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Answer:

[tex]\sin(\theta) = -\dfrac{\sqrt2}{2}[/tex]

[tex]\cos(\theta) = -\dfrac{\sqrt2}{2}[/tex]

Step-by-step explanation:

The sine of any given angle on the unit circle is the y-coordinate of the point on the circle at the given angle.

The cosine of any given angle on the unit circle is the x-coordinate of the point on the circle at the given angle.

See the attached image for a labeled unit circle.

The point on the unit circle that is at angle 5π/4 is:

[tex]\left(-\dfrac{\sqrt2}{2},-\dfrac{\sqrt2}{2}\right)[/tex]

This means that:

[tex]\sin\left(\dfrac{5\pi}{4}\right) = \cos\left(\dfrac{5\pi}{4}\right) = \boxed{-\dfrac{\sqrt2}{2}}[/tex]

The longest flagopole that could fit in the box is 15.26 feet

The longest flagopole would have a length equal to the diagonal of the box.

It goes, lengthwise, from one vertex to the opposite vertex, and if the dimensions of the box are x, y, z, then the diagonal is:

d = √(x² + y² + z²)

In this case the box is 2ft by 2 ft by 15ft, then the diagonal is:

d = √(2² + 2² + 15²) = 15.26

That is the maximum length that can fit in the box, 15.26ft

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Answer:

The common difference in an arithmetic sequence is the constant difference between any two consecutive terms. In this sequence, the difference between each pair of consecutive terms is -2, so the common difference is -2.

Therefore, the answer is -2.

The average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

Deviation is a statistical measure that indicates how much a set of data varies from its average or expected value. It is calculated by finding the difference between each data point and the mean value of the data set.

Absolute deviation is a measure of how far apart a set of numbers is from their average, or mean, value. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences.

Here are the basic steps to find the absolute deviation:

1) Find the mean of the data set by adding up all the numbers and dividing by the total number of values.

2) For each value in the data set, subtract the mean from the value to find the difference.

3) Take the absolute value of each difference (ignore the positive or negative sign) by simply dropping the minus sign if there is one.

4) Add up all the absolute differences found in step 3.

5) Subtract the total number of values in the data set from the sum of the absolute differences.

The result is the average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

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The radian measure of an angle is directly proportional to the length of the arc intercepted by that angle on the unit circle.

Proportional is a mathematical concept that describes the relationship between two or more values that have a constant ratio. It is commonly used to describe the relationship between two or more variables, such as the size of an object in relation to another or the amount of a certain item in relation to the total amount. In proportionality, the ratio of the amounts remains consistent, no matter what the size of the values.

This means that as the angle increases, so does the length of the arc. This is because the length of an arc is determined by the angle measure of the central angle created by the arc, and the radian measure of an angle is the ratio of the arc length to the radius of the circle. Therefore, if the angle measure increases, so does the arc length.

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The largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is 8.5 (if x is οdd) οr 5.5 (if x is even)

The median is the middle value in a set οf numbers arranged in οrder. It is the value that separates the higher half frοm the lοwer half.

Tο find the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5), we need tο cοnsider the different cases when x is an integer.

First, let's arrange the numbers in οrder:

{2, 3, 2x, 5, x}

Tο find the median, we need tο determine the middle number in the set. If the set has an οdd number οf elements, the median is the middle number. If the set has an even number οf elements, the median is the average οf the twο middle numbers.

Case 1: x is even

If x is even, then 2x is even and x < 2x. Therefοre, the middle numbers are 2x and 3, and the median is (2x + 3) / 2.

Case 2: x is οdd

If x is οdd, then 2x is even and 2 < 2x. Therefοre, the middle numbers are 2 and 2x, and the median is (2 + 2x) / 2.

Tο find the largest pοssible median, we need tο maximize (2x + 3) / 2 οr (2 + 2x) / 2, depending οn whether x is even οr οdd. This οccurs when x is the largest pοssible integer, which is:

x = 4 (if x is even)

x = 7 (if x is οdd)

Therefοre, the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is:

(2x + 3) / 2 = (2(7) + 3) / 2 = 8.5 (if x is οdd)

οr

(2x + 3) / 2 = (2(4) + 3) / 2 = 5.5 (if x is even)

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Let's use algebra to solve this problem.

Let x be one of the integers, and y be the other integer.

From the problem, we know that:

x = 4y + 17 (one integer is 17 more than 4 times the other)

xy = -15 (the product of the two integers is -15)

We can use substitution to solve for one of the variables. From the first equation, we can write:

y = (x - 17)/4

Substituting this expression for y into the second equation gives:

x(x - 17)/4 = -15

Multiplying both sides by 4 and expanding gives:

x^2 - 17x = -60

Rearranging gives:

x^2 - 17x + 60 = 0

This is a quadratic equation that can be factored as:

(x - 5)(x - 12) = 0

So the solutions are:

x = 5, y = (-12/4) = -3

x = 12, y = (-5/4) = -1.25

Since the problem states that the integers are both integers, the only valid solution is:

x = 5, y = -3

Therefore, the two integers are 5 and -3.

Answer:

a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal curve to the left of 44. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 44 inches:

z = (44 - 40.9) / 5.3 = 0.585

The area to the left of z = 0.585 is approximately 0.7202. Therefore, about 72.0% of years will have an annual rainfall of less than 44 inches.

b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal curve to the right of 38. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 38 inches:

z = (38 - 40.9) / 5.3 = -0.717

The area to the right of z = -0.717 is approximately 0.4713. Therefore, about 47.1% of years will have an annual rainfall of more than 38 inches.

c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal curve between the corresponding z-scores:

z1 = (37 - 40.9) / 5.3 = -0.736

z2 = (43 - 40.9) / 5.3 = 0.396

Using a standard normal distribution table or a calculator, we find the area between z = -0.736 and z = 0.396 is approximately 0.6181. Therefore, about 61.8% of years will have an annual rainfall between 37 inches and 43 inches.

Step-by-step explanation:

Step-by-step explanation:

a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal distribution curve to the left of 44 inches.

Using a standard normal distribution table or calculator, we can find the z-score:

z = (44 - 40.9) / 5.3 = 0.585

The area to the left of this z-score is approximately 0.72, or 72%.

Therefore, approximately 72% of years will have an annual rainfall of less than 44 inches.

b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal distribution curve to the right of 38 inches.

Using a standard normal distribution table or calculator, we can find the z-score:

z = (38 - 40.9) / 5.3 = -0.736

The area to the right of this z-score is approximately 0.77, or 77%.

Therefore, approximately 77% of years will have an annual rainfall of more than 38 inches.

c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal distribution curve between the z-scores for 37 inches and 43 inches.

Using a standard normal distribution table or calculator, we can find the z-scores:

z1 = (37 - 40.9) / 5.3 = -0.736

z2 = (43 - 40.9) / 5.3 = 0.394

The area between these z-scores is approximately 0.53, or 53%.

Therefore, approximately 53% of years will have an annual rainfall between 37 inches and 43 inches.

Answer:

To subtract two fractions, you need to have a common denominator. The common denominator for 8 and 3 is 24.

-5/8 = -15/24 (multiply both the numerator and denominator by 3)

-4/3 = -32/24 (multiply both the numerator and denominator by 8)

Now, we can subtract the two fractions by subtracting their numerators while keeping the common denominator.

-15/24 - (-32/24) = -15/24 + 32/24 = 17/24

Therefore, -5/8 - -4/3 = 17/24 in its simplest form.

Answer: the answer is C $912.

Step-by-step explanation: The interest on the loan is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:

Interest = $800 x 0.14 x 1

Interest = $112

Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:

Total amount = Principal + Interest

Total amount = $800 + $112

Total amount = $912

Answer:

Luke has saved $21

Step-by-step explanation:

Answer:

According to the problem, Ramona has saved 3 times as much money as Luke, so:

Ramona's savings = 3x

Luke's savings = x

The problem tells us that Ramona has saved $63, so we can write an equation:

3x = 63

To solve for x, we can divide both sides by 3:

x = 21

Therefore, Luke has saved $21.

Answer:6

Step-by-step explanation:

24------100%

x--------25%

100x=25*24

x=25*24/100=24/4=6

Answer:

the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).

Step-by-step explanation:

We can use the standard normal distribution to solve this problem. We first need to calculate the z-scores for the given diameters.

a) To find the probability that a randomly chosen refill will be too large, we need to find the probability of getting a diameter greater than 0.520 mm.

z-score = (0.520 - 0.5) / 0.007 = 2.857

Using a standard normal table or calculator, we find that the probability of getting a z-score of 2.857 or greater is 0.0021.

Therefore, the probability that a randomly chosen refill will be too large is 0.0021 (rounded to three decimal places).

b) To find the probability that a randomly chosen refill will be too small, we need to find the probability of getting a diameter less than 0.485 mm.

z-score = (0.485 - 0.5) / 0.007 = -2.143

Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.143 or less is 0.0164.

Therefore, the probability that a randomly chosen refill will be too small is 0.0164 (rounded to three decimal places).

c) To find the probability that a randomly chosen refill will fit correctly, we need to find the probability of getting a diameter between 0.485 mm and 0.520 mm.

First, we find the z-scores for each diameter:

z-score for 0.485 mm = (0.485 - 0.5) / 0.007 = -2.143

z-score for 0.520 mm = (0.520 - 0.5) / 0.007 = 2.857

Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.143 and 2.857 is 0.9780.

Therefore, the probability that a randomly chosen refill will fit correctly is 0.9780 (rounded to three decimal places).

Answer: Second answer, (5,2)

Step-by-step explanation:

To reflect across the y axis, it would be: (x,y) -> (-x,y)

So, (-5,2) reflected across the y axis would be (5,2)

Answer: 86.5

Step-by-step explanation:  

(83.5 + x )/2= 85

2(85)= 83.5 + x

170-83.5 =x

x= 86.5

Answer: Budgeting for electricity is important because it allows you to plan and allocate your financial resources in a way that ensures that you can pay your electricity bills on time and avoid late payment fees, disconnection, or debt accumulation. Electricity bills can fluctuate significantly from month to month, depending on factors such as the weather, the number of people living in your home, your electricity usage patterns, and changes in electricity rates.

To create a plan to adjust your monthly budget as bills fluctuate month by month, you can take the following steps:

- Review your past electricity bills to identify patterns and trends in your usage and costs. Look for any changes that may have occurred, such as the addition of new appliances, a change in occupancy, or a change in electricity rates.

- Use this information to estimate your average monthly electricity costs. This will be your baseline budget.

- Consider setting aside a buffer amount, such as 10-15%, to account for unexpected changes or fluctuations in your electricity bills.

- Monitor your electricity bills closely each month to compare your actual costs with your budgeted amount. If your bills are consistently higher or lower than your budgeted amount, adjust your budget accordingly for the following month.

- Look for ways to reduce your electricity usage and costs, such as turning off lights and appliances when not in use, using energy-efficient light bulbs and appliances, and adjusting your thermostat settings.

- Consider enrolling in a budget billing or level payment plan offered by your electricity provider, which allows you to pay the same amount each month based on your estimated annual usage.

By budgeting for electricity and adjusting your budget as bills fluctuate month by month, you can better manage your finances, avoid surprises, and ensure that you can pay your bills on time.

Step-by-step explanation:

Therefore, the unit price of the potatoes per ounce is $0.036875.

The unitary method is a mathematical technique that involves finding a single unit value in order to solve a problem involving multiple units. In other words, the unitary method involves finding the value of one unit of a given quantity, and then using that value to calculate the value of another quantity that is related to it.

Here,

First, we need to convert pounds to ounces since the unit price is usually measured in terms of ounces. There are 16 ounces in one pound, so:

5 pounds = 5 x 16

= 80 ounces

The bag of potatoes costs $2.95 for 80 ounces, so the unit price per ounce can be found by dividing the total cost by the number of ounces:

Unit price per ounce = Total cost / Number of ounces

Unit price per ounce = $2.95 / 80

= $0.036875

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Answer:

B. (-3, 4)

Step-by-step explanation:

x=0-3=-3

y=0+4=4

(-3, 4)

Answer:

(-3, 4)

Second answer choice

Step-by-step explanation:

The coordinates of A(0, 0) are shifted to the left by 3 units. A shift to the left means the new x- coordinate = old x-coordinate -3 = 0 -3

A shift up means the new y-coordinate = old y-coordinate + 4 + 0 + 4 = 4

Therefore the new coordinates of A are (-3, 4)

Answer:

a)g(x) = 2f(x+1)

B) the point (-1, 3) would end up at (-4, 1) on the new graph.

Step-by-step explanation:

The total resistance of three resistors in parallel s 2 Ohms. Option A

Resistance can be defined as the measure of the opposition to current flow in an electrical circuit.

Resistance is measured in Ohms, using the Greek symbol for omega (Ω).

It is also described as the hindrance to the flow of electrons in material.

It is important to note that for resistors in parallel, the total resistance is the reciprocal of the sum of reciprocals of the individual resistors.

This is represented as;

1/Rt = 1/R₁ + 1/R₂ + 1/R₃ ...

Where the variables , 'R' represented the resistors

Now, substitute the values, we have;

1/Rt = 1/4 + 1/8 + 1/8

Find the lowest common multiple

1/Rt = 2 + 1 + 1/8

1/Rt = 4/8

Take the reciprocal of the values

Rt = 8/4 = 2 Ohms

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The vertex form is:y(x-3)2-4

:) Good luck

Use the method of completing the square to express in vertex form.

Given

[tex]y = x^2 - 6x + 11[/tex]

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 6x

[tex]y = x^2 + 2(- 3)x + 9 - 9 + 11[/tex], then

[tex]y = (x - 3)^2 + 2[/tex]

Carter is a salesperson who sells computers at an electronics store.

He gets paid a base pay amount each day and a commission for every computer sale he makes.

Carter's total pay on a day depends on the number of computers he sells, represented by x.

The relationship between x and Carter's total pay, represented by P, is linear.

linear means the graph is a straight line, not a curve

A table with select values of x and P is given.

The task is to determine Carter's base pay regardless of computer sales.

Table of select values of x and P:

x P

0 30

1 40

2 50

3 60

4 70

5 80

To determine Carter's base pay, we need to identify the amount he earns when he doesn't sell any computers, represented by x = 0. Looking at the table, we see that when x = 0, Carter's total pay is $30. Therefore, his base pay is $30.

ChatGPT

The probabilities are given as follows:

a) All 10: 0.0163 = 1.63%.

b) Exactly eight: 0.3483 = 34.83%.

c) At least nine: 0.1518 = 15.18%.

The mass probability formula, giving the probability of x successes, is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

N = 20, k = 15, n = 10.

Hence the probability of answering all 10 is given as follows:

[tex]P(X = 10) = h(10,20,10,15) = \frac{C_{15,10}C_{5,0}}{C_{20,10}} = 0.0163[/tex]

The probability of exactly 8 is given as follows:

[tex]P(X = 8) = h(8,20,10,15) = \frac{C_{15,8}C_{5,2}}{C_{20,10}} = 0.3483[/tex]

The probability of nine successes is of:

[tex]P(X = 9) = h(9,20,10,15) = \frac{C_{15,9}C_{5,1}}{C_{20,10}} = 0.1355[/tex]

Hence the probability of at least nine successes is of:

P(X >= 9) = P(X = 9) + P(X = 10) = 0.1355 + 0.0163 = 0.1518 = 15.18%.

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The solution to the system of equations on the graph is (0, 0)

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

y = -2x and y = 4/3x represented on a graph

On the graph, we have two lines that intersect at a point

Using the above as a guide, we have the following:

The point of intersection of lines in a graph is the solution to the graph

In this case, they intersect at (0, 0)

So, the solution is (0. 0)

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The hiker's altitude after 4.5 hours is 448 feet.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: A hiker is climbing a local peak. After 1.5 hours of hiking, he is at an altitude of 220 feet. After 4 hours, he is at an altitude of 410 feet.

We have to find the hiker's altitude after 4.5 hours.

We have height as a function of time:

x = time, y = height

Our two points are (1.5, 220), (4, 410), and (4.5,x)

(4-1.5) = (410-220)

2.5 = 190

1 = 190/2.5

1 hours = 76 feet

0.5 hours = 38 feet

4.5 hours = 410 + 38 feet = 448 feet

Hence,  the hiker's altitude after 4.5 hours is 448 feet.

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Nate made 18 loaves of bread and gave an equal number to each of his 9 neighbors, resulting in each neighbor receiving 2 loaves of bread.

The problem provides us with some information about Nate's bread-making and bread-giving activities. We know that he made 8 loaves of bread on Monday and 10 more on Tuesday, for a total of 18 loaves. We also know that he gave an equal number of loaves to each of his 9 neighbors.

To find out how many loaves each neighbor received, we need to divide the total number of loaves (18) by the number of neighbors (9). This gives us:

18 loaves / 9 neighbors = 2 loaves per neighbor.

This means that each neighbor received 2 loaves of bread from Nate. We can check this by multiplying 2 (the number of loaves per neighbor) by 9 (the number of neighbors):

2 loaves/neighbor x 9 neighbors = 18 loaves

So, we can see that the math checks out and each neighbor received 2 loaves of bread from Nate.

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In the above prompt involving a trajectory calculation, the correct option is: "The kick is not successful. The ball is approximately 5 feet too low." (Option A)

x component of trajectory =   73 cos 34   f/s  

   Now how long will it take to travel 49 yards (= 147 feet) ?

         147 / (73 cos 34) = 2.43 seconds

Initial y component of trajectory = 73 sin 34 f/s = 40.82 f/s  

    but this velocity is acted upon by gravity

       y = y0 + vot - 1/2 a t^2      

                         y0 = 0        

Now we need to know the y value at 2.43 seconds to see if it will clear the uprights.

y = 40.82 (2.43)  - 1/2 (32.174)(2.43)2  

= 4.2 Feet      
Thus, it is correct to state that the "The kick is not successful. The ball is approximately 5 feet too low."

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