Answer:50 in 1.5 hours.
Step-by-step explanation:
If Joan can do 50 in 3 hours, then in 1 hour, that’s 50/3.
Jill completes the rest of the 50, so 50-(50/3) is how many letters Jill can type in an hour.
50-(50/3)=(150/3)-(50/3)=100/3 letters in an hour. If Jill can write 100 letters in 3 hours, then she can write 50 in 1.5 hours.
Simplify. 1/4 (-12+4/3)
The simplification of 1/4 (-12+4/3) first involves simplifying the operation in the parentheses which gives -10.67. Multiplying this by 1/4 we get -2.67.
Explanation:To simplify the expression 1/4 (-12+4/3), first simplify the operation in the parentheses.
-12 + 4/3 equals -12 + 1.33 (approx.), which simplifies to -10.67.
Then, multiply this result by 1/4. So, 1/4 of -10.67 equals -2.67 (approx.).
So, 1/4 (-12+4/3) simplifies to -2.67.
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Which are zeros of the following polynomial?
6x 2 - 11x - 10 = 0
A x = 6, x = 10
B x = ; x =
C x = -2; x = 5
D x = ; x =
Answer:
x = -2/3; x = 5/2.
Step-by-step explanation:
6x 2 - 11x - 10 = 0
Use the 'ac' method:
6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.
That would be -15 and +4. So we write:
6x^2 - 15x + 4x - 10 = 0 Factor by grouping:
3x(2x - 5) + 2(2x - 5) = 0
(3x + 2)(2x - 5) = 0
x = -2/3; x = 5/2.
Use what you know about compound statements to determine if "A piece of paper is an object that can be drawn on " would be considered a good definition. Explain.
A compound statement can be represented in symbolic logic as p ∧ q
The statement "A piece of paper is an object that can be drawn on" is not a compound statement
Reason:
A compound statement is a statement that consists of two simple statements combined into one statementThe given statement is "A piece of paper is an object that can be drawn on"
The given statement is made up of just one subject which is 'a piece of paper'. The statement also has just one predicate, which is 'is an object that can be drawn on'
Therefore;
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Laura sends an average of 27 text messages per month to each of f friends. Her cell phone provider charges her a flat rate of $3.50 per month and $0.04 per text message. The function t(f) gives the total number of text messages Laura sends each month to f friends, and g(t) gives the amount Laura is charged by her cell phone provider for t text messages.
find t(f) and g(t)
t(f) = 27*f
g(t) = $0.04*27*f
without the value for f (the number of friends) that is the farthest this can be solved.
A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder
A family has five children. the probability of having a girl is 1/2. what is the probability of having at least 4 girls?
The department store where you work is having a sale. Every item is to be marked down 15% What will the sale price of a $152 coat be
multiply 152 by 15%
152 * 0.15 = 22.80 ( amount of discount
152 - 22.80 = 129.20 ( sale price)
Which data set is represented by the box plot below?
A. 10, 10, 10, 14, 23, 25, 26, 28, 30, 31, 34, 34, 44, 50, 50
B. 10, 10, 11, 12, 14, 18, 18, 18, 19, 20, 22, 26, 36, 42, 50
C. 10, 14, 18, 18, 19, 22, 31, 32, 33, 34, 40, 42, 43, 46, 50
D. 10, 14, 17, 24, 27, 32, 34, 34, 37, 38, 39, 39, 40, 43, 50
How do you find absolute extrema for a function?
f(x)= (8+x)/(8-x); Interval of [4,6]
a country's people consume 7.7 billion pounds of candy per year Express this quantity in terms of pounds per person per month. note that the population of the country is 303 million
Describe the transformation of the graph from f(x) to g(x)
1) f(x)=2x+1
g(x)=2x+4
2) f(x)=x+3
g(x)=-x+1
3) f(x)=x^2
g(x)=(x-1)^2 +3
Transformations of the functions include a vertical shift, reflection and vertical shift, and a horizontal and vertical shift for three different pairs respectively. Specific (x, y) data pairs demonstrate these transformations on the graphs.
Explanation:We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:
Vertical Shift: For the functions f(x)=2x+1 and g(x)=2x+4, g(x) represents a vertical shift up by 3 units from f(x).Reflection and Vertical Shift: For f(x)=x+3 and g(x)=-x+1, g(x) is f(x) reflected across the x-axis (due to the negative sign before x) and then a vertical shift down by 2 units.Horizontal Shift and Vertical Shift: Lastly, from f(x)=x^2 to g(x)=(x-1)^2+3, the graph of g(x) is the graph of f(x) shifted to the right by 1 unit and then up by 3 units.The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.
a bicycle costs $198.99. If the sales tax is 8%, what will be the final cost of the bicycle including tax (in dollars)?
What is 2 3/4 - 1/2? A. -2 1/4 B. 1 1/4 C. 2 1/4 D. 3
A heap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters.
Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.
---------------------
The volume of a cube of edge e is given by:
[tex]V = e^3[/tex]
In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.
[tex]V = e^3[/tex]
[tex]125 = e^3[/tex]
[tex]e = \sqrt[3]{125}[/tex]
[tex]e = 5[/tex]
Now, for the rate of change, we need to apply the implicit differentiation, thus:
[tex]V = e^3[/tex]
[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]
Volume decreases at a rate of 4 cubic meters per minute, thus:
[tex]\frac{dV}{dt} = -4[/tex]
The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:
[tex]-4 = 75\frac{de}{dt}[/tex]
[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]
[tex]\frac{de}{dt} = -0.0533[/tex]
The rate of change is of -0.0533 cubic meters per minute.
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A manufacturing company has developed a cost model, C(X)= 0.15x^3 + 0.01x^2 +2x +120, where X is the number of item sold thousand. The sales price can be modeled by S(x) + 30- 0.01x. Therefore revenues are modeled by R(x)= x*S(x).
The company's profit, P(x) = R(x)-C(x) could be modeled by
1. 0.15x^3+ 0.02x^2- 28x+120
2. -0.15x^3-0.02x^2+28x-120
3. -0.15x^3+0.01x^2-2.01x-120
4. -0.15x^3+32x+120
A solid lies above the cone z = x2 + y2 and below the sphere x2 + y2 + z2 = z. write a description of the solid in terms of inequalities involving spherical coordinates
The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).
Explanation:In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).
The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.
The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.
In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).
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The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.
Explanation:To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.
Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.
As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).
Therefore, the solid can be described using the following inequalities in spherical coordinates:
0 ≤ r ≤ cos(θ) 0 ≤ θ ≤ 2π 0 ≤ ϕ ≤ π Learn more about Solid described in spherical coordinates here:
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An accepted relationship between stopping distance, d in feet, and the speed of a car, in mph, is d(v)=1.1v+0.06v^2 on dry, level concrete.
a) how many feet will it take a car traveling 45 mph to stop on dry, level concrete?
b) if an accident occurs 200 feet ahead, what is the maximum speed at which one can travel to avoid being involved in the accident?
The distance it will take a car traveling at 45 mph to stop on dry, level concrete is 171 feet. If an accident occurs 200 feet ahead, one can travel at a maximum speed of approximately 58.4 mph to avoid the accident. The answers were calculated using the given equation for stopping distance and the speed of the car.
Explanation:To address this question, we first need to make use of the equation d(v)=1.1v+0.06v²
First, let's answer part a): to find how many feet it will take a car traveling at 45 mph to stop, we simply substitute v with 45 in the equation, resulting in d = 1.1(45) + 0.06(45)² = 49.5 + 121.5 = 171 feet.
For part b), we need to solve the equation for v when d is equal to 200 feet. This is a quadratic equation (1.1v + 0.06v^2 = 200) and can be solved using the quadratic formula, or a method such as factoring or completing the square. Using the quadratic formula, we find that v ≈ 58.4 mph.
Therefore, if an accident happens 200 feet ahead, the maximum speed at which one can travel to avoid being involved in the accident is approximately 58.4 mph.
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a) At 45 mph, stopping distance is 171 feet. b) To avoid a 200-ft accident, max speed is 48.33 mph.
a) To find the stopping distance when the car is traveling at 45 mph, substitute v = 45 into the equation:
d(45) = 1.1(45) + 0.06(45)^2
= 49.5 + 121.5
= 171 feet
b) To find the maximum speed to avoid a 200 feet accident, set d(v) = 200 and solve for v:
1.1v + 0.06v^2 = 200
0.06v^2 + 1.1v - 200 = 0
Using the quadratic formula:
v = [-b ± √(b^2 - 4ac)] / (2a)
v = [-1.1 ± √(1.1^2 - 4(0.06)(-200))] / (2 * 0.06)
v ≈ [-1.1 ± √(1.21 + 48)] / 0.12
v ≈ [-1.1 ± √49.21] / 0.12
Now, solve for v:
v ≈ [-1.1 ± 7] / 0.12
This gives two solutions:
v ≈ (-1.1 + 7) / 0.12 ≈ 48.33 mph (Approx.)
v ≈ (-1.1 - 7) / 0.12 ≈ -63.33 mph (Not applicable)
Therefore, the maximum speed to avoid the accident is approximately 48.33 mph.
If 5x=3x-8, evaluate 4x+2
What is the solution of the equation f(x) = g(x) ?
A. x = -4
B. x = -2
C. x = 2
D. x = 4
tiffany and Adele sold cookies and brownies to raise money for their school. They sold a total of 25 sweets. If each cookie costs 1$ and the brownies cost a 1.50 each and they made a total of 32$, how many did each sell?
By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.
To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.
The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.
Solving this system of equations will give us the number of each type of sweet sold.
To solve the system of equations, we can use substitution or elimination. I'll use substitution:
From the first equation, we can express y as y = 25 - x.Next, we substitute y in the second equation: 1*x + 1.50*(25 - x) = 32.Simplify and solve for x: X + 37.50 - 1.50x = 32, which simplifies further to 0.50x = 5.50. Divide both sides by 0.50 to find x = 11.Now that we have the value for x, substitute it back into the equation for y: y = 25 - 11 = 14.Tiffany and Adele sold 11 cookies and 14 brownies.
round 26,891 to the nearest ten-thousands place
Candidates for employment at a city fire department are required to take a written aptitude test. scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. a random sample of nine test scores was taken.
The question asks for statistical analysis of aptitude test scores for firefighters, requiring an understanding of probability, statistics, normal distribution, and sample observations.
Explanation:The question concerns the statistical analysis of employment test scores, specifically discussing aptitude tests for a firefighter position. These tests are normally distributed with a given mean and standard deviation. Understanding this concept is an application of probability and statistics, which involves analyzing data to make inferences about a population based on sample observations. Knowledge of the normal distribution and its properties is key to answering questions about what proportion of test scores fall within certain intervals, or to calculate probabilistic outcomes such as percentile ranks or cutoff scores.
Daniel is completing a home project. He needs 13 pieces of wood, each 112 feet long, to complete the project. How much wood does Daniel need to complete his home project? 823 ft
Answer:
its a
Step-by-step explanation:
Answer:
19 1/2 ft
Step-by-step explanation:
hope this helped
can someone help me please
to convert feet to miles you would use a ratio of feet over miles
so the answer would be B
solve the system of linear equations. separate the x- and y- with a coma.
6x=-14-8y
-12x=20+8y
Answer:
-16 81 19
Step-by-step explanation:
A fisherman drops his net to a depth of -8 feet below the surface of the water. How far does he need to raise the net to bring it back to the surface of the water?
Suppose Georgette buys 400 shares of Google at $250 a share. She sells them at $350 a share. What is her capital gain?
a. 400 times $100
b. 400 times $250
c. 400 times $350
d. 400 times $600
Answer: A
Step-by-step explanation:
The shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?
What is the gcf for 84
Jack has 702 acres of land which requires 1.2 acre-feet of water to grow crops successfully. Currently it cost 12.95 per acre-foot to purchase water. How much will it cost to water all his crops
A) 9,090.90
B) 10,909.08
C) 15,540.00
D) none