To solve this equation, begin by expanding the parentheses.
y = 4x² + 40x + 100 + 16
Then, collect like terms on the left hand side.
y = 4x² + 40x + 116
Finally, rearrange the equation to get y on the left side.
4x² + 40x - (y - 116) = 0
The final answer will be a quadratic equation.
To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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Christine has a six-sided dice numbered from 1 to 6. She rolled it a total of 50 times. It landed on an odd number 21 times. a) Work out the relative frequency of the dice landing on an odd number. Give your answer as a decimal. b) If the dice were fair, what would the theoretical probablity of it landing on an odd number be? Give your answer as a decimal. c) Is the dice definitely biased or definetely not biased, or is it impossible to tell? Write a sentence to explain your answer.
A) Relative frequency is number of times an event happened over total number of events:
Answer is 21/50 = 0.42
B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50
C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.
What is the solution for those?
And if you can please add the explanations
The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.
What is Equation?the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.
According to question:Simplified forms of the equation are
[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]
[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]
[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]
[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]
f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]
[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]
[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]
[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]
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Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP
Step-by-step explanation:
"increase" means to take the original 100% and put an additional 3.5% of these 100% on top of it.
so, we have to calculate
100% + 3.5% of £16470.45
100% of £16470.45 = £16470.45 × 100/100
3.5% of £16470.45 = £16470.45 × 3.5/100
the sum is therefore
£16470.45 × (100/100 + 3.5/100) =
= £16470.45 × (1 + 0.035) = £16470.45 × 1.035 =
= £17,046.91575 ≈ £17,046.92
which statemnt is ture when the dimensions of a two-dimensional figures are dilated by a scale factor of 2
When a shape is dilated, the size of the shape changes. The true statement is (d) The scale factor is 2.5.
Dilation:
Dilation is the process of changing the size of an object or shape by reducing or increasing its size by a specific scale factor. For example, a circle with a radius of 10 units shrinks to a circle with a radius of 5 units. Applications of this method are in photography, arts and crafts, sign making and more.
According to the Question:
How to determine the scale factor
In figure A, we have:
Length = 0.6
In figure B, we have:
Length =1.5
The scale factor is then calculated as:
K = 1.5/0.6
Dividing the equation:
k = 2.5
Hence, the true statement is (d) The scale factor is 2.5.
Complete Question:
The first figure is dilated to form the second figure. Which statement is true?
The scale factor is 0.4.
The scale factor is 0.9.
The scale factor is 2.1.
The scale factor is 2.5.
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Mr. and Mrs. Davenport have 3 kids, ages 3, 6, and 13. Their financial matters for 2019 are as follows:Adjusted Gross Income: $65,000Un-reimbursed Medical Expenses: $5,250How much would the Davenports' medical expenses contribute to their total itemized deductions?
The Davenports' medical expenses contribute to their total itemized deductions are $375 (7.5% for 2019).
The costs you incurred for state and local income or sales taxes, real estate taxes, personal property taxes, mortgage interest, and disaster losses are all included in itemised deductions. You can also count charitable donations and a portion of your out-of-pocket medical and dental costs.
Currently for the 2019 (due 2020), you can deduct medical expenses that exceed 7.5% of your AGI, but back then in 2019, the threshold was 7.5%, not 10%.
So the Davenports can only deduct
$5,250 - ($65,000 x 7.5%) = $375
if they decided to itemize their deductions.
The threshold will increase back to 10% starting 2020 (due 2021) tax returns.
