There are 8 pencils in package.how many packages will be needed for 28 children if each child get 4 pencils

Answer:

Angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min

Step-by-step explanation:

Angular velocity, ω = 2πf , where f is the frequency.

Here frequency, f = 20 revolutions per minute

Substituting frequency value in angular velocity equation,

Angular velocity, ω = 2πf = 2 x π x 20 = 40π rad/min

So angular velocity of a wheel which makes 20 revolutions per minute is 40π rad/min

The final answer is 55,800

Answer:

21.

Step-by-step explanation:

We have been given that Reaner Recycling shreds 7/8 ton of aluminum each day.The machines can shred 1/24 ton aluminum per cycle.

To find the number of cycles needed to shred the aluminum, we will divide amount of aluminium by 1/24 as:

[tex]\text{Number of cycles}=\frac{7}{8}\div \frac{1}{24}[/tex]

Convert into multiplication problem by flipping the 2nd fraction:

[tex]\text{Number of cycles}=\frac{7}{8}\times \frac{24}{1}[/tex]

[tex]\text{Number of cycles}=\frac{7}{1}\times \frac{3}{1}[/tex]

[tex]\text{Number of cycles}=7\times 3[/tex]

[tex]\text{Number of cycles}=21[/tex]

Therefore, 21 cycles will be needed to shred the aluminum.

The reference angle for a 240° angle is 60 degree.

Reference Angle is the acute angle between the terminal side and the x axis. The value of reference angle is always positive and less than 90 degree.

The angle is 240 degree, for which the reference angle has to be determined.

The angle 240 degree lies in the third quadrant between 180 and 270 degree.

To determine the reference angle, the given angle will be subtracted by 180 degree.

=> 240 - 180

=> 60 degree

To know more about Reference Angle

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Answer:

The value of y is [tex]\frac{198}{5}[/tex] or 39.6.

Step-by-step explanation:

It is given that y varies directly as x and y. It means y is directly proportional to x.

[tex]y\propto x[/tex]

[tex]y=kx[/tex]            .... (1)

where, k is constant of proportionality.

It is given that y is 18 when x is 5.

Substitute y=18 and x=5 in equation (1).

[tex]18=k(5)[/tex]

Divide both sides by 5.

[tex]\frac{18}{5}=k[/tex]

The value of k is [tex]\frac{18}{5}[/tex]. So, the relation between x and y is

[tex]y=\frac{18}{5}x[/tex]            .... (2)

We need to find the value of y when x=11.

[tex]y=\frac{18}{5}(11)[/tex]

[tex]y=\frac{198}{5}[/tex]

[tex]y=39.6[/tex]

Therefore the value of y is [tex]\frac{198}{5}[/tex] or 39.6.

To find the difference between the number of condos available at Sunset Beach and Playa Del Mar, we need to set up an equation and solve for the unknown. The number of timeshare condos available at Sunset Beach is 3/5 of the number available at Playa Del Mar. By solving the equation, we find that the difference is 60 condos.

To solve this problem, we can set up an equation. Let's say the number of timeshare condos available at Playa Del Mar is x. According to the question, the number of condos available at Sunset Beach is 3/5 of x, or 3/5x.

So, the total number of condos available at both beaches is x + 3/5x = 240. We can combine the like terms to get 8/5x = 240.

To solve for x, we divide both sides of the equation by 8/5, which is the same as multiplying by its reciprocal, 5/8. Simplifying, we get x = 240 * 5/8 = 150.

Therefore, the number of condos available at Sunset Beach is 3/5 * 150 = 90, and the difference between the number of condos available at Sunset Beach and Playa Del Mar is 150 - 90 = 60.

134 = 14 +6x

subtract 14 from each side

120 = 6x

 divide each side by 6

x = 120/6 = 20

x = 20

ANGLE GOF = (360 - (134+134)) /2 = 92/2 = 46 degrees

Answer:

∠EFG=104° and ∠GFH=76°

Step-by-step explanation:

Given information:∠EFG = (4n+20)°, ∠GFH = (3n+13)° and ∠EFG and ∠GFH are a linear pair.

If two angles are a linear pair, then the sum of those angles is 180°.

It is given that ∠EFG and ∠GFH are a linear pair.

[tex]\angle EFG+\angle GFH=180^{\circ}[/tex]

Substitute the given values.

[tex](4n+20)+(3n+13)=180[/tex]

Combined like terms.

[tex](4n+3n)+(20+13)=180[/tex]

[tex]7n+33=180[/tex]

Subtract 33 from both sides.

[tex]7n+33-33=180-33[/tex]

[tex]7n=147[/tex]

Divide both sides by 7.

[tex]n=21[/tex]

The value of n is 21.

[tex]\angle EFG=4n+20=4(21)+20=104^{\circ}[/tex]

[tex]\angle GFH=3n+13=3(21)+13=76^{\circ}[/tex]

Therefore, the measure of ∠EFG and ∠GFH are 104° and 76° respectively.

 2 3/2 =  3 1/2  ( 3/2 = 1 1/2 + 2 = 3 1/2)

so area = 3 1/2 ^2

3 1/2 x  3 1/2 = 12 1/4

Area = 12 1/4

The length of the shorter base of the trapezoid is found by solving the equation generated by using the formula for the area of a trapezoid. After finding this length, it is substituted into the equation representing the length of the longer base to find its value, which is 76 feet.

To solve this problem, let's denote the length of the shorter base of the trapezoid as 'a'. According to the problem, the length of the longer base is then 5a - 19. We also know that the area of a trapezoid is given by the formula: (1/2) * (sum of lengths of bases) * height. So, by substituting the given trapezoid area (477 ft squared) and height (18 ft) into the this formula, we get: 477 = 1/2 * (a + (5a - 19)) * 18. Solving this equation will give us the value of 'a'. As calculating 'a' we find it to be 19. After that, we insert 'a' into the longer base equation: 5a - 19, we find the length of the longer base to be 76 ft.

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Answer:

y = 4x - 14 is equivalent from of y = 4x - 14.

Step-by-step explanation:

Given : 4x-y= 14

To find : Which is an equivalent form of the equation.

Solution : We have given 4x - y = 14.

We can write it in slope intercept form y = mx  + b

Where, m = slope , b = y intercept.

4x - y = 14.

On subtracting both sides by 4x

- y= -4x + 14.

On dividing both sides by -1.

y = 4x - 14.

Therefore, y = 4x - 14 is equivalent from of y = 4x - 14.