Joan can type 50 letters in three hours. When Jill helps, they can do the job in one hour. How long would it have taken Jill to do the job alone?

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:

Tiffany and Adele sold 11 cookies and 14 brownies.

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.

to convert feet to miles you would use a ratio of feet over miles

 so the answer would be B

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.

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.

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.

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.

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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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:

The 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;

Learn more about compound statements here:

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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).

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.

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:

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Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.

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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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The question asks for statistical analysis of aptitude test scores for firefighters, requiring an understanding of probability, statistics, normal distribution, and sample observations.

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.

Answer: A

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

Answer:

19 1/2 ft

Step-by-step explanation:

hope this helped

Answer:

-16         81       19

Step-by-step explanation:

multiply 152 by 15%

152 * 0.15 = 22.80 ( amount of discount

152 - 22.80 = 129.20 ( sale price)

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.

We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:

The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.