It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs.
Work done by Bill, Bob, and Barry collectively take the working efficiency in a defined time interval.
Barry's work in 3 hours:
[tex]\(3 \times \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \text{ sign}\)[/tex]
Bob's work in 3.5 hours:
[tex]\(3.5 \times \frac{1}{4} = \frac{7}{8} \text{ sign}\)[/tex]
Bill's work for the same time until Bob leaves (3.5 hours):
[tex]\(3.5 \times \frac{1}{8} = \frac{3.5}{8} = \frac{7}{16} \text{ sign}\)[/tex]
Total work done by all three in the first 3.5 hours:
[tex]\[ = \frac{1}{2} + \frac{7}{8} + \frac{7}{16}\\= \frac{8}{16} + \frac{14}{16} + \frac{7}{16} \\= \frac{29}{16} \text{ signs} \][/tex]
Remaining work to be done:
[tex]\[ = 2 - \frac{29}{16} \\= \frac{32}{16} - \frac{29}{16} = \frac{3}{16} \text{ signs} \][/tex]
Time for Bill to complete remaining work:
Bill’s rate: [tex]\( \frac{1}{8} \text{ signs per hour}\)[/tex]
Time to paint [tex]\( \frac{3}{16} \text{ signs}\):[/tex]
[tex]\[ =\frac{\frac{3}{16}}{\frac{1}{8}} \\= \frac{3}{16} \times 8 = \frac{24}{16} = 1.5 \text{ hours} \][/tex]
Thus, It will indeed take Bill 1.5 hours to finish the remaining [tex]\( \frac{3}{16} \)[/tex] signs. This confirms that the correct answer is 1.5 hours.
A box has dimensions of 17 inches long 1.3 feet wide and 8 inches high what is the volume of the box the formula of the volumes is v=l•w•h
The length of a rectangle is twice its width. if the area of the rectangle is 162 m2 , find its perimeter.
The width of the rectangle is 9m and the length is 18m. The perimeter of the rectangle is 54m.
Explanation:Let's assume the width of the rectangle as 'w'. According to the given information, the length would be twice the width, so the length can be represented as '2w'.
The formula for the area of a rectangle is length multiplied by width, which can be written as 'A = lw', where 'A' is the area. By substituting the given area value of 162m2, the equation becomes '162 = 2w * w'.
Solving this equation, we get 'w = 9m' which represents the width. The length can be found by doubling the width, so the length is '2 * 9m = 18m'.
The perimeter of a rectangle can be calculated using the formula 'P = 2(l + w)', where 'P' is the perimeter, 'l' is the length, and 'w' is the width. Plugging in the values, the perimeter of the rectangle is 'P = 2(18m + 9m) = 54m'.
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Factor polynomial 2x^2-11x+15
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▹ Answer
(2x - 5) * (x - 3)
▹ Step-by-Step Explanation
2x² - 11x + 15
Rewrite:
2x² - 5x - 6x + 15
Factor:
x(2x - 5) - 6x + 15
x(2x - 5) - 3(2x - 5)
Factor:
(2x - 5) * (x - 3)
Hope this helps!
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Chad bought 8 pounds of strawberries for $25.25. What is the cost, c, of 1 pound of strawberries?
10 more than the quotient of a number and 8 is at least 12
Can you write a linear inequality whose solution contains only points with positive x-values and y-values? why or why not?
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values.
Explanation:A linear inequality is a mathematical statement that expresses a relationship between two linear expressions using inequality symbols (>, <, ≥, or ≤). It describes a region of values that satisfy the inequality, often represented on a coordinate plane as a shaded area.
Yes, a linear inequality can be written whose solution contains only points with positive x-values and y-values. One example of such an inequality is y > 0. This inequality represents all the points above the x-axis in the coordinate plane, where both x-values and y-values are positive.
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Which expression means 7 more than a number?
A.
d × 7
B.
d + 7
C.
d ÷ 7
D.
d – 7
***PLEASE HELP*** ***50 POINTS***
Construct a system of two linear equations where (−2, 3) is a solution to the first equation but not to the second equation, and where (5, −2) is the solution to your system.
You need to write the equations of your system and graph them on the same graph.
Explain how your graph shows that your system satisfies the 2 required conditions.
see attached picture:
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
(A.) {(-8, -12)}
(B.) {(3, 2)}
(C.) {(-4, 6)}
Final answer:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 is found by eliminating y, yielding x=3 and y=2, which is option B, (3, 2).
Explanation:
The solution to the system of equations x + 2y = 7 and x - 2y = -1 can be found by adding or subtracting the two equations to eliminate one of the variables. By adding the two equations, we eliminate y and get 2x = 6, which results in x = 3. Substituting x = 3 back into either of the original equations yields y = 2. Therefore, the solution to the system is (3, 2), which corresponds to option B.
What is m∠D ?
Enter your answer in the box. __°
Answer
Find out the m∠D .
To proof
In Δ ABE
∠EAB + ∠ABE + ∠AEB = 180 °
(By using the angle sum property of a triangle.)
As given and shown in the diagram
∠EAB = 14° , ∠ABE = 45 °
Put in the above equation
14° + 45° + ∠AEB = 180 °
∠AEB = 180 °- 59°
∠AEB = 121 °
∠AEB = ∠DEC = 121°
(by using the vertical opposite angles property)
Now in ΔCED
∠DEC + ∠EDC + ∠ECD = 180 °
(Angle sum property of a triangle)
(as given ∠DEC = 121° ,∠ECD = 27° shown in the diagram )
∠EDC = 180 ° - 27 ° - 121 °
∠EDC = 32°
therefore
∠ D = 32 °
Hence proved
Evaluate the expression below when x = -1.
2x2 − 5
x + 9
-7
8
-3
8
-1
8
-1
Answer:
-3/8
Step-by-step explanation:
plato
The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies. which equation describes the number of people that went to the movies?
The equation that describes the number of people that went to the movies could be 5x = 105
What is a solution to a system of equations?For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs,
So solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)
Given; The cost of a movie ticket is $5. it costs a group of friends $105 to go to the movies.
Each ticket cost is $5,
The tickets were $105.
So, multiplied 5 x 105 = 525.
Let x be the number of people that went to the movies.
So, 105 / 5 = x = 21
OR
5x = 105
Therefore, the equation that describes the number of people that went to the movies could be 5x = 105
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The product of some negative number and 3 less than twice that number is 209. find the number
a model rocket is 3 inches long. the real rocket is 120 feet long. what is the unit rate that describes the relationship of the real rocket to the model rocket? a.360 ft/in. b.360 in./ft c.40 in./ft d.40 ft/in.
Assume that the set s has 8 elements. how many subsets of s have at most 2 elements?
six times the reciprocal of a number equals 2 times the reciprocal of 6. find the number.
Find an equation of the line that satisfies the given conditions. through (−5, −13); perpendicular to the line passing through (−2, −1) and (2, −3)
Find the equation in standard form of the line with slope − 4 7 -47 that passes through the point ( 2 , 5 ) (2,5)
I need Help with 9??
A parabola has vertex (2, 3) and contains the point (0, 0). find an equation that represents this parabola.
The required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
f(x) = ax² + b x + c.
The parabola equation into the vertex form:
(y-k) = a(x-h)²
Where (h,k) are the x and y-coordinates of the vertex.
The parabola has vertex (2, 3) which is given in the question
Here h = 2,and k = 3
Substitute the values of h = 2 and k = 3 in the above equation
y - 3 = a(x - 2)²
y = a(x - 2)² + 3
If the parabola contains the point (0, 0)
Substitute the point (0, 0) in the above equation
0 = a((-2)² + 3
4a = -3
a = -3/4
Thus, the equation becomes y = (-3/4)(x - 2)² + 3
Hence, the required equation is y = (-3/4)(x - 2)² + 3 that represents given parabola.
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Sam's bedroom has a perimeter of 46 feet. If the length of the bedroom is 11 feet, what is the width of the bedroom?
How many 3 digit positive integers are odd and do not contain the digit 5?
2(x+3) + 6 = 3x - 9 written in word form? HELP!!!
Two angles are supplementary. one angle measures 12 degrees less than 5 times the other. find the measure of each angle
The measures of the two supplementary angles are 32 degrees and 148 degrees, respectively.
Explanation:The question is about finding the measures of two supplementary angles given the relationship between them. Supplementary angles are two angles whose measures add up to 180 degrees. If we let x be the measure of the first angle, then the measure of the second angle is 5x - 12 degrees, according to the problem statement.
Since the angles are supplementary, we can set up the following equation: x + (5x - 12) = 180. This simplifies to 6x - 12 = 180. Solving for x gives us x = 32, so the first angle measures 32 degrees.
Substitute x = 32 into the equation for the second angle gives us: 5x - 12 = 5(32) - 12 = 148 degrees. Therefore, the two angles measure 32 degrees and 148 degrees, respectively.
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Which of the following does not have a measure of 40 degrees?
∠AOX
∠DOA
∠COA
Answer:
the correct answer is C) COA
Which equation is related to the equation shown? x + 3 = 12
a. x = 12 + 3
b. x = 12 ÷ 3
c. x = 12 − 3
d. x = 12 • 3 open study?
Morgan needs gas for her jeep, which gets 26 miles per gallon for gas mileage. When she stops at the gas station, she already has 10 gallons of gas in her tank. She buys more gas for $1.60 per gallon. If Morgan spends $21 on gas, what is the total distance she could travel? Round, if necessary, to the nearest tenth.
Answer:
The answer 601.3 miles.
Step-by-step explanation:
Write an inequality for the given statement: The sum of y and 20 is more than 50.
Hey!
Hope this helps...
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We know that we will be using the greater than symbol...
By know this we can assume that the start of the problem looks like this:
> 50
This is because the answer of said question MUST be greater than 50...
We also know that the question states "the sum of y and 20"
So... that will look like this:
y + 20
We also know that it says "the sum of y and 20 is more than 50", so we set that up like this:
y + 20 > 50
So the inequality for this is: y + 20 > 50
HIJK is a rectangle. Find the value of x and the length of each diagonal. HJ=x and IK= 2x-7
The value of x will be equal to 7 for the two diagonals HJ and IK.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position. A geometer is a mathematician who works in the field of geometry.
Given that the length of each diagonal is HJ=x and IK= 2x-7
HJ and IK are diagonals.
By definition of the rectangle, the diagonals are congruent or equal.
HJ=IK
x=2x-7
-x+x=2x-x-7
0=x-7
0+7=x-7+7
7=x and 2x-7=2 (7)-7=14-7=7
For the two diagonals, the value of x is 7.
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A right triangle has exterior angles at each of its acute angles with measures in te ratio 13:14. find the measures o the two acute angles of the right triangle.