A portion of Raul's check register is shown. His checking account had a balance of $539.50 on April 2. Based on the information in the check register, what was the balance of Raul's checking account after the transaction on April 13 in dollars and cents?
​

The vectors v1 and v2 are:v1 = -3/5 i - 3/10 jv2

= 18/5 i - 47/10 j which is approximately 3.6i - 4.7j.

The option that represents the vectors v1 and v2 is (C) v1 = 56/13 i + 52/13, v2 = 59/13 i - 527/65 j.

To find vectors v1 and v2 , the following steps should be followed:

Compute the projection of vector v onto vector w which gives the parallel component of vector v to vector w which is v1 = projw(v).

Compute the vector which is perpendicular to w by subtracting v1 from vector v which is v2 = v - v1.

Given vectors are v = 3i - 5j and

w = 3i + j.

We have to decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to w.

First, we need to calculate the projection of vector v onto vector w as follows:v1 = project (v)

= (v⋅w/||w||^2) w

where v⋅w is the dot product of vectors v and w and ||w|| is the magnitude of vector w.v⋅w = (3i - 5j)⋅(3i + j)

= 9 - 15 + 0

= -6||w||^2

= (3i + j)⋅(3i + j)

= 9 + 1

= 10v1

= (-6/10) (3i + j)

= -3/5 i - 3/10 j

The projection of vector v onto vector w is v1 = -3/5 i - 3/10 j.

Next, we can find the vector which is orthogonal to w by subtracting v1 from vector v:v2 = v - v1

= (3i - 5j) - (-3/5 i - 3/10 j)

= 18/5 i - 47/10 j

Therefore, the vectors v1 and v2 are:v1 = -3/5 i - 3/10 jv2

= 18/5 i - 47/10 j which is approximately 3.6i - 4.7j.

The option that represents the vectors v1 and v2 is (C) v1 = 56/13 i + 52/13, v2 = 59/13 i - 527/65 j.

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Answer:

(A)\((-\infty, 2)(2, \infty)\)

(−[infinity], 2) (2, [infinity])

Step-by-step explanation:

Given the rational function, f(x) such that:

\(f(x)=\dfrac{x+1}{x-2}\)

The domain of the function are the values of x for which f(x) is defined.

A rational function is undefined when its denominator equals zero.

Denominator of f(x)=x-2

x-2=0

x=2

Therefore, f(x) is undefined at x=2.

The domain of f(x) is all therefore all real numbers excluding 2.

This is written in set notation as:

\((-\infty, 2)(2, \infty)\)

The correct option is A.

Answer: A (-infinity,2) (2,infinity)

Step-by-step explanation:

The Laplace transform of f2(t) is, L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

To find the Laplace transform of f2(t), we use the definition of the Laplace transform:

L{f(t)} = \(\int_0^{\infty} e^{-st} f(t) dt\)

where L{f(t)} denotes the Laplace transform of f(t), s is a complex number, and u(t) is the unit step function.

Substituting f2(t) into this formula, we get:

L{f2(t)} = \(\int_0^{\infty} e^{-st} (27t^2sin(6t-60)u(t)) dt\)

Using the properties of the Laplace transform, we can simplify this expression. First, we can factor out the constant 27:

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2sin(6t-60)u(t)) dt\)

Next, we use the identity sin(a-b) = sin(a)cos(b) - cos(a)sin(b) to write the sin function as a sum of exponential functions:

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2(sin(6t)cos(60) - cos(6t)sin(60))u(t)) dt\)

L{f2(t)} = \(27 \int_0^{\infty} e^{-st} (t^2sin(6t)u(t)cos(60) - t^2cos(6t)u(t)sin(60)) dt\)

We can now apply the Laplace transform to each term separately. Using the formula L{t^n} = n!/s^(n+1), we get:

L{t^2sin(6t)u(t)cos(60)} = (2!/(s^3)) L{sin(6t)u(t)} = 12/(s^3(s^2+36))

L{t^2cos(6t)u(t)sin(60)} = (2!/(s^3)) L{cos(6t)u(t)} = (2s)/(s^2+36)^2

Substituting these expressions back into the original equation, we get:

L{f2(t)} = 27 (12/(s^3(s^2+36))cos(60) - (2s)/(s^2+36)^2sin(60))

Simplifying this expression, we get:

L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

Therefore, the Laplace transform of f2(t) is:

L{f2(t)} = 216/(s^3(s^2+36)) - 6s/(s^2+36)^2

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The answer would be x=14.5

I got this answer by dividing all the values (Miles) by the hours and got 14.5.

Answer:

20

Step-by-step explanation:

substitute 5 for 'x':

6(5) - 2(5) = 30-10 = 20

a. the probability that a student in this class passes the course is approximately 1 - 0.0301 = 0.9699 (or 96.99%). b. the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale is approximately 0.9992 (or 99.92%). c. the percentage score required to be in the top 10% of students is approximately 75.24%. d. the student's z-score in statistics (1.875) is higher than their z-score in microeconomics (1.818).

a. To find the probability that a student in the class passes the course (assuming a passing grade is 50%), we need to calculate the area under the normal distribution curve for scores greater than or equal to 50%.

Using Table A or a standard normal distribution calculator, we can find the z-score corresponding to a score of 50% in a normal distribution with a mean of 65% and a standard deviation of 8%.

The z-score can be calculated as:

z = (x - mean) / standard deviation

z = (50 - 65) / 8

z = -1.875

From Table A, the corresponding area (probability) for a z-score of -1.875 is approximately 0.0301.

Therefore, the probability that a student in this class passes the course is approximately 1 - 0.0301 = 0.9699 (or 96.99%).

b. To find the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale, we need to find the corresponding z-score for 3.3.

Since the Queen's University GPA Scale is not explicitly mentioned in the question, we will assume a standard normal distribution with a mean of 0 and a standard deviation of 1.

Using Table A, the area (probability) for a z-score of 3.3 is approximately 0.9992.

Therefore, the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale is approximately 0.9992 (or 99.92%).

c. To find the percentage score required to be in the top 10% of students, we need to find the z-score corresponding to the area under the normal distribution curve that leaves a probability of 10% in the upper tail.

Using Table A, the z-score corresponding to the top 10% (or 90th percentile) is approximately 1.28.

Now, we can calculate the percentage score using the z-score:

z = (x - mean) / standard deviation

1.28 = (x - 65) / 8

Solving for x, we get:

x - 65 = 1.28 * 8

x - 65 = 10.24

x = 75.24

Therefore, the percentage score required to be in the top 10% of students is approximately 75.24%.

d. To compare the student's performance in the statistics and microeconomics classes, we can use z-scores to standardize the scores relative to their respective class distributions.

For statistics:

z_stats = (x_stats - mean_stats) / standard_deviation_stats

z_stats = (80 - 65) / 8

z_stats = 1.875

For microeconomics:

z_micro = (x_micro - mean_micro) / standard_deviation_micro

z_micro = (80 - 60) / 11

z_micro = 1.818

Comparing the z-scores, we see that the student's z-score in statistics (1.875) is higher than their z-score in microeconomics (1.818).

Since z-scores represent the number of standard deviations above or below the mean, a higher z-score indicates better performance relative to the class. Therefore, the student has performed better in statistics relative to their peers compared to their performance in microeconomics.

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Answer: 14

Step-by-step explanation:

P(6)- Q(2) = 4

Q(5) - R(2) = 3

R(6) - S(2) = 4

S(5) - P(2) = 3

4 + 3 + 4 + 3 = 14

Brainliest is appericiated!

