Valerie bought 3 storybooks and 2 notebooks for 4 $73. krithik bought 4 storybooks and 1 notebook for $84. find the cost of 1 storybook

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

C) 33 inches

Step-by-step explanation:

A^2 + B^2 = C^2

812.25 + 256 = C^2

1068.25 = C^2

32.684 = C

Hope this helps! Pls mark me as brainliest :)

There are no non-trivial ring homomorphisms from Z20 to Z6, where "non-trivial" refers to mappings other than the trivial homomorphism that sends every element to 0. The ring homomorphisms from Z6 to Z6 can be determined by mapping each element of Z6 to its corresponding element in Z6.

However, there are no non-trivial ring homomorphisms from Z20 to Z6. To determine the ring homomorphisms from Z6 to Z6, we need to find the mappings that preserve the ring structure. In this case, Z6 consists of the elements {0, 1, 2, 3, 4, 5}. Since Z6 is a cyclic ring, any ring homomorphism can be uniquely determined by its mapping of the generator. Let's consider the generator, 1, in Z6. It can be mapped to any element in Z6: 0, 1, 2, 3, 4, or 5. Each mapping corresponds to a different ring homomorphism. Therefore, there are six ring homomorphisms from Z6 to Z6.

On the other hand, when determining the ring homomorphisms from Z20 to Z6, we encounter a different situation. Z20 consists of the elements {0, 1, 2, 3, ..., 18, 19}. Again, we focus on the generator, 1, in Z20. However, no matter how we map the generator to an element in Z6, we cannot preserve the ring structure. This means that there are no non-trivial ring homomorphisms from Z20 to Z6, where "non-trivial" refers to mappings other than the trivial homomorphism that sends every element to 0.

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The average value of the function f(x) = x² - 5 on the interval [0,6] is approximately -2. The average value, we need to find the definite integral of the function over the given interval and divide it by the length of the interval. In this case, the interval is [0,6].

1. Find the definite integral of the function f(x) = x² - 5 with respect to x. The integral of x² - 5 is (1/3)x³ - 5x.

2. Evaluate the integral at the upper limit of the interval (6) and subtract the value of the integral at the lower limit of the interval (0). (1/3)(6)³ - 5(6) - [(1/3)(0)³ - 5(0)] = 72 - 30 = 42.

3. Divide the value obtained in step 2 by the length of the interval, which is 6 - 0 = 6. Therefore, 42/6 = 7.

4. Round the result to the nearest integer. The average value, favg, is approximately -2.

the average value of the function f(x) = x² - 5 on the interval [0,6] is approximately -2. The calculation involves finding the definite integral of the function over the interval and dividing it by the length of the interval.

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Analytics will count three goal conversions if a user completes the newsletter sign-up three times in three separate sessions.

When a goal is set up in analytics, it is assigned a unique ID. When a user completes the desired action that triggers the goal, the ID is recorded in the user's session data. Each time the user completes the action, a new session is created, and a new goal completion is recorded with a unique ID.

Therefore, if the user completes the newsletter sign-up three times in three separate sessions, analytics will count three goal conversions, each with a unique ID.

It's worth noting that while this behavior is typical for most analytics platforms, it's possible to configure goals in different ways, so the behavior may vary depending on the specific implementation. Therefore, it's important to consult the analytics documentation or work with a knowledgeable analyst to confirm the expected behavior.

Therefore, the correct answer is three goal conversions will be counted in analytics.

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Answer:

I think option 3 but not sure

Step-by-step explanation:

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.

From the calculations, we can see that Phone A would use a total of 1.69 hours of battery life in a day. Therefore, the answer is Phone A.

To find out which mobile phone would use a total of 1.69 hours of battery life in a day, we need to calculate 8.45% of the battery life of each mobile phone and compare it to 1.69 hours.

Let's calculate the battery usage for each mobile phone:

For Phone A: 8.45% of 20 hours = 0.0845 * 20 = 1.69 hours

For Phone B: 8.45% of 25 hours = 0.0845 * 25 = 2.1125 hours

For Phone C: 8.45% of 10 hours = 0.0845 * 10 = 0.845 hours

For Phone D: 8.45% of 18 hours = 0.0845 * 18 = 1.521 hours

From the calculations, we can see that Phone A would use a total of 1.69 hours of battery life in a day. Therefore, the answer is Phone A.

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After calculating the given equation we can conclude the resultant equations are:
\(21x - 16y - 22z = 9\\x + y + z = 6\)

To solve the system of equations:
\(2x + 3y + z = 13\\5x - 2y - 4z = 7\\4x + 5y + 3z = 25\)
You can use any method you prefer, such as substitution or elimination. I will use the elimination method:

First, multiply the first equation by 2 and the second equation by 5:
\(4x + 6y + 2z = 26\\25x - 10y - 20z = 35\)
Next, subtract the first equation from the second equation:
\(25x - 10y - 20z - (4x + 6y + 2z) = 35 - 26\\21x - 16y - 22z = 9\)

Finally, multiply the third equation by 2:
\(8x + 10y + 6z = 50\)

Now, we have the following system of equations:
\(4x + 6y + 2z = 26\\21x - 16y - 22z = 9\\8x + 10y + 6z = 50\)

Using elimination again, subtract the first equation from the third equation:
\(8x + 10y + 6z - (4x + 6y + 2z) = 50 - 26\\4x + 4y + 4z = 24\)
This equation simplifies to:
\(x + y + z = 6\)

Now, we have two equations:
\(21x - 16y - 22z = 9\\x + y + z = 6\)

You can solve this system using any method you prefer, such as substitution or elimination.

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The solution to the given system of equations is x = 2, y = 3, and z = 1.

To solve the given system of equations:
2x + 3y + z = 13  (Equation 1)
5x - 2y - 4z = 7   (Equation 2)
4x + 5y + 3z = 25  (Equation 3)

Step 1: We can solve this system using the method of elimination or substitution. Let's use the method of elimination.

Step 2: We'll start by eliminating the variable x. Multiply Equation 1 by 5 and Equation 2 by 2 to make the coefficients of x the same.

10x + 15y + 5z = 65 (Equation 4)
10x - 4y - 8z = 14  (Equation 5)

Step 3: Now, subtract Equation 5 from Equation 4 to eliminate x. This will give us a new equation.

(10x + 15y + 5z) - (10x - 4y - 8z) = 65 - 14
19y + 13z = 51          (Equation 6)

Step 4: Next, we'll eliminate the variable x again. Multiply Equation 1 by 2 and Equation 3 by 4 to make the coefficients of x the same.

4x + 6y + 2z = 26   (Equation 7)
16x + 20y + 12z = 100  (Equation 8)

Step 5: Subtract Equation 7 from Equation 8 to eliminate x.

(16x + 20y + 12z) - (4x + 6y + 2z) = 100 - 26
14y + 10z = 74          (Equation 9)

Step 6: Now, we have two equations:
19y + 13z = 51   (Equation 6)
14y + 10z = 74   (Equation 9)

Step 7: We can solve this system of equations using either elimination or substitution. Let's use the method of elimination to eliminate y.

Multiply Equation 6 by 14 and Equation 9 by 19 to make the coefficients of y the same.

266y + 182z = 714    (Equation 10)
266y + 190z = 1406   (Equation 11)

Step 8: Subtract Equation 10 from Equation 11 to eliminate y.

\((266y + 190z) - (266y + 182z) = 1406 - 7148z = 692\)

Step 9: Solve for z by dividing both sides of the equation by 8.

z = 692/8
z = 86.5

Step 10: Substitute the value of z into either Equation 6 or Equation 9 to solve for y. Let's use Equation 6.

\(19y + 13(86.5) = 5119y + 1124.5 = 5119y = 51 - 1124.519y = -1073.5y = -1073.5/19y = -56.5\)

Step 11: Finally, substitute the values of y and z into any of the original equations to solve for x. Let's use Equation 1.

2x + 3(-56.5) + 86.5 = 13

2x - 169.5 + 86.5 = 13

2x - 83 = 13

2x = 13 + 83

2x = 96

x = 96/2

x = 48

So, the solution to the given system of equations is x = 48, y = -56.5, and z = 86.5.

Please note that the above explanation is based on the assumption that the system of equations is consistent and has a unique solution.

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Based solely on the mileage of the Eurovan, it is likely to be in above-average condition.

The condition of a vehicle is influenced by several factors, including mileage, maintenance history, usage, and overall care. While high mileage can generally indicate wear and tear on a vehicle, it does not necessarily imply poor condition. Eurovans are known for their durability and reliability, so even with 81,718 thousand miles, it is possible for the van to be in above-average condition.

To determine the true condition of the Eurovan, additional information beyond mileage is required. Factors such as regular maintenance, service records, and the overall care provided by the previous owner(s) play a crucial role in assessing the van's condition. If the van has been well-maintained, with routine servicing and repairs, it is more likely to be in above-average condition despite the higher mileage. Additionally, the overall usage of the van should be considered. If the majority of the mileage consists of long highway trips rather than stop-and-go city driving, it can contribute to less wear and tear on the engine and components. Furthermore, factors such as storage conditions, accident history, and the quality of the driving surface can also impact the condition of the Eurovan.

In summary, while the mileage of the Eurovan may initially suggest a below-average condition, it is essential to consider additional factors such as maintenance history, usage patterns, and overall care to make a more accurate assessment. Without this additional information, it is reasonable to assume that the Eurovan is likely to be in above-average condition based on its reputation and durability.

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To show that each function is O(x^2) using the Definitional proof, we need to find a constant c and a positive number k such that |f(x)| ≤ c|x^2| for all values of x greater than some value k.

(a) For function f(x) = x:

We need to find a constant c and k such that |x| ≤ c|x^2| for all x > k.

Let's choose c = 1 and k = 1.

|f(x)| = |x| ≤ 1 * |x^2| for all x > 1.

Therefore, f(x) = x is O(x^2).

(b) For function f(x) = 9x + 5:

We need to find a constant c and k such that |9x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 14 and k = 1.

|f(x)| = |9x + 5| ≤ 14 * |x^2| for all x > 1.

Therefore, f(x) = 9x + 5 is O(x^2).

(c) For function f(x) = 2x^2 + x + 5:

We need to find a constant c and k such that |2x^2 + x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 8 and k = 1.

|f(x)| = |2x^2 + x + 5| ≤ 8 * |x^2| for all x > 1.

Therefore, f(x) = 2x^2 + x + 5 is O(x^2).

(d) For function f(x) = 10x^2 + log(x):

We need to find a constant c and k such that |10x^2 + log(x)| ≤ c|x^2| for all x > k.

Let's choose c = 11 and k = 1.

|f(x)| = |10x^2 + log(x)| ≤ 11 * |x^2| for all x > 1.

Therefore, f(x) = 10x^2 + log(x) is O(x^2).

In each case, we have found a constant c and a value k such that the inequality |f(x)| ≤ c|x^2| holds for all x greater than k. This satisfies the definition of f(x) being O(x^2).

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The initial bird population density is 3713.

Given info;

A certain county received a new species of bird 25 years ago. According to biologists, the population doubles every ten years and is currently 21,000 people.

To get the initial size of the bird population;

We use the formula,

\(P(t)=Po* 2^\frac{t}{10}\)

Where Po is the initial population and t is the time in years.

\(21000= P(25)=Po*2^\frac{25}{10}\)

\(21000= Po*2^\frac{5}{2}\)

\(21000= 4\sqrt{2}*Po\)

\(Po = 21000/4\sqrt{2}\)

\(Po = 3712.31\\Po = 3713\)

Hence, the initial size of the bird population is 3713.

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The correct answers for the expression T(n) are:

- T(n) = O(81log₃n)

- T(n) = O(n³lg(n⁷))

- T(n) = Ω(n³lg(n⁷))

These answers are correct because:

- T(n) = O(81log₃n): This indicates that T(n) has an upper bound of 81log₃n, meaning it grows at most logarithmically with base 3.

- T(n) = O(n³lg(n⁷)): This signifies that T(n) has an upper bound of n³lg(n⁷), indicating it grows no faster than n³ multiplied by the logarithm of n⁷.

- T(n) = Ω(n³lg(n⁷)): This means that T(n) has a lower bound of n³lg(n⁷), suggesting it grows at least as fast as n³ multiplied by the logarithm of n⁷.

However, T(n) = O((31ⁿ)​) is not a correct answer. This is because the expression (31ⁿ) grows exponentially with n and is not an upper bound for T(n).

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Answer:

I don't know I just got the app

Step-by-step explanation:

; /

a)  The probability that six or more cell phone owners used their phones for guidance on purchasing decisions is approximately: P(X ≤ 5) = 0.8406

b) The probability that fewer than ten cell phone owners used their phones for guidance on purchasing decisions is approximately: P(X ≤ 9) = 0.9641

c) The probability that exactly eight cell phone owners used their phones for guidance on purchasing decisions is approximately: P(X = 8) = 0.1144

d) It would be considered unusual if more than 12 cell phone owners had used their phones for guidance on purchasing decisions.

a. Probability that six or more of them used their phones for guidance on purchasing decisions:

Let X be the number of cell phone owners using their phones for guidance on purchasing decisions. Here, X follows the binomial distribution with n = 15 and p = 0.58.

We need to find the probability of six or more phone owners using their phones for guidance on purchasing decisions.

P(X ≥ 6) = 1 - P(X ≤ 5)

We can find the probability using a binomial distribution calculator or cumulative binomial distribution table. Using the binomial distribution table,

P(X ≤ 5) = 0.1594P(X ≥ 6)

= 1 - P(X ≤ 5)

= 1 - 0.1594

= 0.8406

Therefore, the probability that six or more of them used their phones for guidance on purchasing decisions is 0.8406.

b. Probability that fewer than 10 of them used their phones for guidance on purchasing decisions: We need to find the probability of fewer than 10 cell phone owners using their phones for guidance on purchasing decisions.

P(X < 10) = P(X ≤ 9)

We can find the probability using a binomial distribution calculator or cumulative binomial distribution table. Using the binomial distribution table,

P(X ≤ 9) = 0.9641P(X < 10)

= P(X ≤ 9)

= 0.9641

Therefore, the probability that fewer than 10 of them used their phones for guidance on purchasing decisions is 0.9641.

c. Probability that exactly eight of them used their phones for guidance on purchasing decisions: We need to find the probability that exactly eight of them used their phones for guidance on purchasing decisions.

P(X = 8) = 15C8 × 0.58⁸ × 0.42⁷

We can find the probability using the binomial distribution formula, where n = 15 and p = 0.58.

P(X = 8) = 15C8 × 0.58⁸ × 0.42⁷

= 6435 × 0.009505198 × 0.186096542

= 0.1144

Therefore, the probability that exactly eight of them used their phones for guidance on purchasing decisions is 0.1144.

d. Would it be unusual if more than 12 of them had used their phones for guidance on purchasing decisions?

We can find out if it would be unusual for more than 12 cell phone owners to use their phones for guidance on purchasing decisions by calculating the probability of P(X > 12) and comparing it with the significance level.

Here, we can use a binomial distribution calculator or cumulative binomial distribution table.

Using the binomial distribution table, P(X > 12) = 0.0001

Since the probability is less than the significance level (0.05), it would be considered unusual if more than 12 of them had used their phones for guidance on purchasing decisions.

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The confidence level is 90%

The correct option is (B)

We have the following information from the question is:

The sample mean and he sample standard deviation were measured

x bar = 190cm, s = 5cm respectively.

The confidence interval for the mean is [188.29; 191.71]

Now, According to the question:

The confidence interval is given by:

CI = \([x (bar)-z\sigma_x_(_b_a_r_),x (bar)+z\sigma_x_(_b_a_r_)]\)

If x (bar) is 190, we can find the value of \(z\sigma_x_(_b_a_r_)\) :

\(x(bar) -z\sigma_x_(_b_a_r_)=188.29\)

Put the value of x (bar)

\(190-z\sigma_x_(_b_a_r_)=188.29\)

\(z\sigma_x_(_b_a_r_)=1.71\)

We have to find the value of \(\sigma_x_(_b_a_r_)\)

\(\sigma_x_(_b_a_r_)=\frac{s}{\sqrt{n} }\)

\(\sigma_x_(_b_a_r_)=\frac{5}{\sqrt{25} }\)

\(\sigma_x_(_b_a_r_)=1\)

The value of z will be 1.71

Now, Find the value of z-score from the table of z-table:

Hence, The value z-score at 1.71 is 0.0436

This value will occur in both sides of the normal curve, so the confidence level is:

CI = 1- 2 × 0.0436= 0.9128 = 90%

The nearest CI is 90%,

So, the correct option is (B)

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Answer:

800

Step-by-step explanation:

= 2 (13 x 11 + 11 x 11 + 11 x 13 )

= 2 (143 + 121 + 143)

= 2 x 407

= 814 inch^2

nearest hundred = 800

80, answer = 800 inch^2

Answer: Since it is not a perfect square my answer is the square root of 261 or 16.16  which is rounded to the nearest hundredth.

Step-by-step explanation:

10^2 + b^2 = 19^2

100  + b^2 =  361

-100              -100

b^2 = 261

b= \(\sqrt{261}\)

Answer

40%

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

3.60 divided by 12

Random sampling is most important to quantitative research methods.

Quantitative research relies on collecting numerical data and analyzing it statistically to draw conclusions about a population. Random sampling is a crucial aspect of quantitative research as it ensures that the sample selected is representative of the population being studied. By randomly selecting participants or data points from the population, researchers can minimize bias and increase the generalizability of their findings.

This allows them to make accurate inferences about the larger population based on the characteristics observed in the sample. Random sampling helps to reduce the potential for selection bias and ensures that each member of the population has an equal chance of being included in the sample, which enhances the validity and reliability of the research results.

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Answer:

Part A:

To calculate the measures of center, we need to find the mean and median of each set of data.

For Bay Side School:

Mean = (2 x 12 + 1 x 10 + 1 x 8 + 3 x 6 + 1 x 5 + 1 x 4 + 1 x 3 + 1 x 2) ÷ 15 = 6.4

Median = (5 + 5) ÷ 2 = 5

For Seaside School:

Mean = (2 x 10 + 1 x 8 + 2 x 7 + 2 x 6 + 1 x 5 + 1 x 2) ÷ 9 ≈ 7.11

Median = (5 + 6) ÷ 2 = 5.5

Part B:

To calculate the measures of variability, we need to find the range and interquartile range (IQR) of each set of data.

For Bay Side School:

Range = Largest value - Smallest value = 8 - 2 = 6

IQR = Q3 - Q1 = (6 + (8 ÷ 2)) - (3 + (5 ÷ 2)) = (6 +4) - (3+2.5) =4.5

For Seaside School:

Range = Largest value - Smallest value =8 -2=6

IQR=Q3-Q1=(7+(8÷2))−(5+(0÷2))=(7+4)−(5+0)=6

Part C:

If you are interested in a smaller class size, Seaside School is a better choice for you because it has a smaller mean and median than Bay Side School. The mean and median are both measures of center, so they give us an idea of what the typical class size is like at each school. Since Seaside School has smaller values for both measures of center, it is likely that the classes are smaller on average at Seaside School.

After the 6-for-1 stock split, the stock price will be $16.41 per share, assuming no market imperfections or tax effects.

A stock split is a process in which a company increases the number of shares outstanding while proportionally reducing the price per share. In this case, the company plans a 6-for-1 stock split, which means that for every existing share, shareholders will receive six new shares.

To determine the post-split stock price, we divide the original stock price by the split ratio. The original stock price is $98.48, and the split ratio is 6-for-1. Therefore, we calculate:

$98.48 / 6 = $16.41

Hence, after the 6-for-1 stock split, the stock price will be $16.41 per share. This means that each shareholder will now hold six times more shares, but the value of their investment remains the same.

It is important to note that in practice, market imperfections, investor sentiment, and other factors can influence the stock price after a split. However, assuming no market imperfections or tax effects, the calculated value of $16.41 represents the theoretical post-split stock price.

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Answer:

Step-by-step explanation:

a-As he had earned $45.00 for cutting lawns and had earned $35.75 for yard work during the week and had not earned more than that, in order to find the total amount of money he earned during the week, we have to add $45.00 and $35.75 together which will be $80.75. So we can say that he had earned $80.75 during the week.

b- Since he had spent $25.23 on food and $22.12 on gas, we have to add them to get the total amount of money spend during the week. So after adding the amount of moneys spent, we will get $47.35.

c- Finally, to find out how many money he was left with, we have to subtract the amount of moneys spent from the total amount of earnings for the week. So, after subtracting $47.35 from $80.75 he is left with $33.4.

The total number of seconds (s) that a jump takes can be found using the equation:

           \(s = \sqrt{(2h / g)}\)

where h is the height of the jump and g is the acceleration due to gravity.

The required details for equation in given paragraph

An equation is a formula that expresses the equality of  expressions, with the aid of using connecting them with the equals signal =. The word equation and its cognates in different languages can also additionally have subtly extraordinary meanings; for example, in French an équation is described as containing one or more variables, whilst in English, any well-shaped formula which includes expressions associated with an equals signal is an equation. Solving an equation containing variables includes figuring out which values of the variables make the equality true. The variables for which the equation must be solved also are called unknowns, and the values of the unknowns that fulfill the equality are called solutions of the equation.

This equation is based on the kinematic equation for vertical motion with constant acceleration, which states that the time it takes for an object to fall a distance h under the influence of gravity is given by the formula:

           \(t = \sqrt{(2h / g)}\)

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Answer:

B. 60ft

Step-by-step explanation:

if a 6ft box casts a 2ft shadow, then the water towers height would be 3 times its shadow. 20 x 3 = 60ft