If solids above are boxes being measured for moving, which of the solids above uses the best units?

A. Solid A

B solid B

C solid C

Answer:

\(C.\)  \(400\)

Step-by-step explanation:

\(19.7/0.0485\)

\(=406.18556701030927835051546391752577319587628865979381443298969\)

The number closest in value to 19.7/0.0485 is 400.

The correct option is C.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

We have the expression,

19.7/0.0485 = 406.1855

From the options,

400 is closest to 406.1855.

Therefore, 400 is closest to 406.1855.

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Answer:

3 and 3/4

Step-by-step explanation:

Answer:

121.5 :) hope this helped

Answer:23

Step-by-step explanation:

Answer:

113, 118, 151, 162, 167, 181, 206, 207, 228, 232, 232, 233, 233, 247, 248, 251, 253, 255, 256, 276

Step-by-step explanation:

Good luck man :)

Answer: looks at the picture

Step-by-step explanation: hope this help :)

The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Answer:116,600

Step-by-step explanation:5,500 x 20 = 110,000 + 6% = 116,600

\(answer \\ = (4.5 , 1.5) \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps\)

Answer:

(-1,-1)

Step-by-step explanation:

If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).

Answer:

The slope of line q is -7/6

Step-by-step explanation:

To find the slope of a perpendicular line, you need to find the opposite reciprocal. So, flip the fraction (7/6) and then take the opposite, (-7/6).

Hope this helps!

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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Answer:

x = 14

Step-by-step explanation:

∠A = (8x – 12) and ∠B = (6x + 14)

∠A = ∠B because they are vertical angles

then:

(8x – 12) = (6x + 14)

reduce:

2x = 28

x = 14

Answer:

3 is known as the power of 2.

Answer:

The three is the exponent, it is also called power so 2 to the power of 3

Step-by-step explanation:

Answer:

yes it can be

Answer:

Step-by-step explanation:

1.33 and 1.3 are not the same, although they share the digits 1.3.

1.33 is accurate to the hundredths place, whereas 1.3 is accurate only to the tenths place.

So:  1.33 and 1.3 are in the same ball park, but are not the same.

This is because of the rule that if we have rational coefficients, then one root of \(a+\sqrt{b}\) must have a conjugate pair of \(a-\sqrt{b}\). Multiplying the conjugates will have the square roots cancel out.

For more information, check out the difference of squares rule.

Answer:

$448

Step-by-step explanation:

Answer:

2.9661582

Step-by-step explanation:

2.9661582e+16 this is the answer

Therefore, $3292213⁴¹ \mod 100$ is equal to $71$. In this calculation, we required $2$ multiplications ($69⁵$ and $4761²$), and all the numbers we multiplied had $2$ digits.

To compute $3292213⁴¹ \mod 100$ efficiently, we can use the property of modular arithmetic that states $(a \cdot b) \mod m$ is equal to $[(a \mod m) \cdot (b \mod m)] \mod m$.

Let's break down the calculation step by step:

Step 1: Simplify $3292213 \mod 100$

Since the remainder when dividing $3292213$ by $100$ is $13$, we have $3292213 \mod 100 = 13$.

Step 2: Simplify the exponent $41$

We can divide $41$ by $4$ and find that the remainder is $1$. Therefore, we can write $41$ as $4 \cdot 10 + 1$.

Step 3: Rewrite the expression using modular arithmetic property

Using the property mentioned earlier, we can rewrite the expression as $(3292213⁴ \cdot 3292213¹⁰ \cdot 3292213¹) \mod 100$.

Step 4: Calculate $3292213⁴ \mod 100$

To calculate $3292213⁴ \mod 100$, we compute $13⁴ \mod 100$. This simplifies to $169 \mod 100$, which is $69$.

Step 5: Calculate $3292213¹⁰ \mod 100$

To calculate $3292213¹⁰ \mod 100$, we compute $13¹⁰ \mod 100$. This simplifies to $169⁵ \mod 100$, which further simplifies to $69⁵ \mod 100$. This can be computed by repeatedly squaring: $69² = 4761 \mod 100$, $69⁴ = 4761² \mod 100$, and $69⁵ = 4761² \cdot 69 \mod 100$. The result is $89$.

Step 6: Calculate $3292213¹ \mod 100$

To calculate $3292213¹ \mod 100$, we compute $13¹ \mod 100$, which is $13$.

Step 7: Multiply the simplified expressions

To find the final result, we multiply the three simplified expressions together: $69 \cdot 89 \cdot 13 \mod 100$. This simplifies to $71 \mod 100$.

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The remainder when 3292213⁴¹ is divided by 100 is 13, and the calculations required 5 multiplications. The maximum number of digits in the numbers we had to multiply was 18.

To compute 3292213⁴¹ mod 100 efficiently, we can use modular arithmetic properties and simplify the calculations.
First, let's find the remainders when 3292213 is divided by 100. 3292213 divided by 100 gives us a quotient of 32922 and a remainder of 13. So, we can rewrite the expression as (100 * 32922 + 13)⁴¹ mod 100.
Next, we can apply the binomial theorem to expand the expression. However, most terms in the expansion will have powers of 100, which will not affect the remainder when divided by 100. So, we only need to focus on the terms involving 13⁴¹.
To calculate 13⁴¹ efficiently, we can use exponentiation by squaring. We can start by squaring 13, then repeatedly squaring the result to get the desired power.

Here's the breakdown:
13^2 = 169
13^4 = (13²)² = 169² = 28561
13^8 = (13^⁴)² = 28561² = 815372721
13^16 = (13^⁸)² = 815372721² = 664383887546445441
13^32 = (13^¹⁶)² = 664383887546445441² = 441806812314554874942185426169281
Finally, we multiply 13³² by 13⁸ to get 13⁴⁰, and then multiply the result by 13 to get 13⁴¹.
The number of multiplications required was 5, as we squared 13 five times.
The numbers we had to multiply had a maximum of 18 digits (441806812314554874942185426169281).

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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Answer:

I would go with answer option A.

Step-by-step explanation:

Hope this helps. Also  have an Amazing Day!

A reasonable prediction for the number of times a pink paper clip will be drawn is 18. Option D.

To determine a reasonable prediction for the number of times a pink paper clip will be drawn when a random paper clip is drawn and replaced 50 times, we need to consider the relative proportions of each color of paper clip in the bag.

The bag contains a total of 9 pink paper clips out of a sum of 9 + 7 + 5 + 4 = 25 paper clips in total. To find the probability of drawing a pink paper clip in a single draw, we divide the number of pink paper clips by the total number of paper clips: 9 / 25 = 0.36.

Since each draw is independent and the paper clip is replaced after each draw, the probability of drawing a pink paper clip remains constant at 0.36 for each subsequent draw. This means that in a large number of draws, we would expect approximately 36% of the draws to result in a pink paper clip.With 50 draws in total, we can predict the number of times a pink paper clip will be drawn by multiplying the probability of drawing a pink paper clip (0.36) by the total number of draws (50): 0.36 * 50 = 18.

Therefore, a reasonable prediction for the number of times a pink paper clip will be drawn is 18, SO Option D is correct.

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The sum of the first $20$ terms of the arithmetic sequence is $420$.

In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:

Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.

Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:

$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.

To find the twentieth term, we use the following equation:

$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.

Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:

Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.

Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.

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Answer:

x  =  500 yd

y  =  250 yd

A(max) = 125000 yd²

Step-by-step explanation:

Let´s call x the side parallel to the stream ( only one side to be fenced )

y the other side of the rectangular area

Then the perimeter of the  rectangle  is  p  =  2*x  + 2* y  ( but only 1 x will be fenced)

p  =  x  +  2*y

1000  =  x   +  2 * y         ⇒    y  =  (1000 - x )/ 2

And   A(r)  =  x * y

Are as fuction of x

A(x)  =  x  *  (  1000  -  x ) / 2

A(x)  =   1000*x / 2 -  x² / 2

A´(x)  =  500  -  2*x/2

A´(x)  =  0              500   -  x   =  0

x  =  500 yd

To find out if this value will bring function A to a maximum value we get the second derivative

C´´(x)  =  -1         C´´(x) < 0  then efectevly we got a maximum at  x  = 500

The side  y  = ( 1000  -  x ) / 2

y  =  500/ 2

y  =  250 yd

A(max)  =  250 * 500

A(max) = 125000 yd²

The value of R(x) term is 36.

We are given that;

The equation x³ + 2x² - 72x - 28

Now,

We divide the first term, 8x, by the first term of d(x), which is x. This gives us 8, which is the third term of Q(x). We write 8 above the division bar and multiply it by d(x), which gives us 8x - 64. We subtract this from the new dividend, which gives us 36.

Since we cannot divide 36 by x-8 any further, we stop here and write 36 as the remainder R(x).

   x² + 10x + 8

  _______________

x-8 | x³ + 2x² - 72x - 28

    - (x³ - 8x²)

    -------------

        10x² - 72x

      - (10x² -80x)

      -------------

             8x -28

           - (8x -64)

           ----------

                36

Q(x) = x² + 10x + 8 and R(x) = 36.

Therefore, by the equation the answer will be R(x) = 36.

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a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

To write a rational number as a decimal, you need to divide the numerator by the denominator. Let's go through each option to determine which decimal is repeating or terminating.

a. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

b. 0: This decimal is also terminating because there are no numbers after the decimal point. The rational number is 0.

c. 0.16 overbar: This decimal has a line over the 16, indicating that it is repeating. The rational number is 0.161616...

d. 0: This decimal is terminating because there are no numbers after the decimal point. The rational number is 0.

So, to summarize:

a. The decimal is terminating and the rational number is 0.

b. The decimal is terminating and the rational number is 0.

c. The decimal is repeating and the rational number is 0.161616...

d. The decimal is terminating and the rational number is 0.

.

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Answer:

86 degrees

Step-by-step explanation:

94+86=180

Answer:

A supplementary angle is an angle that completes 180 degrees.

Thus, an 86 degree angle would be supplementary to a 94 degree angle.

Step-by-step explanation:

Answer:

a + b + c = m

=> (a + b+ c)³= m³

⇔m³ = a³ + b³ +c³ + 3(a + b)(a + c)(c + b)

=> m³ + 2p³ = 3a³ + 3b³ + c³ + 3(a + b)(a + c)(b + c)

with c = 0 => m³ + 2p³ = 3a³ + 3b³ + 3ab(a + b)

have:

3mn = 3(a + b + c)(a² + b² + c²)

with c = 0

=> 3mn = 3(a + b)(a² + b²) = 3[a³ + ab² + ba² + b³]

=  3a³ + 3b³ + 3(a²b + ab²)

= 3a³ + 3b³ + 3ab(a + b)

= m³ + 2p³

=> 3mn = m³ + 2p³

Step-by-step explanation:

Given the conditions a + b + c = m, a² + b² + c² = n, and a³ + b³ + c³ = p, we are required to prove that if c = 0, then m³ + 2p³ = 3mn.

If c = 0, then the equations become a + b = m, a² + b² = n, and a³ + b³ = p.

Using the sum of cubes identity (a³ + b³ = (a + b)(a² - ab + b²)), we can rewrite the third equation as (a + b)(a²- ab + b²) = p.

Since a + b = m, we can substitute this value into the above equation: m(a² - ab + b²) = p.

Now, we'll square the first equation (a + b = m) to get a² + 2ab + b² = m². Rearranging, we find ab = (m² - n)/2.

Substituting this value of ab into the equation m(a² - ab + b²) = p, we get m(a² + b² - (m² - n)/2) = p.

Now, we know that a² + b² = n, so we can replace a² + b² in the equation: m(n - (m² - n)/2) = p.

Simplifying the equation further, we get

mn - (m³ - mn)/2 = p.

Finally, rearranging the equation, we find that

m³ + 2p³ = 3mn.

Thus, we have proved that if c = 0, then m³ + 2p³ = 3mn.

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Answer:

v/5*3

Step-by-step explanation:

The volume of 5 balls is V cm. Express the volume of 3 balls in terms of V

v/5*3

Step-by-step explanation:

5 balls volumes = V cm

1 ball volume = V/5 cm

:. 3 balls volumes = 3×V/5 = 3V/5 cm

the volume of 3balls is 3V/5 cm.

hope this helps you.