The radius of each cylinder is approximately 3.49 cm and the length of the plastic strip is approximately 65.84 cm.
Cylinder is a basic 3 dimensional solid with a curved surface. A cylinder can be identified as a prism with circular base.
The cross-section of a cylinder gives a circle whose area can be represented by πr² where r is the radius of the base of the cylinder.
Here the plastic wire encloses the area of cross-section of three cylinders.
Therefore area of cross-section of one cylinder=115÷3=(115/3) cm ²
Since area of cross-section of a cylinder=πr²
Therefore πr²=(115/3)
or, r=3.4931...
or, r≈3.49 cm
Hence the radius of each cylinder is approximately 3.49 cm
Now the plastic strip covers 3 cylinders .
Circumference of each cross-section of cylinder is given by =2πr
Total length of 3 cylinders = 2πr×3 = 6πr cm
Therefore total length= 64.843...cm ≈ 65.84 cm
Therefore the length of the plastic strip is approximately 65.84 cm
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Nick was scuba diving at -32 1/2 feet. If he descends another 8 3/5 feet, what is his location?
Answer:
-41.1 feet
Step-by-step explanation:
-32.5-8.6=-41.1
1/2=0.5
3/5=6/10=0.6
There are two teams of customer service representatives at a call center for a software company. The call center manager wants to give a prize to the team who most consistently has customer service calls with the least total call times. The two graphs show the distributions of the total call times of the two different teams. Team A 0 3 4 5 1 2 Total Call Times (minutes) Team B 0 I 2 3 4 5 Total Call Times (minutes) Which of the following provides a correct argument in support of the team that should be awarded the prize?
The correct argument in support of the team that should be awarded the prize is; Team A because their distribution of total call times is skewed to the right, which shows the majority of total call times are less than the mean.
How to interpret Skewed Graphs?
A skewed distribution is a distribution which is non-symmetric and also it has no mirror-imaging.
One common characteristic of skewed distributions, is that one tail of the distribution will be quite longer or drawn out relative to the other tail.
A distribution is said to be skewed right when one of the tail is on the right side.
A distribution is said to be skewed left when one of the tail is on the left side.
Now, we want to find the correct argument in support of the team that should be awarded the prize.
Looking at the two graphs of team A and B, we see that team A has a distribution that is skewed to the right which means majority of total call times are less than the mean.
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three times the smaller of three consecutive even integers is four less than twice the larger
The required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
What is integer?
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.
Given:
The statement is three times the smaller of three consecutive even integers is four less than twice the larger
According to given question we have
Let the even integers be x and x + 2 .
Here, x is the smaller integer
(x + 2) the bigger integer.
By the equation is
3x =2(x + 2)-4
compare the like terms we get
x=4-4
x=0
The smaller integer=0
The bigger integer= 0+2=2
Therefore, the required solution of the given statement is 0 the smaller integer and 2 for the bigger integer.
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Wayne charges a flat photography fee of $100 to take pictures. He also charges $35 per hour. If Wayne made $240 to take pictures at an event, how many hours did he spend taking pictures at the event?
Answer:
100 + 35x = 240
240 - 100 = 140 = 35x
140/35 = 4
Step-by-step explanation:
4 hours, not a bad pay o.o
Answer:
4 Hours
Step-by-step explanation:
Let y=money
Let x= Hours
y=mx+b
240=35x+100
minus 100
140=35x
divide 35
4=x
12 = -4(-6X - 3) what is x
Answer:
x=0
Step-by-step explanation:
12 = -4(-6x-3)
12 = 24x+12
-12 -12
0 = 24x
/ /
24 24
0 = x
Check
12 = -4(-6(0)-3)
12 = -4(0-3)
12 = 0 + 12
12 = 12
Melvin ordered a cinnamon roll, 3 doughnuts, and 2 dozen doughnut holes. The sales tax was $0.72. He paid with a $20 bill. How much change should Melvin receive from a $20 bill? Responses A $9.66 B$10.34 C$11.78 D$11.06
The amount of change that Melvin would receive from a $20 bill is equal to: C. $11.78.
How to determine Melvin's change?In order to determine the amount of change that Melvin would receive from a $20 bill, we would first of all calculate the total cost before tax.
For the cinnamon roll, we have:
Cinnamon roll's cost = $2.59.
For three (3) doughnuts, we have:
Doughnut's cost = 0.95 × 3
Doughnut's cost = $2.85.
For two (2) dozen doughnut holes, we have:
Doughnut hole's cost = 1.75 × 2
Doughnut hole's cost = $3.5.
Total cost = $2.59 + $2.85 + $3.5
Total cost = $8.94
Next, we would determine the new cost after applying sales tax:
New cost = 8.94 - 0.72
New cost = $8.22.
Now, we can determine Melvin's change:
Change = Dollar bill - New cost
Change = $20 - $8.22.
Change = $11.78.
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Answer:
4 C$11.78
Step-by-step explanation:
Reasoning Relation r has one element in its domain and two elements in its range. Is r a function? Is the inverse of r a function? Explain.
Relation r is not a function and Inverse function because a single
input gives several outputs.
What is the Reasoning Relation R?A subset of AB is a relation between two sets A and B. Consequently, an ordered pair (a,b) of a relation R is one where a=A and b=B. If (a,b)R, we say that it is connected to and write aRb.Sets are defined as a collection of well-defined objects. Relation refers to a relationship between the elements of 2 sets A and B. It is represented by R. We say that R is a relation from A to A, then R ⊆ A×A1. Identity Relation: In an identity relation, every element is related to itself. Its notation is I = (a, a), A.
2. Empty relation: In an empty relation, there will be no connection between the set's components. This is a subset of.
3. Reflexive relation: Each element is mapped to itself in a reflexive relation. If (a, a) R for all aR, a relation R in a set A is automatic.
4. An irreflexive relation exists when two elements are not related to one another.
5. Inverse relation: An inverse relation exists when a set contains elements that are inverse pairs of those in another set. For instance, R-1 = (q,p), (s,r) if A = (p,q), (r,s), etc.
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SOMEONE PLEASE HELP ME
1st - 3
2nd-1
3rd-4
5th-2
George jumps off a tire swing into a circular pond causing circles of waves. One of the waves travels at a rate of 16 ft/sec .
d. If the area of the pond is 22,000 square feet, how long will it take the circle to cover the area of the pond? Use this information to determine the diameter of the pond.
The wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.
We are given that the area of the pond = 22,000 square feet
Area = 22,000 feet²
π r² = 22,000
22 / 7 r² = 22,000
r² = 22000 × 7 / 22
r² = 7000
r = √ 7000
r = 10 √70
r = 83.76 feet
Also, since the wave travels 16 feet per second,
Time taken to cover the entire area = 83.76 / 16 = 5.23 seconds
The diameter of the lake = 83.76 + 83.76
d = 167.52 feet
Therefore, we get that the wave will take 5.23 seconds to cover the area of the pond and the diameter of the lake is 167.52 feet when the area of the lake is given as 22000 feet.
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i need help and this is IXL how do you do this?
Answer:
Q= (1, -1), R = (7,-1), S = (7,-10), P =. (1,-10)
Step-by-step explanation:
Look at the coordinate grind then look at the coordinates (x) vertically, then look at the coordinates(y) horizontally.
then plot it as (x, y)
Problem Solving
Use the table for Exercises
13-16 that shows the average
weights of popular dog breeds.
13. Complete the table.
14. Which weight(s) have a prime
factorization of exactly three
factors?
Breed
Cocker Spaniel
German Shepherd
Labrador Retriever
Beagle
Golden Retriever
Siberian Husky
Weight (lb)
20
81
67
25
70
50
Prime Factorization
Prime numbers are those numbers that are divisible only by the number itself and by 1. Such numbers are 2, 3, 5, and 7 etc.
Factorization is when we write a given mathematical term in product of its various factors. Suppose we are provided with a mathematical expression of:
x^2 + 3x + 2
We will undergo its Factorization and write the expression in its possible factors:
( x + 1 ) ( x + 2)
By multiplying these factors, we will get the actual expression x^2 + 3x + 2.
Prime Factorization is a method of identifying which prime numbers multiply together to give the original value/expression.
Suppose we have a number 60, then the prime factors of it will be:
60
6 x 10
2 x 3 2 x 5
In the problem statement above, we are provided with some popular dog breeds, and we are expected to find the prime factors of each of the given weights of the breed.
The weights that have a prime factorization of exactly three number are as follows:
Prime factors of 20 (Cocker Spaniel)
= 2 x 2 x 5
Prime factors of 50 (Siberian Husky)
= 2 x 5 x 5
Prime factors of 70 (Golden Retriever)
= 2 x 5 x 7
Weights that have the same number in their prime factorization are:
Prime factors of 81 (German Shepherd)
= 3 x 3 x 3 x 3
Prime factors of 25 (Beagle)
= 5 x 5
So, the prime factorization of the weights of the dog breeds are being found. While Labrador Retriever 67 is a prime number itself.
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Need an answer!! Please and thank you.
Answer: 110 degrees
Step-by-step explanation:
We know that all the angles of a triangle add to 180 degrees. Notice how there are already 60 and 50 degrees on the triangle. In order to find the last angle, we subtract 110 (60+5) from 180 to get 70.
Now, we know that the angle of a straight line is 180.
So, in order to find <BCD, take 70 and subtract it from 180.
Doing this, we find that m<BCD is 110 degrees
Which of the following functions are continuous for all real numbers?
f(x) = e²
g(x)=√x
Choose 1 answer:
f only
g only
Both f and g
Neither f nor g
APR include:
the principle and the term on the loan
finance and interest charges on the loan
finance charges on the loan
the principle and the interest on the loan
Interest on the loan
APR include: Interest on the loan
What does APR mean?
The APR which means annual percentage rate, is the interest rate on the loan, it is expressed in annual terms which is normally compounded monthly, by monthly compounding I mean the interest is computed on monthly basis.
APR has does not have anything to do with the principle and term of the loan since the principle is the loan amount and the term is the number of periods that the borrower is allowed to make repayments until the loan is fully repaid
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Find the highest common factor (HCF) of 90
jackie has fewer than 20 h to work on her jewelry. it takes her half an hour to make a necklace and an hour to make a bracelet. she wants to make x necklaces and y bracelets, and she wants at least twice as many bracelets as necklaces. select all inequalities that model this situation.
The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.
Let Jackie wants to make x necklace and y bracelets.
Now, Since it take her half an hour to make a necklace and one hour to make a bracelet.
Also since she has fewer than 20 h total to work on the jewelry. So we have
0.5x + 1y < 20
=> 0.5x + y < 20
and she want at least twice as many bracelets as necklace, so we have
y ≥ 2x
also the number of necklace should be greater than 0. So x > 0
So the required inequalities are:
0.5x + 1y < 20
y ≥ 2x
and x > 0
Hence, The inequalities that model the given situation are 0.5x+y<20, y≥2x and x>0.
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Given g(x)=5x-3g(x)=5x−3, find g(-2)g(−2).
What is the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6?
The the equation of a line that passes through the point (2, −10) and is parallel to 14x+2y=6 is 7x + y + 8 = 0.
A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.
The equation of a line parallel to a given line will have the same slope as the given.
The equation of a line having a slope m and passing through the point (x', y') is written as
y - y' = m (x - x').
This is called point - slope equation of a straight line.
In the given equation,
14x+2y=6
⇒ 2y = -14x + 6
⇒ y = -7x + 3
Comparing it with standard equation of a straight line; y = m x + c, the slope m of the given line = -7
Therefore equation of the line parallel to the given line and passing through point (x', y') = (2, -10) would be:
y - (-10) = -7x + 2
⇒ y + 10 = -7x + 2
⇒ 7x + y + 8 = 0
Hence the required equation of line 7x + y + 8 = 0
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Please help is this true or false
Answer:
True
Step-by-step explanation:
How do I solve this?
Answer:times 5 and 5 =25 7 and 7=49 add answers 74
Step-by-step explanation:
Evaluate each logarithm.
log₇49
After evaluating the logarithm log ₇ 49, we get the result as 2.
The common logarithm is also known as the base 10 logarithm. It is represented by log10 or simply log.
For example, the common logarithm of 1000 is written as log(1000). The common logarithm defines how many times we need to multiply by 10 to get the required output. The natural logarithm is called the logarithm of base e. The natural logarithm is represented by ln or loge. Here, "e" stands for Euler's constant which is approximately equal to 2.71828.
We need to evaluate log ₇ 49
x = log₇ 49
We can also write it as:
7ˣ = 49
7ˣ = 7²
Comparing the bases, we get that:
x = 2
Therefore, after evaluating the logarithm log ₇ 49, we get the result as 2.
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3. An example of an irrational number is _____.
A. -17 square root
B. square root of 16
C, -9 square root
D. square root for 1
A parking area at a department store is shaped like a quarter circle with a radius of 123 meters. Due to the fact that the department store is to be rebuilt, the parking area must be temporarily reduced to 1/3 of its original area. What is the radius of the new parking area assuming it is still a quarter circle?
a. 91 m
b. 71 m
c. 77m
d. 82 m
The radius of the new parking area is 82 meters
How to determine the radius of the new parking area?The radius of the old parking area is given as
Radius, R = 123 meters
From the question, we understand that:
The parking area must be temporarily reduced to 1/3 of its original area
This means that
New Radius = Old radius - Old radius * 1/3
So, we have
New Radius = 123 meters - 123 meters * 1/3
Evaluate the product
So, we have
New Radius = 123 meters - 41 meters
Evaluate the difference
New Radius = 82 meters
Hence, the radius of the new parking area is 82 meters
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Factor the ff.
1.) 2x² + 17x + 35
2.) 2y² - 5y - 3
3.) 3x² - 8x + 4
1.
[tex] 2x {}^{2} + 17x + 35 \\ = 2x {}^{2} + 10x + 7x + 35 \\ = 2x(x + 5) + 7(x + 5) \\ = (2x + 7)(x + 5)[/tex]
2.
[tex]2y {}^{2} - 5y - 3 \\ = 2y {}^{2} -6y + y - 3 \\ = 2y(y - 3) + 1(y - 3) \\ = (2y + 1)(y - 3)[/tex]
3.
[tex]3x {}^{2} - 8x + 4 \\ = 3x {}^{2} - 6x - 2x + 4 \\ = 3x(x - 2)( - 2)(x - 2) \\ = (3x - 2)(x - 2)[/tex]
dave earns his salary by making a 12.5% commision on all of his sales.if he sells $25000 this month,how much did he earn this month
PLEASE SHOW WORK
The total amount did he earn this month is $3125.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Dave earns his salary by making a 12.5% commission.
sales= $25000 this month.
According to given question we have
The basic formula is
Sales × Commission Percent/100 = Commission
$25000 ×12.5/100= Commission
Commission=$3125
Therefore, the total amount did he earn this month is $3125.
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△LMN with vertices L(4, 8), M(4, 3), and N(8, 8) is rotated 270° clockwise about the origin.
What are the coordinates of L′?
The image of the triangle at point L is L' = (-8, 4)
How to determine the image of the triangle when rotated?The vertices of the triangle are given as:
L(4, 8), M(4, 3), and N(8, 8)
The transformation rule is given as
270 degrees rotation
The rule of 270 degrees rotation is
(x,y) = (-y , x)
When the above rule is applied to the vertices of the triangle, we have:
L' = (-8, 4)
Hence, the image of the triangle at point L is L' = (-8, 4)
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Solve the system of equations using a matrix
x+5 y=-4
x+6 y=-5
The solution of system of equations is (1,-1).
Given that the system of equations is x+5y=-4, x+6y=-5.
The system of equations can be written in matrix form as
x+5y=-4
x+6y=-5
[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]
Write the matrix on the left as the product of coefficients and variables.
[tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}-4\\ -5\end{array}\right][/tex]
Firstly, find the inverse of the coefficient matrix.
The inverse of [tex]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right][/tex] is
[tex]\begin{aligned}\left[\begin{array}{ll}1& 5\\ 1&6\end{array}\right]&=\frac{1}{6(1)-5(1)}\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right] \\ &=\left[\begin{array}{ll}6&-5\\ -1&1\end{array}\right]\end{aligned}[/tex]
Next, multiply each side of the matrix equation by the inverse matrix . Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.
[tex]\begin{aligned}\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{ll}1&5\\ 1&6\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{ll}6&-5\\ -1& 1\end{array}\right]\left[\begin{array}{l}-4\\ -5\end{array}\right]\\ \left[\begin{array}{ll}1&0\\ 0&1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]&=\left[\begin{array}{l}1\\ -1\end{array}\right]\end{aligned}[/tex]
The identity matrix on the left verifies that the inverse matrix was calculated correctly.
[tex]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}1\\ -1\end{array}\right][/tex]
The solution is (1,-1).
Hence, the solution of the system of equtions using matrix is x+5y=-4, x+6y=-5 is (1,-1).
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x
10
8
What is the value of x?
X =
your ans
Step-by-step explanation:
the value of x is 6
The value of x will be 6 for the given triangle.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.
The value of x will be calculated as:-
x² = 10² - 8²
x² = 100 - 64
x² = 64
x = √36
x = 6
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Please help me please help me
Answer:
the third option I think it says (-1,4)
Step-by-step explanation:
So the directions are basically asking to turn in the paper 3 times ending up in the 1st quadrant. Because 90*3 equals 270 degrees. There would be only one point in the negative and there are 2 options. So, we would immediately know that the first option or the last option is wrong. I don't really know how to explain this without drawing so if you could try turning your paper 3 times then you'll see what I mean. Comment if you need any more help. Or if you have any questions. My explanation is pretty bad I apologize.
What is the image point of (-1,8)after a translation right 1 unit and up 2 units?
Answer:
so your first number in your plotted points is the x value and the next is the y value as shown here (x,y) so if it needs to go up 2 and right 1 what we do is increase the -1 to a 0 because you are moving right on the graph which makes it become a positive. now if you were to move up 2 that is your y coordinate because y controls up and down movement while x controls left and right movement so you would increase the 8 to 10 so you'll find no coordinates would end up being (0,10)