Plug the corresponding R(s) for each input type and the transfer functions of the given systems into the equations above to find yss and ess for each case. Keep in mind that some systems might not have a finite steady-state response or error for specific input types, depending on the system's type (order and poles).
To determine the steady-state response (yss) and steady-state error (ess) values for the given systems, we need to use their transfer functions and input types (unit step, unit ramp, and unit parabolic). Unfortunately, without information about the specific transfer functions for figures 5.74 a, b, 5.75, and 5.76, it is not possible to provide a definitive answer.
In general, for a system with transfer function G(s), you can calculate the steady-state response and error using the Final Value Theorem:
yss = lim (s -> 0) s * Y(s), where Y(s) = G(s) * R(s) is the system's output.
ess = lim (s -> 0) s * E(s), where E(s) = R(s) - Y(s) is the system's error.
For different input types:
- Unit step input: R(s) = 1/s
- Unit ramp input: R(s) = 1/s^2
- Unit parabolic input: R(s) = 1/s^3
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Solve the system of equations by elimination.
Answer:
(-1,1)
Step-by-step explanation:
You have the option to pick between an action, horror, or
romantic comedy movie. You can also go at either 5pm, 7pm,
8pm, or 9pm. What is the total number of possible outcomes?
a. For which angle measures, 0, between 0 and
2π radians is cos(0) = 0? Label the
corresponding points on the unit circle.
b. What are the values of sin(x) for these angle
measures?
for the angle measures where cos(0) = 0, sin(x) equals 1 for π/2 radians and -1 for 3π/2 radians.
cos(0) = 0 when the angle is π/2 or 3π/2 radians.
To label the corresponding points on the unit circle, we can use the following conventions:
The angle 0 radians (or 0 degrees) starts at the positive x-axis and goes counterclockwise.
The angle π/2 radians (or 90 degrees) is at the positive y-axis.
The angle π radians (or 180 degrees) is at the negative x-axis.
The angle 3π/2 radians (or 270 degrees) is at the negative y-axis.
So, for cos(0) = 0, the corresponding angle measures are π/2 and 3π/2 radians. On the unit circle, these correspond to the points (0, 1) and (0, -1), respectively.
the values of sin(x) for these angle measures:
sin(π/2) = 1
sin(3π/2) = -1
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A top tv costs r50 000. The dealer offers you two payments options
Option1:20% deposit and the balance paid back over 36 months (3 years) at 12% simple interest p. A
Option 2:no deposit ,but the product needs to be paid off in 42 months (3 1,2years )at 9% compound interest p. A
Calculate the deposit amount if option 1 is chosen
The deposit amount need to be paid in option 1 with 20% of the cost is equal to R10,000.
Cost of a tv = R50,000
Option 1.
Deposit amount = 20% of the cost.
Balance to be paid in 36 months
Simple interest = 12% p.a.
Deposit amount
= 20% of R50,000
= 0.2 x R50,000
= R10,000
Now,
Let x be the balance amount that needs to be paid.
x = R50,000 - R10,000
⇒ x = R40,000
Simple Interest = ( Principal × Rate of interest × time ) / 100
Total amount to be paid = Principal + Simple Interest
= R40,000 + (R40,000 x 0.12 x 3)
= R40,000 + R14,400
= R54,400
Therefore, the deposit amount for option 1 as per the given details is equal to R10,000.
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In a lab experiment, 80 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 5 hours. How long would it be, to the nearest tenth of an hour, until there are 136 bacteria present?
Answer:
Step-by-step explanation:
We can use the formula for exponential growth to solve this problem:
N = N0 * 2^(t/T)
where N is the final number of bacteria, N0 is the initial number of bacteria, t is the time elapsed, and T is the doubling time.
We know that N0 = 80, and T = 5 hours. We want to find t when N = 136.
136 = 80 * 2^(t/5)
Dividing both sides by 80, we get:
1.7 = 2^(t/5)
Taking the logarithm of both sides (base 2), we get:
log2(1.7) = t/5
Solving for t, we get:
t = 5 * log2(1.7) ≈ 3.4 hours
Therefore, it would take approximately 3.4 hours, to the nearest tenth of an hour, until there are 136 bacteria present.
Shirts are on sale for 30% off the oringal price of one shirt is 15 what is the total cost of 2 of these shirts at the sales price including a 7% sales tax
The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.
Original price of one shirt = $15
Number of shirts bought = 2
Sale discount = 30% off on original price
Sale price of one shirt = Original price - 30% of the original price
Substitute the value we get,
⇒Sale price of one shirt = 15 - (0.30)(15)
⇒Sale price of one shirt = $10.50
The cost of two shirts is equal to,
2 x $10.50 = $21.00
Sales tax = 7% of the total cost.
Substitute the value we have,
⇒Sales tax = 0.07 x $21.00
= $1.47
Total cost of two shirts = Cost of two shirts + Sales tax
⇒ Total cost of two shirts = $21.00 + $1.47
⇒ Total cost of two shirts = $22.47
Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.
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A company has hired 14 new employees and must assign 10 to the dayshift and for to the Night Shift how many ways can the assignment be made ?
There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe
WHAT IS COMBINATION ?
Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.
To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:
C(n, k) = n! / (k! * (n - k)!)
where n! means n factorial (i.e. n multiplied by all the positive integers less than n).
In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:
C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))
Simplifying this expression, we get:
C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1
C(14, 10) * C(4, 4) = 1001 * 1
C(14, 10) * C(4, 4) = 1001
So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe
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what is the 1ooth digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 ?
The 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
First, let's convert the number (1 .fi.)3000 into its decimal representation. This is done by dividing 3000 by 10 raised to the power of the number of digits following the decimal point, which in this case is 3. We get the answer 1000, or 1.000.
Now, we can look at the 100th digit to the right of the decimal point. This will be the 0th digit from the right of the decimal point, which is 0. Therefore, the 100th digit to the right of the decimal point in the decimal representation of (1 .fi.)3000 is 0.
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emma buys a gift basket online for 30% off the list price. she has to pay $5.50 for shipping. the total charge is $45.20. what is the list price of the gift basket?
The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.
Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.
This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.
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I need help with question
Check the picture below.
so the ball hits the ground when g(x) = 0
[tex]\stackrel{g(x)}{0}=-16t^2+30t\implies 0=-2t(8t-15) \\\\[-0.35em] ~\dotfill\\\\ 0=-2t\implies \boxed{0=t} \\\\[-0.35em] ~\dotfill\\\\ 0=8t-15\implies 15=8t\implies \cfrac{15}{8}=t\implies \stackrel{ seconds }{\boxed{1.9\approx t}}\qquad \textit{falls to the ground}[/tex]
we get two values for "t", once at 0, because that's when the ball was at rest before being kicked.
A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
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Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
During a series of spins, a spinner landed on blue 7 times and on other colors 7 times. Considering this data, how many of the next 10 spins should you expect to land on blue?
Answer:
5
Step-by-step explanation:
Landing 7 times on blue and 7 times on other colors means it landed on blue half of the time.
I expect it will land on blue half of the next 10 spins.
Answer: 5
ʙʀᴀɴᴅᴏɴ ᴡᴀs ᴏɴ ᴠᴀᴄᴛɪᴏɴ ꜰᴏʀ 2 weeks ᴀɴᴅ 1ᴅᴀʏ ᴀɴᴅ ʜᴇ sᴘᴇɴᴅ ᴛʜᴇ sᴀɴᴇ ᴀᴍᴏᴜɴᴛ ᴏɢ ᴛɪᴍᴇs ᴡɪᴛʜ ᴇᴀᴄʜ 3 ʙʀᴏ ʜᴏᴡ ᴍᴀɴʏ sᴀʏs ᴅɪᴅ ʜᴇ sᴘᴇɴᴅ ᴡɪʀʜ ᴇᴀᴄʜ ʙʀᴏ ?
Answer:
5 days
Step-by-step explanation:
You want to know the amount of time that is 1/3 of 2 weeks and 1 day.
Total timeThere are 7 days in a week, so 2 weeks and 1 day will be a total of ...
2·7 +1 = 14 +1 = 15 . . . . days
Part timeIf this time is split into 3 equal parts, each part is 1/3 of the total.
1/3 · 15 days = 5 days
Brandon spent 5 days with each of his 3 bro.
I have been stuck on this question and I can't solve it.
Please help me!!
Answer:
Step-by-step explanation:
it is either Graph A or B pick one of them
Answer:
Graph D is correct
Step-by-step explanation:
if you choose a point, let's say 0,0 and plug in the values for x and y, you'll get
[tex]0 \leqslant - 2[/tex]
Since this equation isn't true, 0,0 can't be filled.
to choose between graphs c and d, you look at the line and because c is dotted, it means it isn't solution. because your sign is less than or equal to, the line has to be solid.
therefore, graph d is the correct answer
Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: x = h + r cos(), y = k + r sin()
the parameter and obtain the standard form of the rectangular equation would be: [tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]
[tex]x=h+rcos\theta ,y=k+rsin\theta\\x-h=rcos\theta\\\frac{x-h}{r}=cos\theta...................(1)y=k+rsin\thetay-k=rsin\theta[/tex]
[tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]
square and add both the equations
[tex]\frac{(x-h)^2}{(r^2)} + \frac{(y-k)^2}{(r^2)} = sin^2\s\theta + cos^2\s\theta\\\\\frac{(x-h)^{2}}{r^{2}}+\frac{(y-k)^{2}}{r^{2}}=1\\\\ the value of (sin^{2}\theta+cos^{2}\theta=1)\\\\(x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
The overall rectangular (or standard) form of the perplexing numbers is a + b I. We can change over complex numbers in rectangular form, by tracking down r = a 2 + b 2 and θ = tan − 1 .
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6. complete the interpretation for the p-value: if delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of or any statistic (larger, smaller) is .
If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.
This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.
The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.
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The complete question is:
Complete the interpretation for the p-value:
If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .
The manager at Braums recorded the orders of their customers over the last hour and had the following number of ice cream cones 4 vanilla, 5 chocolate, 2 peanut butter cup, 3 strawberry, and 2 coffee. Based on these numbers, what is the probability of the next customer ordering peanut butter cup? Write your answer as a decimal
Answer:
To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.
The total number of cones is:
4 + 5 + 2 + 3 + 2 = 16
The number of cones that are peanut butter cup is 2.
Therefore, the probability of the next customer ordering peanut butter cup is:
2/16 = 0.125
So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.
if shoulders bought twice as many footballs as basketballs and the footballs cost $60 and the basketballs cost $30 and he spends $450, then how many footballs did he purchase?
Using equations, we can find that he purchased 6 footballs.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.
Here in the question,
Let the number of footballs purchased be f.
Let the number of basketballs purchased be b.
Cost of each football = $60.
Cost of each basketball = $30.
Total amount spent = $450
Now,
60f + 30b = 450
Given,
2b = f
⇒ b = f/2
Putting the value of b in the equation,
60f + 30(/2f) = 450
⇒ 60f + 15f = 450
⇒ 75f = 450
⇒ f = 6
Therefore, he purchased 6 footballs.
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Choose the equation that represents the line passing through the point (2, −5) with a slope of −3
The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).
To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:
y - (-5) = -3(x - 2)
Simplifying this expression, we get:
y + 5 = -3x + 6
y = -3x + 1
Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.
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Complete Question:
Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.
A.) y = −3x − 13
B.) y = −3x + 11
C.) y = −3x + 13
D.) y = −3x + 1
Answer:
The answer is y = -3x + 1
During a space shuttle launch, a maneuver is scheduled to begin at T minus 80
seconds, which is 80 seconds before liftoff. The maneuver lasts 1 1/2 minutes. At
what time will the maneuver be complete?
Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.
What is the order of rotation?The amount of rotations a shape can undergo around its center before returning to its initial position is referred to as the order of rotation in mathematics and geometry. It is also referred to as a shape's circular symmetry. A circle, for instance, has an order of rotation of infinite because it can be rotated indefinitely around its center without changing how it appears. A cube has an order of rotation of four because it will remain the same in shape whether it is rotated 90, 180, 270, or 360 degrees around its center.
given
At T minus 80 seconds, or 80 seconds prior to liftoff, the move is slated to start.
We must multiply the duration of the maneuver by the beginning time to determine the time at which it will be finished.
The move is estimated to take 1 and a half minutes. Since there are 60 seconds in a minute, we can change this to seconds by multiplying it by 60:
1 and a half minutes is equal to 1.5 minutes, 1.5 minutes multiplied by 60 seconds is equal to 90 seconds.
The move lasts 90 seconds as a result.
We multiply the duration of the move (90 seconds) by the start time (T minus 80 seconds) to determine the time at which the maneuver will be finished:
The move will be finished in T minus 80 seconds plus 90 seconds.
By adding the integers, we can make this simpler:
When the move is finished, the time will be T minus 80 seconds + 90 seconds + T plus 10 seconds.
Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.
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If a bus car 1km and 2 minutes what is the m/s
the speed of the bus in meters per second is 8.33 m/s. If a bus travels a distance of 1 kilometer in 2 minutes, we can use the formula for speed to calculate its speed in meters per second (m/s).
The formula for speed is:
Speed = Distance ÷ Time
Here, the distance is 1 kilometer, which is equal to 1000 meters (since 1 kilometer = 1000 meters), and the time is 2 minutes, which is equal to 120 seconds (since 1 minute = 60 seconds).
So, we can plug these values into the formula:
Speed = 1000 meters ÷ 120 seconds
Simplifying this expression, we get:
Speed = 8.33 meters per second (rounded to two decimal places)
Therefore, the speed of the bus in meters per second is 8.33 m/s.
To put this into context, it's important to understand that speed is the rate at which an object moves, while velocity is the rate at which it moves in a specific direction. So, in this case, we have only calculated the speed of the bus, not its velocity. However, knowing the speed of the bus can be useful for a variety of applications, such as determining how long it will take to travel a certain distance, or calculating the fuel efficiency of the vehicle
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a new product is being tested by zed electronics to determine if it will continue to operate in a stable fashion under a variety of conditions. a sample of 400 items were tested, and 60 failed the test. determine a 90 percent confidence interval for the population proportion.
The 90% confidence interval for the population proportion is (0.1171, 0.1829).
To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:
p-bar = x/n = 60/400 = 0.15
where x is the number of items that failed the test and n is the sample size.
Next, we need to find the margin of error, which is given by:
ME = z*√(p_bar(1-p_bar)/n)
where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.
For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:
ME = 1.645*√(0.15(1-0.15)/400) = 0.0329
Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:
CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)
Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.
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two cars leave the same parking lot, with one heading north and the other heading east. after several minutes, the northbound car has traveled 6 miles, and the eastbound car has traveled 8 miles. measured in a straight line, how far apart are the two cars?
The two cars are 10 miles apart, measured in a straight line.
We can use the Pythagorean theorem to find the distance between the two cars. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's imagine that the cars have traveled for some time, forming a right triangle where the distance between them is the hypotenuse. The northbound car has traveled 6 miles, which corresponds to the length of one of the legs of the triangle. The eastbound car has traveled 8 miles, which corresponds to the length of the other leg of the triangle. Therefore, the distance between the two cars is
distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles
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A certain computer can perform a maximum number of operations per second. If this computer is running at 65%
of the maximum and is performing 30 operations per second, what is the maximum number of operations the
computer can perform per second? Round your answer to the nearest whole number.
1. 20 operations per second
2. 46 operations per second
3. 1,950 operations per second
4. 95 operations per second
Answer:
Let the maximum number of operations the computer can perform per second be x.
According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:
0.65x = 30
Solving for x, we get:
x = 30/0.65
x ≈ 46.1538
Rounding to the nearest whole number, we get:
x ≈ 46
Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.
Eugene had some paper with which to make note cards. on his way to his room he found 3 more pieces to use. in his room he cut each piece of paper in half. when he was done he had 12 half-pieces of paper. with how many sheets of paper did he start with?
On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with [tex]3[/tex] pieces of paper.
What is the equation?Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.
After finding the 3 more pieces, he had a total of [tex]x + 3[/tex] pieces of paper.
He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with [tex]2 \times (x + 3) = 2x + 6[/tex] half-pieces of paper.
We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:
[tex]2x + 6 = 12[/tex]
Solving for x, we get:
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Therefore, Eugene started with 3 pieces of paper.
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Find the center and radius of a circle with the equation x^2 + y^2 = 20.
x 2 + y 2 = 20
This is the form of a circle. Use this form to determine the center and radius of the circle.
( x − h ) 2 + ( y − k ) 2 = r 2
Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.
r = 2 √ 5
h = 0
k = 0
The center of the circle is found at ( h , k )
. Center: ( 0 , 0 )
These values represent the important values for graphing and analyzing a circle.
Center: ( 0 , 0 )
Radius: 2 √ 5
if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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HELP ASAP!!! What is the length of LN if the figure is a rectangle? (Attachment)
The length of the LN in the given rectangle is 33.
What is the intersection spot called?
The point of intersection is the location where two lines meet one another. If two straight lines are not parallel, they will eventually meet at some point. The meeting place of two straight lines is known as the point of intersection. The intersection location can be determined by simultaneously solving the equations for two straight lines that are passing.
In a rectangle, diagonals intersect at the right angle. The interesting point divides the lines into equal halves.
By solving the two equations, we can get the value of x.
LN = 4x-7
MO = 2x+13
Now, by equating two diagonal equations:
4x-7 = 2x+13
⇒4x-2x = 13+7
⇒2x = 20
⇒ x = 10
The required is LN = 4x-7
= 4(10) - 7
= 40-7
∴ LN = 33
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PLS HELP ASAP .a vacuum cleaner costs the owner $220 to buy. They then mark up the cost to sell it by 30%. What as the amount of the mark up? What is the selling price?
The amount of the mark up is $66 and the selling price is $286.
What is markup percentage?The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:
Markup percentage = (Selling price - Cost price) / Cost price x 100%
Given that, the mark up is 30%.
Thus,
Mark up = 0.3 x $220 = $66
The selling price is:
Selling price = $220 + $66 = $286
Hence, the amount of the mark up is $66 and the selling price is $286.
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Which fractions are the equivalent to 4/10 + 40/100 ? A. 80/100 B. 4/5 C. 20/100 D. 8/10 (multiple choice)