What is 8 1/3 - 3 1/2?

Answer:

This sum is the sum of an arithmetic sequence.  There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.

A nice approach for this sequence is the following.  Notice  that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.

There are n of these pairs.  So the desired sum is n x (first number + last number).   But the first number is 1 and the last on is 2n.   Thus the desired sum is n(1 + 2n).

Hope this helps!!

Mark Brainleast!!!!!!!!!!!

Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.

Now let's say we wanted to add everything in that set.

What we can do is write out the terms

1, 2, 3, 4, ..., m

then just underneath, we write the reverse of that set

m, ..., 4, 3, 2, 1

Here's an example of what I mean. I'll use m = 7

[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}[/tex]

For each column, add straight down

The third row will be nothing but 8's

[tex]\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}[/tex]

We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.

Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.

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

That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.

We could write that as 7(1+7)

Then divide that by 2 to fix the double-counting error.

We have 7(1+7)/2

Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2

Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2

We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.

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

The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2

In this case, m = 2n because we want the first 2n natural numbers.

Therefore,

m(1+m)/2

2n(1+2n)/2

n(1+2n)

n(2n+1)

represents the sum 1+2+3+...+n+...+2n

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

Try out a value like n = 5 to find that 2n = 2*5 = 10, and,

1+2+3+4+5+6+7+8+9+10 = 55

also

n(2n+1) = 5(2*5+1) = 5*(11) = 55

Showing that the formula works for n = 5. I'll let you try other values of n.

Answer:

it's the last one, and the missing number is 70 (the P)

The expression that represents this scenario is 35/p = 70/100.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Alex has 70% of her weekly paycheck automatically deposited into a savings account.

This week $35  is deposited,

∴ The expression that represents this situation is 35/p = 70/100.

learn more about numerical expressions here :

https://brainly.com/question/29199574

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Answer:

f(-8) = 64

Step-by-step explanation:

Given conditions :

We have x = -8

⇒ It follows x < 0

Therefore, substituting x = -8 in the function :

[tex]5x^2-14x+8\\\\=5x^2-10x-4x +8\\\\=5x(x-2) -4(x-2)\\\\=(x-2)(5x-4)[/tex]

Answer:

6 and 9

Step-by-step explanation:

Because if 6 is substituted,

And if 9 is substituted,

Considering that the mile counter increases by 50 every hour, a linear function should be empathized.

A linear function is modeled by:

y = mx + b

In which:

In this problem, they start at mile 62, and the counter increases by 50 every hour, which is a fixed amount, hence a linear function should be used.

More can be learned about linear functions at https://brainly.com/question/24808124

Answer:

B

Step-by-step explanation:

its b bc its inclusive and rhe others font make much sense

Answer:

sine

.....................

Answer:

9.21954445729

Step-by-step explanation:

A^2 + B^2 = C^2

7^2 = 6^2 = 85

The square root of 85 is...

9.21954445729

Answer:

124

Step-by-step explanation:

4*5*3

+

2*4*8

=124

Formula for volume of a rectangular prism is base x height.

Answer:

79-22=57.

Your answer is correct. You also have to fill in the second one (B)

Answer:

79-22=57

Step-by-step explanation:

I can explain on phone

Answer:

The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.

Step-by-step explanation:

Recall our formula for the probability of A or B:

We are given are variables already, which we can once again define:

To find P(A ∩ B), we start by plugging in the values into our formula:

We can add the RHS of the equation:

Subtracting 0.97 on both sides, we get closer to our answer:

To obtain our final answer, we can simply just divide both sides by -1:

Therefore, the probability of A and B is equal to 0.331.

Answer:

Trees are important to one's health as they produce oxygen and reduce climate change. Also, bees pollinate our crops leading to more crop production and increase in revenue.

It should be noted that health simply means the state of being free from illness or diseases.

In this case, trees are important for one's health as they help in the production of oxygen which are needed by human beings. Bees are also important for the generation of higher profits though the pollination of crops which leads to increase in crop production.

Learn more about health on:

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Answer:

3 laps per day

Step-by-step explanation:

Divide 45 laps by 5 days to get how many laps they ran per day

45/5 = 9 laps per day

The tennis players run 6 less laps per day than the soccer players so subtract 6 laps from 9 laps to get their daily laps

6-9 = 3 laps per day

Answer:

The cost of one T-shirt is £4

The cost of a hat is £1

Step-by-step explanation:

The ship movement is an illustration of distance and bearing

The ship is 31.97 miles from its point of departure

The given parameters are:

See attachment for the image of the above parameters

The distance (x) from the point of departure is then calculated using the following cosine function

a^2 = b^2 + c^2 - 2bc * cos(Ф)

So, we have:

x^2 = 40^2 + 70^2 - 2 * 40 * 70 * cos(12)

Evaluate the exponent and the product

x^2 = 6500 - 5477.63

Evaluate the difference

x^2 = 1022.37

Evaluate the exponent

x = 31.97

Hence, the ship is 31.97 miles from its point of departure

Read more about distance and bearing at:

https://brainly.com/question/24142612

Answer:

  c. 33.0%

  d. 14.5%

Step-by-step explanation:

For answering questions about percentages in different categories or combinations of categories, it is convenient to find the totals of rows and columns in the table. These totals are shown in the attached.

__

Students who surf total 32+65 = 97. Of those, 32 also skateboard. The requested percentage is ...

  32/97 × 100% ≈ 33.0% . . . . surfers who also skateboard

__

The total number of students is 166. Of those, the number who neither surf nor skateboard is 24. That percentage is ...

  24/166 × 100% ≈ 14.5% . . . . students who don't surf or skateboard

_____

Additional comment

a. 97/166 ≈ 58.4% surf

b. 89/166 ≈ 53.6% do not skateboard

__

This sort of table is called a "two-way table." One set of categories is represented in rows, another set is represented in columns. This table is filled with frequencies. Such tables can also display relative frequencies by dividing the entire table by the total of totals in the lower right corner.

Step-by-step explanation:

[tex]y = \frac{3}{4} x - 2[/tex]

is the required equation

I hope it helped you

Answer:

y = [tex]\frac{3}{4} x-2[/tex]

Step-by-step explanation:

y = mx + c

m = gradient= [tex]\frac{-5-(-2)}{-4-0}[/tex]= [tex]\frac{3}{4}[/tex]

c = y-intercept = -2

Answer:

21

Step-by-step explanation:

You can tell that AB=2x7

BC=4x7

So, you're increasing each by multiplying each by 7.

3x7=21.

Answer:

8 inches

Step-by-step explanation:

Nacho cheese

v= Pi×radius×2×height

v = 3.14×8×2×4 = 200.96

jalapeño

3.14×4×2=25.12

200.96÷25.12=8

the height is 8

to check your work you can do

(multiply by 8 and see if it equals 200.96)

3.14×4×2×8 = 200.96

since the volume is the same as the volume for nacho cheese we can say that 8 inches for height is correct

Answer: Times it

Step-by-step explanation:

Answer:

90 square feet

Step-by-step explanation:

area of this figure = area of 1 rectangle + area of 2nd rectangle

= L×B + l × b

= 18 × 3 + 12 × 3

= 54 + 36

= 90 feet²

Answer:

There isn't any data, maybe you could put the rest of the question in the comment area.

Step-by-step explanation:

(sinx/cosx - cosx/sinx) + sinxcosx

sin²x - cos²x = 1

I can't prove

I only know sin²x + cos²x = 1 : )

Answer:

[tex] \: [/tex]

Step-by-step explanation:

In the question, it is given that a cone has a diameter of 14 feet and a height of 11 feet and we have to find the volume of the cone.

[tex] \: [/tex]

To Find the volume of the cone, we must know this formula :

[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]

Where,

Now, we will substitute the values in the formula :

[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(7)}^{2} \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 49 \times 11 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 539 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1692.46 }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1692.46}{3} }}}}}}} \\ \\[/tex]

[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \: \: \underline{ \boxed{ \frak{564.15 } }} }}}}}}} \: \: \bigstar \\ \\[/tex]

Therefore,

Step-by-step explanation:

Given :-

To Find :-

Solution:-

Formula for volume of cone = 1/3πr²h

Volume = 1/3×3.14×7²×11 cubic ft.

Volume = 564.15 cubic ft.

Answer:

i think it would be 45

hope im right

if not i can change it

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

The circle is divided into 8 equal arcs, each arc measuring an angle of:

360/8 = 45°

Hope this helps

Answer:

20/2.5 =? (Answer is 8)

Step-by-step explanation:

Aaden needs 40 points.

He gets 20 at the start, just for signing up, so he needs only 20 now.

If he gets 2.5 points for each visit, after 8 days he will have been given 20 more points, allowing him to get a free movie ticket.

Brainliest please?

Answer:

Step-by-step explanation:

Given the equation: y = 8 * 2ˣ, substitute the x-values in the table for x in your equation, to find the y-values.

For x = -1

[tex]y = 8 * 2^x\\y=8*2^{-3}\\y=8*\frac{1}{2^3} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{8}\\y=8*0.125\\y=1\\\\(-1,1)[/tex]

For -2:

[tex]y = 8 * 2^x\\y=8*2^{-2}\\y=8*\frac{1}{2^2} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{4}\\y=8*0.25\\y=2\\\\(-2,2)[/tex]

For -1:

[tex]y = 8 * 2^x\\y=8*2^{-1}\\y=8*\frac{1}{2^1} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{2}\\y=8*0.5\\y=4\\\\(-1,4)[/tex]

For 0:

[tex]y = 8 * 2^x\\y=8*2^0\\y=8*\frac{1}{2^2} < ==zero\ exponent\ property: x^0=1\\y=8*1\\y=8\\\\(0,8)[/tex]

For 1:

[tex]y = 8 * 2^x\\y=8*2^1\\y=8*2\\y=16\\\\(1,16)[/tex]

For 2:

[tex]y = 8 * 2^x\\y=8*2^2\\y=8*4\\y=32\\\\(2,32)[/tex]

For 3:

[tex]y = 8 * 2^x\\y=8*2^3\\y=8*8\\y=64\\\\(3,64)[/tex]

Hope this helps!

Answer:

the

• the population of the first germ is represented by the function a(x) = (1. 3)+9