what pyramid???????
i think you forgot the pyramid
A deep-cone clarifier tank is being built. The radius is 5 feet, the height of the cylinder is 8 feet and the height of the cone is 6 feet. Assuming there is no sheet metal overlap, how much sheet metal is needed to build this tank including the top? Must show work
Answer:
Is needed [tex]452.32\ ft^{2}[/tex] of sheet metal to build this tank
Step-by-step explanation:
we know that
To find how much sheet metal is needed to build this tank including the top, calculate the lateral area of the cone plus the lateral area of the cylinder plus the area of the top of the cylinder
[tex]A=\pi rl+2\pi rh1+\pi r^{2}[/tex]
we have
[tex]r=5\ ft[/tex]
[tex]h1=8\ ft[/tex] ----> height of the cylinder
[tex]h2=6\ ft[/tex] ----> height of the cone
Find the slant height of the cone l
Applying Pythagoras Theorem
[tex]l^{2}=r^{2}+h2^{2}[/tex]
substitute
[tex]l^{2}=5^{2}+6^{2}[/tex]
[tex]l^{2}=61[/tex]
[tex]l=\sqrt{61}\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]A=(3.14)(5)(\sqrt{61})+2(3.14)(5)(8)+(3.14)(5)^{2}[/tex]
[tex]A=122.62+251.2+78.5=452.32\ ft^{2}[/tex]
If a || b and _____, then a || c.
b perpendicular c
b || c
a perpendicular c
b perpendicular a
The answer is:
The correct option, is the second option:
b || c ( b and c are parallel).
Why?To solve the problem, let's remember the following relationship:
If:
[tex]a=b[/tex]
and
[tex]b=c[/tex]
Then:
[tex]a=c[/tex]
So, from the statement we know that a and b are parallel (a || b), so, if a and c are parallel ( a || c) it means that b and c are parallel ( b || c).
Hence, the correct option is:
The second option, b || c ( b and c are parallel)
Have a nice day!
If the company has set a goal of producing 20 radios for a cost of 2,500, which statement is true?
(1.Plant A is producing at a cost that is farthest from the goal
(2. Plant C is producing at a cost greater than the goal.
(3. Plant B is at the goal
Answer: 2) Plant C is producing at a cost greater than the goal.
Explains which plant is achieving the goal set by the company regarding radio production costs.
Correct Statement: Plant B is at the goal of producing 20 radios for a cost of $2,500.
Explanation:
Plant A being farthest from the goal is inaccurate since the question mentions Plant B is producing at the goal cost.
Plant C producing at a cost greater than the goal is incorrect as Plant B is already reaching the goal cost.
Plant B is indeed at the goal, as stated in the question, producing 20 radios for a cost of $2,500.
You can work at most 20 hours next week. You need to earn at least $90 to cover your weekly expenses. Your dog walking job pays $9.00 per hour and your job as a car wash attendant pays $10.00 per hour. This situation can be represented by a system of inequalities, where x = dog walking hours and y = car washing hours. Identify two possible combinations of hours you can work at both jobs. Create a system of linear inequalities and solve.
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x ----> the dog walking hours
y ----> the car washing hours
we know that
The system of linear inequalities is equal to
[tex]x+y\leq20[/tex] -----> inequality A
[tex]9x+10y\geq 90[/tex] -----> inequality B
Solve the system of inequalities by graphing
The solution is the shaded area
see the attached figure
Two possible combinations of hours are
(10,10) and (0,9)
Verify
For (10,10)
Substitute the value of x and the value of y in both inequalities
Inequality A
[tex]10+10\leq20[/tex]
[tex]20\leq20[/tex] -----> is true
Inequality B
[tex]9(10)+10(10)\geq 90[/tex]
[tex]190\geq 90[/tex] ----> is true
therefore
(10,10) is a possible solution
For (0.9)
Substitute the value of x and the value of y in both inequalities
Inequality A
[tex]0+9\leq20[/tex]
[tex]9\leq20[/tex] -----> is true
Inequality B
[tex]9(0)+10(9)\geq 90[/tex]
[tex]90\geq 90[/tex] ----> is true
therefore
(0,9) is a possible solution
Final answer:
The situation can be described by two inequalities: x + y <= 20 and 9x + 10y >= 90. Two possible combinations of hours that meet these requirements are 0 hours of dog walking and 9 hours of car washing, or 8 hours of dog walking and 2 hours of car washing.
Explanation:
To represent this situation with a system of linear inequalities, we will let x be the number of hours working as a dog walker and y be the number of hours working as a car wash attendant. The two inequalities based on the constraints of the problem are:
x + y \<= 20 (because you can't work more than 20 hours).
9x + 10y >= 90 (because you need to earn at least $90).
Solving this system can be done graphically or algebraically. Let's see two possible solutions:
If you want to work at both jobs, you could work 8 hours dog walking (x=8) and 2 hours at the car wash (y=2). This means you would earn 8*$9 + 2*$10 = $92, which is also enough to cover the expenses.
One letter is selected from the word "statistics." What is the probability that an "s" or "t" is chosen?
1/5
2/5
1/2
3/5
Answer:
3/5
Step-by-step explanation:
There are 10 letters in the word "statistics".
Out of which, there are 3 s's and 3 t's.
So, the question asks what's the probability to get a S or a T out of 10 letters.
Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.
6/10 or if we simplify/reduce it... we get 3/5.
the correct answer is 3/5
The question is asking for the probability of selecting either an 's' or a 't' from the word 'statistics'. To solve this, we need to look at the total number of each letter and the total number of letters in the word. The word 'statistics' has 10 letters in total, with 3 's' letters and 3 't' letters.
To calculate the probability, we add the number of 's' letters to the number of 't' letters, which gives us 6. Then we divide this sum by the total number of letters in the word:
Probability('s' or 't') = (Number of 's' + Number of 't') / Total number of letters
Probability('s' or 't') = (3 + 3) / 10 = 6/10 = 3/5.
Thus, the correct answer is 3/5, meaning there is a 60% chance of picking either an 's' or a 't' from the word 'statistics'.
Please help!!!!!!!!!!!!!!
Answer:
51.3°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
For angle y, the opposite side is 10 cm, and the adjacent side is 8 cm. Then you have ...
tan(y) = (10 cm)/(8 cm)
y = arctan(1.25) ≈ 51.3402° ≈ 51.3°
The image of (triangle) ABC is (triangle) A'B'C. What transformations would result in this image?
A.(triangle)ABC is reflected over the y-axis, then is rotated -90° around the origin.
B.(triangle)ABC is reflected over the line y = x.
C.(triangle)ABC is rotated -90° around the origin, then is reflected over the x-axis.
D.(triangle)ABC is rotated 90° around the origin, then is reflected over y-axis.
Answer:
The triangle ABC is reflected over the line y = x ⇒ answer B
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
* Lets find the vertices of ABC and A'B'C' to solve the problem
- In Δ ABC
# A = (5 , -5) , B = (5 , -4) , C = (2 , -4)
- In Δ A'B'C'
# A' = (-5 , 5) , B = (-4 , 5) , C = (-4 , 2)
∵ The image of (5 , -5) is (-5 , 5)
∵ The image of (5 , -4) is (-4 , 5)
∵ The image of (2 , -4) is (-4 , 2)
∴ The point (x , y) is (y , x)
- From the rule above
∴ The triangle ABC is reflected over the line y = x
Answer:
The triangle ABC is reflected over the line y = x ⇒ answer B
Step-by-step explanation:
Help with this question, please!!
Answer:
72°
Step-by-step explanation:
You correctly found x, but the measure of the angle is ...
4x-22 = 4·23.5-22 = 72°
___
or (6x-69)° = (141-69)° = 72°
The number which is repeated as a factor in an exponential expression exponent 2. the fixed amount multiplied by a term to get to the next term in a geometric sequence radical expression 3. the (superscript) number in an exponential expression which tells how many times a factor is repeated index 4. a sequence in which there is a common ratio between the terms geometric sequence 5. the small number preceding a radical symbol that indicates the desired root of the radicand rationalize 6. expressions having the same root index and the same radicand like radicals 7. an expression that contains a radical; √7 and √21y are examples of radical expressions term 8. the expression under a radical symbol common ratio 9. eliminate the radical from the denominator of a fraction radicand 10. a set of numbers that follows a pattern, with a specific first number sequence 11. an individual quantity or number in a sequence base
An exponential expression refers to an expression where a base number is raised to a certain power or exponent. The exponent indicates how many times the base number is repeated as a factor. Exponential expressions can be simplified or evaluated using the rules of exponents.
Explanation:In mathematics, an exponential expression refers to an expression where a base number is raised to a certain power, or exponent. The exponent indicates how many times the base number is repeated as a factor. For example, in the expression 23, 2 is the base and 3 is the exponent, so it means that 2 is repeated as a factor three times. Exponential expressions can be simplified or evaluated using the rules of exponents.
For example, in the expression 42, 4 is the base and 2 is the exponent, so it means that 4 is repeated as a factor two times. This can be evaluated as 42 = 4 x 4 = 16.
Exponential expressions are commonly used in various mathematical applications, such as in compound interest, population growth, and scientific calculations.
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What fraction is equal to the percent? Simplify the fraction. 16% =
Answer: 16% as a fraction is 4/25
Step-by-step explanation:
convert 16% into a decimal then put it over 100 and simplify which gives you 4/25
Answer: [tex]=\frac{4}{25}[/tex]
Step-by-step explanation:
First, you need to convert 16% to decimal form. To do this, you must divide it by 100. Then, the numerator will be 16 and the denominator will be 100:
[tex]=\frac{16}{100}[/tex]
And finally, you need to simplify the fraction by reducing it. Notice that the numerator and the denominator can be both divided by 4. Then, dividing by 4 you get:
[tex]=\frac{4}{25}[/tex]
Since the numerator and the denominator cannot be divided by the same number anymore, then the fraction is simplified.
Therefore, the fraction equal to 16% (simplified) is:
[tex]=\frac{4}{25}[/tex]
The ratio of Melanie's allowance to Jacob's allowance is 4.1 to20.5.If Jacob gets 5.00 dollars, how much allowance does Melanie get
[tex]\bf \cfrac{Melanie}{Jacob}\qquad \stackrel{ratio}{\cfrac{4.1}{20.5}}\qquad \qquad \cfrac{4.1}{20.5}=\cfrac{m}{5}\implies 20.5=20.5m \\\\\\ \cfrac{20.5}{20.5}=m\implies 1=m[/tex]
Malia solved an equation, as shown below: Step 1: 6x = 48 Step 2: x = 48 – 6 Step 3: x = 42 Part A: Is Malia's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. Part B: How many solutions will this equation have?
Answer:
a. the answer is incorrect
b. 1
Step-by-step explanation:
step 1) 6x=48
step 2) 48/6
step 3)x=3
Help plzzzz I have until 12 am
Answer:
To complete the square move the non-x term to the right
2x^2 + 13x = -20 then divide equation by x^2 coefficient
x^2 + 6.5x = -10
then coefficient of x (which is 6.5) divide by 2 (3.25) square the number
=10.5625 Then add 10.5625 to both sides of the equation:
x^2 + 6.5x + 10.5625 = -10 + 10.5625
x^2 + 6.5x + 10.5625 = .5625
Take the square root of both sides
(x + 3.25)^2 = .75
Step-by-step explanation:
Drag the correct classification for each graph into the boxes to complete the table.
neither even or odd, odd, even
Answer:
Odd, neither, neither
Step-by-step explanation:
A function is even if f(x) = f(-x). That means that it passes through the origin and is symmetrical about the y-axis.
A function is odd if f(x) = -f(-x). That means that it passes through the origin and is symmetrical about the origin.
The first graph, the line, passes through the origin and is symmetrical about the origin. So it is odd.
The second graph does not pass through the origin, nor is it symmetrical. So it is neither odd nor even.
The third graph does not pass through the origin, nor is it symmetrical about the y-axis. So it is neither odd nor even.
Help with this question, please!!
Answer:
∠XMZ = 74°
Step-by-step explanation:
Since the arcs XZ and BC are congruent, then
∠BNC = ∠XMZ ← substitute values
6x - 88 = 3x - 7 ( subtract 3x from both sides )
3x - 88 = - 7 ( add 88 to both sides )
3x = 81 ( divide both sides by 3 )
x = 27
Hence
∠XMZ = 3x - 7 = (3 × 27) - 7 = 81 - 7 = 74°
Marie is purchasing a $108,000 home with a 30 year ortgage at 5.25%. What is her monthly principal and interest payment
Answer:
Monthly interest rate is r=0,004375
Monthly principal c=590,625
Step-by-step explanation:
Monthly interest payment rate :
[tex]r=\frac{5.25}{12}:100=0,0004375[/tex]
Now, we need to find monthly principal payment : [tex]c=\frac{rP}{1-(1+r)^{-N}}[/tex]
Use this rule : [tex]N=30*12=360[/tex]
P=108000
r=0,004375
[tex]c=\frac{0.004375*108000}{1-(1+0.004375)^{-360}} =\frac{472.5}{0.8}=590,625[/tex]
Answer: 596.38
Step-by-step explanation:
In the figure. What is the value of x?
180-40-60=80 degrees
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The graph of the function y = x2 is shown. How will the graph change if the equation is changed to y = 2x^2?
Answer:
The parabola will become narrower.
Step-by-step explanation:
Because of the coefficient 2, every value of x² is doubled, which means higher value on the same X coordinate, compared to the y = x² function.
Answer: B) The parabola will become narrower
Step-by-step explanation:
The vertex form of a quadratic equation is: y = a (x - h)² + k where
"a" is the vertical stretch (shrink/compression if |a| < 1)(h, k) is the vertexIn the given equation of y = 2x², the a-value has increased so it is stretched. When the graph stretches, the sides will get closer together thus the parabola will become narrower.
Please help me with this
Answer:
h = 40 cm
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the radius and h the height )
here V = 3240π, thus
π × 9² h = 3240π
81πh = 3240π ( divide both sides by 81π )
h = [tex]\frac{3240\pi }{81\pi }[/tex] = [tex]\frac{3240}{81}[/tex] = 40
Find the first six terms of the sequence.
a1 = -7, an = 2 • an-1
Answer:
The first 6 terms are -7,-14,-28,-56,-112,-224
Step-by-step explanation:
The given sequence is defined recursively by:
[tex]a_1=-7[/tex] and [tex]a_n=2(a_{n-1})[/tex]
When n=2
[tex]a_2=2(a_{2-1})[/tex]
[tex]a_2=2(a_{1})[/tex]
[tex]a_2=2(-7)=-14[/tex]
When n=3
[tex]a_3=2(a_{3-1})[/tex]
[tex]a_3=2(a_{2})[/tex]
[tex]a_3=2(-14)=-28[/tex]
When n=4
[tex]a_4=2(a_{4-1})[/tex]
[tex]a_4=2(a_{3})[/tex]
[tex]a_4=2(-28)=-56[/tex]
When n=5
[tex]a_5=2(a_{5-1})[/tex]
[tex]a_5=2(a_{4})[/tex]
[tex]a_5=2(-56)=-112[/tex]
When n=6
[tex]a_6=2(a_{6-1})[/tex]
[tex]a_6=2(a_{5})[/tex]
[tex]a_6=2(-112)=-224[/tex]
The first 6 terms are -7,-14,-28,-56,-112,-224
How many solutions will the following system of linear equations have? –2x + 4y = –7 y= -1/2x + 5 A. 0 B. 1 C. 2 D. infinite
Answer:
B. 1
Step-by-step explanation:
they only cross at one point... look below
ANSWER
B. 1
EXPLANATION
The given system of equations is;
–2x + 4y = –7
y= -1/2x + 5
We rewrite the first equation is slope intercept form:
4y = 2x–7
[tex]y = \frac{1}{2}x - \frac{7}{4} [/tex]
The two equations have different slopes.
This means that they will intersect at one point in the XY plane.
Hence the system has a unique solution.
RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.
The area of rectangle ABCD is 18 square units.
Step 1: Calculate the length of the rectangle.
The length of the rectangle is the distance between points A and B (or C and D). Using the distance formula:
[tex]\[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For the points A(-5,2) and B(-5,4), the length is:
[tex]\[ \text{Length} = \sqrt{(-5 - (-5))^2 + (4 - 2)^2} \][/tex]
[tex]\[ \text{Length} = \sqrt{(0)^2 + (2)^2} \][/tex]
[tex]\[ \text{Length} = \sqrt{0 + 4} \][/tex]
[tex]\[ \text{Length} = \sqrt{4} \][/tex]
[tex]\[ \text{Length} = 2 \][/tex]
Step 2: Calculate the width of the rectangle.
The width of the rectangle is the distance between points B and C (or A and D).
For the points B(-5,4) and C(4,4), the width is:
[tex]\[ \text{Width} = \sqrt{(4 - (-5))^2 + (4 - 4)^2} \][/tex]
[tex]\[ \text{Width} = \sqrt{(4 + 5)^2 + (0)^2} \][/tex]
[tex]\[ \text{Width} = \sqrt{9^2 + 0} \][/tex]
[tex]\[ \text{Width} = \sqrt{81} \][/tex]
[tex]\[ \text{Width} = 9 \][/tex]
Step 3: Calculate the area using length and width.
Now that we have the length and width of the rectangle, we can use the formula:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
[tex]\[ \text{Area} = 2 \times 9 \][/tex]
[tex]\[ \text{Area} = 18 \][/tex]
The length of the rectangle, calculated as the distance between points A and B (or C and D), is 2 units. The width of the rectangle, calculated as the distance between points B and C (or A and D), is 9 units. Multiplying the length and width together gives us the area of the rectangle, which is 18 square units. Therefore, the correct answer is that the area of rectangle ABCD is 18 square units.
Complete question :
RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.
If (x-2) is a factor of x^3 + bx^2 - 4 , what is the value of b?
Answer:
b= -1
Step-by-step explanation:
Step 1: Find out value of x
x-2 = 0
x= 2
Step 2: Substitute value of x in the equation
x^3 + bx^2- 4 = 0
(2)^3 + b (2)^2 - 4 = 0
8 + 4b - 4=0
4 - 4b = 0
4b = -4
b = -1
Maxim and Salma were asked to find an explicit formula for the sequence 54,63,72,81,... Maxim said the formula is f(n)=54+9n Salma said the formula is f(n)=9+54nf(n)=9+54n. Which one of them is right?
ANSWER
The explicit rule is
[tex]f(n) = 45+9n [/tex]
EXPLANATION
The given sequence is :
54,63,72,81,...
The first term of this sequence is
[tex]a = 54[/tex]
The common difference is
[tex]d =63 - 54 = 9[/tex]
The explicit rule is given by:
[tex]f(n) = a + d(n - 1)[/tex][tex]f(n) = 54+9(n -1 )[/tex]
We expand to get:
[tex]f(n) = 54+9n -9[/tex]
[tex]f(n) = 45+9n [/tex]
None of them is correct .
Answer:Neither Maxim nor Salma
Step-by-step explanation:
i just answered ed the question
What is the cos of angle y
Answer:
its cos:48/80
Step-by-step explanation:
cos-1(48/80)=53.13
For this case we have by definition of trigonometric relations that the cosine of an angle is given by the leg adjacent to said angle on the hypotenuse of the triangle. So:
[tex]Cos (Y) = \frac {64} {80} = \frac {32} {40} = \frac {16} {20} = \frac {8} {10} = \frac {4} {5}[/tex]
After simplifying we have to:
[tex]Cos (Y) = \frac {4} {5}[/tex]
ANswer:
[tex]Cos (Y) = \frac {4} {5}=0.8[/tex]
MA 912. G.1.4
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3.6) and (1, -2)?
Answer:
Step-by-step explanation:
Going from (1, -2) to (3,6), x increases by 2 and y increases by 8. Thus, the slope m of this line is m = rise / run = 8/2 = 4.
I think you meant, "What is the EQUATION of the line that passes through the point (-1, 1) and is parallel to a line that passes through
(3, 6) and (1, -2)? We have seen that this slope is -4.
Starting with the point-slope equation of a line, we have:
y - 6 = -4(x - 3)
Solve the system of equations. (3x + 4y = 5) (2x - 3y = -8)
A)y = -x = 2
B)x = -1, y = 2
C)x = -4, y = 0
D)x = 3, y = -1
Answer:
the solution is (-1, 2)
Step-by-step explanation:
Let's solve the system
(3x + 4y = 5)
(2x - 3y = -8)
using the method of elimination by addition and subtraction. Notice that if we multiply all terms of the first equation by 3 and all terms of the second by 4, y as a variable will temporarily disappear:
9x + 12y = 15
8x - 12y = -32
-----------------------
17x = - 17, so x = -1.
Replacing x in the second equation by -1, we get:
2(-1) - 3y = -8, or
2 + 3y = 8,
or 3y = 6. Thus, y = 2, and the solution is (-1, 2).
The solution to the given system of equations is x = -1 and y = 2. We found these values using the elimination method, first by making the coefficients of x in both equations the same, then eliminating x and solving for y, and finally substituting y = 2 into the first equation and solving for x.
Explanation:To solve the given system of equations, we can use the elimination method. First, we need to make the coefficients of either x or y the same in both equations. We can do so by multiplying the first equation by 2 and the second equation by 3:
⟹ (3x * 2 + 4y * 2 = 5 * 2) and (2x * 3 - 3y * 3 = -8 * 3)
When simplified, we get:
⟹ 6x + 8y = 10 and 6x - 9y = -24
Now, we subtract the second equation from the first one to eliminate x:
⟹ (6x + 8y) - (6x - 9y) = 10 - (-24)
⟹ 17y = 34
Finally, we solve for y by dividing both sides of the equation by 17:
⟹ y = 34 / 17
⟹ y = 2
Substitute y = 2 into the first original equation:
⟹ 3x + 4 * 2 = 5
⟹ 3x + 8 = 5
⟹ 3x = -3,
On simplifying, we get x = -1. So, the solution to the system is x = -1, y = 2.
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Evaluate (5 + 2)2 − 40 + 3 = __________.
NUMERICAL ANSWER EXPECTED!
Answer for Blank 1:
Answer:
-28
Step-by-step explanation:
(5+2) = 7
7 + 2 - 40 = -31
-31 + 3 = -28
Fill in the exponent
Answer:
3
Step-by-step explanation:
12/4 = 3
so
(a^2/b^3)^4 = a^8 / b^12
A piggy bank was filled during a calendar year, by a coin placed in it every day except some Sundays. If the quantity of coins in the piggy bank is distributed evenly among 6 children, two coins remain. If this quantity is distributed evenly among 7 children, four coins remain. If the quantity of coins in the piggy bank is distributed evenly among 8 children, how many coins will remain?
Answer:
probably 6////////////
Answer:
The answer is 6
Step-by-step explanation:
In a year there is 365 days.
From the first condition, 6x + 2 = to a unknown number of coins
From the second condition, 7x + 4 = to the same number of unknown coins.
The number which satisfies this given condition is 326 coins.
If we divide this number by 8 to share it among 8 students =
326 ÷ 8 = 40 coins/ student and 6 coins remaining. Therefore, the answer is
6 Coins