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In Linguistics 101, the ratio of the number of juniors to the number of seniors is 3:2.  When six more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes 2:3.  How many students are in the class after these changes?  

I answered this question a couple of days ago and the thread was removed.  

I thought probably a moderator had deleted it because it was a bogus problem.  

If you start with the ratio of juniors to seniors 3:2, and then add even more juniors,  

the ratio can not invert to 2:3.  

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Let's denote the number of pies in each row at the downtown location as "x" and the number of pies in each row at the uptown location as "y."

We are given that the downtown location has 4 rows, and the uptown location has 6 rows. Additionally, we know that one of the locations has a square display, which means that the number of pies in each row is equal to the number of rows.

If the downtown location has a square display, then the number of pies in each row at the downtown location is 4 (since there are 4 rows).

Therefore, x = 4.

To find the number of pies in each row at the uptown location, we can set up a proportion using the given information:

4 (pies in each row at the downtown location) / 6 (number of rows at the uptown location) = y (pies in each row at the uptown location) / 6 (number of rows at the uptown location)

Simplifying the proportion:

4/6 = y/6

Cross-multiplying:

4 * 6 = 6 * y

24 = 6y

Dividing both sides by 6:

24/6 = y

4 = y

Therefore, if the downtown location has a square display with 4 rows, then the uptown location will have 4 pies in each of its 6 rows.

Angular velocity =angular acceleration*time (when starting from zero angular velocity), so  \(\omega=0.75\times4.7\text{ rad/s}\)

Linear velocity = angular velocity*radius, so \(v = \omega\times21\text{ cm/s}\)

You can crunch the numbers.

The number of regions created by the intersection of lines in a plane can be calculated using a formula known as Euler's formula. Euler's formula states that for a planar graph, the number of regions (including the infinite region) is equal to the number of edges minus the number of vertices plus 1.

In this case, we have 10 lines in the plane. The number of intersections can be calculated as the sum of the first 9 positive integers since each line intersects with every other line exactly once. The sum of the first 9 positive integers is (9 * 10) / 2 = 45.

So, the number of vertices is 45, and the number of edges is the number of lines, which is 10.

Using Euler's formula, the number of regions is given by:

Number of regions = Number of edges - Number of vertices + 1 = 10 - 45 + 1 = -34 + 1 = -33

However, it doesn't make sense to have a negative number of regions, so in this case, we should consider the value of 1 for the infinite region. Therefore, the number of regions created by the intersection of the lines in the plane is 1 -(- 33) = 34.

The equation of the circle can be rewritten in the standard form by completing the square for both the x and y terms:

(x^2 + 4x) + (y^2 - 6y) = -12

To complete the square for the x terms, we need to add (4/2)^2 = 4 to both sides, and for the y terms, we need to add (-6/2)^2 = 9 to both sides:

(x^2 + 4x + 4) + (y^2 - 6y + 9) = -12 + 4 + 9

Simplifying, we have:

(x + 2)^2 + (y - 3)^2 = 1

Comparing this to the standard form of a circle equation, we find that the center of the circle is (-2, 3), and the radius is sqrt(1) = 1.

The distance between the center of the circle (-2, 3) and the point (1, 7) can be found using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((1 - (-2))^2 + (7 - 3)^2)
= sqrt(3^2 + 4^2)
= sqrt(9 + 16)
= sqrt(25)
= 5

Find the coefficient of y^4 in the expansion of (2y-5+3y^2)^6.   

That's way too much multiplying to try to do it manually.  

Luckily, we have been provided a handy tool to use, at

https://www.symbolab.com/solver/expand-calculator

You'll find that it's 375 but go ahead and see for yourself.  

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?   

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

RV = SU is the FALSE statement.  

RV is just half a diagonal.  

SU is an entire diagonal.  

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?    

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

^.

In a store window, there was a box of berries having a total weight of 200 kg.  The berries were 99% water, by weight.  After two days in the sun, the water content of the berries was only 90%, by weight.  What was the total weight of the berries after two days, in kg?   

You're starting with 200 kg of berries, and 99% of that is water.  

Since they're 99% water, that means that there's 1% of solid stuff.  

1% of 200 kg means that there are 2 kg of solid stuff.   

Some of the water evaporates in the sun, but the solid stuff doesn't.  

So there still remains 2 kg of solid stuff.  

Since the new water content is 90%, that means that now the solid stuff is 10%.  

So 2 kg (the solid stuff) is 10% of the total weight.  

That means the new total weight is 20 kg.  

_.

This has been answered a ton of times. Find my answer at https://web2.0calc.com/questions/help-help_29#r1

You don't have to call everyone on this website a homework cheater. Sometimes, you just can't solve a problem, and you need some help. If you understand after someone helps you, then what is the problem?

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