Answer:
26.a
27 c
28.a
Step-by-step explanation:
Please send an answer quick I really need it the picture is above.
Answer:
-132
Step-by-step explanation:
When you plug in -8 to every x you get -2(8)^2+2(8)-20 which gives you -132.
I am wondering about chapter 8, problem #4. The answer says 0.8 but why wouldn't the correct answer be 80%?
If the whole school has 800 students, and the 9th grade has 250 students, what percentage of the 9th grade population did you sample?
The percentage of the 9th grade population did you sample is 80%.
First, let's find out how many students were in the sample. The problem doesn't provide this information directly, so we'll assume that the sample size was given to you. For the sake of this explanation, let's say that the sample size was 200 students.
Next, we need to find out the total number of 9th-grade students in the school. The problem tells us that there are 250 9th-grade students in the school, so we'll use that number.
Using the values we've found, we can plug them into the formula:
percentage = (200/250) x 100%
percentage = 0.8 x 100%
percentage = 80%
In this problem, the fraction we calculated was 0.8, which means that 80% of the 9th-grade population was included in the sample. So the answer is indeed 80%, as you suspected.
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13 points if someone gets it right.
You spin this spinner twice.
1 polka-dot section, 2 white sections, 1 shaded section
Whta is the probability of the spinner stopping at a polka- dot section and then say stopping a solid white section? Write your answer as a fraction
The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.
The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.
When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.
Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.
Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).
To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8
Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.
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5 3/4 divided by 1/3
Answer:
23/12 (or) 1.917
Step-by-step explanation:
5 3/4 = 5+3/4
(23)/4=5.75
5.75/(1/3) (or) 5.75/3
=1.916666
5 less than the square of a number
x^2 - 5 this will be the equation formed.
What is exponents?An exponent is the number of times a number is multiplied by itself. For example, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of one is itself.
Calculationlet the number be x
x^2 - 5 this will be the equation formed
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Question 5 (3 points) For a Normal distribution with mean 0 and standard deviation 1, which of the following Python lines outputs the probability p(-0.15 < x < 1.88)? Select one. O import scipy.stats as st print(st.norm.cdf(1.88, 0, 1) - st.norm.cdf(-0.15, 0, 1)) O import scipy.stats as st print(st.norm.pdf(1.88, 0, 1) - st.norm.pdf(-0.15, 0, 1)) O print(st.norm.cdf(1.88, 0, 1) - st.norm.cdf(-0.15, 0, 1)) O import scipy.stats as st print(st.norm.cdf(1.88, 0, 1))
The probability distribution at each point x along the horizontal axis.
Why Python lines outputs the probability?For a Normal distribution with mean 0 and standard deviation 1,
the following Python line outputs the probability p(-0.15 < x < 1.88):
print(st.norm.cdf(1.88, 0, 1) - st.norm.cdf(-0.15, 0, 1))
Probability is the likelihood or chance that an event will occur. It is a number between 0 and 1, with 0 indicating that an event will never occur and 1 indicating that an event will always occur.
Probability values range from 0 to 1, with a value of 0 indicating that the event will never occur and a value of 1 indicating that the event will always occur.
The probability is the value between 0 and 1 that indicates the likelihood of an event occurring. The probability is obtained by dividing the number of ways an event can occur by the total number of possible outcomes.
Scipy.stats.norm is the normal distribution's probability density function (pdf) in SciPy.
The PDF function is a part of the scipy.stats library in Python. The probability density function of the normal distribution is the function scipy.stats.norm.pdf(x, loc=0, scale=1). It is the height of the probability distribution at each point x along the horizontal axis.
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Draw the graph of y = x² – 4x + 3. Identify the intercepts (x and y), the vertex, and the axis of symmetry.
Answer:
y-intercept : 3
x-intercepts are 1 and 2
Vertex is at (2,-1)
Axis of symmetry is at x = 2
Step-by-step explanation:
See attached graph.
The equation y = x² – 4x + 3 represents a parabola
y-intercept at is at B(0,3); y-intercept is 3
x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3
The vertex is the lowest point on this parabola (2-1)
Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2
If ABC~ DEF, what is the scale factor of ABC to DEF?
Answer:
that would be 1/2 because its the only one that could reduce the numbers.
Step-by-step explanation:
hope this helps,
kleann
The scale factor of the triangle ΔABC to ΔDEF will be 1/2. Then the correct option is A.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The triangle ΔABC is similar to the triangle ΔDEF. Then the ratio of the corresponding sides will be constant. Then the scale factor is calculated as,
SF = 10 / 20
SF = 1 / 2
The scale factor of the triangle ΔABC to ΔDEF will be 1/2. Then the correct option is A.
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The radius of a circle is 3 inches. What is the area of a sector bounded by a central angle measuring 240°?
Answer:
the area of the sector is 6π square inches.
Step-by-step explanation:
First, we need to find the length of the arc that bounds the sector.
The circumference of the circle is 2πr, where r is the radius, so the circumference of this circle is 2π(3) = 6π inches.
To find the length of the arc that bounds the sector, we need to find what fraction of the circumference the central angle measures. The whole circle has a central angle of 360°, so if the central angle of the sector is 240°, then the fraction of the circle that it bounds is 240°/360° = 2/3.
Therefore, the length of the arc that bounds the sector is (2/3) * 6π = 4π inches.
Now, to find the area of the sector, we need to use the formula:
area of sector = (central angle / 360°) * πr^2
Plugging in the values we have:
area of sector = (240° / 360°) * π(3)^2
area of sector = (2/3) * 9π
area of sector = 6π
So the area of the sector is 6π square inches.
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over the time interval 0
Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.
To find the maximum displacement, we need to first determine the particle's velocity and acceleration.
The velocity of the particle is given by the derivative of its position function:
\(v(t) = y'(t) = 3t^2 - 12t + 9\)
The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12
Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.
This occurs when its velocity is zero:
\(3t^2 - 12t + 9 = 0\)
Simplifying this equation, we get:
\(t^2 - 4t + 3 = 0\)
This quadratic equation factors as:
(t - 1)(t - 3) = 0
So the particle comes to rest at t = 1 or t = 3.
Next, we need to determine whether the particle is at a maximum or minimum at each of these times.
To do this, we look at the sign of the acceleration:
When t = 1, a(1) = 6(1) - 12 = -6, which is negative.
Therefore, the particle is at a maximum at t = 1.
When t = 3, a(3) = 6(3) - 12 = 6, which is positive.
Therefore, the particle is at a minimum at t = 3.
Finally, we need to find the displacement of the particle at each of these times:
\(y(1) = 1^3 - 6(1)^2 + 9(1) = 4\)
\(y(3) = 3^3 - 6(3)^2 + 9(3) = 0.\)
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Simplify.
6a2−4b2+4abc−9b2−4a2+8abc
Answer:
\(\huge\boxed{\sf 2a^2-13b^2+12abc}\)
Step-by-step explanation:
Given expression:\(=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}\)
Answer:
Hello! The answer is: \(2a^2 - 13b^2 + 12abc\)
Step-by-step explanation:
\(6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc\)
Rearrange to combine like terms:
\(6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc\)
Combine like terms:
\(2a^2 - 13b^2 + 12abc\)
what is 4 2/3 in a proper fraction.
Answer:
14/3(I believe you mean improper fraction)
Step-by-step explanation:
4 mutiply 3 plus 2
Suppose that the future price pt) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and t is thenumber of years from today.p (t) = 800(1.041)^tFind the initial price of the item.Does the function represent growth or decay?By what percent does the price change each year?
Answer:
The population function is given below as
\(P(t)=800(1.041)^t\)Step 1:
To figure out the initial price of the item, we will substitute the value of t=0
\(\begin{gathered} P(t)=800(1.041)^t \\ P(0)=800(1.041)^0 \\ p(0)=800\times1 \\ P(0)=800 \end{gathered}\)Hence,
The initial pice of the item is = $800
Step 2:
To determine if the function represents a growth or decay, we will use the relation below
The function for exponential growth is given below as
\(\begin{gathered} y=ab^t \\ b=1+r(\text{growth)} \\ b=1-r(\text{decay)} \end{gathered}\)By comparing coefficients, we can see that
\(b=1.041>1\)Hence,
The function represents GROWTH
STEP 3:
To figure out the percentage of price change each year, we will use the formula below
\(\text{percentage change=}\frac{new\text{ price-initial price}}{in\text{itial price}}\times100\%\)To figure out the thenew price, we will substitute the value of t=1
\(\begin{gathered} P(t)=800(1.041)^t \\ P(1)=800(1.041)^1 \\ P(1)=800\times1.041 \\ P(1)=832.8 \end{gathered}\)By substituting the values, we will have the percentage to be
\(\begin{gathered} \text{percentage change=}\frac{new\text{ price-initial price}}{in\text{itial price}}\times100\% \\ \text{percentage change}=\frac{P(1)-P(0)}{P(0)}\times100\% \\ \text{percentage change}=\frac{832.8-800}{800}\times100\% \\ \text{percentage change}=\frac{32.8}{800}\times100\% \\ \text{percentage change}=\frac{3280}{800}\% \\ \text{percentage change}=4.1\% \end{gathered}\)Hence,
The percentage = 4.1%
y= 4x - 3
How do I graph this equation?
Answer:
y intercept is -3, go up 4 over 1
Step-by-step explanation:
write the trigonometric expression in terms of sine and cosine
The trigonometric simplified form of sinθ secθ is tanθ.
To write the trigonometric expression sinθ secθ in terms of sine and cosine, we can use the reciprocal identity for secant:
secθ = 1/cosθ
Substituting this into the expression, we have:
sinθ secθ = sinθ (1/cosθ)
Now, to simplify the expression, we can multiply sinθ by 1/cosθ:
sinθ (1/cosθ) = sinθ/cosθ
Using the quotient identity for tangent, we can rewrite sinθ/cosθ as tanθ:
sinθ/cosθ = tanθ
Therefore, the simplified form of sinθ secθ is tanθ.
The complete question is:
Write the trigonometric expression in terms of sine and cosine, and then simplify.
sinθ secθ
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Let X1,..., Xn ~ F and let F be the empirical distribution function. Let a < b be fixed numbers and define theta = T(F) = F(b) - F(a). Let theta = T(Fn) = Fn(b) - Fn(a). Find the estimated standard error of theta. Find an expression for an approximate 1 - alpha confidence interval for theta.
The confidence interval is given by: [F(b) - F(a)] - z_alpha/2 * sqrt{ [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n } <= theta <= [F(b) - F(a)] + z_alpha/2 * sqrt{ [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n }
Find the estimated standard error of theta?The estimated standard error of theta can be found using the following formula:
SE(theta) = sqrt{ [F(b)(1 - F(b)) / n] + [F(a)(1 - F(a)) / n] }
where n is the sample size.
To find an approximate 1 - alpha confidence interval for theta, we first need to find the standard error of the estimator. Let X1, X2, ..., Xn be the random sample. Then, the estimator T(Fn) is given by:
T(Fn) = Fn(b) - Fn(a)
The variance of T(Fn) can be estimated as:
Var(T(Fn)) = Var(Fn(b) - Fn(a)) = Var(Fn(b)) + Var(Fn(a)) - 2Cov(Fn(b), Fn(a))
Using the fact that Fn is a step function with jumps of size 1/n at each observation, we can calculate the variances and covariance as:
Var(Fn(x)) = Fn(x)(1 - Fn(x)) / n
Cov(Fn(b), Fn(a)) = - Fn(a)(F(b) - F(a)) / n
Substituting these into the expression for Var(T(Fn)), we get:
Var(T(Fn)) = [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)(F(b) - F(a))] / n
Simplifying this expression, we get:
Var(T(Fn)) = [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n
Now, the standard error of T(Fn) can be calculated as the square root of the variance:
SE(T(Fn)) = sqrt{ [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n }
To construct an approximate 1 - alpha confidence interval for theta, we use the following formula:
T(Fn) +/- z_alpha/2 * SE(T(Fn))
where z_alpha/2 is the (1 - alpha/2)th quantile of the standard normal distribution. Therefore, the confidence interval is given by:
[F(b) - F(a)] - z_alpha/2 * sqrt{ [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n } <= theta <= [F(b) - F(a)] + z_alpha/2 * sqrt{ [F(b)(1 - F(b)) + F(a)(1 - F(a)) - 2F(a)F(b) + 2F(a)^2] / n }
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Find the volume of a cone with a base diameter of 6 in and a height of 7 in.
Use the value 3.14 for , and do not do any rounding.
Be sure to include the correct unit in your answer.
Answer:
65.94cubic inch
Step-by-step explanation:
volume of cone = 1/3πr²h
=1/3×3.14×3²×7
=3.14×3×7
= 3.14×21
=65.95
unit is inch
then
65.94cubic inch
Help please and Thankyou
a) A square with sides of length 8 units, sits on a graph with is lower left hand corner at the origin. This square is translated 5 units up,and 7 units left. What are the coordinates of the upper right hand corner after translation.
b) Explain
Answer: not correct reset an-[ERROR]
Step-by-step explanation:
Identify the height of a triangle in which b=(x−2) m and A=(x2−4) m2. A) h = (2x + 4) m B) h = (2x + 2) m C) h = (x + 2) m D) h = (x + 4) m
The height of the given triangle is given by option c) h = (x+2)m.
Given the triangle with base b = (x - 2) m and area A = (x² - 4) m²,
we are to determine the height of the triangle using the formula for the area of a triangle.
Area of a triangle = (1/2) × base × height
We have the base and area of the triangle, but the height is unknown.
Therefore, let's find the height of the triangle, h.
A = (1/2) × b × h(x² - 4)
= (1/2) × (x - 2) × h
h = [(x²- 4) / (x - 2)] × 2h
= [(x - 2)(x + 2)] / (x - 2)h
= x + 2
Therefore, the height of the triangle is h = x + 2, which is option C). h = (x + 2) m.
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Compare A and B, if 120 % of A is equal to 150 and 105 % of B is equal to 165.
A....B
The comparison between A and B is as follows:A < B.
We are given that:120 % of A is equal to 150 => (120/100)A = 150
Divide both sides by 120/100: A = 150 × 100/120 = 125
And, 105 % of B is equal to 165 => (105/100)B = 165
Divide both sides by 105/100: B = 165 × 100/105 = 157.14
Therefore, A = 125 and B = 157.14
Compare A and B:It can be seen that B is greater than A. Therefore, B > A. Hence, the comparison between A and B is as follows:A < B.
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Find the slope of a line if it goes through (2, 5) and (-2,9)
Hello!
The slope of a line is found using the following formula:
\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{9-5}{-2-2}\)
\(m=\frac{4}{-4}\\m=-1\)
So the slope is -1.
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\(GraceRosalia\)
Where is the meidpoint
What is the midnumber between 1 and 7 ?
( 1 + 7 ) ÷ 2 =
8 ÷ 2 = 4
That was the direction now tell me what is the midpoint of point A and point B ?
midpoint of AB = ( A + B ) ÷ 2
m o AB = ( ( 14 , 15 ) + ( - 2 , 9 ) ) ÷ 2
m o AB = ( ( 14 - 2 , 15 + 9 ) ) ÷ 2
m o AB = ( ( 12 , 24 ) ) ÷ 2
m o AB = ( 12 ÷ 2 , 24 ÷ 2 )
m o AB = ( 6 , 12 )
0.0063 x 100 i do not know what I’m doing-
Answer:
0.63
Step-by-step explanation:
0.0063×100
you will move the point two times to the right hand side (backward )
it will be 0.63
Write an algebraic expression for the verbal expression
the quotient for 45 and r
Answer:
45/r
Step-by-step explanation:
You're just doing 45 divided by r.
A truck can be rented from company. How many miles must be driven in a day to make the rental cost for a company a better deal than company b
We have the following parameter
Company A
The charges is given by
\(\begin{gathered} \text{ 120 + }0.8x \\ \text{where x is the number of miles} \end{gathered}\)Company B
The charges is given by
\(60+0.9x\)To determine how many miles it will take for the rental cost of company A to exceed B, we will set up the inequality
\(120+0.8x<60+0.9x\)To find the number of miles, we will make x the subject of the formula
\(\begin{gathered} 120-60<0.9x-0.8x \\ 60<0.1x \end{gathered}\)Re-arranging
\(\begin{gathered} 0.1x>60 \\ x>\frac{60}{0.1} \\ x>600\text{ miles} \end{gathered}\)Therefore, for the rental cost of company A to be better than company B, the number of miles driven in a day must be greater than 600 miles
The graph represents the relationship between the number of employees scheduled per estimated customer at a restaurant.
The table represents the relationship between the number of employees scheduled per estimated customer at a grocery store
Answer: 8 8 4
Step-by-step explanation:the first one is 8 then 8 and then 4
The answers will be ;
a) No. of customers , one employee can help at restaurant is 5.
b) No. of customers , one employee can help at grocery store is 12.
c) The grocery rate of customer per employee is 7 more than restaurant's rate.
A graph for restaurant is given and a table for grocery store is given which represents relation of no. of employees per customer.
We have to solve the subparts of the given question.
What will be the rate if there are 12 customers per 2 employee at a shop ?
The rate at the shop will be 12 ÷ 2 or 6 customers per employee.
As per the question ;
Graph for restaurant is given and a table for grocery store is given.
a)
At restaurant ;
For 2 employees , no. of customers = 10
For 4 employees , no. of customers = 20
So ,
With increase of 2 in number of employees , no. of customers increases by 10.
⇒ No. of customers , one employee can help at restaurant is ;
= 10 ÷ 2
= 5 customers
b)
At grocery store ;
For 2 employees , no. of customers = 24
For 4 employees , no. of customers = 48
So ,
With increase of 2 in number of employees , no. of customers increases by 24.
⇒ No. of customers , one employee can help at grocery store is ;
= 24 ÷ 2
= 12 customers
c)
So ,
The restaurant rate of customers per employee = 5 customers/employee
The grocery store rate of customers per employee = 12 customers / employee
And
The grocery rate of customer per employee is more than restaurant rate by ;
= 12 - 5
= 7
Thus , the answers will be ;
a) No. of customers , one employee can help at restaurant is 5.
b) No. of customers , one employee can help at grocery store is 12.
c) The grocery rate of customer per employee is 7 more than restaurant's rate.
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Did I do it right ? I NEED HELP
Answer:
The correct y-increment should be 50 instead of 1, and it will solve the problem.
Hence, you are right!
Step-by-step explanation:
Yes, you did right.Because with Min. x=0 and Max. x=20 and with increment 5 the x values will be:
x=0x=5x=10x=15x=20Now, putting all the x-values in the equation
y=10x+50
For x=0
y=10(0)+50=50
so, for x=0, the value of y=50 i.e. (0, 50)
For x=5
y=10(5)+50=100
so, for x=5, the value of y=100 i.e. (5, 100)
For x=10
y=10(10)+50=150
so, for x=10, the value of y=150 i.e. (10, 150)
For x=15
y=10(15)+50=200
so, for x=15, the value of y=200 i.e. (15, 200)
For x=20
y=10(20)+50=250
so, for x=20, the value of y=250 i.e. (20, 250)
It means, for every x-increment of 5 units, the y-increment goes to 50 units.
Therefore, the correct y-increment should be 50 instead of 1, and it will solve the problem.
Hence, you are right!
