The seller earns $116.04 on each furnace microwave sold.
If 314% is the seller's profit, then the cost price of the furnace microwave can be found by dividing the selling price by (100% + 314%) or 4.14,
Cost price of the furnace microwave = Selling price / 4.14
= $153 / 4.14
= $36.96
(rounded to two decimal places)
The profit earned by the seller on each furnace microwave is equal to the selling price minus the cost price,
Profit per furnace microwave = Selling price - Cost price
= $153 - $36.96
= $116.04
Hence, On each furnace microwave sold, the seller receives $116.04 in profit.
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Problem #4: Depletion Mode Inverter Analysis Find the VH and V₁ for the depletion mode inverter. Assume VDD = 3.3 V, VTN = 0.6 V, P = 9 250 μW, Kn' = 100 μA/V², y = 0.5 √V, 20F = 0.6 V, Vro2 = -2.0 V, (W/L) of the switch is (1.46/1), and (W/L) of the load is (1/2.48)
The VH and V₁ for the depletion mode inverter is provided: VH = 2.3475 V and V₁ = 2.448 V.
Given data: VDD = 3.3
VVTN = 0.6
VP = 9 250
μWKn' = 100
μA/V²y = 0.5
√V20F = 0.6 V
Vro2 = -2.0 V(W/L) of the switch is (1.46/1)(W/L) of the load is (1/2.48)
Inverter Circuit:
Image credit:
Electronics Tutorials
Now, we need to calculate the threshold voltage of depletion mode VGS.
To calculate the VGS we will use the following formula:
VGS = √((2I_D/P.Kn′) + (VTN)²)
We know the values of I_D and P.Kn′:
I_D = (P)/VDD = 9.25 mW/3.3 V = 2.8 mA.
P.Kn′ = 100
μA/V² × (1.46/1) × 2.8 mA = 407.76.μA
Using the above values in the formula to find VGS we get:
VGS = √((2 × 407.76 μA)/(9.25 mW) + (0.6)²) = 0.674 V
Now, we can calculate the voltage drop across the load, which is represented as V₁:
V₁ = VDD - (I_D.Ro + Vro2)
V₁ = 3.3 - (2.8 mA × (1.46 kΩ/1)) - (-2 V) = 2.448 V
We can also calculate the voltage at the output of the switch, which is represented as VH.
To calculate the VH we will use the following formula:
VH = V₁ - (y/2) × (W/L)(VGS - VTN)²
We know the values of VGS, VTN, and y, and the ratio of (W/L) for the switch.
W/L = 1.46/1y = 0.5 √V = 0.5 √VGS - VTN = 0.5 √(0.674 - 0.6) = 0.0526
VH = 2.448 - (0.0263 × 1.46/1 × (0.0526)²) = 2.3475 V
Therefore, VH = 2.3475 V and V₁ = 2.448 V.
Hence, the solution to the given problem of finding VH and V₁ for the depletion mode inverter.
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Factor completely 16x8 − 1.
Answer:
Step-by-step explanation:
(4x^4 - 1)(4x^4 + 1)
(2x^2 - 1)(2x^2 + 1)(4x^4 + 1)
I am learning ratio and proportion
Answer:
Unit Quantity is the answer
if the sun is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the sun? (the sun is 92,960,000 miles from the earth, and there are 5,280 feet in 1 mile.)
What is the probability of getting a sum 10, when two dice are thrown simultaneously?
1/12
1/6
1/9
1/8
The probability of getting a sum 10 when two dice are thrown simultaneously is 1/12.
What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of an event happening. The probability of a specific event is a number between 0 and 1.
The closer the probability is to 1, the more likely it is that the event will occur.
The closer the probability is to 0, the less likely it is that the event will occur.
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Which set Doesnt describe a function??
Answer:
set c is the answer
Step-by-step explanation:
for a pair to be a function it can't have 2 different numbers for the same x value
Tom went on a bike ride to the store 3 miles away. If it took Tom 12 of an hour to get there and 23 of an hour to get back, what was his average rate of speed (miles per hour) for the entire trip?
Answer: 0.1714 miles / hour
Step-by-step explanation:
Given the following :
Distance to the store = 3 miles
Time taken to get to store = 12 hours
Time taken to return = 23 hours
The average rate of speed for the trip =?
Average Speed = total distance traveled / total time taken
Total distance traveled = 2 × 3 miles = 6 miles
Total time taken = 12 + 23 = 35 hours
Average speed = 6 miles / 35 hours
Average speed = 0.1714 miles / hour
Answer:
0.1714 mph
5.14 mph
Step-by-step explanation:
Solve the following system of equations.
