Answer:
The number of days it takes to complete the work is 15 days.
Step-by-step explanation:
Given:
Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them
Find:
the numbers of days it takes to complete the work
Step 1 of 1
Because 5 workers can build a road in 20 days, each worker can build [tex]$\frac{1}{5}$[/tex] of a road in 20 days.
Therefore, each worker can build 1 road working alone in [tex]$20 \cdot 5=100$[/tex] days.
So, each worker builds [tex]$\frac{1}{100}$[/tex] road each day.
Therefore, three workers together build [tex]$\frac{3}{100}$[/tex] of a road each day, so in 10 days they build $10.
[tex]$\frac{3}{100}=\frac{3}{10}$[/tex] of a road.
At this point, they have [tex]$1-\frac{3}{10}=\frac{7}{10}$[/tex] of the road to the finish.
After the 11 extra workers join in, the 14 workers build [tex]$\frac{14}{100}$[/tex] of the road each day.
So, to finish the remaining [tex]$\frac{7}{10}$[/tex] of a road, the workers must work for
[tex]$$\begin{aligned}\frac{\frac{7}{10} \text { road }}{\frac{14}{100} \frac{\text { ruad }}{\text { day }}} &=\frac{7}{10} \cdot \frac{100}{14} \text { days } \\&=5 \text { days. }\end{aligned}$$[/tex]
Therefore, the road is built in 10+5=15 days
It will take 15 days to finish the road.
What is Proportion?Proportion is defined as where two or more ratios are set to be equal to each other.
If two quantities are directly proportional, if one increases or decreases, other also increases or decreases simultaneously.
If two quantities are inversely proportional, if one increases, other decreases and vice versa.
Here,
Number of days and number of workers are directly proportional to the road built.
Number of workers to build the road is inversely proportional to number of days to build the road.
Let R be the total road need to be built.
Five workers together can build a road in 20 days.
Road built by 5 workers in 20 days = R
Road built by 1 worker in 20 days = R/5
Road built by 1 worker in 1 day = (R/5) / 20
= R/100
Now, three workers work on the road for 10 days.
We have,
Road built by 1 worker in 1 day = R/100
Road built by 3 workers in 1 day = 3R/100
Road built by 3 workers in 10 days = (3R/100) × 10
= 30R/100
Remaining road to complete = R - (30R/100)
= 70R/100
= 7R/10
This is the time when eleven more workers joined.
That is, total number of workers = 3 + 11 = 14
We have,
Number of days taken by 5 workers to complete R = 20 days
Number of days taken by 1 worker to complete R = 20 × 5 = 100 days
Number of days taken by 1 worker to complete 7/10 of R = 100 × [tex]\frac{7}{10}[/tex]
= 70 days
Number of days taken by 14 workers to complete 7/10 of R = 70/14
= 5 days
Total number of days taken = 10 + 5 = 15 days
Hence if three workers work on the road for 10 days before eleven more workers join them, then it will take a total of 15 days to build the road.
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Circle the correct option: A, B, C, or D.
3. What is the value of 0.008 km in meters?
A 0.8
B 80
C 8
D 1.8
Answer:
Recall 1000m=1km
hence
0.008*1000=8
Ans 8m
7.6.7. Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute. Four minutes later, Christen joined him and peeled at the rate of 5 potatoes per minute. When they finished, how many potatoes had Christen peeled?
Answer:
When they finished, the number of potatoes had Christen peeled is 20 potatoes.
Step-by-step explanation:
Given:
Homer began peeling a pile of 44 potatoes at the rate of 3 potatoes per minute.
Four minutes later, Christen joined him and peeled at the rate of 5 potatoes per minute We have to find the number of potatoes Christen has peeled.
Step 1 of 1
Homer peels 3 potatoes a minute, so in the four minutes he works alone, he peels [tex]$3 \cdot 4=12$[/tex] potatoes.
This leaves 44-12=32 potatoes for them to peel together.
Together, they peel 3+5=8 potatoes per minute, so they need
[tex]$\frac{32 \text { potatoes }}{8 \frac{\text { potatuos }}{\text { minute }}}=4$[/tex]minutes
to peel the rest of the potatoes.
Christen peels 5 potatoes a minute for 4 minutes, so she peels [tex]$5 \cdot 4=20$[/tex] potatoes.
A lightbulb manufacturer must test
a
to ensure
sample of lightbulbs
that quality and safety standards are being met.
Which of these methods will produce the most representative sample
of the
population of lightbulbs made by this company?
O A. The manufacturer tests every lightbulb made on Monday.
O B. The manufacturer tests the last 100 lightbulbs produced each
month.
O C. The manufacturer tests the first lightbulb off the production line
each day.
manufacturer tests every 1000th lightbulb off the production
• D. The
line.
an algebraic expression with square of the sum of two numbers is 49
(x+y)=7
Step-by-step explanation:
because the x plus y was squared,we find the square root of the 49 which is 7 and the answer remains (x+y)=7
The Crawfords drove for 4000 miles. This was 1/3 the distance the Blake family drove. How many miles did the jones family drive.
Evaluate the following expression. -8 x (-10 + (-7))
please help!
Answer:
136
Step-by-step explanation:
Answer:136
Step-by-step explanation: 136
-10+-7 equals -17
-17x-8 equals 136
a negative times a negative equals a positive
which ratio is greater than 5/8
Answer:
4/5 is greater thwn 5/8
Step-by-step explanation:
because ot just is
Answer:
Possible answers are 5/6, 3/4, etc.
Step-by-step explanation:
Many different ratios are greater than 5/8. If I wrote them all it would take FOREVER...
5/8 is greater than 1/2, therefore, ratios: 3/6, 2/4, etc. would not work.
I think you wrote the question wrong and forgot to type the options.
Sorry.
8.28 Katie wants a fancy new music player that costs $300. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax. How much does Katie save on the player if she drives to the neighboring state?
Answer:
Explanation
Given:- Katie wants a fancy new music player that costs $300
. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax
To Find:- To determine the cost Katie saves on the player if she drives to the neighboring state
The difference between the sales tax of the home state and the neighboring state provides the percentage of sales tax . Then, multiplying the determined percentage of sales tax on the new music player would be the cost Katie saves on the player if she drives to the neighboring state.
Step-by-step explanation:
The sales tax in the home state is 8% and the sales tax in the neighboring state is 5%The percentage of sales tax saved when travelling from home state to neighboring state will be=8%-5%
=3%
Therefore, the cost Katie saves on the new music player which costs $300 if she drives to the neighboring state will be=300*3%
=300*(3/100)
=3*3
=$9
The amount Katie saves on the new music player if she drives to the neighboring state is $9
Answer:
Katie saves $9.
Step-by-step explanation:
Buy it in her home:
8% of $300 = $24
Buy it in neighbouring state:
5% of $300 = $15
How much she save's (Answer):
She saves $9 because 24 - 15 = 9.
Please Help!
What is 3,198.7 as a fraction
Answer:
31987/10 or 3198 7/10
Step-by-step explanation:
Hi!! Here's how to solve your problem!!
Step 1: Convert decimal to fraction.
3198.7 = 31987 over 10 (31987/10)
(You add a 1 under the decimal point and there is a 7 next to the decimal point so you add one 0 since there aren't any numbers after 7.)
Step 2: Change the fraction (if you want)
31987/10 = 3198 and 7 over 10
31987 ÷ 10 = 3198 remainder 7 so it will be 3198 7/10.
I hope this helps!!!
16. During a choir rehearsal, 25 students were standing in a line at equal distances. The distance between the first and the fourth student was 2.7 m. What was the distance between the first and the last student?
Answer:
Step-by-step explanation:
25 - 4 = 21
2.7*21=56.7m
PLEASE HELP!!!
Due in 10 minutes!
Answer:
41ft²
Step-by-step explanation :
8ft - 2ft = 6ft
6ft - 2ft = 4ft
4ft - 1ft = 3ft
3ft * (8ft + 2ft) / 2 = 15ft²
1ft * (8ft + 2ft) = 10ft²
8ft * 2ft = 16ft²
Total : 16 + 15 + 10 = 41ft²
−11−(−5)/2×3 is an example of
A. an algebraic expression
B. a numerical equation
C. a numerical expression
D. an algebraic equation
Answer:
C, numerical expression
Step-by-step explanation:
B and D mean equations, not expressions. Equations are when one side is equal to the other so we can rule those out. A algebraic expression has variables like X in it, but this doesn't have any variables, so C is your answer, a numerical expression.
PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?
Answer:
[tex]-\frac{77}{3}[/tex]
Step-by-step explanation:
So we have the equation: [tex]3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2})[/tex]. and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so: [tex]2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}[/tex]. And you do this for the 1/2 as well: [tex]1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}[/tex].
Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM. [tex]\frac{8}{3} * \frac{2}{2} = \frac{16}{6}[/tex]. And now do this to the 3/2 you get: [tex]\frac{3}{2} * \frac{3}{3} = \frac{9}{6}[/tex]. Now the inside of the parenthesis is: [tex]\frac{9}{6} + \frac{16}{6} = \frac{25}{6}[/tex]. So now we have the equation: [tex]3\frac{1}{2} -7 * \frac{25}{6}[/tex] . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.
Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you: [tex]\frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}[/tex]. Now we have the equation: [tex]3\frac{1}{2} - \frac{175}{6}[/tex]. And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation: [tex]\frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}[/tex]. Which can simplify by dividing both sides by 2 to get: [tex]-\frac{77}{3}[/tex]
please answer correctly.
Answer:
The answer is the second option down.
Compare the expressions using >, < or =
-5 + (-3) and -5- (-3)
Answer:
-5 + (-3) < -5 - (-3)
Step-by-step explanation:
so -5 + (-3) evaluates to -5 - 3 which then evaluates to -8, because you're "going back" on the number line by 3.
-5 - (-3) evaluates to -5 + 3 since the negatives cancel out. this further evaluates to -2. this is greater than the previous value so we use the < (if you put this equation on the right side, since you can technically use > if you put the equation on the left side, just depends on what side you put it on)
-5 + (-3) < -5 - (-3)
Find the amount of discount using the following numbers.
Original price: $60; Rate of discount: 20%
PLEASE HELP ME
I GOT STUCK
THANK YOU!!
Answer:
Discount = 20%
Original price = $60
Discounted price = $48
Step-by-step explanation:
To find the amount of the discount, we take the original price and multiply it by the rate of the discount. In this case, we would take $60 and multiply it by 0.20 to get $12. This is the amount of the discount.
Find the degree of 3m^2·n^4
Hello!
The degree of the term will be the highest power to which a variable in the term is raised.
Hence, the degree of 3m²n⁴ is [tex]\fbox {4}[/tex]
PLEASE ANSWER ASAP: After moving to a new house the McGraths budgeted $250 for landscaping. On their visit to a local nursery they chose 8 sunflowers priced at $10.95 a piece and 12 roses priced at $11.95 each. By how much did they exceed their budget?
Answer:
They did not exceed their budget.
Step-by-step explanation:
8(10.95) + 12(11.95) = $231
250 - 231 = $19 savings
Answer: They didn't exceed the budget
Step-by-step explanation:
FACTS:
their budget is $250 dollars.
They buy:
8 sunflowers at 10.95 each
12 roses at 11.95 each.
How much did they exceed their budget? (in other words, by how much did they go over their spending limit?)
Step 1: Find the total amount of money spent on sunflowers.
We know they got 8 sunflowers, and each sunflower cost $10.95.
Total on sunflowers= 10.95x8= $87.60
Step 2: Find the total amount spent on roses
12 roses, each one costs 11.95.
total on roses= 11.95x12=$143.40
Step 3: Find how much was spent
143.4+87.6= 231
They didn't exceed their budget. In fact, they were $19 under their spending limit because 250-231= 19. I double checked my answer.
The lengths of the sides of triangle ABC are consecutive whole numbers. The median from angle A is perpendicular to the angle bisector of ∠B. Find the lengths of the sides of the triangle.
help i dont know how to find the surface area. a step by step explanation would help me better.
Answer:
256
Step-by-step explanation:
so there is 4 rectangles, 1 square, and 4 triangles within the composite figure in the question.
so basically you find the area of each of those shapes and add them together and that's your answer.
the rectangles width is 4 and length is 12, to find the area of a rectangle you do length times width so 4 times 12 which is 48, you have 4 rectangles so 48 times 4, which is 192.
the squares sides are 4 so you multiple two of the sides so 4 times 4 which is 16.
now we have the triangles, the formula for the area of a triangle is A=[tex]\frac{hx_{b}b }{2}[/tex], so b is base, the base is 4, h is height, the height is 6, so you plug in those numbers in the formula and you get 12. you have 4 triangles so 12 times 4 which is 48.
so now you add them all together 192 + 16 + 48 = 256
How many arrangements of all eight letters in TRESPASS do not have S as the final letter?
Answer:
i think its 16
Step-by-step explanation:
Tell which number is greater.
11. 0.12, 1.2%
Answer: 11
Step-by-step explanation:
Out of the 3 choices, the last two both give decimals less than one, so we know they won't be greater than 11.
how many more cartons are needed to hold 1500 books in cartons of 10 than in cartons of 15?
The cartoons of 10 be 150 and cartoons of 15 be 100.
What is Unitary method?It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Steps to Use Unitary MethodFirst, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.
Given:
total books = 1500
So, cartoons of 10 needed
=1500 / 10
=150 cartoons
and, cartoons of 15 needed
=1500/15
=100 cartoons
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Which ratio is leColleen compared the ratios 3:8 and One-half. Her work is shown below.
Write the ratios as fractions: Three-eighths and One-half
The common denominator is 8.
Write each fraction using the common denominator: Three-eighths and One-eighth
Compare the numerators: 3 > 1
Write the correct statement: Three-eighths > One-half
Where did Colleen make her first mistake?ss than 15/24 ?
Answer:
Step #3 is where Colleen messed up.Step-by-step explanation:
When Colleen was making a common denominator for the two fractions, she should have multiplied the numerator by 8/denominator.
For example,
1/2 with a denominator of 8 would be 4/8 since we must multiply the numerator by 4. (8/2 = 4)
So, her answer should have been 3/8 < 4/8 (which is also 3/8 < 1/2)
Answer:
Step 3 is where Colleen messed up.
Step-by-step explanation:
7.24. If you walk for 45 minutes at a rate of 4 \mathrm{mph}$ and then run for 30 minutes at a rate of 10 mph, then how many miles have you gone at the end of one hour and 15 minutes? What was your average speed for the journey?
Answer:
The average speed for the journey is 6.4 mph.
Step-by-step explanation:
Given:
If you walk for 45 minutes at a rate of [tex]$4 \mathrm{mph}$[/tex] and then run for 30 minutes at a rate of [tex]$10 \mathrm{mph}$[/tex], then how many miles have you gone at the end of one hour and 15 minutes Find the average speed for the journey
Step 1 of 1
We can compute the walking distance and running distances separately, then add them.
You walk for 45 minutes, which is [tex]\frac{3}{4}$[/tex] hours, at a rate of [tex]$4 \mathrm{mph}$[/tex], so the walking distance is [tex](4 \mathrm{mph})\left(\frac{3}{4}\right.$ hours $)=3$[/tex] miles. You run for 30 minutes, which is [tex]\frac{1}{2}$ hour, at a rate of $10 \mathrm{mph}$[/tex], so the running distance is [tex]$(10 \mathrm{mph})\left(\frac{1}{2} h o u r\right)=5$[/tex] miles.
So the total distance you cover is 3+5=8 miles.
Now we can also compute the average speed for the journey.
You covered 8 miles in [tex]$\frac{5}{4}$[/tex] hours, so your average speed was
[tex]$$\begin{aligned}&\frac{8 \text { miles }}{\frac{5}{4} \text { hours }}=\frac{8}{\frac{5}{4}} \mathrm{mph} \\&\frac{32}{5} \mathrm{mph}=6.4 \mathrm{mph}\end{aligned}$$[/tex]
8.41 Compute 40% of 20% of 10% of 80,000.
Answer: 640
Step-by-step explanation:
In this case, we can substitute the word "of" with multiplication.
we have:
40% ×20%×10%×80000
solving this out, you get the answer!
(and yes, I recognize this problem from the aops textbook, if you want a different solution, check 8.21 in the solutions manual)
Answer:
The 40% of 20% of 10% of 80000 is 640.
Step-by-step explanation:
We are given with a number 80000We are asked to find the 40% of 20% of 10% of the numberWe can do this in one single stepStep 1: Computing the value
Step 1 of 1
We are asked to find the value 40% of 20% of 10% 80,000 40% of 20% of 10% of 80000
[tex]&=\frac{40}{100} \times \frac{20}{100} \times \frac{10}{100} \times 80000 \\&=\frac{40}{100} \times 1600 \\&=640\end{aligned}$$[/tex]
What is the volume of a rectangular prism with side lengths 15.8 m, 24.5 m, and 4.2 m? Round to the nearest cubic meter.
Answer: 1,626 cubic meters
Step-by-step explanation:
V= lwh
V= length x with x height
Each number isn't specified (i dont know which numbers represent the width, length, and height since it isn't said) but that doesn't matter because according to the commutative property , you can multiply in any order and still get the same result.
So V= 15.8 x 24.5 x 4.2
V= 1,625.82
Rounded to the nearest cubic meter: 1,626 because 1625.82 becomes 1625.8, which, to the nearest whole number, is 1,626.
What steps should be taken to calculate the volume of the right triangular prism? Select three options.
A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters.
A. Use the formula A = one-half b h to find the area of the base.
B. Use the formula A = b h to find the area of the base.
C. The area of the base, A, is One-half (7) (8) = 28 meters squared.
D. The area of the base, A, is One-half (8) (14) = 56 meters squared.
E. The volume of the prism, V is (56) (7) = 392 meters cubed.
Answer:
A D E
Step-by-step explanation:
A) The formula for the area of a triangle is [tex]\frac12 bh[/tex]
D) The base is 8 and the height is 14 so the area of the triangle is 56 meters squared.
E) Volume is [tex]56\times7=392[/tex] meters cubed.
Have a nice day :)
I REALLY NEED HELP: A cook is planning a banquet dinner a recipe that serves 8 people calls for 2 cups of milk. How many cups of milk will be needed for 36 servings?
The cook will need 9 cups of milk for the banquet dinner.
How many cups of milk will be needed for 36 servings?Since the recipe calls for 2 cups of milk per 8 servings. We can say:
cups of milk / servings = 2 / 8 = 1/4
We can solve for the cups of milk by multiplying both sides of the proportion by 36.
cups of milk for 36 servings = (cups of milk / servings) * 36
= (1 / 4) * 36
= 9
Therefore, 9 cups of milk will be needed for the banquet dinner.
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The difference of two odd numbers is a multiple of ______ 11. | -56 | = ____
Answer:
1. The difference of two odd numbers is a multiple of 2
2. | -56 | = 56
Step-by-step explanation:
1. Since the difference between two odd numbers is always even, this means the difference of two odd numbers is a multiple by 2. This is because all even numbers are divisible by 2.
2. The absolute value of | -56 | would be 56