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Angelina_Jolie [31]
2 years ago
5

Suppose a charity received a donation of $24.6 million. If this represents 49% of the charity's donated funds, what is the total

amount of its donated funds?
Round your answer to the nearest million dollars.
Mathematics
1 answer:
Marrrta [24]2 years ago
6 0

Answer:

73.6

Step-by-step explanation:

this is an addition question so we're going to answer it with an equation let's put 24.6 + 49 =73.6

You might be interested in
3,6,11,18,27,38
MakcuM [25]

Answer:  The pattern is x^2+2

where x is the term number

Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27

=================================================

Explanation:

  • The jump from 3 to 6 is +3
  • The jump from 6 to 11 is +5
  • The jump from 11 to 18 is +7
  • The jump from 18 to 27 is +9
  • The jump from 27 to 38 is +11

The pattern of jumps is: 3, 5, 7, 9, 11

Those increments are going up by 2 each time.

Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.

Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.

-----------

If x is the term number and y is the term itself, then we have these points

(1,3)

(2,6)

(3,11)

(4,18)

(5,27)

(6,38)

The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.

Pick exactly 3 of those points. I'll pick the first 3.

Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.

  • Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
  • Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
  • Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11

-----------

We have this system of equations

\begin{cases}a+b+c = 3\\ 4a+2b+c = 6\\9a+3b+c = 11\end{cases}

There are a number of methods to solve this system. Substitution is what I'll go for.

Solve the first equation for c

a+b+c = 3

c = 3-a-b

Then use substitution.

4a+2b+c = 6

4a+2b+(3-a-b) = 6

3a+b+3 = 6

3a+b = 6-3

3a+b = 3

and

9a+3b+c = 11

9a+3b+(3-a-b) = 11

8a+2b + 3 = 11

8a+2b = 11-3

8a+2b = 8

We now have this reduced system of equations.

\begin{cases}3a+b = 3\\8a+2b = 8\end{cases}

I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.

Use those values to find c

c = 3-a-b

c = 3-1-0

c = 2

-----------

To summarize the previous section, we have these solutions:

a = 1, b = 0, c = 2

Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.

Let's test it out.

  • If x = 1, then y = x^2+2 = 1^2+2 = 3
  • If x = 2, then y = x^2+2 = 2^2+2 = 6
  • If x = 3, then y = x^2+2 = 3^2+2 = 11

And so on. I'll let you test the other x values (4 through 6).

Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.

Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.

7 0
2 years ago
Please answer plz
djyliett [7]

x + y = 3.36 --> the boys are splitting $3.36

x = 3y - .12 --> one boy received $.12 less than 3 times as much as the other

--> substitute the second equation for the x in the first equation


(3y - .12) + y = 3.36 --> combine like terms

4y - .12 = 3.36 --> add .12 to both sides of the equation

4y = 3.48 --> divide both sides by 4

y = .87

the other boy gets $0.87

substitute into x = 3y - 12


x = 3(.87) - .12

x = 2.61 - .12

x = 2.49

the first boy gets $2.49

4 0
3 years ago
In the Minnesota Northstar Cash Drawing, you pick five different numbers between 1 and 35. What is the probability of picking th
maw [93]

Answer:

\frac{1}{324632} probability of picking the winning combination

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Since the order is not important, the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

Desired outcomes:

The correct five numbers from a set of 5. So

D = C_{5,5} = \frac{5!}{5!0!} = 1

Total outcomes:

Five numbers from a set of 35. So

T = C_{35,5} = \frac{35!}{5!30!} = 324632

Probability:

p = \frac{D}{T} = \frac{1}{324632}

\frac{1}{324632} probability of picking the winning combination

5 0
2 years ago
Factor 64x² + 114x + 81
slavikrds [6]
The answer is 64x^2+114x+81. Hope this helps.
3 0
2 years ago
The length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of 0.7 m
zloy xaker [14]
The probability of the message lasting longer than six minutes is 0.955. I hope this helps!
8 0
2 years ago
Read 2 more answers
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