Based on the information in the table, is the cost of the apples proportional to the weight of apples?
A pound of apples:
2
3
4
5
Cost of apples:
$3.76
$5.64
$7.52
$9.40

[tex] \frac{3x {}^{2} }{5x {}^{2} } = \frac{3}{5} [/tex]

Considering the perimeter of the rectangle, it is found that 44 feet will be needed to go all the way around the room.

The perimeter of a rectangle of length l and width w is given by:

P = 2(l + w)

In this problem, we have that the length and the width, are respectively, given by l = 12 and w = 10, hence:

P = 2(l + w) = 2(12 + 10) = 44.

44 feet will be needed to go all the way around the room.

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Answer: 8109/77 in decimal form 105.31169

Step-by-step explanation: simplify 153/4

189 811  212  153

 ((———+———)+———)+———

   11  14   11   14

212

Simplify   ———

           11

Find the Least Common Multiple

     The left denominator is :       11  

     The right denominator is :       14  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

11 1 0 1

2 0 1 1

7 0 1 1

Product of all  

Prime Factors  11 14 154

Least Common Multiple:

     154

Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 14

  Right_M = L.C.M / R_Deno = 11

Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.      14535

  ——————————————————  =   —————

        L.C.M              154  

  R. Mult. • R. Num.      153 • 11

  ——————————————————  =   ————————

        L.C.M               154    

Adding fractions that have a common denominator :

7.4       Adding up the two equivalent fractions

14535 + 153 • 11     8109

————————————————  =  ————

      154             77

8109              

 ———— = 105.31169  

  77            

Answer:

  144

Step-by-step explanation:

For a bitstring of length n, there are Fibonacci(n+2) strings containing no two consecutive zeros. This can be seen by constructing the strings starting with n=1.

1-bit strings: 1, 0 -- 2 strings not containing consecutive 0s

2-bit strings: 11, 10, 01 -- 3 strings not containing consecutive 0s

Note that we have added 1 to all the 1-bit strings, and added 0 only to the string ending in 1.

3-bit strings: 111, 110, 101, 011, 010 -- 5 strings not containing consecutive 0s

Note that these 5 strings consist of all (3) of the 2-bit strings with 1 appended, and all (1) of the 2-bit strings ending in 1 with 0 appended. The number that now end in 0 is the number previously ending in 1.

__

If (x, y) represents the numbers of n-bit strings ending in (0, 1), then the number of (n+1)-bit strings ending in (0, 1) is (y, x+y). That is, the recursive relation is ...

  [tex](x_1,y_1)=(1,1)\\(x_n,y_n)=(y_{n-1},\,x_{n-1}+y_{n-1})\\b_n=x_n+y_n\quad\text{number of n-bit strings without consecutive 0s}[/tex]

For n=1 to n=10, these pairs are ...

  (1, 1), (1, 2), (2, 3), (3, 5), (5, 8), (8, 13), (13, 21), (21, 34), (34, 55), (55, 89)

The sequence of b[n] values is ...

  2, 3, 5, 8, 13, 21, 34, 55, 89, 144

which are the n=3 to n=12 numbers from the Fibonacci sequence.

That is, there will be Fibonacci(12) = 144 10-bit strings with no consecutive 0s.

Answer:

........................................

Answer:

The equation of the circle with centre (5, 6) and radius = 3 is x2 +y2 - 10x - 12y + 52 = 0.

I believe this is the answer.

Answer:

B

Step-by-step explanation:

If a=2, then a+5 is still less than 8. This counter example proves that b is not less than 5, but is less than 6.

The counterexample of the given statement is;

⇒ b = 5

Option B is true.

What is Function?

A relation between a set of inputs having one output each is called a function.

The conditions is given as;

If a + b < 8 and a = 2, then b < 5.

Now,

Let b = 5

Then, a + b = 2 + 5 = 7, is less than 8.

But b= 5 is not less than 5.

So, The counterexample of the given statement is;

⇒ b = 5

Option B is true.

Learn more about the function visit:

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Answer: 1/12

Step-by-step explanation:

Multiply the top which is 2. Multiply the bottom which is 24. Simplified by 2 is 1/12.

Lets have the younger person be x.
The older person will be 8x + 3.

The sum of their ages is 21, so we can get this equation:

x + (8x+3) = 21

9x+3 = 21
Subtract 3 from both sides
9x = 21

x=3 --> The younger person is 3 years old, and now we can substitute that for the older person (8x+3):

(3 * 8) + 3 = 27

The younger person is 3 years old, and the older person is 27.

eg. the first loan is x, the second loan will be (9,000 - x)

First, we need to make an equation based on the problem

first interest + second interest = 492

5% of x + 6% of (9,000 - x) = 492

This is the equation

Second, solve the equation and find out the value of x (first loan)

0.05x + 0.06(9.000 - x) = 492

0.05x + 540 - 0.06x = 492

-0.01x + 540 = 492

-0.01x = 492 - 540

-0.01x = -48

x = -48/-0.01

x = 4,800

Third, find the second loan

9,000 - x

= 9,000 - 4,800

= 4,200

SUMMARY

The first loan that has interest of 5% is $4,800

The second loan that has interest of 6% is $4,200

Answer:

(5-7)^2 because g(x) is the value of h(x) squared

x-7, s = 5

5-7)^2

Step-by-step explanation:

To find the degree of this function, you would look at the first term of the function, which is 3. So, the degree of this function would be 3.

Answer:

20

Step-by-step explanation:

The input (X) is 10. The output (Y) is 2X Which means 2 times X. So your answer is 2 × 10 which is 20.

Answer:

7.5 mph

Step-by-step explanation:

Answer:

Okay so all you need to know is the percentage of the hydrogen peroxide.
We know that the total solution is 400 ml and the hydrogen peroxide solution is 8ml.
8/400

Percent means out of a hundred, this can go multiple ways.

Way #1, benchmarking.

So 8/400 simplified is 1/50 or 2/100.
1/50 is basically 2/100.

And percent means out of a hundred so 2/100 is basically 2percent.

Way #2, proportions

We want to know the percentage of hydrogen/ fabric dye

If you put it in numbers int he same fraction and put “x” as the unknown 8ml hydrogen peroxide solution you’d get.

8/400 = x/100
X/100 because percent means out of a hundred.
Now solve3

Cross multiply,

800 = 400x
divide 400 on both sides

2=x

Now plug it back in the proportion.

8/400 = 2/100

If you simplify to check if they are equal then it’s correct

Answer:

It's a palindrome - in that it reads the same backwards as forwards - so long as the decimal point remains in the same place.

Step-by-step explanation:

Answer:

2/5?

Step-by-step explanation:

Answer:

4/10

Step-by-step explanation:

1/5 = 2/10

6/10 - 2/10 = 4/10

(if simplifyed your answer would be 2/5)

Answer:

5

Step-by-step explanation:

Answer:

x = 10, y = 20

Step-by-step explanation:

7x + 20 + 90 = 180 (adj angle on st line)

therefore x = 10

5x + 2y = 90 (vertically opposite angle)

2y = 40

y = 20

Answer:

Ray AC.

Step-by-step explanation:

They are the same; if you look at the figure, you can see that A and C are the same distance from each other and a ray in either direction would be equivalent to its counterpart.

Answer:

AC

Step-by-step explanation:

Answer:

The y intercept is 92, this is because:

In slope intercept equations, it is formatted like:

y = mx + b

where y is the dependent variable and x is the independent variable

m is the slope

and b is the y - intercept

In terms of this situation, 92 means I think probably the start of their latest grades.

Answer:

straight angle and right angle virtually opposite angle

Answer:

c

Step-by-step explanation:

Exponent division rule: If base are same for any two variables, then subtract the powers.

[tex]\dfrac{a^{m}}{a^{n}}=a^{m-n}[/tex]

[tex]\dfrac{f^{6}h^{9}}{f^{3}h^{7}}=f^{6-3}h^{9-7}\\\\\\ =f^{3}h^{2}[/tex]

Answer:A

Step-by-step explanation:

I just did this one and that was correct

Answer:

1/3 x 10 = 10/3, 10/3 = 3 1/3

Step-by-step explanation:

For 10 people he only would need 3 cups and 1/3 so he does have enough

Answer:

Step-by-step explanation:

Here we have relation between gallons of gas and the distance

The range depends on the domain which is limited up to 12 gallons

The range is:

Data set: