1. Compare two spheres. The first has a diameter of 4 inches.
The second sphere has a diameter of 428 inches.
Determine the ratio of the volume of the large sphere to the volume
of the small sphere.
Ratio =

Answer:

Step-by-step explanation:

See screenshot
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lol I'm improve my rank so brainliest would help a lot :]

I think your answer is 10 minutes and 30 seconds. . .

What I did was I took 6 and 7 and multiplied them together, then i divided 42 by 4, and got 10.5. which would give you 10 minutes and 30 seconds.

6*7=42/4=10.5 (aka 10min 30sec)

If the bottom of the ladder slides away from the wall, then x changes by 12cosθ with respect to theta and when  θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.

Here, we are given that a ladder 16 ft long rests against a vertical wall and theta is the angle between the top of the ladder and the wall.

We know that, sin of an angle = opposite / hypotenuse

Thus, sinθ = x/16

⇒ x = 16 sinθ

The rate of change of x with respect to θ will be given by dx/dθ

dx/dθ = d/dθ (12sinθ)

= 12 d/dθ (sinθ)

= 12cosθ

Now, we need to find the value of dx/dθ when θ = π/6,

= 12 cosπ/6

= 12 ([tex]\sqrt{3}[/tex]/2)

= 6[tex]\sqrt{3}[/tex]

Thus, when  θ = π/6, x changes by 6[tex]\sqrt{3}[/tex] inches with respect to θ.

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A ladder 12 feet long rests against a vertical wall. Let θ be the angle between the top of the ladder and the wall, and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to θ when θ = π/6?

Answer:

Step-by-step explanation:

[tex]\displaystyle\\(64x^\frac{2}{3})^{-\frac{1}{3}} =\\\\(4^3x^\frac{2}{3})^{-\frac{1}{3}}=\\\\ 4^{3*(-\frac{1}{3})}x^ {\frac{2}{3}*(-\frac{1}{3} )}=\\\\ 4^{-1}x^{-\frac{2}{9} }=\\\\\frac{1}{4} x^{-\frac{2}{9} }=\\\\\frac{1}{4} (\frac{1}{x^\frac{2}{9}} } )=\\\\\frac{1}{4\sqrt[9]{x^2} }[/tex]

Using angle sum property we found that ∠ x = 113°, ∠y = 67°  and ∠z = 49°

The angle sum property of triangle states that the sum of all the interior angles of a triangle is 180°.

If ΔABC is a triangle then,

m ∠A + m ∠B + m ∠C = 180°

Given from the figure in the question that 28°, 39° and x° are interior angles of a triangle, then using angle sum property:

28° + 39° + x° = 180°

⇒ 67° + x° = 180°

⇒ x° = 180° - 67° = 113°

∠x and ∠y are on the same line same point therefore their sum will be 180°

⇒ x° + y° = 180°

⇒ 113° + y° = 180°

⇒ y° = 180° - 113° = 67°

Also an exterior angle of a triangle is equal to sum of interior opposite angles.

∴ y ° = 28° + 39° = 67°

Now, 64° , y° and z° are interior angles of same triangle from the figure in the question.

∴ Using angle sum property,

64° + y° + z° = 180°

⇒ y ° + z° = 180° - 64° = 116°

⇒ y° + z° = 116°

⇒ z° = 116° - y° = 116° - 67°  = 49°

Therefore ∠x, ∠y , ∠z are 113° , 67° and 49° respectively

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Answer: 30 minutes to get to the playground

Step-by-step explanation:

Answer:

Step-by-step explanation:

1slice=280 and 6 slices so 280x6 so 0x6=0 then 80x6=6+6x4=48x10=480
then 200x6= 6x2=12x100=1200

add all 0+480+1200=1680

sry i'm not used to showing work i usually do it all in my head

The value of g(f(x)) will be 3(1-x²) and the value of g(f(2)) will be -9 for the f(x)=4-3x² and g(x)=x-1.

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Functions are broadly classified into four categories. Element-based: one-to-one function, many-to-one function, onto function, one-to-one and onto function, into function.

Here, f(x)=4-3x² and g(x)=x-1

g(f(x))=(4-3x²)-1

g(f(x))=4-3x²-1

=3-3x²

=3(1-x²)

g(f(2))=3(1-2²)

=3*-3

=-9

For f(x)=4-3x² and g(x)=x-1, the value of g(f(x)) is 3(1-x²) and the value of g(f(2)) is -9.

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Check the picture below.

[tex]\textit{internal division of a line segment using ratios} \\\\\\ Q(6,2)\qquad R(18,18)\qquad \qquad \stackrel{\textit{ratio from Q to R}}{3:1} \\\\\\ \cfrac{Q\underline{S}}{\underline{S} R} = \cfrac{3}{1}\implies \cfrac{Q}{R} = \cfrac{3}{1}\implies 1Q=3R\implies 1(6,2)=3(18,18)[/tex]

[tex](\stackrel{x}{6}~~,~~ \stackrel{y}{2})=(\stackrel{x}{54}~~,~~ \stackrel{y}{54}) \implies S=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{6 +54}}{3+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{2 +54}}{3+1} \right)} \\\\\\ S=\left( \cfrac{ 60 }{ 4 }~~,~~\cfrac{ 56}{ 4 } \right)\implies {\Large \begin{array}{llll} S=(15~~,~~14) \end{array}}[/tex]

The equation of line is y= 5/2x -7.

The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

One of the significant forms used to express a straight line algebraically is the two point form.

Written as, y- y1= m (x- x1), where m is slope.

Given:

a line passes through the point (2, -2) and parallel to 5x-2y = 4

Now, writing the given equation of line in the form of slope intercept form

5x- 2y=4

2y = 5x -4

y= 5/2x -2

Here the slope is 5/2 and the required line will also have the same slope as parallel line.

then, m=5/2

Now using y=mx +c

put y=-2 and x=2

-2 = 5/2(2) + c

-2 -5 = c

c=-7

Hence, the equation of line is y= 5/2x -7.

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Answer:

6/7

Step-by-step explanation:

2Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 1/3 is 3/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two sevenths divided by one third is six sevenths.

Answer:11

Step-by-step explanation:

The inches that are expected more in September than in February is 3.94

What is average and how to calculate it?

Average is ratio of the sum of all elements of dataset and total number of elements in the dataset. To calculate first find the sum of all elements of the dataset and then divide it by total number of elements in the dataset

The average rainfall for key west is 1.52 inches in February and 5.45 inches in month of September

To find the more inches we subtract the two We get,

[tex]5.45-1.51=3.96[/tex] inches

Hence The inches that are expected more in September than in February is 3.94 inches

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40% of 8 is 3.2

hope this helped

Answer:

Step-by-step explanation:

We all know that any number multiplied by zero equals zero. Consequently, the division by zero operation is impossible.

so, your answer is undefined

The cost of the phone  before the discounted price is $160.

Given that, Refurbished phone 45% OFF now only £88.

Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. The List price or Marked price is the price of an article as declared by the seller or the manufacturer, without any reduction in price. Selling price is the actual price at which an article is sold after any reduction or discounts in the list price.

Let the original price of the phone be x.

Now, x - 45% of x = 88

⇒ x - 45/100 × x = 88

⇒ x - 0.45x = 88

⇒ 0.55x = 88

⇒ x = 88/0.55

⇒ x = 160

Therefore, the cost of the phone  before the discounted price is $160.

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Answer:

12 weeks

Step-by-step explanation:

if 280=420

then 8=×

cross multiply

280×=420×8

280×=3360

divide both sides with the co efficient of x

280×/280=3360/280

leaving the answer to be 12

Answer:

16c - 48

Step-by-step explanation:

combine like terms : 18c - 2c - 49 + 1

then you get              16c - 48

The mark up is $30.

As stated, markup is the distinction between a product's selling price and its cost price. Retail minus Cost is markup. The term "markup" describes the discrepancy between a product's selling price and its actual cost. It is specified as a percentage over the price. In other words, the seller makes a profit when the price of the commodity or service is higher than the overall cost. A unit's gross profit, which is the sales price less the cost to create or buy it for resale, is divided by its cost to determine the markup %. The markup percentage is computed as (12 - 8) / 8 and is equal to 50% if an item costs the business $8 to produce but is sold for $12.

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Answer: 3.32 * 10^4

Step-by-step explanation:

1) Set up the equation

4.00 * 10^4 - 6.8 * 10^3

2) Set the scientific notions the same

You can do this by multiplying 10 or dividing 10 on a notion

4.00 * 10^4 - 0.68 * 10 ^4

3) Factor the scientific notions out

10^4(4.00 - 0.68)

4) Subtract

10^4(3.32)

3.32 * 10^4

The friend's explanation is not correct.

