Solve for k : (5k - 2 )/ 3k =7

Answer:

We have the sentence:

"X by the power of 5 times y to the power of 6 over 2 by the power of -2 times x by the power of 0times x by the power of 9"

Let's break it into parts.

"X by the power of 5 times y to the power of 6..."

This can be written as:

x^5*y^6

"...  2 by the power of -2 times x by the power of 0times x by the power of 9"

This can be written as:

2^(-2)*x^(0)*x^(9)

And we have the quotient between the first thing and the second thing, then the equation is:

\(\frac{x^5*y^6}{2^{-2}*x^0*x^9}\)

And any number by the power of 0 is equal to 1, then:

x^0 = 1, then we can rewrite the equation as:

\(\frac{x^5*y^6}{2^{-2}*x^9}\)

We can keep simplifying this.

We know that:

a^(-n) = (1/a)^(n)

Then:

2^(-2) = (1/2)^2 = 1/4

Then we get:

\(\frac{x^5*y^6}{2^{-2}*x^9} = \frac{x^5*y^6}{x^9}*4\)

And we also know that:

a^n/a^m = a^(n - m)

Then:

\(\frac{x^5*y^6}{x^9}*4 = 4*y^6*\frac{x^5}{x^9} = 4*y^6*x^{5 - 9} = 4*y^6*x^{-4} = \frac{4*y^6}{x^4}\)

And we can't simplify this anymore.

To solve this problem, we can use a recursive approach to calculate the sum of all subtrees and keep track of the frequency of each subtree sum using a dictionary. We then find the most frequent subtree sum and return all the values with the highest frequency.

Here's a detailed explanation of how to solve this problem:

We start by defining a recursive function that takes a node as input and returns the sum of the subtree rooted at that node. The function calculates the sum of the left subtree, the right subtree, and the node value, and returns their sum as the result.

Next, we create a dictionary to keep track of the frequency of each subtree sum. We traverse the tree using the recursive function and update the frequency of each subtree sum in the dictionary.

After traversing the entire tree, we find the most frequent subtree sum by iterating over the dictionary and keeping track of the maximum frequency. We then iterate over the dictionary again and add all the subtree sums with the highest frequency to a list.

Finally, we return the list of most frequent subtree sums.

Here's a Python implementation of the solution:

```
from collections import defaultdict

class TreeNode:
   def __init__(self, val=0, left=None, right=None):
       self.val = val
       self.left = left
       self.right = right

def findFrequentTreeSum(root):
   freq_dict = defaultdict(int)
   
   def sum_subtree(node):
       if not node:
           return 0
       left_sum = sum_subtree(node.left)
       right_sum = sum_subtree(node.right)
       subtree_sum = left_sum + right_sum + node.val
       freq_dict[subtree_sum] += 1
       return subtree_sum
   
   sum_subtree(root)
   max_freq = max(freq_dict.values())
   result = [key for key, value in freq_dict.items() if value == max_freq]
   return result
```

Note that this solution has a time complexity of O(n) and a space complexity of O(n), where n is the number of nodes in the tree.

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Answer:

first quarter

Step-by-step explanation:

Based on the price the computer was reduced by and the profit the shopkeeper still made, if the computer was sold at full price, the profit percentage would have been 50%.

First assume a price the computer was sold at. We'll go with $100.

At this price, the shopkeeper still made a profit of 20% which means that the cost price was;

= 100 / (1 + 20%)

= $83.33

Based on the discounted price of $100, the full price was:

= 100 / (1 - 20%)

= $125

The profit the shopkeeper would have made is:

= (Full price - Cost price) / Cost price x 100%

= (125 - 83.33) / 83.33 x 100%

= 50%

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Considering the definition of an inequality, an inequality that represent the possible values for the number of hotdogs purchased and the number of drinks purchased is \(\bold{4.50h + 3d \leq 70}\).

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

In this case, you know that:

Each hotdog costs $4.50 and each drink costs $3.

Mamadou has a total of $70 to spend on hotdogs and drinks.

Being:

the inequality that expresses the previous relationship is

\(\bold{4.50h + 3d \leq 70}\)

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The inequality that represents the possible values for the number of hotdogs and drinks purchased is 4.50ℎ + 3d ≤ 70.

To write an inequality that represents the possible values for the number of hotdogs purchased, ℎ h, and the number of drinks purchased, �, we can use the following equation:

4.50ℎ + 3d ≤ 70

This inequality states that the sum of the cost of the hotdogs (4.50 multiplied by the number of hotdogs) and the cost of the drinks (3 multiplied by the number of drinks) should be less than or equal to 70, which is the total amount of money Mamadou has to spend.

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ANSWER

a. 1.25 + 1.5x = 8.75

b. 5 games

EXPLANATION

We have that:

Shoe rental = $1.25

Games = $1.50 per game

He spent a total of $8.75.

a. Let the number of games played be x.

This means that the cost of shoe rental and the total cost of x games must be equal to $8.75. Therefore:

1.25 + (1.50 * x) = 8.75

1.25 + 1.5x = 8.75

That is the equation that represents Frank's situation.

b. To find the number of games he bowled, we have to find x:

1.25 + 1.5x = 8.75

=> 1.5x = 8.75 - 1.25

1.5x = 7.5

Divide both sides by 1.5:

x = 7.5 / 1.5

x = 5

He bowled 5 games.

Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9

Answer:

7

Step-by-step explanation:

If you divide 8y / 8  then you have to do the same thing to 56. When you do, y  = 7

Answer:

Step-by-step explanation:

I got it right on I-ready.

Hope this helps!

From: Aug1e

Answer:

37

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

You can use absolute value to solve this. l-12l+l25l=12+25=37

Absolute value is the distance from 0.

Answer:

51

Step-by-step explanation:

A^2+b^2=c^2

That's the formula

Answer:

Trevon is 15

Step-by-step explanation:

If Issac is 5 years older than Trevon, and the ratio is 4:3, then we can multiply one or both of them to be compared by.

If Issac is 10, for example, then Trevon would be 5, giving a 2:1 ratio

When we multiply the ratio, we eventually see a point where Issac's (first number) age is 5 more than Trevon's (second number) age:

( 4:3 ) 3 = 12:9
( 4:3 ) 4 = 16:12
( 4:3 ) 5 = 20:15

Issac is 20 and Trevon is 15

There's probably an easier way to solve problems like these but this was what came to mind at first hope this helps

Answer:

Trevon is 15

Step-by-step explanation:

let Trevon's age be x then Issac is x + 5

the ratio of Issac : Trevon = 4 : 3

set up a proportional equation

\(\frac{Issac}{Trevon}\) , that is

\(\frac{x+5}{x}\) = \(\frac{4}{3}\) ( cross- multiply )

4x = 3(x + 5)

4x = 3x + 15 ( subtract 3x from both sides )

x = 15

So Trevon is 15 and Issac is x + 5 = 15 + 5 = 20

Answer:

2) x=11

Step-by-step explanation:

1) u got the first one right x=90°

2)

2x-1+69=90

2x-1=21

2x=22

x=11

Answer:

y=2205

Step-by-step explanation:

5+y-5/34+3*7-6=45

combine terms on each side

y/49=45

multiply 49 on each side

y=2205

i hope this helps you

Answer:

y=855/34 or 25 5/34

Step-by-step explanation:

Rewrite

5+y-5/34+3x7-6=45

Calculate Sum or differnce

5+y-5/34+21-6=45

Caculate difference

20+y-5/34=45

Move constant to the right

675/34+y=45

Caculate Difference

y=45-675/34

y=855/34 or you could put 25 5/34

Answer:

− 3 w 2 + 9 w + 1

The runner has to run more 8.808 km to finish the race.

So, the runner ran 1.192 km out of 10 km.

Then, the remaining distance:

Therefore, the runner has to run more 8.808 km to finish the race.

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The half-life of a certain chemical in the human body is 4 hours. In the second part, we will calculate the exponential decay rate and the time it takes for 91% of the chemical to leave the body.

a) The exponential decay rate can be calculated using the formula: decay rate = ln(2) / half-life. The natural logarithm of 2 is approximately 0.693. Therefore, the decay rate is 0.693 / 4 = 0.17325 or approximately 17.3%.

b) To determine how long it will take for 91% of the chemical to leave the body, we can use the formula for exponential decay: N(t) = N₀ * e^(-kt), where N(t) is the amount remaining after time t, N₀ is the initial amount, e is the base of the natural logarithm, k is the decay rate, and t is the time.

We need to find the value of t for which N(t) is equal to 91% of the initial amount, which is 0.91 * N₀. Substituting the values, we have:

0.91 * N₀ = N₀ * e^(-0.17325t).

By canceling out N₀ from both sides and taking the natural logarithm of both sides, we can solve for t:

ln(0.91) = -0.17325t.

Dividing both sides by -0.17325, we find:

t = ln(0.91) / -0.17325.

Using a calculator, we can evaluate this expression to find the value of t. It turns out to be approximately 4.018 hours.

Therefore, the answers to the given questions are:

a) The decay rate of the chemical is approximately 17.3%.

b) It will take approximately 4.0 hours for 91% of the chemical consumed to leave the body.

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Answer:

6x - 4

Step-by-step explanation:

Perimeter is equal to double the length plus double the width, and if you use this to find perimeter, you would get that the perimeter = 2(2x-7)+2(x+5), which simplifies to 4x - 14 + 2x + 10, which simplifies to 6x - 4. That means that the rectangle's perimeter is 6x-4.

Answer: D

Step-by-step explanation:

\(V=\frac{1}{3}\pi r^{2} h\) is the general formula for the volume of a cone with radius r and height h.

Substituting in s for both r and h, \(V=\frac{1}{3}\pi s^{3}\).

Answer: $40.95

Step-by-step explanation:

65 times 40%=26

So 40% off is 26 dollars off

The price is $39

Then when you add the sales tax by  doing 39 times 5%, you see that the sale tax is $1.95

39+1.95= $40.95 for the jacket

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer is 3a - 2b =  \(\sqrt{(13 - 6\sqrt3)}\angle(tan_(-1)[(3a - 2b) / \sqrt3])\)

Vectors a and b have a magnitude of 1. The angle between ä and b is 30°. We have to calculate 3a - 2b.

Step 1: Magnitude of the vector a and b
Magnitude of vector a = 1
Magnitude of vector b = 1

Step 2: Dot Product of vector a and b. The dot product of two vectors is the product of their magnitudes and cosine of the angle between them.

Formula: a . b = |a||b|cosθ Where, θ is the angle between vectors a and b.

|a| = 1,

|b| = 1θ

= 30°cos 30°

= √3/2a . b

= |a||b|cosθ

= 1 × 1 × √3/2

= √3/2

Step 3:

3a - 2b = |3a - 2b|∠(3a - 2b)

Here,

3a - 2b

= 3(a) - 2(b)3a - 2b

= 3a - 2b

Since the vectors are not perpendicular to each other.

Therefore, the magnitude of

\(3a - 2b\)  is  \(\sqrt{(3)^2 + (-2)^2 + 2(3)(-2)cos30}\)

= √[(9 + 4 - 12 × √3/2)]

= √[(13 - 6√3)]∠(3a - 2b)

=\(tan^_{(-1)}\)[(3a - 2b) sin30°/ (3a - 2b) cos30°]

=\(tan^_(-1)[(3a - 2b)\)\(/ \sqrt3]\)

Therefore,

3a - 2b

= \(\sqrt{(13 - 6\sqrt3)}\angle(tan_(-1)[(3a - 2b) / \sqrt3])\)

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Answer:

1/2

Step-by-step explanation:

Answer:

it is 1/2 or 9/18

Step-by-step explanation:

there was 18 shirts all together and half were white

good luck!

Answer:

There are 5 shifts per day

Step-by-step explanation:

7 1/2 is equal to 7.5 and 1 1/12 is equal to 1.5

7.5/1.5= 5

Answer:

Step-by-step explanation:

Depends on what you mean by multiplying by - 1.  I assume you are not going to multiply the y or f(x) term by - 1.

If that is so, take an example. Suppose you have a graph that is y=x^2

That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.

When you multiply the right hand side by - 1, the graph you get will be y = - x^2.

That opens downward and the focus is on the - y axis.

That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.

Answer:

c

Step-by-step explanation:

ape x

Answer:

Step-by-step explanation:

The statement describes a set of interest in a study, which is the set of all elements being investigated or under consideration. It is not a sample, which refers to a subset of the population being studied.

The set of all elements of interest in a study is called the population. It refers to the entire group of individuals, objects, or measurements that are being studied and from which data can be collected. The population can be finite or infinite and can include people, animals, plants, materials, or any other object or concept of interest. In statistical analysis, researchers use samples of the population to make inferences or draw conclusions about the entire population. By selecting a representative sample, researchers can reduce the cost and time required for data collection and analysis while still obtaining valid and reliable results.

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To find how many interfere lie between 168 and 15, simply subtract them!

Thus the answer is:

= 168- 15

= 153

153 integers lie between 168 and 15

Answer:

a is 1

Step-by-step explanation:

\(a+\dfrac{1}{a}=2\)

Multiply both sides by a:

\(a^2+1=2a\)

Move everything to one side:

\(a^2-2a+1=0\)

Factor:

\((a-1)^2=0\)

By the zero product rule, a is 1.

Therefore, the expression is true, because:

\((1)^2+\dfrac{1}{a^2}=a^4+\dfrac{1}{a^4}=1+1=2\)

Hope this helps!

Hello,

I hope you and your family are doing well!

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the difference between consecutive terms is 6, so the common difference is 6.

The explicit formula for the nth term of an arithmetic sequence with first term a1 and common difference d is:

a_n = a1 + (n-1)d

Plugging in the values from the given sequence, we have:

a_n = 7 + (n-1)6

This is the explicit formula for the nth term of the arithmetic sequence.

For example, if you want to find the fifth term of the sequence, you would plug in n = 5:

a_5 = 7 + (5-1)6 = 7 + 4*6 = 7 + 24 = 31

So the fifth term of the sequence is 31.

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