Answer:
D
Step-by-step explanation:
y = x² - 4x - 5 → (1)
y = x - 9 → (2)
substitute y = x² - 4x - 5 into (2)
x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )
x² - 5x + 4 = 0 ← in standard form
(x - 1)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )
x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )
8. Determine if the following integral converges or if it diverges. If it converges find its value 1 L²dx 9. Determine if the following series is convergent or divergent by expressing S½ as a telescoping sum. If it is convergent, finds its sum. 00 n=2 2 n² - 1 10. Determine if the following series is convergent or divergent by expressing Sk as a telescoping sum. If it is convergent, finds its sum. Σ(1) n=1 11. Determine if the following series is convergent or divergent by expressing S as a telescoping sum. If it is convergent, finds its sum. 1 Σ( √²+1) √n n=4
The first integral converges to \(\frac{1}{3}\)L³ from 0 to L. The second series is convergent and its sum is 2.
For the first integral, we can calculate it using the power rule and evaluate it from 0 to L. Therefore, the integral converges and its value is \(\frac{1}{3}\)L³. For the second series, we can express the sum as a telescoping sum by taking the common denominator of the terms in the series.
We can see that this is a telescoping sum because each term cancels out with the next term except for the first and last terms. Therefore, we can evaluate the sum by substituting n=2 and infinity into the formula, which gives us:
S2 = \(\frac{1}{2}\)[(1)-(\(\frac{1}{3}\))] = \(\frac{1}{3}\)
S∞ = lim (n→∞) S_n = [1-0] = \(\frac{1}{2}\)
Therefore, the series is convergent and its sum is 2.
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36 of 4436 of 44 items question mr. jones was 4 times as old as his daughter 5 years ago. how old is mr. jones now if the sum of their present age is 55 years?
Mr. jones now if the sum of their present age is 55 years is 41 years from the given information mr. jones was 4 times as old as his daughter 5 years ago and formulated linear equation..
Given that, Mr. Jones and their daughter are currently 55 years old.
Let Mr. Jones' age at this time be x years.
His daughter is currently y years old.
Since Mr. Jones's and his daughter's combined age as of right now is 55
Therefore, we can write linear equation x + y = 55.... I (i)
The current age of Mr. Jones is equal to (x - 5) years, and their ages prior to 5 years.
His daughter is currently (y - 5) years old.
Since Mr. Jones was four times as old as his daughter five years ago,
(x - 5) = 4 (y - 5), where x = 5 and y = 20 and 15, respectively. ... (ii) (ii)
When you solve for |(i) and (ii), you get y = 14.
And, x = 41
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In a group of 75 student 20 liked football only 30 liked cricket only and 18 did not like any of two game? i) How many of them liked at least on game? ii) find the number of student who liked both game. iii)how many of them liked cricket. iv) how many of them liked football. v) represent the result in venn diagram
Answers:
i) 57ii) 7iii) 37iv) 27v) See the venn diagram below====================================================
Explanation:
We have these given facts
A. There are 75 students total.B. There are 20 students who like football onlyC. There are 30 students who like cricket onlyD. There are 18 students who don't like either sportFact D indicates that 18 goes on the outside of the two circles, but inside the universal set shown by the rectangle.
We'll use facts A and D to find that 75-18 = 57 students like either football, cricket, or both. So the numbers inside the regions in the circles must add up to 57.
Now use the values from facts B and C. They add to 20+30 = 50. This is the number of students who either like football only OR like cricket only. None of these 50 students like both sports. But we found that 57 like one or the other or both. So that must mean 57-50 = 7 students like both sports.
We have enough info to fill out the venn diagram as shown below.
--------------
Now to answer the questions your teacher asked:
i) How many of them liked at least on game? This would be the 57 value mentioned earlier.ii) Find the number of student who liked both game. It's the value 7 found in the middle of the two circles.iii)how many of them liked cricket. Add up the numbers in the "Cricket" circle to get 7+30 = 37.iv) how many of them liked football. Add up the numbers in the "Football" circle to get 20+7 = 27PLEASE HELP!!
Given two consecutive integers whose sum is 45, find the smaller of the two integers.
Answer:
22
Step-by-step explanation:
Let x represent the smaller integer. Then x+1 is the larger. Their sum is ...
x +(x+1) = 45
2x = 44 . . . . . subtract 1
x = 22 . . . . . divide by 2
The smaller of the two integers is 22.
simplify
25x-16y-25x+16y
Answer:
Step-by-step explanation:
25x-16y-25x+16y
-16y and 16y cancels out
25x-25x
25x and -25x cancels out too
This means the answer is 0
Do number 2 please ……
Answer:
huh
Step-by-step explanation:
Write the expression in standard form a+bi: (8-i)/(2+i)
Answer:
The expression (8-i)/(2+i) in standard form is, 3 - 2i
Step-by-step explanation:
The expression is,
(8-i)/(2+i)
writing in standard form,
\((8-i)/(2+i)\\\)
Multiplying and dividing by 2+i,
\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)
Hence we get, in standard form, 3 - 2i
The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).
To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.
The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:
(8-i)/(2+i) * (2-i)/(2-i)
Using the distributive property, we can expand the numerator and denominator:
(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))
Simplifying further:
(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)
Since i^2 is equal to -1, we can substitute -1 for i^2:
(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))
Combining like terms:
(15 - 10i) / (3 + 4i)
Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).
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Find the number of outcomes in the complement of the given event. out of 301 apartments in a complex, 138 are available for rental.
The number of outcomes in the complement of the event is 163
How to find the number of outcomes in the complement of the event?The statement is given as:
Out of 301 apartments in a complex, 138 are available for rental.
This means that
Apartments = 301
Rental = 138
The complement is calculated as:
Complement = Apartment - Rental
So, we have
Complement = 301 - 138
Evaluate
Complement = 163
Hence, the number of outcomes in the complement of the event is 163
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suppose the matrix, , has eigenvectors , , and whose eigenvalues are , and respectively. then, using the same order, can be written in the form where
We can write A = PAP where 1 P= and A= where P is an invertible matrix that maps the null space of A to itself.
To find the matrix P, we need to solve the following system of linear equations:
λ_1 1 = 1
λ_2 (-4) 1 = 1
λ_3 (-1) 1 = 1
The eigenvalues are real and non-negative, so they can be written as λ = λ_1, λ_2, λ_3 = λ_1, -4, -1 respectively.
Using Cramer's rule, we have:
\(λ_1 * 1^T = 1 * 1^T = 1\)
\(λ_2 * (-4)^T = -4 * 1^T = -4\)
\(λ_3 * (-1)^T = (-1) * 1^T = -1\)
Multiplying the first and third equations, we get:
\(-λ_1 * λ_3 = -4 * (-1) = 4\)
Multiplying the second and third equations, we get:
\(-λ_2 * λ_3 = -4 * (-1) = 4\)
Subtracting the second equation from the first, we get:
\(λ_1^2 - λ_2^2 = 1^2 - (-4)^2 = 5\)
Multiplying the first and third equations, we get:
\(-λ_1 * λ_2 = -4 * (-1) = 4\)
Dividing the third equation by the second equation, we get:
\(-1/λ_2 = -1/λ_3\)
Taking the reciprocal of both sides, we get:λ_2 = λ_3
Substituting this into the second equation, we get:
-\(λ_1 * λ_3 = -4 * (-1) * λ_3 = -4\)
Simplifying, we get:
-4 = -4
This equation has no solution, so the matrix A cannot be written in the form A = PAP where 1 P= and A= Thus, the answer is no.
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Full Question: the matrix, A, has eigenvectors and whose eigenvalues are 1, –4 and – 1 respectively. Then, using the same order, A can be written in the form A = PAP where 1 P= and A=
Find the percent of change
if the price of a $10 game is
marked up to $15.
Answer:
50%
Step-by-step explanation:
10 divided by 2 is 5. 5 is 50% of 10, and if you add 5 to 10, you get 15.
The growth of a certain bacteria can be modeled by C(t) = 100(1.03)^24t, where C(t) is the total number of bacteria after t hours. Which function is approximately equivalent to C(t)?
A) C(t) = 100(2.03)^t
B) C(t) = 2,400(2.03)^t
C) C(t) = 100(2.03)^t/24
D) C(t) = 2,400(2.03)^t/24
Answer:A
Step-by-step explanation:
alan's camping troop is raising money for a camping trip. the camping troop is selling boxes of popcorn, b, for $3.75 each. each camper starts with a credit of $25. to make the first deposit on the camping trip, alan total sales, f(b), needs to be at least $1100. write an inequality to represent the problem:
Answer:
$3.75b + $25 >= $1100
Step-by-step explanation:
Answer the question mentioned below
9.5 divide by 0.05
Answer:
190
Step-by-step explanation:
14. (10.0 points) Given f(x)=sin(2πx), when x = 0.3, f(x) = 0.951057. Approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1. (Write your answer to 6 decimal points).
Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.
We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,
we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.
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A speedboat moving at 30 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of 3.0 m/s
2
by reducing the throttle. What is the velocity of the boat when it reaches the buoy?
The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.
To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.
We can use the equation: v² = u² + 2as
Substituting the given values, we have:
v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)
v² = 900 m²/s² - 600 m²/s²
v² = 300 m²/s²
Taking the square root of both sides, we find:
v = √300 m/s
v ≈ 17.32 m/s
Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.
The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.
In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.
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87. Which of the following is an equation of the line tangent to the graph of f(x) = x² + 2x² at the
point where f'(x)=1?
(A) y=8x-5
(B) y=x+7
(C) y=x+0.763
(D) y=x-0.122
(E) y=x-2.146
Juan mowed the same number of lawns each week as Mark. Which equation represents Juan’s rate of mowing lawns, where x represents the number of weeks and y represents the total number of lawns mowed?
Answer:
y=20x is correct
Step-by-step explanation:
i took the quiz
Answer:
y = 20x
i got the question right on the quiz
PLEASE HELP ME
7. (37:10) Kevin finds Buzz's life savings. If Buzz
had $47 and had been saving for 17 years, how
much could we expect him to save in 30 years?
Based on the information given, the amount that he'll be expected to save in 30 years will be $83.
From the question given, since Buzz had $47 and had been saving for 17 years, the amount saved per year will be:
= $47/17
= $2.7647
Therefore, the amount that'll be saved in 30 years will be:
= 30 × $2.7647
= $82.941
= $83
The amount saved will be $83.
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A is at (-2, 1) and B is at (4, -1).
P is a point on y-axis which is equidistant from A and B.
What are the coordinates of P?
Answer:
The coordinates of P are (1,0)
Step-by-step explanation:
Midpoint
The midpoint (xm,ym) of a segment defined by points (x1,y1) and (x2,y2) is calculated as follows:
\(\displaystyle x_m=\frac{x_1+x_2}{2}\)
\(\displaystyle y_m=\frac{y_1+y_2}{2}\)
We need to find the coordinates of P which is equidistant from the endpoints A=(-2,1) and B=(4,-1).
Calculate the midpoint:
\(\displaystyle x_m=\frac{-2+4}{2}=1\)
\(\displaystyle y_m=\frac{1-1}{2}=0\)
Thus, the coordinates of P are (1,0)
Note the midpoint does not lie on the y-axis but on the x-axis.
Need help with 1-6 pls
1. The value of n in 3n + 19 = 28 will be 3.
2. The value of b in 34 - 4b = 18 will be 4.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The value of n in 3n + 19 = 28 will be:
3n + 19 = 28
Collect the like terms
3n = 28 - 19
3n = 9
Divide
n = 9 / 3
n = 3.
The value of b in 34 - 4b = 18 will be:
34 - 4b = 18
4b = 34 - 18
4b = 16
Divide.
b = 16 / 4
b = 4
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Which of the following are ways to find the rate of change or slope
1 . Rise over run
2 . Subtract Y coordinates over subtract X coordinates
3 . Change in Y over change in X
4 . All of the above
The rate of change or slope can is the ratio of the change in horizontal axis to the change in the vertical axis, Hence, all the equations stated above can be used to obtain the slope.
The slope or rate of change can be obtained using the following expression :
Slope = Rise / Run Slope = (y2 - y1) ÷ (x2 - x1) Slope = (△Y ÷ △X)Therefore, all the given equations in the option can be used to obtain the slope value of a line.
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L.B. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. Altogether, they sold 486 items that totaled $2,673 b.Explain the value of each digit in your answer to 1(a) using place value terms.
Answer: $5.5
Step-by-step explanation:
Here is the complete question:
L.B. Johnson Middle School held a track and field event during the school year. The chess club sold various drink and snack items for the participants and the audience. Altogether, they sold 486 items that totaled $2,673 a. If the chess club sold each item for the same price, calculate the price of each item. b. Explain the value of each digit in your answer to a using place value terms
Item sold = 486
Total amount = $2673
Price of each item = Total amount/items sold
= 2673/486
= $5.5
Each item costs $5.5.
5.5 = 5 units and 5 tenths.
The first number after the decimal point by the right is the tenths.