cos theta = 3/5 and sin theta < 0. Identify the quadrant of the terminal side of theta and
find sin theta

Answer:

94

Step-by-step explanation:

The mean score is the sum of the test scores divided by the number of tests.

Let s = sum of the scores of the first 6 tests.

s/6 = 80

s = 80 × 6

s = 480

The sum of the scores of the first 6 tests is 480.

The next test is the 7th test.

Let x = score of the 7th test.

mean score of the first 7 tests = (s + x)/7

(s + x)/7 = 82

(480 + x)/7 = 82

480 + x = 574

x = 94

Answer: 94

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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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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Given:

A recipe uses 4 pounds of rice and 5 quarts of boiling water.

To find:

The rate of rice to quarts of water for this recipe.

Solution:

We need to divide the amount of rice by amount of water to get the rate of rice to quarts of water for this recipe.

\(\text{Required rate}=\dfrac{\text{Rice in pounds}}{\text{Water in quarts}}\)

\(\text{Required rate}=\dfrac{4}{5}\)

\(\text{Required rate}=0.8\)

Therefore, the  rate of rice to quarts of water for this recipe is 0.8.

Equation V + Iwh , I = 32, w = 14, and h = 7, V = -3,136. The correct answer is B.

To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:

1. V + Iwh = V + (32)(14)(7)
2. V + 3,136 = V + 3,136
3. Subtract 3,136 from both sides of the equation: V = -3,136

The correct answer is option B: 3,136. Here is the solution in HTML format:

To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:

V + Iwh = V + (32)(14)(7)
V + 3,136 = V + 3,136
Subtract 3,136 from both sides of the equation: V = -3,136

The correct answer is option B: 3,136.

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Answer:

9 inches

Step-by-step explanation:

We see all sides are the same length:

4x+3=3(2x-5)

4x+3=6x-15

18=2x

x=9

Therefore 9 inches.

The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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Answer: 4=X

Step-by-step explanation:

You divide 4x by itself, and divide 16 by 4x leaving you with X and 4 (I'm pretty sure)

Answer:

x=2,-2

Step-by-step explanation:

first you subtract x^4 from both sides

second subtract 16  from both sides

third Divide both sides by -1

fourth take root.

The measure of angle 2 and angle3 are 133 ad 47 degrees respectively

From the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)

Given he following parameters

m<1 = 133 degrees

Since m<1 = m<2, hence m<2 = 133 degrees

Also;

m<2 + m<3 = 180

133 + m<3 = 180

m<3 = 180 - 133

m<3 = 47 degrees

Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively

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Answer: 1, 4, and 5 are 125

2, 3, 6, 7 are 55

Step-by-step explanation:

1 and 8 are congruent by opposite exterior angles and I forgot how to explain 4 and 5 but you know 7 is 55 because a straight line is 180 degrees so is you subtract 125 (8) you get 55 (7)

the second option is more profitable

if she sells more than $ 18000 per month

Explanation

Step 1

let's check the options we have

a)

one paying ​$3,000 per month

it means, in a month , she will receive 3.000

b)$2,100 per month plus a​ 5% commission on all sales made during the month

if x represents the sales, then the formula would be

Step 2

now, to make the option 2 more profitable

solve for x

therefore, the second option is more profitable

if she sells more than $ 18000 per month

I hope this helps you

Answer:

slope = \(\frac{3}{5}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (6, 2)

m = \(\frac{2+1}{6-1}\) = \(\frac{3}{5}\)

Answer:

60

Step-by-step explanation:

Answer: Difference of Cubes

Step-by-step explanation:

                          \(\boxed {a^3-b^3=(a-b)(a^2+ab+b^2)}\)

\(8x^3-27=\\\\(2x)^3-3^3=\\\\(2x-3)((2x)^2+2x(3)+3^2)=\\\\(2x-3)(4x^2+6x+9)\)

Answer

Option C is correct.

Sandra will be paid 72.30 dollars for babysitting for 12 hours.

Explanation

We are told that Sandra earned 60.25 dollars babysitting 10 hours.

If she babysits at the same rate, we are asked to calculate the amount she would earn if she babysits for 12 hours.

Let the amount Sandra is paid for babysitting for 12 hours be x dollars

10 hours = 60.25 dollars

12 hours = x dollars

We can write a mathematical relationship by cross multiplying

10 × x = 12 × 60.25

10x = 723

Divide both sides by 10

(10x/10) = (723/10)

x = 72.3 dollars

Hope this Helps!!!

Answer: 1.11

Step-by-step explanation:

To find the range of the data set all you have to do is subtract the higher number with the lowest number, so in this math problem, we will take 1.75- 0.64 and we get 1.11 :]

Answer:

1) true

2) false

3) true

4) true

5) false

Step-by-step explanation:

1) they are across from each other, making them vertical

2) they are not next to each other

3) they add up to 180 degrees

4) they add up to 180 because both lines form a right angle

5) they are adjacent, not vertical

Answer:

Step-by-step explanation:

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

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Answer:

Side  Original length  Copy length    

a               4                          1     =4                                  

b               6                         1.5     =4                              

c               20                        5         =4                            

d               16                         4                 =4                    

In this section, we demonstrate a simple numerical technique that makes use of the Intermediate Value Theorem to determine a polynomial's zeros. Assess g (a + b 2). The root is x = a + b 2 if g (a + b 2) = 0.

The essential premise of the intermediate value theorem (IVT) is as follows: Assume that a continuous function has a line segment (between points a and b, inclusive) that crosses a horizontal line. Given these details, point c—where the two lines intersect—must exist.

Solving Intermediate Value Theorem Problems :

Define a function y=f(x).

Define a number (y-value) m.

Establish that f is continuous.

Choose an interval [a,b].

Establish that m is between f(a) and f(b).

Now invoke the conclusion of the Intermediate Value Theorem.

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Based on the information provided, we cannot conclusively determine how drivers react to sudden large increases in the price of gasoline. However, we can use the recorded speeds of cars passing the service station before and after the price increase to determine if there is a statistically significant difference in speeds.

A hypothesis test can be conducted to determine if there is a significant difference in means between the two groups. If the p-value is less than the significance level, we can conclude that the speeds differ and suggest that the price increase had an impact on driver behavior. However, if the p-value is greater than the significance level, we cannot conclude that there is a significant difference in speeds and suggest that other factors may have influenced driver behavior.

To determine how drivers react to sudden large increases in the price of gasoline, we can follow these steps:

1. Collect data: The statistician recorded the speeds (mph) of cars passing a large service station before and after the price of gasoline increased by 15 cents.

2. Analyze the data: Compare the recorded speeds before and after the price increase to see if there's a noticeable difference.

3. Conduct a hypothesis test: Perform a statistical test to determine if the observed differences in speeds are significant or due to chance. For example, you can use a paired t-test or another appropriate test based on the data collected.

4. Draw conclusions: If the test shows a significant difference in speeds, we can conclude that drivers' behavior changed in response to the price increase. Otherwise, we cannot confidently say that the speeds differ due to the price increase.

By following these steps, you can determine if drivers' speeds differ as a result of sudden large increases in the price of gasoline.

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Answer:

10

Step-by-step explanation:

30/3 = 10

If all bags have the same number of apples, then each bag has 10 apples.

Answer: 10

Answer:

10 apples

Step-by-step explanation:

Given:

30 apples Total

3 Bags

Note:

Hence, Apples/Bags = Solution

Solve:

30/3 = 10

Thus, Aiden have 10 apples in each bag.

[RevyBreeze]

Answer:

-5

Step-by-step explanation:

-7 - (-2)

-7 + 2

Example: If you owe someone $7, and you give them $2, how much do you still owe? You are owing him $7 so it's a negative and you give him $2 which is a negative as well since you are giving it to him. So, to answer how much do you still owe, you would add $2  to the $7 you owed, so now, you owe him $5, which is a negative since you OWE him.

Hope this helps:)

Answer:

It will take 500 seconds before the scientist sees the solar flare

Step-by-step explanation:

From the question, the Earth-Sun distance is 1.5×10¹¹ m and the speed of light is approximately 3×10⁸ m/s.

Now, we are to determine how long it will take before a scientist sees a solar flare after it has occurred. That is, we are to determine time.

From the formula

Speed = Distance / Time

Time = Distance / Speed

From the question,

Distance = 1.5×10¹¹ m

and speed = 3×10⁸ m/s

Therefore,

Time = 1.5×10¹¹ m / 3×10⁸ m/s

∴ Time = 0.5 × 10³ s

Time = 500 s

Hence, it will take 500 seconds before the scientist sees the solar flare.

Answer:

15

Step-by-step explanation:

9/6=x/10

why? they segments are similar

Answer:

193

Step-by-step explanation:

Let's "cheat" a little on this one

We know that the numbers are consecutive

so lets take the square root of 9312 to get close

√9312 = 96.4987046545

Consecutive numbers around 96.4987046545

96 * 97 = 9312

96 + 97 = 193

-------------------------------

The "correct" method would be to set up an equation

x(x + 1) = 9312

x² + x = 9312

x² + x - 9312 = 0

Then use the quadratic equation to solve for x

Which you can do if you're so inclined.

Me, I'm happy to have "cheated"

The height of the swing path for a performer whose maximum speed is 7 meters per second is 0. 35m

The formula for calculating the maximum speed of the swing is given by the function:

v = 2gh

Given that the parameters are;

From the information given, we have that;

v = 7 meters per second

g = 9. 8 meters per square second

Now, substitute the values into the formula, we get;

7 = 2× 9. 8 × h

Multiply the values, we get'

7 = 19.6 h

Divide both sides by the coefficient of h, we get;

h = 7/19.6

h = 0.35 m

Thus, the value is 0.35 m

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The given function [cos(7y) cos (3y) - sin (7y) sin (3y)] is equal to cos(10y) as per trigonometric identities.

"Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle."

Given, trigonometric function is: cos(7y) cos (3y) - sin (7y) sin (3y)

We know, cos(A + B) = cos(A) cos(B) - sin(A) sin(B)

Therefore, cos(7y) cos (3y) - sin (7y) sin (3y)

= cos(7y + 3y)

= cos(10y)

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