Surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].
How to find the surface area of the cylinder?The surface area of a cylinder can be calculated by adding the area of the two bases (which are circles) and the lateral area (which is the area of the curved surface).
The radius of the cylinder is given as 36m and the height as 46m. Therefore, the diameter of the cylinder is 72m (twice the radius). Using the formula for the area of a circle, we can calculate the area of each base:
[tex]$A_{base} = \pi r^2 = \pi (36m)^2 = 1296\pi m^2$[/tex]
The lateral area of the cylinder can be calculated using the formula:
[tex]$A_{lateral} = 2\pi r h$[/tex]
Substituting the given values, we get:
[tex]$A_{lateral} = 2\pi (36m) (46m) = 3312\pi m^2$[/tex]
Therefore, the total surface area of the cylinder is:
[tex]$A_{total} = A_{base} + A_{lateral} + A_{base} = 2A_{base} + A_{lateral}$[/tex]
Substituting the values we calculated, we get:
[tex]$A_{total} = 2(1296\pi m^2) + 3312\pi m^2 = 5904\pi m^2$[/tex]
So the surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].
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which statement explains the best measure of variability to use to compare the data sets? the mean is the best measure because the data sets have the same minimum weight. the range is the best measure because the distribution of zucchini weights is skewed left. the median is the best measure because the data sets have different medians. the standard deviation is the best measure because both data distributions are symmetric.
The correct option is D, The best measure of variability to use to compare the data sets is the standard deviation is the best measure because both data distributions are symmetric.
Let's examine each of the possibilities we've been provided so we can select the best one.
A. Since the data sets have the same minimum weight, the mean is the best indicator.
Option A is untrue about the measure of variability since the mean measures the central tendency of a data collection.
B. The distribution of zucchini weights is tilted to the left, making the range the most accurate measurement.
Given that both of our box plots are symmetric, option B cannot be true, as can be seen.
C. Because the medians of the data sets differ, the median is the best indicator.
Since the median is a measure of a data set's central tendency rather than variability, option C is the correct answer. not true.
D. Because both data distributions are symmetric, the standard deviation is the most accurate measurement.
Option D is the best option since standard deviation is the best measurement for symmetric data sets and both of our provided box plots are symmetric.
Distributions can take on many different forms, depending on the type of random variable being described. Some common distributions include the normal distribution, the uniform distribution, and the binomial distribution. In statistics, a distribution is a function that describes the probabilities of different outcomes in a random variable. A random variable is a variable whose value is determined by chance, such as the outcome of a coin toss or the height of a randomly selected person.
The normal distribution is perhaps the most well-known and is often used to model real-world phenomena, such as heights or weights of people, IQ scores, or measurements of physical characteristics. Understanding distributions is important in statistics because they allow us to make predictions and draw conclusions about populations based on a sample of data.
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Complete Question:-
The box plots show the distributions of weights of cucumbers and zucchini collected from a garden.
(see attachment)
Which statement explains the best measure of variability to use to compare the data sets?
A.The mean is the best measure because the data sets have the same minimum weight.
B. The range is the best measure because the distribution of zucchini weights is skewed left.
C. The median is the best measure because the data sets have different medians.
D. The standard deviation is the best measure because both data distributions are symmetric.
An phone playlist has songs of various genres
according to the table below. What is the probability
that, of three random songs, the first two are country
and the third is R&B? Once a song is played it will not
be repeated until all other songs are played.
Genre :Number of Songs
Rock: 12
Country :15
R&B :10
Classical :3
The probability of selecting two country songs followed by an R&B song is 0.0202.
What is the probability?The probability of selecting two country songs followed by an R&B song is determined below as follows:
The total number of songs in the playlist = 40
The probability of the first song being country = 15/40.
The probability of the second song also being country = 14/39
The probability of the third song being R&B =s 10/38
Therefore, the probability of selecting two country songs followed by an R&B song is:
Probability(country, country, R&B) = (15/40) x (14/39) x (10/38)
Probability(country, country, R&B) = 0.0202
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Identify the volume of the composite figure. The figure shows a rectangular prism with a cube removed. The prism is 9 meters long, 8 meters wide, and 3 meters high. The cube has a side of 4 meters
The volume of the composite figure is 152 m³.
How to solve for the volume of the shapeThe volume of a rectangular prism can be found using the formula V = lwh, where l is the length, w is the width, and h is the height.
