Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an average rate of 6.6 kilometers per hour. The equation that models the distance he runs for t hours is d=6.6t


Find the theoretical and practical domains of the equation.

Select ALL correct answers.

Question 4 options:

The practical domain is all real numbers.


The theoretical domain is all real numbers.


The theoretical domain is all real numbers greater than or equal to one and less than or equal to two.


The practical domain is all real numbers greater than or equal to one and less than or equal to two.

Answer:

a,b,d

Step-by-step explanation:

a constant rate means it is constantly/repeatedly changing the same amount over time a,b,d keeps on changing (a is by 12% each year) (B is by 3 points each decade) (D is by 2.5% each year) C on the other hand changes every six months but stops at the end of the second year. therefore the answers are A,B and D

Answer:

B

This is a 30-60-90 Triangle which means that the long side is twice the short side and the hypotenuse is Square Root 3 times bigger

Circumference of circle is 2πr

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14). How do you calculate a circle's circumference? The circle's radius is necessary to calculate the circumference: To calculate the diameter, multiply the radius by two. Divide the outcome by, or an estimate of 3.14. You have now successfully determined the circle's circumference.

Given,

Radius - r

Circumference of circle:

2πr

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the cell in g1 in a 2n=4 configuration

The below illustration represents a cell in the G1 phase with a 2n=4 configuration.

To draw a cell in the G1 phase with a 2n=4 configuration, follow these steps:

1. Begin by drawing a circular or oval shape to represent the cell.

2. Inside the cell, draw a smaller circle or oval to represent the nucleus.

3. In the nucleus, draw four chromosomes (X-shaped structures) to represent the 2n=4 configuration.

Since it is in the G1 phase, the chromosomes have not duplicated yet.

4. Label the cell as "G1" to indicate that it is in the G1 phase of the cell cycle.

This illustration represents a cell in the G1 phase with a 2n=4 configuration.

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The required points that are on the top for every rotation is,
90 clockwise                    =      A
90 counterclockwise       =     B , C
180 clockwise                   =     A , D
360 counterclockwise     =     A , D

Given that,
To determine, for each rotation, write the point or points that are the uppermost points of the rotated figure.

A quadrilateral is a four-sided shape as given in the picture in question.

Here,
For 90 clockwise,
Point A, will be on the top

For 90 counterclockwise|
The figure retraces its shape, so Point B and C be on the top,

For 180 clockwise,
Figure flip, the upper side will go down the side and the downside will go upper side
And point A and D will be on the top

360 counterclockwise

Point A and D remains on the top,

Thus, the required point that is on the top for the revolution of the figure is mentioned above.

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The 19 circles are possible within the same center and not more than 18 units.

The radius of each circle must be different if we wish to draw many circles around a single Centre point.

We can draw a circle with a radius of 18 units that is centered at (-3, 8) to make the largest circle feasible because each circle can have a maximum radius of 18 units.

We can create a circle with simply the Centre point if we assume that the radius is 0. (-3, 8).

We can continue this process, increasing the radius by 1 unit each time, until we reach a radius of 18 units. Therefore, we can draw 19 circles in total, including the circle of radius 0 units.

Therefore, the 19 circles are possible within the same center and not more than 18 units.

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The parametric equation for y in terms of the parameter t, when x = t + 1, is: y = (-1/2)t + 3/2.

What is equation?

An equation is used to represent a relationship or balance between quantities, expressing that the value of one expression is equal to the value of another.

To find the parametric equation for y in terms of the parameter t when x = t + 1, we need to determine the relationship between x and y based on the given line passing through the points (2,1) and (-2,3).

First, let's find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

where (x1, y1) = (2,1) and (x2, y2) = (-2,3).

m = (3 - 1) / (-2 - 2)

= 2 / (-4)

= -1/2

Now that we have the slope, we can express the line in point-slope form:

y - y1 = m(x - x1)

Using the point (2,1), we have:

y - 1 = (-1/2)(x - 2)

Simplifying:

y - 1 = (-1/2)x + 1

Next, let's express x in terms of the parameter t:

x = t + 1

Now, substitute the expression for x into the equation of the line:

y - 1 = (-1/2)(t + 1 - 2)

y - 1 = (-1/2)(t - 1)

y - 1 = (-1/2)t + 1/2

y = (-1/2)t + 1/2 + 1

y = (-1/2)t + 3/2

Therefore, the parametric equation for y in terms of the parameter t, when x = t + 1, is:

y = (-1/2)t + 3/2.

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The given relation is not an equivalence relation.

To show that a relation is an equivalence relation, it must satisfy three properties: reflexive, symmetric, and transitive.

Reflexive property: Every element should be related to itself. In this relation, we have (0, 0), (1, 1), and (6, 6), so the reflexive property holds.

Symmetric property: If (a, b) belongs to R, then (b, a) must also belong to R. Here, we have (0, 1), (1, 0), (1, 6), and (6, 1), which satisfy the symmetric property.

Transitive property: If (a, b) and (b, c) belong to R, then (a, c) must also belong to R. In this relation, we have (0, 1) and (1, 6), which implies (0, 6) should belong to R for the transitive property to hold. However, (0, 6) is not part of the relation R, so the transitive property is violated.

Therefore, the given relation is not an equivalence relation.

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Answer:

5

Step-by-step explanation:

25% of 20 is 5

Answer:

Ice would be the correct answer.

Answer:

if u want go to the doctor but use ice but if its to cold use a little heat not too much tho

Step-by-step explanation:

If you have injured your neck and are experiencing swelling, you should ice the area for at least 72 hours. After icing, you can use heat to help any lingering pain. Tight neck muscles and old injuries can benefit from heat only, as long as there isn’t any swelling.

Answer:

Pmt Amt     $12.50      $23.50      $64.00      $82.00

Fee             $0.25        $0.47        $1.28         $1.64

Step-by-step explanation:

The top line is the payment amount.

The bottom line is the 2% fee.

Let's do the middle columns first.

For any payment amount, the fee is 2%.

To find a percent of a number, change the percent to a decimal by moving the decimal point of the percent to places to the left, and multiply the decimal by the number.

2% as a decimal is 0.02

To find 2% of a number, multiply 0.02 by the number.

The second column has payment amount of $23.50

We need to find 2% of $23.50

2% of $23.50 = 0.02 × $23.50 = $0.47

The third column has payment amount of $64.00

We need to find 2% of $64.00

2% of $64.00 = 0.02 × $64.00 = $1.28

Now we do the first and 4th columns. Here we know the fee, and we are looking for the payment amount.

Let the amount be x.

The fee is 2% of x, so the fee is

0.02x

We set the expression equal to the actual fee and solve for x.

The first column has a fee of $0.25

0.02x = $0.25

x = $0.25/0.02

x = $12.50

The 4th column has a fee of $1.64

0.02x = $1.64

x = $1.64/0.02

x = $82

Answer:

Pmt Amt     $12.50      $23.50      $64.00      $82.00

Fee             $0.25        $0.47        $1.28         $1.64

There is a solvability constraint on this problem which is B₀ = 0.Note: The function u(r,θ) is not uniquely defined if B₀ ≠ 0.

The Laplace's equation inside a circular annulus (a < r < b) with the following boundary conditions is given as;∂u/∂r (a,θ) = f(θ),∂u/∂r (b,θ) = g(θ)

The expression for Laplace's equation inside a circular annulus is given as;∂²u/∂r² + 1/r ∂u/∂r + 1/r² ∂²u/∂θ² = 0.

The general solution of the above Laplace's equation is given as;

u(r,θ) = (A₀ + B₀ ln(r)) + ∑ [Aₙ rⁿ + Bₙ r⁻ⁿ] (n = 1,2,3,....)×[Cₙ cos(nθ) + Dₙ sin(nθ)]where, A₀, B₀, Aₙ, Bₙ, Cₙ and Dₙ are constants.

The solvability constraint on this problem is the problem of uniqueness. The function u(r,θ) has a unique solution if the constant B₀ = 0 which is the solution of the Laplace's equation inside a circular annulus (a < r < b) with the following boundary conditions.

Therefore, there is a solvability constraint on this problem which is

B₀ = 0.

Note: The function u(r,θ) is not uniquely defined if B₀ ≠ 0.

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The area between the curves, or the area bounded by the curves, y = x² + 10x and y = 2x + 9 is 58/3 square units.

To find the area between two curves, we need to determine the points of intersection and integrate the difference between the curves over the given interval.

First, let's find the points of intersection by setting the two equations equal to each other:

x² + 10x = 2x + 9

Rearranging the equation, we get:

x² + 8x - 9 = 0

Now we can solve this quadratic equation. Using the quadratic formula, we have:

x = (-8 ± √(8² - 4(-9)))/(2)

Simplifying further, we get:

x = (-8 ± √(100))/(2)

x = (-8 ± 10)/(2)

So we have two possible solutions for x:

x₁ = 1 and x₂ = -9

Now we can integrate the difference between the curves over the interval from x = -9 to x = 1. The area between the curves is given by:

Area = ∫[a,b] (f(x) - g(x)) dx

where f(x) is the upper curve and g(x) is the lower curve.

Using the given curves, we have:

f(x) = 2x + 9

g(x) = x² + 10x

Now we can integrate:

Area = ∫[-9,1] (2x + 9 - (x² + 10x)) dx

Simplifying:

Area = ∫[-9,1] (-x² - 8x + 9) dx

To find the exact value of the area, we need to evaluate this integral. Integrating term by term, we have:

Area = (-1/3)x³ - 4x² + 9x |[-9,1]

Evaluating this expression at the limits of integration:

Area = [(-1/3)(1)³ - 4(1)² + 9(1)] - [(-1/3)(-9)³ - 4(-9)² + 9(-9)]

Area = (-1/3 - 4 + 9) - (-243/3 + 324 - 81)

Area = (4/3) - (-54/3)

Area = (4 + 54)/3

Area = 58/3

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By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Bill can hit 437 golf balls in 23 hours while it takes him 17 hours to hit 323 balls using the unitary approach.

The goal of this method is to determine values in reference to a single unit. The unitary technique can be used, for instance, to determine how many kilometers a car can go on one litre of gas if it can travel 44 km on two litres of gas.

calculation

You can resolve it using the unitary technique.

because 323 golf balls were affected by the bill in 17 hours

so in an hour  = 323/17

so in a 23 hours  = (323×23)/17

=  437

so , Bill can hit 437 golf balls in 23 hours while it takes him 17 hours to hit 323 balls using the unitary approach.

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Answer:

Step-by-step explanation:

C

Answer:

C.) Rich lost 20 pounds

Step-by-step explanation:

I hope you have a good rest of your day!

Volume of a Sphere Formula:
\(\displaystyle V = \frac{4}{3} \pi r^3\)

Diameter/Radius Relationship:
\(\displaystyle r = \frac{d}{2}\)

Let us clearly sort out what information this specific problem gives us:

We can consolidate this into mathematical symbols:

Given what we know, we now need to find the volume of the sphere. With knowledge implied, found under the General Formulas and Concepts section above, we can first solve for the radius \(\displaystyle r\):

\(\displaystyle\begin{aligned}r & = \frac{d}{2} \\& = \frac{10 \ \text{in}}{2} \\& = \boxed{5 \ \text{in}} \\\end{aligned}\)

∴ the radius of the sphere is equal to 5 inches.

Now that we have our radius, we can substitute this value into our volume of a sphere formula and evaluate:

\(\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \boxed{ \frac{500}{3} \pi \ \text{in}^3 } \\\end{aligned}\)

∴ the volume of the sphere is equal to \(\boxed{ \frac{500}{3} \pi \ \text{in}^3 }\).

To estimate our answer, we can simply substitute the value of \(\displaystyle \pi\) for 3.14, as defined by the problem, and evaluate once more:

\(\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \frac{500}{3} \pi \ \text{in}^3 \\& = \frac{500}{3} (3.14) \ \text{in}^3 \\& \approx \boxed{ 523.333 \ \text{in}^3 }\end{aligned}\)

∴ the volume of the sphere is approximately equal to \(\displaystyle \boxed{ 523.333 \ \text{in}^3 }\).

∴ the best answer choice that corresponds to our gathered result is answer choice b. 523.333 cu. in.

___

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Topic: Geometry

Unit: Volume

Answer:

breadth= 18.75 inches

length= 56.25 inches

Step-by-step explanation:

if the breadth = x inches

length = 3x inches

perimeter of rectangle= 2(l+b)= 2(3x+x)= 2(4x)= 8x

we know that perimeter = 150inches

so x= 150/8= 18.75

breadth= 18.75 inches

length= 518.75x3 =6.25 inches

If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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Based on the fact that 6 consecutive integers will add up to 447, the first integer is therefore 72.

The integers have to be consecutive so you can test the options for consecutive integers that will add up to 447.

First option is 72 so the consecutive integers are:

= 72 + 73 + 74 + 75 + 76 + 77

= 447

This shows that the first integer is 72.

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A country's population in 1995 was 23 million. In 2001 it was 25 million, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

For this problem, we have the final population P, the starting population A, and the time passed t.

We still need to determine the value of the growth factor k.

This can be done using the information for the years 1995 and 2001.

In this case, A will be 23 million (the population in 1995), P will be 25 million (the population in 2001), and t will be 6 years (the number of years between 1995 and2001):

\(P=Ae^{kt}\)

\(25=23e^{k 6}\)

\(e^{6k} =\frac{25}{23}\)

\(k = \frac{ln(25) - ln(23)}{6}\)

k = 0.013897

Now, let's use this information to determine P in 2013.

A will still be 23 million, but t will be 18 years.

\(P= 23e^{0.013897*18} \\P= 23e^{0.250146} \\P=23 * 1.28421\\P=29.5368\\\)

Therefore, the population in 2013 using the exponential growth formula in 2013 will be around 30 million.

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Answer:

C,

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is B.the equation of the line

Answer:2.43

Step-by-step explanation:

Answer:

The correct option is;

An isosceles triangle

Step-by-step explanation:

The parameters given are;

Line segments XY and ZY are tangents to circle O.

ΔXYZ has points X and Z on the circle.

XY and ZY are tangents that intersect at point Y outside the circle'

Therefore, given the circle has center O, then;

OY ≅ OZ = Radius of circle with center O

∠OXY ≅ ∠OZY = 90°  (The radius line from the circle center to the tangent point is perpendicular)

OY ≅ OY (Reflexive property)

ΔOYX and ΔOYZ are right triangles (Triangle with one angle = 90°

ΔOYX ≅ ΔOYZ (Hypotenuse Leg, HL, rule of congruency)

Therefore;

XY = ZY (Corresponding Parts of Congruent Triangles are Congruent CPCTC)

Triangle XYZ is an isosceles triangle (Triangle with two equal sides).

Answer:

B. an isosceles triangle

Step-by-step explanation: