What property justifies the equation: 3(x - 5) = 3x - 15*
associative
distributive
addition property of equality
commutative

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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Answer:

A.336 cubic centimeter

Step-by-step explanation:

6cm×8cm×7cm=336

Answer:

b=10

Step-by-step explanation:

I think the other part would be √-300   √3   but that's the best i could do

(a) The value of #C(5) = 13.

(b) In the brute-force method, all binary strings of length n are listed and those that contain consecutive 1s are rejected. So a brute-force approach used to compute #C(5).

(c) Using the Theorem of Induction, we proved that #C(C) = #C(l – 1) + #C(l – 2) for l ≥ 2.

Let #C(l) denote the number of binary strings with length l that have no consecutive occurrences of a 1.

For example #C(3) 5; we can list all binary strings of length 3 and determine by inspection that only the strings 000, 001, 010, 100, and 101 have no consecutive occurrences of a 1.

(a) We have to compute #C(5).

All binary strings with length five include:

00000, 00001, 00010, 00100, 00101, 01000, 01001, 01010, 10000, 10001, 10010, 10100, 10101

Strings that don't have successive 1s in them.

So #C(5) = Total number of binary strings with length five

#C(5) = 13

(b) We have to describe why a brute-force approach used to compute #C(5).

In the brute-force method, all binary strings of length n are listed and those that contain consecutive 1s are rejected. The complexity is at least exponential, thus even for modest values of n (like 40 or 50), it will take a long time to process the number of binary strings of length n = 2n.

(c) We have to show that #C(C) = #C(l – 1) + #C(l – 2) for l ≥ 2 and derive a recursive algorithm to compute #C(C).

No empty string contains two consecutive ones.

So #C(0) = 1,

#C(1) = 2 ( 0 and 1)

Base Case : For l = 2,

#C(2) = |{00, 10, 11}|

#C(2) = 3

#C(2) = #C(1) + #C(0)

Consequently, the recurrence is true, for l = 2.

Number of strings with the character 0 = 2 = #C (1)

Theorem of Induction

Assume that the recurrence holds for every l < k and the quantity of strings with 0 = #C(l-1)

Induction Step :

For l = k+1,

#C(k+1): Only those strings of length k that do not include consecutive 1s will be the first string in such strings. These strings will never result in consecutive 1s when a 0 is added.

Thus, the number of strings that end in 0 = #C(k)

Only strings of length k that finish in 0 can be added to.

The number of such strings, by induction = #C(k-1)

Hence, #C(k+1) = #C(k) + #C(k-1)

Recursive Algorithm:

NoCon1(n)

{

1. if n < 0 : return 0

2. if n == 0 : return 1

3. if n==1 : return 2

4. return NoCon1(n-1) + NoCon1(n-2);

}

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The maximum sustainable rate of harvest which is possible for the growth of fish P(t)  according to the differential equation " P' = 4P - 4P^2 - h " will be at the harvest rate of h=3.

In order to calculate the maximum sustainable harvest rate possible, we are required to find the equilibrium solutions of the differential equation firstly. Equilibrium solutions occur when P' = 0, so we can set the right-hand side of the differential equation at 0.

4P - 4P² - h = 0

Now a quadratic equation is formed in terms of P, which can be used to obtain P.

P = (1 ± √(1 + h))/2

There are two equilibrium solutions, obtained by these two values of P.

Now, in order to obtain a maximum sustainable harvest rate, we are required to have both equilibrium solutions to as positive ( as negative populations don't make any sense in this context).

Therefore, we have to find the largest value of h for which both of these equations have positive solutions:

(1 + √(1 + h))/2 > 0

(1 - √(1 + h))/2 > 0

On camparing both the inequalities, it can be concluded that the first inequality is always true, since the square root of a positive number is always positive. The second inequality is true when h < 3.

Hence, the maximum sustainable harvest rate is is found to be at h = 3. If the harvesting rate is greater than 3, then there will be no positive equilibrium solutions and the population will eventually be perished.

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Answer:

increases

Step-by-step explanation:

on on the side, it looks like you need to enter stuff into the table. All you need to do is copy the numbers from the table and transfer them to the empty one.

also this answer just makes sense. If you look at the table, you can see for the x values, they are always increasing. For The y values they are also increasing. Therefore, is the number of hours studying increases the corresponding test scores also increase

Answer:

If it's multiple choice, I'd say B and D. If it's only one, those are the ones I'd narrow it down to.

Step-by-step explanation:

All you have to do is imagine the question's answers as a statistic. With A, you can't say "There are 56% theaters in my city." So that's out. C is the same, you cant say "The students in my class watch 47% movies in a month." Also out. Sorry if this answer is incorrect, but that's your best bet.

Answer:

g(x)=6 and f(x)=3 these are your answers for this equation

Answer:

4 feet wide because to find the perimeter you add all the numbers around

Using proportions, it is found that one sandwich costs $4.25.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Considering x as the cost of a sandwich, the total cost is given as follows:

1.08(3x + 1.75) + 5 = 20.66.

The multiplication by 1.08 is because of the sales tax. We solve for x to find the cost of one sandwich, hence:

1.08(3x + 1.75) = 15.66

3x + 1.75 = 14.5

3x = 12.75

x = 12.75/3

x = 4.25.

Hence one sandwich costs $4.25.

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We have to calculate the absolute value of (-5+2+6)

Answer:

65

Step-by-step explanation:

using the ratio we can find the side lengths of the other triangle.

since it is 2:5

6:x=2:5

so x = 15(first side)

8:x=2:5

so x = 20(second side)

12:x=2:5

x=30(third side)

so then we add them up

15+20+30

65

hope this was helpful

Answer:

3.82165605 and rounded is 4

Step-by-step explanation:

The radius would be 4 cm or to be exact 3.82165605 cm

Answer:

4:5

Step-by-step explanation:

A pair of complementary add up to 90, given that one of them is 50, we can do this: x + 50 = 90

solve it and we get x = 40

40 + 50 = 90, so 40 and 50 are the pair of complementary angles.

As for it's Ratio, we can just get the pair and have it as 40:50 but we can reduce it to 4:5

Answer: 3 hours and 15 minutes

Step-by-step explanation:

Answer:

Time taken by Rahm to write the essay and finish the science project = 12.5 hours    

Step-by-step explanation:

Now, we need to find the total time spent by Rahm to finish the both writing the essay and the science project.

Hence, Time taken by Rahm to write the essay and finish the science project = 12.5 hours

Answer:adjective. damaged or spoiled to a certain extent; made less perfect, attractive, useful, etc.: We can all get preoccupied with the marred aspects of our character.

Step-by-step explanation:

adjective. damaged or spoiled to a certain extent; made less perfect, attractive, useful, etc.: We can all get preoccupied with the marred aspects of our character.

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

\(2.8 \times 4.6 \\ \\ = 12.88\)

it's was helpful to you

Step-by-step explanation:

a + b = 16

a = 16 - b

45a + 30b = 585 | divide both sides by 15

3a + 2b = 39

now we are using the first in the second equation :

3(16 - b) + 2b = 39

48 - 3b + 2b = 39

48 - b = 39

48 = 39 + b

9 = b

he sold 9 pairs of type b socks.

FYI :

a = 16 - b = 16 - 9 = 7

Answer:

The second store with the 6 foot is better pricing.

Step-by-step explanation:

find out how much each foot cost on each sandwich

42.5/5=8.5

49.5/6=8.25

The first store sells each foot of sandwich for 25 cents cheaper.

Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the System of equations.

To determine the duration of each workout plan, let's assume that both Plan A and Plan B have a fixed duration. Let's denote the duration of Plan A as "x" hours and the duration of Plan B as "y" hours.

From the given information, we can form the following equations:

On Wednesday:

5 clients did Plan A, so the total duration for Plan A is 5x hours.

6 clients did Plan B, so the total duration for Plan B is 6y hours.

The total training duration on Wednesday is 7 hours, so we have the equation: 5x + 6y = 7   ... Equation (1)

On Thursday:

3 clients did Plan A, so the total duration for Plan A is 3x hours.

2 clients did Plan B, so the total duration for Plan B is 2y hours.

The total training duration on Thursday is 3 hours, so we have the equation: 3x + 2y = 3   ... Equation (2)

We now have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.

Multiplying Equation (1) by 2 and Equation (2) by 5 to eliminate the y variable, we get:

10x + 12y = 14   ... Equation (3)

15x + 10y = 15   ... Equation (4)

Multiplying Equation (3) by 3 and Equation (4) by 2 to create a new system of equations:

30x + 36y = 42   ... Equation (5)

30x + 20y = 30   ... Equation (6)

Subtracting Equation (6) from Equation (5), we can eliminate the x variable:

(30x + 36y) - (30x + 20y) = 42 - 30

16y = 12

y = 12/16

y = 0.75

Substituting the value of y into Equation (2), we can solve for x:

3x + 2(0.75) = 3

3x + 1.5 = 3

3x = 3 - 1.5

3x = 1.5

x = 1.5/3

x = 0.5

Therefore, the duration of Plan A is 0.5 hours, and the duration of Plan B is 0.75 hours.

Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the system of equations.

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The time it would take you to run 3.1 miles given the time it takes you to run a mile is 24 minutes 48 seconds.

Multiplication is a mathematical operation that is used to determine the product of a number. The sign used to represent multiplication is ×.

In order to determine the time, multiply 3.1 miles by 8 minutes

3.1 x 8 = 24.8 =  24 minutes 48 seconds.

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The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Step-by-step explanation:

The coordinates and vertices

which reflected over the y- axis are

r(-2,0) , s(2,-3) , and t(2,3).

well, we know the pants are 25% off, that means the current sale price is only 75% of the original price, say the original price is "x" or 100%.  So we know that $24.60 is 75%, what is the 100%?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 24.6&75\\ x&100 \end{array}\implies \cfrac{24.6}{x}=\cfrac{75}{100}\implies \cfrac{24.6}{x}=\cfrac{3}{4} \\\\\\ 98.4=3x \implies \cfrac{98.4}{3}=x\implies 32.8=x\)

Answer: Hope this helps you!

B

Step-by-step explanation:

A, B, and C don't have are numbers without a square route that is rational.

However D is rational as the square route of 25 is 5, hence making it rational.