For the rectangular prism:
V_prism = lwh = 9m * 8m * 3m = 216 m³
For the cube:
V_cube = s^3 = 4m * 4m * 4m = 64 m³
Now, subtract the volume of the cube from the volume of the prism:
V_composite = V_prism - V_cube = 216 m³ - 64 m³ = 152 m³
The volume of the composite figure is 152 m³.
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Tell whether finding the answer requires finding a greatest common factor or a least common multiple. You do not need solve the problem. A string of holiday lights at a store have three colors that flash at different times. Red lights flash every fifth second. Blue lights flash every third seconds. Green light flashes every four seconds. The store owner turns on the lights. After how many seconds will all three lights flash at the same time for the first time?
A. ) Greatest Common Factor
B. ) Lest Common Multiple
Finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer B. ) Least Common Multiple.
To determine whether finding the answer requires finding a greatest common factor (GCF) or a least common multiple (LCM), we need to analyze the given information.
In this scenario, the red lights flash every fifth second, the blue lights flash every third second, and the green lights flash every fourth second. We want to find the first time when all three lights flash simultaneously.
To find this time, we need to find the smallest number that is divisible by all three given numbers (5, 3, and 4). This means we are looking for the least common multiple (LCM) of these numbers.
To calculate the LCM, we can use the formula:
LCM(a, b) = (a * b) / GCF(a, b),
where GCF(a, b) represents the greatest common factor of numbers a and b.
Therefore, in this case, finding the answer requires finding the least common multiple (LCM) of 5, 3, and 4, making the correct answer:
B. ) Least Common Multiple.
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solve the equation sin theta equals to Cos 35
Answer:
55 degrees
Step-by-step explanation:
sin Φ = cos 35
sin Φ = .81915
Φ = arc sin (.81915) = 55 degrees
Or you could just know that the cos of an angle is equal to the sin of its comeplement
Find the composite volume of the figure
The volume of the composite figure is 96.3 cm³
How to find the volume?First we need to find the volume of the cylinder, and then remove the volume of the rectangular prism.
The radius of the prism is 3cm and the height is 5cm, then the volume is:
V = 3.14*R²*H
V = 3.14*(3cm)²*5cm
V = 141.3 cm³
And the volume of the prism is:
V' = 3cm*3cm*5cm = 45 cm³
The difference gives:
volume = 141.3 cm³ - 45 cm³
volume = 96.3 cm³
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John has $23. 65 spend on a book and magazines. The book costs $5. 95z the magazines cost $2. 95 each. A) write an equation that models the number of magazines that John can afford. B) solve the equation
John can afford approximately 6 magazines.
A) To write an equation that models the number of magazines John can afford, let's denote the number of magazines as 'm'. Since each magazine costs $2.95 and John has a total of $23.65 to spend, the equation can be expressed as:
2.95m + 5.95 = 23.65
B) To solve the equation, we can isolate the variable 'm' by subtracting 5.95 from both sides:
2.95m = 23.65 - 5.95
2.95m = 17.70
Then, divide both sides by 2.95:
m = 17.70 / 2.95
m ≈ 6
Therefore, John can afford approximately 6 magazines.
In conclusion, the equation 2.95m + 5.95 = 23.65 models the number of magazines John can afford, and by solving it, we find that he can purchase approximately 6 magazines with the given amount of money.
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square peg sydney smith wrote in ""on the conduct of the understanding"" that it is im-possible to fit a square peg in a round hole.
On the basic of square peg sydney smith written point the probability that it is im-possible to fit a square peg in a round hole is equals to the zero.
Probability is defined as the number of chances of occurrence of an event. It is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Mathematical formula is written as, probability of an event, P(E) = (Number of favorable outcomes)/(Total possible outcomes). Now, we have specify that according to sydney smith written in on the conduct of the understanding about square peg that it is impossible to fit a square peg in a round hole. Let consider an event A of fit a square peg in a round hole. We have specify that it is impossible to fit a square peg in a round hole. So, the favourable possible outcomes for event A = 0. Therefore, the probability that to fit a square peg in a round hole, P(A) = 0
Hence, required probability value is zero.
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The function h is given by h(x)=log_2(x^2 -6). For what positive value of x does h(x)=4?
The function h is given by h(x)=log2(x² -6). The positive value of x that makes h(x) equal to 4 is approximately 4.69
We have the function:
h(x) = log2(x² - 6)
We want to find the value of x that makes h(x) equal to 4:
h(x) = 4
log2(x² - 6) = 4
We can rewrite this equation as:
2⁴ = x² - 6
16 = x² - 6
x²= 22
x = √22 (because we are looking for a positive value of x)
Therefore, the positive value of x that makes h(x) equal to 4 is approximately 4.69 (rounded to two decimal places).
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Evaluate the following using suitable identities:
(i) (99)^3 (ii) (102)^3 (iii) (998)^3
We may use the identity (a + b)³ = a³ + 3a²b + 3ab² + b³ to get 970299, 1061208, and 992016008 for (i), (ii), and (iii), respectively.
Using the identity (a + b)³ = a³ + 3a²b + 3ab² + b³ allows us to expand and simplify the expressions by distributing and collecting like terms. Any integer's cubes can be calculated using this method.
(i) Using the identity, we can write 99 as 100 - 1 and get:
= (99)³
= (100 - 1)³
= 100³ - 3(100²)(1) + 3(100)(1²) - 1³
= 970299
(ii) We can denote 102 as 100 + 2 and use the identity to obtain:
= (102)³
= (100 + 2)³
= 100³ + 3(100²)(2) + 3(100)(2²) + 2³
= 1061208
(iii) Using the identity, we may write 998 as 1000 - 2 and get:
= (998)³
= (1000 - 2)³
= 1000³ - 3(1000²)(2) + 3(1000)(2²) - 2³
= 992016008
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Choose the function table that matches the given rule. Output = Input – 3 (1 point) Input Output –2 –5 1 –2 6 3 Input Output 2 –1 –2 3 0 –6 Input Output 5 2 2 –5 0 9 Input Output 6 3 –6 –3 5 0
The function table that matches the given rule output = input - 3 is
Input = -2, 1, 6 and output = -5, -2, 3
A) first function table
Output = Input - 3
Value of input:- -2
Putting the value of the input
Output = -2 -3
The value of output we get
Output = -5
Value of input:- 1
Putting the value of the input
Output = 1 -3
The value of output we get
Output = -2
Value of input:- 6
Putting the value of the input
Output = 6 -3
The value of output we get
Output = 3
Hence function table A is correct match
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To synthesize information regarding when books were written, alex should create a a. timeline c. venn diagram b. chart d. none of these please select the best answer from the choices provided a b c d
To synthesize information regarding when books were written, Alex should create a timeline. So, the correct option is A.
A timeline is a visual representation of chronological events, which can be used to arrange information in order based on their time of occurrence. In this case, Alex can plot the publication dates of the books on a timeline, allowing him to see how the dates relate to each other and to other events. This will help him to identify patterns and trends in the publication history of the books.
A Venn diagram, on the other hand, is a tool used to compare and contrast two or more sets of information. It is not well-suited for presenting chronological information.
A chart may be useful in presenting data in a visual manner, but it may not be as effective as a timeline in showing the order of events over time.
Therefore, the best answer from the choices provided is A. timeline.
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THIS IS FOR 20 POINTS
What is the value of a?
27.5
50
90
45
The measure of arc a must be 2 times measure of inscribed angle, which is 90 degrees.
What is arc?
In geometry, an arc is a segment of a circle's circumference. It is defined by two endpoints and all the points on the circle's circumference between them.
What is inscribed angle?
An inscribed angle is an angle formed by two chords in a circle that have a common endpoint.
According to given information:For any inscribed angle in a circle, the measure of the angle is always half the measure of the arc that it intercepts. This is known as the inscribed angle theorem.
So, if we have an inscribed angle with a measure of 45 degrees, then the measure of its corresponding arc would be 2 times that, which is 90 degrees.
Therefore, if the inscribed angle is associated with arc a, and the measure of the corresponding angle is 45 degrees, then we know that the measure of arc a must be 2 times that, which is 90 degrees.
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Use the equation, 8^2x = 32^x+3 , to complete the following problems.
(a) rewrite the equation using the same base.
(b) solve for x. write your answer in the simplest form.
side note: don't respond with a link because your answer is deleted immediately, and i therefore i have no way of accessing the answer, also please show your work!
The solution to the equation is x = 15.
(a)How to rewrite the exponential equation?To rewrite the exponential equation using the same base, we need to express both 8 and 32 as powers of the same base. Since both 8 and 32 are powers of 2, we can rewrite the equation as:
[tex](2^3)^(2x) = (2^5)^(x+3)[/tex]
Here, we used the fact that[tex](a^b)^c = a^(b*c)[/tex]to simplify the exponents. We also used the property that 8 is equal to 2 raised to the power of 3, and 32 is equal to 2 raised to the power of 5.
(b)How to solve for x?Now that we have rewritten the equation with the same base, we can equate the exponents on both sides of the equation to solve for x:
[tex]2^(6x) = 2^(5x + 15)[/tex]
Since the bases on both sides of the equation are equal, we can equate the exponents and solve for x:
6x = 5x + 15
Subtracting 5x from both sides, we get:
x = 15
Therefore, the solution to the equation is x = 15.
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Neil is creating a computer game in which bubbles represented by circles collide, merge, and separate in different ways. A bubble may be enclosed in a square whose side length is equal to the bubble's diameter. Four bubbles in squares collide and merge into one large bubble in a square. The area of the large bubble is equal to the sum of the areas of the small bubbles. How is the side length of the large square related to the side length of the small square?
the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.
what is length ?
Length is a physical quantity that refers to the measurement of a one-dimensional distance or extent, such as the distance between two points. It is typically measured in units such as meters, feet, inches, or centimeters. Length can be used to describe the size or dimensions
In the given question,
Let's assume that the side length of the small square is equal to the diameter of each small bubble.
When four bubbles in squares collide and merge into one large bubble in a square, the total area of the small squares is equal to the area of the large square. Since the side length of each small square is equal to the diameter of the small bubble, the area of each small square is equal to the square of the diameter of the small bubble.
So, if we let d be the diameter of each small bubble, then the area of each small square is equal to d². Therefore, the total area of the four small squares is equal to 4d², and the area of the large square is equal to the sum of the areas of the four small squares, which is 4d².
The area of a circle is equal to πr², where r is the radius of the circle. If we let R be the radius of the large bubble, then its area is equal to π².
We know that the area of the large square is equal to the area of the large bubble, so we have:
4d² = πR²
Solving for R, we get:
R =√(4d²/π)
R = 2d/√(π)
Since the side length of the large square is equal to twice the radius of the large bubble, we have:
Side length of large square = 2R = 4d/√(π)
Therefore, the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.
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Which scatter plot below would best be modeled by using linear regression?
Answer:
Top
Step-by-step explanation:
The closer the data points come to forming a straight line when plotted, the higher the correlation between the two variables, or the stronger the relationship. Therefore, the top option has the most closest lines to a linear function.
(Ex. 1) Y=4x-2
This example shows the corresponding possibilities of a linear regression because of the way the line is represented as graphed, making a straight line as similar to the top option
(Ex. 2) f(x) = x^2-5+15
This example dialates to a similar option like the third option, which isnt linear regression because of it being a quadratic function.
In a nut shell, all data plotted on the graph that are formed closer together and corresponds to a linear equation is a linear regression
Consider ABC.
What is the length of AC
A. 32units
B.48units
C.16units
D.24units
On the math exam,5 tasks were given. 25% of students solved at least two tasks. Prove that there was at least one task that no more than 12 students solved if 32 students wrote that test
Given that 25% of students solved at least two tasks and there were 32 students who wrote the test, we can prove that there was at least one task that no more than 12 students solved.
There was at least one task that no more than 12 students solved, we can use a proof by contradiction.
Assume that all five tasks were solved by more than 12 students. This means that for each task, there were at least 13 students who solved it. Since there are five tasks in total, this implies that there were at least 5 * 13 = 65 students who solved the tasks.
However, we are given that only 25% of students solved at least two tasks. If we let the number of students who solved at least two tasks be S, then we can write the equation:
S = 0.25 * 32
Simplifying, we find that S = 8.
Now, let's consider the remaining students who did not solve at least two tasks. The maximum number of students who did not solve at least two tasks is 32 - S = 32 - 8 = 24.
If all five tasks were solved by more than 12 students, then the total number of students who solved the tasks would be at least 65. However, the maximum number of students who could have solved the tasks is 8 (those who solved at least two tasks) + 24 (those who did not solve at least two tasks) = 32.
This contradiction shows that our initial assumption is false. Therefore, there must be at least one task that no more than 12 students solved.
Hence, we have proven that there was at least one task that no more than 12 students solved if 32 students wrote the test.
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What is the area of the curved surface of a right circular cone of radius 15 and height 8? The area of the curved surface is | | units. (Type an exact answer in terms of π.)
Curved surface area of cone: 255π or approx. 801.41 sq units with radius 15 and height 8.
The curved surface area of a right circular cone can be calculated using the formula:
A = πrℓ
where A is the area of the curved surface,
r is the radius of the base of the cone, and
ℓ is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem:
ℓ² = r² + h²
where h is the height of the cone.
Substituting the given values, we get:
ℓ² = 15² + 8²
ℓ² = 225 + 64
ℓ² = 289
ℓ = √289
ℓ = 17
Now, substituting the values of r and ℓ in the formula for curved surface area, we get:
A = πrℓ
A = π(15)(17)
A = 255π
Therefore, the area of the curved surface of the cone is 255π square units, or approximately 801.41 square units.
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list all the Factors. circle the GCF.
6:
9:
list 7 multiples.Circle the LCM.
5:
2:
Answer:
List all the factors
6: 3, 2, 1 (6)
9:3,(9),1
5:(5),1
2:(2),1
Step-by-step explanation:
Help me with homework
Therefore, the perimeter of the rectangle is 38 units that is option C.
What is coordinate?A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.
Here,
First, we need to find the distance between points A and B to determine the length of the rectangle:
Distance AB = |yB - yA|
= |8 - 2|
= 6
Next, we need to find the distance between points B and C to determine the width of the rectangle:
Distance BC = |xC - xB|
= |6 - (-7)|
= 13
Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * (length + width)
Perimeter = 2 * (13 + 6)
Perimeter = 2 * 19
Perimeter = 38
So the answer is (C) 38.
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just need help with this
The rate of change between August and October is
What is rate?Rate is how a quantity changes over a period of time.
Therefore rate = change in quantity/change in time.
For example acceleration is defined as the rate of change of velocity with time. This means that acceleration = change in velocity/time
change in quantity = 85-81 = 4
change in time = 2 months
therefore rate of change = 4/2 = $2 per month
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Shandra has $760 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. ⢠She buys a new bicycle for $433. 54. ⢠She buys 2 bicycle reflectors for $18. 41 each and a pair of bike gloves for $10. 76. ⢠She plans to spend some or all of the money she has left to buy new biking outfits for $66. 40 each. Write and solve an inequality which can be used to determine o, the number of outfits Shandra can purchase while staying within her budget. â
We can use an inequality to determine the number of biking outfits Shandra can purchase while staying within her budget.
Let o represent the number of outfits she can purchase. Here are the given terms and costs:
- Initial budget: $760
- Bicycle cost: $433.54
- 2 reflectors cost: 2 * $18.41 = $36.82
- Bike gloves cost: $10.76
- Outfit cost: $66.40 each
Now, we can set up the inequality:
760 >= 433.54 + 36.82 + 10.76 + 66.40 * o
First, combine the constants:
760 >= 481.12 + 66.40 * o
Now, subtract 481.12 from both sides:
278.88 >= 66.40 * o
Finally, divide both sides by 66.40:
o <= 4.2
Since Shandra can only purchase whole outfits, the maximum number of outfits she can buy is 4. So the inequality representing this situation is o <= 4.
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How would I solve this equation by factoring m²-64 = 0
A shoe store orders shoes from the manufacturer and sells them at a mall. Storing shoes at the store costs $6 per shoe pair for a year. When reordering shoes from the manufacturer, there is a fixed cost of $14 per order as well as $7 per shoe pair. The retail store sells 1750 shoe pairs each year. Find a function that models the total inventory costs as a function of x x the number of shoe pairs in each order from the manufacturer
The total inventory costs consist of two parts: the cost of storing the shoes and the cost of reordering the shoes. The cost of storing the shoes is given by the formula:
Cost of storing = $6 per shoe pair per year x number of shoe pairs
Since the shoes are stored for a year, this cost is incurred annually. The cost of reordering the shoes is given by the formula:
Cost of reordering = $14 per order + $7 per shoe pair x number of shoe pairs
This cost is incurred each time the store places an order with the manufacturer.
Let x be the number of shoe pairs in each order from the manufacturer. The number of orders needed to sell 1750 shoe pairs each year is given by:
Number of orders = 1750 shoe pairs / x shoe pairs per order
The total inventory costs can be expressed as:
Total cost = Cost of storing + Cost of reordering
Substituting the formulas for the two costs and the expression for the number of orders, we get:
Total cost = $6 per shoe pair per year x 1750 shoe pairs + ($14 per order + $7 per shoe pair x x shoe pairs) x (1750 shoe pairs / x shoe pairs per order)
Simplifying this expression, we get:
Total cost = $10,500 + $14(1750/x) + $7(1750)
Total cost = $10,500 + $24,500/x
Therefore, the function that models the total inventory costs as a function of x is:
Total cost(x) = $10,500 + $24,500/x
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Leslie works for Blank Chemical Corporation. Her annual salary is $57,285. 50. She is
paid biweekly (26 weeks). Each pay period, Leslie's employer deducts $418. 63 for
federal tax withholding. City tax for Blank Chemical employees is 3. 65%. What is Leslie’s annual social security (6. 2%) deduction?
Leslie’s annual social security deduction is $3551.70.
How to determine Leslie’s annual social security deduction?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Leslie’s annual salary is $57,285. 50 and her annual social security deduction is 6.2% of the annual salary. We can say:
Annual social security deduction = 6.2/100 * 57,285. 50
Annual social security deduction = $3551.70
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. The volume of a sphere is 6,000π m^3. What is the surface area of the sphere to the nearest square meter?
*
18850 m^2
33 m^2
1090 m^2
3425 m^2
The correct option is the last one, the surface is 3425 m²
How to get the surface area of the sphere?Remember that for a sphere of radius R, the volume is:
V = (4/3)pi*R³
S = 4pi*R²
Where pi = 3.14
Here the volume is 6,000π m³, then the radius will be:
R =∛( (3/4)*6,000m³)
R = 16.51 m
Then the surface area is:
[tex]S = 4*3.14*( 16.51 m)^2 = 3,424 m^2[/tex]
The option that is closser to it is the fourth one, so that is the correct option.
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A dessert has both fruit and yogurt inside.Altogether,the mass of the dessert is 185g.The ratio of the mass of fruit to the mass of yogurt is 2:3 What is the mass of yogurt?
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F (X) = X + 3
G (X) = 7X + 4
WHAT DOES (F + G) (X) EQUAL??
The solution to the composite function (f + g)(x) is: 8x + 7
How to solve Composite Functions?Composite functions are said to occur when the output of one function is used as the input of another. If we have a function f and another function g, it means that the function fg(x), said as “ f of g of x”, is the composition of the two functions.
Now, we are given two functions as:
f(x) = x + 3
g(x) = 7x + 4
Thus, we can say that:
(f + g)(x) = f(x) + g(x)
= x + 3 + 7x + 4
= 8x + 7
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Victoria has $200 of her birthday gift money saved at home, and the amount is modeled by the function h(x) = 200. She reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1. 05)x−1. Explain how Victoria can combine the two functions to model the total amount of money she will have in her bank account as interest accrues after she deposits her $200. Justify your reasoning.
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The total amount of money Victoria will have in her bank account after x years can be modeled by the function f(x) = 200 * (1.05)ˣ.
How can we model Victoria's bank account growth over time?To model the total amount of money Victoria will have in her bank account after depositing her $200 and accruing interest over time, we can combine the two functions h(x) and s(x).
We can use the following formula to represent the total amount of money Victoria will have in her bank account after x years:
f(x) = h(x) + h(x) * s(x)
where h(x) represents the $200 that Victoria has saved at home, and h(x) * s(x) represents the amount of interest accrued on that $200 in x years according to the function s(x).
The justification for this formula is that the total amount of money Victoria will have in her bank account after x years is the sum of the initial amount of $200 and the interest accrued on that amount over x years.
The interest accrued can be calculated by multiplying the initial amount by the interest rate function s(x).
For example, if Victoria leaves her $200 in the bank for 5 years, the total amount of money she will have in her account can be calculated using the formula:
f(5) = h(5) + h(5) * s(5) = 200 + 200 * (1.05)⁴ ≈ $273.04
Therefore, the total amount of money Victoria will have in her bank account after x years can be modeled using the function f(x) = h(x) + h(x) * s(x).
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