Complete each exercise.
Order from least to greatest.
1. 1, 7, -1, -7

Answer:

10y + 15

Step-by-step explanation:

5(2y + 3)

= 5x2y + 5x3

= 10y + 15

Answer: Convergent; converges to 9/5 = 1.8

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

Explanation:

The expression 8/(n^2-1) is the same as 8/( (n+1)(n-1) )

Use partial fraction decomposition to get

8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)

8 = (n+1)(n-1)*( A/(n+1) + B/(n-1) )

8 = A(n-1) + B(n+1)

8 = An-A + Bn+B

0n + 8 = (A+B)n + (-A+B)

We can see that

[tex]\begin{cases}A+B = 0\\-A+B = 8\end{cases}[/tex]

Use elimination to get 2B = 8 which leads to B = 4

Plug B = 4 into either equation of that system to solve for A getting A = -4

Therefore,

8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)

8/( (n+1)(n-1) ) = -4/(n+1) + 4/(n-1)

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

Why do all this? Because it'll be helpful to set up the telescoping sum

Let's plug in a few values of n. Let's say from n = 5 to n = 10

If we do so, then we have...

 -4/(5+1)+4/(5-1)   =    -4/6 + 4/4

 -4/(6+1)+4/(6-1)   =    -4/7 + 4/5

 -4/(7+1)+4/(7-1)   =    -4/8 + 4/6

 -4/(8+1)+4/(8-1)   =    -4/9 + 4/7

 -4/(9+1)+4/(9-1)   =    -4/10 + 4/8

 -4/(10+1)+4/(10-1) =    -4/11 + 4/9

I'm not evaluating or simplifying further because we'll have cancellations as shown in the diagram below. The left panel is what you see before cancelling happens, and the right hand panel is what happens after the terms pair up and cancel (since those pairs add to 0).

Note the color coding so you can see what terms pair up and cancel. The only stuff left is the 4/4 and the 4/5

So,

4/4 + 4/5 = 1 + 4/5 = 5/5+4/5 = 9/5 = 1.8

is what the infinite sum converges to. You can use a tool like wolfram alpha to confirm this answer.

Answer:

[tex] 25\frac{1}{2} [/tex]

Step-by-step explanation:

[tex]5 \frac{2}{3} \times 4 \frac{1}{2} \\ \\ = \frac{5 \times 3 + 2}{3} \times \frac{4 \times 2 + 1}{2} \\ \\ = \frac{15 + 2}{3} \times \frac{8 + 1}{2} \\ \\ = \frac{17}{3} \times \frac{9}{2} \\ \\ = \frac{17}{1} \times \frac{3}{2} \\ \\ = \frac{51}{2} \\ \\ = 25 \frac{1}{2} [/tex]

Answer:

-1

Step-by-step explanation:

slope=m

(keep in mind your equation is written in the form y=mx+b)

Answer:

Step-by-step explanation:

rate of change for y = -x - 1

so its the inverse of -x - 1 = -1 - x

therefore, the rate of change = -1

Answer:

Option (3)

Step-by-step explanation:

Given:

Horizontal side of a triangle ABC is side AC.

AB and BC are the perpendicular lines.

BD is perpendicular to side AC.

Solution:

Option (1).

Slopes of AB and BC are reciprocal.

False.

Option (2)

Angle DAB and BCD are equal.

False.

Option (3).

Since, sides AB and BC are perpendicular lines,

Slopes of AB and BC will be negative reciprocals.

True.

Option (4).

Triangles ABD and BCD are similar.

False.

Therefore, Option (3) will be the answer.

Answer:

150

Step-by-step explanation:

Answer:

152

Step-by-step explanation:

you want to be my friend

Hello! Your answer to this question is Yes!

Step-by-step explanation:

About 90% of babies born with a certain ailment recover fully. A hospital is caring for sixsix babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment.

Answer:

plants sbbsjdjdhdhhs

Answer:

B

Step-by-step explanation:

7 x 4 = 28

12 x 4 = 48

The higher numbers might be higher on the line but still in the same line :)

Answer:

A

Yes, because they are similar triangles

Step-by-step explanation:

Each angle increases by four

Triangle one is 7 and 12

Triangle two is 28 and 48

7 x 4 = 28

12 x 4 = 48

Answer: johnny will beat up ava and take his three apples back

Answer:

I'm assuming you mean how many would Johnny have left. If not I am providing both answers. Johnny has 3 apples leftover. Ava has 3 apples, now.

Step-by-step explanation:

Johnny's apples: 6-3 = 3

Ava's apples: 0+3 = 3

13.86 would be about how much that is

Answer:it’s 13

Step-by-step explanation:

Answer:

Last option; 5/2+ i5/2

Answer:

Non Proportional

Step-by-step explanation:

A proportional figure relates to two or more figures that correspond in size or amount to one another. The gallon of milk which costs 1.99 is nonproportional to the half-gallon which costs 3.89.

On the other hand, a nonproportional figure does not correspond to in size or amount to one another.

From the given information;

A half-gallon cost 3.89

i.e.

[tex]\mathbf{= \dfrac{1}{2} \times 3.89}[/tex]

= 1.945

Therefore, we can conclude that the gallon of milk which cost 1.99 is nonproportional to the half-gallon which cost 3.89.

Learn more about proportionality here:

https://brainly.com/question/18707816?referrer=searchResults

Answer:

D.

Step-by-step explanation:

(x-3)(x+1)(x+5)

The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given as,

⇒ x³ + 3x² - 13x - 15

Factorize the polynomial, then we have

⇒ x³ + 3x² - 13x - 15

⇒ x³ - 3x² + 6x² - 18x + 5x - 15

⇒ x²(x - 3) + 6x(x - 3) + 5(x - 3)

⇒ (x - 3)(x² + 6x + 5)

⇒ (x - 3)(x² + 5x + x + 5)

⇒ (x - 3)[x(x + 5) + 1(x + 5)]

⇒ (x - 3)(x + 5)(x + 1)

The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ5

Answer:

I think it's 1/3

Step-by-step explanation:

because yo can see that in y-1, x=1 then in y0, x=1.3 and it keep going

When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

Answer:

Ok sorry but I have a very strong feeling that this isn't a college question because I am in an 8th grader taking Algebra 1 and this is sooooo simple.

Step-by-step explanation:

the answer is

8=m

Answer:

4) x=110º

5) x=90º (so does y)

6) x=109

7) x=15º and y=5º

8) x=7

9) x=95

10) x=33

Step-by-step explanation:

4), 5) and 6) were a little hard to read but they were mostly simple to solve from what I saw. Using the verticle angles theorem and corresponding theorem you can easily find the values.

7) I plugged in the two first equations to solve x which is (3x+60)=(6x+15)

and for y I had to plug in x to find one of the angles' values to plug in with 15y and then created a second equation which should look like this 105+15y=180º (Since they should be supplementary angles)

8) This one's similar to 7) and even a little simpler. The equation should look like this 4x=3x+7

9) The equation to solve it that I used is x + (x-10)=180º

10) The equation to solve it that I used is (4x+5)=137

Hope this was helpful and (to other people too) if I made any mistakes or didn't explain properly feel free to let me know! :)

Answer:

Jeannie sent/received 572 text messages

Step-by-step explanation:

60$ are payed at the beginning

0.15$ is payed for every extra text.

the total is 70.80$

if t is the number of extra text messages, then

60 + 0.15t = 70.80

subtract 60 from both sides

0.15t = 70.80 - 60

0.15t = 10.80

divide both sides by 0.15

t = 10.80/0.15

t = 72

remember, Jeannie was able to send 500 free texts at the beginning.

so, her total texts would be 572

let me know if I did something wrong!

