1. Depreciation expense = $7,400 per year
2. Incremental net operating income = $10,000 per year
3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
4. The simple rate of return on the new bottling machine is 13.5%.
What is investment?Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.
Annual Depreciation Expense:
The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:
Depreciation expense = (Cost of the machine - Salvage value) / Useful life
Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year
Annual Incremental Net Operating Income:
To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.
Annual operating cost of the old machine = $19,000
Annual operating cost of the new machine = $9,000
Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine
Incremental net operating income = $19,000 - $9,000 = $10,000 per year
Initial Investment:
The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
Simple Rate of Return:
The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.
Simple rate of return = Annual incremental net operating income / Initial investment
Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)
Therefore, the simple rate of return on the new bottling machine is 13.5%.
To know more about investment:
https://brainly.com/question/17252319
#SPJ1
1. Depreciation expense = $7,400 per year
2. Incremental net operating income = $10,000 per year
3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
4. The simple rate of return on the new bottling machine is 13.5%.
What is investment?
Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.
Annual Depreciation Expense:
The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:
Depreciation expense = (Cost of the machine - Salvage value) / Useful life
Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year
Annual Incremental Net Operating Income:
To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.
Annual operating cost of the old machine = $19,000
Annual operating cost of the new machine = $9,000
Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine
Incremental net operating income = $19,000 - $9,000 = $10,000 per year
Initial Investment:
The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
Simple Rate of Return:
The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.
Simple rate of return = Annual incremental net operating income / Initial investment
Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)
Therefore, the simple rate of return on the new bottling machine is 13.5%.
To know more about investment:
brainly.com/question/17252319
#SPJ1
Fred, a frequent business traveler, is considering signing up for a hotel rewards program.
Hotel Elegance is currently offering 881 points for signing up, plus 22 points for every night
Fred books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 851
points, plus 23 points per night. If Fred books a certain number of nights, the points he earns
with either hotel will be the same. How many points will he have? How many nights will that
be?
If Fred books a certain number of nights, If Fred books 30 nights at either hotel, he will earn 1,661 points.
What are the points?
Let's assume that Fred books "n" nights at the hotel.
For Hotel Elegance, the total number of points that Fred will earn is:
881 + 22n
For Hotel Paradiso, the total number of points that Fred will earn is:
851 + 23n
According to the problem, Fred will earn the same number of points at both hotels if:
881 + 22n = 851 + 23n
Solving for "n", we get:
n = 30
Therefore, if Fred books 30 nights at either hotel, he will earn the same number of points. To find out how many points he will earn, we can substitute "n=30" into either equation:
For Hotel Elegance:
881 + 22n = 881 + 22(30) = 1,661 points
For Hotel Paradiso:
851 + 23n = 851 + 23(30) = 1,621 points
Therefore, if Fred books 30 nights at either hotel, he will earn 1,661 points.
To know more about points, visit:
https://brainly.com/question/14765384
#SPJ1
Describe the number of faces, edges, and vertices of a
math book.
Answer:
Step-by-step explanation:
I can cover this, so a math book is a rectangle, I hope you knew that, there is the front, back, and sides of a math book, given 2 faces and 4 sides of a book, there will be 6 faces, now for the vertices, there are 6 faces, so the edges will make 8 vertices, a vertex is where 2 or more edges meet, so now we will count the edges, given the 6 faces, we can count all of the edges and end up with 8 edges, I hope this helped you
Please I want answer!
The subtraction expression for each length is given as follows:
OB = 3 - (-3).AB = 4 - (-2).How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance OB is given as follows:
OB = sqrt((3 - (-3))² + (4 - 4)²)
OB = 3 - (-3).
The distance AB is given as follows:
AB = sqrt((-2 - (-2))² + (4 - (-2))²)
AB = 4 - (-2)
More can be learned about the distance between two points at https://brainly.com/question/30347465
#SPJ1
Sin and cos
Solve: 2 sin ϕ cos ϕ + 2 sin ϕ + cos ϕ + 1 = 0 for 0 < ϕ < 2π
Answer:
We can start by using the identity 2 sin ϕ cos ϕ = sin 2ϕ to simplify the left-hand side of the equation:
2 sin ϕ cos ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + cos ϕ + 1
Next, we can use another identity, sin^2 ϕ + cos^2 ϕ = 1, to eliminate the cosine term:
sin 2ϕ + 2 sin ϕ + cos ϕ + 1 = sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1
Now, we can substitute u = sin ϕ to obtain a quadratic equation in u:
sin 2ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1 = sin^2 ϕ + 2 sin ϕ + √(1 - sin^2 ϕ) + 1
sin 2ϕ = sin^2 ϕ
2 sin ϕ cos ϕ = sin^2 ϕ - cos^2 ϕ
2 u √(1 - u^2) = u^2 - (1 - u^2)
2 u √(1 - u^2) = 2 u^2 - 1
4 u^2 (1 - u^2) = (2 u^2 - 1)^2
4 u^4 - 4 u^2 + 1 = 0
This is a quadratic equation in u^2, which can be solved using the quadratic formula:
u^2 = [4 ± √(16 - 16)] / 8 = 1/2 or u^2 = 1
Since 0 < ϕ < 2π, we have 0 < u < 1, so u^2 = 1/2. Therefore, sin ϕ = u = ±√(1/2) and cos ϕ = ±√(1 - u^2) = ±√(1/2).
We can summarize the solutions as follows:
sin ϕ = √(1/2) or sin ϕ = -√(1/2)
cos ϕ = √(1/2) or cos ϕ = -√(1/2)
Therefore
what is the volume of this figure ?
The volume of the figure is 1795.5 m³.
How to find the volume of the figure?The volume of the figure can be found as follows:
volume of the figure = base area × height
Therefore, the base of the figure is a trapezium.
Hence,
base area = 1 / 2 (a + b)h
where
a and b are the basesh = height of the pyramidTherefore,
base area = 1 / 2 (11 + 16)9.5
base area = 1 / 2 (27)9.5
base area = 256.5 / 2
base area = 128.25
Hence,
volume of the figure = 128.25 × 14
volume of the figure = 1795.5 m³
learn more on volume here: https://brainly.com/question/17101095
#SPJ1
HELPPPP PLEASEEEEEEEEE
So, the length of WZ is 24 in kite WXYZ with diagonals WY and XZ.
What is triangle?A triangle is a closed, two-dimensional geometric shape that is formed by three line segments, called sides, that intersect at three points, called vertices. Triangles are one of the most basic shapes in geometry and are studied extensively in mathematics. The properties of triangles depend on the length of their sides and the size of their angles. Triangles can be classified based on the length of their sides as equilateral, isosceles, or scalene, and based on the size of their angles as acute, right, or obtuse. In an equilateral triangle, all three sides are of equal length. In an isosceles triangle, two sides are of equal length, while the third side is of a different length. In a scalene triangle, all three sides are of different lengths.
Here,
Since WXYZ is a kite, we know that its diagonals, WY and XZ, intersect at a right angle and bisect each other. Let M be the point of intersection of the diagonals, so that MW = MY and MX = MZ.
We can use the Pythagorean theorem to find MW and MX, and then use the fact that they are equal to find WZ.
Using the Pythagorean theorem in right triangles WMX and WMY, we have:
MW² = WX² - MX²
= 17² - 5²
= 264
MY² = WY² - MW²
= 13² - 264
= 25
MX² = XZ² - MZ²
= 17² - 13²
= 144
Since MW = MY, we have MW = √(25)
= 5
Therefore, WZ = 2MX
= 2√(144)
= 2*12
= 24
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
Graph of polygon ABCDE with vertices at negative 1 comma negative 4, negative 1 comma negative 1, 3 comma negative 1, 3 comma negative 4, 1 comma negative 6. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma negative 4, 13 comma negative 1, 9 comma negative 1, 9 comma negative 4, 11 comma negative 6.
Determine the line of reflection.
Reflection across the x-axis
Reflection across x = 6
Reflection across y = −3
Reflection across the y-axis
The reflection line that maps polygon ABCDE to polygon A' B' C' D' E' is the y-axis.
What do you mean by reflective line?The image is reflected through a line known as a reflection line. A pattern is said to mirror another pattern, and then every point in the pattern is equidistant from every corresponding point in the other pattern. The reflected image must be the same shape and size, but the image is in the opposite direction.
In order to determine the line of reflection that maps polygon ABCDE to polygon A' B' C' D' E', we must find a symmetrical line equidistant from each corresponding pair of points. If you project the image across the x-axis, vertex A (-1, -4) is mapped to A' (13, -4) and vertex E (1, -6) is mapped to E'. (11, 6). Therefore, the reflection line must be the x-axis.
If we map the image to the cross x=6, vertex A (-1, -4) would correspond to A' (13, -4) and vertex E (1, -6) would correspond to E' (3, 6). ). Therefore, the reflection line cannot be x=6.
If we project the pattern perpendicular to y=-3, the point A (-1, -4) is opposite to the point A' (-7, -4) and the vertex E (1, -6) to the point E . (7, 6). Therefore, the reflection line cannot be y=-3.
If you project the image across the y-axis, point A (-1, -4) is mapped to point A' (-13, -4) and vertex E (1, -6) is mapped to E. (-11 , 6). Therefore, the reflection line must be the y-axis.
Therefore, the reflection line that maps polygon ABCDE to polygon A' B' C' D' E' is the y-axis.
Learn more about Reflection line here
https://brainly.com/question/29248743
#SPJ1
Can you please show your work
The average velocity is given by the displacement during the time thus,[3, 4]: Average Velocity = 40 m/s. [3, 3.5]: Average Velocity = 40 m/s. [3, 3.1]: Average Velocity = 40 m/s. [3,3.01]: Average Velocity = 40 m/s.
What is speed and velocity?Unaffected by direction, speed is a scalar quantity that describes how quickly an object is travelling. The speed and direction of an object's motion are both described by its velocity, which is a vector quantity. In other terms, velocity is the rate of positional change of an object in a specific direction. Therefore, if two objects are travelling in separate directions or if one is accelerating while the other is not, they can have the same speed but distinct velocities.
The average velocity is given by the displacement during the time, thus we have:
Displacement = h(t2) - h(t1) = (40t2 - 0.8312) - (40t1 - 0.8312) = 40(t2 - t1)
Now, the average velocity between t2 - t1 is:
Average Velocity = Displacement / Duration = 40(t2 - t1) / (t2 - t1) = 40 m/s
Using the different values of t2 and t1 we see that:
[3, 4]:
Average Velocity = 40 m/s
[3, 3.5]:
Average Velocity = 40 m/s
[3, 3.1]:
Average Velocity = 40 m/s
[3,3.01]:
Average Velocity = 40 m/s
[3, 3.001]:
Average Velocity = 40 m/s
Learn more about average velocity here:
https://brainly.com/question/862972
#SPJ1
What’s the answer????
The equation of the circle in standard form with a center at (-6, 5) and passing through the point (-11, 3) is (x + 6)² + (y - 5)² = 29.
What is the equation of the circle?
The equation of a circle in standard form with a center at (h, k) and a radius r is:
(x - h)² + (y - k)² = r²
Center: (h, k) = (-6, 5)
Point on circle: (-11, 3)
Substituting these values into the standard form equation:
(x - (-6))² + (y - 5)² = r²
(x + 6)² + (y - 5)² = r²
Now we need to find the value of r, which is the radius of the circle.
The distance between the center (-6, 5) and the point (-11, 3) is equal to the radius of the circle.
Using the distance formula:
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-11 - (-6))² + (3 - 5)²)
r = √((-5)² + (-2)²)
r = √(25 + 4)
r = √29
r² = 29
The equation of the circle:
(x - h)² + (y - k)² = r²
(x + 6)² + (y - 5)² = 29
Learn more about equation of circle here: https://brainly.com/question/1506955
#SPJ1
What two numbers multiply to -35 and add to get -18
he two numbers that multiply to -35 and add to get -18 are -5 and 3.
To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.
Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:
-5 + 3 = -2
So, -5 and 3 are the two numbers that multiply to -35 and add to -18.
What number decreased by 25% is equal to 7?
the dahlia is the national of Mexico. a florist sold bouquets of dahlias to 15 of the first 20 customers who came into his shop. Based on the experimental probability, how many bouquets of dahlias should the florist expect to sell on a day with 120 customers?
120 × 5 ÷ 20
= 120 × 5/20
= 6 × 15
= 90 Answer.
The number of dahlias should the florist expect to sell on a day with 120 customers is 90 bouquets.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Sold bouquets=15
Total customers=120
Now,
In this case, the number of successful outcomes is 15, and the number of total outcomes is 20.
So the experimental probability is:
2015=43
To find the expected number of bouquets of dahlias to sell on a day with 120 customers, you need to multiply the experimental probability by the number of customers.
In this case, you need to multiply 3/4 by 120:
3/4×120=3×120/4
=360/4
=90
Therefore, by the unitary method the answer will be 90 bouquets
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and
the probability of obtaining a success. Round your answer to four decimal places.
P(X ≤ 3).n = 7, p = 0.4
The probability of success for given number of trials is 0.4751.
What is probability?
Probability can be used to determine the likelihood of an event. The likelihood that an event will happen is the only useful outcome. a scale where 0 indicates impossibility and 1 indicates a specific occurrence.
We know that the probability is given by:
P = nCx * [tex]p^{x}[/tex] * [tex]q^{n-x}[/tex]
P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)
Now,
⇒ P(0) = 7C0 * [tex]0.4^{0}[/tex] * [tex]0.6^{7}[/tex]
⇒ P(0) = 1 * 1 * 0.0279936
⇒ P(0) = 0.02799
Similarly,
⇒ P(1) = 7C1 * [tex]0.4^{1}[/tex] * [tex]0.6^{6}[/tex]
⇒ P(1) = 7 * 0.4 * 0.046656
⇒ P(1) = 0.13064
Similarly,
⇒ P(2) = 7C2 * [tex]0.4^{2}[/tex] * [tex]0.6^{5}[/tex]
⇒ P(2) = 21 * 0.16 * 0.07776
⇒ P(2) = 0.02613
Similarly,
⇒ P(3) = 7C3 * [tex]0.4^{3}[/tex] * [tex]0.6^{4}[/tex]
⇒ P(3) = 35 * 0.064 * 0.1296
⇒ P(3) = 0.2903
So, now we get
⇒ P (x ≤ 3) = P(0) + P(1) + P(2) + P(3)
⇒ P (x ≤ 3) = 0.02799 + 0.13064 + 0.02613 + 0.2903
⇒ P (x ≤ 3) = 0.4751
Hence, the probability of success for given number of trials is 0.4751.
Learn more about probability from the given link
https://brainly.com/question/29848579
#SPJ1
A company uses six filling machines of the same make and model to place detergent into cartons that show a label of 32 ounces. The production manager has complained that the six machines do not place the same amount of fill into the cartons. A consultant requested that 20 filled cartons be selected randomly from each of the six machines and the content of each carton carefully weighed. The response is the deviation from 32 ounces.
(a) Is this study experimental, observations, or mixed?
(b) Identify all factors, factor levels, and factor-level combinations. For each factor indicate if it is experi- mental or observational.
(c) What type of design is being implemented here?
(d) We import the data and display the structure of the dataframe. We also coerse the variable Machine to a factor, and display the factor levels.
(a) This study is observational because the consultant is not manipulating any variables or imposing treatments on the machines.
(b) The factors are:
Machine (experimental factor): There are six machines, labeled A through F.
Carton (observational factor): There are 20 cartons selected randomly from each machine.
Deviation from 32 ounces (response variable): This is the weight difference between the actual fill amount and the target fill amount of 32 ounces.
The factor levels are:
Machine: A, B, C, D, E, F
Carton: 1, 2, 3, ..., 20
The factor-level combinations are all possible pairs of machine and carton, such as A-1, A-2, ..., F-20.
(c) This is a nested design because the 20 cartons selected from each machine are not interchangeable between machines.
(d) Here's an example code snippet in R to import the data and display the structure of the dataframe:
data <- read.csv("filling_machine_data.csv")
data$Machine <- factor(data$Machine)
levels(data$Machine)
Assuming the data is stored in a CSV file called "filling_machine_data.csv", the code reads in the data, coerces the Machine variable to a factor, and displays the factor levels of Machine
learn about deviation,
https://brainly.com/question/475676
#SPJ11
The decimal grid shown below is shaded and marked with Xs to model an expression
(Picture shown below)
Which expression could be modeled by this decimal grid?
A. 0.20 x 0.30
B. 0.020 x0.030
C. 0.020 x 0.30
D. 0.20 x 0.030
The expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator).
We have a total of 10 columns and 10 rows.
Total boxes = 10×10 ⇒ 100
Number of shaded boxes = 3×10 ⇒ 30
Each box contains X's out of 100 that is:
= 30/100
= 0.30
We can represent a number of columns in decimal such that:
= 20/100 = 0.20
The expression becomes 0.20×0.30.
Thus, the expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.
Learn more about expression
brainly.com/question/14083225
#SPJ1
Need help will give brainliest and 5 stars! :)
Answer:
2.362
Step-by-step explanation:
Use calculator: 2.361727836
Round: 2.362
Suppose the probability that an adult watches the news at least once per week is 0.60. We randomly survey 8 people. Let X = the number that watch the news at least once per week. Find the probability that at least 6 adults watch the news.
The answer of the given question based on the probability is , the probability that at least 6 adults watch the news is approximately 0.755.
What is Probability?Probability is measure of likelihood or chance of event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability is used to analyze random experiments and events, and it is an essential concept in statistics, mathematics, and many other fields.
This is a binomial probability problem, where X follows a binomial distribution with n = 8 and p = 0.60. We want to find the probability that at least 6 adults watch the news, which can be written as:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ...
To solve , we use binomial probability formula:
P(X = k) =(n choose k) *p^k *(1 - p)^(n - k)
where "n choose k" is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Using this formula, we can find the probabilities for each value of k:
P(X = 6) = (8 choose 6) * 0.60⁶ * 0.40² = 0.311
P(X = 7) = (8 choose 7) * 0.60⁷ * 0.40¹ = 0.276
P(X = 8) = (8 choose 8) * 0.60⁸ * 0.40⁰ = 0.168
Note that we can also use binomial probability table or calculator with binomial probability function to find the probabilities.
Then, we can add these probabilities to get the probability that at least 6 adults watch the news:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ... = 0.311 + 0.276 + 0.168 + ...
This is a infinite series, but we can stop at P(X = 8) since the probabilities become very small after that.
P(X ≥ 6) = 0.755
Therefore, the probability that at least 6 adults watch the news is approximately 0.755.
To know more about Binomial probability visit:
https://brainly.com/question/30764478
#SPJ1
4. A rectangular prism has height of 2¾ cm, the length is 1¼ cm and the height 4 cm, what is the volume?
Answer:
13.75 cm³
Step-by-step explanation:
In order to find the area of a rectangular prism you only need to multiply the width height and length together:
2.75 * 1.25 = 3.4375
3.4375 * 4 = 13.75
Hope this helps!
6) Given the points A(-4, 5) and B(6, 0), find
bolthe coordinates of the point P on the line
segment AB that partitions AB into the
ratio 2:3. Plot P along with segment AB.
Answer: (0, 3)
If you don't know how to do this or have difficulties doing these types of of Questions Please visit: youtu.be/XBktwjl6swg
What are the solution(s) of -1/2x + 4 = x+1
Answer:
2
Step-by-step explanation:
just did it on end 2022 test quiz
32 to the power of negative 4 fifths
Answer:
0.0625
Step-by-step explanation:
hope this helps :)
look at the picture.
Answer:
Using order of operations:
[tex] \frac{12a}{2} - 3a \times 5[/tex]
[tex]6a - 3a(5)[/tex]
[tex]6a - 15a = - 9a[/tex]
[tex] - 9 \times 4 = - 36[/tex]
can anyone help please either one
The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d
How many students know the rumor on day 0Here, the number of students are the students that start the rumor i.e. Susanna and Liz
So, we have
JB = 2 studentsRihanna = 2 studentsHow many students know the rumor on day 2For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day
So, we have
JB day 2 = 2 + 5(2) = 7
For the Rihanna rumor, the rumor spreads at an exponential rate of 3
So, we have
Rihanna day 2 = 2 * (3)^2 = 18
Days for students to knowUsing the functions, we have
JB
2 + 5x = 32 students
5x = 30
x = 6 days
Rihanna
2(3)^x = 162 students
3^x = 81
x = ln(81)/ln(3)
x = 4 days
The function N for d daysJB
N(d) = 2 + 5d
Rihanna
N(d) = 2(3)^d
So, we have
d JB Rihanna
0 2 2
1 7 6
2 12 18
3 17 54
4 22 162
5 27 486
6 32 1458
7 37 4374
8 42 13122
9 47 39366
Read more about functions at
https://brainly.com/question/28532394
#SPJ1
If the area of a rectangle is 15x²+12x and
the length is 5x+4 find the width
Answer:
width = 3x
Step-by-step explanation:
Area of a rectangle = Length × width
Length = 5x + 4
Breadth = y
15x² + 12x = 5x + 4 × y
y = 15x² + 12x
---------------
5x + 4
y = 3x
please help with this question
The probability of the sample mean being less than 25.3 is given as follows:
0.9713 = 97.13%.
The sample mean would not be considered unusual, as it has a probability that is greater than 5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576[/tex]
The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:
Z = (25.3 - 25)/0.1576
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
1. Harold and his pet chicken, Simone, leave their home traveling by bicycle at a constant-
speed that allows them to cover 500 feet in 2 minutes.
a) Express the rate of speed of Harold and Simone traveling on their bicycle in feet per
minute.
In miles per hour.
Answer:
Step-by-step explanation:
minute= 250 per minute
mph = 1500/5280
1. What is 2x + 4 = 10?
A. x = 3
B. x = 4
C. x = 5
D. x = 6
2. 25 / 5 x 7 = ?
A. 175
B. 185
C. 195
D. 205
3. 100 - 50 + 10 - 5 = ?
A. 55
B. 60
C. 65
D. 70
4. 24 / 6 = ?
A. 4
B. 5
C. 6
D. 7
5. A triangle has base 6 inches and height 8 inches. What is the area?
A. 24 sq in
B. 32 sq in
C. 40 sq in
D. 48 sq in
6. What is the greatest common factor of 36 and 56?
A. 4
B. 8
C. 12
D. 16
7. What is the square root of 121?
A. 11
B. 12
C. 13
D. 14
8. If 2x + 4 = 14, what is x?
A. 5
B. 6
C. 7
D. 8
9. (3x - 5) + (7x + 1) = ?
A. 10x - 4
B. 11x - 4
C. 12x - 4
D. 13x - 4
10. What fraction is 5/12?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Required Answers :
1. 2x + 4 = 10
[tex]\: :\implies [/tex] 2x = 10 - 4
[tex]\: :\implies [/tex] 2x = 6
[tex]\: :\implies [/tex] x = 6/2
[tex]\: :\implies [/tex] x = 3.
Hence, Option (A) x = 3 is the answer.
2. 25/5 × 7 = ?
[tex]\: :\implies [/tex] 5 × 7
[tex]\: :\implies [/tex] 175/5
[tex]\: :\implies [/tex] 35
Hence, The required answer is 35.
3. 100 - 50 + 10 - 5 = ?
[tex]\: :\implies [/tex] 50 + 5
[tex]\: :\implies [/tex] 55
Hence, Option (A) 55 is the answer.
4. 24 / 6 = ?
[tex]\: :\implies [/tex] 24 ÷ 6
[tex]\: :\implies [/tex] 4
Hence, Option (A) 4 is the answer.
5. A triangle has base 6 inches and height 8 inches. What is the area?
Area of triangle = ½ × Base × Height
[tex]\: :\implies [/tex] 1/2 × 6 × 8
[tex]\: :\implies [/tex] 1/2 × 48
[tex]\: :\implies [/tex] 48/2
[tex]\: :\implies [/tex] 24 sq. in
Hence, Option (A) 24 sq in is the answer.
6. What is the greatest common factor of 36 and 56?
36 = 1,2,3,4,6,9,12, 18 and 36.
56 = 1,2,4,7,8,14,28 and 56.
Hence, Option (A) 4 is the answer.
7. What is the square root of 121?
[tex]\: :\implies [/tex] 11 × 11
[tex]\: :\implies [/tex] 121
Hence, (A) 11 is the answer
8. If 2x + 4 = 14, what is x?
[tex]\: :\implies [/tex] 2x + 4 = 14
[tex]\: :\implies [/tex] 2x = 14 - 4
[tex]\: :\implies [/tex] 2x = 10
[tex]\: :\implies [/tex] x = 10/2
[tex]\: :\implies [/tex] x = 5
Hence, Option (A) 5 is the answer
9. (3x - 5) + (7x + 1) = ?
[tex]\: :\implies [/tex] 3x - 5 + 7x + 1
[tex]\: :\implies [/tex] 10x - 5 + 1
[tex]\: :\implies [/tex] 10x - 4
Hence, Option (A) 10x - 4 is the answer.
10. What fraction is 5/12?
[tex]\: :\implies [/tex] 1/2 (approximately)
Hence, Option (A) 1/2 is the answer.
If the volume of the sphere below is 36 in3, what is the volume of a hemisphere of the same ball?
Answer:
R = 3
Step-by-step explanation:
V = 4 π r³/3 = 36
Multiply both of the sides by 3
4π · r³ =108 πcm³
Now your going to divide by 4π
r³ = 27cm³
Square off the ³
r = 3
Lily has 4 cups of apples, 5-½ cups of watermelon, and cups of
grapes. She needs 2½ times of each fruit to make her fruit bowl. How
much of each fruit does she need? Do not round. Write your answer as
a whole number or as a mixed number. Use "/" as a fraction bar. Do
not label your answers.
a. Apples
b. Watermelons
c. Grapes
a. Apples: Lily needs 10 cups of apples for her fruit bowl.
b. Watermelons: Lily needs 13-3/4 cups of watermelons for her fruit bowl.
c. Grapes: The amount of grapes that Lily has is not given
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
To make her fruit bowl, Lily needs 2½ times the amount of each fruit she currently has.
a. Apples:
2½ × 4 cups = 10 cups
Therefore, Lily needs 10 cups of apples for her fruit bowl.
b. Watermelons:
2½ × 5-½ cups = (2 × 5 + 1/2) × 5/2 cups = 13-3/4 cups
Therefore, Lily needs 13-3/4 cups of watermelons for her fruit bowl.
c. Grapes:
The amount of grapes that Lily has is not given, so we cannot calculate how much she needs for her fruit bowl.
To learn more about arithmetic sequence from the given link:
https://brainly.com/question/15412619
#SPJ1
A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During
one particular week, the two cars went a combined total of 1725 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week?
First car: gallons
Second car: gallons
The first car consumed 15 gallons of gas
The second car consumed 30 gallons of gas during the week
To solve this problemLet's denote the number of gallons consumed by the first car as x, and the number of gallons consumed by the second car as y.
We know that the total gas consumption is 45 gallons, so:
x + y = 45
We also know that the total distance traveled is 1725 miles, and that the fuel efficiency (miles per gallon) of the first car is 35, and of the second car is 40. Using this information, we can write another equation:
35x + 40y = 1725
We now have two equations with two unknowns, which we can solve simultaneously to find x and y.
Multiplying the first equation by 35, we get:
35x + 35y = 1575
Subtracting this equation from the second equation, we get:
5y = 150
y = 30
Substituting y = 30 into the first equation, we get:
x + 30 = 45
x = 15
Therefore, the first car consumed 15 gallons of gas, and the second car consumed 30 gallons of gas during the week.
Learn more about equation here : brainly.com/question/28871326
#SPJ1
