I typically give 12% of money I receive to my church. My uncle died recently and left me some money. I donated $408 to my church in his memory. How much did he leave to me in his will?

Answer:a=10 b=35

Step-by-step explanation:

1*8=8  1.25*8=10

1*28=28 1.25*28=35

Answer:

84

Step-by-step explanation:

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

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

Explanation:

Let [tex]f(n) = \frac{(-1)^{n+1}}{n!}[/tex]

The summation given to us represents the following

[tex]\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\[/tex]

There are infinitely many terms to be added.

-------------------

The partial sums only care about adding a finite amount of terms.

The partial sum [tex]S_1[/tex] is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say [tex]S_1 = f(1) = 1[/tex]

I'm skipping the steps to compute f(1) since you already have done so.

-------------------

The second partial sum is when things get a bit more interesting.

We add the first two terms.

[tex]S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\[/tex]

The scratch work for computing f(2) is shown in the diagram below.

-------------------

We do the same type of steps for the third partial sum.

[tex]S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\[/tex]

The scratch work for computing f(3) is shown in the diagram below.

-------------------

Now add the first four terms to get the fourth partial sum.

[tex]S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\[/tex]

As before, the scratch work for f(4) is shown below.

I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.

This means something like [tex]S_3 = S_2 + f(3)[/tex] and [tex]S_4 = S_3 + f(4)[/tex]

In general, [tex]S_{n+1} = S_{n} + f(n+1)[/tex] so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.

-------------------

Let's use that recursive trick to find [tex]S_5[/tex]

[tex]S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333[/tex]

The scratch work for f(5) is shown below.

Answer:

10138 is the answer to 12x12x77-38x 25

Step-by-step explanation:

I added these step by step 12x12 = 144 x 77 = 11088 -38x 25 10138

let's recall that d = rt, or namely distance = rate * time.

b = speed of the boat

c = speed of the current

now, we know that going downstream the boat went 16 miles total, that's going only one way, so the distance the boat travels downstream as well as upstream to return is 16 miles flat.

when going downstream, the boat is not really going at "b" speed, is really going at "b + c" speed, because the current is adding its speed to it, so is really going faster than "b".

when going upstream, the boat is not really going at "b" speed" either, is really going slower at "b - c" speed, because the current is against it and thus subtracting speed from "b".

let's take a look at those in a table

[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Downstream&16&b+c&2\\ Upstream&16&b-c&4 \end{array}\qquad \qquad \begin{cases} 16=(b+c)(2)\\\\ 16=(b-c)(4) \end{cases} \\\\\\ \stackrel{16}{(b+c)(2)}~~ = ~~\stackrel{16}{(b-c)(4)}\implies 2b+2c~~ = ~~4b-4c\implies 2c=2b-4c[/tex]

[tex]6c=2b\implies \cfrac{6c}{2}=b\implies \boxed{3c=b} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{16~~ = ~~(\stackrel{b}{3c}+c)(2)}\implies 16=4c(2)\implies 16=8c \\\\\\ \cfrac{16}{8}=c\implies \blacktriangleright \stackrel{mph}{2}=c \blacktriangleleft~\hspace{10em}3(2)=b\implies \blacktriangleright \stackrel{mph}{6}=b \blacktriangleleft[/tex]

Answer:

D, [tex]\frac{7(x-4)}{6}[/tex]

Step-by-step explanation:

Basically you have to simplify the (x² - 16). Since it is the difference of 2 squares, it's simplified as (x + 4)(x - 4). Now that everything is simplified, you can start doing the multiplication.

[tex]\frac{(x+4)(x-4)}{6x} *\frac{7x}{(x+4)}[/tex], You can cancel out the (x+4)'s

[tex]\frac{(x-4)}{6x} *{7x}[/tex], There is a common factor between 7x and 6x. The common factor is x. So cancel out both "x".

You end up with this, [tex]\frac{7(x-4)}{6}[/tex]

Answer:

128 because formula is bh

Step-by-step explanation:

Answer:

5m - 10

Step-by-step explanation:

Use distributive property;

5(m - 2)

(5 x m) (5 x -2)

5m - 10

Answer:

the answer is D...... ..........

Answer:

226,080 cm3

Step-by-step explanation:

The probability that Natalie got at least two correct on the last three

true-or-false questions is 1/4.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The sample space is 2. The question is either correct or wrong.  

The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4

To learn more about probability, please check: https://brainly.com/question/795909

Answer:

7x+4+2y is your answer

Answer:

53

Step-by-step explanation:

[tex] \frac{sin(56)}{78.6} = \frac{sin(90)}{ab} \\ \\ absin(56) = sin(90) \times 78.6 \\ \\ ab = \frac{sin(90) \times 78.6}{sin(56)} \\ ab = 94.8 \\ \\ {x}^{2} + {78.6}^{2} = {94.8}^{2} \\ {x}^{2} = {94.8}^{2} - {78.6}^{2} \\ {x}^{2} = 8987.04 - 6177.96 \\ {x}^{2} = 2809.08 \\ x = \sqrt{2809.08} \\ x = 53[/tex]

Answer:

8

Step-by-step explanation:

Now consider an experiment of tossing three coins simultaneously. The possible outcomes will be HHH, TTT, HTT, THT, TTH, THH, HTH, HHT. So the total number of outcomes is 23 = 8.

Answer:

8

Step-by-step explanation:

Answer:

[tex]\sf \theta=\dfrac34 \ radians=42.97 \textdegree \ (nearest \ hundredth)[/tex]

Step-by-step explanation:

Formulae

[tex]\sf radius (r)=\dfrac12 d[/tex]

(where d is the diameter of a circle)

[tex]\sf arc \ length =r\theta[/tex]

(where r is the radius and [tex]\theta[/tex] is measured in radians)

Calculation

Given:

Substituting these values into the formula for arc length:

[tex]\implies \sf 3 =4\theta[/tex]

[tex]\implies \sf \theta=\dfrac34 \ radians[/tex]

To convert radians to degrees use

[tex]\sf 1 \ rad \cdot \dfrac{180\texrdegree}{\pi}[/tex]

[tex]\implies \sf \dfrac34 \cdot \dfrac{180\texrdegree}{\pi}=42.97183463...\textdegree[/tex]

Now

[tex]\\ \rm\rightarrowtail \theta=\dfrac{l}{r}[/tex]

[tex]\\ \rm\rightarrowtail l=r\theta[/tex]

[tex]\\ \rm\rightarrowtail 3=4\theta[/tex]

[tex]\\ \rm\rightarrowtail \theta=\dfrac{3}{4}^c[/tex]

Answer:

x=7

Step-by-step explanation:

In a 45 45 90 triangle the two legs are equal so you set 33=5x-2 and then solve the equation.

Answer:

4x+4=16

4x= 16–4

4x= 12

x= 12/4

x= 3

Alternatively,

4x+4=16

Taking 4 common,

4 (x+1) = 16

x+1 = 16/4

x+1 = 4

x = 4–1

x = 3

Step-by-step explanation:

The value of x is 68.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Parts of an Equation

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators. An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables. As opposed to this, an equation with variables is an algebraic equation.

Given equation:

4/(x - 4) = 1 /16

Now, solving for x

4/(x - 4) = 1 /16

64 = x - 4

x= 68

Hence, the value of x is 68.

Learn more about equation here:

https://brainly.com/question/10413253

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Answer:

=(-1,-5)

Step-by-step explanation:

y=X1=4

y=-2x-5-2

try your best

Step-by-step explanation:

Answer:

Study!

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

[tex]9x^2-18x+36\\\\=(3x)^2- 3x \cdot 6+6^2\\\\\text{It is not in the form of}~ A^2-2AB+B^2[/tex]

Answer:

16641

Step-by-step explanation:

Thank you!

Answer:

5sqroot3

Step-by-step explanation:

see image.

An integer is just a whole positive or negative (positive in this case) number that's not a fraction or decimal or mixed number. In the answer that is the 5.

To simplify a radical, look for a factor that is a perfect square. Radicals and multiplying are very friendly to each other and you can separate the "radicand" (the inside number) into factors inside the radical also into separate radicals to simplify. See image

Answer:

(x² -1) + y² = 9

Step-by-step explanation:

diameter=6 so radius means 6/2=3 (thus,radius²=3²=9)

centre (1 and midpoint of diameter is at y=0, so 1,0)

Answer:

-1/1

Step-by-step explanation:

=64/-8

over

36-30+2

= -8

over

8

= -1

over

1

Answer:

[tex] \rightarrow - 1[/tex]

Step-by-step explanation:

[tex] \rightarrow \frac{ {4}^{3} }{ \frac{ - 12 + {2}^{2} }{(2 \times 3) {}^{2} + ( - 5 \times 2 \times 3) + 2 }} \\ [/tex]

[tex] \rightarrow \frac{ {4}^{3} }{ \frac{ - 12 + {2}^{2} }{ {6}^{2} + ( - 30) + 2 }} \\ [/tex]

[tex] \rightarrow \frac{ 64 }{ \frac{ - 12 + 4 }{ 36 + ( - 30) + 2 }} \\ [/tex]

[tex] \rightarrow \frac{ 64 }{ \frac{ - 8 }{ 8 }} \\ [/tex]

[tex] \rightarrow - \: \frac{ 64 }{ \frac{ 8 }{ 8 }} \\ [/tex]

[tex] \rightarrow - \frac{ 8 }{ 8 } \\[/tex]

[tex] \rightarrow \: - 1[/tex]

Answer:

Step-by-step explanation:

firstly the area for teh rectangle is 12 x 15 = 18are0

the area for the circle is 113.1 sq inches because  pi x r squared

Step-by-step explanation:

what is that called into the comet or ok

Step-by-step explanation:

The number 1 is a common factor of C) all whole numbers

Answer:

C

Step-by-step explanation:

6 / 1 = 6. 5 / 1 = 5. every whole number is divisble by 1, even prime numbers.