The greatest number of cans each stack can have is 10.
What is Greatest Common Divisor (GCD)?
The number that divides two or more numbers most precisely by itself is said to be the greatest common divisor (GCD) of those numbers. It is also defined as the highest common factor (HCF).
If a and b are two numbers then the greatest common divisor of both numbers is denoted by GCD(a, b).
Given, Total number of cola cans = 150
Total number of fruit juice cans = 260
According to the question condition, we need to find GCD (150,260)
Now, the prime factorization of 150 and 260 are:
150= 2 x 3 x 5 x 5
260 = 2 x 2 x 5 x 13
So, common factor = 2 x 5 = 10
Then, GCD (150,260) = 10
Hence, the greatest number of cans in each stack can have 10.
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HELPP ME PLEASEEEEEE
Answer:
We can see that as x increases, y decreases. This indicates a negative slope meaning that the two variables are negatively related.
Hope this helps! :)
Calculate the simple interest and maturity value.
Note: Do not round intermediate calculations. Round your answers to the nearest cent.
S
Principal
19,500
Interest rate
6 1/2 %
Time
20 month
Simple interest
< Prev
C
a
2 of 14
Maturity value
Next >
DELL
The simple interest is 2112.5 and the maturity value is 21,612.5
In the given question,
We have to find the simple interest and maturity value.
The given principal amount (P)= 19,500
The interest rate (r)= 6 1/2%
We write the interest in improper fraction. We can write it as 6 multiple with 2 then adding the result of multiplication with 1.
So the simplest form (r)=13/2%
Time = 20 months.
Now converting the months into years.
As we know that in one year have 12 months.
So the Time = 20/12
Time (T)= 5/3
The formula of simple interest is
I = P*R*T/100
Now putting the value
I = 19,500*(13/2)*(5/3)/100
Simplifying
I = 19,500*13*5/100*2*3
I = 1,267,500/600
I = 2112.5
Hence, the simple interest is 2112.5.
Now finding the maturity value(MV).
MV=P+I
MV=19,500+2112.5
MV=21,612.5
Hence, the maturity value is 21,612.5
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Please Help
Find(f+g)(x)if f(x)-/16x4 and g(x)=3x2-3x-5
The function operation (f + g)(x) of the functions f(x) = √( 16x⁴ ) and g(x) = 3x² - 3x - 5 is -5x² + 5x - 7.
What is the function operation (f + g)(x) of the given functions?A function is simply a relationship that maps one input to one output.
Given the functions in the question;
f(x) = √( 16x⁴ )g(x) = 3x² - 3x - 5To determine the function operation (f + g)(x), replace the function designators with the functions and simplify.
(f + g)(x) = f(x) + g(x)
(f + g)(x) = √( 16x⁴ ) + ( 3x² - 3x - 5 )
Replace √( 16x⁴ ) with 4x²
(f + g)(x) = 4x² + 3x² - 3x - 5
Collect and add like terms
(f + g)(x) = 7x² - 3x - 5
Therefore, the function operation (f + g)(x) is 7x² - 3x - 5.
Option A is the correct answer.
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Complete the table: (Enter your answers as a whole dollar amount.) Units Unit Cost Dollar Cost Beg. Inventory Jan. 1 8 $ 6.00 A Apr. 11 24 $ 11.00 B May 17 30 $ 14.00 C Dec. 5 19 $ 16.00 D 21 units sold
The completion of the inventory table is as follows:
A = $48
B = $264
C = $420
D = $304.
What are the inventory methods?The above inventory table is completed using some of the inventory methods including:
FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
The weighted-average method uses the average cost of goods to determine both the ending inventory and the cost of goods sold.
Specification Identification does not base allocating the costs of goods sold and ending inventory on any assumptions. Instead, it uses specific costs.
Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 8 $6.00 $48 ($6 x 8)
Apri. 11 Purchases 24 $11.00 $264 ($11 x 24)
May 17 Purchases 30 $14.00 $420 ($14 x 30)
Dec. 5 Purchases 19 $16.00 $304 ($16 x 19)
Total 81 $1,036
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List 1 4/5, -7/4, 41%, and -1.3 from greatest to least.
The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.
What us descending order?
When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.
Main Body:
To solve this question we need to convert all numbers into decimal system.
calculate:
1 can be written as 1.00
4/5 can be written as 0.8
-7/4 = -1.75
41% = 41/100 = 0.41
-1.3 can remain as it is because it itself is in decimal form.
Hence the order from greatest to smallest is as
1 > 0.8 > 0.41 > -1.3 > -1.75
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Whats the answer please
The domain of the given function f(x) = (-x - 9)^(1/2) is; C) (-∞, -9)
What is the domain of the function?The domain of a function is defined as the set of all possible input values that make the function possible.
Now, we are given the function;
f(x) = (-x - 9)^(1/2)
This can also be written as;
f(x) = √(-x - 9)
Now, since the item in bracket seems to be negative, we can say that we want to find the lowest term for which the function in bracket is zero because when the function in the bracket is negative, then the function is a complex number. Thus;
At (-x - 9) = 0
-x = 9
x = -9
This will be the maximum value of x while the minimum value will be negative infinity.
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Solve the system of equations.
y = 3x+2
y=x²-4x+2
Answer:
a) -2/3
b) x^2-1/2
Step-by-step explanation:
On a coordinate plane, the position of two friends can be defined by the points A(1,3) and B(7,6). Their teacher is standing at point C, the teacher’s distance from point A is twice the distance from Point B. What are the coordinates of point C?
A.) (5,5)
B.) (-5,5)
C.) (4, 9/2)
D.) (8/3, 3)
Please show work if possible!
The coordinate of point C will be (5, 5). Then the correct option is A.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.
The ratio is given as 2:1.
x = (7 × 2 + 1 × 1) / (2 + 1)
x = 15 / 3
x = 5
y = (6 × 2 + 1 × 3) / (2 + 1)
y = 15 / 3
y = 5
The coordinate of point C will be (5, 5). Then the correct option is A.
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f: x → x + 5 9: x→ 8x What is the value of fg(4.5)?
The mapping of the function f of g(x) will result to 41
What is a functionA function in mathematics is a rule that defines a relationship between one variable. This is a mapping whose codomain is the set of real numbers.
By mapping of the functions f and g defined as;
f : x » x + 5 and g : x » 8x
then;
f of g(x) = f of 8(4.5)
f of g(x) = f of 36
f of g(x) = 36 + 5
f of g(x) = 41
Hence, with proper mapping of the defined functions of f and g, the correct value for f of g(x) is 41.
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0.8421 as a fraction
Answer:
8421/10000
Step-by-step explanation:
8421/10000
Choose the answer.
The difference between 3 times a number and 7 is 5. Write and solve an equation to
determine the number. Select the solution and graph that represents the number.
5 is the difference between the two numbers 12 and 7.
Given,
In the question;
The difference between 3 times a number and 7 is 5.
Write and solve an equation to determine the number.
Now, According to the question:
Let's assume the unknown number to be x,
so three time the number would be 3x.
The difference between 3 times a number (3x) with 7 is 5, so we can write it as:
3x - 7 = 5
Now we can solve this equation to the find x (the unknown number).
3x = 5 + 7
3x = 12
x = 12/3
x = 4
Therefore 3x= 12
So, 5 is the difference between the two numbers 12 and 7.
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screenshot included with question
Answer:
48 fl oz = 6 c
4 gal = 16 qt
Step-by-step explanation:
4 times 4 is 16
48 divided by 8 is 6
Nolan went shopping for a new pair of sneakers because of a sale. The store was offering a 25% discount. What number should he multiply the prices on the tags by to find the price he would have to pay, before tax, in one step?
The number is 0.75.
From the question, we have
The store was offering a 25% discount.
number = 1-0.25
=0.75
Subtraction:
Subtraction serves as a representation for the act of removing items from a collection. The minus sign stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above figure) are then moved to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, or equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.
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Two rockets are to be launched at the same time from NASA headquarters in Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 19,200 miles per hour and the second rocket will travel at 18,000 miles per hour. If the first rocket is scheduled to reach the space station 0.5 of an hour before the second rocket, how far is the space station from NASA headquarters?
By solving a linear equation, it can be calculated that
The space station is at a distance of 144000 miles from NASA headquarters
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let the space station be d miles from NASA headquarters
Speed of the first rocket = 19200 miles/hour
Speed of the second rocket = 18000 miles /hour
Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]
Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]
By the problem,
[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]
The space station is at a distance of 144000 miles from NASA headquarters
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When Nathaniel moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 38 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6
The equations of the growth of both treesFrom the question, we have the following parameters that can be used in our computation:
Tree A
Initial height = 38 inchesRate = 6 inches each yearTree B
Initial height = 20 inchesRate = 9 inches each yearThe height after t years is
Tree = Initial height + rate * t
So, we have
Tree A = 38 + 6t
Tree B = 20 + 9t
The interval of timeRecall that
Tree A = 38 + 6t
Tree B = 20 + 9t
When Tree A is taller than Tree B, we have
38 + 6t > 20 + 9t
Evaluate the like terms
-3t > -18
Divide
t < 6
Hence, the interval is t < 6
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Jamal has 54 marbles.
Lucas has 70 marbles.
How many more marbles
does Lucas have than
Jamal?
Answer: 16
Step-by-step explanation:
What is the slope of the line that passes through the points (−4, −4) and (6, 4
Answer: no slope
Step-by-step explanation:
m= y2-y1/x2-x1
m= 6-(-6)/4-4
m=12/0
m= no slope
Answer:
y = 0.8x - 0.8
Step-by-step explanation:
Δy ÷ Δx = gradient (x)
4 - -4 = 8
6 - -4 = 10
8 ÷ 10 = 0.8
equation of line; y = mx + c
substitute one of the coordinates into the equation
(6, 4) y = 4, x = 6
4 = 0.8(6) + c
4 = 4.8 + c
- 4.8 to get the y intercept on it's own
-0.8 = y intercept (c)
confirmation
substitute the new values to get the other y
(-4, -4) y = -4 <-- should be the answer, x = -4
y = mx + c
y = 0.8(-4) - 0.8
y = -3.2 - 0.8
y = -4 the gradient and the y intercept have been proven right
write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation (0,0) y=-3x+2
Triangle PQR is isosceles, Q being the right angle. If the hypotenuse is 38.47cm, find: i. Lengths of sides PQ and QR. ii. The size of angle QPR
The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm
What are Isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,
since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).
Therefore 90+x+x= 180°
2x= 90
x= 45°
To find line PQ and QR, we use trigonometry ratio
cos 45°= adj/hyp
I/√2= QR/38.47
QR= 38.47/√2
= 27.20cm
QR= PQ= 27.20
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Which expression is equivalent to 1 2/9 x 6/16
Answer:
0.45833333333 or 11/23
Step-by-step explanation:
1 2/9*6/16 is simply 11/23, cross multiply and simplify
Determine the period.
2 y
-2
1
10
Answer:
8
Step-by-step explanation:
You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.
PeriodThe period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.
Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:
period = 9 - 1 = 8
The period of the function is 8 units.
__
Additional comment
In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).
How you find interest rates
17).
A chef has 31 litres of cooking oil. He uses 7, of it during an evenings cooking.
How much does he
a).
use,
b).
have left over ?
Answer:
a) He obviously used 7 liters of cooking oil.
b) He has 24 liters of cooking oil left.
20 points Describe another way you could have solved the equation. Tell which of these two ways of solving the equation you prefer and why.
In the equation 2[(4m * 3.5) / 400] = 171.5, the value of m is 2450
EquationsEquations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
In the equation given;
2[(4m * 3.5) / 400] = 171.5
To solve for m, we have to expand the bracket and make m the subject of formula.
2[(4m * 3.5) / 400] = 171.5
2[14m/400] = 171.5
28m / 400 = 171.5
28m = 400 * 171.5
28m = 68600
m = 68600 / 28
m = 2450
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Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. What is the current price of the bonds?
b. By what percent will the price of the bonds increase between now and maturity? (Round "PV Factor" to 3 decimal places, intermediate and final answers to 2 decimal places. Omit the "%" sign in your response.) Price increases by %
a) The current bond price (present value) is $420.03.
b) The percentage by which the price of bonds will increase between now (current) and maturity (18 years) is 138%.
How is the bond price determined?The current bond price represents its present value.
The present value is the discounted future cash inflows.
We can compute the present value using an online finance calculator as follows:
N (# of periods) = 18 years
I/Y (Interest per year) = 12$
PMT (Periodic Payment) = $40 ($1,000 x 4%)
FV (Future Value) = $1,000
Results:
PV = $420.03
Sum of all periodic payments = $720.00
Total Interest = $1,299.97
Percentage increase in bond price = [(Future value - Present value)/Present value x 100]
= 138% [($1,000 - $420.03)/$420.03 x 100]
Thus, the present value of the bonds $420.03 will grow by 138% at maturity.
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Please help with the ones that have a red x beside it would greatly and would give 100 pts so please help me!!!!!
Answer:
huhh
Step-by-step explanation:
Hi im new can u guys tell me how this work pease??
Answer:
Step-by-step explanation:
idek idek
What is the volume of a cylinder, in cubie centimeters, with a height of 2 centimeters
and a base diameter of 20 centimeters? Round to the nearest tenths place?
The volume of the cylinder in cubie centimeter is 628 [tex]cm^{3}[/tex]
How to find the volume of cylinder?
1. Find the radius of the circular base: Since both circles are the same size, either one will work. Move on if you are aware of the radius. If you don't know the radius, you can divide the diameter of the circle by 2.
2. Find the height of the cylinder : Continue if you already know the height. Otherwise, measure it with a ruler. The height is determined by the separation of the two bases' edges.
diameter (d) = 20
radius = [tex]\frac{20}{2}[/tex]
r = 10
height (h) = 2cm
volume v = [tex]\pi r^{2} h[/tex]
v = 3.14(10*10)2
= 628 [tex]cm^{3}[/tex]
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(10-x)+(12-x)
how do you do this i can't do this at all.
Answer:
[tex]\sf -2x+22[/tex]Step-by-step explanation:
[tex]\sf (10-x)+(12-x)[/tex]
Simplify:-
[tex]\sf 10-x+12-x[/tex]
Combine like terms:-
[tex]\sf -x-x+10+12[/tex]
[tex]\sf (-x-x)=\bf -2x[/tex]
[tex]\sf (10+12)=\bf 22[/tex]
[tex]\sf -2x+22[/tex]
__________________Hope this helps!
Have a great day!
4. Solve for y.
q
116° +15y - 4=180
After simplifying the expression, the value of y is 4.53.
In the given question,
We have to solve for y.
The given expression is 116° +15y - 4=180.
To solve for y we simplify the expression.
The expression is 116° +15y - 4=180
Now simplifying the expression.
Add 4 on both side
116° +15y - 4+4=180+4
116° +15y=184
Subtract 116 on both side
116° +15y-116°=184-116°
Simplifying
15y=184-116°
15y = 68
Divide by 15 on both side
15/15 y=68/15
y=4.53
Hence, the value of y is 4.53.
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Gardner Pete wanted to fertilize his garden. The garden has a radius of 10 feet. Each bag of fertilizer covers 50 feet. How many bags will he need to buy?
He needs to buy 7 bags of fertilizer to fertilize the garden
The radius of the garden = 10 feet
The area of the garden A = π × [tex]r^2[/tex]
Where A is the area of the garden
r is the radius of the garden
Substitute the values in the equation
A = π × [tex]10^2[/tex]
= π × 100
= 314.16 feet square
Each bag of fertilizer covers 50 square feet
Then the number of bags required to fertilize the garden = The area of the garden / 50
Substitute the values in the equation
= 314.16 / 50
= 6.28
≈ 7 bags
Hence, he need to buy 7 bags of fertilizer to fertilize the garden
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