Can someone help me with my mid term click download document

Answer:

3075

Step-by-step explanation:

So we have the sequence:

\(-12, -9, -6...\)

As given, this is an arithmetic sequence and we want to find the sum of the first 50 terms.

The formula for the sum of an arithmetic sequence is:

\(S=\frac{k}{2}(a+x_k}\)

Where k is the number of terms, a is the initial term, and x_k is the last term.

We already know that k is 50 because we want to find the sum of the first 50 terms. a is -12 because it's the first number in our sequence. To find our last term, we need to do some more work.

To find the 50th term, let's write an explicit formula for our sequence. The standard form for the explicit formula for an arithmetic sequence is:

\(x_n=a+d(n-1)\)

Where a is the first term, d is the common difference, and n is the nth term.

We already know that a, the first term, is -12. From the sequence, we can see that the common difference d is +3 because each term is 3 more than the previous one. -12 plus 3 is -9, plus 3 is -6, and so on.

So, substitute -12 for a and 3 for d gives us:

\(x_n=-12+3(n-1)\)

So, to find the 50th term for our sum, substitute 50 for n:

\(x_{50}=-12+3(50-1)\)

Subtract:

\(x_{50}=-12+3(49)\)

Multiply:

\(x_{50}=-12+147\)

Add:

\(x_{50}=135\)

So, the last term of our 50 number sequence is 135.

Now, let's go back to our original formula:

\(S=\frac{k}{2}(a+x_k})\)

Now we know all the values. So, substitute 50 for k (the amount of terms), -12 for a (the first term), and 135 for k (the 50th and last term). So:

\(S=\frac{50}{2}(-12+135)\)

Divide:

\(S=25(-12+135)\)

Add:

\(S=25(123)\)

Multiply:

\(S=3075\)

So, our sum is 3075.

And we're done!

Answer:

S₅₀ = 3075

Step-by-step explanation:

Find the sum, S50, of the first 50 terms of the following arithmetic series:(−12)+(−9)+(−6)

an = a₁ + (n - 1) d

where:

a₁ = 1st term                      = -12

n = nth term                      = 50

d = common difference  

  = a₂-a₁ = -9 - (-12)            =3

plugin values into the formula:

an = -12 + (50 - 1) 3

    = 135

sum of an arithmetic sequence:

Sn = n (a1 + an)  

              2

S₅₀  = 50 ( -12 + 135 )

                    2

S₅₀ = 3075

Answer:

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Step-by-step explanation:

SA=2B+Ph

Find the area of each face. Add up all areas.

Answer:

Step-by-step explanation:

A= 189.06cm2

Answer:

Step-by-step explanation:

189.06cm2

By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042

Answer:

By proportion that is:(54/150) * 8450= 54 * 56 1/3= 3042

Step-by-step explanation:

Answer:B,C

Step-by-step explanation:

6/9=2/3=18/27=30/54

Answer: 18/27

: that’s the only one I know sorry

Answer:

25

Step-by-step explanation:

\(105+3x=180 \\ \\ 3x=75 \\ \\ x=25\)

Answer:

The answer is 25 degrees

Step-by-step explanation:

If you subtract 180 - 105 then you get 75.
Then you divide it by 3.
One circle is 360 degrees thus half of it is 180.
If you know one angle is 105 degrees then subtract it from 180.
If the number is 3x then you have to divide it by 3 to get x alone.
Hope it helps! :)

Answer:

C

Step-by-step explanation:

It isn't B because the point does not start at 600 and it is not A because it shows the entire decrease of the mass in one millennium. The correct answer is c.

Explanation:

The data from the stem-and-leaf plot is:

10,

24,25,26,

30,30,32,33,

40,45,46

Add up those values

10+24+25+26+30+30+32+33+40+45+46 = 341

Then divide over n = 11 which is the sample size.

341/11 = 31 is the arithmetic mean.

Answer:

341/11 = 31 is the arithmetic mean.

Step-by-step explanation:

Step-by-step explanation:

If you are multiplying a fraction and a whole number just make the whole number a fraction by using the whole number as the numerator and a 1 as the denominator.

Answer:

20 cm

Step-by-step explanation:

Height is AE.

Find height.

600 = 1/3 × (18 × 5) × h

Base area is the area of square.

Volume is given, solve for h.

600 = 30h

600/30 = h

20 = h

Answer:

\(\boxed{Height = 20 cm}\)

Step-by-step explanation:

Base Area = \(Length *Width\)

Base Area = 5*18

Base area = 90 square cm

Volume = 600 cubic cm

Volume = \(\frac{(BaseArea)(Height)}{3}\)

For Height, it will be:

=> \(Height = \frac{3(Volume)}{BaseArea}\)

=> H = \(\frac{3(600)}{90}\)

=> H = 20 cm

Answer:

b

Step-by-step explanation:

Answer: 110

Step-by-step explanation: Write 275% as

275

100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

275

100

of 40 =

275

100

× 40

Therefore, the answer is 110

If you are using a calculator, simply enter 275÷100×40 which will give you 110 as the answer.

Answer:

4/5 -  2/ 15=

0.66666666666

0.66666666666 in fraction form is 2/3

Step-by-step explanation:

I hope this helps <3  

Answer:

2/3 (0.6)

Step-by-step explanation:

To subtract fractions find the LCD then combine

Answ

Step-by-step explanation:

The function for the points are  y = -15x - 5

From the information given, we have that;

The points are;

(1/3,0) (-2 3/4,0) and (0,-5)

Using the point-slope form of a linear equation, we have;

y - y₁ = m(x - x₁)

Such that;

Using (1/3, 0) and (0, -5), we have that the slope is;

m = (0 - (-5))/0 -1/3)

expand the bracket

= 5 / (-1/3)

= -15

Now, take any of the given points and substitute the values

Using (1/3, 0), we get;

y - 0 = -15(x - 1/3).

y = -15x - 5.

Learn more about functions at: https://brainly.com/question/25638609

#SPJ1

The function for the points solved by  (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)

We have given the points:

(1/3,0) (-2 3/4,0) and (0,-5)

Using the formula of linear equation

\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)                                                          

Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)

that is 1/3 = \(a\), 0 = \(a_{1}\) and

0 = \(b\), -5 = \(b_{1}\)

\(x\) refers to the slope of line (take any variable)

Now for finding the value of \(x\),

\(x=a-a_{1}/b-b_{1}\)

inserting the values,

\(x=[0-[-5]]/[0-1/3]\\x= -15\)

Substitute the value of \(x\) in the equation

\(a-0=-15[b-1/3]\)

By simplifying the equation, we get

\(a=-15b-5\)

To know more about functions and points:

https://brainly.com/question/30721594

Answer:

50.23 and 50.24 are both rational numbers.

Step-by-step explanation:

Rational numbers can be written like a ratio.

●Whole numbers (2, 15, 77) are rational bc just put a 1 underneath it (2/1, 15/1, 77/1) now its a ratio.

●Fractions are rational bc the fraction is exactly the ratio (1/2, 5/8, 65/111)

●Decimals that "terminate" that is end or stop are rational like your problem (50.23, 50.24) and ALSO decimals that repeat (2.33333..., 7.666666...) We can do some math on these and find the ratio that is equal to the decimal.

50.23

= 50 + 23/100

= 50•(100/100) + 23/100

= 5000/100 + 23/100

= 5023/100

50.23 is equal to 5023/100.

50.24 = 5024/100 = 2512/50 = 1256/25

Briefly, decimals that do not end either with no pattern or even with a pattern, but not repeating...they are Irrational. (pi, e, and any weird 4.531874569131187732678...no pattern, and 3.1121231234pattern but not a repeat)

Square roots of not-a-perfect square are Irrational (sqrt3, sqrt7, sqrt24) probably tmi, but hope this helps!

Answer:

145

Step-by-step explanation:

105 + 40 = 145

I hope this helps!!!!

Answer:

52

Step-by-step explanation:

Answer:

x= 12

Step-by-step explanation:

Please see attached picture for full solution.

Feel free to ask if you have any queries :)

Answer:

slope : opposite of a

y-intercet:b/c

x-intercet:a/b

Step-by-step explanation:

Answer:

18-3

It should be 18-3 since that's the only way to write it as an expression. If you want to add a variable, the answer would be something like x=18-3 or x+3=18, which is not an expression..

Step-by-step explanation:

It asks for an expression for 3 fewer than 18. Since it is an expression, you should not include any equal signs, thus the only possible answer would be 18-3.

Answer:

18-3

Step-by-step explanation:

The required expression is 18-3 (The given phrase is '3 fewer than 18')

We need to find the algebraic expressions for the given phrase.

Algebraic expressions:

The algebraic expressions for the phrase "a fewer than b" is:

b - a

Similarly, the algebraic expressions for the phrase "3 fewer than 18" is:

18 - 3 (18 being b and 3 being a)

This means that our expression is 18 - 3 because that's the only way this is possible. You can add other things (like complicate it/ turn it into a 'find a' algebra question or a linear equation, I gave an example below- not the best i know but its like 1 am and I can't lol) like:

Find x: 18 - x = 16

x = 16

Answer:

10

Take 10 and add it 5 times

Step-by-step explanation:

5 divided by 50 is 10

Answer:

1/10

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

Let's break down this problem step by step.

First, let's understand what's happening here. There's a carnival game where you can pick one duck from a pond. Each duck has a mark under it that might make you a winner of a prize. Some ducks are marked with large prizes, some with medium, some with small, and the rest don't win you any prize.

The total number of ducks in the pond is 73.

Out of these 73 ducks:

- 5 are marked for a large prize,

- 11 are marked for a medium prize,

- 24 are marked for a small prize.

We are asked to find the theoretical probability of picking a duck that has a medium prize mark. The theoretical probability is basically a fraction that compares the number of ways something can happen with the total number of outcomes.

Here, the number of ways you can win a medium prize is equal to the number of ducks that have a medium prize mark, which is 11.

The total number of outcomes is just the total number of ducks you can choose from, which is 73.

The probability (P) of winning a medium prize is then:

P(medium prize) = (Number of medium-prize ducks) / (Total number of ducks)

= 11/73

To convert this fraction to a decimal, simply divide 11 by 73:

= 11 ÷ 73

≈ 0.1507 (rounded to the nearest thousandth)

So, the probability of winning a medium prize at the duck pond is about 0.151 or 15.1%. Imagine, for every 100 ducks you pick (if there were that many), about 15 of them would win you a medium prize.

The theoretical probability of winning a medium prize at the duck pond is ≈ 0.150

To find the theoretical probability of winning a medium prize at the duck pond, we need to determine the ratio of the number of medium-prize-winning ducks to the total number of ducks in the pond.

The total number of ducks in the pond is given as 73.

The number of medium-prize-winning ducks is given as 11.

Therefore, the probability can be calculated as follows:

Probability of winning a medium prize = (Number of medium-prize-winning ducks) / (Total number of ducks)

Probability of winning a medium prize = 11 / 73

To express the answer as a decimal, we divide 11 by 73:

Probability of winning a medium prize ≈ 0.150

Rounded to the nearest thousandth, the theoretical probability of winning a medium prize at the duck pond is approximately 0.150

To better understand how to find theoretical probability of winning medium prize at the duck pond:

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