Evaluate the expression for a = 3.8, a = 7, and a - 7.2

The expression a ÷ 4 is equal to __ a = 3.8

The value of the trigonometric identities are;

1. cos R = 15/17

cos S = 8/17

2. cos R = 12/13

cos S = 5/13

Trigonometric Identities are simply seen as the equalities involving trigonometry functions.

It also 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. They are;

We have cosine represented as;

cos θ = adjacent/hypotenuse

For the first triangle, we have;

cos R = 30/34 = 15/17

cos S = 16/34 = 8/17

For the second triangle;

cos R = 24/26 = 12/13

cos S = 10/26 = 5/13

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1) The solution is (2, 4).

2) The solutions are (-1, -5) and (2, 4).

3) The solutions are (3, -5) and (-2, 5).

1) Y = x^2 and y = 4x - 4

Substitute y from the second equation into the first equation to get:

x^2 = 4x - 4

Simplifying and rearranging:

x^2 - 4x + 4 = 0

(x - 2)^2 = 0

x = 2

Substitute x = 2 into the second equation to get:

y = 4(2) - 4 = 4

Therefore, the solution is (2, 4).

2) Y = -x^2 + 2x - 4 and y = 3x - 2

Substitute y from the second equation into the first equation to get:

-x^2 + 2x - 4 = 3x - 2

Simplifying and rearranging:

-x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1 or x = 2

Substitute x = -1 into the second equation to get:

y = 3(-1) - 2 = -5

Substitute x = 2 into the second equation to get:

y = 3(2) - 2 = 4

Therefore, the solutions are (-1, -5) and (2, 4).

3) Y = x^2 - 3x - 5 and y = -2x + 1

Substitute y from the second equation into the first equation to get:

x^2 - 3x - 5 = -2x + 1

Simplifying and rearranging:

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3 or x = -2

Substitute x = 3 into the second equation to get:

y = -2(3) + 1 = -5

Substitute x = -2 into the second equation to get:

y = -2(-2) + 1 = 5

Therefore, the solutions are (3, -5) and (-2, 5).

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Answer:

Interest charged for the loan will be calculated based on the price of the car minus the down payment.

Step-by-step explanation:

Plato

Jethro must get a mark of 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.

To work out the least mark that Jethro needs to get for the last test, we can use the Mean formula: Mean = (Sum of all scores) / (Number of scores).

We know that the Mean of the 5 tests that Jethro has already sat is 74, so we can calculate the sum of the 5 test scores by multiplying the mean by the number of tests (74 x 5 = 370). We also know that Jethro wants his mean mark for all 6 tests to be at least 77, so the sum of all 6 test scores must be higher than (77 x 6 = 462).

To calculate the least mark Jethro needs to get for the last test, we can combine these two facts. We know the sum of the 5 test scores is 370, so the sum of all 6 test scores must be 462 or higher. This means the least mark Jethro needs to get for the last test must be (462 – 370) = 92. This means that Jethro must get a mark of at least 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.

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The number οf attendees at Harry's Hοedοwn is 42.

A data set is a cοllectiοn οf cοnnected data. In the case οf tabular data, a data set is assοciated with οne οr mοre database tables, where each rοw alludes tο a particular recοrd in the assοciated data set and each cοlumn tο a particular variable.

Suppοse the number οf Harry's Hοedοwn attendees be "x"

Given, Mean οf the data = 41 attendees

We knοw,

Mean = sum οf οbservatiοns / number οf οbservatiοns

41 = (48+33+x) / 3

48 + 33 + x = 123

x = 123 - (48+33)

x = 42

Hence the correct answer is 42 attendees.

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Answer:

42

Step-by-step explanation:

Answer: 54 cubic yd^2

Step-by-step explanation: The volume formula for a cube is [tex]s^3[/tex] where s represents a side length.

To get the side length to solve for the surface area just do

[tex]\sqrt[3]{27} =3[/tex]

Which means that the side length is equal to 3

Now plug it into the surface area formula [tex]6s^2[/tex]

[tex]6(3)^2[/tex]

[tex]6(9)\\[/tex]

=54!

Answer:

54 yards^2

Step-by-step explanation:

Volume of a cube = side x side x side or [tex]s^3[/tex]

[tex]s^3 = 27yards^3[/tex]

s = [tex]\sqrt[3]{27}[/tex]

s = 3

Surface Area of a cube = A [tex]= 6 * s^2[/tex]

= [tex]6 * (3)^2[/tex]

= [tex]6 * 9[/tex]

=[tex]54[/tex][tex]yards^2[/tex]

Hope this helps!

Brainliest is much appreciated.

As a result, the answer to the following question, As a result, the length triangle of side JS is 18.

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.  

We must apply the Pythagorean theorem to answer question 19. We know that JN is the hypotenuse of a right triangle with legs of 6 and 8 lengths. As a result, we may apply the formula:

[tex]JN^2 = 6^2 + 8^2\\JN^2 = 36 + 64\\JN^2 = 100\\JN = square root (100)\\JN = 10\\[/tex]

As a result, the length of side JN is 10.

JS/NS = JM/JN

When we substitute the provided values, we get:

12/10 = JS/NS

When we simplify the left side, we get:

6/5 = JS/NS

When we multiply both sides by NS, we get:

JS = (6/5)NS

We also know that NS is 15, therefore we may substitute that number for:

[tex]JS = (6/5) * 15\sJS = 18[/tex]

As a result, the length of side JS is 18.

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From the given data, the vertical intercept, vertical asymptotes and slant asymptote are 2, -5/3 and 4, y = x² - 5x + 13 respectively.

To find the horizontal intercepts, we need to set f(x) = 0 and solve for x:

x³ - 2x² - 29x - 42 / (3x² - 7x - 20) = 0

We can factor the denominator using the quadratic formula:

3x² - 7x - 20 = (3x + 5)(x - 4)

Now, we can write the function as:

f(x) = (x³ - 2x² - 29x - 42) / (3x + 5)(x - 4)

To find the vertical intercept, we need to set x = 0:

f(0) = -42/(-5)(-4) = 2.1

To find the vertical asymptotes, we need to find the values of x that make the denominator equal to zero:

3x + 5 = 0 or x - 4 = 0

Solving for x, we get:

x = -5/3 or x = 4

Therefore, the vertical asymptotes are x = -5/3 and x = 4.

To find the horizontal or slant asymptote, we need to look at the degree of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is a slant asymptote, which we can find by dividing the numerator by the denominator:

x³ - 2x² - 29x - 42 / (3x + 5)(x - 4) = (x² - 5x + 13) + (-2x - 2) / (3x + 5)(x - 4)

The slant asymptote is the line y = x² - 5x + 13.

Now, we can sketch the graph of the function. The graph will approach the vertical asymptotes at x = -5/3 and x = 4. The function will intersect the x-axis at x = -2, x = 3, and x = 7. The function will intersect the y-axis at y = 2.1. The graph will approach the slant asymptote y = x² - 5x + 13 as x approaches infinity or negative infinity.

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Answer ! :)

If Jazmin spent  $38.75 on all

Then it would 15miles ( 15m ) to get home.

As your adding the extra $5 which starts the process.

Basically a equation could be:

(5 + 2.25 = 7.25) + ( 2.25 x 14 )

Extra info if needed more explanation: ( 2.25 x 14 = 31.5 ) Which 31.5 + 7.25 = 38.75

Info on counting:

7.25, 9.50, 11.75, 14, 16.25, 18.50, 20.75, 23, 25.25, 27.50, 29.75, 32, 34.25, 36.50, 38.75

a) 6 adult tickets and 6 child tickets cost  is £102. b) 4 adult tickets and 7 child tickets cost  is  £77 c) 3 child tickets cost is £21

The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.

Let x be the cost of one adult ticket and y be the cost of one child ticket.

From the given information, we can write two equations:

2x + 2y = 38 (equation 1)

2x + 5y = 59 (equation 2)

To solve for x and y, we can use elimination method.

Multiplying equation 1 by 5 and equation 2 by 2, we get:

10x + 10y = 190

4x + 10y = 118

Subtracting equation 2 from equation 1, we get:

6x = 72

x = 12

Substituting x = 12 into equation 1, we get:

2(12) + 2y = 38

2y = 14

y = 7

Therefore, one adult ticket costs £12 and one child ticket costs £7.

a) 6 adult tickets and 6 child tickets:

Cost = 6(£12) + 6(£7) = £102

b) 4 adult tickets and 7 child tickets:

Cost = 4(£12) + 7(£7) = £77

c) 3 child tickets:

Cost = 3(£7) = £21

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After using the npr formula, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.

There are a total of 13 players on the youth basketball team, and there are five different positions that need to be filled. To determine the number of ways that the players can be assigned to these positions, we can use the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of players, and r is the number of positions. In this case, n = 13 and r = 5. Plugging these values into the formula, we get:

P(13, 5) = 13! / (13 - 5)!
= 13! / 8!
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (13 * 12 * 11 * 10 * 9) / 1
= 154440

Therefore, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.

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The cοrrect answer is οptiοn B, t-statistic =1.841, p-value= 0.0748 there is nοt suffient evidence tο reject the null hypοthesis.

The null hypοthesis is a sοrt οf suppοsitiοn used in statistical tests, which are fοrmal prοcedures fοr drawing inferences οr taking judgements based οn evidence. Based οn a sample οf the pοpulatiοn, the hypοtheses are suppοsitiοns regarding a statistical mοdel οf the pοpulatiοn. In οrder tο distinguish between statistical nοise and scientific claims, tests, which are fundamental cοmpοnents οf statistical inference, are frequently utilised in the interpretatiοn οf scientific experimental data.

The null hypοthesis is the prοpοsitiοn under cοnsideratiοn in a test οf statistical significance. Tο evaluate the strength οf the evidence cοntradicting the null hypοthesis, the significance test is used. A claim οf "nο effect" οr "nο difference" is the null hypοthesis. Frequently, H0 is used tο represent it. The alternative hypοthesis is the assertiοn being examined in relatiοn tο the null hypοthesis. Included are symbοls H1 and Ha.

Marcellο's Pizza, Mean – 11.25, Varience- 10.1974, Standard deviatiοn – 3.1933, n- 20

Pizza a Gο-Gο,  Mean – 9.6, Varience – 4.4, Standard deviatiοn – 2.0976 , n – 15

H0  - u1=u2 , Ha – u1≠u2

Test Statistics =(11.25-9.6)/ (√ {(3.1933 ×3.1933)÷20}+√{(2.097×2.097)÷15 }

=1.841

P-value = 2p (±≥1.841) ≈0.0748>0.05

Sο there is nοt sufficient evidence tο reject the null hypοthesis.

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Rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, 50% is equal to 50/100, which simplifies to 0.5. Percentages are often used to express proportions or ratios in a way that is easier to understand. For instance, if there are 20 red balls and 80 blue balls in a bag, we could say that the ratio of red balls to blue balls is 1:4, or we could express this as a percentage by saying that 20% of the balls are red and 80% are blue.

To calculate the total carbon emissions over the 5-year period, we need to calculate the emissions for each year and then add them up.

Starting with the current emission level of 150,000 kilotons, the emissions in each of the next 5 years will be:

Year 1: 150,000 kilotons (no reduction)

Year 2: 150,000 * (1 - 0.005) = 149,325 kilotons

Year 3: 149,325 * (1 - 0.005) = 148,654 kilotons

Year 4: 148,654 * (1 - 0.005) = 147,987 kilotons

Year 5: 147,987 * (1 - 0.005) = 147,323 kilotons

To get the total emissions over the 5-year period, we add up the emissions for each year:

150,000 + 149,325 + 148,654 + 147,987 + 147,323 = 743,289 kilotons

Therefore, rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.

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Answer:742537

Step-by-step explanation: I did the  math, and this is the correct answer

You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.

Suppose you compile all possibilities samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of elementary school age in your school district.

1. All possible samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) is 11.03 the expected population mean:

E(μ) = 11.03

2. The standard error of M for this distribution of samples when n = 100 will be equal to 1.964

σ/√n = 19.64/ √100 = 1.964

3. The standard error of M for all the possible samples of 100 is twice (2 times) the standard error of M for all of the possible samples of 25.

σ/√n= 19.64/√25 = 3.928 = 2( σ/√n = 19.64/√100=1.964)

4. As both the sample has a same population with different sample size, therefore we can predict the standard error on the basis of sample observation. large sample size lower stanadrd error and vice versa.

If you were interested in how much time children spend reading on weekdays among this population of 2, 431 children, would you actually compile all possible samples of a certain size, Option: No

5. If we are traying to know the reading habit of 2431 children, we do not actually compile all possible sample rather we use some specific sample on the basis of sampling distribution.

You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.

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Q: Suppose you compile all possible samples of 100 children of preschool age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of preschool age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to The standard error of M for all the possible samples of 100 is the standard error of M for all of the possible samples of 25. You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the If you were interested in how much time children spend with siblings on weekends among this population of 2,431 children, would you actually compile all possible samples of a certain size? ОО Yes No

The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.

The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is given by 0.0032. Probability is a concept of Mathematics. It is a measure of the likelihood of an event taking place. The concept of probability is very essential in the study of Mathematics. It helps us in determining the chance of occurrence of an event.What is the formula for probability?The probability of an event is represented by a number between 0 and 1. A probability of 0 indicates that the event is impossible while a probability of 1 indicates that the event is certain to happen.

The formula for probability is given by;Probability (P) = Number of favourable outcomes/ Total number of outcomes.The given event is to find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker.In a deck of cards, there are 13 clubs. Out of these, we have to select 4 cards. This can be done in (13C4) ways. Similarly, one card can be chosen from each of the remaining three suits. This can be done in (13C1) * (13C1) * (13C1) ways.

Therefore, the total number of ways in which we can choose 7 cards is given by (52C7).Thus, the required probability is given by;Probability = Number of favourable outcomes/ Total number of outcomes.Number of favourable outcomes = (13C4) * (13C1) * (13C1) * (13C1)Total number of outcomes = (52C7)Probability = Number of favourable outcomes/ Total number of outcomes= [(13C4) * (13C1) * (13C1) * (13C1)]/ (52C7)= 0.0032 (rounded to 6 decimal places).Therefore, the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.

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The total expense for producing 2 widgets is $18,006.00.

To find the total expense for producing 2 widgets, we need to find the total revenue from selling 2 widgets and then subtract the total expense of producing them.

The total revenue from selling 2 widgets is simply the price per widget times the quantity demanded at that price. Since the price is not specified in the problem, we can use the demand function to find it.

We know that the quantity demanded when 2 widgets are produced is:

q = 2

So we can solve the demand function for p:

q = -112p + 4,500

2 = -112p + 4,500

-112p = -4,498

p ≈ 40.16

Therefore, the price per widget is approximately $40.16.

The total revenue from selling 2 widgets at this price is:

revenue = price × quantity demanded

revenue = $40.16 × 2

revenue = $80.32

Now we need to find the total expense of producing 2 widgets. The problem gives us an expression for the total expense:

E = 3.00q + 18,000

Substituting q = 2, we get:

E = 3.00(2) + 18,000

E = $18,006.00

Therefore, the total expense for producing 2 widgets is $18,006.00.

Finally, we can calculate the profit as the difference between the revenue and the expense:

profit = revenue - expense

profit = $80.32 - $18,006.00

profit ≈ -$17,925.68

Since the profit is negative, Willie's Widgets would not make any profit from producing 2 widgets at this price. They would lose money.

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The given sequence 22, 12, 2, -8 is arithmetic, and the common difference is -10.

An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if k is that common difference, we can write the recursive formula as:

a(n) = a(n - 1) + k

Here we have the sequence:

22, 12, 2, -8

Taking the differences between consecutive terms we get:

12 - 22 = -10

2 - 12 = -10

-8 - 2 = -10

The differences are all equal, then this is an arithmetic sequence, and the common difference is -10.

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Answer:

Step-by-step explanation:

Multiply both sides by 2.

Splitting the middle term, we get

In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.

So, the value of the function is 10 at  (its way up) and at  (its way down.

Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.

For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.

The basic definition of a one-to-one function is the mapping of two sets. If each element in the range of a function g matches precisely one in the domain of g, then the function g is one-to-one. 1-1 is another way to represent one-to-one. A function or formula, such as f() connects the values of two variables in such a way that the values of the first variable's elements determine the values of the second variable in exactly the same ways.

We have:

{(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}

We can see the number of the 2nd position is prime and in sequence so, we can easily determine that 2, 3, 5, 7, 11, and next will be 13.

For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.

