===================================================
Explanation:
Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.
Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.
Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.
--------------------------
Another approach
Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is
1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute
x = number of minutes
(combined rate)*(time) = number of jobs done
(1/24)*x = 1
x = 1*24
x = 24 is the time it takes if they worked together without getting in each other's way.
Effectively, we are solving the equation
1/A + 1/B = 1/C
with
A = time it takes Wilma to do the job on her own
B = time it takes Rocky to do the job on his own
C = time it takes the two working together to get the job done
The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.
So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.
Together they can mow the lawn in 24 minutes.
What are the relation between time, work, and efficiency?Time and efficiency are inversely proportional to each other.
Time and work are directly proportional to each other.
Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.
Assuming total work to be 120 as it is the LCM of 40 and 60.
So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is
(120/40) = 3.
Now together their efficiency is (2 + 3) = 5.
∴ Together they can complete the work in (120/5) = 24 minutes.
learn more about time and work here :
https://brainly.com/question/3854047
#SPJ2
Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:
A. 2 √34 units
B. √85 units
C. 2 √17 units
D. √17 units
Answer:
Step-by-step explanation: Answer is 2√17 units
Distance =√ (−2−0) ^2−(5−(−3)) ^2
=√ (−2) ^2−(5+3) ^2
=√4+64
=√68
=2√17 units
How many gallons of fuel costing $1.15 a gallon must be mixed with a fuel costing $0.85 per gallon to get 40
gallons of a fuel that costs $1 per gallon? Formulate an equation and then solve it in order to determine how
many gallons of fuel costing $1.15.
Answer:
multiply 0.85x40
Step-by-step explanation:
9(d − 93) = –36 d = _______
Steps to solve:
9(d - 93) = -36d
~Distribute
9d - 837 = -36d
~Subtract 9d to both sides
-837 = -45d
~Divide -45 to both sides
18.6 = d
Best of Luck!
Use the box-and-whisker plot below to identify the lower quartile, upper quartile, and interquartile range of the
data set the plot represents.
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
A lower quartile - 38, upper quartile = 47. interquartile range = 9
B lower quartile = 45, upper quartile -50, interquartile range = 5
cu lower quartile 47 upper quartile = 53, interquartile range 6
D. lower quartile = 45, upper quartile = 47. interquartile range = 2
Answer:
The answer should be B.
The lower quartile is the one that is 45, the upper quartile is the one on 50, and the interquartile range is the difference between upper and lower quartile, which is 5.
Hope this helps!
You take a multiple choice test that you are not prepared for, so you have to guess on all twenty questions. The probability that you guess correctly on any given question is 20% (since there are five choices on each question). What is the probability that you are able to guess ten or more correct answers? You must show correct inputs to either binompdf or binomcdf to receive credit.
Answer:
The probability that you are able to guess ten or more correct answers is P(x≥10) = 0.0026
Step-by-step explanation:
This can be modeled by a binomial random variable, with sample size n=20 and probabillity of success p=0.2.
The probability of getting k answers right can be calculated as:
[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{20}{k}\cdot0.2^k\cdot0.8^{20-k}[/tex]
Now, we have to calculate the probabiltiy that 10 or more answers are correctly answered guessing. This is P(x≥10).
[tex]P(x\geq10)=P(x=10)+P(x=11)+P(x=12)+P(x=13)+P(x\geq14)[/tex]
Note: the expression is simplified for x≥14 because we know the additional probability is less than 0.00005.
[tex]P(x=10)=\dbinom{20}{10}\cdot0.2^{10}\cdot0.8^{10}=184756\cdot0.0000001\cdot0.1074=0.0020\\\\\\P(x=11)=\dbinom{20}{11}\cdot0.2^{11}\cdot0.8^{9}=167960\cdot0.00000002\cdot0.1342=0.0005\\\\\\P(x=12)=\dbinom{20}{12}\cdot0.2^{12}\cdot0.8^{8}=125970\cdot0\cdot0.1678=0.0001\\\\\\P(x=13)=\dbinom{20}{13}\cdot0.2^{13}\cdot0.8^{7}=77520\cdot0.000000001\cdot0.2097=0.0000\\\\\\P(x\geq14)=0.0000[/tex]
[tex]P(x\geq10)=0.0020+0.0005+0.0001+0.0000+0.0000=0.0026[/tex]
The probability that you are able to guess ten or more correct answers is P(x≥10) = 0.0026
O número inteiro positivo, cujo produto de seu antecessor com seu sucessor é igual a 8, é
A) 5
B) 4
C) -3
D) 3
El 2
Answer:
Olá!
`~~~~~~~~~~~~~~~~~~
3 (número inteiro positivo)
2 (antessor)
4 (sucessor)
Para provar isso, simplesmente multiplicamos entre 4 e 2:
4 x 2 = 8
Espero que isso tenha ajudado! Também seria bom se você me desse Brainliest!
On Wednesday and Thursday
a total of 32 records were sold.
The number of records sold on
Thursday was 3 times the number
of records sold on Wednesday.
c) How many records were (2)
sold on Wednesday?
d) How many records were (1)
sold on Thursday?
Total marks: 5
Answer:
8 records were sold on Wednesday, and 24 records were sold on Thursday
Step-by-step explanation:
Let's call the number of records sold on Wednesday w, and the number sold on Thursday t.
t+w=32
t=3w
Substituting:
(3w)+w=32
4w=32
w=8
t=3w=3(8)=24
Hope this helps!
I NEED HELP PLEASE, THANKS! :)
Answer:
D. No solution
Step-by-step explanation:
Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all. Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.
Hope you understand :)
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set B is about 41.56 with standard deviation of about 6.07. The mean for Set A is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set A means that Set A’s low temperatures have a greater variability than Set B temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.4. The mean for Set B is about 41.5 with standard deviation of about 6.7. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures. The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 43.8 with standard deviation of about 14.8. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set B’s low temperatures have a greater variability than Set A temperatures.
Answer:
Explained below.
Step-by-step explanation:
The question is:
Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.
Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}
Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}
The five-number summary is:
MinimumFirst Quartile Median Third Quartile MaximumThe five-number summary for set A is:
Variable Minimum Q₁ Median Q₃ Maximum
Set A 36.00 38.25 44.00 50.75 54.00
The five-number summary for set B is:
Variable Minimum Q₁ Median Q₃ Maximum
Set B 22.00 28.75 48.00 58.50 65.00
Compute the mean for both the data as follows:
[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]
Both the distribution has the same mean.Compare mean and median for the two data:
[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]
This implies that set A is positively skewed whereas set B is negatively skewed.Compute the standard deviation for both the set as follows:
[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]
The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.Parker wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3 2% and the other bank is offering a rate of 3%
compounded annually. If Parker decides to deposit $7,000 for 25 years, which bank would be the better deal?
A.)a simple interest rate of 3.2%
B.)a compound interest rate of 3%
Answer:
The better deal would be simple interest rate of 3.2%
Step-by-step explanation:
In order to calculate which bank would be the better deal If Parker decides to deposit $7,000 for 25 years, we would have to make the following calculation:
A. simple interest rate of 3.2%.
Therefore, FV= P*r*t
=$7,000*3.2%*25
=$5,600.
B. compound interest rate of 3%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.03)∧25
FV=$14,656
The better deal would be simple interest rate of 3.2%
Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight. Which are knights
Answer:
w and y are knights
Step-by-step explanation:
Of the six natives, W and Y are the knights.
What is the reasoning?In mathematics, reasoning entails making logical deductions from data or presumptions. Making sense of something can be defined as gaining comprehension of a situation, setting, or idea by relating it to what is already known or has already happened.
Given that you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight.
From the given data it is concluded that W and Y are the knights because their statement is W says: At most three of us are knights and Y says: Exactly two of us are knights.
To know more about reasoning follow
https://brainly.com/question/28015404
#SPJ2
If a carpenter nails a 15-ft brace to the wall 9 feet above the floor, how far (in ft) from the base of the wall should he nail the brace to the floor? ___________________________________ ft.
Answer:
c = 12ft
Step-by-step explanation:
Given that the wall is 9ft from the ground.
Brace nailed to the wall is 15ft.
Note that the brace to the wall will be slant hence it will look like the hypotenus side of a triangle.
The question requires the solution to the distance from the base of the wall to the brace.
Note from Pythagoras theorem
a^2 = b^2+c^2
Where a = 15ft
b = 9ft
Hence, from the base of the wall, the brace will be nailed 9ft
c = ?
15^2 = 9^2+c^2
225 = 81+c^2
225-81 = c^2
144 = c^2
c =√144
c = 12ft
In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into 0.25-kmsquared regions. They then counted the number of rockets that landed in each region, with the results shown in the table below. Complete parts (a) through (e). Number of rocket hits 0 1 2 3 4 5 6 7 Observed number of regions 228 214 94 32 7 0 0 1 (a) Estimate the mean number of rocket hits in a region by computing mu equals Summation from nothing to nothing xP left parenthesis x right parenthesis.
Answer:
The estimated mean number of rockets hits in the region is 533.
Step-by-step explanation:
We are given the following information,
Number of rocket hits | Observed number of regions
0 | 228
1 | 214
2 | 94
3 | 32
4 | 7
5 | 0
6 | 0
7 | 1
We are asked to estimate the mean number of rocket hits in the region.
The mean or expected value is given by
[tex]\mu = \sum (x \cdot P(x)) \\\\\mu = (0 \cdot 228) + (1 \cdot 214) + (2 \cdot 94) + (3 \cdot 32) + (4 \cdot 7) + (5 \cdot 0) + (6 \cdot 0) + (7 \cdot 1) \\\\\mu = 0 + 214 +188+ 96 +28 +0+ 0 + 7 \\\\\mu = 533[/tex]
Therefore, the mean number of rockets hits in the region is 533.
write your answer without using negative exponents (u^4)^-7
Answer:
[tex] \frac{1}{ {u}^{28} } [/tex]solution,
[tex] {(u}^{4} \: )^{ - 7} \\ = {(u)}^{4 \times ( - 7)} \\ = {(u)}^{ - 28} \\ = \frac{1}{ {u}^{28} } [/tex]
Hope this helps...
Good luck on your assignment..
Two particles travel along the space curves r(t) and u(t). A collision will occur at the point of intersection if both particles are at P at the same time. (If an answer does not exist, enter DNE. Enter your answers as a comma-separated list.)
r(t) = t^2i + (9t - 20)j + t^2k u(t) = (3t + 4)i + t^2j + (5t - 4)k point of intersection (x, y, z) =
1. Do the particles collide?
a. Yes
b. No
2. Do their paths intersect?
a. Yes
b. No
Answer:
Point of intersection (x, y, z) = (16, 16, 16)
1. a. Yes
2. a. Yes
Step-by-step explanation:
In order for the particles to colide (and therefore have their paths intersect), the values for the i, j, and k coordinates must be equal for a given 't':
For the i coordinate:
[tex]i_{r(t)} =i_{u(t)}\\t^2=3t+4\\t=\frac{3\pm\sqrt{9-4*1*(-4)} }{2}\\t=4\ or\ -1[/tex]
For the j coordinate:
[tex]j_{r(t)} =j_{u(t)}\\9t-20=t^2\\t=\frac{9\pm\sqrt{81-4*1*20} }{2}\\t=4\ or\ 5[/tex]
For the k coordinate:
[tex]k_{r(t)} =k_{u(t)}\\t^2=5t-4\\t=\frac{5\pm\sqrt{25-4*1*4} }{2}\\t=4\ or\ 1[/tex]
As we can see, for t =4, both paths have the same coordinates and therefore they intersect and the particles will colide.
[tex]r(4) = 4^2i + (9*4 - 20)j + 4^2k \\r(4)=16i+16j+16k\\u(4) = (3*4 + 4)i + 4^2j + (5*4 - 4)k\\u(4)=16i+16j+16k[/tex]
Point of intersection (x, y, z) = (16, 16, 16)
Please answer this correctly
Answer:
1/4
Step-by-step explanation:
The probability of landing on an odd number is 2/4.
The probability of landing on a number greater than 5 is 2/4.
2/4 × 2/4
4/16 = 1/4
Gregoire sold 24 cars to his friend for $71.76. What was the price per car?
a. $47.76
b. $2.99
c. $17.22
d. $3.25
Answer:
2.99
Step-by-step explanation:
Take the total cost and divide by the number of cards
71.76/24 = 2.99
The cost per car is 2.99
Answer:
b. $2.99.
Step-by-step explanation:
To get the price per car, you get the total price divided by the total number of cars.
That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!
Hope this helps!
The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid Als
y the volume of pyramid B. If the helght of pyramid B increases to twice that of pyramid A, the
new volume of pyramid B is
the volume of pyramid A.
Answer:
a. The volume of Pyramid A is double that of Pyramid B.
b. The new volume of B is equal to the volume of A.
Step-by-step explanation:
The base of pyramid A is a rectangle with length 10 meters and width 20 meters.
The base of pyramid B is a square of side length 10 meter.
Both pyramids have the same height, h.
The volume of a pyramid is given as:
V = lwh / 3
where l = length
w = width
h = height
The volume of Pyramid A is:
V = (10 * 20 * h) / 3 = 66.7h cubic metres
The volume of Pyramid B is:
V = (10 * 10 * h) / 3 = 33.3h cubic metres
By comparing their values, the volume of Pyramid A is double that of Pyramid B.
If the height of B increases to 2h, its new volume is:
V = (10 * 10 * 2h) / 3 = 66.7h cubic metres
The new volume of B is equal to the volume of A.
Find the third term in a geometric sequence if a = 8 and r = -1. Use the formula a(subscript n) = arⁿ⁻¹
Answer:
[tex]a_{3} = 8[/tex]
Step-by-step explanation:
=> [tex]a_{n} = ar^{n-1[/tex]
Where n = 3, a = 8 and r = -1
=> [tex]a_{3} = (8)(-1)^{3-1}[/tex]
=> [tex]a_{3} = (8)(1)[/tex]
=> [tex]a_{3} = 8[/tex]
Determine whether the lines L1:x=25+7t,y=17+6t,z=t and L2:x=−12+8ty=−17+8tz=−11+4t intersect, are skew, or are parallel. If they intersect, determine
Answer: The lines are skew.
Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:
1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:
[tex]\frac{7}{8} \neq \frac{6}{8} \neq \frac{1}{4}[/tex]
Since they are not equal, L1 and L2 are not parallel.
2) If the lines intersect, when you equal the equations the variable is a valid statement:
25 + 7t = - 12 + 8t (1)
17 + 6t = - 17 + 8t (2)
t = - 11 + 4t (3)
Using (3) to solve the system:
t - 4t = - 11
3t = 11
t = [tex]\frac{11}{3}[/tex]
Substituing t in (1):
25 + 7(11/3) = -12 + 8(11/3)
25 + 77/3 = - 12 + 88/3
[tex]\frac{152}{3} = \frac{52}{3}[/tex]
Which is not true, so, the lines does NOT intersect.
As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.
What is 62 in expanded form?
A. 2 x 2 x 2 x 2 x 2 x 2
B. 6 x 6
C. 12
D. 36
Answer:
I think so you meant to write 62 as 6^2
If this is the question , then the answer is 6 x 6
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
Answer:
B. 6 × 6
Step-by-step explanation:
6²
The square of a number means that the number is multiplied by itself.
6 × 6 (expanded form)
Suppose you draw a single sample of size 64 from a large population and measure its sample proportion. What is the margin of error for 95% confidence?
(a) 5% (b) 6.25% (c) 12.5% (d) 95%
Answer:
(b) 6.25%
Step-by-step explanation:
Margin of error is the chances of percentage deviation that may differ from original population data. The margin of error for 95% confidence interval can be 6.25%. To find this we divide population standard deviation with square root of sample size. The margin of error is the estimate of the deviation from actual and real value of population.
Skylar has 4 times as many books as Karen. If Skylar has 164 books, how many books does Karen have?
Answer:
41
Step-by-step explanation:
If Skylar has 4 times as many books as Karen, that means that you have to do a division problem to figure out how books Karen has. Because Skylar has 4 times as many books, and she has 164 books, the division problem is 164÷4=41 books.
The number of books Karen has will be 41.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Let,
Skylar has x number of books
Karen has y number of books = 164
Given condition;
y=4x
164=4x
x=41 books
Hence Karen has 41 books.
To learn more about the simplification, refer to:
https://brainly.com/question/23509407
#SPJ2
Which shapes have the same volume as the given rectangular prism?
helpppppppppp give bralienst
Answer:
1
Hope that helps.
Answer:
1
Step-by-step explanation:
16/16=1
Hope this helps, if you have any questions, feel free to ask
Have a good day! :)
Which of the following lists of ordered pairs is a function?
Α. (Ο, 2), (2, 3), (ο, - 2), (4, 1)
Β. (1, 2), (1,2), 2), (3, 4)
C. 1, 5). 2, 1, 4, 9), το, 5)
D. (2, 4), (0, 2), (2, -4), (5, 3)
Answer:
the answer will be D
Step-by-step explanation:
V’s Warehouse has a market value of $880,000. The property in V’s area is assessed at 35% of the market value. The tax rate is $58.90 per $1,000 of assessed value. What is V’s property tax?
Answer:
$18,141.20
Step-by-step explanation:
The assessed value is $880,000 × 0.35.
The tax will be ...
(58.90/1000) × (0.35 × $880,000) = $18,141.20
Find the equation of a line perpendicular to 4x+2y=3 that contains the point (1,5)
Answer:
x -2y = -9
Step-by-step explanation:
We can start by swapping the coefficients of x and y, then negating one of them. We can finish by evaluating the expression at the given point to find the constant.
2x -4y = constant
2(1) -4(5) = -18 = constant
So, an equation could be ...
2x -4y = -18
We notice that all of the coefficients of this equation are divisible by 2, so we can remove a factor of 2 from the equation:
x -2y = -9
–735 = 15(m + 929) m = _______
Answer:
-978
Step-by-step explanation:
1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935
2.) Subtract 13,935 on both sides, to move that value to the left side, to further isolate the variable m.
-735-13935=15m + 13935 - 13935
3.)-Simplify/Combine Like Terms
-14,670=15m
4.) Divide both sides by 15 to isolate and solve for m
-14,670/15=15m/15
5.) Simplify
-978=m
6.) Rearrange so m is on left side and value is on right side
m=-978
Which of the following is false? Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation measures the strength of linear association between two numerical variables.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
If the correlation coefficient is 1, then the slope must be 1 as well.
The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.
Correlation coefficient and the slope both quantify the direction and strength of the relationship between two numeric variables. When the correlation (r) is negative, the regression slope (b) will be negative. When the correlation is positive, the regression slope will be positive.If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them.
So, the false statement is:
If the correlation coefficient is 1, then the slope must be 1 as well.
Learn more:https://brainly.com/question/16557696