9x-8y= 1
18x - 16y= 2

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:

multiply second eqyation by 9

Step-by-step explanation:

then subtract with 1 st eqn

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:

21 minutes of game time.

Step-by-step explanation:

Since its every 7 minutes he reads he gets one minute of game time and reads fir 147 minutes you would divide 147 by 7 to get 21 minutes of game time. hope this helped :)

Answer:

C) x=1.5

Step-by-step explanation:

Hope This Helps!

Answer:

it is c!

Step-by-step explanation:

top one is correct

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:

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.

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Answer:

[tex]-\frac{1}{2}[/tex] is the slope value.

Step-by-step explanation:

By using the definition of slope (Δy/Δx), we can reason that the slope is:

[tex]\frac{-1}{2} = -0.5[/tex]

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:

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:

plants sbbsjdjdhdhhs

Answer:

150

Step-by-step explanation:

Answer:

152

Step-by-step explanation:

you want to be my friend

Answer:

g(x) = 2x² + 1

Step-by-step explanation:

The parabola got thinner, so to show that, you put a 2 before x² to show that the graph was dilated (or thinned) by a factor of 2 (Note: this number can also be negative, so if the dilation factor is negative, it's okay). Since the parabola shifts up by 1, you then add + 1 after x² to show the positive upward shift.

Your full equation would look like this: g(x) = 2x² + 1

Dilation: this just means that every point on the parent function was double (or whatever the factor is) in the transformed function.

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! :)

13.86 would be about how much that is

Answer:it’s 13

Step-by-step explanation:

Answer:

2.333333333

Step-by-step explanation:

divide 3 into 7 and it's is repeating

Answer:

Step-by-step explanation:

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:

10y + 15

Step-by-step explanation:

5(2y + 3)

= 5x2y + 5x3

= 10y + 15

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.

Generally, the number of turns is one less than the degree of the polynomial.

Hence,  the polynomial f(x) that has a degree of 8 will have 7 turning points.

Learn more about Polynomials:

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Answer: y

Step-by-step explanation:

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

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:

$2.25

Step-by-step explanation:

The first thing you do is multiply the prices of tickets by how many they bought.

$8.50 x 2= $17

$5.50 x 3= $16.50

You then add these two numbers together and subtract that from $40.25.

$17+$16.50=$33.50

$40.25-$33.50=$6.75

You then divide $6.75 by 3 to find the answer

$6.75/3=$2.25

Answer:

I believe the answer is D) 26.

Step-by-step explanation:

Xavier will need 26 weeks to first bike more than 500 miles.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the successive terms is the same.

The distance biked by Xavier during his first week of training is 15 miles.

The increase in the distance biked each week is 0.4 miles.

And we have to find the number of weeks required to first bike more than 500 miles total.

The given situation represents an arithmetic progression (AP) in which,

First term, a = 15

The common difference, d = 0.4

And the sum of n terms, Sn = 500

The formula to find the sum of n terms of an AP is,

[tex]\text{S}_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

We will check which option is correct by putting them in the above equation.

For n = 8, we have

[tex]\text{S}_n = \dfrac{8}{2}[2\times15+(8-1)0.4][/tex]

Sn = 4[30+2.8]

Sn = 131.2

Which is not more than 500, so option (A) is incorrect.

For n = 15, we have

[tex]\text{S}_n = \dfrac{15}{2}[2\times15+(15-1)0.4][/tex]

Sn = 7.5[30+5.6]

Sn = 267

Which is not more than 500, so option (B) is incorrect.

For n = 19, we have

[tex]\text{S}_n = \dfrac{19}{2}[2\times15+(19-1)0.4][/tex]

Sn = 9.5[30+7.2]

Sn = 353.4

Which is not more than 500, so option (C) is incorrect.

For n = 26, we have

[tex]\text{S}_n = \dfrac{26}{2}[2\times15+(26-1)0.4][/tex]

Sn = 13[30+10]

Sn = 520

Which is more than 500, so option (D) is the correct answer.

Hence, Xavier would bike more than 500 miles in 26 weeks.

Learn more about arithmetic progression here - https://brainly.com/question/27029595

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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:

one over five (m-100)

Step-by-step explanation:

the answer to your question is the 2nd one

Answer:

1 / [ 5(m - 4) ] is equivalent to one over five m -20

Step-by-step explanation:

one over five(m − 4)

5(m − 4)

Factor the denominator:

1 / [ 5m - 20 ]  =  1 / [ 5(m - 4) ]

Answer:

[tex]\frac{16}{10000}[/tex]

Step-by-step explanation:

Answer:

4/25

Step-by-step explanation: