what is 4p−5(p+6) simplified

Answer:

The angular velocity of the wheel in radians per minute is 96·π·rad/min

Where π = 22/7 then the angular velocity is [tex]301\frac{5}{7} \ rad/min[/tex]

Step-by-step explanation:

The number of revolutions completed per 3 seconds = 2.4 revolutions

∴ The number of revolutions completed per second = 2.4/3 = 0.8 = 4/5 revolutions

The angle per revolution = 2π radians

∴ Angular velocity per second = 0.8×2×π rad/sec

The angular velocity of the wheel in radian per second = 1.6·π·rad/sec

1 minute = 60 Seconds

∴The angular velocity of the wheel in radians per minute = 96·π·rad/minute

Where π = 22/7 then the angular velocity = [tex]301\frac{5}{7} \ rad/min[/tex].

Answer:96pi

Step-by-step explanation:

Answer:

840

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

If all the 300 students were surveyed, 220 would have been in favor of the photo booth.

Step-by-step explanation:

Sample size = 15

People out of 15 in favor of photo booth = 11

Percentage of people in favor of school dance = [tex]\frac{11}{15} \times 100\% = 73\frac{1}{3} \%[/tex]

We have to find if all 300 students are surveyed how many will be in favor of photo booth. Remember that, the sample data is the best estimator of the population data. So, the sample data of 15 students will be the best estimator for the entire population of 300 students.

Since, in the sample of 15 students, [tex]73\frac{1}{3} \%[/tex] were in favor of photo booth, we would expect that if all the 300 students were surveyed, the same percentage will be in favor of photo booth. So we need to calculate [tex]73\frac{1}{3} \%[/tex] of 300.

[tex]73\frac{1}{3} \% \text{ of 300}\\\\ = 73\frac{1}{3} \% \times 300\\\\ =\frac{220}{3} \% \times 300\\\\ =\frac{220}{300} \times 300\\\\ = 220[/tex]

This means if all the 300 students were surveyed, 220 would have been in favor of the photo booth as per the sample data.

Approximately 220 out of 300 students are likely to be in favor of the photo booth.

To determine how many of the 300 students are likely to be in favor of the photo booth, we can use the proportion given by the sample.

1. Calculate the proportion of students in favor from the sample:

Proportion = Number in favor / Total surveyed = 11 / 15

Proportion = 0.7333 (rounded to four decimal places)

2. Apply this proportion to the entire school population:

Expected number in favor = Proportion × Total school population

Expected number in favor = 0.7333 × 300

Expected number in favor ≈ 220

Therefore, out of 300 students, approximately 220 students are likely to be in favor of the photo booth.

Answer:

$62.17

Step-by-step explanation:

Answer:

The answer is 62.17.Because you would add 18.62 + 43.55 to get your answer of 62.17

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Answer:C

Step-by-step explanation:

Answer:

40 days

Step-by-step explanation:

A barrel contains 50 gallons of water leaked out of the barrel at a rate of 5 gallons every 4 days at this rate

5 gallons leaked out in 4 days

50 gallons will leak out in (50x4)/5 = 10 ×4 = 40 days

It will take 40 days for the 50 gallons(1 barrel) to leak out

Answer:

(a)The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+c[/tex]

(b)The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+3[/tex]

Step-by-step explanation:

We know that, the first order derivative of the position of an object is the velocity of the object.

(a)

Given that, the velocity of a particle moving in straight line is

[tex]V(t)=t^2+9[/tex]

[tex]\Rightarrow \frac{dS(t)}{dt}=t^2+9[/tex]

[tex]\Rightarrow {dS(t)}=t^2dt+9\ dt[/tex]

Integrating both sides

[tex]\int {dS(t)}=\int t^2dt+\int9\ dt[/tex]

[tex]\Rightarrow S(t)=\frac{t^3}3+9t+c[/tex]  [ c is an arbitrary]

The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+c[/tex]

(b)

Given that S= 3 at time t=0

[tex]\therefore 3=S(t)=\frac{0^3}3+9.0+c[/tex]

[tex]\Rightarrow c=3[/tex]

The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+3[/tex]

The position function is computed by integrating the given velocity function v(t) = t^2 + 9. The constant of integration C was found to be 3 using the given initial condition of s(0) = 3. Thus, the position function without any unknown constants is S(t) = (1/3)t^3 + 9t + 3.

The velocity function given for the particle moving in a straight line is v(t) = t2 + 9. This function can be used to find the position function using integral calculus.

hen t=0 the position function S(t) =  (1/3)*03 + 9*0 + C = C = 3.

Thus, using the constant of integration we found, we can write the position function without any unknown constants as S(t) = (1/3)t3 + 9t + 3.

(a) Finding the Position Function

To find an expression for the position, we integrate the velocity function. Here, the integral of the given velocity function v(t) = t2 + 9 is S(t) = ∫(t2 + 9)dt = (1/3)t3 + 9t + C, where C is the constant of integration.

(b) Finding the Constant of Integration

Given that s(0) = 3, w

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Answer:

C) 6

Step-by-step explanation:

19 - 7 = 12

5 - 3 = 2

12/2 = 6

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Answer:

G, I, H

Step-by-step explanation:

6 and 4 force H to be the largest and G to be the smallest.

For any right triangle, the 90 degree angle is always the largest. The longest side of a triangle is always opposite the largest angle. Similarly, the shortest side of a triangle is always opposite the smallest angle.

Angle G is opposite side HI = 4 which is the smallest side, so angle G is the smallest angle.

Angle H is the middle angle as this is the longer leg, but it is not longer than the hypotenuse. The hypotenuse is always the longest side.

Answer: it is c. 10.7 cm

Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.

To find the length of CD in a right triangle ABC where:

BA = 10 cm (the side adjacent to angle B)

angle B = 30 degrees

angle C = 90 degrees (a right angle)

angle D = 25 degrees

We can use the trigonometric ratio for tangent (tan) since we know the measure of angle B and the length of side BA. The tangent of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

In this case, we want to find CD, which is the side opposite to angle B. So, we can use the following relationship:

tan(B) = CD / BA

First, find the tangent of angle B (30 degrees):

tan(30 degrees) ≈ 0.5774 (rounded to four decimal places)

Now, we can solve for CD:

CD = tan(B) * BA

CD ≈ 0.5774 * 10 cm

CD ≈ 5.774 cm

Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.

for such more question on length

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For a sphere of radius r the volume V is

V=(4/3)πr³

We have r=10 so

V = (4/3) π 10³ = 4000π/3

Answer: 4000π/3

The volume of a sphere can be calculated using the formula V = 4/3 * π * r³. Assuming the radius is 10 units, the calculated volume is 4186.67 cubic units.

The volume V of a sphere can be found using the formula V = 4/3 * π * r³, where π is a constant (approximately 3.14) and r is the radius of the sphere. In your question, it appears there may be missing information as the value for the radius is not provided. Assuming that 10 is the radius of the sphere, we can substitute this value into the formula. So, V = 4/3 * 3.14 * 10³ = 4186.67 cubic units. Therefore, the volume of a sphere with a radius of 10 units is approximately 4186.67 cubic units.

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Answer:

(2,1) is a solution

Step-by-step explanation:

y = 3x-5

Substitute the point into the equation and see if it is true

1 = 3(2)-5

1 = 6-5

1=1

This is true so the point is a solution

Answer:

A

Step-by-step explanation:

A is the right answer

f has the greater slope, 3. The slope of g is 2.

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Answer:

Let play build royale together

Step-by-step explanation:

b. y = r cosa

Answer: A. y= r sin e

Step-by-step explanation: I just did it

Answer:

C

Step-by-step explanation:

Answer:

178.85

Step-by-step explanation:

Answer:

153 !

Step-by-step explanation:

begin by multiplying 180 by .15 then you should get 27. next, subtract 27 from 180 and you're left with 153.

Answer:

34

Step-by-step explanation:

Answer:

1.68 km

Step-by-step explanation:

You want the horizontal distance (on the ground) from beneath the helicopter to the vertex of the 37 degree angle.  The hypotenuse is given and is 2.1 km.

We want to find the horizontal distance when we already know the angle and the hypotenuse.

That horizontal distance could be called 'x.'   Then:

x/r = adj/hyp = cos 37 degrees, which becomes adj = (2.1 km)cos 37 degrees, which is found using a calculator:  adj = (2.1 km)(0.7987)  =  1.68 km

Answer:

The answer to your question is    Volume = 125 π in³

Step-by-step explanation:

Data

Volume = ?

Base area = 25π in²

height = radius

Process

1.- Find the radius

   Area of the base = πr²

-Equal

               πr² = 25π

-Solve for r

                r² = 25π/π

-Simplify

                r² = 25

-Result

                r = 5 in

2.- Find the volume of the cylinder

     Volume = πr²h

-Substitution

                   = (25π)(5)

-Simplification

     Volume = 125 π in³

Answer:

[tex]y=27x+20[/tex]

8 people went to the game.

Step-by-step explanation:

Let x represent number of tickets.

We have been given that the family parked the car in a parking lot which charged ​$20. The cost per ticket was ​$27.

The cost of x tickets would be [tex]27x[/tex].

The total cost of going to baseball game would be equal to cost x tickets plus parking cost that is [tex]27x+20[/tex].

Therefore, the equation [tex]y=27x+20[/tex] represents the total cost (y) of going to the baseball​ game.

To find the number of people who went to game, we will equate total cost with 236 as:

[tex]236=27x+20[/tex]

[tex]236-20=27x+20-20[/tex]

[tex]216=27x[/tex]

[tex]\frac{216}{27}=\frac{27x}{27}[/tex]

[tex]8=x[/tex]

Therefore, 8 people went to the game.

Answer:

The shop did not meet their goal of selling 65 per month. You can tell this because if you look at the graph you see that January, May, and June are all under the 65 mark.

Hope this helps ;)

Answer:

( -[tex]\sqrt{3}[/tex]/2 , -1/2)

Step-by-step explanation:

-210 degrees in standard position corresponds to an angle in the 3rd quadrant  30 degrees below the negative x-axis

The hypotenuse of the triangle here is 1, and we want the coordinates.

_______________________(0,0)

|(x = -root(3)/2)

|

| (y = -1/2)

The coordinates of the point at which the terminal side intersects the unit circle are (-√3/2, -1/2).

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given  -210 degrees is in standard position,

-210° lies in the third quadrant,

which is 180° + 30° or π + 30°

the coordinate are x = cos(π + 30°)

and y = sin(π + 30°)

cos(π + Ф) = -cosФ and

sin(π + Ф)  = -sinФ

x = cos(π + 30°) = -cos30° = -√3/2

y = sin(π + 30°) = -sin30° = -1/2

Hence the coordinates of points are (-√3/2, -1/2).

Learn more about the cartesian plane;

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Answer:

-

[tex] \frac{ - \sqrt{2} }{10} [/tex]

step by step:

[tex] \frac{ - 1}{5 \sqrt{2 } } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ - \sqrt{2} }{5 \times 2} = \frac{ - \sqrt{2} }{10} [/tex]

multiply by the square root of 2 to get rid of the square root of 2 on the bottom, then simplify. hope this helped :)

[tex]\\ \sf{:}\longrightarrow \dfrac{-1}{5\sqrt{2}}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-1(5√2)}{(5√2)^2}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{25(2)}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-5√2}{50}[/tex]

[tex]\\ \sf{:}\longrightarrow \dfrac{-√2}{10}[/tex]

Answer:

The volume of the Perfume bottle is 128 cubic cm.

Step-by-step explanation:

We are given the following in the question:

Height of bottle, h = 6 cm

Base edge of perfume bottle, a = 8 cm

The perfume bottle in the shape of square pyramid.

Volume of perfume bottle = Volume of square pyramid.

[tex]V = a^2\times \dfrac{h}{3}[/tex]

Putting values, we get,

[tex]V = (8)^2\times \dfrac{6}{3}\\\\V = 128\text{ cubic cm}[/tex]

Thus, the volume of the Perfume bottle is 128 cubic cm.

The total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.

The fence segments are determined by the vertices A, B, C, D, E, and F. The distances between consecutive vertices can be calculated using the distance formula:

[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Let's calculate the lengths of the segments:

1. Length of AB: [tex]\(\sqrt{(-4 - 4)^2 + (-4 - (-4))^2} = \sqrt{64 + 0} = 8\) yards[/tex]

2. Length of BC: [tex]\(\sqrt{(-4 - (-4))^2 + (3 - (-4))^2} = \sqrt{0 + 49} = 7\) yards[/tex]

3. Length of CD: [tex]\(\sqrt{(1 - (-4))^2 + (3 - 3)^2} = \sqrt{25 + 0} = 5\) yards[/tex]

4. Length of DE:[tex]\(\sqrt{(1 - 1)^2 + (-1 - 3)^2} = \sqrt{0 + 16} = 4\) yards[/tex]

5. Length of EF: [tex]\(\sqrt{(4 - 1)^2 + (-1 - (-1))^2} = \sqrt{9 + 0} = 3\) yards[/tex]

Now, sum up these lengths:

[tex]\[ 8 + 7 + 5 + 4 + 3 = 27 \][/tex]

So, the total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that x varies directly with y, if we introduce a constant of proportionality, k, the expression becomes

x = ky

If x = - 4 when y = 6, then

- 4 = 6k

k = - 4/6 = - 2/3

Therefore, the equation that relates x and y is

x = -2y/3

Answer:

3/2

Step-by-step explanation:

Answer:

10 yd

Step-by-step explanation:

The length of the top is

6+4 = 10 yd

The bottom must be the same length

To find the length of the bottom side, we can look around the shape to see if there are any similar sides. The sides 6ft and 4ft make up the same length as the bottom side, so, we can add.

6 + 4 = 10ft.

Best of Luck!

The inequality that represents Max's situation with renting a bicycle is 5 + 3h <= 20. Max can rent the bicycle for up to 5 hours with his $20 budget, and renting for 4 hours would satisfy the inequality.

The inequality to represent Max's situation with renting a bicycle, considering his budget constraints, would be:

5 + 3h \<= 20

Where h represents the number of hours Max can rent the bike. To solve for h, you subtract 5 from both sides of the inequality (which represents the fixed insurance fee) and then divide by 3 (the hourly rate for renting the bike):

3h \<= 15

h \<= 5

Thus, Max can rent the bicycle for up to 5 hours to stay within his budget of $20. An example value that satisfies this inequality is 4 hours, which would cost Max $5 for insurance plus $12 for the rental time, totaling $17.