there are 324 students in a college who have taken a course in calculus, 211 who have take a course in discrete mathematics, and 135 who have taken a course in both calculus and discrete mathematics. how many students at this college have taken a course in either calculus or discrete mathematics?

The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is  M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .

in the question ,

it is given that the

formula to find , "gravitational  force" between two objects is

[tex]F_{g}[/tex] = (G*M₁*M₂)/r²

to express the formula in terms of M₁ ,

we first multiply both the sides by r² ,

on multiplying , we get

[tex]F_{g}[/tex]*r² = G * M₁ * M₂

On dividing both sides by G ,
we get

( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂

we have to find the formula for M₁ ,

we divide both sides  by M₂,

So , on dividing both  sides by M₂ , we get

( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁

hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )

Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is  M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .

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We are given

Therefore the value of x can be gotten by simplifying the above equation

Given that x is 5, we can proceed to find the value of the expression.

This implies that

$3

the amount paid after adding tip is $21

the amount for the meal is $18

$21-$18=$3

In the first graph, we have that the whole figure is 1

it is divided in 4 parts:

Then, we want to divide 1 into 4 parts. That is

Then, we have that:

It is the same for the second figure:

Each 1/4 corresponds to each part. Then if we add them:

Solution:

Let the score for the seventh test be represented below as

The mean score t be attained after the sevent tests is

The scores from the 6 tests are given below as

To figure out the seventh score, we will do the calculation below

Hence,

The final asnwer is

The sentence that represents the expression (5 + 5)ve y(5-5) u is:

love you.

The expression is given as follows:

(5 + 5)ve y(5-5)u

There are two operations in the expression, as follows:

Then the expression, with the numbers, is given as follows:

10ve y0o.

The number 10 can be interpreted as the two letters lo, as l and 1 are very similar symbols, as are 0 and o, then the updated expression is:

love y0u.

The same is applied to the final zero, as 0 and o are very similar symbols, hence the sentence that represents the expression is:

love you.

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The required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
1.

The sum of the vertical angle is 180°. So,
∠A + ∠B = 180
Substitute value in the above equation,
x + 4x - 24 = 180
5x - 24 = 180
5x = 204
x = 204 / 5
x = 40.8°
∠A = 40.8°
Similarly,
2. ∠L = 83°
3. ∠J = 95°

Thus, the required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.

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Answer:

A. [tex]9n - 190 = 5n[/tex]

Step-by-step explanation:

Dora earning 5 dollars per song is represented by [tex]5n[/tex].

Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.

The graph of the equation is attached to the solution.

We can graph the equation of the line by finding the x and y intercept of the line.

We know that the equation is in the slope intercept form.

Hence, we can write the y-intercept of the line as 2.

The coordinates of the point will be (0,2).

To find the x - intercept, we can put y = 0

0 = 2x + 2

-2 = 2x

x = -2/2 = -1

x = -1

The coordinates of the point will be (-1,0).

We can find another point on the line.

Let x = 1

y = 2(1) + 2

y = 2 + 2

y = 4

The coordinates of the point will be (1,4).

We can plot these points on the graph and get our graph.

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Answer:

(7,-3)

Step-by-step explanation:

x = 7

-2x - 9y = 13

* Substituition is the easieat way to solve such a function.

- Firstly, put "7" instead of "x" in the equation.

- multiply "7" by "-2"

- Solve for "y"

* -2x-9y = 13

* -2×7-9y = 13

* -14-9y = 13

* -9y = 27

* -9y/-9 = 27/-9

* y = -3

# Since x = 7, the output/"y" will be -3

(7,-3)

Average speed is 35.56 mph.

Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.

We have to find the average speed of the whole journey.

First we have to find total distance for whole journey and then total time for whole journey.

Total distance for whole journey = 30 miles + 50 miles = 80 miles

Time for 30 miles = distance/speed = 30/40 = 3/4 hrs  = 0.75 hrs

Total time = 1.5 + 0.75 hrs = 2.25 hrs

Average speed =  total distance/ total time

= 80/2.25

= 35.56 mph.

The average speed is 35.56 mph.

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The given function F(x) is,

Take the limit of the function when x ix close to 2.

Hence, the function diverges.

The value of x in the right triangle is 15√2.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.

Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:

cos 45 = adjacent / hypotenuse

cos 45° = x / 30

cross multiply

30 cos 45° = x

Therefore,

x = 30 × 1 / √2

x =  30 / √2 × √2 / √2

x = 30√2 / 2

x = 15√2

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The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.

Given that,

One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.

To find:

What is the most effective gaming approach and what is the highest possible return on investment

By Central Limit Theorem,

It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.

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The answer after simplifying the expression, [tex]x^{-10} *x^{6}[/tex], will be [tex]1/x^{4}[/tex].

According to the question,

We have the following expression:

[tex]x^{-10} *x^{6}[/tex]

Now, we know that if two numbers are being multiplied with the same base but different powers then their powers are added.

(More to know: if the numbers are in division with the same base but different powers then their powers are subtracted.)

So, we have:

[tex]x^{-10+6}[/tex]

[tex]x^{-4}[/tex]

Now, we know that if powers are in negative then the number can be inverted to make the power positive (because it is given that the answer should have only positive exponents).

[tex]1/x^{4}[/tex]

Hence, the value after solving the expression is [tex]1/x^{4}[/tex].

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When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 1/2.

Given,

An envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2

That is,

When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 1/2.

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Answer:

(I) y=10-6x. (ii) y=x/-2 - 3

In this equation the solution for x in terms of a and b is 8.

What is equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.

Sol- As per the question given that- ax-3= bx+5------(equation 1)

Let ax=3-----(equation 2)

And bx =5------(equation 3)

On adding equation(1)and (2) we get

(ax)+(bx)= 3+5

(ax)+(bx)=8

x(a+b)+y(a+b)=8

(x+y)+(a+b)=8

1×(a+b)=8

Thus

a+b=8

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We are given a graph and we are asked to determine if it is a function or not. To do that we will use the vertical line test. We will draw a vertical line and if the line touches the graph in more than two places in any given value of "x" then it is not a function. Therefore, the vertical line we get is:

Since the vertical line touches the graph in two axes this means that the given graph is not a function.

Answer:

1. [tex]a=\frac{b}{zm-1}[/tex] 2. [tex]x=\frac{p-n-m}{1-y}[/tex] 3. [tex]a=\frac{z}{m+n+p}[/tex]

Step-by-step explanation:

1. zma = a+b  :    [tex]z=\frac{a+b}{ma} ;[/tex] [tex]m\neq 0[/tex]

zma = a + b  Divide both sides by ma: [tex]m\neq 0[/tex]

[tex]\frac{zma}{ma} =\frac{a}{ma} +\frac{b}{ma} ;[/tex] [tex]m\neq 0[/tex]

2. Subtract m from both sides

x + m - m = p - n + yx - m

Simplify

x = p - n + yx - m

Subtract yx from both sides

x - yx = p - n + yx - m - yx

simplify

x - yx = p - n - m

Factor x - yx:      x(1 - y)

x(1 - y) = p - n - m

simplify x = [tex]\frac{p -n-m}{1-y} ;y\neq 1[/tex]

3.Apply the sum /Different Rule :   (f + g)' = f ' + g'

= [tex]\frac{d}{dp} (am)+\frac{d}{dp} (an)+\frac{d}{dp} (ap)[/tex]

[tex]\frac{d}{dp} (am)=0[/tex]

[tex]\frac{d}{dp} (an)=0[/tex]

[tex]\frac{d}{dp} (ap)=a[/tex]

= 0 + 0 + [tex]a[/tex]

simplify

= a

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Using concept of Linear equations, we find $40 is the daily fee for renting a moving truck.

Linear equations are generally equations of the first order. The linear equations are defined for the lines in the coordinate system. When the equation having  a homogeneous variable of degree 1 (i.e. only one variable), then it is called as a linear equation in one variable. A linear equation can have more than one variables. If the linear equation has two variables, then it is known as  linear equations in two variables and so on. Some of the examples of linear equations which are listed here 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

So, lets suppose daily fee for renting a movie a truck is $x

Then according to question,

Daily fee+ total distance travelled × charge per mile=total cost

=>x+48×0.50=64

On solving x, we get x=40

Hence, daily fee cost is $40 which is required for renting a moving truck.

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Answer:

Choice A. 1.1

Explanation:

Using the information of the factors f ( x ) are

The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include

The given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:

Therefore they are the correct choice

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This is an example of a geometric distribution with success probability p=0.102

The expected number of rolls is 10.

This is an example of a geometric distribution with success probability p=0.102 The expected value of the random variable of a geometric distribution is 1/p=1/0.102=9.80

Therefore, the expected number of rolls is 10.

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The given expression is,

Multiplying all the terms with 5, we get

Thus, the solution is, x = 75.

Answer:

mA = 69 degrees

Step-by-step explanation:

A complementary angle has a measure of 90 degrees.

(2x + 27) + (2x - 21) = 90

Simplify

4x + 6 = 90

-6

4x = 84

/4

x = 21

mA: 2(21) + 27 = 69

Answer:

A = 69°

Step-by-step explanation:

Complementary angles sum 90°

A + B = 90°

(2x + 27) + (2x-21) = 90°

4x + 27 - 21 = 90°

4x + 6 = 90°

4x = 90 - 6

4x = 84°

x = 84°/4

x = 21

Then A:

A = 2x + 27

A = 2*21  +  27

A = 42 + 27

A = 69°

B = 2x - 21

B = 2(21)  + 27

B = 42 - 21

B = 21°

Check:

69 + 21 = 90

Explanation

Step 1

let x represents the numbers of days you can stay at the beach

then,

You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.

so

but, you have only $1200, so the total needs to be smaller or equal than 1200

Step 2

solve the inequality

it means you can stay maximum 6 days

I hope this helps you

Let

x -----> number of rides

y ----> the total cost

so

The linear equation that represents both situations are

y=40 -----> equation A

y=x+15 ----> equation B

equate both equations

40=x+15

solve for x

x=40-15

x=25

therefore

According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.

The probability that mn has a units digit of 1 = 2/5

By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.

Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex],  [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).

We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).

We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is  [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].

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