The after-tax present worth according to the given values is $732,140.56 and the internal rate of return is 22.65%.
(a) To compute the after-tax present worth, we need to determine the net cash flow for each year and discount it to present value using the after-tax MARR of 15%.
Year 0: Initial cost of equipment = -$18,600
Years 1-10:
Revenue from bags = (100.3 bags/carton) x ($0.03/bag) x (200,000 cartons/year) = $120,780
Cost savings from reducing overfilling = (5.5%) x ($0.03/bag) x (200,000 cartons/year) = $3,300
Operating cost of equipment = -$16,000
Depreciation expense = -$1,800 (($18,600 - $3,600 salvage value) / 10 years)
Net cash flow for each year:
Year 0: -$18,600
Year 1: $107,280 ($120,780 + $3,300 - $16,000 - $1,800)
Year 2: $109,160 ($120,780 + $3,300 - $16,000 - $1,800)
...
Year 10: $113,640 ($120,780 + $3,300 - $16,000 - $1,800)
Discounting each year's net cash flow to present value and summing them up, we get:
PV = -$18,600 + ($107,280 / (1+0.15)^1) + ($109,160 / (1+0.15)^2) + ... + ($113,640 / (1+0.15)^10)
PV = -$18,600 + $750,740.56
PV = $732,140.56
Therefore, the after-tax present worth is $732,140.56.
(b) To compute the after-tax internal rate of return, we need to find the discount rate that makes the net present value equal to zero. We can use trial and error or a financial calculator to solve this.
Using trial and error, we find that a discount rate of approximately 22.65% makes the net present value equal to zero. Therefore, the after-tax internal rate of return is approximately 22.65%.
(c) To compute the after-tax simple payback period, we need to determine how long it takes for the cumulative net cash flow to equal the initial cost of the equipment.
Year 0: -$18,600
Year 1: $107,280
Year 2: $109,160
Year 3: $110,960
Year 4: $112,680
Year 5: $114,320
Year 6: $115,880
Year 7: $117,360
Year 8: $118,760
Year 9: $120,080
Year 10: $121,320
The cumulative net cash flow becomes positive in year 3, so the after-tax simple payback period is approximately 1.9 years (between year 2 and year 3).
To learn more about After-tax, visit:
https://brainly.com/question/25790997
#SPJ11
Consider the equation y=2x²+4x+26.
Part A. Find the value of the discriminant. Show your work.
Part B. Based on the value of the discriminant found in part A, how many real roots does y=2x³+4x+26 have?
Part C. Use the quadratic formula to find the values of x when y-o. Show each step.
Answer:
A. 4^2 - 4(2)(26) = 16 - 208 = -192
B. This equation has no real roots.
C. (-4 + √-192)/(2×2) = (-4 + 8i√3)/4
= -1 + (2√3)i
Helppp (Fill in all the blanks)
The answers are explained in the solution.
Given is a circle F,
The central angle = ∠GFH
The semicircle = arc GJI
The major arc = arc GJH
Since, the measure of semicircle is 180°, therefore,
The semicircle = arc GJI = 180°
We know that the measure of arc intercepted by the central angle is equal to the measure of the central angle.
Therefore, ∠GFH = 125°
Learn more about circles, click;
https://brainly.com/question/29142813
#SPJ1
There are 60 seats on a train. 35% of the seats are empty. How many empty seats are there on the train?
Answer:
21
Step-by-step explanation:
35% of 60=60% of 35
10% of 35=3.5
3.5*6=21
Which of the following is true regarding a regression model with multicollinearity, a high r2 value, and a low F-test significance level? a.The model is not a good prediction model. b.The high value of 2 is due to the multicollinearity. c.The interpretation of the coefficients is valuable. d.The significance level tests for the coefficients are not valid. e.The significance level for the F-test is not valid.
The correct answer is d. The significance level tests for the coefficients are not valid.
Multicollinearity is a statistical term that refers to the presence of high correlation among predictor variables in a regression model. This can cause issues in the model, such as unstable or unreliable coefficients, and can lead to incorrect conclusions about the relationships between the predictors and the response variable.
When multicollinearity is present, the R-squared value of the model can become inflated because the model is able to explain more of the variation in the response variable due to the high correlation among the predictor variables. This can give the impression that the model is a good predictor when in fact it may not be. Additionally, multicollinearity can cause the F-test significance level to be low, indicating that the model is a good fit, even though the individual coefficients may not be statistically significant.
Multicollinearity can cause inflated R-squared values and low F-test significance levels. However, it does not necessarily mean that the model is a poor predictor. The interpretation of coefficients may also be affected by multicollinearity.
However, the most significant issue with multicollinearity is that it can lead to unreliable significance tests for individual coefficients, making it difficult to determine which predictors are contributing significantly to the model.
To learn more about significance level visit: https://brainly.com/question/13947717
#SPJ11
Consider a random variable that can take values {1,2,3,4,5,6,7} with probabilities 0.1,0.1,0.15,0.15,0.15,0.15,0.2. How many bits, on average, will be required to encode this source using a Huffman code? a) 2.500 bits b) 2.771 bits c) 2.800 bits d) 3.771 bits
To find the average number of bits required to encode this source using a Huffman code, we need to first construct the Huffman code for the given probabilities. The Huffman code assigns shorter codes to more probable values and longer codes to less probable values. We can start by listing the probabilities in descending order:
0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1
Next, we group the two least probable values and assign them a code of 0. We then repeat this process, grouping the next two least probable values and assigning them a code of 10. We continue until we have assigned codes to all values:
7: 0
1: 1000
2: 1001
3: 1010
4: 1011
5: 110
6: 111
We can see that the average number of bits required to encode this source using the Huffman code is:
(0.2 x 1) + (0.1 x 4) + (0.1 x 4) + (0.15 x 4) + (0.15 x 4) + (0.15 x 3) + (0.2 x 3) = 2.771 bits
Therefore, the correct answer is b) 2.771 bits.
To find the average number of bits required to encode this source using a Huffman code, follow these steps:
1. Arrange the probabilities in descending order: 0.2, 0.15, 0.15, 0.15, 0.15, 0.1, 0.1.
2. Build the Huffman tree:
- Combine the two smallest probabilities (0.1 and 0.1) into a single node with a probability of 0.2.
- Combine the next two smallest probabilities (0.15 and 0.15) into a single node with a probability of 0.3.
- Combine the next smallest probability (0.2) with the previously created 0.2 nodes to create a node with a probability of 0.4.
- Combine the remaining 0.3 and 0.4 nodes to create the root node with a probability of 0.7.
3. Assign binary codes to each value based on the Huffman tree:
- Value 1: 111
- Value 2: 110
- Value 3: 101
- Value 4: 100
- Value 5: 011
- Value 6: 010
- Value 7: 00
4. Calculate the average number of bits required to encode the source using the assigned binary codes and their probabilities:
- (3 * 0.1) + (3 * 0.1) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (3 * 0.15) + (2 * 0.2) = 0.9 + 0.9 + 1.35 + 1.35 + 0.4 = 2.771 bits
So, the average number of bits required to encode this source using a Huffman code is 2.771 bits, which corresponds to option (b).
Learn more about average here:- brainly.com/question/27646993.
#SPJ11
Look at the transformation from the green triangle to the blue triangle
Draw and label the "Line of Reflection."
Describe the transformation from green triangle to blue triangle in words
The reflection from green triangle to blue triangle is a reflection over the x-axis
What is reflection over x-axis?Reflecting a two-dimensional shape over the x-axis is a geometric transformation that represents an image flipping or mirroring itself across the fixed x-axis.
This axis appears as the horizontal marker in a Cartesian coordinate system, providing the reference line to then split the plane into its top and bottom elements.
When which this action is fullfilled, all the y-coordinates of each point within the figure will be reversed while the x-coordinate remains unchanged;
The image of the reflection is attached and the reflection line labeled
Learn more about reflection over x-axis at
https://brainly.com/question/28655129
#SPJ1
Assume there are 14 homes in the Quail Creek area and 5 of them have a security system. Three homes are selected at random: a. What is the probability all three of the selected homes have a security system? (Round your answer to 4 decimal places.)
The probability is approximately 0.0549 or 5.49%. So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.
To answer your question, we'll use the concept of probability. In this case, we want to find the probability that all three randomly selected homes in the Quail Creek area have a security system.
1. First, determine the probability that the first home has a security system:
There are 5 homes with security systems out of 14 total homes, so the probability is 5/14.
2. Next, determine the probability that the second home also has a security system:
Since one home with a security system has been "selected," there are now 4 homes with security systems out of the remaining 13 homes. So, the probability is 4/13.
3. Finally, determine the probability that the third home has a security system:
Since two homes with security systems have been "selected," there are 3 homes with security systems left out of the remaining 12 homes. So, the probability is 3/12, which simplifies to 1/4.
4. Multiply the probabilities from steps 1, 2, and 3 to get the probability that all three selected homes have a security system:
(5/14) * (4/13) * (1/4) = 20/364.
5. Round your answer to 4 decimal places:
The probability is approximately 0.0549 or 5.49%.
So, there is a 5.49% probability that all three randomly selected homes in the Quail Creek area have a security system.
Learn more about probability here:
brainly.com/question/27342429
#SPJ11
An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?
40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches
Answer:
To find the dimensions of the actual painting, we need to use the scale factor of 4:1. This means that the actual dimensions of the painting are four times larger than the scaled dimensions.
Let's start with the width of the actual painting:
8 inches (scaled width) × 4 = 32 inches (actual width)
Now, let's find the height of the actual painting:
10 inches (scaled height) × 4 = 40 inches (actual height)
Therefore, the dimensions of the actual painting are 32 inches by 40 inches.
Solve each system by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure described in this section.
2x 1+4x 2=−4 5x1+7x 2=11
The solution to the system is [tex]$\$\left(x_{-} 1, x_{-} 2\right)=(4,-3) \$$[/tex].
To solve the system, we can use the method of elimination or Gaussian elimination.
We start by writing the system in augmented matrix form:
[tex]$$\left[\begin{array}{cc|c}2 & 4 & -4 \\5 & 7 & 11\end{array}\right]$$[/tex]
We can eliminate the [tex]$\$ x_{-} 1 \$$[/tex] variable from the second equation by subtracting 5 times the first equation from the second:
[tex]$$\left[\begin{array}{cc|c}2 & 4 & -4 \\5-5(2) & 7-5(4) & 11-5(-4)\end{array}\right] \Rightarrow\left[\begin{array}{cc|c}2 & 4 & -4 \\-3 & -13 & 31\end{array}\right]$$[/tex]
Next, we can eliminate the [tex]$\$ x_{-} 2 \$[/tex]$ variable from the first equation by subtracting twice the second equation from the first:
[tex]$$\left[\begin{array}{cc|c}2-2(-13) & 4-2(7) & -4-2(31) \\-3 & -13 & 31\end{array}\right] \Rightarrow\left[\begin{array}{cc|c}28 & -10 & -66 \\-3 & -13 & 31\end{array}\right]$$[/tex]
We can simplify this further by dividing the first row by 2 :
[tex]$$\left[\begin{array}{cc|c}14 & -5 & -33 \\-3 & -13 & 31\end{array}\right]$$[/tex]
Now we can solve for [tex]$\$ x_{-} 2 \$$[/tex] in terms of [tex]$\$ x_{-} 1 \$$[/tex] by multiplying the first equation by 13 and adding it to the second equation:
[tex]$$13(14) x_1-13(5) x_2-13(33)-3(-13) x_1-3(-13) x_2=13(31)-3(14) x_1$$[/tex]
Simplifying:
[tex]$$\begin{aligned}& 169 x_1-91 x_2-429+39 x_1+39 x_2=403 \\& 208 x_1=832 \\& x_1=4\end{aligned}$$[/tex]
Substituting back into the first equation, we get:
[tex]$$2(4)+4 x_2=-4 \Rightarrow x_2=-3$$[/tex]
Therefore, the solution to the system is [tex]$\$\left(x_{-} 1, x_{-} 2\right)=(4,-3) \$$[/tex].
To learn more about elimination visit:
https://brainly.com/question/29625952
#SPJ11
At a construction site, the brace used to retain a wall is 9.6 m in length. The distance from the wall to the lower end of the brace (on the ground) is 5.3 m. Calculate the angle at which the brace meets the wall.
The angle at which the brace meets the wall is approximately 56.51 degrees.
To calculate the angle at which the brace meets the wall at a construction site, we can use the right triangle trigonometry. Here, the brace is the hypotenuse of a right-angled triangle, with the distance from the wall to the lower end of the brace being one of the legs. We will use these terms: construction, brace, and angle in our explanation.
Step 1: Identify the given measurements
- Length of the brace (hypotenuse) = 9.6 m
- Distance from the wall to the lower end of the brace (adjacent leg) = 5.3 m
Step 2: Use the cosine function to find the angle
cos(angle) = adjacent leg / hypotenuse
cos(angle) = 5.3 m / 9.6 m
Step 3: Calculate the angle using the inverse cosine function
angle = cos^(-1)(5.3 m / 9.6 m)
Step 4: Find the angle using a calculator
angle ≈ cos^(-1)(0.5521) ≈ 56.51°
So, at the construction site, the angle at which the brace meets the wall is approximately 56.51 degrees.
inverse cosine functionhttps://brainly.com/question/31149456
#SPJ11
A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1200 square meters, what is the width of the path?
Answer:
The area of the pool is 10*20 = 200 square meters. Let's assume the width of the path is x. Then the dimensions of the entire region would be (10+2x) by (20+2x). The area of the entire region would be (10+2x)*(20+2x) = 400 + 60x + 4x^2. We know that the area of the pool and the path combined is 1200 square meters. So we can set up the equation as follows:
200 + 1200 = 400 + 60x + 4x^2
Simplifying the equation, we get:
4x^2 + 60x - 1000 = 0
Dividing both sides by 4, we get:
x^2 + 15x - 250 = 0
Factoring the equation, we get:
(x + 25)(x - 10) = 0
x = 10 or x = -25
Since the width of the path can't be negative, the width of the path is 10 meters.
Step-by-step explanation:
Mark Brainliest!!
You started your day out with $120 in your bank account. You paid your electricity bill that was $67. Then, you went out with friends and spent $44 on your night out. On your way home, you stopped and purchased gas for $35. How much do you have to deposit into your bank account to not receive an overdraft fee?
You need to deposit at least $74 into your bank account to avoid an overdraft fee.
We have,
Start with the initial balance = $120
Subtract the first expense, the electricity bill = $120 - $67 = $53
Subtract the second expense, the night out with friends = $53 - $44 = $9
Subtract the third expense, the gas purchase = $9 - $35 = -$26
Now,
Since the remaining balance is negative, you would receive an overdraft fee if you left it at this amount.
To avoid the overdraft fee, you need to deposit enough money to bring your account balance back to $0 or higher.
To do this, you need to add the absolute value of the negative balance to your desired minimum balance, which in this case is:
$0 = |-26| + $0 = $26
Therefore,
You need to deposit at least $74 into your bank account to avoid an overdraft fee.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Write a Variable equation for each sentence
Danika's new running route is 4 miles longer than
her old route.
Answer:
Let x be the length of Danika's old running route in miles.
Then, her new running route can be represented by x + 4, since it is 4 miles longer than her old route.
Step-by-step explanation:
11. Solve the following inequality Express your answer in interval notation. 2x - 75 5x + 2
The answer for the following inequality expressed in interval notation is (-77/3, infinity)
To solve the inequality 2x - 75 < 5x + 2,
we need to isolate the variable x on one side of the inequality sign.
Starting with 2x - 75 < 5x + 2:
Subtracting 2x from both sides:
-75 < 3x + 2
Subtracting 2 from both sides:
-77 < 3x
Dividing both sides by 3 (and flipping the inequality sign because we are dividing by a negative number):
x > -77/3
So the solution to the inequality is x > -77/3.
Expressing this in interval notation, we have:
(-77/3, infinity)
Learn more about inequality: https://brainly.com/question/25275758
#SPJ11
1. A train 600 m long is running at the speed of 40 km/hr. Find the time taken by it to pass a man standing near the railway line. Not yet answered A 54 B. 10 sec C. 15 sec D. 10.5
The time taken by the train to pass the man is 54 seconds
To find the time taken by the train to pass a man standing near the railway line, we need to convert the train's speed to meters per second and then use the formula time = distance/speed.
1. Convert the speed of the train from km/hr to m/s: 40 km/hr * (1000 m/km) / (3600 s/hr) = 40000/3600 = 40/3.6 = 10/0.9 = 100/9 m/s.
2. Now, use the formula: time = distance/speed. The distance is the length of the train (600 m) and the speed is 100/9 m/s.
time = 600 m / (100/9 m/s) = 600 * 9 / 100 = 54 seconds.
Therefore, the time taken by the train to pass the man is 54 seconds (Option A).
To learn more about Time and speed visit
https://brainly.com/question/13388824
#SPJ11
2,8km a m:
27,55dm a m:
27,9hm a m:
275dam a m:
The conversions are :
a) 2.8 km = 2800 m.
b) 27.55 dm = 2.755 m.
c) 27.9 hm = 2790 m.
d) 275 dam = 2750 m.
What is the conversion about?By multiplying the value by 1000 will help us to change kilometers (km) to meters (m). In order to change decimeters into meters, it is necessary to divide the figure by 10.
To convert, Note that:
km = kilometers m = meters,d= decimetershm = hectometersdam =decameters
a) 2.8 km to m:
= 2.8 x 1000 m
= 2800 m
b) 27.55 dm to m:
= 27.55 ÷ 10 m
= 2.755 m
c) 27.9 hm to m:
= 27.9 x 100 m
= 2790 m
d) 275 dam to m:
= 275 x 10 m
= 2750 m
Learn more about conversion from
https://brainly.com/question/97386
#SPJ1
Convert the following to meter
2,8km
27,55dm
27,9hm
275dam
eleanor robson regarding plimpton 322, she lists six criteria for interpreting ancient mathematical texts what are the 6 criteria
The 6 criteria are Internal consistency, Contextual consistency, Intelligibility, Mathematical plausibility, Historical plausibility and Replicability.
According to Eleanor Robson's interpretation of Plimpton 322, she lists six criteria for interpreting ancient mathematical texts. These six criteria are as follows:
1. Internal consistency: The mathematical text should be internally consistent and coherent in its logic.
2. Contextual consistency: The mathematical text should be consistent with the historical and cultural context in which it was written.
3. Intelligibility: The mathematical text should be understandable and intelligible to the intended audience.
4. Mathematical plausibility: The mathematical content of the text should be mathematically plausible and in line with known mathematical principles.
5. Historical plausibility: The mathematical text should be historically plausible and fit within the known historical context.
6. Replicability: The mathematical text should be replicable, meaning that other mathematicians should be able to reproduce the calculations and results presented in the text.
Learn more about the mathematical text here: brainly.com/question/1146295
#SPJ11
4. Find maximum/minimum / Inflection points for the function y = 5 sin x + 3x Show all work including your tests for max/min. (0 < x < 2phi )
The points of inflection are (0, 3π), (π, 4π), and (2π, 9π).
To find the maximum/minimum and inflection points of the function y = 5 sin x + 3x, we need to take the first and second derivatives of the function with respect to x, and then find the critical points and points of inflection by setting these derivatives equal to zero.
First derivative:
y' = 5 cos x + 3
Setting y' = 0 to find critical points:
5 cos x + 3 = 0
cos x = -3/5
Using a calculator or reference table, we can find the two values of x between 0 and 2π that satisfy this equation: x ≈ 2.300 and x ≈ 3.840.
Second derivative:
y'' = -5 sin x
At x = 2.300, y'' < 0, so we have a local maximum.
At x = 3.840, y'' > 0, so we have a local
To check whether these are global maxima/minima, we need to examine the behavior of the function near the endpoints of the interval 0 < x < 2π.
When x = 0, y = 0 + 0 = 0.
When x = 2π, y = 5 sin (2π) + 6π = 6π, since sin(2π) = 0.
So the function is increasing on the interval [0, 2.300], reaches a local maximum at x = 2.300, is decreasing on the interval [2.300, 3.840], reaches a local minimum at x = 3.840, and then is increasing on the interval [3.840, 2π]. Therefore, the maximum value of the function occurs at x = 2π, where y = 6π, and the minimum value of the function occurs at x = 3.840, where y ≈ 1.221.
To find the points of inflection, we set y'' = 0:
-5 sin x = 0
This equation is satisfied when x = 0, π, and 2π. We can use the second derivative test to determine whether these are points of inflection or not.
At x = 0, y'' = 0, so we need to examine the behavior of the function near x = 0.
When x is close to 0 from the right, y is positive and increasing, so we have a point of inflection at x = 0.
At x = π, y'' = 0, so we need to examine the behavior of the function near x = π.
When x is close to π from the left, y is negative and decreasing, so we have a point of inflection at x = π.
At x = 2π, y'' = 0, so we need to examine the behavior of the function near x = 2π.
When x is close to 2π from the right, y is positive and increasing, so we have a point of inflection at x = 2π.
Therefore, the points of inflection are (0, 3π), (π, 4π), and (2π, 9π).
To learn more about minimum visit:
https://brainly.com/question/21426575
#SPJ11
Plane A has just 1 ton of fuel left and has requested plane B to refuel it. Plane B has 21 tons of fuel. Fuel transfer happens at the rate of 1 ton per minute. Use this information as you work through the activity and find how long it will take to refuel plane A until both planes have the same amount of fuel. Let x be the time in minutes and y be the amount of fuel in tons. The equation y = x + 1 represents the quantity of fuel with respect to time in plane A, and y = -x + 21 represents the quantity of fuel with respect to time in plane B. For each equation, find two points that satisfy the equation
The time for which plane B will take to refuel plane A is equals to 10 minutes. The two points who satisfy the equation, y = x + 1, are (0, 1), (-1,0). The two points who satisfy the equation, y = -x + 21, are (0,21), (21,0).
We have a fuel left in Plane A = 1 ton
fuel left in Plane B = 21 tons
Fuel transfer rate = 1 ton per minute
In order that for them to have the same amount of fuel, We add up the fuel left in Plane A and Plane B = 21 + 1 = 22 tons. This implies each plane will have fuel of 11 tons. Time that plane B will take to refuel plane A until both planes have the same amount of fuel is calculated by : Plane B will transfer 10 tons of fuel to A.
Plan A has a total of 11 tons. Since, the transfer rate = 1 ton per minute
=> 1 ton will transfer in 1 minute
So, 10 tons fuel will need 10 minutes. Hence, required time value is 10 minutes. Now, The equation for quantity of fuel with respect to time in plane A is, y = x + 1 --(1). If x = 0 => y = 1
and y = 0 => x = -1. So, (0, 1) and (-1,0).
The equation for quantity of fuel with respect to time in plane B is, y = -x + 21 --(2). For it, x = 0 => y = 21 and y= 0 => x = 21. Hence, two points that satisfy the equation(1) and equation(2) are (0, 1), (-1,0) and (0,21), (21,0) respectively.
For more information about time, visit:
https://brainly.com/question/31020192
#SPJ4
Five students enter a school talent competition the scatter plot shows the number of hours each student has rehearsed and the score of the students Calculate the balance point of the data
The balance point of the data, given the number of hours rehearsed and the score would be (5, 50).
How to find the balance point ?The balance point on the graph is simply the average of the x vertices and the y vertices.
The average of the x vertices is:
= ( 1 + 3 + 4 + 8 + 9 ) / 5
= 25 / 5
= 5
The average of the y vertices is:
= ( 30 + 50 + 20 + 90 + 60 ) / 5
= 250 / 5
= 50
This then means that the balance point would be ( 5, 50 ).
Find out more on balance point at https://brainly.com/question/27142077
#SPJ1
Factor the expression, and use the factors to find the x-intercepts of the quadratic relationship it represents. Type the correct answer each box, starting with the intercept with the lower value The x- intercepts occur where x = and x =
The factors to the given expression are -1(x+3)(x-8)
The x-intercepts of the quadratic relationship are -3, 8. When we write an expression in its factors and multiplying those factors gives us the original expression, then this process is known as factorization.
How do we factorize the given expression?
We equate the given expression to f(x)
(-[tex]x^{2}[/tex] + 5x + 24) = f(x)
⇒ -1([tex]x^{2}[/tex] - 5x - 24) = f(x)
⇒ -1([tex]x^{2}[/tex] - (8-3)x - 24) = f(x)
⇒ -1([tex]x^{2}[/tex] + 3x - 8x -24) = f(x)
⇒ -1(x(x+3) -8(x+3)) = f(x)
⇒ -1(x+3)(x-8) = f(x)
∴The factor to the given expression is -1(x+3)(x-8)
How do we find the x-intercepts?
We equate f(x) = 0 to find the x-intercepts.
⇒ -1(x+3)(x-8) = 0
⇒ (x+3)(x-8) = 0
The roots of the above equation are x-intercepts.
Therefore, the x-intercepts occur where x = -3 and x = 8
To learn more about the x-intercepts;
brainly.com/question/3951754
#SPJ4
The complete question is "Factor the expression (-x^2 + 5x + 24.) and use the factors to find the x-intercepts of the quadratic relationship it represents.
Type the correct answer in each box, starting with the intercept with the lower value.
The x-intercepts occur where x =
and x = "
Using the following data, determine if the normal distribution gives a reasonable approximation: 71 42 77 84 46 93 94 63 82 88 57 32 79 67 68 83 60 65 58 70 Calculate the mean and standard deviation for these data using the appropriate equations. Compare these values to those you would get from the distribution line that you draw through the data by eye.
Hi, I'm glad to help you with this question. To determine if the normal distribution gives a reasonable approximation using the given data, we need to calculate the mean and standard deviation. Here are the steps:
1. Calculate the mean (average): Add all the data points together and divide by the number of data points.
(71+42+77+84+46+93+94+63+82+88+57+32+79+67+68+83+60+65+58+70) / 20 = 1380 / 20 = 69
Mean = 69
2. Calculate the standard deviation: First, find the difference between each data point and the mean, square the differences, and then find the average of those squared differences. Finally, take the square root of that average.
a. Differences from the mean: (-2, 27, 8, 15, -23, 24, 25, -6, 13, 19, -12, -37, 10, -2, -1, 14, -9, -4, -11, 1)
b. Squared differences: (4, 729, 64, 225, 529, 576, 625, 36, 169, 361, 144, 1369, 100, 4, 1, 196, 81, 16, 121, 1)
c. Average of squared differences: (4520) / 20 = 226
d. Square root of the average: √226 ≈ 15.03
Standard Deviation ≈ 15.03
Now that we have the mean (69) and the standard deviation (15.03), you can compare these values to the distribution line that you draw through the data by eye. If the distribution line follows a bell-shaped curve with the mean at the center and the data points spread around it following the standard deviation, then the normal distribution provides a reasonable approximation for this data set.
#SPJ11
Standard deviation:https://brainly.com/question/475676
The chart below represents data collected from 10 eighth grade boys
showing their height in inches and their weight in pounds.
Height
(inches)
60 63 65 61 70 55 58 61 64 57
Weight
(pounds) 125 139 155 136 170 108 116 139 129 121
Which statement best describes the association between height and
weight of the ten boys?
A. The data shows a negative, linear association.
B. The data shows a positive, linear association.
C. The data shows a non-linear association.
D. The data shows no association.
B. The data shows a positive, linear association.
To determine the association between height and weight of the ten boys, we will first observe the data points provided. We can compare the increase or decrease in height with the corresponding increase or decrease in weight to identify a pattern.
Here's a list of height and weight pairs:
(60, 125), (63, 139), (65, 155), (61, 136), (70, 170), (55, 108), (58, 116), (61, 139), (64, 129), (57, 121)
Upon observing these pairs, we can see that as height increases, weight generally increases as well. For example, when height increases from 55 inches to 70 inches, weight increases from 108 pounds to 170 pounds. This pattern can also be seen in other data pairs.
This means that there is a direct relationship between the height and weight of the boys, where taller boys tend to weigh more, and shorter boys tend to weigh less.
To learn more about linear association : brainly.com/question/29299187
#SPJ11
I NEED HELP ASAP
BRAINIEST WILL GET 10 POINTS!!!
PLEASE ITS DUE IN MINUTS
Answer:
1) 4 pounds / $5.48 = .73 pounds / dollar
2) 5 pounds / $4.85 = 1.03 pounds / dollar
3) $3.51 / 3 pounds = $1.17 / pound
4) $9.12 / 6 pounds = $1.52 / pound
pls help me with Question B only
a. The nth term of the sequence is 11 - 3n.
b. The nth term of the sequence is 14- 5n.
How to find the nth term of a sequence?The sequence is an arithmetic progression. Therefore, the expression for the sequence can be represented as follows:
nth term = a + (n + 1)d
where
n = number of termsd = common differencea = first termTherefore,
a.
a = 8
d = 11 - 8 = - 3
Therefore,
nth term = 8 + (n - 1)-3
nth term = 8 - 3n + 3
nth term = 11 - 3n
b.
a = 19
d = 14 - 19 = -5
nth term = 19 + (n - 1)-5
nth term = 19 - 5n - 5
nth term = 14 - 5n
learn more on sequence here: https://brainly.com/question/1582366
#SPJ1
Henry predicted whether he got answers right or wrong in his 50 question exam.
He identified the 31 questions he thought he got right.
It turns out that Henry got 6 questions wrong that he thought he got correct and he only got 12 of the questions wrong he had predicted.
What is the percentage accuracy he had with predicting his scores?
You are going to cut a circle out of the triangle piece of wood below how much wood will be left over after you cut the circle if the base is six the height is five
Answer:
6.03
Step-by-step explanation:
In math terms, we can model the area left when cutting a circle out of a triangle as subtracting the area of a circle inscribed in a triangle.
There was only one side length of the triangle given (its base), so we can assume that it is an isosceles triangle with the given height.
To find the radius of the triangle, we can use the formula:
r = (A / s)
where r is the radius of the inscribed circle, A is the area of the triangle, and s is the semiperimeter (half-perimeter) of the triangle.
Finding the area of the triangle:
A = (1/2) * b * h
A = (1/2) * 6 * 5
A = 15
Finding the length of the congruent sides of the triangle:
[tex]a^2 + b^2 = c^2[/tex]
[tex]c^2 = 5^2 + 3^2[/tex]
[tex]c^2 = 34[/tex]
[tex]c \approx 5.83[/tex]
Finding the semiperimeter:
s = (side1 + side2 + side3) / 2
s = (5.83 + 5.83 + 6) / 2
s ≈ 8.83
Plugging these values into the radius formula:
r = A / s
r = 15 / 8.83
r ≈ 1.69
From here, we can get the area of the circle cutout:
A(circle) = πr²
A(circle) = π(1.69)²
A(circle) ≈ 8.97
Finally, we can get the leftover area by subtracting the area of the circle from the area of the triangle:
A = A(triangle) - A(circle)
A = 15 - 8.97
A = 6.03
find the equation of P
The equation of circle P include the following: D. x² + (y - 3)² = 4
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.By critically observing the graph of this circle, we have the following parameters:
Radius, r = 2 units.Center, (h, k) = (0, 3).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 2²
x² + (y - 3)² = 4.
Read more on equation of a circle here: brainly.com/question/15626679
#SPJ1
Given the linear inequality graph, which two statements are true? A) Point (8, 3) is a solution. B) The graph represents y < − 1 3 x + 5. C) The graph represents y ≤ 3x + 5. D) All points in the blue area are solutions. E) All points above the broken line are solutions.
Given the linear inequality graph, which two statements are true include the following:
B) The graph represents y < −1/3(x) + 5.
D) All points in the blue area are solutions.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 7)/(3 + 6)
Slope (m) = -3/9
Slope (m) = -1/3
At data point (3, 4) and a slope of -1/3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -1/3(x - 3)
y - 4 = x/3 + 1
y = x/3 + 5
y < x/3 + 5
Read more on point-slope here: brainly.com/question/24907633
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Find the exact value of the expressions (a) sec
sin−1 12
13
and (b) tan
sin−1 12
13
On solving this trigonometry, we find that (a) sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{13}{5}[/tex] and (b) tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{12}{5}[/tex]
(a) To find the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that sec(x) = [tex]\frac{1}{cos}[/tex](x). Let's draw a right triangle with opposite side 12 and hypotenuse 13. Using the Pythagorean theorem, we can find the adjacent side:
a² + b² = c²
a² + 12² = 13²
a² = 169 - 144
a = √25
a = 5
So our triangle has sides of length 5, 12, and 13. Now we can find cos(sin⁻¹ [tex]\frac{12}{13}[/tex]) by looking at the adjacent/hypotenuse ratio in this triangle:
cos(sin⁻¹ [tex]\frac{12}{13}[/tex]) = [tex]\frac{5}{13}[/tex]
Therefore, sec(sin⁻¹(12/13)) = 1/cos(sin⁻¹ [tex]\frac{12}{13}[/tex])
= 1/[tex]\frac{5}{13}[/tex]
= [tex]\frac{13}{5}[/tex].
So the exact value of sec(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{13}{5}[/tex].
(b) To find the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]), we can use the fact that tan(x) = sin(x)/cos(x). Let's use the same right triangle as before.
Then sin(sin⁻¹ [tex]\frac{12}{13}[/tex])= [tex]\frac{12}{13}[/tex] and cos [tex]\frac{12}{13}[/tex]) = [tex]\frac{5}{13}[/tex] , so
tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) = sin(sin⁻¹ [tex]\frac{12}{13}[/tex])/cos(sin⁻¹[tex]\frac{12}{13}[/tex])
= [tex]\frac{12}{13}[/tex] / [tex]\frac{5}{3}[/tex]
= [tex]\frac{12}{5}[/tex]
So the exact value of tan(sin⁻¹ [tex]\frac{12}{13}[/tex]) is [tex]\frac{12}{5}[/tex].
To learn more about trigonometry, refer to:
https://brainly.in/question/2685053
#SPJ4