– A BOX CONTAINS 9 RED AND 2 BLUE MARBLES. IF YOU SELECT
ONE MARBLE AT RANDOM FROM THE BOX, DETERMINE THE ODDS AGAINST
SELECTING A RED MARBLE.

Answer:

108

Step-by-step explanation:

11+61=72

We use 180 and subtract it by 72 because we know that all angles in a triangle add up to 180.

180-72=108

The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

By mechanical physics we know that the function velocity is the integral of function acceleration and the function position is the integral of function velocity. Hence, we need to integrate twice to obtain the function position of the particle:

Velocity

v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt

v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁

Position

s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt  + C₁ ∫ dt

s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂

Now we find the values of the integration constants by solving the following system of linear equations:

0 = C₂

63 / 4 = C₁ + C₂

The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function position of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.

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Answer:

2

Step-by-step explanation:

Use pemdas

4a*(3-2b)

4(1/2)*(3-2(-1))

4* 1/2 = 2

2*(3-2(-1)

-2*-1 = 2

2(3-2)

3 -2 = 1

2(1) = 2

Answer:

none

Step-by-step explanation:

A. -7 <= x < 0

B. x <= -7 or x > 0

C. -7 < x <= 0

D. x < -7 or x >= 0

To create a graph to represent -7 < x < 0, draw empty circles at -7 and 0, then connect the two with a line.

The inequalities are matched with the respective graphs as shown in the attached image.

In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'

Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.

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By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

Herein we have a trigonometric equation which has to be simplified. Simplification procedure consists in applying trigonometric expressions and algebra properties to transform the function from the form f(cos 12x) to the form f(cos 6x). Now we present the solution in detail:

By applying trigonometric expressions and algebra properties, the trigonometric equation 1 - cos 12x is equivalent to the trigonometric equation 2 · sin² 6x. (Correct choice: D)

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Answer:

10 m/s

Step-by-step explanation:

Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.

x + y = 14

x - y = 6

2y = 8

y = 4

x - 4 = 6

x = 10

The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.

Answer:

Speed of fish in still water = 10 m/s

Speed of current = 4 m/s

Step-by-step explanation:

Let the speed of the fish in still water = x m\s

Let the speed of the current  = y m/s

Speed of the fish with the current = x + y

 x +y = 14 m/s ------------------(I)

Speed of the fish against current = x -y

 x - y = 6 m/s ----(II) &

Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.

     x + y = 14

     x - y =  6      {Now, add)

     2x    = 20

           x = 20/2

          x = 10

[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]

Plugin x = 10 in equation (I)

    10 + y = 14

            y = 14 - 10

           y = 4

[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]

Answer: x = -1 or x = 5/3

Step-by-step explanation:

|3x - 1| = 4

=> 3x - 1 = 4 or 3x - 1 = -4

=>x = 5/3 or x = -1

Answer:

18 miles

Step-by-step explanation:

hihihihihiuijihihihi

If the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.

Given the distance between trains be 664 miles and the speed of one train is 16 miles more than the other train.

We are required to find the speed of both the trains.

Speed is basically the distance that a thing covers in a particular time period.

Speed=Distance/Time

let the speed of first train be x miles per hour.

According to question the speed of the second train be (x+16) miles per hour.

Taking first train:

Speed =Distance/Time

x=664/4

=166

Taking second train:

Speed=Distance/Time

x+16=664/4

x+16=166

x=150

Hence if the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.

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The number of times Ken visits, given the £3.6 pool charge, and 1/3 savings per visit is 5 times.

The entry fee = £3.60

Amount saved on entry fee by having a membership card = 1/3 of the entry fee

Amount Ken spends on the membership card and the reduced entry fee = £5

Therefore;

Reduced entry fee = £3.60×(1 - 1/3) = £2.4

Amount saved per visit = £3.6 - £2.4 = £1.2

The number of visits, n, before he gets back his £5 is therefore;

Ken has to visit the swimming pool more than 4 times to get his £5 back.

Rounding to the next larger whole, therefore;

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The required steps are

2x^2 + 12x – 3 = 0.

2x2 + 12x  = 3

2(x^2+6x) = 3

2[(x+3)^2 - 9] = 3

Quadratic equations are equations that has a leading degree of 2

Given the equation below;

2x^2 + 12x – 3 = 0.

Add 3 to both sides

2x2 + 12x  = 3

Factor out 2

2(x^2+6x) = 3

Complete the square

2(x^2+6x+3^2-3^2) = 3

2[(x+3)^2 - 9] = 3

This gives the required steps to solve the equation

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Answer:

150.8 in³

Step-by-step explanation:

The volume of the 5 inch ball is

[tex]\frac{4}{3}\pi (5/2)^{3}[/tex]

The volume of the 13 inch ball is

[tex]\frac{4}{3}\pi (13/2)^{3}[/tex]

Subtracting these volumes, we get about 150.8 in³.

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³,

where r is the radius of the sphere, which is half the measure of the diameter.

Diameter of the smaller spherical ball = 5 inches

Radius = 5/2 = 2.5 inches

Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³

Volume ≈ 65.5 in.³

Diameter of the larger spherical ball = 13 inches

Radius = 13/2 = 6.5 inches

Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³

Volume of the larger spherical ball ≈ 1,150.3 in.³

The amount of space (volume) that is in the larger spherical ball than the smaller.

= 1,150.3  - 65.5

The amount of space (volume) that is in the larger spherical ball than the smaller will be 1,084.8 in.³

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Answer:

I think it would be D

Based on the fact that there is no country which had won more than 900 silver medals, set E using the roster method would be E = {  }.

Set E is meant to include the set of countries who have attained more than 900 silver medals in the Olympic games.

The highest number of silver medals attained is that of the United States which is 860 silver medals.

This means that no single country has attained more than 900 silver medals.

Set E would therefore be null. Using the roster method, the way to show set E would be:

E = {  }

In conclusion, set E is E = {  }.

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Answer: y = -1/4x + 4

Step-by-step explanation:

slope intercept form = y = mx + b

since you are given m and b, plug in the points into the formula

-1/4 goes in for m and 4 goes in for b

leaving us with:

[tex]y=-\frac{1}{4} x+4[/tex]

Answer:

[tex]y=-\frac{1}{4}x+4[/tex]

Step-by-step explanation:

Ok, so the slope-intercept form is generally expressed as: [tex]y=mx+b[/tex]

y-intercept:

Let's start by explaining why the "b" value represents the y-intercept. So I attached a graph to make this a bit more understandable, but the gist is that anywhere on the y-axis, is going to have x=0, any point on the y-axis can generally be expressed as (0, y).

This means, if we want to find the y-intercept, using the slope intercept form, we simply plug in 0 as x, since that's what x will always be equal to at the y-intercept.

We get the following equation: [tex]y=m(0) + b[/tex], and since anything times zero is just zero, we can simplify this to: [tex]y=b[/tex], meaning the y-intercept will be the "b" value in any slope-intercept form equation.

The slope:

By definition the slope is just how much the y-value changes as x increase by one. Whenever we increase the x-value by one, in the equation y=mx+b, we have one more "m", or the value is increasing by m.

Let's look at an example:

[tex]y=m(1) +b\implies m+b[/tex]

[tex]y=m(2) + b \implies m + m + b[/tex]

[tex]y = m(3) + b \implies m + m + m +b[/tex]

See how each time we increase the value "x" by one, the value of "y" increases by m. So by definition "m" is the value of the slope.

So putting this all together with your example, we get the following equation:

[tex]y=-\frac{1}{4}x+4[/tex]

Answer:

$78.60

Step-by-step explanation:

0.14x + 31 = 0.14*340 + 31 = 78.6

Answer:

100, 25, 50

Step-by-step explanation:

[tex]700: \frac{700}{700} \times 100=100 \\ \\ 175: \frac{175}{700} \times 100=25 \\ \\ 350: \frac{350}{700} \times 100=50[/tex]

Answer:

See image

Step-by-step explanation:

It cant be wrong

Answer: 184

(I am not sure if I have misunderstood the question, but the final answer I got was 184, which wasn't any one of the choices. I was wrong in understanding, please let me know and I will modify my answer)

Step-by-step explanation:

Given expression

6 (4 + 2)² - 32

Simplify values in the parenthesis

6 (6)² - 32

Simplify exponents

6 × 36 - 32

Simplify multiplication

216 - 32

Simplify subtraction

[tex]\Large\boxed{184}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

[tex]f(x)=\left( \cfrac{3x^2-2}{2x+3} \right)^3\implies \cfrac{df}{dx}=\stackrel{\textit{\LARGE chain~ ~~ rule}}{3\left( \cfrac{3x^2-2}{2x+3} \right)^2\underset{quotient~rule}{\left( \cfrac{6x(2x+3)~~ - ~~(3x^2-2)2}{(2x+3)^2} \right)}} \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{12x^2+18x-6x^2+4}{(2x+3)^2} \right) \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{6x^2+18x+4}{(2x+3)^2} \right)[/tex]

[tex]\cfrac{df}{dx}=3 \cfrac{(3x^2-2)^2}{(2x+3)^2} \left( \cfrac{2(3x^2+9x+2)}{(2x+3)^2} \right)\implies \cfrac{df}{dx}=\cfrac{6(3x^2-2)^2(3x^2+9x+2)}{(2x+3)^4}[/tex]

now, we could expand the polynomials, but there isn't much simplification, so no much point doing so.

The feasible reason for inequality y>2 is attached.

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Answer:

  ∠a = 39°

  ∠b = 129°

Step-by-step explanation:

Vertical angles are congruent. An exterior angle of a triangle is equal to the sum of the remote interior angles.

Angle y and angle 'a' are vertical angles, so congruent.

  ∠a = ∠y = 39°

The angle marked 'b' is an exterior angle to the triangle. Its remote interior angles are 'a' and the one marked 90°.

  ∠b = ∠a +90° = 39° +90°

  ∠b = 129°

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

In the given figure, angles a and y are vertically opposite angles. The measure of vertical angles is equal, therefore :-

[tex]\small\longrightarrow\sf{m<a = m<y}[/tex]

[tex]\small\longrightarrow\sf{m<a= \: 39^\circ}[/tex]

Next, angles a and 90° are the opposite interior angles to the exterior angle b. By the triangle theorem below :-

[tex]\small\longrightarrow\sf{m<b=m<a+90^\circ}[/tex]

[tex]\small\longrightarrow\sf{39^\circ+90^\circ}[/tex]

• [tex]\small\longrightarrow\sf{m<b= 129^\circ}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

m<a= [tex]\large\sf{\boxed{\sf 39^\circ}}[/tex]

m<b = [tex]\large\sf{\boxed{\sf 129^\circ}}[/tex]

Answer:

1.24

Step-by-step explanation:

because 1.24>1.215>0.365>0.095

Step-by-step explanation:

it's 2x²+8x

and I cannot understand your question

Answer:

x = - 6, x = - 1

Step-by-step explanation:

[tex]\frac{2x}{x+2}[/tex] = - [tex]\frac{6}{x+4}[/tex] ( cross- multiply )

2x(x + 4) = - 6(x + 2) ← distribute parenthesis on both sides )

2x² + 8x = - 6x - 12 ( subtract - 6x - 12 from both sides )

2x² + 14x + 12 = 0 ( divide through by 2 )

x² + 7x + 6 = 0 ← in standard form

(x + 6)(x + 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x + 1 = 0 ⇒ x = - 1

0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out. This can be obtained by using the formula for probability.

Probability is the chance of occurrence of an event.

⇒ The formula for finding probability,

Probability = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Here it is given in the question that,

Therefore by using the formula of probability we get,

⇒ Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ events\ sold\ out}{Total\ number\ of\ events}[/tex]

Probability (Junior Athletics being sold out) = 5/7

⇒ Probability (Junior Athletics being sold out) = 0.7

Hence 0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out.

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Answer:

correct

Step-by-step explanation:

dividing both quantities in a ratio by the same non zero number does indeed find an equivalent ratio.

for example

60 : 36 ( divide both parts by 6 )

= 10 : 6 ← equivalent ratio ( divide both parts by 2 )

= 5 : 3 ← equivalent ratio in simplest form

in fact dividing the original by the HCF of the 2 quantities gives the ratio in simplest form immediately , that is

60 : 36 ( divide both parts by 12 )

= 5 : 3