The formula to find the 10th term of the sequence is -512(x-1).
How to find sequenceThe given sequence is generated by starting with the term x-1 and then multiplying each term by -2 to get the next term.
Therefore, the nth term of the sequence can be expressed as:
[tex](-2)^(n-1) * (x-1)[/tex]
To find the 10th term of the sequence, we substitute n = 10 into the formula
[tex](-2)^(10-1) * (x-1) = (-2)^9 * (x-1)[/tex]
= -512(x-1)
So the formula to find the 10th term of the sequence is -512(x-1).
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Determine any data values that are missing from the table, assuming that the data represent a linear function. x y 1 2 2 6 4 a. 2 c. 14 b. 10 d. 16
The equation of the linear function is y = 4x - 2. The missing value in the table is 14.
The missing value in the given table is 10. Assuming that the data represent a linear function, we can use the slope formula (m = (y2 - y1) / (x2 - x1)) to find the missing value.
We can choose any two sets of coordinates from the table to find the slope, then use that slope to find the missing value. For example, using the coordinates (1, 2) and (2, 6), we get:m = (6 - 2) / (2 - 1) = 4
Therefore, the equation of the linear function is y = 4x + b, where b is the y-intercept. To find b, we can plug in any set of coordinates into the equation and solve for b.
For example, using the coordinates (1, 2), we get:2 = 4(1) + bSimplifying the equation, we get:b = -2Therefore, the equation of the linear function is y = 4x - 2. We can now use this equation to find the missing value when x = 4:y = 4(4) - 2 = 14Therefore, the missing value in the table is 14.
We are given a table of x and y values. We need to find the missing value assuming that the data represent a linear function. To find the missing value, we can use the slope formula (m = (y2 - y1) / (x2 - x1)).
This formula gives us the slope of the line passing through two points, which is the rate at which y changes with respect to x. We can then use this slope to find the missing value in the table.
Using the coordinates (1, 2) and (2, 6), we get a slope of 4. This means that for every 1 unit increase in x, y increases by 4 units. Therefore, the equation of the linear function is y = 4x + b, where b is the y-intercept.
To find b, we can plug in any set of coordinates into the equation and solve for b. Using the coordinates (1, 2), we get b = -2. Therefore, the equation of the linear function is y = 4x - 2.
Finally, we can use this equation to find the missing value when x = 4. Plugging in x = 4, we get y = 4(4) - 2 = 14. Therefore, the missing value in the table is 14.
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PLEASE HELP ASAP
select the correct answer from the drop down menu
Graph Y represents the equation [tex]y=\frac{x}{x \;+\;1}[/tex].
What is a rational function?In Mathematics and Geometry, a rational function simply refers to a type of function which is expressed as a fraction that is composed of two (2) main parts and these include the following:
NumeratorDenominatorBased on the information provided above, we can logically deduce the following rational function;
[tex]y=\frac{x}{x \;+\;1}[/tex]
Next, we would set the denominators equal to 0 in order to determine the restrictions on the variable as follows;
x + 1 = 0
x = 0 - 1
x = -1.
In conclusion, this rational function [tex]y=\frac{x}{x \;+\;1}[/tex] has a horizontal asymptote at y = 1 and a vertical asymptote at x = -1.
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6. Which term best describes the figure shown below?
M
line LM
Opoints LM
Oray LM
Oplane LM
The term that best describes the figure shown is (a) line LM
How to determine the term of the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have
Points L and M
On the figure, we have two arrows that extend indefinetely
By definition of lines, lines extend indefinetely
This means that the term that best describes the figure shown is (a) line LM
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Travel Expenses, Meals And Entertainment, Educational Expenses (LO 3.4, 3.5, 3.6) Bob is a self-employed lawyer and is required to take a week of continuing legal education every year to maintain his license. This year he paid $1,400 in course fees for his continuing legal education in a different city. He also paid $500 for airfare and a hotel room and paid $300 for meals, all of which were provided by the hotel’s restaurant. Bob also purchased a $10 bag of snacks from a newsstand while waiting for his plane in the airport because he missed lunch. What is the total amount he can deduct on his Schedule C related to these expenses? fill in the blank 1 of 1$
Bob can deduct a total of $2,210 on his Schedule C related to these expenses.
How to calculate deductible amount?To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:
Course fees for continuing legal education: $1,400
Airfare and hotel room: $500
Meals provided by the hotel's restaurant: $300
Snacks from the newsstand: $10
To calculate the total amount that Bob can deduct, add up these expenses:
$1,400 + $500 + $300 + $10 = $2,210
Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.
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Use the diagram in the box to convert the given measurements to the unit indicated. 18.8 hm to m
How to convert 18.8 hm (hectometers) to meters using the diagram. So, 18.8 hm is equal to 1,880 m after converting using the diagram.
Here is how to convert 18.8 hm to m using the diagram:
1. Start with the given measurement, which is 18.8 hm.
2. Locate "hecto" on the diagram and see that it is 2 units away from "m" (meter).
3. Since you want to convert from hm to m, you need to move 2 units to the left on the diagram.
4. Moving 2 units to the left on the diagram brings you to the meter (m) unit.
5. Each time you move one unit to the left on the diagram, you divide the original measurement by 10. Since you moved 2 units to the left, you need to divide 18.8 by 100 (10 raised to the second power).6. Therefore, 18.8 hm is equal to 1,880 m after converting using the diagram.
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When plotting points on the coordinate plane below, which point would lie on both the x-axis and the y-axis?
A coordinate plane.
The point that would lie on both the x-axis and the y-axis is (0, 0)
How to determine the point on the x-axis and the y-axisFrom the question, we have the following parameters that can be used in our computation:
Plotting points on a coordinate plane
The general rule is that
The point on the x-axis and the y-axis is the origin
This means that the point that would lie on both the x-axis and the y-axis is (0, 0)
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A water taxi carries passengers from harbor to another. Assume that weights of passengers are normally distributed with a mean of 180 lb and a standard deviation of 43lb. The water taxi has a stated capacity of 25 passengers, and the water taxi was rated for a load limit of 3500 lb.
Once upon a time in a land not so far away, there was a bright and sprightly water taxi. Let's call it 'HappiNess'. She was known far and wide for her distinct yellow hue, and her chirpy charm was the talk of the harbor. She carried people from one harbor to another with pride and style, and had quite a reputation for always being on time.
Now, passengers, as varied and vibrant as the rainbow itself, came from all walks of life. It just so happened that on average, they tipped the scales at around 180 lb. You'd think that's a bit too precise for an estimate, wouldn't you? But you see, in this magical realm, statisticians have fairy dust. And, just like how fairy godmothers knew the exact size of Cinderella's shoe, our statisticians sprinkled their dust and found that passenger weights in our story followed a 'normal distribution'. Quite like the shape of a bell, but let's imagine it as an enchanted hill with the most common weights at the peak and the rare, lighter and heavier weights as the slopes on either side. The enchantment was such that the weights of passengers varied by around 43 lb on either side of 180 lb.
Now, HappiNess was as robust as she was sprightly, but every ship, no matter how bright and yellow, has its limits. She could carry a merry crowd of 25 passengers at a time. Any more than that and she'd risk becoming the 'GrumpiNess', and no one wanted that! Besides, she was rated for a load limit of 3500 lb - that's the magic number beyond which HappiNess would start losing her cheer.
Imagine one fine day, a crowd of 25 average-sized passengers (each 180 lb) decided to board HappiNess. That would be quite an adventure, right? Because 25 passengers, each weighing 180 lb, totals to 4500 lb - a number that exceeds the HappiNess' load limit of 3500 lb. And we'd never want to risk her becoming GrumpiNess, would we?
So, we better make sure that we don't overburden HappiNess, even if that means fewer tales of seafaring adventures. The key is to ensure a balance, quite literally, so she can continue to be the HappiNess we all love and enjoy. After all, it's all about staying afloat and riding the waves with a smile, isn't it?
An image of a rhombus is shown.
a rhombus with a base of 18 centimeters and a height of 15.5 centimeters
What is the area of the rhombus?
16.75 cm2
33.5 cm2
139.5 cm2
279 cm2
The area of the rhombus with a base of 18 centimeters and a height of 15.5 centimeters is 139.5 cm² (option c).
To find the area of a rhombus, we can use the formula:
Area = (base * height) / 2.
Given that the base of the rhombus is 18 centimeters and the height is 15.5 centimeters, we can substitute these values into the formula:
Area = (18 cm * 15.5 cm) / 2.
Multiplying the base and height gives us:
Area = (279 cm²) / 2.
Dividing 279 cm² by 2 gives us the final area:
Area = 139.5 cm².
Therefore, the area of the rhombus is 139.5 cm².
Thus, the correct option is c.
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Seema invested $4,000 at 5% interest and x dollars at 3% interest. If her return on both investments at
the end of the year is same, what is the value of x?
The value of x is $6,666.67.
Let the value of x dollars invested at 3% interest rate be X .If the return on both investments at the end of the year is the same, the two investments should give the same amount of money after one year. The formula for calculating the simple interest on an investment is:
I = P × R × T
Where, I is the simple interest P is the principal amount R is the interest rate T is the time duration Seema invested $4,000 at 5% interest. Using the above formula, her return after 1 year is:
I1 = 4000 × 0.05 × 1 = $200
The value of x dollars was invested at 3% interest. Using the above formula, her return after 1 year on x dollars will be:
I2 = X × 0.03 × 1 = 0.03X dollars
If the return on both investments at the end of the year is the same, then we can equate the two equations obtained for I1 and I2, then solve for X dollars.
4000 × 0.05 × 1 = X × 0.03 ×
1Simplifying this equation, we get:200 = 0.03XDividing both sides by 0.03, we get:
X = 200 / 0.03X = 6666.67
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Write an algebraic equation for the following problem and then solve it.
When Angela and Walker first started working for the supermarket, their weekly salaries totaled $650. Now during the last 25 years
Walker has seen his weekly salary double. Angela has seen her weekly salary become three times larger. Together their weekly
salaries now total $1730. How much did they each make 25 years ago?
How is the product of 2 and -5 shown on a number line
The product of 2 and -5 can be shown on a number line as a movement in the negative direction. To represent this on a number line, we start at zero and move 2 units to the right (in the positive direction) to the point labeled +2. Then, since the product is negative, we move 5 units to the left (in the negative direction) from the point +2. This brings us to the point labeled -3.
Start at zero on the number line.
Move 2 units to the right (in the positive direction) to the point labeled +2.
Since the product is negative, we need to move in the opposite direction (left) from the point +2.
Move 5 units to the left (in the negative direction) from the point +2.
The point we reach after moving 5 units to the left from the point +2 is labeled -3.
Therefore, on the number line, the product of 2 and -5 is represented by the point labeled -3. This indicates that starting from zero and moving 2 units to the right and then 5 units to the left results in a position of -3.
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The probable question could be:
How is the product of 2 and -5 shown on a number line?
enter the number that belongs in the green box 37 5 120
The number that fit in into missing value is 7.707
What is Law of Sines?Rule of Sines The sine law, sine formula, sine rule, or law of sines is an equation in trigonometry that connects the lengths of any triangle's sides to the sines of its angles. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle.
[tex]\frac{sin A}{a} = \frac{sinB}{b} = \frac{sin C}{c}[/tex]
The value of the third angle = 180-(37+120)
=23 degree
let x be the missing side
[tex]\frac{sin 23}{5} =\frac{sin37}{x}[/tex]
x=[tex]\frac{ sin37 *5}{ sin23 }[/tex]
x =[tex]\frac{0.6018 * 5}{ 0.39073}[/tex]
=7.707
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in the poisson probability calculation, why does the 3! of the 3yr become 6?
The 3! is used to calculate the number of permutations of three objects, and is included in the Poisson probability formula to account for the number of ways in which three events can occur in a specific order over a given period.
In Poisson probability calculation, 3! (3 factorial) is used to find the number of ways in which three independent events can occur in a specific order over a given period. In other words, 3! refers to the number of permutations of 3 objects.
The formula used in Poisson distribution is as follows: [tex]P (X = x) = (e^{-\lambda } \lambda^x)/x![/tex], where λ is the mean rate of the event occurring over a specific time interval, and x is the number of events that occur within that time interval.
The x! term is included in the formula because it represents the number of ways in which x events can occur in a specific order over the given time period. The exponents of λ are used to represent the probability of an event occurring in the interval.
In the case of 3! we are calculating the number of ways that three independent events can occur in a specific order over a given period. This can be expressed as 3 x 2 x 1 = 6, which is why 3! becomes 6 in the Poisson probability calculation.
The term 3! (6) is included in the formula to account for the number of ways in which three events can occur in a specific order over a given period.
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PLSSS HELP!! Ty whoever helped me! :) Question: Select the statement that is true about the two-dimensional figure.
