Answer:
1 ¹/₉ hours
Step-by-step explanation:
Let's say L is Larry's speed, C is Curly's speed, and M is Moe's speed.
1 = 2 (L + C)
1 = 1 ⅔ (C + M)
1 = 1 (L + C + M)
Solve the system of equations. First, simplify the equations:
1 = 2L + 2C
3 = 5C + 5M
1 = L + C + M
Double the third equation and subtract the first equation from it:
2 = 2L + 2C + 2M
1 = 2L + 2C
1 = 2M
M = 1/2
Plugging into the second and third equations, we get:
C = 1/10
L = 2/5
Therefore, the time it takes Larry and Moe together is:
1 = t (L + M)
t = 1 / (L + M)
t = 1 / (2/5 + 1/2)
t = 1 / (4/10 + 5/10)
t = 1 / (9/10)
t = 10/9
t = 1 ¹/₉ hours
It takes them 1 ¹/₉ hours, or 1 hour 6 minutes 40 seconds.
Larry and Moe would take 5/3 hours, or 1 hour and 40 minutes, to build a bookcase together, based on the rates of building individually and in different pairs.
Larry and Curly together build a bookcase in 2 hours. This means that together they have a rate of 0.5 bookcases per hour, since 1 divided by 2 is 0.5. Similarly, Curly and Moe together can build one in 1 2/3 hours, which is the same as 5/3 hours. Therefore, their collective rate is 3/5 bookcases per hour. Larry, Curly, and Moe together can build a bookcase in 1 hour, which means their combined rate is 1 bookcase per hour.
Let's denote the rates of work for Larry, Curly, and Moe as L, C, and M respectively. When working together the sum of their rates equates to the rate at which they finish the job together. Hence:
L + C = 0.5 (Larry and Curly's rate)
C + M = 3/5 (Curly and Moe's rate)
L + C + M = 1 (Larry, Curly, and Moe's rate)
Using the first two equations, we can solve for L and M by substituting the values into the third equation:
L + 3/5 = 1
L = 1 - 3/5 = 2/5
C + 0.5 = 1
C = 1 - 0.5 = 0.5
Now we know that Larry's rate is 2/5 bookcase per hour, and Curly's rate is 0.5 bookcase per hour. We can use Curly's rate to find Moe's rate:
C + M = 3/5
0.5 + M = 3/5
M = 3/5 - 0.5 = 1/5
Larry and Moe's combined rate is L + M = 2/5 + 1/5 = 3/5 bookcases per hour.
To find the time it takes for Larry and Moe to build one bookcase together, we take the reciprocal of their combined rate:
Time = 1 / (L + M) = 1 / (3/5) = 5/3 hours, which is equal to 1 hour and 40 minutes.
Complete the table. In the row with x as the input, write a rule as an algebraic expression for the output. Then complete the last row of the table using the rule.
Input Output
Tickets Cost ($)
2 60
6 180
9 270
x
10
Final answer:
The rule for determining the cost based on the number of tickets is Cost = 30 × Tickets. Using this rule, the cost for 10 tickets is calculated to be 300 dollars.
Explanation:
The question requires us to determine a rule for the output based on the given input of tickets and then use this rule to find the cost for 10 tickets. By examining the input and output values provided, we see a consistent pattern: the cost increases by 30 dollars with each additional ticket. Given this pattern, the rule can be formulated as an algebraic expression: Cost = 30 × Tickets.
Applying this rule to an input of x tickets, the expression becomes Cost = 30 × x. To find the cost for 10 tickets, we replace x with 10: Cost = 30 × 10 = 300 dollars.
Brad wants to open a new savings account. He finds one that returns 3% on his investment each year.
Question 1
Assign a variable to each of the following pieces of information
Final balance
Initial investment
Return rate
Answer:
Step-by-step explanation:
Return rate, r = 3% = 0.03
x = initial investment
b = final balance
After 1 year, the balance i
b = initial investment + interest
b = x + r*x = (1 + r)*x
Because r = 0.03,
b = 1.03x (after 1 year)
The cost to take a car across a bay on a ferry is $16.00. The ferry has a capacity of 42cars. The revenue collected is a function of the number of cars, c . R()=16 Use the drop-down menus to complete the statements below about the domain of this function.
The domain of this function is first restricted to all nonnegative integers because the ferry can carry only a whole number number of cars.
