If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be? If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be

Answer:

a1=6 a2=15 a3=33 a4=69 a5=141

Step-by-step explanation:

an=2an-1+3

We should attempt n=2 to find the second term

a2=2a1+3= 2*6+3=15

n=3 to find the third term

a3=2a2+3= 2*15+3=33

n=4 to find the fourth term

a4=2a3+3=2*33+3=69

n=5 to find the fifth term

a5= 2a4+3=2*69+3= 141

9514 1404 393

Answer:

  x, y ∈ all real numbers

Step-by-step explanation:

For your function ...

  f(x, y) = 2x^3·y -xy

there appear to be no values of x or y for which the function is undefined. The domain for both x and y is "all real numbers."

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]

∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]

                   [tex]$=P(27.5 \leq x \leq 28.5)$[/tex]

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5

Answer:

Standard error of: 2.47%

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

18% are older than 25.

This means that [tex]p = 0.18[/tex]

Simple random sample of 242 of the students.

This means that [tex]n = 242[/tex]

Standard error:

By the Central Limit Theorem:

[tex]s = \sqrt{\frac{0.18*0.82}{242}} = 0.0247[/tex]

0.0247*100% = 2.47%

Standard error of: 2.47%

Answer:

(x1 + x2) , (y1+y2)

   2              2

Step-by-step explanation:

Answer: 15 cups

Step-by-step explanation:

Answer:

-6/5

Step-by-step explanation:

- 2/3 (2 - 1/5)

Distribute

-2/3 *2 -2/3 *(-1/5)

-4/3 + 2/15

Get a common denominator

-4/3 *5/5 +2/15

-20/15 +2/15

-18/15

Simplify

-6/5

Answer:

3cx - 2c + 21x - 14

Step-by-step explanation:

( c + 7 ) ( 3x - 2 )

= c ( 3x - 2 ) + 7 ( 3x - 2 )

= c ( 3x ) - c ( 2 ) + 7 ( 3x ) - 7 ( 2 )

= 3cx - 2c + 21x - 14

Answer:

3cx-2c+21x-14

Step-by-step explanation:

try to expand it by multiplying everything in the first brackets by every thing in the second brackets.

c(3x-2)+7(3x-2)

3cx-2c+21x-14

I hope this helps

Answer:

y > -1/2 x + 4

Step-by-step explanation:

Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-4)/(2-4)= (x-0)/(4-0)

(y-4)/-2 = x/4

(-y+4)/2 = x/4

-y+4 = 1/2 x

-y = 1/2 x - 4

y = -1/2 x + 4

the solutions of the inequality are the points above this line, so

y > -1/2 x + 4

Answer:

2.5+2.5+45+45

=95.0m

therefore area of the square= 95.0m

45m×0.5=45.5÷95=

Step-by-step explanation:

2.5m

2.5 m tiles are required

[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]

Answer:

We should get a 3 about 5 times

Step-by-step explanation:

Possible outcomes 1,2,3,4,5,6

P(3) = number of 3's / total = 1/6

Expect a 3 = number of rolls * probability of a three

                  = 30 * 1/6

                       =5

Answer:

yes how can I help you???

Answer:

85%

Step-by-step explanation:

100% = 20

1% = 100%/100 = 20/100 = 0.2

now, how often does 1% fit into the actual result of 17 ? and that tells us how many %.

17/0.2 = 17/ 1/5 = 17/1 / 1/5 = 5×17 / 1 = 5×17 = 85%

Answer:

17/20×100=

85%

=85%

hope this helps

Answer:

8.6

Step-by-step explanation:

VW = WX / cos (36°)

= 7 / 0.81

= 8.6

Answer:

8.65

Step-by-step explanation:

cos 36° = 7 / VW

VW = 7 /  cos 36°

VW = 8.65

Answer:

3/4y +5/3 = x

Step-by-step explanation:

y = 4(3x-5)/9

Multiply each side by 9

9y = 4(3x-5)/9*9

9y = 4(3x-5)

Divide each side by 4

9/4 y = 4/4 (3x-5)

9/4y = 3x-5

Add 5 to each side

9/4y +5 = 3x-5+5

9/4y +5 = 3x

Divide by 3

9/4 y *1/3 +5/3 = 3x/3

3/4y +5/3 = x

Answer:

∠ DBC = 60°

Step-by-step explanation:

BD is an angle bisector , so

∠ DBC = ∠ ABD = 60°

angel ABD =60°

BD line is bisector

angel DBC=60° because both the angel are similar

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the ratio of the rectangle base to the triangle side length. Then the height of the small triangle above the rectangle will be x times the height of the equilateral triangle. Then the height of the rectangle is (1-x) times the height of the equilateral triangle. The rectangle's area will be ...

  A = bh

  A = (xL)(1-x)(L·√3/2) = (L²√3/2)(x)(1-x)

This graphs as parabola opening downward with x-intercepts at x=0 and x=1. The vertex is on the line of symmetry, halfway between these zeros, at x = 1/2.

The base of the rectangle is L/2.

The height of the rectangle is L√3/2.

_____

The general solution to this sort of problem is that one side of the rectangle is the midsegment of the triangle.

Answer:

626949

Step-by-step explanation:

Answer:

Part a: The correct answer is A, reject H0 because p value is less than . Part B: The correct answer is C, the percentage of adults that would erase their personal information online if they could is more than 51%.

Step-by-step explanation:

part a. The essential idea of hypothesis testing in statistics is to evaluate the probability p (p value) of some representative parameter, compared to a level of likelihood that is set before starting the test (). In this case, we are interested in a level of likelihood , which means that if the probability of the parameter is less than 5%, we will reject the hypothesis that this parameter is representing, since it's so unlikely. Of course, the significance level is arbitrary and must be payed attention, according to the particular situation. Therefore, the correct anser is A.

part b. Since we rejected the hypothesis to a 5% significance level, we reject the fact that less than 51% of adults would erase their personal information online if they could. This is equivalent to saying that a percentage of adults equal to or more than 51% would erase their personal information if they

9514 1404 393

Answer:

  -4

Step-by-step explanation:

The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...

  x = 1, y = -4

  y/x = -4/1 = -4

The slope of the line is -4.

Answer:

[tex](y - 0) = \frac{1}{3} (x - 0)[/tex]

[tex]y = \frac{1}{3} x[/tex]

Answer:

25827165

Step-by-step explanation:

from the question that we have here

the total population = 54 students

the sample size = 6 students

So given this information carol has to pick the total samples from the 54 students that we have here

the total ways that she has to do this

= 54 combination 6

= 54C6

= [tex]\frac{54!}{(54-6)!6!}[/tex]

= 25827165

this is the total number of possible samples that could occur given the total population of 54 students.

Answer:

the answer is A

okay that it have a nice day

Answer:

the answer above me is correct!

Step-by-step explanation:

Edge 2021

9514 1404 393

Answer:

  the correct choice is marked

Step-by-step explanation:

The end behavior matches that of an odd-degree polynomial. The only function shown that has that behavior is the one marked:

  [tex]f(x)=\dfrac{x^2-36}{x-6}=\dfrac{(x+6)(x-6)}{(x-6)}=x+6\qquad x\ne6[/tex]

__

Additional comment

The other functions have horizontal (not slant) asymptotes, so do not have the described end behavior.

  B: y=0

  C, D: y=1

The rate of change of R with time in the given equation is 0.004 ohm/s

Given parameters:

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]

To find:

First determine the value of R from the given equation;

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]

Finally, to determine the rate of change of R, differentiate the given equation.

[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]

[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]

Thus, from the given equation the rate of change of R with time is 0.004 ohm/s

Learn more here: https://brainly.com/question/14796851

Answer:

the verified answer is wrong.

Step-by-step explanation:

OP forgot to square R (34.286)

Answer:

$2884.62

Step-by-step explanation:

A year has 52 weeks

The number of times Charlie will receive a paycheck will be 52w ÷ 2w = 26 times

Charlie's gross income each paycheck will be 7500÷26 = $2884.62 every two weeks

75000 ÷ (52 ÷2)

7500 ÷ 26

$2884.62

Answer:

y=3.6

Step-by-step explanation:

The scale factor is 3/2.4. So 4.5/y=3/2.4. y=3.6

Sector area

Area of whole = 51.313

Area of unshaded = 9.424

Area of shaded = 41.8886

Answer:

Step-by-step explanation:

Find the area of the bigger circle:

Find the area of 120° sector AOC:

Find the area of smaller circle:

Find the area of 120° sector of DOB:

Now find the shaded area, the difference of areas of sectors:

Step-by-step explanation:

I'm not sure about it

Try it find examples

Step-by-step explanation:

so at the end 2=1

not sure but hopefully you get the idea :)