A quadrilateral with the vertices labeled L, M, N and O. Angles M L O and L M N are greater than 90 degrees, and angles L O N and M N O are less than 90 degrees.
∠LMN is an acute angle.
∠LMN is an obtuse angle.
∠MNO is an obtuse angle.
∠MNO is a right angle.
∠LMN is an obtuse angle.
==========================================
Explanation
Let's go through the answer choices to see which are true, and which are false.
A. This is false. It is stated that "LMN is greater than 90 degrees", so this angle is obtuse. Acute angles are less than 90 degrees.B. This is true. See choice A above.C. This is false. We're told that "angle MNO is less than 90 degrees". That makes the angle acute. D. This is false. See choice C above. Right angles are 90 degrees exactly. Often a small square marker is used to denote a 90 degree angle.What is the first step in sketching the graph of a rational function
Answer:
Answer is A. Find the functioning zeros and vertical asymptotes
solve using the quadratic formula
16x^2-8x=-1
Answer:
Step-by-step explanation:
To solve the quadratic equation 16x^2 - 8x = -1 using the quadratic formula, we need to rearrange the equation in the standard form ax^2 + bx + c = 0.
Given equation: 16x^2 - 8x = -1
We bring all terms to one side to obtain: 16x^2 - 8x + 1 = 0
Comparing this with the standard form ax^2 + bx + c = 0, we have:
a = 16
b = -8
c = 1
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
x = (-(-8) ± √((-8)^2 - 4 * 16 * 1)) / (2 * 16)
x = (8 ± √(64 - 64)) / 32
x = (8 ± √0) / 32
Since the discriminant (b^2 - 4ac) is zero, the quadratic equation has only one real root.
x = 8 / 32
x = 1/4
Therefore, the solution to the equation 16x^2 - 8x = -1 is x = 1/4.
Consider the two triangles shown below. Two triangles. The first triangle has a side length of seven units and a side length of five units. The second triangle has a side length of seven units and a side length of five units. Two triangles. The first triangle has a side length of seven units and a side length of five units. The second triangle has a side length of seven units and a side length of five units. Note: The triangles are not drawn to scale. Are the two triangles congruent?
The two triangles are congruent because they have identical side lengths, implying that all corresponding angles and side lengths are equal.
What are Congruent Triangles?Congruent triangles are triangles that have the same shape and size, with corresponding angles and side lengths being equal.
The image shows two triangles with given side lengths where the corresponding side lengths are each equal to each other.
Therefore, we can conclude that the two triangles are congruent since they have the exact same side lengths, which indicates that all corresponding angles and side lengths are equal.
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How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?
Using the principle of inclusion-exclusion, we can see that the total number of numbers with the given restrictions is:
586,071
How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?o find the number of 7-digit numbers where the digits 1, 2, and 3 each appear at least once, we can use the principle of inclusion-exclusion.
Step 1: Find the total number of 7-digit numbers without any restrictions.
Since each digit can be chosen independently from 0 to 9 (excluding leading zeros), there are 9 options for the first digit (1-9) and 10 options for each subsequent digit (0-9). Therefore, the total number of 7-digit numbers without any restrictions is 9 * 10⁶.
Step 2: Subtract the number of 7-digit numbers that do not contain 1, 2, or 3.
The number of 7-digit numbers that do not contain 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding 1, 2, and 3). So for each digit position, there are 7 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without 1, 2, or 3 is 7⁷.
Step 3: Add back the number of 7-digit numbers that do not contain two of the digits 1, 2, or 3.
The number of 7-digit numbers that do not contain two of the digits 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding two of 1, 2, and 3). For each digit position, there are 6 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without two of 1, 2, or 3 is 6⁷.
Step 4: Subtract the number of 7-digit numbers that do not contain all three digits 1, 2, and 3.
The number of 7-digit numbers that do not contain all three digits 1, 2, and 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding all three of 1, 2, and 3). For each digit position, there are 4 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without all three of 1, 2, and 3 is 4⁷.
Now we can apply the principle of inclusion-exclusion to find the desired count:
Total number of 7-digit numbers = 9 * 10⁶ - 7⁷ + 6⁷ - 4⁷
Calculating this expression, we find:
Total number of 7-digit numbers = 586,071
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Earth has more than 60,000 tree species. Each look different and grows at a different rate. Pick a tree species below. If you planted a seed in year 0, calculate the dimensions of the trees trunk in years 1,2,3, and 10. Would you say that the tree grows by the same amount each additional year?
One of the species of trees is the Oak. If a seed of an Oak tree is planted, and it is assumed that the diameter of the seed is 0, the tree would grow by approximately 3.3 inches in year 1, 6.6 inches in year 2, 9.9 inches in year 3, and 33 inches in year 10. It cannot be said that the Oak tree would grow by the same amount each additional year.
Some years, the tree might grow more, while other years, it might grow less.Trees are perennial plants that have a single main stem, a supporting structure of branches and leaves, and the ability to produce wood.
A tree that is mature and has a single stem is known as a "single-trunked" or "single-stemmed" tree; trees with several stems originating at or near the ground are known as "multi-stemmed" or "clonal" trees.The height and trunk diameter of a tree increase as it matures.
The growth rate of each tree species is determined by various variables such as weather, altitude, and soil fertility.
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The graphs of f(x) and g(x) are shown below.
On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6).
Which of the following is the graph of (g – f)(x)?
On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6)
On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
On a coordinate plane, a straight line with a positive slope goes through points (negative 6, negative 6), (0, 0), and (6, 6).
Mark this and return
The correct statement regarding the graph of the linear function (g - f)(x) is given as follows:
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
How to define the functions?The function f(x) in this problem is defined as follows:
f(x) = -x.
The function g(x) in this problem is defined as follows:
g(x) = 2x.
Hence the subtraction of the two functions is given as follows:
(g - f)(x) = g(x) - f(x)
(g - f)(x) = 2x - (-x)
(g - f)(x) = 3x
Which has a positive slope, hence the correct option is given as follows:
On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
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b) The following information was got from an international market in relation to United states and Britain.
Amount available to invest $ 1 000000
Spot exchange rate: $ 1.618 per sterling pound
180 days forward rate: $ 1.6052 per sterling pound
Annual interest rate in U.S 8%
Annual interest rate in Britain 15%
Required:
i. Compute arbitrage profit (if any) (5 marks)
ii. What are the possible moves which can eliminate the arbitrage profit in short run?
(3 marks)
iii. Which name do we give to the situation such that the arbitrage profit is nil.
(2 marks)
The arbitrage profit is $1,750,801.62.Borrow $1,000,000 in the U.S. at an annual interest rate of 8%.
Convert the borrowed amount to sterling pounds at the spot exchange rate.
Invest the borrowed sterling pounds in Britain at an annual interest rate of 15%.
Enter into a forward contract to exchange the future value of the investment back to U.S. dollars at the forward exchange rate.
To determine the arbitrage profit, we need to compare the potential gains from two different investment strategies: investing in the U.S. and investing in Britain.
i. Compute arbitrage profit:
1. Investing in the U.S.:
If we invest $1,000,000 in the U.S. at an annual interest rate of 8%, after 180 days (half a year), the investment will grow to:
$1,000,000 * (1 + 0.08/2) = $1,040,000
2. Investing in Britain:
To invest in Britain, we convert the $1,000,000 to sterling pounds using the spot exchange rate:
$1,000,000 * 1.618 = £1,618,000
Then, we invest the £1,618,000 in Britain at an annual interest rate of 15%:
£1,618,000 * (1 + 0.15/2) = £1,737,850
Now, we need to convert the future value of the investment back to U.S. dollars using the forward exchange rate:
£1,737,850 * 1.6052 = $2,790,801.62
Arbitrage profit = Future value of investment in Britain - Future value of investment in the U.S.
= $2,790,801.62 - $1,040,000
= $1,750,801.62
Therefore, the arbitrage profit is $1,750,801.62.
ii. Possible moves to eliminate arbitrage profit in the short run:
To eliminate the arbitrage profit, investors could take advantage of the discrepancy in interest rates and exchange rates by performing the following actions:
- Borrow $1,000,000 in the U.S. at an annual interest rate of 8%.
- Convert the borrowed amount to sterling pounds at the spot exchange rate.
- Invest the borrowed sterling pounds in Britain at an annual interest rate of 15%.
- Enter into a forward contract to exchange the future value of the investment back to U.S. dollars at the forward exchange rate.
By executing these actions, the arbitrage profit would be eliminated as the gains from the investment in Britain would be offset by the interest payments on the borrowed amount.
iii. The situation where the arbitrage profit is nil is referred to as "Arbitrage equilibrium" or "Arbitrage-free market." In this state, there are no opportunities for risk-free profits through exploiting discrepancies in prices, interest rates, or exchange rates. The market prices and rates are in balance, reflecting all available information and preventing arbitrage opportunities.
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What is the distance from point N to M in the figure below?
L
8.3
N
7.5
0
OA. 7.7
7.7
B. 1.74
C. 8,3
OD. 7.5
OE. 0.8
OF. 3.55
M
Answer:
Step-by-step explanation:
Distance from point N to M can be calculated using the Pythagoras theorem. According to Pythagoras theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, side LN is the hypotenuse, and NM and ML are the other two sides. Therefore, LM can be calculated using the Pythagorean theorem as follows:
NM² + ML² = LN²
7.5² + 8.3² = LM²
56.25 + 69.29 = LM²
125.54 = LM²
LM = √125.54
LM ≈ 11.2
Therefore, the distance from point N to M is equal to the length of the side LM which is approximately 11.2. Hence, the correct option is not available in the given alternatives.
Un automóvil de 860 kg se desplaza a 50 km/h ¿cuál será su energía cinética?
The kinetic energy of this car is equal to 77160.49 Joules.
How to calculate the kinetic energy of this car?In Mathematics, the kinetic energy of a physical object can be calculated by using the following equation (formula):
K.E = 1/2 × mv²
Where:
K.E represent the kinetic energy.m represent the mass.v represent the speed or velocity.Note: 50 km/h to m/s = 50 × 1000/3600 = 13.89 m/s
By substituting the given parameters into the formula for the kinetic energy of a physical object, we have the following:
Kinetic energy, K.E = 1/2 × 800 × 13.89²
Kinetic energy, K.E = 400 × 192.90
Kinetic energy, K.E = 77160.49 Joules.
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Complete Question:
An 860 kg car moves at 50 km/h, what will its kinetic energy be?
A body moves on a coordinate line such that it has a position s=f(t)=16/t^2-4/t on the interval 1≤t≤4, with s in meters and t in seconds.
a. Find the body's displacement and average velocity for the given time interval.
b. Find the body's speed and acceleration at the endpoints of the interval.
c. When, if ever, during the interval does the body change direction?
A) Average Velocity = Displacement / Time Interval = -9 / (4 - 1) = -3 meters per second.
B) Acceleration(4) = 96/4^4 - 8/4^3 = 1/8 meters per second squared.
C) The body changes direction when the velocity changes sign.
a. To find the body's displacement, we need to find the difference between the initial and final positions. The position function is given as s [tex]= f(t) = 16/t^2 - 4/t.[/tex]
[tex]For t = 1, the position is:s(1) = 16/1^2 - 4/1 = 12For t = 4, the position is:s(4) = 16/4^2 - 4/4 = 3[/tex]
The displacement is given by the difference in position:
Displacement = s(4) - s(1) = 3 - 12 = -9 meters
To find the average velocity, we divide the displacement by the time interval:
Average Velocity = Displacement / Time Interval = -9 / (4 - 1) = -3 meters per second
b. The speed of the body at the endpoints of the interval can be found by taking the absolute value of the derivative of the position function. The acceleration can be found by taking the derivative of the velocity function.
At t = 1:
[tex]Velocity = f'(t) = d(s)/dt = d/dt(16/t^2 - 4/t) = -32/t^3 + 4/t^2[/tex]
[tex]Speed at t = 1: |Velocity(1)| = |-32/1^3 + 4/1^2| = 28[/tex] meters per second
At t = 4:
[tex]Velocity = f'(t) = d(s)/dt = d/dt(16/t^2 - 4/t) = -32/t^3 + 4/t^2[/tex]
[tex]Speed at t = 4: |Velocity(4)| = |-32/4^3 + 4/4^2|[/tex]= 4 meters per second
To find the acceleration, we take the derivative of the velocity function:
[tex]Acceleration = f''(t) = d^2(s)/dt^2 = d/dt(-32/t^3 + 4/t^2) = 96/t^4 - 8/t^3[/tex]
At t = 1:
[tex]Acceleration(1) = 96/1^4 - 8/1^3[/tex]= 88 meters per second squared
At t = 4:
Acceleration(4) = 96/4^4 - 8/4^3 = 1/8 meters per second squared
c. The body changes direction when the velocity changes sign. From the velocity function, we can see that the velocity will change sign when the denominator of the expression becomes zero, as that would result in a zero in the denominator, making the velocity undefined.
For the given position function, the velocity will change sign when t = 0 or t = 2. However, these values are not within the interval 1 ≤ t ≤ 4. Therefore, the body does not change direction during the interval 1 ≤ t ≤ 4.
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10. Convert 78% to a decimal
Answer:
0.78
Step-by-step explanation:
Move the decimal place 2 spots to the left (i.e., imagine the decimal is already to the right most):
100% = 100/100 = 1 = 1.00
78% = 78/100 = 0.78
What is the y-intercept of the function f(x)=4-5x?
Answer: the y-intercept is at four
Step-by-step explanation: 4 is the point which the function cross the y axis on a graph
washington plastic products pays kim 2420 monthly salary plus 11% commission each month.assume her sales were 74000 last month what's commission and gross
Kim's commission was $8140, and her gross pay was $10560 for last month.
Washington Plastic Products pays Kim $2420 monthly salary plus 11% commission each month.
If her sales were $74000 last month, her commission and gross pay can be calculated as follows:
Kim's commission = 11% of $74000
= $8140Kim's gross pay
= $2420 + $8140 = $10560
Therefore, Kim's commission was $8140 and her gross pay was $10560 last month.
In the given problem, Kim's monthly salary is $2420, and she earns an 11% commission on her sales.
Assuming her sales last month were $74000, her commission and gross pay for the month can be found by multiplying her sales by the commission rate and adding her monthly salary.
Commission = 11% of $74000 = $8140Gross Pay = $2420 + $8140 = $10560
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Which expression is equivalent to the given expression?
[tex] 2x^2 - 11x - 6 [/tex]
Hello!
2x² - 11x - 6
= (2x² + x) + (-12x - 6)
= x(2x + 1) - 6(2x + 1)
= (x - 6)(2x + 1)
What is the domain of y=√x+7 +5?
x20
O x27
x2-7
Oall real numbers
DONE
The domain of the function y = √(x + 7) + 5 is all real numbers (all real numbers). Option D.
To determine the domain of the function y = √(x + 7) + 5, we need to identify the values of x for which the function is defined.
In this case, the function includes two operations: addition and square root. To ensure the function is defined, we need to consider the restrictions imposed by each operation.
The square root function (√) is defined only for non-negative real numbers. In other words, the expression inside the square root (√(x + 7)) must be greater than or equal to zero for the function to be defined.
Setting x + 7 ≥ 0, we can solve for x:
x ≥ -7
Therefore, the expression inside the square root (√(x + 7)) is defined for x values greater than or equal to -7.
Additionally, there are no restrictions on the addition operation (+5). It can be applied to all real numbers.
Combining both restrictions, we find that the function y = √(x + 7) + 5 is defined for all real numbers x, since there are no limitations or exclusions. Option D is correct.
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3.2.4 Practice: modeling: slope-intercept equation of a line b) The y-intercept (1 point)
The y-intercept of the line with a slope of 2 and passing through the point (3, 5) is -1.
The y-intercept of a line is the point where the line intersects the y-axis. In the slope-intercept form of a linear equation, y = mx + b, the y-intercept is represented by the value of b.
To determine the y-intercept, we need to have information about the line, such as its slope and at least one point it passes through.
If we are given the slope, m, and a point (x₁, y₁) on the line, we can use the point-slope form of the equation, y - y₁ = m(x - x₁), to find the equation of the line and determine the y-intercept.
For example, let's say we are given the slope m = 2 and a point (3, 5) on the line. We can substitute these values into the point-slope form:
y - 5 = 2(x - 3)
Expanding the equation:
y - 5 = 2x - 6
Next, we can rearrange the equation to isolate y:
y = 2x - 6 + 5
y = 2x - 1
From this equation, we can see that the y-intercept is -1. The point where the line crosses the y-axis is (0, -1), and the value of b in the slope-intercept form is -1.
Therefore, the y-intercept of the line with a slope of 2 and passing through the point (3, 5) is -1.
In general, to determine the y-intercept of a line, we need to know the slope and at least one point it passes through. With this information, we can use the point-slope form of the equation and solve for the y-intercept.
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