A paintball court charges an initial entrance fee plus a fixed price per ball. P represents the total price (in dollars) as a function of the number of balls used n P=0.80n+5.50 What is the price for 10 balls, not including the entrance fee?

Answer:

12π inches

Step-by-step explanation:

s = rθ

s = (21) (4π/7)

s = 12π

The length of the arc will be;

⇒ Arc = 37.68 inches

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The central angle = 4π/7

And, A circle has a radius of 21 inches.

Now,

We know that in circle;

⇒ Arc = Radius × Angle

Substitute all the values, we get;

⇒ Arc = 21 × 4π/7

⇒ Arc = 3 × 4 × 3.14

⇒ Arc = 37.68 inches

Thus, The length of the arc will be;

⇒ Arc = 37.68 inches

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The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

The table of values is given as:

Gallons       Cost

1                      1.25

2                     2.50

5                     6.25

15                     18.75

20                    25.00

The inverse of the above table would have the following header

Cost     Gallons

When the inverse table is populated, we have:

Cost    Gallons

1.25          1

2.50        2

6.25         5

18.75        15

25.00      20

The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

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Answer:

Step-by-step explanation:

Given the total number of games played by the softball team = 18 games

Total games won = 15 games

Ratio of the softball team's wins to its total number of games played can be gotten by simply dividing the total games won by the total games played

Ratio = [tex]\frac{total \ teams's win}{total\ number\ of \ games\ played}[/tex]

[tex]Ratio = \frac{15}{18}[/tex]

Expressing the ratio in its lowest term

[tex]Ratio = \frac{3*5}{3*6} \\\\Ratio = \frac{5}{6}[/tex]

Hence, the ratio of the softball team's wins to its total number of games played is 5:6

Answer:

Amount of solution = 15 liter

Step-by-step explanation:

Given:

One third of solution is acid

Amount of acid = 5 Liter

Find:

Amount of solution

Computation:

Amount of solution = Amount of acid (1 / One third of solution is acid)

Amount of solution = Amount of acid (3)

Amount of solution = (5)(3)

Amount of solution = 15 liter

Answer:

(g + f) (x) = (2^x + x – 3)^1/2

Step-by-step explanation:

The following data were obtained from the question:

f(x) = 2^x/2

g(x) = √(x – 3)

(g + f) (x) =..?

(g + f) (x) can be obtained as follow:

(g + f) (x) = √(x – 3) + 2^x/2

(g + f) (x) = (x – 3)^1/2 + 2^x/2

(g + f) (x) = (x – 3)^1/2 + (2^x)^1/2

(g + f) (x) = (x – 3 + 2^x)^1/2

Rearrange

(g + f) (x) = (2^x + x – 3)^1/2

Answer:

x = -2 and y = 3

Step-by-step explanation:

In linear combination method we try one of the variables from bopth of equations by

first making the variable equal in vlaue

then either subtracting or adding the two equation as required to eliminate the variable.

_____________________________________________

7x-2y=-20   equation 1

and 9x+4y=-6   equation 2

we see that y has

has value -2 and +4

4 = 2*2

thus, if we multiply equation1 with 2 we will give value for variable y as 4y and hence y can be eliminated easily.

7x-2y=-20  

multiplying the LHS and RHS with 2

2(7x-2y)=-20 *2

=> 14x - 4y = -40   eqaution 3

now that we have got 4y

lets add equation 2 and equation 3

  9x +4y=   -6

+14x - 4y = -40

________________________________

=> 23x + 0 =  -46

x = -46/23 = -2

Thus, x = -2

substituitinng x = -2 in 7x-2y=-20

7*-2 -2y=-20

=> -14 -2y = -20

=> -2y = -20+14 = -6

=> y = -6/-2 = 3

Thus, y = 3

solution is x = -2 and y = 3

Answer:

45

Step-by-step explanation:

Given the legs of the right triangle.

Then using Pythagoras' identity

The square oh the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 36² + 27² = 1296 + 729 = 2025 ( take the square root of both sides )

h = [tex]\sqrt{2025}[/tex] = 45

Answer:

45

Step-by-step explanation:

When you are given the opposite and adjacent sides of a triangle, the easiest way to find the hypotenuse is through the Pythagorean theorem!

The formula is a^2 + b^2= c^2

Plugging in the values, your formula would now look like 36^2 + 27^2= c^2

Once you do square your values and add them up, the result would end up being 2025, but since that is squared, to find the actual value of c you have to take the square root of this number, this will result in 45.

Answer:

6/100x

Step-by-step explanation:

Answer:6/100x

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]

[tex]\bold{METHOD\ 2}[/tex]

[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]

[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome of event

Given the total amount of chocolate in a box = 39chocolates

Amount of nuts = 16

Mount of caramel = 13

Amount of solid chocolate = 10

If he randomly selects a nut chocolate and eat, the probability of selecting a nut chocolate = Amount of nuts/total chocolate in the box = 16/39

IF he selects a seconnd piece (caramel chocolate) and eat, the probability of selecting a caramel chocolate = Amount of caramel/total chocolate in the box = 13/39 = 1/3

The probability of selecting a nut chocolate followed by a caramel chocolate will be 16/39*1/3 = 16/117

Answer:

u = [tex]\sqrt{6}[/tex].

Step-by-step explanation:

This is a 45-45-90 triangle.

That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.

[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]

1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]

u = [tex]\sqrt{6}[/tex].

Hope this helps!

Answer:

53.076923

Step-by-step explanation:

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Answer:

30

Step-by-step explanation:

The unknown number is x.

Start with x.

To increase x by 130%, you need to add 130%of x to x.

x + 130% of x

The sum equals 69.

x + 130% of x = 69

x + 130% * x = 69

1x + 1.3x = 69

2.3x = 69

x = 30

Answer: The number is 30.

Answer:

The common difference is -5/4

T(n) = T(0)  - 5n/4,

where T(0) can be any number. d = -5/4

Assuming T(0) = 0, then first term

T(1) = 0 -5/4 = -5/4

Step-by-step explanation:

T(n) = T(0) + n*d

Let

S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240

S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220

S2 - S1

= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)

= (5+6+7+8 - 1 -2-3-4)d

= 4(4)d

= 16d

Since S2=220,  S1 = 240

220-240 = 16d

d = -20/16 = -5/4

Since T(0) has not been defined, it could be any number.

Answer:

i believe a=105, b=29, and c=45

Answer:

Sine angle of <ACB = 38.68°

Step-by-step explanation:

Hello,

To solve this problem, we need a good representation of the sides and the angle.

See attached document for better illustration.

Assuming it's a right angled triangle,

AC = hypothenus

AB = opposite

BC = adjacent

AC = 40

BC = 25

AB = 25

From trigonometric ratios

Sinθ = opposite/ hypothenus

Sinθ = AB / AC

Sinθ = 25 / 40

Sinθ = 0.625

θ = sin⁻¹0.625

θ = 38.68°

Sine angle of <ACB = 38.68°

Answer:

All numbers greater than 5, i.e., [tex]x>5[/tex] .

Step-by-step explanation:

The given inequality is  

[tex]80x>150+50x[/tex]

Isolate variable terms on one side to find the solution.

Subtract  50x from both sides.

[tex]80x-50x>150+50x-50x[/tex]

[tex]30x>150[/tex]

Divide both sides by 30.

[tex]\dfrac{30x}{30}>\dfrac{150}{30}[/tex]

[tex]x>5[/tex]

It means, all the numbers which are greater than 5, are the solutions of the given inequality and 5 is not included in the solution set.

Answer:

Multiply every coordinate from the old one by 0.75

Step-by-step explanation:

I just did this question so I didn't need your photo. And I got it right. Hope this helps anyone else stuck on a similar question.

The rule is to multiply the old coordinates/sides by the scale factor, if its a fraction convert it to a decimal and then multiply like I did.

Answer:

x, y ----> 3/4x, 3/4y

Step-by-step explanation:

Answer:

Number of pieces of candy in the bowl=64

Step-by-step explanation:

Let

x=number of pieces of candy in a bowl

Shirley took=1/2 of x

=1/2x

Remaining

x-1/2x

= 2x-x/2

=1/2x

Rose took half of the pieces left in the bowl=1/2 of 1/2x

=1/2*1/2x

=1/4x

Remaining

1/2x-1/4x

=2x-x/4

=1/4x

Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x

=1/2*1/4x

=1/8x

Remaining 8

1/8x=8

x=8÷1/8

=8*8/1

=64

x=64

Answer:

120 degrees

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Add all the number then subtract it with 360.

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

BHF

Step-by-step explanation:

Definition of inscribed

Answer:

8 inches

Step-by-step explanation:

3/4+(3/4*2)=3/4+6/4=9/4=2 1/4

2 1/4+6=8 1/4=8.25

Answer: 8.25 inches

Step-by-step explanation:

Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer:

Two remote interior angles.

Answer: x=10

Step-by-step explanation:

We can use the pythagorean theorem here: a^2 + b^2 = c^2, where c is the hypotenuse.

The values for c and one of the legs are already given, so we can plug them into the equation to find the length of the other leg x:

(square root of 200)^2 + x^2 = (square root of 300)^2

200 + x^2 = 300

x^2 = 100

x = 10

Answer:

Step-by-step explanation

square root  300 square - square root 200 square = x square

300 - 200 = x square

100 = x square

square root 100 = x

10= x

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

Answer:

C = 314 m

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

Using 3.14 for pi

C = 3.14 * 100

C = 314 m

Answer:

The answer is option D.

Step-by-step explanation:

Circumference of a circle = πd

Where d is the diameter

From the question

d = 100m

Circumference of the circle is

100π

= 314.2

Which is 314m to the nearest whole number

Hope this helps you

Answer:

[tex]Probability = 51\%[/tex]

Step-by-step explanation:

Given

Radius of inner circle = 5ft

Radius of outer circle = 7ft

Required

Determine the probability that the thumbtack will be placed on the inner circle

We start by calculating the area of both circles;

Inner Circle

[tex]Area = \pi r^2[/tex]

[tex]Area = 3.14 * 5^2[/tex]

[tex]Area = 3.14 * 25[/tex]

[tex]Area = 78.5[/tex]

Outer Circle

[tex]Area = \pi R^2[/tex]

[tex]Area = 3.14 * 7^2[/tex]

[tex]Area = 3.14 * 49[/tex]

[tex]Area = 153.86[/tex]

At this point, the probability can be calculated;

The probability = Area of Inner Circle / Area of Outer Circle

[tex]Probability = \frac{78.5}{153.86}[/tex]

[tex]Probability = 0.51020408163[/tex]

Convert to percentage

[tex]Probability = 0.51020408163 * 100\%[/tex]

[tex]Probability = 51.020408163\%[/tex]

Approximate

[tex]Probability = 51\%[/tex]

Answer: 4

Step-by-step explanation:

Because there are two equal angles, this is an isoceles triangle. Line JP and HP are equal. To find the variable, write the equation which would be 3x-6=x+2. X is 4.

hope this helped:)

Answer: 4 AKA D

Step-by-step explanation:

Well to start off, we must first establish that line JP and line HP are equal because of the red ticks in the corner. So once we figured that out, then 3x-6 = x+2

»Next we add 6 to both side to make 3x = x+8

»Then we subtract x from both sides to equal 2x = 8

»Then we divide both sides by 2 which equals x=4

»So the final answer would be D. 4

Hope i helped

-lvr

Answer:

15w - 10x + 30.

Step-by-step explanation:

-5(2x - 3w - 6)

= (-5 * 2x) + (-5 * -3w) + (-5 * -6)

= -10x + 15w + 30

= 15w - 10x + 30.

Hope this helps!

Answer:

Step-by-step explanation:

[tex] - 5(2x - 3w - 6)[/tex]

Multiply each term in the parentheses by -5

[tex] - 5 \times 2x - 5 \times ( - 3w) - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x - 5 \times ( - 3x) - 5 \times ( - 6)[/tex]

Multiplying two negatives equals a positive [tex]( - ) \times ( - ) = ( + )[/tex]

[tex] - 10x + 5 \times 3w - 5 \times ( - 6)[/tex]

Calculate the product

[tex] - 10x + 15w - 5 \times ( - 6)[/tex]

Multiply the numbers

[tex] - 10x + 15w + 30[/tex]

Hope this helps..

Best regards!!

Answer:

6√5

Step-by-step explanation:

We have to solve the expression [tex]\sqrt{180}[/tex]

Break 180 into its factors which are in the perfect square form.

Since, 180 = 9 × 4 × 5

                 = 3² × 2² × 5

Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]

                           = [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]

                           = 3 × 2 × √5

                           = 6√5

Therefore, solution of the given square root will be 6√5.