They are mixing up x and y intercepts.

To find the y intercept, plug in x = 0 to find y.

To find the x intercept, plug in y = 0 and solve for x.

The angle measures formed by the parallel lines are:

9. m∠10 = 69°

10. m∠6 = 115°

11. m∠7 = 118°

12. m∠11 = 108°

13. m∠14 = 66°

14. m∠12 = 86°

The angle measures can be determined by using the special angle relationship between the angles involved when a transversal crosses two lines that are parallel.

9. x and y are parallel lines

m∠5 = 69°

m∠10 = m∠5 [alternate interior angles theorem]

m∠10 = 69° [substitution]

10. x and y are parallel lines

m∠9 = 115°

m∠6 = m∠9 [alternate interior angles theorem]

m∠6 = 115° [substitution]

11. x and y are parallel lines

m∠12 = 118°

m∠7 = m∠12 [alternate interior angles theorem]

m∠7 = 118° [substitution]

12. x and y are parallel lines

m∠4 + m∠11 = 180 [supplementary angles]

72 + m∠11 = 180 [substitution]

m∠11 = 180 - 72

m∠11 = 108°

13. m∠4 + m∠14 = 180 [supplementary angles]

114 + m∠14 = 180 [substitution]

m∠14 = 180 - 114

m∠14 = 66°

14. m∠5 = 86° [given]

m∠12 = m∠5 [congruent angles]

m∠12 = 86°

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Applying the scale factor the actual dimension of the ramp in the blueprint Mark was looking at was found to be 0.158 inches

Scale factor represent the amount the image is increased or reduced in the map.

information from the question include

the scale on the blueprint is 1 inch: 6 feet

the ramp's length that is 11.4 inches

finding the scale factor

1 inch ⇒ 6feet = 72 inches

the scale factor is 1/72

finding the actual dimension

1 inch ⇒  72 inches

? = 11.4 inches

cross multiplying gives

72 * ? = 1 * 11.4

? = 1/72 * 11.4

? = 0.158 inches

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Answer:

Step-by-step explanation:

its 3 4

R' (-3,-4) are the resulting coordinates of the purpose R.

A rotation may be a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point. The fixed point is named the center of rotation . The quantity of rotation is called the angle of rotation and it is measured in degrees. Use a protractor to live the specified angle counterclockwise.

Using the rule for a 180° rotation to seek out the vertices of the rotated triangle.

T: (x, y) ⇒ (-x, -y)

Given points of triangle: S(1,1) , R (3, 4) and Q (7, 0).

Rotation 180° about the origin.

S (1, 1) → S' (-1,-1)

R (3,4) → R' (-3,-4)

Q (7,0) → Q' (-7,0)

Hence, the coordinate of the R is: R' (-3,-4).

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Answer:

A

Step-by-step explanation:

x² - 2x + y² + 6y - 4 = 0 ( add 4 to both sides )

x² - 2x + y² + 6y = 4

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

= x² + 2(- 1)x + 1 + y² + 2(3)y + 9 = 4 + 1 + 9

(x - 1)² + (y + 3)² = 14 ← in standard form

Answer:

$26.99

Step-by-step explanation:

17.50 original cost plus a 54.2% increase

First, divide percentage by 100 to get a decimal to divide by 54.2/100=0.542

Then multiply the new decimal by the original cost to find the amount marked up. 17.50 x 0.542= 9.485

Now add 9.485 to the original cost

17.50+9.485=26.985-> 26.99 rounded for the final answer

[tex]\huge\boxed{\sf 16}\\\\ \sf The\ two\ right\ triangles\ are\ a\ reflection\ of\ each\ other.\\ Both\ sides\ are\ equal\ in\ size. \\\\ 5x+1=4x+4\\5x-4x=4-1\\1x=3\\\\ Plug\ the\ value\ of\ x\ back\ into\ any\ of\ the\ two\ equations.\\\\ 5(3)+1 =15+1=16[/tex]

Given the volume of the box is 100 cm^3

And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.

so, the height of the box = 4 cm

so, the volume = height * area of the base

100 = 4 * area of the base

Area of the base = 100/4 = 25 cm^2

so, the side length of the base of the box =

so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm