[tex]\lim_{t\to 0} \det\left(\begin{bmatrix} \displaystyle \int_0^t \frac{u}{\sinh(u)} du & \cos(t) & \displaystyle \sum_{n=1}^{\infty} \frac{1}{n+t+i} \\ \displaystyle \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right) & \binom{5}{2} t^2 & \displaystyle \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right) \\ i\binom{5}{3} t^3 \sin(2t) & \displaystyle \sum_{n=1}^{5} n^2 e^{int} & \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) \end{bmatrix}\right)[/tex]
The limit of the determinant as [tex]t[/tex] approaches 0 is [tex]-\infty[/tex].
To evaluate this limit, we can use the fact that the determinant is a linear function of each row, and that the limit of a sum is the sum of the limits. Therefore, we can compute the limit of each row separately.
Starting with the first row, we have:
[tex]\lim_{t\to 0} \int_0^t \frac{u}{\sinh(u)} du
= \lim_{t\to 0} \frac{\int_0^t \frac{u}{\sinh(u)} du}{t} \cdot t
= \lim_{t\to 0} \frac{\frac{t}{\sinh(t)} - 1}{t} \cdot t
= \lim_{t\to 0} \frac{1-\sinh(t)}{t\sinh(t)} = 1[/tex]
[tex]\lim_{t\to 0} \cos(t)
= 1[/tex]
[tex]\lim_{t\to 0} \sum_{n=1}^{\infty} \frac{1}{n+t+i}
= \sum_{n=1}^{\infty} \lim_{t\to 0} \frac{1}{n+t+i}
= \sum_{n=1}^{\infty} \frac{1}{n+i}
= \psi(i+1) \approx 0.643 + 0.41i[/tex]
where [tex]\psi(z)[/tex] is the digamma function.
Therefore, the limit of the first row is [tex]1 \cdot 1 \cdot \psi(i+1) = \psi(i+1)[/tex].
Moving on to the second row, we have:
[tex]\lim_{t\to 0} \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)
= \lim_{t\to 0} \frac{e^t}{t} - \lim_{t\to 0} \frac{e^t}{t^2}
= 1 - \infty = -\infty[/tex]
[tex]\lim_{t\to 0} \binom{5}{2} t^2
= 0[/tex]
[tex]\lim_{t\to 0} \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right)
= \prod_{n=1}^4 \lim_{t\to 0} \left(\sqrt{1+nt} - 1\right)
= \prod_{n=1}^4 \sqrt{1+n} - 1
= 4\sqrt{2} - 5[/tex]
Therefore, the limit of the second row is [tex]-\infty \cdot 0 \cdot (4\sqrt{2} - 5) = 0[/tex].
Finally, for the third row, we have:
[tex]\lim_{t\to 0} i\binom{5}{3} t^3 \sin(2t) = 0[/tex]
[tex]\lim_{t\to 0} \sum_{n=1}^{5} n^2 e^{int}
= \sum_{n=1}^{5} n^2 \lim_{t\to 0} e^{int}
= \sum_{n=1}^{5} n^2
= 55[/tex]
[tex]\lim_{t\to 0} \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) = 28[/tex]
Therefore, the limit of the third row is [tex]0 \cdot 55 \cdot 28 = 0[/tex].
Putting everything together, we get:
[tex]\lim_{t\to 0} \det\left(\begin{bmatrix} \displaystyle \int_0^t \frac{u}{\sinh(u)} du & \cos(t) & \displaystyle \sum_{n=1}^{\infty} \frac{1}{n+t+i} \\ \displaystyle \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)
& \binom{5}{2} t^2 & \displaystyle \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right) \\ i\binom{5}{3} t^3 \sin(2t) & \displaystyle \sum_{n=1}^{5} n^2 e^{int} & \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) \end{bmatrix}\right) = \det\left(\begin{bmatrix} \psi(i+1) & 1 & 0 \\ -\infty & 0 & 4\sqrt{2}-5 \\ 0 & 55 & 28 \end{bmatrix}\right) = -\infty[/tex]
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need help on this please
Answer:
z = 8Step-by-step explanation:
To find:-
The value of z .Answer:-
We are here given that the right angle is made up of two angles viz 8z° and (3z+2)° .
As we know that the measure of a right angle is 90° , so the sum of the two angles would also be 90° . Hence here ,
→ 8z + 3z + 2 = 90
→ 11z + 2 = 90
→ 11z = 90-2
→ 11z = 88
→ z = 88/11
→ z = 8
Hence the value of z is 8 .
Suppose that Mars rotates on its axis once every hours. The equator lies on a circle with a diameter of miles.
(a) Find the angular speed of a point on its equator in radians per day ( hours).
(b) Find the linear speed of a point on the equator in miles per day.
Do not round any intermediate computations, and round your answer to the nearest whole number.
The answer of the given question based on the Angular speed is (a) the angular speed of a point on Mars' equator is π/2 radians per day. (b) the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.
What is Linear speed?Linear speed, also known as tangential speed, is the distance traveled by an object in a straight line per unit of time. It is the speed at which an object is moving along its path, tangent to the path at any given point. Linear speed is calculated by dividing the distance traveled by the time taken to travel that distance. The units of linear speed are typically expressed in meters per second (m/s), miles per hour (mph), or kilometers per hour (km/h), depending on the system of measurement used.
(a) The angular speed of a point on Mars' equator is the angle (in radians) that a point on the equator sweeps out as Mars rotates on its axis. Since Mars completes one rotation every 24 hours, the angular speed is:
angular speed =(2πradians)/ (24 hours)= π/12radians per hour
To find the angular speed in radians per day, we need to multiply by the number of hours in a day:
angular speed = (π/12 radians per hour) * (24 hours per day) = π/2 radians per day
Therefore, the angular speed of a point on Mars' equator is π/2 radians per day.
(b) The linear speed of a point on the equator is the distance traveled by a point on the equator in a certain amount of time. The distance traveled by a point on the equator in one rotation is equal to the circumference of the circle with a diameter of miles, which is:
C = πd = π(6794) ≈ 21343.98 miles
Since Mars rotates once every 24 hours, a point on the equator travels the circumference of the circle in 24 hours. Therefore, the linear speed of a point on the equator in miles per day is:
v = C/24 ≈ 889.33 miles/day
So the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.
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please help i will rate braainliest and 100 points
Answer:
1 : I will give you the first one answer and trying later to answer all as possible!Step-by-step explanation:
First one are given in attachment!Can someone please solve step by step. I'm having trouble understanding.
A multiple choice test consists of five questions, each of which has four choices. Each
question has exactly one correct answer. How many ways are there to fill out the answer sheet so that four answers are correct and one is incorrect?
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
What is possible way?It involves finding the most efficient and effective solution to a problem by exploring multiple options and assessing the pros and cons of each.
This can be found by calculating the number of possible ways to fill out the answer sheet.
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024..
To explain why this is happening, it is helpful to look at an example. Let's say the five questions are A, B, C, D, and E.
If a person wants to fill out the answer sheet so that four answers are correct and one is incorrect, they can either choose the correct answer for four of the questions, and then choose an incorrect answer for the fifth question, or they can choose the incorrect answer for four of the questions, and then choose the correct answer for the fifth question.
In terms of calculating the number of ways to fill out the answer sheet, this means that for each of the five questions, there are four possible ways to answer (four choices for each question). This means that there are 4
The answer to this question is 1024. This can be found by calculating the number of possible ways to fill out the answer sheet. Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
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(essay making) how important factoring polynomials in our lives
1. What is the relationship between AD and AB?
2. What is the relationship between ACD and BDC?
3. What is the relationship between AC and CB? Explain.
4. True or False? Because BD is the angle bisector of ABC, AB = CB
1. The Similarity between AD and AB is that AD is half the length of AB.
2. The areas of triangles ACD and BDC are equal.
3. We can say that if AC is the longest side, then CB is the shortest side
4. False, The relationship between AD and AB is that AD is half the length of AB.
What do you mean by Triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
1) Since D is the midpoint of AB, we know that AD and DB have the same length. Therefore, we can say that:
AD = DB
Substituting AB for AD + DB, we can simplify to:
AB = AD + AD
or
AB = 2AD
So, the relationship between AD and AB is that AD is half the length of AB.
2) The areas of triangles ACD and BDC are equal, and we can write:
Area of ACD = (1/2) * AC * AD
Area of BDC = (1/2) * BC * DB
Since AD = DB, we can substitute and get:
Area of BDC = (1/2) * BC * AD
So, we can see that the areas of ACD and BDC are equal, and their bases AD and DB have the same length. Therefore, triangles ACD and BDC are equal in area and shape (they are congruent).
3) we can say that if AC is the longest side, then CB is the shortest side
4) False,
The relationship between AD and AB is that AD is half the length of AB.
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What is the vertical distance between (5, –12) to (5, 17)?
5 units
29 units
–29 units
–5 units
The vertical distance between two points is just the distance between the two y coordinates. Distance is positive.
|-12|+17 = 29 units
Answer: the answer is 29 trust me
Step-by-step explanation: don't have time for explanation sorry
By using math to strategize and organize aspects of personal and professional life that involve numbers, such as budgets and other finances, individuals display their __________ skill.
The required answers to fill in the blank is Numeracy or mathematical.
What is Numeracy or mathematical skill ?Numeracy or mathematical skill is the ability to understand and use numbers to solve real-world problems. In personal and professional life, math skills are essential for managing finances, creating budgets, analyzing data, and making informed decisions.
By using math to plan and organize their finances, individuals can effectively manage their income, expenses, and savings. This skill also helps in making decisions related to investments, loans, and other financial products.
Developing math skills can lead to better financial stability, as well as improved problem-solving and decision-making abilities in various aspects of life.
Thus, required answers to fill in the blank is Numeracy or mathematical.
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2 + 5 + 8 + 11 + 14
Use the arithmetic explicit formula to find n for the number 14 in the sequence. Use the formula.
Write the arithmetic sum formula.
Using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.
What is an arithmetic sequence?An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,...
The common difference of the sequence is d, and the number an is the first term.
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
So, we have the sequence:
2, 5, 8, 11, 14
Common difference = 5 - 2 = 3
Then, the formual is:
aₙ = a + (n - 1)d
Then, insert values:
aₙ = a + (n - 1)d
a₁₄ = 2 + (14 - 1)3
a₁₄ = 2 + (13)3
a₁₄ = 2 + 39
a₁₄ = 41
Therefore, using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.
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helppp please
A population of bacteria is growing according to the equation p(t)=1000e^0.21t
Use a graphing calculator to estimate when the population will exceed 2627.
t =------------
The population will exceed 2627 after approximately 6.08 units of time.
What is logarithm?A lοgarithm is a mathematical functiοn that tells us what expοnent is needed tο prοduce a given number, when that number is expressed as a pοwer οf a fixed base. In οther wοrds, lοgarithms tell us hοw many times we need tο multiply the base by itself tο get the desired number.
To solve for t when the population exceeds 2627, we can set the equation equal to 2627 and solve for t:
p(t) = 1000[tex]e^{(0.21t)}[/tex] = 2627
Dividing both sides by 1000, we get:
[tex]e^{(0.21t)}[/tex] = 2.627
Taking the natural logarithm of both sides, we get:
0.21t = ln(2.627)
Solving for t, we get: t = ln(2.627)/0.21 ≈ 6.08
Therefore, the population will exceed 2627 after approximately 6.08 units of time.
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1. The table lists the length of time in seconds it takes for each student in Ms. Sousa's class to say the alphabet. Make a line plot of the data. 2. Meghan says the difference between the least amount of time it takes a student to say the alphabet and the greatest amount of time is 4 seconds. Do you agree? Explain.
Answer:
The file is attached below.
I disagree with Meghan.
Step-by-step explanation:
Hello!
The line plot is attached below.
I disagree with Meghan as the least amount of time someone recited the alphabet is 4 seconds and the greatest is 7.5 seconds.
The difference between these two numbers would be 3.5 seconds, which is not the same as 4 seconds.
how do it prove this without approximately calculating the logarithm ?
Answer:
[tex]10 < {e}^{8} [/tex]
[tex] ln(10) < 8[/tex]
[tex] ln(10) - 8 < 0[/tex]
Since ln(10) > 0, it follows that ln(10) + 1 > 0, and so:
[tex]( ln(10) + 1)( ln(10) - 8) < 0[/tex]
[tex] {( ln(10)) }^{2} - 7 ln(10) - 8 < 0[/tex]
[tex]( { ln(10) })^{2} - 7 ln(10) + 1 < - 9[/tex]
[tex] {( ln(10)) }^{2} + 2 ln(10) + 1 < 9 ln(10) - 9[/tex]
[tex] {( ln(10) )}^{2} + 2 ln(10) + 1 < 9( ln(10) - 1)[/tex]
(ln(10) + 1)^2 < 9(ln(10 - 1)
ln(10) + 1 < 3√(ln(10) - 1)
(1 + ln(10))/3 < √(ln(10) - 1)
√(ln(10) - 1) > (1+ ln(10))/3
can somebody please do this with proof?
The length of the side AC is 4.00cm
How to determine the valueWe have different trigonometric identities and their ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Line CD = hypotenuse
Line Cy = Opposite = 4cm
Using the sine identity, we have;
sin 45 = 4/CD
cross multiply
CD = 4/0. 7071
Divide the values
CD = 5. 66cm
To determine the length of AC
sin 45 = AC/5.66
cross multiply the values
AC =sin 45 ×5.66
AC = 0. 7071 × 5. 66
multiply the values
AC = 4. 00cm
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HWLP PLEASE HWLP ASAP!! SHOW WORK
The required perimeter of the given triangle is 23 units respectively.
What is the triangle?Triangles are closed, two-dimensional shapes with three sides, three angles, and three vertices.
A triangle is part of a polygon. A triangle is a polygonal form with three sides.
These points meet at the vertex, which forms an internal angle at the junction of two triangle sides.
Every triangle has three sides, three vertices, and three internal angles.
So, to get the perimeter of the triangle, count the unit as follows:
7 units + 7 units + 9 units
To find the triangle, we need to add the length of the 3 sides as follows:
7 + 7 + 9 = 23 units
Therefore, the required perimeter of the given triangle is 23 units respectively.
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A ferris wheel can accommodate 60 people in 25 minutes. How many people
could ride the ferris wheel in 4 hours? What was that rate per hour?
The rate per hour for the ferris wheel is 144 people per hour.
What is rate per hour?Your pay for each hour of labour is expressed as an hourly rate. You might need to estimate your income for other applications or modify your personal budget after comparing the hourly and salaried pay rates.
The ferris wheel can accommodate 60 people in 25 minutes.
To find out how many people could ride the ferris wheel in 4 hours, we need to convert 4 hours to minutes, since the given rate is in minutes.
1 hour = 60 minutes
4 hours = 4 x 60 minutes = 240 minutes
So, in 4 hours, the ferris wheel could accommodate 240/25 = 9.6 (rounded to the nearest whole number) cycles of 60 people.
The total number of people that could ride the ferris wheel in 4 hours would be 9.6 x 60 = 576 people.
Now, to find the rate per hour, we divide the total number of people (576) by the number of hours (4):
Rate per hour = Total number of people / Number of hours
Rate per hour = 576 / 4 = 144 people/hour
Therefore, the rate per hour for the ferris wheel is 144 people per hour.
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The rival football team is predicted to score 35 points at the next game. How many field
goals (3 points) and how many touchdowns (assume 7 points) does your team need to
score in order to win? Let f = field goal and t = touchdown. Create an inequality to
represent this situation and determine values for the variables in an organized way that
makes your inequality true. List at least 3 possible game winning combinations and
justify your answer.
To win the game, your team needs to score more than [tex]35[/tex] points, which means: 3f + 7t > 35 three possible game-winning combinations are:
[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]
[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]
[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]
Each of these combinations would result in your team scoring more than 35 points and winning the game.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).
For example, the argument [tex]"2x + 3 = 9"[/tex] asserts that the phrase [tex]"2x + 3"[/tex] equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that allows the equation to be true.
Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation. [tex]"x2 + 2x - 3 = 0."[/tex] Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Let's let f be the number of field goals scored by your team and t be the number of touchdowns scored by your team.
a) To win the game, your team needs to score more than 35 points, which means:
3f + 7t > 35
We can simplify this inequality by dividing both sides by 1:
3f + 7t/1 > 35/1
3f + 7t > 35
b) Now, we need to find possible values for f and t that make this inequality true. Since we are looking for positive integer values for f and t, we can start by testing different values for t and solving for f:
If t = 5, then 3f + 7(5) > 35, so 3f > 0 and f > 0. Possible solutions are f = 1, f = 2, f = 3, and so on.
If t = 6, then 3f + 7(6) > 35, so 3f > 7 and f > 2. Possible solutions are f = 3, f = 4, f = 5, and so on.
If t = 7, then 3f + 7(7) > 35, so 3f > 14 and f > 4. Possible solutions are f = 5, f = 6, f = 7, and so on.
c) So, three possible game-winning combinations are:
[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]
[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]
[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]
Each of these combinations would result in your team scoring more than 35 points and winning the game.
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Select the correct answer.
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently
two candidates. The results of the poll are shown in the two-way frequency table belo
Candidate A Candidate B
Total
Center City
152
198
350
Carsonville
205
266
471
Appleton
260
203
New Thomas
180
138
463
318
Total
797
805
1.602
a survey to gauge support for each of the
Based on the data shown, which of the following statements are true?
I. The two cities with the highest number of respondents both show more support for candidate A.
The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New
II. Thomas.
III. More residents of Center City responded to the poll than the number who responded from New Thomas
IV. Overall, more residents support candidate A than candidate B.
Options I and II contain claims regarding the two-way frequency table that are accurate.
How to interpret two-way frequency table?We are given the two-way frequency table that shows the newspapers recently conducted survey that gauges support for each of the two candidates.
Let us now analyze the options;
I) The two cities with the highest number of respondents are Carsonville and Appleton and from the table, they both show more support for candidate A and thus this option is true.
II) There are 266 supporters of candidate B in Carsonville. While there are 138 supporters of candidate B in New Thomas, we can see that 266 is not twice 138.This choice is untrue.
III) The number of residents that responded from Center city is 350 and we see that this is more than the number of residents that responded from New thomas which is 318 people.
The statement is true.
IV) This is untrue because candidate B has 805 supporters, which is greater than candidate A's 797 supporters. The assertion is thus untrue.
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((30/180)*2.80 + (40/180)*11.20
Answer:
0.47?
Step-by-step explanation:
What is the x-intercept of the line illustrated in the graph below? (Enter your answer as a number. If necessary, round to the nearest tenth.)
The line passes through the horizontal axis 2.5 units to the left of the origin. It passes through the vertical axis 1 unit above the origin.
Using the point-slope form of the equation of a line. the x-intercept of the line is [tex]-2.5[/tex].
What is the intercept of the line?To find the x-intercept of the line, we need to find the point where the line intersects the x-axis. We know that the y-coordinate of this point is zero, because it is on the x-axis. Let's call the x-coordinate of this point "x".
We also know that the line passes through the point (-2.5,0), because it is 2.5 units to the left of the origin. Using the point-slope form of the equation of a line, we can write the equation of the line as:
[tex]y - 0 = m(x - (-2.5))[/tex]
where m is the slope of the line. To find the slope, we can use the fact that the line passes through the point [tex](0,1)[/tex] and [tex](-2.5,0)[/tex]:
[tex]m = (1 - 0) / (0 - (-2.5)) = 1 / 2.5 = 0.4[/tex]
Substituting this into the equation of the line, we get:
[tex]y = 0.4(x + 2.5)[/tex]
To find the x-intercept, we set y to zero and solve for x:
[tex]0 = 0.4(x + 2.5)[/tex]
[tex]-2.5 = x[/tex]
Therefore, the x-intercept of the line is [tex]-2.5.[/tex]
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George invests a sum of money into a savings account with a fixed annual interest rate of 5.5% and compounded 6 times a year. After 7 years the account has a balance of $3,820. What is the initial investment?
Group of answer choices
a. $1506.30
b. $2603.88
c. $7082.77
d. $5604.10
The initial investment was approximately $2,603.88, which is option (b).
What is probability?Probability is a measure of the likelihood of an event occurring.
We can use the formula for compound interest:
A = [tex]P(1+r/n)^{nt}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, we know that the final amount A is $3,820, the annual interest rate r is 5.5% (or 0.055 as a decimal), the interest is compounded 6 times a year (n = 6), and the time period is 7 years.
So we can rearrange the formula to solve for P:
P = A/[tex]P(1+r/n)^{nt}[/tex]
Plugging in the values, we get:
P = 3820 / [tex](1+0.055/6)^{6*7}[/tex]
P ≈ $2,603.88
Therefore, the initial investment was approximately $2,603.88, which is option (b).
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Whats is the value of this expression [45-(6+3)]x 27
Answer:
972
Step-by-step explanation:
1. 6+3=9
2. 45-9=36
3. 27x36=972
If these solids were If these solids were candles that you could sell, and the cylinder shaped candie was $12.00. What would be the price of the cone shaped candle and the sphere shaped candle? (
The volume of wax is required to make 1 candle is 22.92 cu. in.
Explain about the shape of cone:A cone is a tri solid geometric object with an apex that is pointed at the top and a circular base. A cone has a vertex and one face.
The length of a line segment from a cone's apex to any point along the circumference of a cone's base is known as the slant height of the cone.An oblique cone is one that doesn't have its apex directly over the base's circle.Given data:
Candle's shape is cone.height h = 6 in.circumference c = 12 inchesLet the radius of the cone be 'r'.
circumference c = 2*π*r
c = 2*π*r
12 = 2*3.14*r
r = 6/3.14
r = 1.91
Volume of cone V = 1/3 * π * r² *h
Put the values:
V = 1/3 * 3.14 * 1.91² *6
V = 22.92 cu. in.
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Correct question:
A company makes candles in the shape of the cones. Their best selling candles has a height of 6 inches and the circumference of 12 inches What is the volume of wax is needed to make 1 candle.
how much is 2 1/6 years in months in a fraction
2 1/6 years in months is 26/1 as a fraction.
Answer:26 months or 26/1 months
Over what interval is the graph of y = |x + 6| decreasing? A. (–∞, –6) B. (–∞, 6) C. (–6, ∞) D. (6, ∞)
The function is decreasing for x < -6, or over the interval (–∞, –6).
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines). Graphs are often used to represent relationships between objects or to model complex systems.
The derivative of the function y = |x + 6| is equal to -1 for x < -6 and 1 for x > -6. At x = -6, the derivative is undefined, but the function is not decreasing there, so we don't need to consider that point.
Thus, the function is decreasing for x < -6, or over the interval (–∞, –6). Therefore, the answer is A. (–∞, –6).
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Ryan and Kayley launch their rockets at the same time. The height of Ryan’s rocket, in
meters, is given by the function () = −3.4
2 − 64, where x is the number of seconds
after the launch. The height of Kayley’s rocket, in meters, is given by the function
() = −3.4
2 − 25 − 45 where x is the number of seconds after the launch.
Algebraically find the moment when the rockets are at the same height, and then use that
to calculate the height. Round to the nearest hundredth. Show all work.
At the moment when the rockets are at the same height, their height is approximately -223.34 meters. Note that this negative value indicates that they are both below the ground level.
How to find moment?
To find the moment when the rockets are at the same height, we need to set the two height functions equal to each other and solve for x:
-3.4x²- 64 = -3.4x² - 25x - 45
Simplifying and rearranging:
0 = 25x + 19
x = -19/25
So the rockets are at the same height after -19/25 seconds, or about 0.76 seconds.
To find the height at this moment, we can plug this value of x into either of the height functions. Let's use Ryan's function:
h(-19/25) = -3.4(-19/25)²- 64
= -3.4(361/625) - 64
= -223.34
So at the moment when the rockets are at the same height, their height is approximately -223.34 meters. Note that this negative value indicates that they are both below the ground level.
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1/3 (16a-8) expandesch expression
Answer: To expand the expression 1/3(16a-8), we can distribute the 1/3 to each term inside the parentheses:
1/3(16a-8) = 1/3(16a) - 1/3(8)
Simplifying each term:
1/3(16a) = (1/3)16a = (16/3)*a
1/3(8) = (1/3)*8 = 8/3
So the fully expanded expression is:
1/3(16a-8) = (16/3)*a - 8/3
Step-by-step explanation:
Calculate the come tax on salary of Birr 5200. Derive formule to calculate income tax and on Birr x, in terms of x. here x falls on the interval 5251 to 7800
the income tax payable on a salary of Birr 5200 is Birr 320.
In Ethiopia, income tax is calculated based on a progressive tax system where the tax rate increases as the taxable income increases. The formula for calculating income tax on monthly salary is as follows:
Taxable income = Gross monthly salary - Deductions
Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances
Where:
1. Gross monthly salary: Total salary before any deductions.
2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.
3. Taxable income: Gross monthly salary minus deductions.
4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.
5. Tax threshold: The minimum amount of taxable income before tax is applicable.
6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.
To calculate the income tax on a salary of Birr 5200, we need to determine the taxable income first. Let's assume that the gross monthly salary is Birr 5200, and there are no deductions.
Taxable income = Birr 5200 - 0 = Birr 5200
Next, we need to determine the tax rate applicable to this taxable income based on the tax bracket. For the taxable income range of Birr 5251 to 7800, the tax rate is 10%. Therefore, the tax rate applicable to Birr 5200 is 10%.
Tax rate = 10%
Now, we need to determine the tax threshold and the allowances applicable to this taxable income. Let's assume that the tax threshold is Birr 2000, and there are no allowances.
Tax threshold = Birr 2000
Allowances = 0
Using the formula mentioned earlier, we can calculate the income tax payable as follows:
Tax payable = 10% * (Birr 5200 - Birr 2000) - 0
Tax payable = Birr 320
Therefore, the income tax payable on a salary of Birr 5200 is Birr 320.
To derive the formula to calculate income tax on Birr x, we can use the same formula mentioned earlier. We can express the formula in terms of x as follows:
Taxable income = x - Deductions
Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances
Where:
1. x: Gross monthly salary.
2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.
3. Taxable income: Gross monthly salary minus deductions.
4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.
5. Tax threshold: The minimum amount of taxable income before tax is applicable.
6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.
We can use this formula to calculate the income tax payable on any salary falling within the Birr 5251 to 7800 taxable income range.
In conclusion, income tax in Ethiopia is calculated based on a progressive tax system, where the tax rate increases as the taxable income increases. To calculate income tax on a salary of Birr 5200, we need to determine the taxable income, tax rate, tax threshold, and allowances applicable to that salary. We can use the same formula to calculate income tax on any salary within the Birr 5251 to 7800 taxable income range.
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I NEEDDD HELPPPPPPPP
Answer:
VX=33
Step-by-step explanation:
VW=2z-1
WX=z+3
XV=3z
VW=a
WX=b
XV=c
a+b+c=2z-1+z+3+3z
Perimeter=6z+2
P=68
68=6z+2
66=6z
z=11
VX=3x11
VX=33
oscar corporation produces and sells three products. unit data concerning each product is shown below. the company has 2000 hours of labor available to build inventory
Oscar Corporation can effectively allocate its 2000 labor hours to build Inventory for its three products, ensuring efficient production and maximizing profits
Based on the information provided, let's assume that the three products produced by Oscar Corporation are Product A, Product B, and Product C.
1. Determine the labor hours required for each product.
First, we need to know the labor hours required to produce one unit of each product. This information is essential in order to allocate the available labor hours effectively.
Calculate the labor efficiency for each product.
Divide the total number of units produced by the labor hours required for each product. This will help us determine the most efficient product in terms of labor utilization.
Allocate the available labor hours.
Using the labor efficiency data, allocate the 2000 available labor hours among the three products. Prioritize the most efficient product to maximize production.
Calculate the number of units produced for each product.
Multiply the allocated labor hours for each product by its respective labor efficiency to determine the number of units that can be produced.
Evaluate and adjust if necessary.
Review the results and adjust the allocation of labor hours if needed to meet the company's goals or demand for each product.
By following these steps, Oscar Corporation can effectively allocate its 2000 labor hours to build inventory for its three products, ensuring efficient production and maximizing profits.
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