Answers
Jack can mow 10% of the yard in 0.3 hours
Marilyn can mow 10% of the yard in 0.7 hours
Jack will mow 70% of the yard : 0.3 hours ( 10% ) × 7
= 2.1 hours . Jack can mow 70% of the yard in 2.1 hours
Marilyn will mow 30% of the yard : 0.7 hours ( 10%) × 3 = 2.1 hours. Marilyn can mow 30% of the yard in 2.1 hours.
John mowwing for 2.1 hours + Marilyn mowwing for 2.1 hours = 100% of the yard in 4.2 hours.
Awnser : 4.2 hours
First, figure out their mowing rates per hour.
Jack's is [tex] \frac{1}{3} [/tex] since he mows 1 lawn in 3 hours; Marilyn's is [tex] \frac{1}{7} [/tex] since she mows 1 lawn in 7 hours.
We now know that their combined rate of mowing 1 lawn is [tex] \frac{1}{3} + \frac{1}{7} [/tex]. Use the variable t for time and multiply it by their combined rate to figure out their combined time of mowing 1 lawn.
[tex]( \frac{1}{3} + \frac{1}{7})t =1[/tex]
[tex]( \frac{7}{21} + \frac{3}{21} )t=1[/tex]
[tex] \frac{10}{21} t =1[/tex]
[tex]t= \frac{21}{10} [/tex]
Answer:
Jack and Marilyn could mow the lawn in [tex] \frac{21}{10} [/tex] or 2.1 hours if they work together.
Related Questions
HELP WILL MARK BRAINLIEST
Use the net to find the lateral area of the cylinder
height is 9inch and radius is 5inch
Answers
Lateral Area = 2 x π x 5 x 9
Lateral Area = 282.74 in²
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Answer: The lateral area of the cylinder is 282.74 in²
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Carlos’s hockey team has ten players, not counting the goalie.Five non goalie players need to be selected for a starting line-up.
A)How many different starting lineups are possible if positions are not assigned?
B)How many starting lineups are possible if positions are assigned?
Answers
Final answer:
There are 252 different starting lineups possible if positions are not assigned, and 30,240 starting lineups are possible if positions are assigned.
Explanation:
For part A of the question, where positions are not assigned, we can calculate the number of different starting lineup combinations by using the combination formula. Since we are choosing 5 players out of 10 without regard to order, we use:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of players to choose from, and k is the number of players we want to choose. Therefore, we have:
C(10, 5) = 10! / (5! (10-5)!) = 252
There are 252 different starting lineups possible if positions are not assigned.
For part B, where positions are assigned, we use the permutation formula because the order in which we select the players matters. This formula is:
P(n, k) = n! / (n-k)!
Since the order in which the players are chosen matters, we have:
P(10, 5) = 10! / (10-5)! = 30,240
There are 30,240 different starting lineups possible with positions assigned.
Rodney bought a 25-pound bag of dog food. His dog ate 10 2/5 pounds of the food in the first month and 10 4/5 pounds in the second month. How much dog food, in pounds, was remaining in the bag at the end of the two months?
Answers
10 2/5 + 10 4/5 = 21 1/5.
25 - 21 1/5 = 3 4/5.
Answer:
[tex]3\frac{4}{5}[/tex] pounds of food
Step-by-step explanation:
We have been given that Rodney bought a 25-pound bag of dog food. His dog ate [tex]10\frac{2}{5}[/tex] pounds of the food in the first month and [tex]10\frac{4}{5}[/tex] pounds in the second month.
Let us find the amount of dog-food eaten by dog in two months.
[tex]\text{Dog-food eaten in 2 months}=10\frac{2}{5}+10\frac{4}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{52}{5}+\frac{54}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{52+54}{5}[/tex]
[tex]\text{Dog-food eaten in 2 months}=\frac{106}{5}[/tex]
Now we will subtract amount of food eaten by dog from the amount of food initially to find the remaining amount of dog food.
[tex]\text{Remaining amount of dog-food}=25-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog-food}=\frac{5*25}{5}-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog-food}=\frac{125}{5}-\frac{106}{5}[/tex]
[tex]\text{Remaining amount of dog food}=\frac{125-106}{5}[/tex]
[tex]\text{Remaining amount of dog food}=\frac{19}{5}[/tex]
[tex]\text{Remaining amount of dog food}=3\frac{4}{5}[/tex]
Therefore, [tex]3\frac{4}{5}[/tex] pounds of food was remaining in the bag at the end of the two months.
There are four steps in solving one’s personal financial challenges:
1. considering opportunity costs
2. assessing risks and returns
3. setting short- and long-term goals
4. assessing needs and wants
Which of these is the correct order of these steps?
2, 3, 1, 4
1, 2, 3, 4
4, 1, 2, 3
3, 1, 4, 2
Answers
Answer: C. 4, 1, 2, 3.
I hope this helps :)
Answer: Third option is correct.
Step-by-step explanation:
Since there are four steps in solving one's personal financial challenges:
1) First he needs to assessing the needs and wants .
2) Then, he will consider opportunity costs, i.e. next best alternative.
3) Then, he will assessing the risks and returns associated with the opportunity costs.
4) Last, but not the least, he will be setting short and long term goals.
So, The correct order of these steps is 4,1,2,3.
Hence, Third option is correct.
A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet is uniform. what is the x-coordinate of its center of mass?
Answers
1. The long way
We know that the base of the triangle is along the x-axis, and the length of the base is 20.
The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).
Therefore the centre of mass is located at
x=3+(10-3)*2/3=23/3
y=4/3
2. The short way
It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i.e.
CG=((0+20+3)/3, (0+0+4)/3)=(23/3, 4/3) as before.
What number fills in the blank to complete the factorization of 3x + 24?
(x + 8)
Answers
Answer:
The factor form of given expression is 3(x+8) so the required number is 3.
Step-by-step explanation:
The given expression is
[tex]3x+24[/tex]
Write the factors of each term.
[tex]3x+24=3\times x+3\times 8[/tex]
In both terms, 3 is a common factor.
Take out the common factor 3.
[tex]3x+24=3(x+8)[/tex]
The factor form of given expression is 3(x+8). The factor (x+8) is given, therefore the required number is 3.
At what Kelvin temperature will a sample of gas occupy 12 liters if the same sample occupies 8 liters at 27 °C?
Question 11 options:
45.0K
450K
40.5K
405K
Answers
P
V
=
n
R
T
we can say:
V
T
=
constant
Therefore,
V
1
T
1
=
V
2
T
2
⇒
T
1
=
V
1
×
T
2
V
2
⇒
T
1
=
12
L
×
300
K
8
L
=
450
K
A=450k
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
Answers
Noel is more likely to draw two cards with a sum that is greater than 13.
To determine which outcome is more likely, let's count the number of combinations that meet each criterion.
1. **Sum that is a multiple of 3**:
- Possible sums: 3, 6, 9, 12
- Counting the combinations:
- 3: 1 combination
- 6: 2 combinations
- 9: 3 combinations
- 12: 4 combinations
- Total combinations: 1 + 2 + 3 + 4 = 10 combinations.
2. **Sum greater than 13**:
- Possible sums: 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
- Counting the combinations:
- 14: 1 combination
- 15: 2 combinations
- 16: 2 combinations
- 17: 3 combinations
- 18: 2 combinations
- 19: 3 combinations
- 20: 2 combinations
- 21: 3 combinations
- 22: 1 combination
- 23: 1 combination
- Total combinations: 1 + 2 + 2 + 3 + 2 + 3 + 2 + 3 + 1 + 1 = 20 combinations.
Comparing the total combinations, we see that there are more combinations with a sum greater than 13 (20 combinations) than there are combinations with a sum that is a multiple of 3 (10 combinations). Therefore, Noel is more likely to draw two cards with a sum that is greater than 13.
The probable question may be:
Noel is playing a game where he draws one playing card each out of two stacks of 5 cards. The table below shows all possible sums for the two numbers on the cards.
3, 6, 7, 9, 1
1 = 4, 7, 8, 10, 12
4 = 7, 10, 11, 13, 15
6 = 9, 12, 13, 15, 17
8 = 11, 14, 15, 17, 19
12 = 15, 18, 19, 21, 23
Is Noel more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13?
Noel is more likely to draw two cards with a sum greater than 13, as there are 37 combinations compared to 11 combinations for multiples of 3.
To determine whether Noel is more likely to draw two cards with a sum that is a multiple of 3 or two cards with a sum that is greater than 13, we can analyze the table provided.
1. Sum that is a multiple of 3:
- There are several combinations of card values that result in a sum that is a multiple of 3. We can count these combinations from the table:
- (3, 4), (3, 7), (3, 9), (3, 12)
- (6, 7), (6, 10), (6, 12)
- (7, 8), (7, 11)
- (9, 10), (9, 13)
- (11, 12)
2. Sum greater than 13:
- We need to count the combinations of card values that result in a sum greater than 13:
- (6, 8), (6, 10), (6, 11), (6, 12), (6, 13), (6, 15), (6, 17)
- (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 15), (7, 17), (7, 19)
- (9, 10), (9, 11), (9, 12), (9, 13), (9, 15), (9, 17), (9, 19)
- (11, 12), (11, 13), (11, 15), (11, 17), (11, 19)
- (12, 13), (12, 15), (12, 17), (12, 19)
- (13, 15), (13, 17), (13, 19)
- (15, 17), (15, 19)
- (17, 19)
After counting the combinations, we can compare the number of combinations in each category:
1. Sum that is a multiple of 3:
- Total combinations: 11
2. Sum greater than 13:
- Total combinations: 37
Comparing the totals, we can see that Noel is more likely to draw two cards with a sum that is greater than 13, as there are more combinations resulting in this outcome.
Complete Question:
The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%. I. a food establishment succeeding and earning $50,000 or more II. a service establishment succeeding and earning between $25,000 and $75,000 III. a retail establishment succeeding and earning no more than $50,000 a. I only b. I and II c. II and III d. III only
Answers
Answer:
The answer is D on edge 2020.
Step-by-step explanation:
What is the product of (-1/4) x (-3/7)? Write your answer in simplest fraction form
Answers
Two numbers have a difference of 0.7 and a sum of 1 . What are the numbers ?
Answers
0.85 + 0.15 = 1
0.85 - 0.15 = 0.7
hope this helps
Write an inequality to represent the situation. Twelve times a number increased by four is no more thsn twenty-three.
Answers
The inequality for this situation is
12x + 4 <= 23
Where x is the number.
Hope this helps!
Let x be the number.
Twelve times the number x is 12·x=12x.
The number 12x increased by four is 12x+4. This result is no more than twenty-three, then
12x+4≤23.
Answer: 12x+4≤23.
The speed limit on a highway is 55 miles per hour. This means that vehicles cannot legally drive at speeds over 55 miles per hour. Write an inequality that is true only for speeds in miles per hour, x, at which vehicles can drive legally on the highway.
Answers
Hope it helps! :)
If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year, what will be the balance of the savings account after all the interest is paid for the year?
A. $5300.00
B. $5127.03
C. $5100.00
D. $5370.30
Answers
Answer:
Option D - $5370.30
Step-by-step explanation:
Given : If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year.
To find : What will be the balance of the savings account after all the interest is paid for the year?
Solution :
First we find the interest he paid.
The interest formula is [tex]I=P\times R\times T[/tex]
Where, P is the principal P=$5100
R is the rate of interest R=5.3%=0.053
T is the time T=1 year
Substituting the values,
[tex]I=5100\times 0.053\times 1[/tex]
[tex]I=\$270.3[/tex]
The balance of the saving account is the sum of interest paid and principal value.
Amount = Interest +Principal
Amount = $270.3 +$5100
Amount = $5370.3
Therefore, Option D is correct.
Help please !!!!!!! .......
Answers
A geometric sequence is a sequence of numbers, where the successive values after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In this case the common ratio is 0.6.
5 * 0.6 = 3
3 * 0.6 = 1.8
1.8 * 0.6 = 1.08
the first term in an arithmetic sequence is 5. the foutth term in the sequence is -4. the tenth term is 22. which function can be used to find the nth term of the arithemetic sequence
Answers
if the given terms are a₁=5; a₂=-4; a₁₀= -22, then
1. rule: n-th term of any arithmetic sequence is:
[tex]a_n=a_1+d(n-1), [/tex] where d - difference of this sequence.
2. using the mentioned rule
a₄=a₁+d(4-1), ⇒ -4=5+3d; ⇒ d=-3.
(a₁₀=a₁+9d=5-3*9=-22).
3. if d=-3 and a₁=5, then it is possible to make up an equation for n-th term:
[tex]a_n=5-3(n-1)=8-3n;[/tex]
a₁₀₀=8-3*100=-292.
An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two to do the job together
Answers
1/r1 + 1/r2 = 1/rt
r1 = time for roofer 1 in hours = 26 hours.
r2 = time for roofer 2 in hours = 39 hours.
1/26 + 1/39 = 1/rt
0.03846 + 0.02564 = 1/rt
0.06410 = 1/rt ****** (I've used these stars later on. Ignore them now)
You could go on one of two ways. You could put 1 one under 0.06410 and cross multiply. I'll do that first.
0.06410 / 1 = 1/rt
0.06410 * rt = 1 * 1
0.06410 * rt = 1 Now divide by the number on the left.
rt = 1/0.06410
rt = 15.6
Or you could do this. Go back to the step with the stars.
Turn both steps upside down
0.06410 = 1 / r2 Take the reciprocal of both sides.
1/0.06410 = r2
r2 = 15.6 hours for both roofers working together.
There are other ways of doing this problem. None are any quicker. The point is that your answer should come to a number below either of the workers. It makes sense. The slower worker still does some work, but the faster worker does most of it.
Final answer:
The experienced roofer and the beginning roofer together can complete the job in approximately 15.6 hours, which is found by adding their work rates and taking the reciprocal of the sum.
Explanation:
To find how long it takes for both an experienced and a beginning roofer to roof a house together, we need to sum their work rates and then find the reciprocal of that sum. We'll start by considering the work rates of both the experienced and the beginning roofer. The experienced roofer can roof a house in 26 hours, which means the roofer completes 1/26 of the job per hour. The beginning roofer completes the job in 39 hours, which is 1/39 of the job per hour.
Now, we can calculate their combined work rate:
1/26 + 1/39 = (39 + 26) / (26 * 39) = 65 / 1014 = 1/15.6
These two roofers together complete 1/15.6 of the job per hour. To find out how long it will take them to complete the job together, we take the reciprocal of this rate:
1 / (1/15.6) = 15.6 hours.
Therefore, it would take the experienced and beginning roofer combined around 15.6 hours to roof the house together.
A plot of 1/no2 versus time is linear. using this information, identify the factor by which the rate will increase in model (c) if the number of molecules is increased by a factor of 17.
Answers
We have that b/A= t+c where c is a constant.
Hence A=b/(c+t)
By differentiating, we get that A'=-b/(C+t)^2
Then, we have that -(A)^2=A'/b
Hence at any point, we have that if we make the concentration 17 times, we have that there is a 17 times bigger , the rate will become bigger by 17*17, hence 289 times faster.
solve the system of equations by substitution y=5x-13 and 5x+2y=19
Answers
5x + 2y = 19 --------- (2)
Sub (1) into (2):
5x + 2(5x -13) = 19
5x + 10x - 26 = 19
15x = 19 + 26
15x = 45
x = 3 -------- sub back into (1)
y = 5(3) - 13
y = 15 - 13
y = 2
Ans: x = 3, y = 2
A bag of trail mix weighs 2 lb. By weight, 20% of the bag is oats. How many pounds is the
oats portion of the trail mix?
(a) Write an equation for the situation and label the “part,” “whole,” and “percent.”
HELP DUE TONIGHT
Answers
20% = 20/100 = 0.2. Multiplying the percent by the whole gives us the part; 0.2(2) = 0.4.
It took Eduardo 8 hours to drive from buffalo, NY to new York city, a distance of about 400 miles. Find his average speed.
Answers
Hope this helped!
A gardener crosses tall true-breeding pea plants with short true-breeding ones. Tall plants are dominant to short ones. He collects the seeds to grow F1 plants and then allows them to self-pollinate to form an F2 generation. Which of the following describes the traits of the offspring correctly?
Answers
a) Three–fourths of the F1 and one–half of the F2 plants will be tall.
b) All of the F1 and three–fourths of the F2 plants will be tall.
c) Three–fourths of the F1 and all of the F2 plants will be tall.
Let’s name tall as T and short as t
Since both are true breeding plants
Tall plants have the genotype TT and short plants have the genotype tt
Tall plants will make gametes of type T only
Short plants make gametes of type t only
After cross breeding the offspring would all be of genotype Tt as they’re made of T and t gametes
F1 generation formed have the genotype Tt
Since T is dominant all F1 plants are tall
When F1 self pollinates
F1 * F1
Tt *Tt
Gametes are
T t T t
F2 population offspring genotypes are as follows;
TT -1/4 tall
Tt -1/4 tall
Tt -1/4 tall
tt - 1/4 short
3/4 of the plants are tall
Remaining 1/4 is short
Therefore response b is correct
All f1 plants are tall and 3/4 of f2 plants are tall
help please in eed answers asap
Answers
4.2 x 4.2 x 4.2 = 74.088 cm^3
Answer:
74,088 cm³
Step-by-step explanation:
[tex]whl = V \\ \\ [4,2]^{3} = 74,088[/tex]
I am joyous to assist you anytime.
Vanessa earns a base salary of $400.00 every week with an additional 5% percent commission on everything she sells. Vanessa sold $1650.00 worth of items last week.
What was vanessas total pay last week
Answers
Will someone please find the value of x for these questions
Answers
12) for h=√(10²-6²)=8
then
[tex] \frac{x-6}{8} = \frac{8}{6}; \ =\ \textgreater \ \ x= \frac{50}{3} [/tex]
14) 6:11 as x:10. It means that
[tex] \frac{6}{11} = \frac{x}{10}; \ =\ \textgreater \ \ x=6*10/11= \frac{60}{11} [/tex]
A stained glass window is in the shape of an equilateral triangle. what is the measure of one interior angle of the triangle
Answers
60° x 3 (Angles) = 180°
a store received 500 containers of milk to be sold by Febuary 1. Each container the store sold $0.83 and sold for $1.67. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by Febuary 1. If 470 containers were sold bu February 1, how much profit did the store make?
Answers
The amount of net profit the store makes on each container is given by 1.67-0.83 (the amount it is sold for subtracted by the amount it costs the store), which is $0.84 per container. They sell 470 containers, so the net profit at this point is 470(0.84) = $394.80.
However, since the distributor is giving the store a $0.50 refund on all every container under 500 that the store sells, the store gets additional money back:
500-470 = 30 containers not sold
30(0.50) = 15
So the total profit is $394.80 + 15 = $409.80.
i,ii,iii,iiii,iiiii what is the twentieth term?
Answers
Name all pairs of vertical angles.
Answers
:)
A circle has a circumference of 361π. What is the diameter of the circle?
Answers
Given that the circumference = 361π
πD = 361π
D = 361 units
The formula to find circumference of circle is given by
[tex] C =2\pi r [/tex]
Where r is radius of circle and pi =3.14
We are given Circumference here as 361π
Plugging the value in the formula :
[tex] 361\pi =2\pi r [/tex]
r=361/2 = 180.5
radius of circle is 180.5.
We know that Diameter is double of radius.
So diameter = 2*180.5 = 361
Answer: Diameter of circle is 361.