Use the present value method to select the more cost-effective remediation from two options. Assume a discount rate of 7%. (Hint: When converting annual O&M to present value, an alternative approach is to use tabulated value for the conversion, or use the for- mula P = A [((1 + i)¹ − 1)/i (1 + i)¹] to convert from annual O&M to the present value). = $500K, annual O&M = $15K, salvage value = $50K, life expec- Option 1: Capital cost tancy = 15 years. Option 2: Capital cost = $350K, annual O&M = $10K, equipment replacement $20K every 3 years, salvage value = $5K, life expectancy = 15 years.
The present value method is the more cost-effective remediation method from two options. To determine the present value method for the above option, the given annual O&M needs to be converted into present value.
Given data:
Option 1:Capital cost = $500KAnnual O&M = $15KSalvage value = $50KLife expectancy = 15 yearsDiscount rate = 7%
Option 2:
Capital cost = $350KAnnual O&M = $10KEquipment replacement cost = $20K every 3 yearsSalvage value = $5KLife expectancy = 15 yearsDiscount rate = 7%We can use the below formula for calculating the present value of an annual O&M.P = A [((1 + i)¹ − 1)/i (1 + i)¹]Where,P = Present valueA = Annual O&M ratei = Discount rateOption 1:Present value of Annual O&M:P = A [((1 + i)¹ − 1)/i (1 + i)¹]P = 15,000 [((1 + 0.07)¹⁵ − 1)/0.07 (1 + 0.07)¹⁵]P = 15,000 [7.4693]P = $112,039.50Present value of Salvage value:
P = A [((1 + i)¹ − 1)/i (1 + i)¹]P = 50,000 [((1 + 0.07)¹⁵ − 1)/0.07 (1 + 0.07)¹⁵]P = 50,000 [0.4255]P = $21,276.46Total present value for option 1 = $500K + $112,039.50 - $21,276.46 = $590,763.04
Option 2:
Present value of Annual O&M
:P = A [((1 + i)¹ − 1)/i (1 + i)¹]P = 10,000 [((1 + 0.07)¹⁵ − 1)/0.07 (1 + 0.07)¹⁵]P = 10,000 [5.1395]P = $51,395.26Present value of Salvage value:
P = A [((1 + i)¹ − 1)/i (1 + i)¹]P = 5,000 [((1 + 0.07)¹⁵ − 1)/0.07 (1 + 0.07)¹⁵]P = 5,000 [0.2128]
P = $1,063.91Equipment replacement cost every 3 years needs to be converted into present value:P = A [((1 + i)¹ − 1)/i (1 + i)¹]
P = 20,000 [((1 + 0.07)³ − 1)/0.07 (1 + 0.07)³]P = 20,000 [2.5273]P = $50,546.82
Total present value for option 2 = $350K + $51,395.26 + $50,546.82 - $1,063.91 = $450,877.17Therefore, the more cost-effective remediation method is Option 2, as it has a lower present value of cost of remediation as compared to option 1.
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pls help asap!!! Find the value of z
Effect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. 625p2 − x2 =100
If 37000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number. ) (Hint: To find the value of p when x = 37, solve the supply equation for p when x = 37. )
The supply of average eggs is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.
The equation given states that the weekly supply x (in thousands of cartons) of a certain brand of medium-sized eggs is related to the wholesale price p (in dollars/carton) by the following equation: 625p2 − x2 =100. In order to determine the rate at which the supply is changing, we must first calculate the value of p when x = 37,000, which is the number of cartons available at the beginning of the week. To do this, we can solve the equation for p when x = 37,000\(p = (100 + x2)1/2/625\). When x=37,000, p=3.65. Therefore, if the price is falling at the rate of 7¢/carton/week, then the new price p = 3.65 - 0.07 = 3.58. When we plug this new value of p into the supply equation, we get\(x^2\) = 4,225. Taking the square root of both sides gives us x = 65. Therefore, the supply is decreasing at a rate of approximately -550 cartons per week as the price decreases 7 cents per carton per week.
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