace m with y/x. Substituting y/x for m in the equation above, we get:
(p² - q)(x² - y²) + 2pqxy = 0
Further simplifying the equation, we arrive at:
(p² - q)(x² - y²) + 4pqxy = 0
Hence, we have proven that the equation of the two straight lines through the origin, making an angle of 45° with the line px + qy + r = 0, is given by (p²-q)(x² - y²) + 4pqxy = 0.
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Here is another one sorry there will be a lot
Answer:
2 7/24 gallons
(sorry if its wrong)
A cuboid is placed on top of a cube, as shown in the diagram, to form a solid.
2 cm
3 cm
The cube has edges of length 7 cm.
The cuboid has dimensions 2 cm by 3 cm by 5 cm.
Work out the total surface area of the solid.
Optional working
Ansv
cm²
+
5 cm
7 cm
Answer: 344cm²
Step-by-step explanation:
7x7=49
49x5=245
3x2=6
49-6=43
245+43=288
5x2=10 10x2=20
5x3=15 15x2=30
288+30+20+6=344
Let X be the number of screws delivered to a box by an automatic filling device.
Assume = 1000 and
2 = 25. There are problems with too many screws going
into the box or too few screws going into the box.
a. How many units to the right of is 1009? (5 marks)
b. What X value is 2. 6 units to the left of ? (4 marks
There are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box. When the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
To answer this question, we need to use the normal distribution formula.
a. To find how many units to the right of 1000 is 1009, we need to calculate the z-score:
z = (X - μ) / σ
where X = 1009, μ = 1000, and σ = 25.
z = (1009 - 1000) / 25 = 0.36
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.36 or higher is 0.3520.
To convert this probability to units to the right of the mean, we subtract it from 0.5 (which represents the area to the left of the mean):
units to the right = 0.5 - 0.3520 = 0.1480
Therefore, there are approximately 0.1480 standard deviations (or 3.7 screws) to the right of the mean when there are 1009 screws in the box.
b. To find the X value that is 2.6 units to the left of the mean, we can rearrange the formula:
X = μ - zσ
where z = -2.6 (since we want units to the left of the mean) and μ and σ are the same as before.
X = 1000 - (-2.6) * 25 = 1065
Therefore, when the automatic filling device delivers 1065 screws to the box, there are approximately 2.6 standard deviations (or 65 screws) to the left of the mean.
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A set of data is represented in the stem plot below.
Key: 315= 35
Part A: Find the mean of the data. Show each step of work. (2 points)
Part B: Find the median of the data. Explain how you determined the median. (2 points)
Part C: Find the mode of the data. Explain how you determined the mode. (2 points)
Part A: The mean of the data is approximately 5.79. Part B: The median is 6.5. Part C: The mode of the data is the set of values {5, 9}.
Describe Mean?In statistics, mean is a measure of central tendency that represents the average of a set of numbers. The mean is calculated by adding up all the values in a data set and dividing by the total number of values.
The formula for calculating the mean of a set of n numbers is:
mean = (x1 + x2 + ... + xn) / n
where x1, x2, ..., xn are the individual values in the data set.
Part A:
To find the mean of the data, we need to add up all the values and divide by the total number of values:
3 + 4 + 4 + 5 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 9 + 9 + 9 = 81
There are 14 values in the data set, so we divide the sum by 14 to get:
81/14 ≈ 5.79
Therefore, the mean of the data is approximately 5.79.
Part B:
To find the median of the data, we need to arrange the values in order from lowest to highest:
3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 9
There are 14 values, so the median is the middle value. Since there is an even number of values, we need to find the average of the two middle values, which are 6 and 7. Thus, the median is:
(6 + 7)/2 = 6.5
Therefore, the median of the data is 6.5.
Part C:
To find the mode of the data, we need to look for the value(s) that occur most frequently. From the stem plot, we can see that the values 5 and 9 occur three times each, while all other values occur either once or twice. Therefore, the mode of the data is:
5 and 9
Thus, the mode of the data is the set of values {5, 9}.
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Determine the product of 23.5 and 2.3
Answer:
Therefore, the product of 23.5 and 2.3 is 54.05.
Step-by-step explanation:
To determine the product of 23.5 and 2.3, we can use the following steps:
Align the numbers vertically with the ones digit of the second factor (2.3) under the tenths digit of the first factor (3 in 23.5).
23.5
x 2.3
-----
Multiply the ones digit of the second factor by the first factor and write the result below, shifted one place to the right.
23.5
x 2.3
-----
71
Multiply the tenths digit of the second factor by the first factor and write the result below, shifted two places to the right.
23.5
x 2.3
-----
71
470
Add the two partial products together.
23.5
x 2.3
-----
71
470
-----
54.05
Therefore, the product of 23.5 and 2.3 is 54.05.
The volume of a cylinder is 336m3 . what is the volume of a cone with the same radius and height?
Find the area of the following shape. You must show all work to recive credit.
this is a writting question
The total area of the given figure is 12 units²
In the given figure, we have 3 shapes. One is rectangle and the other two are triangles. We can find areas of all three shapes and add to find the total area.
Finding area of the triangle ABC,
base of the triangle ABC = 4 units
height of the triangle ABC = 4 units
Area of the triangle ABC = 1/2 x base x height = 1/2 x 4 x 4 = 8 units²
Finding area of the triangle CDE,
base of the triangle CDE = 2 units
height of the triangle CDE = 2 units
Area of the triangle CDE = 1/2 x base x height = 1/2 x 2 x 2 = 2 units²
Finding area of the rectangle,
length of the rectangle = 2 units
breadth of the rectangle = 1 unit
Area of the rectangle = length x breadth = 2 x 1 = 2 units²
So, total area of the given figure = 8 units² + 2 units² + 2 units² = 12 units²
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Suppose that your foot length L in inches is related to your height h in inches by L=(3/4)h^0. 5
In one (non-leap) year, you have a growth spurt in which you grow from 64 inches to 69 inches. For simplicity of modeling, assume that your height changes at a constant rate throughout the year. What was the fastest rate of growth that your foot experienced during this time?
Answer for inch/year. Three digits after the decimal points after round off.
The fastest rate of growth that the foot experienced during the year is approximately 0.554 inches/year.
We can use the given relationship between foot length L and height h to determine the rate of change of foot length with respect to time. Taking the derivative of L with respect to time t, we have dL/dt = (3/4) * 0.5 * h^(-0.5) * dh/dt. We can then substitute the given values of L and h at the beginning and end of the growth spurt to find dh/dt.
At the start, h = 64 inches and L = (3/4) * 64^0.5 = 9 inches. At the end, h = 69 inches and L = (3/4) * 69^0.5 = 9.89 inches.
Solving for dh/dt, we have dh/dt = 2.4 inches/year. Substituting this value into the expression for dL/dt, we get dL/dt = (3/4) * 0.5 * 69^(-0.5) * 2.4 = 0.554 inches/year (rounded to three decimal places). Therefore, the fastest rate of growth that the foot experienced during the year is approximately 0.554 inches/year.
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