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The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of nine hours per day. The mowing and raking typically takes six hours and an average of thirty-six bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves?
The average time it takes to fill one bag of leaves is approximately 0.17 hours.
Explanation:To find the average time to fill one bag of leaves, we use the formula
Average Time=Total Time÷Total Bags. In this scenario, the total time spent is the average workday hours, which is 9 hours, and the total number of bags filled is 36.
So,
Average Time=9hours÷36bags=0.25 hours/bag.
Therefore, the average time it takes to fill one bag of leaves is 0.25 hours or 15 minutes. This means, on average, it takes 15 minutes to fill each bag of leaves.
In summary, the staff at Larry's Lawns spends 9 hours a day on lawn-related tasks, with mowing and raking taking 6 hours. Since they fill an average of 36 bags of leaves in that time, each bag takes approximately 0.25 hours or 15 minutes to fill, assuming a constant rate of filling.
To find the average time it takes to fill one bag of leaves at Larry's Lawns, divide the total time spent filling bags by the number of bags filled. Time per bag = 1/6 hours per bag.
Explanation:To find the average time it takes to fill one bag of leaves, we need to divide the total amount of time spent filling bags by the number of bags filled. In this case, the staff at Larry's Lawns spend 6 hours mowing and raking and fill 36 bags of leaves. So to find the average time per bag, we divide 6 hours by 36 bags:
Time per bag = Total time / Number of bags = 6 hours / 36 bags
Since we want the average time per bag, we can simplify the fraction:
Time per bag = 1/6 hours per bag.
what are the domain and range of the function f(x) = 4(3 square root 81)^x?{x| x is a real number}; {y| y > 0}{x| x > 4}; {y| y > 0}{x| x is a real number}; {y| y > 4}{x| x > 4}; {y| y > 4}
we are given
[tex]f(x)=4(3\sqrt{81} )^x[/tex]
Domain:
we know that domain is all possible values of x for which any function is defined
Here , since, x is only exponent
so, we can take any values of x
it will be defined for all values of x
so, domain is all real numbers
{x | x is a real number}
Range:
we know that
range is all possible values of f(x) or y
Since, there is no negative sign here
so, f(x) will always be positive and greater than 0
so, range is y>0
Answer: {x| x is a real number}; {y| y>0}
Step-by-step explanation:
The function y = 3.75 + 2.50(x - 3) can be used to determine the cost in dollars for a uber ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles? PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER.
Multiple choices:
A. $3.75 per mile
B. $6.25 per mile
C. $4.75 per mile
D. $2.50 per mile
The measure of is 126. What is the measure of ABC, the tangent-chord angle?
A. 126
B. 66
C. 63
D. 152
Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC.
By the theorem, the measure of angle is half of the intercepted arc which is 126.
Then, (1/2) · 126 = 63;
The correct answer is C. 63;
Answer:63
Step-by-step explanation:
Subtract. (5z−3)−(3z−8) Enter your answer, in simplified form, in the box.
y=f (x)=-4^x solve for f (x) when x = 3
Answer:
-64
Step-by-step explanation:
Plato/Edmentum users -64 is correct.
What is the value of x to the nearest tenth?
x=2.1
x=3.4
x=9.6
x=13.1
The value of x is 9.6.
To find the value of x to the nearest tenth, we can use the angle bisector theorem, which states that in a triangle, an angle bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Given that:
[tex]\[\frac{6.3}{5.4} = \frac{11.2}{x}\][/tex]
We can solve for x by cross-multiplying:
[tex]\[6.3 \cdot x = 5.4 \cdot 11.2\][/tex]
[tex]\[6.3x = 60.48\][/tex]
Now, divide both sides by 6.3 to isolate x:
[tex]\[x = \frac{60.48}{6.3}\][/tex]
[tex]\[x \approx 9.6\][/tex]
So, the value of x to the nearest tenth is 9.6. Therefore, the correct option is x = 9.6.
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 121212 inches. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many inches of ribbon will Peter need to make the "X"?
Calculate each mountain path grade to the nearest percent. Path A for every 31 meters of horizontal distance, the vertical change is 11 meters Path B for every 4.25 meters of horizontal distance, the vertical change is 3 meters?
The grades of Path A and Path B are calculated by dividing the vertical change by the horizontal distance. Path A has a grade of approximately 35%, while Path B has a grade of approximately 71%.
Explanation:The grade of a path or road is calculated by taking the vertical rise and dividing it by the horizontal distance, typically expressed as a percentage. In Path A, the vertical change is 11 meters and the horizontal distance is 31 meters. Therefore, the grade of Path A is calculated as follows:
(11 / 31) x 100 = 35.48%So, Path A has a grade of approximately 35% when rounded to the nearest percent.
For Path B, the vertical change is 3 meters and the horizontal distance is 4.25 meters. Therefore, the grade of Path B is calculated as follows:
(3 / 4.25) x 100 = 70.59%So, Path B has a grade of approximately 71% when rounded to the nearest percent.
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Which is the appropriate solution to the system y = 0.5x + 3.5 and y = -2/3x+1/3 shown on the graph
HELP!!! BRAINLIEST ANSWER!!!!!!
Arnold and Jeremy are working on a rocket project for math class. Their job is to find the time it takes for a model rocket to reach its maximum height and how long it will take the rocket to return to Earth if the rocket’s parachute fails to deploy.
They are making calculations for three different rocket engines and each engine has a different initial velocity. They are a bit confused on how to make the calculations. Take a look at the information that they were given and show them how to set up the equations and solve for the times requested.
1. A model rocket is launched from the ground with an initial velocity of 160 ft/sec.
a. How long will it take the rocket to reach its maximum height?
b. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched?
since u already have a answer and brainly isn't letting me ask a question i have to ask it here...... how did you figure out what the max height was for the rocket.
The rocket will reach it's maximum height in 4.98 seconds.
The rocket would return to earth in 9.96 seconds from the time it was launched.
What are Equations of Motion?Equations of motion are the equations which relate quantities like velocity, displacement, time and acceleration.
There are three equations of motion, which are:
First equation of motion, v = u + at
Second equation of motion, s = ut + [tex]\frac{1}{2}[/tex] at²
Third equation of motion, v² = u² + 2as
where, u is the initial velocity, v is the final velocity, a is the acceleration, t is the time and s is the displacement.
(a) Given that a model rocket is launched from the ground with an initial velocity of 160 feet/sec.
So, u = 160 feet/sec. = 160 × 0.305 meter/second = 48.8 meter/sec.
At maximum height velocity will be equal to zero.
So, v = 0
Here value of the acceleration will be g, acceleration of gravity = 9.8 m/s². And the sign of g will be negative because motion is in upward direction against gravity.
So, a = -g = -9.8 m/s².
From first equation of motion,
v = u + at
0 = 48.8 + (-9.8)t
9.8 t = 48.8
t = 48.8 / 9.8
t = 4.98 seconds.
(b) If the model rocket’s parachute failed to deploy and the rocket fell back to the ground, the time taken to reach the ground from it's maximum height will be the same as the time taken to reach the maximum height from the ground.
So total time taken = 4.98 + 4.98 = 9.96 seconds
Hence, the rocket will reach it's maximum height in 4.98 seconds.
The rocket would return to the Earth from the time it was launched in 9.96 seconds.
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Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is y = 3x – 1. Which could be the other equation? y = 3x + 2 3x – y = 2 3x – y = 1 3x + y = 1
The larger triangle is a dilation of the smaller triangle with a center of dilation at
(2,???1)
.
What is the scale factor of the dilation?
A. 1/3
B. 1/2
C. 2
D. 3
someone help? Which graph most likely shows a system of equations with two solutions?
Answer:
Option D is correct.
The fourth graph shows a system of equation with two solutions.
Step-by-step explanation:
From the given figure,
we can see that we have a parabola and a straight line.
Since, the line is touching the parabola at two points, one point and no point.
In the first graph, the line touches the parabola at one point.
In the second graph, the line does not touches the parabola at no point.
also,In the third graph,the line touches the parabola at one point and
In fourth graph, the lines touches the parabola at two points.
For the system of equations :
For one solution, the two equations will touch at one point.For Two solution, the two equation will touch at two point.For no solution, the two equation will not touch at no point.Therefore, the graph which is most likely shows a system of equation with two solutions is: In fourth graph
Answer:
Two solution to a system of equation means when we look at the graph of the function the graph of the two equations must intersect at exactly two points.
The graph satisfying such condition is attached to the answer.
in this graph the curve that is downward parabola and a line intersect at exactly two points and hence result in two solutions.
The volume of a rectangular prism is 2x3+9x2-8x-36 with height x + 2. Using synthetic division, what is the area of the base?
we know that
The volume of a rectangular prism as
[tex]V=A*h[/tex]
where
V is volume
A is area
H is height
now, we are given
[tex]V=2x^3+9x^2-8x-36[/tex]
[tex]h=x+2[/tex]
now, we can find A
[tex]V=A*h[/tex]
[tex]A=\frac{V}{h}[/tex]
now, we can plug it
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}[/tex]
now, we can synthetic division method
so, we can write it as
[tex]A=\frac{2x^3+9x^2-8x-36}{x+2}=(2x^2+5x-18)[/tex]
so, the area of base is
[tex]=(2x^2+5x-18)[/tex].............Answer
Select the correct product.
(2x + 9)(x + 1)
2x2 + 11x + 9
3x2 + 11x + 9
2x2 - 7x + 9
2x2 + 11x + 10
Final answer:
To find the product of (2x + 9) and (x + 1), we use the distributive property and combine like terms, resulting in 2x² + 11x + 9.
Explanation:
The student is asking for the correct product when multiplying the binomials (2x + 9) and (x + 1). This is a math problem involving algebraic multiplication.
To find the product, we apply the distributive property (also known as FOIL method in binomials):
Multiply 2x by x to get 2x².Multiply 2x by 1 to get 2x.Multiply 9 by x to get 9x.Multiply 9 by 1 to get 9.Combine the terms to get the final product: 2x² + 2x + 9x + 9, which simplifies to 2x² + 11x + 9.
The correct product of (2x + 9)(x + 1) is 2x² + 11x + 9.
It takes 40 ink cartridges and 200 pages to print a book, and it takes 30 ink cartridges and 80 pages to print a magazine.
Sarah wants to print books and magazines with at most 300 ink cartridges and 1200 pages. Let B denote the number of books she prints and M the number of magazines she prints.
Write an inequality that represents the condition based on the number of ink cartridges.
Write an inequality that represents the condition based on the number of pages.
Answer:
40B+30M≤300
200B+80M≤1200
Step-by-step explanation:
How to find side of triangle if two sides and one angle is known?
What is the value of h when the function is converted to vertex form?
Note: Vertex form is g(x)=a(x−h)2+k .
g(x)=x2−6x+14
Answer: The value of 'h' is 3.
Step-by-step explanation: Given that the vertex form of a function is given by
[tex]g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of 'h' when the following function is converted to the vertex form.
[tex]g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (ii), we have
[tex]g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.[/tex]
Comparing it with the vertex form (i), we get
[tex]h=3.[/tex]
Thus, the value of 'h' is 3.
The value of h in the vertex form is -3.
How to find the value of h?
in the vertex form:
g(x)=a(x−h)^2 + k
h is the x-value of the vertex.
Remember that for the general quadratic equation:
y = a*x^2 + b*x + c
The vertex is at:
h = -b/2a
So in our equation:
g(x) = x^2 - 6x + 14
We will have:
h = -(-6)/2*1 = 3
h = 3
That is the value of h.
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A student's saving account has a balance of $4900 on September 1. Each month the balance declines by $350. What is the slope
Answer:
The slope is [tex]-\frac{350}{month}\[/tex]
Step-by-step explanation:
This saving account is declining a fixed amount every month, this means that the function that represents this decline is linear.
The other thing we know is that originally (september 1), the account has a balance of $4900, and this is the intercept.
Therefore, for a linear function depending of the variable "x", we can write that
[tex]f(x)= (-\frac{350}{month}x+4900)\[/tex]
where the units were factored. Then the slope is
[tex]-\frac{350}{month}\[/tex]
The histogram shows the number of hours volunteers worked one week.
What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?
Enter your answer in the box.
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What is the name of a ray that divides an angle into two equal angles?
Write 7.4 as a mixed number and as an improper fraction. Do not try to simplify your answers.
what are two numbers that when multiplied equal 54, and also when added equals -15
I need help with this
What is the x- intercept of the line with the equation 4x+2y=12?
I dont know on this one, its complicated
PLEASE HELP
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Equivalent expressions are expressions with the same value.
The values of the variables are:
[tex]\mathbf{a = 1}[/tex] [tex]\mathbf{b = 9}[/tex] [tex]\mathbf{c = -2}[/tex] [tex]\mathbf{d = 4}[/tex]
The expression is given as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49}}[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x^2 + 9x - 7x - 21}{-2x^2 +4x -6x + 12} \cdot \frac{2x^2 + 14x + 9x + 63}{6x^2 + 21x - 14x - 49 } }[/tex]
Factorize
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x(x + 3) - 7(x + 3)}{-2x(x -2) -6(x - 2)} \cdot \frac{2x(x + 7) + 9(x + 7)}{3x(2x + 7) - 7(2x - 7) } }[/tex]
Factor out the terms
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(3x - 7) (x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{(3x - 7) (2x - 7) } }[/tex]
Cancel out 3x - 7
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Factor out -2
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{-2(x +3)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Cancel out x + 3
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{1}{-2(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) }}[/tex]
Rewrite as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x + 9)(x + 7)}{ -2(x - 2)(2x - 7) } }[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{2x^2 + 25x + 63}{ -4x^2 + 22x - 28}}[/tex]
Factorize again
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x+ 7)(x + 9)}{(2x + 7)(-2x + 4)}}[/tex]
Cancel out common factors
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{x + 9}{-2x + 4}}[/tex]
From the question, we have:
[tex]\mathbf{\frac{ax + b}{cx + d}}[/tex]
So, we have:
[tex]\mathbf{\frac{ax + b}{cx + d} = \frac{x + 9}{-2x + 4}}[/tex]
By comparison, we have:
[tex]\mathbf{a = 1}[/tex]
[tex]\mathbf{b = 9}[/tex]
[tex]\mathbf{c = -2}[/tex]
[tex]\mathbf{d = 4}[/tex]
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Which statement is NOT always true?
A. The sum of two rational numbers is rational.
B. The product of two irrational numbers is rational.
C. The sum of a rational number and an irrational number is irrational.
D. The product of a nonzero rational number and an irrational number is irrational.
Statement B is the one that is NOT always true.
Explanation of which statement is not always true among given mathematical statements.
To determine which statement is not always true among the given options, let's analyze each one:
A. The sum of two rational numbers is rational - Always TrueB. The product of two irrational numbers is rational - Not Always True. For example, √2 multiplied by √2 equals 2, which is rational.C. The sum of a rational number and an irrational number is irrational - Always TrueD. The product of a nonzero rational number and an irrational number is irrational - Not Always True. For example, 1 (rational) multiplied by √2 (irrational) equals √2 (irrational).Based on the analysis,
Statement B is the one that is NOT always true.
What is the 7th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500?
Answer: The correct option is (C) 62500.
Step-by-step explanation: We are given to find the 7-th term of the following geometric sequence :
4, −20, 100, . . .
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
For the given geometric sequence, we have
first term, a = 4
and common ratio r is given by
[tex]r=\dfrac{-20}{4}=\dfrac{100}{-20}=~~.~~.~~.~~=-5.[/tex]
Therefore, the 7-th term of the given geometric sequence is
[tex]a_7=ar^{7-1}=4\times(-5)^6=4\times 15625=62500.[/tex]
Thus, the required 7-th term is 62500.
Option (C) is CORRECT.