Answer:

Perimeter = 14

Step-by-step explanation:

to find the perimeter first find the distance between the two points :

d=√((x2-x1)²+(y2-y1)²)

PQ:(2,2)(6,2)

d=√(6-2)^2+(2-2)^2

= √16=4

PQ=4

RS: (6,5),(2,5)

d=√(6-2)^2+(5-5)^2

d=4

RS=4

QR:(6,2),(6,5)

QR=3

SP(2,5),(2,2)

SP=3

perimeter=2length+2width

P=2l+2w

p=2(4)+2(3)

p=8+6=14

The rectangular coordinates (x, y) for the point P are:(x, y) = (2.5, 5√3/2)

We can find the rectangular coordinates (x, y) for point P on the polar coordinate plane using the following formulas:

x = r cos θ y = r sin θ

Where r is the distance from the origin to the point P, and θ is the angle between the positive x-axis and the line segment OP (where O is the origin and P is the point).

In the given figure, we can see that the point P has a distance of 5 units from the origin, and the angle θ is 60 degrees (measured counterclockwise from the positive x-axis).

Therefore, we have:

r = 5 θ = 60°

Substituting these values into the formulas above, we get:

x = r cos θ

= 5 cos 60°

= 5 (1/2)

= 2.5 y

= r sin θ

= 5 sin 60°

= 5 (√3/2)

= 5√3/2

Therefore, the rectangular coordinates (x, y) for the point P are:(x, y) = (2.5, 5√3/2).

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Answer:

3850 of those 6 person teams contain at most 3 men.

Step-by-step explanation:

The order in which the people are selected is not important, which means that the combinations formula is used to solve this question.

It drove 30.08 kilometers in an hour.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

0 men:

6 women from a set of 8. So

\(C_{8,6} = \frac{8!}{2!6!} = 28\)

1 men:

5 women from a set of 8

1 men from a set of 7. So

\(C_{8,5}C_{7,1} = \frac{8!}{3!5!} \times \frac{7!}{1!6!} = 392\)

2 men:

4 women from a set of 8

2 men from a set of 7. So

\(C_{8,4}C_{7,2} = \frac{8!}{4!4!} \times \frac{7!}{2!5!} = 1470\)

3 men:

3 women from a set of 8

3 men from a set of 7. So

\(C_{8,3}C_{7,3} = \frac{8!}{5!3!} \times \frac{7!}{3!4!} = 1960\)

How many 6 person teams contain at most 3 men?

28 + 392 + 1470 + 1960 = 3850

3850 of those 6 person teams contain at most 3 men.

Take the root of both sides and solve.

x = 8√−10, −8√−10

Answer:

2/3, 3/7, 2/5.

Step-by-step explanation:

The easiest way to tell which number is larger is by using a common denominator. For example, when comparing 2/3 and 3/7, the common denominator would be 21. I multiplied 3 by 7 to get 21, and multiplied 7 by 3 to get 21. Therefore, we must multiply the  numerator by the same number. Then, our two numbers are 14/21, and 9/21. Now, we can easily see that 2/3 (14/21) is the bigger fraction.

Example Math:

2/3·1/7 = 2/21

2/21·7 = 14/21

3/7·1/3 = 3/21

3/7·3 = 9/21

The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

In the given right angle triangle,

The vertices are A(-3, 2), B(-3, -1) and C(1, -1)

The distance between AB = 3,

And the distance between BC = 4

To find the distance of AC, use Pythagoreans theorem,

AC² = AB² + BC²

       = 3² + 4²

       = 9 + 16

AC² = 25

AC = 5

The perimeter of triangle ABC = AB + BC + AC

= 3 + 4 + 5

= 12

The perimeter of the triangle ABC is 12 unit.

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Answer:

8

Step-by-step explanation:

Given:

Total money Jervane can spend = $20.

Cost of a coffee = $3.

Cost of a donut = $2.

To find: Maximum number of donuts Jervane can buy.

Solution:

Let the number of donuts she can buy be \(x\).

She wants to spend no more than $20 in total.

So,

\(3+2x\leq 20\)

\(\Rightarrow 2x\leqslant 20-3\)

\(\Rightarrow 2x\leqslant 17\)

\(\Rightarrow x\leqslant \frac{17}{2}\)

\(\Rightarrow x\leqslant 8 \frac{1}{2}\)

As the number of donuts can only be a natural number.

Hence, the maximum number of donuts that Jervane can buy are 8.

Answer:

Step-by-step explanation:

\((ax - 2)^{2} = 100\)

(\(3a-2)^{2}\)=\(100\)

\(Using\\ the\\ formula (a + b)^{2} = a^{2} + b^{2} + 2ab\)

(\(3a)^{2}\)\(+ (2)^{2} +2(3a)(2)\)\(=100\)

\(9a^{2}+4^{2} + 12a\)=\(100\)

\(9a^{2}+ 12a+16=100\)

\(9a^{2} +12a+116\)=\(0\)

\(9a^{2} +3a+29\)

Answer:

∠IGH = 50°

Hope this helps! :)

Answer:

  book 25; pen 8

Step-by-step explanation:

If we let b and p represent the cost of a book and a pen, respectively, then the two purchases can be written as ...

  7b +4p = 207

  5b +5p = 165

Multiply the second equation by 4/5 and subtract the result from the first equation:

  (7b +4p) -4/5(5b +5p) = (207) -4/5(165)

  3b = 75 . . . . simplify

  b = 25 . . . . . divide by 3

Dividing the second equation by 5 gives ...

  b + p = 33

Solving for p, we have ...

  p = 33 -b = 33 -25 = 8

The cost of an exercise book is 25; the cost of a pen is 8.

Answer:

False

Step-by-step explanation:

It is a linear equasion because it's in ax+by=c form

The correct statement is- Once the Compromise of 1850 was passed, Northerners and Southerners readily accepted its terms, putting their suspicions to rest.

The statement describes how both Northerners and Southerners were suitable to fluently accept the terms of the concession of 1850 and put their reservations to rest after its end. The Concession of 1850 was a series of legislative measures aimed at resolving the growing pressures between the Northern and Southern countries of the United States over issues similar to slavery and the balance of power.

The statement suggests that the terms of the concession were satisfactory to both sides, allowing for a sense of agreement and resolution. It implies that the concession addressed the enterprises and interests of both Northerners and Southerners, leading to their amenability to accept it. By accepting the concession and its terms, both regions were suitable to palliate their reservations or dubieties, potentially reducing pressures between them.

This statement highlights the significance of the concession of 1850 in furnishing a temporary resolution to the contentious issues of the time, indeed though these issues would latterly contribute to the raising conflicts that ultimately led to the American Civil War.

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The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Answer:

5a+13

Step-by-step explanation:

17-7a+12a+6

combine like terms

-7a+12a+7+6

simplify

5a+13

Answer: 5

Step-by-step explanation:

17 - 7a + 12a + 6  

1. Combine similar terms:

17 - 7a + 12a + 6 = 23 + 5a = 5a+23

The number that goes into the green box is 5.

The number of the one-point shot is 17 and the number of the 2 point shot is 36.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that at a basketball​ game, a team made 53 successful shots. They were a combination of​ 1- and​ 2-point shots.

Let the one-point shot is x and the 2 point shot is y. The equations can be written as below:-

x + y = 53

-x - 2y = -89

_________

y = 36

The value of x will be calculated as:-

x + y = 53

x + 36 = 53

x = 53 - 36

x = 17

Hence, the one-point shot number is 17, and the two-point shot number is 36.

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Answer: This looks like it is a reflection of the y-axis and then an enlarging dilation.