Answer:

your right

Step-by-step explanation:

Answer:

3-√11  must also be a root of f(x)

Step-by-step explanation:

Answer:

If x equals -1 or anything less than -1, then the inequality statement is false

Step-by-step explanation:

So to find the number x has to be for the statement to be false, we have to find what number x would be to make it so both sides equal the same thing. So in this case, it would be -1 because 5-3 equals 2 and -2x=2 only if x=-1. So anything greater than -1 would make the statement true.

I hope this helped.

Answer:

Step-by-step explanation:

Inequality

As per above, the graph covers all numbers to the right from the point -1

The graph is attached

Answer:

i cant see the pic srry dude

Step-by-step explanation:

Answer:

it c

Step-by-step explanation:

it is c because it does cost less by 3.01 per pound and because i did it and got it correct plase mark me as brainliest

Answer:

there's no S .X=1 ,Xc=9.So 91

Answer:

a

 [tex]P(X  < 35) =  32.3 \%[/tex]

b

[tex]P(\= X  < 35) =  0.6 \%[/tex]

Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy

c

A potential confounding variable for this study is  the population of the koalas because in the first question the population was not taken into account and the probability was  [tex]P(X  < 35) =  32.3 \%[/tex] but when the population was taken into account (i.e  n =  30) the probability became

[tex]P(\= X  < 35) =  0.6 \%[/tex]  

Step-by-step explanation:

From the question we are told that

  The mean is  [tex]\mu =  35.6^oC[/tex]

   The standard deviation is  [tex]s =  1.3^oC[/tex]

   The sample size is  n = 30

Generally the  probability that a health koala has a body temperature less than 35.0°C is mathematically represented as

     [tex]P(X  < 35) =  P(\frac{X  - \mu }{s}  < \frac{35 - 35.6}{1.3} )[/tex]

Here  [tex](\frac{X  - \mu }{s} =  Z (The   \ standardized \  value \  of  \  X )[/tex]

So

    [tex]P(X  < 35) =  P(Z < -0.46)[/tex]

From the z-table  P(Z <  -0.46) =  0.323

So  

    [tex]P(X  < 35) =  0.323 [/tex]

Converting to percentage

      [tex]P(X  < 35) =  0.323  * 100 [/tex]

      [tex]P(X  < 35) =  32.3 \%[/tex]

considering question b

The sample mean is  [tex]\= x =  35[/tex]

Generally the standard error of the mean is mathematically represented as

   [tex]\sigma_{\= x} =  \frac{s}{\sqrt{n} }[/tex]

=>  [tex]\sigma_{\= x} =  \frac{1.3}{\sqrt{30} }[/tex]

=>  [tex]\sigma_{\= x} =  0.2373 [/tex]

Generally the probability of the mean body temperature of koalas being less than 35.0°C is mathematically represented as

 [tex]P(\= X  < 35) =  P(\frac{\= X  -  \mu  }{\sigma_{\= x }} <  \frac{35 -35.6}{0.2373 }  )[/tex]

[tex]P(\= X  < 35) =  P(Z< -2.53  )[/tex]

From the z-table  we have that

   [tex]P(Z< -2.53  ) =  0.006[/tex]

So

 [tex]P(\= X  < 35) = 0.006 /tex]

Converting to percentage

      [tex]P(\= X  < 35) =   0.006  * 100 [/tex]

      [tex]P(\= X  < 35) =  0.6 \%[/tex]

Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy

A potential confounding variable for this study is  the population of the koalas because in the first question the population was not taken into account and the probability was  [tex]P(X  < 35) =  32.3 \%[/tex] but when the population was taken into account (i.e  n =  30) the probability became

 [tex]P(\= X  < 35) =  0.6 \%[/tex]  

Answer:

C) x=1.5

Step-by-step explanation:

Hope This Helps!

Answer:

it is c!

Step-by-step explanation:

top one is correct