3-BE
N/14N1
North
16 km
NOT TO
SCALE
9 km
The diagram shows the route of a ship that leaves a port, P.
It travels due west for 16 km and then changes course to due south for 9km.
(a) Calculate the straight line distance PQ.
li

The APR to the nearest tenth percent (one decimal place) can be obtained using the formula provided below;APR = ((Interest + Fees / Loan Amount) / Term) × 12 × 100%.

Interest = Total Interest

Paid Fees = Total Fees Paid

Loan Amount = Amount Borrowed

Term = Loan Term in Years.

Shirley Trembley bought a house for $184,800 and she put 20% down which means the amount borrowed is 80% of the house price;Amount borrowed = 80% of $184,800 = $147,840Simple interest amortized loan for the balance at 1183% for 30 yearsLoan Term = 30 years.

Interest rate = 11.83% per year Total Interest Paid for 30 years = Loan Amount × Rate × Time= $147,840 × 0.1183 × 30= $527,268.00Shirley paid 2 points and $3,427.00 in fees, $1,102.70 of which are included in the finance charge,The amount included in the finance charge = $1,102.70Total fees paid = $3,427.00Finance Charge = Total Interest Paid + Fees included in the finance charge= $527,268.00 + $1,102.70= $528,370.70APR = ((Interest + Fees / Loan Amount) / Term) × 12 × 100%= ((527268.00 + 3427.00) / 147840) / 30 × 12 × 100%= 0.032968 × 12 × 100%≈ 3.95%Therefore, the APR is 3.95% (to the nearest tenth percent).

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The plums that remain with George after sharing 22 with Jude will be equal to 50.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the data mentioned in the question,

We first need to determine how many plums Jude received. Decide to round everything to the sixteenth.

George is having 3/8 = 6/16

Terry is having 1/4 = 4/16

Samuel is having 3/16

So, remaining will go to Jude = (16 - (6 + 4 + 3))/16 = 3/16

Consequently, if Jude received 3/16 of the plums, and she received 36 plums, 1/16 of the total plums is,

= 36/3 = 12 plums (As a side note, there were 192 plums in total).

George has got 6/16 plums = 6 × 12 = 72

Then, he gave 22 plums to Jude, so he has left with,

72–22 = 50 left.

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Answer:

"If the shape is not a rectangle, then the shape doesn't has four sides."

Step-by-step explanation:

Given conditional statement is,

" Is a shape has four sides, then the shape is a rectangle."

Here we have two statements:

Statement p → A shape has four sides

Statement q → The shape is a rectangle.

Contrapositive of the statement will be:

If \(\sim q\) then \(\sim p\).

Therefore, contrapositive will be,

"If the shape is not a rectangle, then the shape doesn't has four sides."

So, Tracy paid $12.50 for the encyclopedia and $45.50 for the math book.

In mathematics, an equation is a statement that shows the equality between two expressions. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. An equation usually has an equals sign (=) between the two expressions. The equals sign indicates that the two expressions have the same value.

Here,

Let's use variables to represent the prices of the math book and the encyclopedia.

Let x be the price of the encyclopedia.

According to the problem, the price of the math book is 8 dollars more than 3 times the price of the encyclopedia. So, the price of the math book can be represented as:

=3x + 8

The total cost of the two books is given as 58 dollars. Therefore, we can write the equation:

x + (3x + 8) = 58

Simplifying and solving for x, we get:

4x + 8 = 58

4x = 50

x = 12.50

So, the price of the encyclopedia is $12.50.

To find the price of the math book, we can substitute x = 12.50 into the expression we derived earlier:

=3x + 8

= 3(12.50) + 8

= 37.50 + 8

= 45.50

Therefore, the price of the math book is $45.50.

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Answer:

53

Step-by-step explanation:

if x is 13, you would simply do the following:

multiply 5 by 13 which is 65.

then subtract 65 by 12 which is your final answer, 53!

The isospin ⊗ spin wavefunctions for the four different spin states of a Δ0 particle, in terms of the wavefunctions of the quarks it is composed of, are:

|3/2, 3/2⟩ = |u↑d↑⟩

|3/2, 1/2⟩ = (√3/2)|u↓d↑⟩ + (√1/2)|u↑d↓⟩

|3/2, -1/2⟩ = (√1/2)|u↓d↑⟩ - (√3/2)|u↑d↓⟩

|3/2, -3/2⟩ = |u↓d↓⟩

The Δ baryons are composed of three quarks: two down (d) quarks and one up (u) quark. The isospin of a particle represents its behavior under rotations in the isospin space, which is related to the behavior of the particle under the strong force. The spin of a particle represents its intrinsic angular momentum.

For the Δ0 particle, which has isospin 3/2, there are four different spin states. Each spin state corresponds to a different combination of up and down quark spin projections along the z axis. The isospin ⊗ spin wavefunctions represent the composite wavefunctions of the quarks that make up the Δ0 particle for each spin state.

In the first spin state, |3/2, 3/2⟩, both the up and down quarks have their spins aligned in the upward direction. In the second spin state, |3/2, 1/2⟩, the up quark has its spin aligned upward while the down quark has its spin aligned downward. The third spin state, |3/2, -1/2⟩, has the up quark with its spin aligned downward and the down quark with its spin aligned upward. Finally, in the fourth spin state, |3/2, -3/2⟩, both the up and down quarks have their spins aligned in the downward direction.

These wavefunctions provide a mathematical description of the different spin states of the Δ0 particle, taking into account the wavefunctions of the constituent quarks. They help us understand the quantum mechanical properties and behavior of the Δ0 baryon in terms of its quark composition.

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The number of miles in 4 weeks is 20 mules

From the question, we have the following parameters that can be used in our computation:

Stone runs 1 mile five times a week

This means that the rate is

Rate = 1 mile * 5 per week

So, we have

Rate = 5 miles per week

For 4 weeks, we have

Distance = 5 * 4

Evaluate

Distance = 20 miles

Hence, the distance is 20 miles

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Answer:

ans of an 1 is option b

Step-by-step explanation:

because x and y both are +ve

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The total number of lollipos that she won is 121.

Let x represent the number of friends that she has.

We were told that she gave 4 to each of her friends. It means that the total number that she gave to her friends is 4x. If she has 9 remaining, it means that

4x + 9 = 121

4x = 121 - 9

4x = 112

x = 112/4

x = 28

She has 28 friends

Answer:

927.3 feet per hour

Step-by-step explanation:

first determine how many seconds are in one hour

there are 60 seconds in one minute and 60 minutes in one hour

so there are 60x60, or 3600 seconds in one hour

now you can create a proportion of inches/seconds = inches/seconds

let 'x' = inches per hour

34/11 = x/3600

cross-multiply to get:

11x = 3600x34

11x = 122,400

x = 122,400/11

x = 11,127.3 inches per hour

to determine how many feet per hour you must divide 11,127.3 inches by 12

this equals 927.3 feet per hour

Hope this help!!!

Have a nice day!!!

Answer:

6

Step-by-step explanation:

2√13 - hypotenuse

4 - leg 1

a^2+b^2=c^2

(2√13)^2-4^2=b^2

52-16=b^2

36=b^2

b=6

The standard normal distribution has a mean of 0 and a standard deviation of 1. M ≈ 30.935. The median of the distribution is also 25.

(a) To find M, we first need to convert the given values of mean and standard deviation to the standard normal distribution. This can be done by using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value of interest, μ is the mean, and σ is the standard deviation. In this case, we have X ~ N(25, 9). Substituting the values into the formula, we get Z = (X - 25) / 3. Now we need to find the Z-score that corresponds to the desired probability of 0.95. Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.645. Setting Z equal to 1.645, we can solve for X: (X - 25) / 3 = 1.645. Solving for X, we get X ≈ 30.935. Therefore, M ≈ 30.935.

(b) The median is the value that divides the distribution into two equal halves. In a normal distribution, the median is equal to the mean. In this case, the mean is given as 25. Therefore, the median of the distribution is also 25.

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As per the binomial distribution, the probability that 6 out of 10 random high school students own a personal media player is 4%.

Binomial distribution:

The general formula to calculate the binomial distribution is written as,

P = aCx pˣ (1 - p)ᵃ⁻ˣ

Where,

x = Total number of successful trails

a = Total number of events

p = Probability of success

1 – p = Probability of failure

nCr = [n!/r!(n−r)]!

Given,

According to a recent survey, 85% of high school students own a personal media player.

Here we need to find the probability that 6 out of 10 random high school students own a personal media player.

While we looking into the given question,

Total number of student = 10

Success rate = 6

Probability percentage = 85%

When we convert this into decimal then we get the probability as 0.85.

Now, according to the binomial distribution, Substituting in values for this problem, n=10, p=0.85, and X=6 on the formula, then we get,

=> P = [10!/6!4!] x (0.85)⁶ x(1- 0.85)¹⁰⁻⁶

When we simplify this one then we get the probability as,

=> P = 0.04

When we convert this into percentage, then we get the probability as 4%.

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Answer:

I think 10%

I am not sure

Step-by-step explanation:

if it's correct I hope it helps

The equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

The slope - intercept form of a line is -

y = mx + c                                                     ... { 1 }

where -

{m} is slope of line.
{c} is y - intercept of the line.

Given is the slope of the line as {m} = 1/4 and the y - intercept as {c} = -2.

From Eq { 1 }, we can write the slope - intercept form as -

y = mx + c

y = (1/4)x - 2

Therefore, the equation of the straight line in slope - intercept form will be y = (1/4)x - 2.

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Answer:

Yes, they would get different values

Step-by-step explanation:

Given

\((4 * 35) + (36 * 8)\)

Required

Would there be different value for the expression?

From the question, we understand that both students made no computational errors. This doesn't mean that the students cannot make other errors.

For instance, the expression can be solved (wrongly) in the following ways;

\((4 * 35) + (36 * 8) \to 4 * 35 + 36 * 8 \to 140 + 36 * 8 \to 176 * 8 = 1408\)

\((4 * 35) + (36 * 8) \to 4 * 35 + 36 * 8 \to 4 * 71 * 8 \to = 2272\)

While the correct solution is:

\((4 * 35) + (36 * 8) \to 140 + 288 =428\)

Hence, it is possible for two students to get different values

The percentage of his income he saved is 44.4%.

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.

In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".

If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:

percentage = (40,000/90,000) x 100% = 44.4%

Hence, she saves 44.4% of his income per month.

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The function f(x) = (x - 8)^(2/3) has no x-intercepts and a y-intercept at (-8)^(2/3). It has no extrema or points of inflection. The function is increasing for x < 8 and decreasing for x > 8. It is concave down for the entire domain. Based on this analysis, a sketch of the function would show a concave-down curve with no intercepts, extrema, or points of inflection.

To analyze the function f(x) = (x - 8)^(2/3), we'll examine its properties step by step.

1. Intercepts:

To find the x-intercept, we set f(x) = 0 and solve for x:

(x - 8)^(2/3) = 0

Since a number raised to the power of 2/3 can never be zero, there are no x-intercepts for this function.

To find the y-intercept, we substitute x = 0 into the function:

f(0) = (0 - 8)^(2/3) = (-8)^(2/3)

The y-intercept is (-8)^(2/3).

2. Extrema:

To find the extrema, we take the derivative of the function and set it equal to zero:

f'(x) = (2/3)(x - 8)^(-1/3)

Setting f'(x) = 0, we get:

(2/3)(x - 8)^(-1/3) = 0

This equation has no real solutions, which means there are no local extrema.

3. Intervals of Increase/Decrease:

To determine the intervals of increase and decrease, we analyze the sign of the derivative. We can see that f'(x) > 0 for x < 8 and f'(x) < 0 for x > 8. Therefore, the function is increasing on the interval (-∞, 8) and decreasing on the interval (8, ∞).

4. Concavity:

To determine the concavity, we take the second derivative of the function:

f''(x) = (-2/9)(x - 8)^(-4/3)

Analyzing the sign of f''(x), we can see that it is negative for all real values of x. This means the function is concave down for the entire domain.

5. Points of Inflection:

To find the points of inflection, we set the second derivative equal to zero and solve for x:

(-2/9)(x - 8)^(-4/3) = 0

This equation has no real solutions, indicating that there are no points of inflection.

Based on the analysis above, we can sketch the function f(x) = (x - 8)^(2/3) as a concave-down curve with no intercepts, extrema, or points of inflection. The y-intercept is at (-8)^(2/3). The function is increasing for x < 8 and decreasing for x > 8.

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Answer:

$1.19

Step-by-step explanation:

Let the cost of a cheeseburger be $b and that of a chicken nugget be $n.

From the given information, we can form 2 equations.

9b +4n= 22.37 -----(1)

3b +4n= 15.23 -----(2)

Notice that the 2 equations have '4n' in them. I'll be using elimination method to solve the equation by getting rid of the 4n.

(1) -(2):

9b +4n -(3b +4n)= 22.37 -15.23

9b +4n -3b -4n= 7.14

6b= 7.14 (simplify)

b= 7.14 ÷6 (÷6 on both sides)

b= 1.19

Thus, a cheeseburger cost $1.19.

Answer:

Step-by-step explanation

1.19

a) The probability that Z lies between -1.05 and 1.76 is 0.8664 to 4 decimal places.

b) The probability that Z is less than -1.05 or greater than 1.76 is 0.1588 to 4 decimal places.

c) The value of Z, where only 1.7% of all possible Z values are larger than it, is 1.41 to 2 decimal places.

a) To find the probability that Z lies between -1.05 and 1.76, we need to find the area under the standard normal distribution curve between these two values. By using the standard normal distribution table, we can find the corresponding probabilities for each value and subtract them. The probability is calculated as 0.8664.

b) The probability that Z is less than -1.05 or greater than 1.76 can be found by calculating the sum of the probabilities of Z being less than -1.05 and Z being greater than 1.76. Using the standard normal distribution table, we find the probabilities for each value and add them together. The probability is calculated as 0.1588.

c) If only 1.7% of all possible Z values are larger than a certain Z value, we need to find the Z value corresponding to the 98.3rd percentile (100% - 1.7%). Using the standard normal distribution table, we can look up the value closest to 98.3% and find the corresponding Z value. The Z value is calculated as 1.41.

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Answer:

5.4

Step-by-step explanation:

x distance = 5 and y distance is 2 so you can use pythagorean theorem which is \(\sqrt{a^{2} +b^{2} }\) and you get 5.4

Answer:

16 x 64 x 4

Step-by-step explanation:

2 x 2 x 2 x 2 = 16

2 x 2 x 2 x 2 x 2 x 2 = 64

2 x 2 = 4

The results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.

To determine if the results support the hypothesis that meditation helps reduce stress levels, we need to perform the necessary statistical analysis. Here are the steps involved:

Step 1: Define the hypothesis:

The null hypothesis (H₀) is that there is no significant difference in stress levels between the two groups.

The alternative hypothesis (Hₐ) is that there is a significant difference in stress levels between the two groups, with meditation reducing stress.

Step 2: Identify the appropriate statistical test:

Since we are comparing the means of two independent groups and want to test if there is a significant difference, we can use an independent samples t-test.

Step 3: Set the significance level:

The significance level (α) is the probability of rejecting the null hypothesis when it is true. In this case, we will use a significance level of 0.05, corresponding to a 95% confidence level.

Step 4: Calculate the sample statistics:

Calculate the means, standard deviations, and sample sizes for both groups.

Group 1:

Mean (x1) = (267 + 245 + 263 + 316 + 246 + 282 + 379 + 300 + 291 + 306 + 425 + 190 + 346 + 150 + 344) / 15 = 290.2

Standard deviation (s1) = 70.764

Sample size (n1) = 15

Group 2:

Mean (x2) = (470 + 222 + 443 + 506 + 455 + 518 + 360 + 408 + 375 + 246 + 189 + 368) / 12 = 377.5

Standard deviation (s2) = 109.057

Sample size (n2) = 12

Step 5: Conduct the statistical test:

We can now perform an independent samples t-test using the sample statistics.

Step 5a: Test for equal variances:

Before conducting the t-test, we need to check if the variances of the two groups are equal. We can use a F-test to compare the variances.

Null hypothesis (H₀): The variances of the two groups are equal.

Alternative hypothesis (Hₐ): The variances of the two groups are not equal.

Using a significance level of 0.02 (98% confidence), we can calculate the F-statistic and compare it to the critical F-value from the F-distribution table.

F = s1² / s2² = 70.764² / 109.057² = 0.428 (approximately)

The critical F-value for a 98% confidence level with (n1-1) = 14 and (n2-1) = 11 degrees of freedom is 3.72.

Since our calculated F-value is smaller than the critical F-value, we fail to reject the null hypothesis. Thus, we can assume equal variances.

Step 5b: Conduct the t-test:

Since the variances are assumed to be equal, we can perform the independent samples t-test using the sample means and pooled standard deviation.

Pooled standard deviation (sp) = √(((n1 - 1) × s1² + (n2 - 1) × s2²) / (n1 + n2 - 2)) = √(((15 - 1) × 70.764² + (12 - 1) × 109.057²) / (15 + 12 - 2)) = 90.362

t = (x1 - x2) / (sp × √(1/n1 + 1/n2)) = (290.2 - 377.5) / (90.362 × √(1/15 + 1/12)) = -2.227

Degrees of freedom (df) = n1 + n2 - 2 = 15 + 12 - 2 = 25

Using the t-distribution table or a statistical software, we can find the critical t-value for a two-tailed test at a significance level of 0.05 with 25 degrees of freedom. The critical t-value is approximately ±2.060.

Since our calculated t-value (-2.227) is smaller than the critical t-value (-2.060), we reject the null hypothesis and accept the alternative hypothesis. Therefore, there is evidence to support the claim that mindfulness meditation helps reduce stress levels, with a 95% confidence level.

In conclusion, the results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.

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Answer:

Commutative Property

Step-by-step explanation:

The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer.