What is the area of triangle abc if a = 12, b = 17, and C = 100°?
For landscape maintenance Gretchen Green uses 2 pounds of fertilizer for every 50 square feet of lawn. At this rate, how many pounds of fertilizer
did she use on a lawn that measures 1700 square feet? Round to the nearest whole number.
The quantity of pounds of fertilizer that she would use on a lawn of given area would be = 68 pounds of fertilizer.
How to calculate the quantity of fertilizer needed for the lawn?To calculate the quantity of fertilizer that is needed for the area of lawn given, the following of carried out.
The total area of lawn that needs fertilizer = 1700 square feet
The quantity lawn that needs 2 pounds of fertilizer = 50ft²
That is;
2 pound = 50ft²
X pound = 1700ft²
make X the subject of formula;
X = 1700×2/50
= 3400/50
= 68 pounds
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The radius of a quarter is 1.21 centimeters. if a quarter is rolled so that it travels in a straight line for exactly 7 revolutions, how far would the quarter travel? express your answer in exact form and as an approximation to the nearest hundredths place.
The circumference of the quarter is approximately 7.60516 centimeters.
To find the distance traveled by the quarter, we need to calculate the circumference of the quarter and then multiply it by the number of revolutions.
The circumference of a circle is given by the formula:
C = 2πr
where C is the circumference and r is the radius.
Given that the radius of the quarter is 1.21 centimeters, we can substitute this value into the formula:
C = 2π(1.21)
Now, let's calculate the circumference:
C = 2 × 3.14159 × 1.21
C ≈ 7.60516 centimeters
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Any ordered arrangement of a given set of objects is called​ a(n)
Any ordered arrangement of a given set of objects is called a permutation. Permutations are used in various fields, including mathematics, statistics, computer science, and cryptography.
Permutations are essentially different ways of arranging objects, and they depend on the number of objects to be arranged and the order in which they are arranged. In a permutation, the order of objects matters, and the same set of objects can have different permutations. The number of permutations of a set of n distinct objects can be calculated by multiplying n by all positive integers less than n.
This is denoted by n!, which is read as n factorial. For example, the number of permutations of the set {1, 2, 3} is 3! = 3 × 2 × 1 = 6. Permutations are important in probability theory, where they are used to calculate the number of possible outcomes of an event.
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In 2000, the average cost for college tuition in the United States was about $14,000. In 2010, the cost was about $18,000. Write a linear model that represents the cost if tuition as a function of the number of years since 2000
The linear model that represents the cost of tuition as a function of the number of years since 2000 is y = 400x + 14000
To write a linear model that represents the cost of tuition as a function of the number of years since 2000, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the cost of tuition, x is the number of years since 2000, m is the slope of the line, and b is the y-intercept (the cost of tuition in the year 2000).
We can use the two data points we have to find the slope of the line:
Slope = (Change in y) / (Change in x)
Slope = (18000 - 14000) / (2010 - 2000) = 4000 / 10 = 400
So the slope of the line is 400, meaning that for every year since 2000, the cost of tuition has increased by $400.
Now we can plug in the slope and the y-intercept to get the equation:
y = 400x + 14000
where x is the number of years since 2000, and y is the cost of tuition in that year.
For example, in the year 2023 (23 years since 2000), the cost of tuition can be estimated as:
y = 400(23) + 14000 = $22,200
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The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 511 people paid admission, the total receipts were $7020. How many who paid were senior citizens
320 senior citizens paid for admission at the Family Fine Arts Center on that weekend evening.
Let's use the given information and these terms in our answer:
Let x represent the number of adult tickets sold, and y represent the number of senior citizen tickets sold.
We have two pieces of information that can be expressed as equations:
The total number of tickets sold: x + y = 511
The total receipts: 20x + 10y = 7020.
Now let's solve this system of equations step by step:
Solve the first equation for x:
x = 511 - y
Substitute the expression for x from Step 1 into the second equation:
20(511 - y) + 10y = 7020
Simplify the equation by distributing the 20:
10220 - 20y + 10y = 7020
Combine like terms:
-10y = -3200
Divide by -10 to find y:
y = 320.
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how do I find the inverse function of [tex]f(x)=\sqrt[3]{x-1}+4[/tex]
The inverse function of f(x) = ∛(x-1) + 4 is f⁻¹(x) = (x - 4)³ + 1
What is the inverse of the given function?Given the function in the question:
f(x) = ∛(x-1) + 4
To find the inverse of f(x), we need to switch the roles of x and y in the equation and then solve for y.
f(x) = ∛(x-1) + 4
Let y = f(x) = ∛(x-1) + 4.
y = ∛(x-1) + 4
Now, we can rewrite this equation in terms of x as follows:
x = ∛(y-1) + 4
Subtracting 4 from both sides, we get:
x - 4 = ∛(y-1)
Cubing both sides, we get:
(x - 4)³ = y - 1
Adding 1 to both sides, we get:
y = (x - 4)³ + 1
Replace y with f⁻¹(x)
f⁻¹(x) = (x - 4)³ + 1
Therefore, the inverse function is f⁻¹(x) = (x - 4)³ + 1.
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Select the correct answer.
Consider the functions graphed below.
-5
b
-3 -2
4
3
2
+
2
-3
4
5
a
1
2
C
3 4 S
X
Determine which function has the greatest rate of change over the interval [0, 2].
We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.
How is this correct?Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula:
m = (y2 - y1 /(x2 - x1)
Rate of change of a :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of :
m = (4-1)/2-0)
m = 1.5
The average rate of change of the function over the interval [0,2] is 1.5
Rate of change of b :
Here the end points are (0,0) and (2,2)
m = (2-0)/2-0)
m = 2/2
m=1
The average rate of change of the function over the interval [0,2] is 1
Rate of change of c:
Here the end points are (0,-1) and (2,0)
m = (0-(-1)/2-0)
m = 1/2
m= 0.5
The average rate of change of the function over the interval [0,2] is 0.5
Rate of change of d:
Here the end points are (0,0.5) and (2,2.5)
m = (2.5-0.5)/2-0)
m = 2/2
m= 1
The average rate of change of the function over the interval [0,2] is 1
We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.
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Full Question:
Determine which function has the greatest rate of change over the interval [0, 2].
See attached image.
It is estimated that 12.6% of drivers are uninsured. part a: what is the probability that exactly 5 drivers are uninsured if a police officer pulls over 30 drivers? round your answer to 4 decimal places. show your work. (5 points) part b: what is the probability the next uninsured driver that the police officer pulls over is the 7th driver? the 20 most populous countries in the world have an average population of 268.35 million with a standard deviation of 370.43 million. the united states has a population of 332 million, egypt has a population of 104 million, and mexico has a population of 128 million. india has a z-score of 2.86 , japan has a z-score of -0.39, and brazil has a z-score of -0.15. part a: calculate the z-scores for the united states, egypt, and mexico. show your work. (6 points) part b: list all 6 countries in order from smallest to largest population and then explain why you ranked them this way. famous basketball player michael jordan had a free throw percentage of 0.83. (he made 83% of his free throw shots.) assume that each free throw shot is independent. show your work. part a: what is the probability that the next free throw he misses will be the 6th throw? round your answer to 4 decimal places. (5 points) part b: what is the expected number of free throws until he misses his first free throw shot?
The probability that exactly 5 drivers are uninsured is approximately 0.3426.
The probability that the next uninsured driver is the 7th driver is approximately 0.000000000123.
Part a: Probability of exactly 5 uninsured drivers out of 30 pulled over
To calculate this probability, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of exactly k successes (5 uninsured drivers)
n is the total number of trials (30 drivers)
k is the number of successes (5 uninsured drivers)
p is the probability of success (12.6% or 0.126)
Using the formula:
P(X = 5) = C(30, 5) * 0.126^5 * (1-0.126)^(30-5)
Calculating the values:
C(30, 5) = 30! / (5! * (30-5)!) = 142506
0.126^5 = 0.00004422936
(1-0.126)^(30-5) = 0.4367520636
Plugging in the values:
P(X = 5) = 142506 * 0.00004422936 * 0.4367520636 ≈ 0.3426
Part b: Probability that the next uninsured driver is the 7th driver
Since each driver is pulled over independently, the probability of the next uninsured driver being the 7th driver is the same as the probability of having 6 insured drivers before encountering an uninsured driver.
Using the same binomial probability formula:
P(X = 6) = C(6, 6) * 0.126^6 * (1-0.126)^(30-6)
Calculating the values:
C(6, 6) = 6! / (6! * (6-6)!) = 1
0.126^6 = 0.00000002645
(1-0.126)^(30-6) = 0.044330365
Plugging in the values:
P(X = 6) = 1 * 0.00000002645 * 0.044330365 ≈ 0.000000000123
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General procedure for factor analysis or PCA
Factor analysis and PCA (Principal Component Analysis) are statistical techniques used to reduce data dimensionality and identify underlying patterns.
Here's a general procedure for both methods:
1. Data collection: Gather a dataset with relevant variables for analysis.
2. Standardization: Standardize the data to ensure variables have equal weight and influence.
3. Covariance or correlation matrix: Calculate the covariance (for PCA) or correlation (for factor analysis) matrix to identify relationships between variables.
4. Eigenvalue decomposition: Perform eigenvalue decomposition on the matrix to obtain eigenvalues and eigenvectors, which represent the amount of variance explained and the direction of the principal components/factors, respectively.
5. Select principal components or factors: Choose the number of components/factors to retain based on the proportion of variance explained and the scree plot, which displays eigenvalues in descending order.
6. Rotation (for factor analysis): Apply a rotation method (e.g., varimax or promax) to the factor loading matrix to simplify interpretation and achieve a more meaningful structure.
7. Interpretation: Analyze and interpret the principal components or factors and their relationships with the original variables.
Remember that PCA and factor analysis have different assumptions and goals: PCA focuses on identifying orthogonal axes maximizing variance, while factor analysis aims to explain the correlation structure among variables using underlying latent factors.
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For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that:
A two-tailed test seeks evidence that the population parameter for sample (1) is either greater than or less than the population parameter for sample (2).
For a two-sample hypothesis which tests for differences in population parameters (1) and (2), a two-tailed test seeks evidence that there is a significant difference between the means of the two populations, regardless of the direction of the difference.
In other words, the null hypothesis is that there is no difference between the two population means, and the alternative hypothesis is that there is a difference between them, either in the positive or negative direction.
The two-tailed test is used when we do not have any prior knowledge about the direction of the difference and want to be able to detect any significant difference, whether it is positive or negative.
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There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria.
1. This diagram shows a bacterium in hour 0 and then hour 1. Draw what happens in
hours 2 and 3.
There are some bacteria in a dish. Every hour, each bacterium splits into 3 bacteria. Hence, in total after 3 hours, we have 27 bacteria.
Bacteria are ubiquitous, largely free-living creatures that frequently only have one biological cell. They make up a significant portion of the prokaryotic microbial kingdom. Bacteria, which tend to be a few micrometres long and were among the initial organisms that appeared on Earth, are found in the majority of its habitats.
n = the number of bacteria at a given hour
at zero hour=1 bacteria.
1 bacteria after an hour is split in to 3 bacteria.
n(1) = 3
n(2) = 3 x 3 = 9 bacteria
n(3) = 9 x 3 = 27 bacteria
Hence, in total after 3 hours, we have 27 bacteria
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Find the solution to the system of equations by graphing.
(Use the answer box with the graph) y = -2x+4 and 6x+3y = 12
Answer:
To graph the system of equations:
1. Rewrite the equations in slope-intercept form (y = mx + b):
y = -2x + 4
3y = -6x + 12
y = -2x + 4
2. Plot the y-intercept of the first equation, which is (0, 4). Then use the slope of -2 (rise of -2 and run of 1) to plot additional points and draw the line.
3. Plot the y-intercept of the second equation, which is (0, 4). Then use the slope of -2 (rise of -2 and run of 1) to plot additional points and draw the line.
The solution to the system of equations is the point where the two lines intersect. From the graph, we can see that the lines intersect at the point (2, 0).
Therefore, the solution to the system of equations by graphing is:
x = 2
y = 0
Answer box: (2, 0)
This table shows the prices of various car models. Car Price 2-door coupe $21,750 4-door hatchback $22,500 Compact sedan $23,000 Compact SUV $23,400 Dean is ready to buy a new car. He has $24,000 to spend. The sales tax where he lives is 6%. He put his research on car prices in this table. What is the most expensive car that he can afford to buy? 2-door coupe 4-door hatchback compact sedan compact SUV
The most expensive car that he can afford to buy is 4-door hatchback.
We have,
Car Price 2-door coupe $21,750
4-door hatchback $22,500
Compact sedan $23,000
Compact SUV $23,400
Sales tax = 6%
So, the most expensive car Dean can buy is the 4-door hatchback.
= 22500 x 0.06
= 13501350 + 22500
= 23850
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Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.
Count the number of distinct islands. An island is considered to be the same as another if they have the same shape, or have the same shape after rotation (90, 180, or 270 degrees only) or reflection (left/right direction or up/down direction).
To count the number of distinct islands in a non-empty 2D array grid of 0's and 1's, we need to first identify the islands. An island is a group of 1's that are connected 4-directionally. We can use depth-first search or breadth-first search to identify the islands.
Once we have identified the islands, we need to check if they have the same shape or not. To check the shape of an island, we can use a hash function that takes into account the shape of the island. The shape of an island can be represented as a sequence of directions that we follow to traverse the island. For example, if we start at the top-left corner of the island and traverse it in a clockwise direction, the shape of the island can be represented as "up-right-down-left".
To check if two islands have the same shape, we can compare their hash values. If the hash values are the same, the islands have the same shape. However, we also need to consider the rotations and reflections of the islands. To handle rotations, we can generate all possible rotations of an island (90, 180, and 270 degrees) and compute their hash values. To handle reflections, we can flip the island horizontally and vertically and compute their hash values. We can then compare the hash values of the original island with the hash values of the rotated and reflected islands to determine if they have the same shape or not.
Finally, to count the number of distinct islands, we can store the hash values of all the islands in a set. The size of the set gives us the number of distinct islands.
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a right triangle has two legs measuring 9 and 40 respectively, what is the length of the hypotenuse?
Answer:
The length of the hypotenuse is 41.
Step-by-step explanation:
The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
In this case, the lengths of the legs are 9 and 40. Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]\sf:\implies h^2 = 9^2 + 40^2[/tex]
[tex]\sf:\implies h^2 = 81 + 1600[/tex]
[tex]\sf:\implies h^2 = 1681[/tex]
Taking the square root of both sides, we get:
[tex]\sf:\implies h = \sqrt{1681}[/tex]
Simplifying the square root, we get:
[tex]\sf:\implies \boxed{\bold{\:\:h = 41\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, the length of the hypotenuse is 41.
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a woman owns 21 pets. Each of her pets is either a cat or bird. If the pets have a total of 76 legs, and assuming that none of the birds legs are protuding from any of the cats jaws, how many cats and how many birds doe the woman own
The solution is taken by solving the linear equations. The woman will have 17 cats and 14 birds.
Let's assume that the woman has x cats and y birds.
Each cat has 4 legs, and each bird has 2 legs. Therefore, the total number of legs can be expressed as:
4x + 2y = 76
We also know that the woman owns a total of 21 pets, so we have:
x + y = 21
We can use these two equations to solve for x and y. First, we can rearrange the second equation to solve for x:
x = 21 - y
Substituting this into the first equation, we get:
4(21 - y) + 2y = 76
Expanding and simplifying, we get:
84 - 2y = 76
2y = 8
y = 4
So the woman owns 4 birds. We can use the second equation to find the number of cats:
x + 4 = 21
x = 17
Therefore, the woman owns 17 cats and 4 birds.
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Estimate the product. Round each factor to the nearest whole number, then multiply. 3 4 7 × 2 3 10
The product of the given numbers by rounding it to the nearest whole number is 8.
Given numbers are 3 4/7 and 2 3/10.
We have to find the product of these numbers by first rounding it to the nearest whole number.
3 4/7 means 3 + 4/7.
When we add 3/7 to it, it will become 4.
So the nearest whole number is 4.
2 3/10 means 2 + 3/10.
When we subtract 3/10 from it, the number is 2.
So the nearest whole number is 2.
The product of 4 and 2 is 8.
Hence the required product is 8.
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Given the head of a singly linked list and an integer k, split the linked list into k consecutive linked list parts.
The length of each part should be as equal as possible: no two parts should have a size differing by more than one. This may lead to some parts being null.
The parts should be in the order of occurrence in the input list, and parts occurring earlier should always have a size greater than or equal to parts occurring later.
Return an array of the k parts.
To split a singly linked list into k consecutive parts with roughly equal sizes, you can use the following algorithm:
1. Calculate the length of the linked list by iterating through it.
2. Determine the size of each part by dividing the length by k, and the remainder by using the modulus operator (%).
3. Initialize an array of linked list nodes with a size of k to store the head of each part.
4. Iterate through the linked list, and for each part:
a. Assign the current node as the head of the current part in the array.
b. Determine the number of nodes for the current part by adding the base size, and if the current part index is less than the remainder, add 1.
c. Move the current node pointer to the last node of the current part by iterating through the determined number of nodes.
d. Set the next pointer of the last node of the current part to null, and move the current node pointer to the next node in the linked list.
5. Return the array of the k parts.
This algorithm ensures that the linked list is split into k consecutive parts with sizes as equal as possible, and parts occurring earlier have a size greater than or equal to parts occurring later.
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Fill in the blank. A polygon is _____ if there are "dents" or indentations in it (where the internal angle is greater than 180°)
A polygon is called non-convex if there are "dents" or indentations in it, where the internal angle is greater than 180 degrees.
In other words, a non-convex polygon is a polygon whose line segments intersect, creating an interior angle greater than 180 degrees. This is in contrast to a convex polygon, where all of the interior angles are less than 180 degrees and none of the line segments intersect.
Non-convex polygons can have a variety of shapes and sizes, and can be composed of any number of sides. However, they are generally more difficult to work with mathematically than convex polygons, and often require more advanced techniques to analyze and understand their properties.
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A car manufacturing company has developed a new tire to endure road wear for longer periods than tires currently on the market. The claim that the new tire is superior to current tires is_______
The claim that the new tire is superior to current tires is the alternative hypothesis.
What is the claim about the new tire developed by a car manufacturing company to endure road wear for longer periods than current tires on the market?In hypothesis testing, we have a null hypothesis and an alternative hypothesis. The null hypothesis is the default assumption, usually that there is no difference or no effect. The alternative hypothesis is the opposite of the null hypothesis and is the claim we are trying to establish evidence for. In this case, the null hypothesis would be that the new tire is not superior to current tires, while the alternative hypothesis would be that the new tire is superior to current tires. We would then collect data on the performance of the new tire and current tires and use statistical methods to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.Learn more about "null hypothesis" and "alternative hypothesis".
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You are going to a Brooklyn nets game with your advisory. During a timeout, the performers are launching t shirts into the crowd! You are sitting in a balcony that is 64 feet above the ground, and you can see that a man is aiming the t-shirt gun right towards your section! The height of the t-shirt in feet can be modeled by the function h(t) = -16t + 80t, where t is the time in seconds since he shot the t-shirt.
A: is the performer launching the t-shirt from a platform or from the court (ground level)? How do you know?
B: After how many seconds will the shirt reach you? Explain whether your solution make sense in context
A: The performer is launching the t-shirt from the court (ground level). We can tell this because the initial height of the t-shirt is 0 feet when t = 0. The height of the t-shirt in feet can be modeled by the function h(t) = -16t^2 + 80t.
B: To find out when the shirt will reach you, we need to solve for t in the equation h(t) = 64. Substituting h(t) with 64, we get 64 = -16t^2 + 80t. Solving this quadratic equation, we get two solutions: t = 1 and t = 4. Since it doesn’t make sense for the shirt to reach you before it’s launched (t < 0), we can conclude that the shirt will reach you after 4 seconds.
The area of a rectangle is. A. Represent the area of the rectangle in factored form. B. Use the factored form to give one possible set of dimensions for this rectangle.
A. Factored form of the area of a rectangle: The area of a rectangle can be represented in factored form as length times width, or A = lw.
B. Possible set of dimensions for a rectangle: Suppose the factored form of the area of a rectangle is A = lw. If we are given the value of A, we can use it to find different combinations of length and width that would result in the same area. For example, if A = 12, one possible set of dimensions for the rectangle could be 3 units by 4 units (3 x 4 = 12). Another possible set of dimensions could be 2 units by 6 units (2 x 6 = 12). In fact, there are infinitely many possible sets of dimensions for a given area. However, it's worth noting that not all combinations of length and width will result in a valid rectangle. For a rectangle to be valid, both the length and width must be positive and non-zero.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 205 , 201 , 197 , . . . Find the 48th term.
Answer:
Step-by-step explanation:
To find the 48th term of the sequence, we need to determine the pattern or rule governing the sequence. From the given sequence, we can observe that each term is decreasing by 4 from the previous term. This means that the common difference between the terms is -4.
Using this information, we can write the general formula for the nth term of the sequence. The formula for the nth term of the sequence would be:
y = x + (n-1)d
where y is the nth term of the sequence, x is the first term, n is the position of the term we want to find, and d is the common difference.
Substituting the given values, we get:
x = 205
d = -4
Now we can plug in n = 48 and solve for the 48th term:
y = x + (n-1)d
y = 205 + (48-1)(-4)
y = 205 - 188
y = 17
Therefore, the 48th term of the sequence is 17.
Answer: 17
Step-by-step explanation:
1. First we find out how to get from 1 term to the next:
205 - 201 = 4, 201 - 197 = 4, and the sequence is decreasing each time so -4, -4n
2. Next we determine the difference between the sequence, and the -4 times table
205 201 197
-4 -8 -12
205 - - 4 = 201, 201 - - 8 = 209, etc...
so the difference is positive 209 (+209)
3. Next, we use the nth term rule (-4n+209), and substitute 48 into n:
-4 x 48 + 209
-4 x 48 = -192, -192 + 209 = 17
4. So 17 is the 48th term.
Find the lateral area of the right prism with height 0.3 dm, if the base of the prism is:
Parallelogram with sides of 6 cm and 20 mm
pls put the answer in cm
The requried, lateral area of the right prism is 4.8 cm².
To find the lateral area of a right prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the base of the prism is a parallelogram with sides of 6 cm and 20 mm, we first need to convert the length of one of the sides to the same unit as the other side.
20 mm is equal to 2 cm (since 1 cm = 10 mm), so the sides of the parallelogram are 6 cm and 2 cm.
The perimeter of the parallelogram base is the sum of the lengths of its four sides, which is:
Perimeter = 2(6 cm) + 2(2 cm) = 12 cm + 4 cm = 16 cm
Therefore, the lateral area of the right prism is:
Lateral Area = Perimeter of Base x Height
Lateral Area = 16 cm x 0.3 dm = 4.8 cm²
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Explain the importance of understanding place value
before you learn how to do multi-digit multiplication.
Answer it is important understanding place value because if u put the number in the wrong place the math will be messed up so it is important to understand we're the place value is before multiplying or any math.
Step-by-step explanation:
one hundred 50 cent coins have a mass of 690g what is the mass of 1 so cent coin
The mass of one cent coin is 6.9 grams.
Let's start by finding the total value of the 100 fifty-cent coins:
100 × 50 cents = 5000 cents
We know that each cent weighs the same amount, so we can set up a proportion to find the mass of one cent:
100 coins / 5000 cents = 1 coin / x cents
where x is the mass of one cent coin.
Simplifying this proportion, we get:
x = 5000 cents / 100 coins = 50 cents/coin
So, the mass of one fifty-cent coin is 50 cents/coin.
Now we can use the given information to find the mass of one cent coin:
690 g / 100 coins = 6.9 g/coin
Therefore, the mass of one cent coin is 6.9 grams.
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If y^3+y=x^2, then dy/dx=
A. 0
B. x/2
C. 2x/3y^2
D. 2x-3y^2
E. 2x/1+3y^2
If [tex]y^3+y=x^2[/tex], then [tex]dy/dx=2x/1+3y^2[/tex]. The correct answer is option e.
To find dy/dx, we first need to implicitly differentiate [tex]y^3 + y = x^2[/tex]with respect to x. Applying the chain rule, we have:
[tex]3y^2(dy/dx) + dy/dx = 2x[/tex]
Now we can solve for dy/dx:
[tex]dy/dx = (2x) / (3y^2 + 1)[/tex]
Substituting [tex]y^3 + y = x^2[/tex], we have:
[tex]dy/dx = (2x) / (3y^2 + 1) = (2x) / (3(x^2 - y))[/tex]
Therefore, the answer is E. [tex]2x/(1+3y^2)[/tex].
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Why is angle IKH a right angle?
Angle IKH must be right angle since line IH is the diameter of the circle.
What is a right angle?
A right angle is an angle that measures exactly 90 degrees, or a quarter of a full turn.
In the given diagram, we can see that line IH is the diameter of the circle.
Also if line IH is the diameter, then the angle at the circumference formed by the lines joining the diameter of the circle must be 90 degrees.
So angle KHI + angle KIH + angle IKH = 180 (sum of angles in a triangle)
angle KHI + angle KIH + 90 = 18
Thus, angle IKH must be right angle since line IH is the diameter of the circle, and angle IBH must also be 90 degrees.
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1.27 A rectangle has a length of 3.24 M and height of .532 m. To the correct number of sig figs is the area?
A 1.72 M
B 1.723 M
C
D
To the correct number of significant figures, the area of the rectangle is 1.723 m². The correct answer is an option (C).
As per the question, we have:
The length of the rectangle = 3.24 m
The width of the rectangle = 0.532 m
To find the area of the rectangle, we can use the formula:
Area of the rectangle = length x height
Substituting the given values, we get:
Area of the rectangle = 3.24 m × 0.532 m
Area of the rectangle = 1.72368 m²
To the correct number of significant figures, the area of the rectangle is 1.723 m².
Therefore, the correct answer is an option (C).
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