Jack, Jill, and Ron share a 2-bedroom apartment. Rent is represented by R. The water bill is $20 per person. The electric bill is $250 a month. Jill will be picking up the water bill for everyone as well as half of the electric. Ron will be paying the other half of the electric bill as well as his third of the rent. Jack will be paying Jill's portion of the rent as well as his own. Match each person with the appropriate algebraic expression.-abcd -abcd 185-abcd -abcd Jill's paymentJack's paymentRon's paymentNo Match

Answers

Answer 1

Answer: Jack: 2R/3
Jill: 3 • 20 + 0.5 • 250 = 185
Ron: R/3 + 125

hope that helps

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F(x)=x^3+ax^2+bx+3 where a and b are constants. bx Given that when f (x) is divided by (x+2) the remainder is 7, (a) show that 2a-b=6 Given also that when f (x) is divided by (x-1) the remainder is 4. (b) Find the value of a and the value of b I don't know how solve it :(((((((

Answers

Part I - First synthetic division

You need to use synthetic division to come up with an expression for a and b:

(x + 2) is a factor, and the remainder is 7, so we can draw a synthetic division table...

coefficients = 1 for X^3; A for X^2; B for X^1; and 3

-2 |    1     A B           3

      -2 -2(A-2) 4(A-2)-2B

   1      (A-2)    -2(A-2)+B    4(A-2)-2B + 3

Remainder = 7

So...

4(A-2)-2B + 3 = 7

4 * (A - 2) - 2B + 3 = 7

4A - 8 - 2B =  4

4A - 2B = 12

2A - B = 6
Proved

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Part II - Second Synthetic Division

We draw another synthetic division table, this time with (x - 1), so the number on the left hand side will be +1

1 |    1        A B           3

      1   (A+1)   A+B+1

         1      (A+1)    A+B+1   A+B+4

    Remainder = 4

So...

A + B + 4 = 4

A + B = 0

A = -B

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Part III - Solving for A and B with our two simultaneous equations

We know that A = -B and we also know that 2A - B = 6

Since we know that A is equal to -B We can substitute in A for -B, to get:

2A - B = 6

Therefore...

2A + A = 6

3A = 6

A = 2

Again, as we know that A = -B, and as we have found that A = 2, we can see:

A = -B

Therefore...

2 = -B

B = -2

So our final answer is A = 2, B = -2

Hopefully this answer is more useful than the last one, and isn't so confusing!

1. Conduct a hypothesis test for the following scenario. SHOW ALL YOUR WORK THE WAY WE DID IN CLASS! Construction zones on highways have a much lower speed limit. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed in miles per hour of a random sample of 10 drivers in a 30 mph speed zone. Here are the data: 26 28 32 21 27 31 29 22 25 34 Is there convincing evidence at the α = .05 level that the average speed is below the speed limit?

Answers

First you want to put the numbers in order 21,22,25,26,27,28,29,31,32,35

Then separate the ones above the limit from below the limit

Above-31,32,35 (a total of 3)

Below-21,22,25,26,27,28,29 (a total of 7)

.5 is equal is 1/2 and over half are below the speed limit

So the average speed is most likely below the speed level

P.S. the average speed is 24.4

I = prt (simple interest).
Find the value of I given that p=300, r=0.14, and t=2

Answers

Hi there, Convert r percent to r a decimal, r=R/100=0.14%/100=0.0014 per year. Now, we have to solve using a equation, the equation is A=300(1+(0.0014*2))=300.84, Therefore, the answer is $300.84

300x0.14=0.42
0.42x2=0.84

The graph of f has the equation of f(x)=x^3-4x²-3x+181.Determine the stationary points of f
2.determine the point of inflection
Please answer any question you know

Answers

Hello,

y= x^3-4x²-3x+18=(x-3)²*(x+2)

y'=3x²-8x-3

y''=6x-8

1) Stationary points

Maximun: x=-1/3 ==>y=18,5185....
Minimum: x=3 ===>y=0 (double root)

2) x=4/3: point of inflection. (y''=0 and change sign)

Can anyone help its due in 10 minuets!

Answers

Answer:

x=30⁰

Step-by-step explanation:

4x-55+3x+25=180

7x-30=180

7x=210

x=30⁰

Proof

3(30)+25=115

4(30)-55=65

115+65=180⁰

If the shadow of a pole 12m high is 2/3 of its length, what is the angle of elevation of the sun?

Answers

To find the angle of elevation of the sun, you can use the tangent function. Given that the shadow of the pole is 2/3 of its length (12 meters), you can set up the following trigonometric relationship:

tan(angle of elevation) = (height of the pole) / (length of the shadow)

tan(angle of elevation) = 12 / (2/3 * 12)

Now, calculate the length of the shadow:

2/3 * 12 = 8 meters

So, tan(angle of elevation) = 12 / 8

tan(angle of elevation) = 3/2

To find the angle of elevation, take the arctan (inverse tangent) of 3/2:

angle of elevation = arctan(3/2)

Using a calculator or trigonometric tables:

angle of elevation ≈ 56.31 degrees

So, the angle of elevation of the sun is approximately 56.31 degrees.

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