A furniture store marks up the price of a desk lamp by 80% from $35. What is the new retail price?

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Ryan was traveling by car at an average speed of 40.3 miles per hour. He will cover 322.4 miles in _____ hours.

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If you divide distance(322.4) by the speed (40.3) you end up with 8. The amount of hours you're traveling the given distance. You can check it by multiplying 40.3 by 8 to ensure that 322.4 miles is in fact how far you will go in that time.

Answer:

i think 8

Step-by-step explanation:

An asprin tablet in a shape of a right circular cylinder has the height of 2/5 cm and the raidus of 1/2cm. the manufacturer also wishes to market the asprin in capsule form. The capsule is to be 5/3cm in total length, in the shape of a right cylinder with hemispheres attached to both ends . find a function that represents the volume of the capsule. fund the radius of the capsule so that it is the same volume of the tablet.

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The function that represents the volume of the capsule will be V = πr²h + (4/3)πR³. And the radius will be 19/30 cm.

What is the volume?

Volume is a measurement of three-dimensional space that is utilized.

An aspirin tablet in a state of a right round chamber has a level of 2/5 cm and a radius of 1/2cm. the producer additionally wishes to advertise the aspirin in container structure. The case is to be 5/3cm in complete length, looking like a right chamber with halves of the globe connected to the two finishes.

The radius of the hemisphere is calculated as,

R = [(5/3) - (2/5)] / 2

R = 19 / 30 cm

The function that represents the volume of the capsule is given as,

V = πr²h + 2[(4/3)πR³ / 2 + (4/3)πR³ / 2]

V = πr²h + (4/3)πR³

V = π(1/2)²(2/5) + (4/3)π(19/30)³

V = 0.1 π + 0.3387 π

V = 1.378 cm³

The function that represents the volume of the capsule will be V = πr²h + (4/3)πR³. And the radius will be 19/30 cm.

More about the volume link is given below.

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Volume of the tablet is height times pi r squared = .4cm x pi x .5^2 = pi cm^3So, the tablet has a volume of pi cubic centimeters (cc).We want the capsule to have the same volume. The two hemispherical ends put together make one sphere. The volume of a sphere is 4/3 pi r^3. And the cylindrical part is the same formula as the first one, but we don't know what r is,height x pi x r^2.pi cc = height x pie x r^2 + 4/3 pi r^3 Here, we took the value from the original problem and made it equal to the two ends of the capsule (together were the sphere) PLUS the rest (which is a cylinder.)Now, divide everything by pi to factor it out of the equation.cc = height x r^2 + 4/3 r^3 The problem told us that the total length is 5/3 cm, this means the cylinder height + the radius times two = 5/3. (Wish I could draw you a picture) So height in the equation at the beginning of this paragraph is 5/3 - 2r.Now we have volume in cc = (5/3 - 2r)r^2 + 4/3 r^3 =5/3r^2 - 2r^3 + 4/3r^3simplified by combining common terms, and written in standard form,volume in cc = 2 r^3 + 5/3 r^2 = 1 = r^2 ( r - 5/3) , factoring out the r^2.this means that r^2 is the reciprocal of r - 5/3, or r^2 = 1/(r - 5/3), and this is a quadratic equation.r^2 - r + .6 = 0 and r^2 -r + .25 = -.6 + .25 by completing the squareor (r - .25)^2 = -.35. Solve for r: square root of r - .25 = square root of .35 or .59r = .84 cm

what is the range of the function g(x) = |x – 12| – 2? {y | y > –2} {y | y > –2} {y | y > 12} {y | y > 12}

Answers

Range = {y | y ≥ –2}

Answer:

The range of function is $R= \left \{ y|y\geq -2 \right \}$

Step-by-step explanation:

Given : Function $g(x) = |x -12| -2$

To find : What is the range of the function?

Solution :

The range is defined as the set of y values for which function is defined.

We have given function $g(x) = |x -12| -2$ in the vertex form.

The general vertex form is $y=a|x-h|+k$ where (h,k) are the vertex of the equation.

On comparing the vertex of the given function is (h,k)=(12,-2)

i.e. The y-values taken is less than -2.

So, the range would be the all y values greater than or equal to -2.

Therefore, The range of function is $R= \left \{ y|y\geq -2 \right \}$

Refer the attached figure below of the function.

Use mental math to find the value of 15/124·230/30÷230/124

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By using mental math the value of 15/124·230/30÷230/124 is 1/2.

How to get better at mental math ?

To get better at mental math or metal calculation we can start by practising doing arithmetic operations of two digit numbers.Then after we can go on increasing the digits when we're getting better at it.Thinking of the easiest way to chunks numbers also helps.

According to the given question

{(15/124)×(230/30)}/(230/124)

First the fraction (230/124) which is in the denominator we flip and multiply.

= (15/124)×(230/30)×(124/230)

Now 124 and 124 on numeration and denominator gets cancelled and same case is applicable for 230 then after we are left with 15/30 which is equal to 1/2.

Learn more about mental math here :

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Okay, the first thing to do is to make it so you're multiplying everything instead of dividing by that last fraction. To divide by a fraction, you just multiply by its reciprocal. So then, it's 15/124 x 230/30 x 124/230. After that, let's organize it into one single giant fraction since order of operations allows us to arrange division and multiplication however we want. Then it's 15x230x124 / 124x30x230. Then, you'll notice that the 230s and 124s can both be canceled out, leaving 15/30. After simplifying, your final answer is 1/2.

Graph the function and identify the domain and range.

y = –0.5x2

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Hello,

y=-0.5 x²
Domain : R (-infinty,+infinity)

Range R- (-infinity,0)

True or False: The value of r represents the reference angle when plotting a point in polar coordinates.

Answers

The answer to the statement above would be false. The value of r does not represent the reference angle when plotting a point in polar coordinates. Instead, it represents the polar distance instead of the angle. The reference angle is represented by t.

Answer:

False

Step-by-step explanation:

In cartesian coordinates, we represents a point as (x,y).

Whereas, in polar coordinates, we represent a point as $(r,\theta)$

Here,

$r=√(x^2+y^2)\n\n\theta=\tan^(-1)((y)/(x))$

The term r is the radial distance from origin and the angle Ф is the polar angle.

Therefore, the term r doesn't represent the reference angle when plotting a point in polar coordinates.

Hence, the given statement is false.

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