Answer:

x = 2, y = 4

Step-by-step explanation:

Given

(x + 1, 8 ) = (3, 2y )

Equate the values in the x and y positions , that is

x + 1 = 3 ( subtract 1 from both sides )

x = 2

and

2y = 8 ( divide both sides by 2 )

y = 4

Answer:

(X+1,8)=(3,2y)

equating corresponding value we get

x+1=3

x=3-1=2

again

8=2y

y=8/2=4

x=2

y=4

Answer:

\(-6\leq x < 5\)

Step-by-step explanation:

Given compound inequality:

\(31 \geq-4x+7\;\;\;\textsf{and}\;\;\;-4x+7 > -13\)

Solve the first inequality:

\(\begin{aligned}31 & \geq -4x+7\\\\31 +4x& \geq -4x+7+4x\\\\4x+31& \geq 7\\\\4x+31-31 & \geq 7-31\\\\4x & \geq -24\\\\\dfrac{4x}{4} & \geq \dfrac{-24}{4}\\\\x & \geq -6\end{aligned}\)

Solve the second inequality:

\(\begin{aligned}-4x+7& > -13\\\\-4x+7-7& > -13-7\\\\-4x& > -20\\\\\dfrac{-4x}{-4}& > \dfrac{-20}{-4}\\\\x& < 5\end{aligned}\)

Therefore, combining the solutions, the solution to the compound inequality is:

\(\large\boxed{-6\leq x < 5}\)

When graphing inequalities:

To graph the solution:

Answer:

A. the slope is negative

Step-by-step explanation:

the slope is going down so it is negative

Answer:

A

Hope this helps if not then let me know!

The percentage increase in the price of a gallon of gas is 80.84 %.

Given,

Jason bought a gallon of gas in 1992 = $1.20

He bought a gallon of gas yesterday = $2.17

Using the formula for the percentage increase in the price,

= ( New Price - Old Price) / Old Price × 100

= ( 2.17 - 1.20) / 1.20 × 100

= 80.84%

Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.

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While there have been studies suggesting potential benefits of cold showers on the immune system and health outcomes, it is important to note that the evidence is still limited and further research is needed to establish conclusive results. The study you mentioned regarding a clinical trial in the Netherlands is not specified, so I cannot provide specific details about it. However, I can provide some general information on the topic.

1. Immune System Stimulation: Cold exposure, such as taking cold showers, has been hypothesized to stimulate the immune system. Cold showers may activate the body's natural defense mechanisms and increase the production of certain immune cells, potentially enhancing immune function. However, more research is required to fully understand the underlying mechanisms and determine the extent of the immune system's response.

2. Reduced Sick Days: Some studies have suggested that cold showers may contribute to a reduction in sick days. The Netherlands clinical trial you mentioned reported a 29% decrease in sick leave from work. Cold exposure might have effects on the body's stress response, blood circulation, and immune function, potentially influencing overall health and decreasing the likelihood of illness. Nonetheless, it is important to consider other factors that could affect sick leave, such as lifestyle, work environment, and individual susceptibility to illness.

3. Cancer Survival: There is limited scientific evidence linking cold showers to improved cancer survival. Cold exposure, specifically in the form of cryotherapy, has been used as an adjunct therapy in some cancer treatments. It is believed that extreme cold temperatures can potentially enhance the effects of traditional cancer therapies, but the research in this area is still ongoing, and more evidence is required to draw definitive conclusions.

It's worth noting that individual responses to cold exposure may vary, and cold showers might not be suitable or beneficial for everyone, particularly those with certain medical conditions or sensitivities to cold. It is always advisable to consult with healthcare professionals or experts in the field before making significant changes to your health routine or treatment plan.

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The functions cosecant and cotangent are undefined when functions sine and tangent are equal to zero.

A function becomes undefined when its denominator becomes zero. In the case of trigonometric functions we know that both sine and tangent of 0° are equal to zero. In addtion, there are two following trigonometric formulas:

csc θ = 1 / sin θ

cot θ = 1 / tan θ

Thus, the functions cosecant and cotangent are undefined when functions sine and tangent are equal to zero.

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