The domain is restricted to number less than or equal to 42 because the ferry cannot carry more cars than capacity .
The domain of this function is the set of non-negative integers.
Explanation:The domain of a function represents the set of possible input values for that function. In this case, the function represents the revenue collected by the ferry, which depends on the number of cars. The number of cars, denoted as c, must be a non-negative integer because the ferry cannot transport a fraction of a car. Therefore, the domain of this function is the set of non-negative integers, or {0, 1, 2, 3, ...}.
Only 6. Please and thanks
Answer:
Part a) [tex]7.536\ m[/tex]
Part b) [tex]\$34.14[/tex]
Step-by-step explanation:
Part 6)
a) How much edging is needed?
we know that
To find out how much edging is needed determine the circumference of the circular garden
The circumference of the circular garden is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]D=2.4\ m[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(2.4)[/tex]
[tex]C=7.536\ m[/tex]
Part b) we know that
To find out the cost to edge the garden, multiply the length of edging plastic needed by the cost of $4.53 per meter
so
[tex](7.536\ m)(4.53\ \$/m)=\$34.14[/tex]
Solve for h
A=1/2(ah/bh)
Answer the answer is in the attachment
To solve for h in the given equation A = (1/2)(ah/bh), divide both sides by (a/b) to isolate h, resulting in h = 2A/b.
Solve for h:
Start with the given equation A = (1/2)(ah/bh).
Divide both sides by (a/b) to isolate h.
Therefore, h = 2A/b.
At age 20 a person deposits $370 in a savings account paying 2% interest compounded quaterly.how much money will be in the account 60 years later, when he is 80 years old? Would his savings have tripled in that time?
Final answer:
After 60 years, with an initial deposit of $370 at a 2% interest rate compounded quarterly, the amount in the savings account would be approximately $996.26. This amount does not triple the initial savings, as it is less than $1110.
Explanation:
To calculate the amount of money in the savings account 60 years later with an initial deposit of $370, an interest rate of 2% compounded quarterly, we use the compound interest formula:
A = P(1 + rac{r}[tex]{n})^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
In this case:
P = $370
r = 0.02 (2% as a decimal)
n = 4 (since the interest is compounded quarterly)
t = 60
So, the equation becomes:
A = 370(1 + rac{0.02}[tex]{4})^{4 imes 60}[/tex]
A = 370[tex](1 + 0.005)^{240}[/tex]
A = 370[tex](1.005)^{240}[/tex]
A = 370(2.69259) = $996.26 (rounded to two decimal places)
So, after 60 years, the amount in the account would be approximately $996.26. To check if the savings have tripled:
370 imes 3 = $1110
Since $996.26 is less than $1110, the savings have not tripled.
How to solve system
X+y=10
X-y=2
Answer:
x=6, y=4. (6, 4).
Step-by-step explanation:
x+y=10
x-y=2
----------
x=y+2
y+2+y=10
2y+2=10
2y=10-2
2y=8
y=8/2=4
x+4=10
x=10-4=6
The memory card on Melchers digital camera can hold about 430 pictures make sure used 18% of the mirror memory card while taking pictures at family reunion about how many pictures did Melcher take out the family room and round to the nearest whole number
Answer:
77
Step-by-step explanation:
0.18*430=77.4
The calculation
add the quotient of 108 and 12 and the quotient of 18 and 2
Answer:
18
Step-by-step explanation:
108/12=9
18/2=9
---------------
9+9=18
If the sum of twice a number and -12 is multiplied by 2 the result is 11 greater than the opposite
of the number find the number
Answer:
The number which satisfy the given statement is 7 .
Step-by-step explanation:
Given statement as :
If the sum of twice a number and -12 is multiplied by 2 the result is 11 greater than the opposite of the number find the number
Now, Let The number be x
So, As per statement
2 × [2 x + ( - 12 ) ] = 11 + ( - x )
Or, 2 × 2 x - 2 × 12 = 11 - x
Or, 4 x - 24 = 11 - x
Or, 4 x + x = 11 + 24
or, 5 x = 35
∴ x = [tex]\frac{35}{5}[/tex]
I.e x = 7
so, number is x = 7
Hence The number which satisfy the given statement is 7 . Answer
I am doing a math problem and i need help. Could you please find the missing fraction?
5/2 - ? = 1/3
Answer:
?=13/6
Step-by-step explanation:
5/2-?+?=1/3+?
5/2-1/3=?
?=15/6-2/6=13/6
Answer:
13/6???
Step-by-step explanation:
I turned 5/2 into 15/6 and 1/3 into 2/6. I multiplied both their numerators and denomonators by 3. I then subtracted the two numbers and got 13/6.
- 4(5a - 3b) simplified is?
Answer:
-20a+12b
Step-by-step explanation:
Answer:
-20a+12b
Step-by-step explanation:
-4(5a-3b)=-20a+12b
please solve 3.4-2.8d+2.8d-1.3
Answer:
2.1
Step-by-step explanation:
3.4-2.8d+2.8d-1.3
3.4-1.3=2.1
The chance that a positive response is obtained from Chicago fro program 1 is %. The chance that a positive response is obtained from Chicago for program 2 is %.
Answer:
The chance that positive response obtained for program 1 is 65.90
And The chance that positive response obtained for program 2 is 87.50
Step-by-step explanation:
Given data as :
The positive response for program of different cities in percentage
Now, The positive response is obtained from Chicago for program 1 is 65.90
The total positive response for program 1 in % = 68.80
So, The chance that positive response obtained = 65.90
Again ,
The positive response is obtained from Chicago for program 2 is 87.50
The total positive response for program 1 in % = 81.70
So, The chance that positive response obtained = 87.50
Hence The chance that positive response obtained for program 1 is 65.90
And The chance that positive response obtained for program 2 is 87.50 answer
70th term of the arithmetic sequence -6, 5, 16, is
Answer:753
Step-by-step explanation:
The value of [tex]n^{th}[/tex] term can be calculated by,
[tex]T_{n} = a+(n-1)d\\[/tex]
where,
a = first number of the series
d = constant difference between the numbers
So, according to the question,
a = -6
d = 11
n = 70
hence, by substituting,
[tex]T_{n} = (-6)+(70-1)11\\T_{n} = 753[/tex]
Final answer:
The 70th term of the arithmetic sequence -6, 5, 16 is calculated using the formula for the nth term of an arithmetic sequence, resulting in the 70th term being 753.
Explanation:
The student is asking for the 70th term of the arithmetic sequence -6, 5, 16. In an arithmetic sequence, the difference between consecutive terms is constant. This difference is referred to as the common difference "d". The formula for finding the nth term an of an arithmetic sequence is:
an = a1 + (n - 1)d
Using the provided sequence, we can find the common difference by subtracting the first term from the second term:
d = 5 - (-6) = 11
Now, apply the formula to find the 70th term:
a70 = a1 + (70 - 1) imes d
a70 = -6 + 69 imes 11
a70 = -6 + 759
a70 = 753
Therefore, the 70th term of the given arithmetic sequence is 753.
A rectangle is 15 ft longer than it is wide it’s area is 1000ft2 what are it’s dimensions
The dimension of the rectangle is 25 by 40
Let :
width = x length = x + 15Area of rectangle = x * (x + 15)
1000 = x² + 15x
x² + 15x - 1000 = 0
solving the quadratic equation
x(x - 25) +40(x - 25)
x = 25 or x = -40
The width cannot be negative.
Hence,
width = 25 Length = 25 + 15 = 40Therefore, the dimension of the rectangle is 25 by 40
#1 Cassie and Anna went out to dinner together. Cassie paid 8 dollars more than
Anna. If Anna paid 40% of the bill, then what was the total price of the bill?
Answer:
$40
Step-by-step explanation:
Let the total bill be "x"
Now,
Anna paid 40% (40/100 = 0.4) of the bill, that means
Cassie paid 100 - 40 = 60% of the bill, that is 60/100 = 0.6
Anna paid 0.4x & Cassie paid 0.6x
Cassie's amount is 8 dollar more, so we can write:
0.6x - 8 = 0.4x
Now, we solve for x:
0.6x - 0.4x = 8
0.2x = 8
x = 8/0.2
x = 40
THe total bill is $40
do the angles 76.2,81.7,and 22.1 make a triangle
The given angles 76.2°, 81.7°, and 22.1° can make a triangle, as the sum of these angles is exactly 180°, aligning with the geometric rule that the sum of the interior angles of a triangle must be 180°.
Explanation:To determine whether the given angles can make a triangle, the law in geometry states that the sum of the measures of the interior angles in a triangle must add up to 180 degrees. To see if the angles 76.2°, 81.7°, and 22.1° can make a triangle, we add them up. The sum is 76.2 + 81.7 + 22.1 = 180 degrees. Thus, yes, these three angles can form a triangle because their sum is exactly 180°.
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Given: g(x) = 2x2 + 3x + 10
k(x) = 2x+16
Solve the equation g(x) = 2x(x) algebraically for x, to the nearest tenth. Explain why you
shose the method you used to solve this quadratic equation.
Answer:
x = 3.576 and x = - 3.076
Step-by-step explanation:
Two functions are given to be, g(x) = 2x² + 3x + 10 and k(x) = 2x + 16.
Now, we have to solve the equation g(x) = 2k(x)
⇒ 2x² + 3x + 10 = 4x + 32
⇒2x² - x - 22 = 0
The expression in the left hand side can not be factorized and therefore we have to use Sridhar Acharya formula which gives the solutions of the equation in the form ax² + bx + c = 0 are given by
[tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} - 4ac} }{2a}[/tex]
Therefore, the solutions of the given equation are
[tex]x = \frac{-(- 1) + \sqrt{(- 1)^{2} - 4 (2)(-22)} }{2(2)} = 3.576[/tex]
and [tex]x = \frac{-(- 1) - \sqrt{(- 1)^{2} - 4 (2)(-22)} }{2(2)} = -3.076[/tex] (Answer)
Final answer:
To solve the equation g(x) = k(x) for x, we simplify it to 2x² + x - 6 = 0 and factor it, resulting in x = 1.5 or x = -2. The method used is factoring due to the simplicity of the equation.
Explanation:
To solve the equation g(x) = k(x) algebraically for x, we set the given functions equal to each other. Given the functions g(x) = 2x² + 3x + 10 and k(x) = 2x + 16, the equation becomes 2x² + 3x + 10 = 2x + 16. To solve for x, we must first simplify the equation by moving all terms to one side and then using the quadratic formula or factoring, if possible.
Step 1: Subtract 2x and 16 from both sides to obtain the quadratic equation 2x² + x - 6 = 0.
Step 2: Factor the quadratic equation if possible. In this case, it factors to (2x - 3)(x + 2) = 0, so the possible solutions for x are x = 1.5 or x = -2.
The chosen method for solving this quadratic equation is factoring because the equation simplifies nicely and the factors are easily observable.
You invest $15,000 in a savings account with an annual interest rate of 2.5% in
which the interest is compounded quarterly. How much money should you expect to
have in the account after 5 years? Show your work to receive full credit!
Answer:
[tex]\$16,990.62[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]
substitute in the formula above
[tex]A=15,000(1+\frac{0.025}{4})^{4*5}[/tex]
[tex]A=15,000(1.00625)^{20}[/tex]
[tex]A=\$16,990.62[/tex]
what is the solution to the system
C= ?
D= ?
Answer:
c=29/20
d=13/5
Step-by-step explanation:
4c+2d=11 A
7d=82-44c 7d+44c=82 B
The first equation multiply by 11
and we get 44c+22d=121 C
C-B=44c+22d-7d-44c=39
15d=39
d=39/15=13/5
so c= 29/20
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 5. If there were 4360 no votes, what was the total
number of votes?
total votes
Answer:
The total number of votes 6976 votes
Explanation:
We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.
Let no. of yes votes be equal to x
So we can write 3:5 = x:4360
total number of yes votes can be obtained by Solving for x
[tex]x = \frac{(4360\times 3)}{5}[/tex]
= 2616
Now total number of votes =
sum of total number of yes votes and total number of no votes
= 2616 + 4360
= 6976
Hence, 6976 is the total number of votes of the residents
Answer:
The total number of votes 6976 votes
Explanation:
We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.
Let no. of yes votes be equal to x
So we can write 3:5 = x:4360
total number of yes votes can be obtained by Solving for x
= 2616
Now total number of votes =
sum of total number of yes votes and total number of no votes
= 2616 + 4360
= 6976
Hence, 6976 is the total number of votes of the residents
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Step-by-step explanation:
If a translation of T-3,-8(x, y) is applied to square ABCD,
what is the y-coordinate of B?
Answer:
It's -6
ur welcome
Step-by-step explanation:
Factor 3x² - 9x - 12
Answer:
3(x-4)(x+1)
Step-by-step explanation:
Step-by-step explanation:
[tex](3x - 12)(x + 1)[/tex]
The diagram shows a cone and its axis of rotation. Which type of cross section is formed when the cone is intersected by a plane containing the axis of rotation?
Answer:
Right-triangle
Step-by-step explanation:
Take a right triangle for example, then twist it 360 degrees, keeping the longest leg at the center of rotation. It will then form a cone.
Answer:
the answer is an isosceles triangle
The area of an interactive whiteboard is 3000 square inches, and its perimeter is 220 inches. find the dimensions of the whiteboard.
Answer:
50, 60, 50, and 60
Step-by-step explanation:
xy = 3000
2x + 2y = 220
Rewrite the second equation
y = -x + 110
Substitute this into the first equation.
x(-x + 110) = 3000
-x^2 + 110x - 3000
Divide by -1
x^2 - 110x + 3000
(x - 60) (x - 50)
x = 60, 50
When x = 60, y = 50 and vice versa, so the sides are 50, 60, 50, and 60.
Answer:
Step-by-step explanation:
Do you still need help
A rectangle has a length of 12 meters and a width of 400 centimeters. What is the perimeter ,in cm of the rectangle
Answer:
perimeter =3200cm
Step-by-step explanation:
l=12m=1200cm
w=400cm
perimeter=2(w+l)
=2(1200+400)
=2(1600)
=3200cm
The perimeter of a rectangle in cm that has a length of 12 meters and a width of 400cm is 3200 cm
perimeter of a rectangle = 2(l + w)
where
l = length
w = width
Therefore,
let's convert meters to centimetres
1m = 100 cm
12m = ?
cross multiply
length = 1200 cm
width = 400 cm
perimeter of the rectangle = 2(1200 + 400)
perimeter of the rectangle = 2(1600)
perimeter of the rectangle = 3200 cm
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1. Eric and four of his friends are taking a trip across the New York State
Thruway. They decide to split the cost of tolls equally.
a. If the total cost of tolls is $8, how much will each person have to
pay?
b. Just before leaving on the trip, two of Eric's friends have a family
emergency and cannot go. What is each person's share of the $8
tolls now?
Answer:
a. $1.60
b. $8/3 which is about $2.67
Step-by-step explanation:
a. five friends in total. 8/5 = 1.6
b. three friends left. 8/3 =~ 2.67
Hence, for
(A) Each person have to pay is $[tex]1.6[/tex].
(B) Each person's share of the $[tex]8[/tex] tolls now is [tex]2.67[/tex].
What is the division?
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.
Here given that,
Eric and four of his friends are taking a trip across the New York State
Thruway. They decide to split the cost of tolls equally.
(A)
If the total cost of tolls is $[tex]8[/tex], how much will each person have to
pay
So, five friends in total cost of trolls is
[tex]\frac{8}{5}=1.6[/tex]
(B)
Just before leaving on the trip, two of Eric's friends have a family
emergency and cannot go.
So, three friends left then,
[tex]\frac{8}{3}=2.67[/tex]
Hence, for
(A) Each person have to pay is $[tex]1.6[/tex].
(B) Each person's share of the $[tex]8[/tex] tolls now is [tex]2.67[/tex].
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on a scale drawing 4 inches represents 25 miles if a line segment on the drawing is 6 inches long what distance dose this like segment represent
Answer:
37.5 miles
Step-by-step explanation:
4in = 25 miles
1in = 25/4
4 + 2 = 6
6 = 25 +(6.25*2)
6 = 37.5
To find the distance represented by a line segment on a scale drawing, set up a proportion and solve for x.
Explanation:To determine the distance represented by a line segment on the scale drawing, we can set up a proportion using the given information. Since 4 inches represents 25 miles, we set up the proportion 4/25 = 6/x, where x represents the distance represented by the line segment. To find x, we can cross-multiply and solve for x: 4x = 150, and dividing both sides by 4 gives x = 37.5. Therefore, the line segment represents a distance of 37.5 miles.
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Which number is a composite number?
17, 29, 37, 31, 47, 27
Answer:
27
Step-by-step explanation:
9x3