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dy If x = a sin 2t, y = a(cos 2t + log tan t), then find dx
Step-by-step explanation:
We have:
x = a sin 2t
Differentiating with respect to t, we get:
dx/dt = 2a cos 2t
Next, we have:
y = a(cos 2t + log tan t)
Differentiating with respect to t, we get:
dy/dt = -2a sin 2t + (1/tan t)(1/ln 10)
Using the identity:
sin^2 t + cos^2 t = 1
We have:
sin 2t = 2sin t cos t
And:
cos 2t = cos^2 t - sin^2 t
cos 2t = 2cos^2 t - 1
Using these identities, we can rewrite dx/dt and dy/dt in terms of x and y:
dx/dt = 2a sqrt(1 - x^2/a^2)
dy/dt = -2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t)
Therefore, we have:
dx/dy = dx/dt ÷ dy/dt
Substituting the expressions for dx/dt and dy/dt, we get:
dx/dy = (2a sqrt(1 - x^2/a^2)) / (-2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t))
Simplifying, we get:
dx/dy = (-2 sqrt(1 - x^2/a^2)) / (2 sqrt(1 - x^2/a^2) - (1/ln 10)(y - a cos 2t))
I'm not sure where I'm going wrong here and need a detailed explanation with a full answer please.
Answer:
g(x) = 1/2|x - 1| + 2
Step-by-step explanation:
You were almost there, you just got the slope wrong.
original vertex (h, k): (0, 0)
transformed vertex (h', k'): (1, 2)
original slope: 1
transformed slope: m = (3-2)/(3-1) = 1/2 pick any 2 points to find the slope
equation for the transformed function shown in the graph:
g(x) = 1/2|x - h'| + k'
g(x) = 1/2|x - 1| + 2
Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, compute the system's impulse response h[n] without using z-transforms.
Given that (1, 2, 3] System{1, 4, 7,6] for a system known to be LTI, the impulse response of the system: h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
To compute the impulse response h[n] of a linear time-invariant (LTI) system given its input-output relationship, we can use the convolution sum:
y[n] = x[n] * h[n]
y[n] = (1/2)*(x[n] + 2x[n-1] + 3x[n-2])
y[n] = (1/2)*(δ[n] + 2δ[n-1] + 3δ[n-2])
y[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2]
Thus, the impulse response of the system is:
h[n] = (1/2)*δ[n] + δ[n-1] + (3/2)*δ[n-2],where δ[n] is the impulse signal.
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59, 60, 61, 62, 63, 64, 65, and 66 Find the values of x for which the series converges. Find the sum of the series for those values of x. 59. § (-5)".z" n=1 Answer + 00 60. Σ(α + 2)" n=1 61. (x - 2)" 3" n=0 Answer + 62. (-4)" (x - 5) n=0 00 63. 2" ch NO Answer
The values of x for which the series converges is x ∈ (-1/5, 1/5). The sum of the series for those values of x is (-5x)/(1 + 5x).
The series is [tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex].
We can write this series as [tex]\Sigma^{\infty}_{n=1}(-5x)^n[/tex].
This is a infinite geometric series with first term a = -5x and common ration r = -5x.
It is convergent when
|r| < 1
|-5x| < 1
|-5| |x| < 1
5|x| < 1
Divide by 5 on both side, we get
|x| < 1/5
The series is convergent when x ∈ (-1/5, 1/5).
Sum of the series is
Sₙ = a/1 - n
Sₙ = (-5x)/{1 - (-5x)}
Sₙ = (-5x)/(1 + 5x)
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The complete question is:
Find the values of x for which the series converges. Find the sum of the series for those values of x.
[tex]\Sigma^{\infty}_{n=1}(-5)^nx^n[/tex]
2 bags of dog food. How many days will 3/4 last?
Answer:
3/4 of a bag of dog food will last 3 days.
g suppose x and y are two random variables. you don't know their distribution, but someone tells you e[x]
When x and y are independent variables with x having uniform distribution (0,1) and y having exponential distribution respectively, then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3, and e (x2 e24) is -1/3 22etyx u (0,1) > Independent y exp (1) > Independent
The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process.
E (x) = 0+1/2 = 1/2
v (x) = [1 – 0]2 / 12 = 1/12
E x2 = v (x) + [Ex]2
= 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3
E (y) = 1 v(y)=1
E y2= 1+1= 2
Eety = ∫0etye-ydy
Eety = ∫0e-y (1 – t)dy
a : E (x+y) = E (x) + E(y)
E (x+y) = 1/2+1 = 3/2
b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2
c: E (x+y)2 = E (x2 - 2xy+ y2)
= 1/3 - 2 x 1/2 + 2
= 1/3 + 1 = 4/3
d. E x2e24
= 1/3 x -1 = - 1/3
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Find the missing length indicated
The value of x is 5
Define the term Similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. To be more specific, two triangles are comparable if their respective sides are proportionate and their corresponding angles are congruent.
Two triangles are similar if corresponding angles are congruent and corresponding sides are proportional.
from the below figure, both the triangles are similar, ∆ABC ≈ ∆EFB
By using Thales's theorem, the ratio of the sides of triangles are;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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The ratio of triangle sides can be calculated using Thales' theory, and it is the value of x is 5
Define the term Similar triangles?Similar triangles are those with the same shape but varying sizes. To be more precise, two triangles are comparable if their matching angles and respective sides are congruent.
If matching sides are proportional and corresponding angles are congruent, two triangles are similar.
Both triangles in the following figure are comparable ∆ABC ≈ ∆EFB
The ratio of triangle sides can be calculated using Thales' theory, and it is;
BE/EA = BF/FC
15/30 = x/10
x = 5
Therefore the value of x is 5
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0.59°C and 0.88°C.
The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.
What is mean?The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.
In this question, using the formula,
z-score = (x – μ) / σ
where:
x: individual data value
μ: population mean
σ: population standard deviation
for x=0.59
μ= 0
σ= 1
z-score= 0.59
Probability=0.7224
for x=0.88
z-score= 0.88
Probability=0.8106
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Orlando skip the rope 125 times in 45 seconds write this as a unit rate
Answer:
g h hh h
Step-by-step explanation:
PLEASE HELPPPPP 30 POINTSSSS!
Answer:
the answer will be 117
Step-by-step explanation:
you need to multiply
Express using algebra:
Z increased by 16%
Answer:
Let's start by expressing "Z increased by 16%" using algebra.
Let Z be the original value of some quantity.
To increase Z by 16%, we need to add 16% of Z to Z:
Z + 0.16Z
Simplifying this expression by factoring out Z, we get:
Z(1 + 0.16)
Combining like terms, we have:
Z(1.16)
Therefore, "Z increased by 16%" can be expressed algebraically as:
Z increased by 16% = Z(1.16)
Answer:
z(1.16)
Step-by-step explanation:
solve please and thank you it’ll help a lot. 15 points.
Parallelogram (Opposite sides have the same length). Parallelogram (Area is one-half the base times the height). Parallelogram (Opposite sides are parallel). Parallelogram (Angles can be right angles)
What is the assertion of the parallelogram?According to the parallelogram law, the sum of the squares of a parallelogram's four sides is equal to the sum of the squares of its two diagonals. It is essential for the parallelogram to have equal opposite sides in Euclidean geometry.
Are a parallelogram's opposing sides parallel?A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another. There are six crucial parallelogram characteristics to be aware of: Congruent sides are those when AB = DC.
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in the right triangle round to your nearest tenth. 18 15 X help please
The value οf the given angle x = 39.8 degree
What is Trigοnοmetric Functiοns?Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.
The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.
In the figure tanx = p/h
[tex]x = tan^{-1(15/18)}[/tex]
x = 39.8
Hence the value οf the given angle x = 39.8 degree
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. (1 point)
help me pls D;
The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
How to find the dimensions of rectangle?Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:
Area of top of bookcase = lb
We want this area to be equal to 300 square inches. Therefore, we can write:
lb = 300
We are solving for "b", so we can rearrange this equation to solve for "b":
b = 300/l
Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:
b = 300/20 = 15
So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
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5) What is the probability of picking a vowel, replacing it
and then picking a consonant from the word "SLEEP"?
The probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is approximately 0.096 or 9.6%.
What is probability?Probability is usually expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain.
According to question:There are two vowels (E) and three consonants (S, L, P) in the word "SLEEP".
The probability of picking a vowel on the first draw is 2/5, because there are two vowels out of five letters total.
Since we replace the vowel we picked, the probability of picking another vowel on the second draw is also 2/5.
The probability of picking a consonant on the third draw is 3/5, because there are three consonants left out of five letters total.
Therefore, the probability of picking a vowel, replacing it, and then picking a consonant from the word "SLEEP" is:
(2/5) x (2/5) x (3/5) = 12/125 or approximately 0.096 or 9.6%.
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Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
A company has a fixed cost of $1277 each day to run their factory and a variable cost of $1.93 for each widget they produce. How many widgets can they produce for $2127?
The company can produce approximately 425 widgets for $2127.
What is cost function ?
The key concept used here is the concept of cost functions, which is an important concept in economics and business. A cost function is a mathematical function that expresses the total cost of production as a function of the level of output produced. In this case, the cost function is a linear function of the form C = a + bx, where C is the total cost, a is the fixed cost, b is the variable cost per unit, and x is the level of output.
Finding the number of widgets the company can produce given a fixed cost and a variable cost per widget :
To solve this problem, we can set up an equation that relates the total cost to the number of widgets produced.
Let x be the number of widgets produced.
The total cost C is given by:
C = fixed cost + variable cost
C = 1277 + 1.93x
We want to find the number of widgets produced for a total cost of $2127. So we can set up an equation:
2127 = 1277 + 1.93x
Subtracting 1277 from both sides gives:
850 = 1.93x
Dividing both sides by 1.93 gives:
x ≈ 439.9
Since we can't produce a fractional number of widgets, we need to round down to the nearest integer. Therefore, the company can produce approximately 425 widgets for $2127.
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The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain of the function is [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.
b) The trip had a duration of 5.1875 hours.
How to obtain the domain and the range of the function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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A firm is a monopoly for the good it produces. Its average cost function is AC = 9+(3/10)q+30/q, where q is the quantity produced. The demand equation for its good is given by q = 40 - (4/3)p where p is the price.
(a) Find expressions, in terms of q, for the total revenue.
(b) What is the equation for the Total cost?
(c) Find the expression for profit. (d) Find the total output and revenue at the break even point.
(e) Find the profit when 20 units are produced.
(f) Find the profit when 7 units are produced.
(g) Find the output required to obtain a profit of RM100.
The answer of the given question is (a) TR = p(40 - (4/3)p), or TR = 40p - (4/3)p² , (b) TC = 9q + (3/10)q² + 30 , (c) π = 40p - (4/3)p² - 9q - (3/10)q² - 30 , (d) TR ≈ 342.67 , (e) the profit when 20 units are produced is approximately RM188.27 , (f) the profit when 7 units are produced is approximately -RM24.44, indicating a loss , (g) the output required to obtain a profit of RM100 is approximately 8.78 units.
What is Equation?An equation is mathematical statement that asserts yhe equality of two expressions. It typically consists of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division, among others. Equations are often used to solve problems, to model real-world phenomena, and to describe mathematical relationships.
(a) The total revenue is given by TR = p x q. Substituting the demand equation q = 40 - (4/3)p, we get TR = p(40 - (4/3)p), or TR = 40p - (4/3)p².
(b) The total cost is given by TC = q x AC. Substituting the given average cost function, we get TC = 9q + (3/10)q² + 30.
(c) The profit is given by π = TR - TC. Substituting the expressions we found in parts (a) and (b), we get π = 40p - (4/3)p² - 9q - (3/10)q² - 30.
(d) At the break even point, the firm earns zero profit, so we set π = 0 and solve for q. Substituting the expression we found in part (a) for p, we get:
0 = 40p - (4/3)p² - 9q - (3/10)q² - 30
0 = 40(40/3 - (3/4)q) - (4/3)(40/3 - (3/4)q)² - 9q - (3/10)q² - 30
0 = 533.33 - 51.25q - 0.22q^2
Solving for q using the quadratic formula, we get:
q = (51.25 ± sqrt(51.25² - 4(-0.22)(533.33))) / 2(-0.22)
q ≈ 22.75 or q ≈ 206.58
We reject the solution q ≈ 206.58 because it is outside the relevant range of output, which is between 0 and 40. Therefore, the total output at the break even point is approximately 22.75 units. To find the total revenue at the break even point, we substitute q = 22.75 into the demand equation from part (a) and get:
p = (40/3) - (3/4)q
p ≈ 15.08
TR = p x q
TR ≈ 342.67
(e) To find the profit when 20 units are produced, we substitute q = 20 into the expression for profit we found in part (c) and get:
π = 40p - (4/3)p² - 9q - (3/10)q² - 30
π ≈ 188.27
Therefore, the profit when 20 units are produced is approximately RM188.27.
(f) To find the profit when 7 units are produced, we substitute q = 7 into the expression for profit we found in part (c) and get:
π = 40p - (4/3)p² - 9q - (3/10)q² - 30
π ≈ -24.44
Therefore, the profit when 7 units are produced is approximately -RM24.44, indicating a loss.
(g) To find the output required to obtain a profit of RM100, we set the profit equation equal to 100 and solve for q:
Profit = TR - TC
100 = pq - ACq
100 = (40-(4/3)p)*q - (9+(3/10)q+30/q)*q
100 = (40-(4/3)p - 9q - 3q²/10)
Multiplying by 10 and rearranging terms, we get a quadratic equation in q:
3q² + 91q - 310 = 0
Solving for q using the quadratic formula, we get:
q = (-91 ± sqrt(91² - 43(-310)))/(2*3)
q ≈ 8.78 or q ≈ -29.44
Since the quantity produced cannot be negative, the output required to obtain a profit of RM100 is approximately 8.78 units.
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(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^{T}[/tex]. Show with an example that the eigenvectors of A and [tex]A^{T}[/tex] are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
If λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
[tex]v^T A^T = \lambda v^T[/tex]
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
[tex]\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right][/tex]
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
[tex]v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T[/tex]
Now, for transpose of A:
[tex]A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right][/tex]
The eigen vectors are:
[tex]u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T[/tex]
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.
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Someone plezzz help me
Neither anushka nor lukas are correct as both of their calculations are wrong.
How are linear equations solved?Basic arithmetic operations like addition, subtraction, multiplication, and division are used to isolate the variable on one side of a linear equation and solve it. The objective is to make the equation as simple as possible until the variable can be identified and its value calculated. In order to solve a linear equation, you must first combine like terms to simplify the expressions on both sides of the problem.
Then, you can use inverse operations to get rid of constants and coefficients. The value of the variable can be ascertained by solving for it once it has been isolated. By looking at the coefficients and constants of the equation, it can be established if the equation has no solution or infinite solutions. In various disciplines, such as science, engineering, and finance, linear equations are used to represent connections between variables.
2/5b + 1 = -11
2/5b = -12
b= -12 x 5/2
b = -30
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Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 JQK
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.
The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.
Actual count of K = 12 - 2 = 10
Total count of 6 and K = 7 + 10 = 17
The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:
Experimental probability = (frequency of K or 6) / (total number of draws)
Experimental probability = 17 / 100
Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.
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These two triangles are similar. What is the missing side measure?
X
5
O x = 9.5
0 x = 2
Ox=7
Ox=4
3.5
20
8
14
According to the given information, the missing side measure is 14.
What is triangle?
A triangle is a polygon with three sides, three angles, and three vertices. It is the simplest polygon and the fundamental shape used in geometry. A triangle can be classified based on the length of its sides and the measure of its angles.
To find the missing side measure, we can set up a proportion between the corresponding sides of the two similar triangles:
(x + 5) / x = 9.5 / 7
We can then solve for x by cross-multiplying:
7(x + 5) = 9.5x
7x + 35 = 9.5x
35 = 2.5x
x = 14
Therefore, the missing side measure is 14.
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