When every element in a function's range and domain match exactly one another, the function is said to be one-to-one. 1-1 is also used to indicate one-to-one. A function or formula, such as f() links the elements and values of one variable to those of another in such a way that the elements of the first variable exactly predict the elements of the second variable.

The complete question is-

For what value of c is the function one-to-one?

{ (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c) }

a)2

b) 5

c)11

d)13

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Answer:YES

Step-by-step explanation:

you should write 1 instead of every x and 5 instead of every y.

6*1+2*5=6+10=16

1+3*5=1+15=16

Answer:

162 and 9

Step-by-step explanation:

The distance he ran for is from - 81 to 0 and to 81

81 +81 = 162 units

Time spent =distance/speed

Time = 162/ 18 = 9mins

Answer:

  (D)

Step-by-step explanation:

You want the graph that shows speed decreasing to zero.

"Slowing down" means speed is decreasing. On a graph of speed that is indicated by a negative slope.

When an object is stopped, its speed is zero. On a graph of speed, points on the horizontal axis indicate the speed is zero.

The attached graph shows the speed of a car that is slowing to a stop.

Answer:

A=[tex]\pi[/tex]r(r+h2+r2)=[tex]\pi[/tex]·7·(7+122+72)≈459.44884

rounded off to 500 square millimetres

Step-by-step explanation:

The total surface area of a cone is the combination of the curved surface as well as the base area of a cone. The formula to calculate the total surface area of the cone is:

TSA of cone = [tex]\pi[/tex]r^2 + [tex]\pi[/tex]r l = r (l + r) square units.

The length of the missing side of the given triangle ABC which is similar to triangle ILN would be = 7cm

Given that triangle ILN and ABC are similar this shows that their sides are equal in measurement too.

Therefore, LI = 25cm = AB = c

AC = 24 cm = LN = b

BC = X = IN = a

Using the Pythagorean formula;

C² = a² + b²

25² = a² + 24²

625 = a² + 576

625 -576 = a²

a² = 49

a = √49

a = 7cm

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Answer:

The potential energy (PE) of an object is given by:

PE = mgh

where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s² near the Earth's surface), and h is the height of the object above a reference level.

In this case, the mass of the clam is 0.11 kg, the height above the beach is 11.5 m, and the acceleration due to gravity is 9.8 m/s². Therefore, the potential energy of the clam is:

PE = (0.11 kg) × (9.8 m/s²) × (11.5 m) ≈ 12.7 J

So the potential energy of the clam is approximately 12.7 Joules.

Answer:

Option 2

Step-by-step explanation:

For two angles to be adjacent they need to have a common side/ray and a common vertex!

Hope this helps!!!

Answer:

Step-by-step explanation:

In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.

->No, the two indicated angles do not share common vertex

According to the given information, the terminal side of an angle of 7 radians is in the second quadrant.

What is the terminal angle?

The terminal angle is the angle formed by the terminal side of an angle in standard position (i.e., with its initial side along the positive x-axis) and the nearest x-axis. It is typically measured in a counterclockwise direction from the positive x-axis.

An angle of 7 radians is greater than 2π radians (which is approximately 6.28 radians), so it corresponds to more than one full revolution around the unit circle.

To find the terminal side of an angle of 7 radians, we can subtract 2π radians (or 360 degrees) from 7 radians until the result is between 0 and 2π radians. We have:

[tex]$$7 \text{ radians} - 2\pi \text{ radians} \approx 1.716 \text{ radians}$$[/tex]

Since 1.716 radians is less than π radians (which is approximately 3.14 radians), the terminal side of an angle of 7 radians is in the second quadrant.

The terminal side of an angle of 7 radians is in the second quadrant.

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Stephen's hourly pay will be $10.42 in two years, calculated by plugging the principal amount of $9.45, the rate of interest of 5%, and the number of times interest is compounded per year of 1 into the compound interest formula.

Stephen's current hourly pay is $9.45. In order to calculate his hourly pay in two years time, we need to use the compound interest formula. The formula is A = P (1 + r/n)^nt, where A is the amount after n years, P is the principal or initial amount, r is the rate of interest, and n is the number of times interest is compounded per year. In this case, the principal is $9.45, the rate of interest is 5%, and the number of times interest is compounded per year is 1. Plugging these into the formula yields A = 9.45(1 + 0.05/1)^2*1, which equals $10.42. That means Stephen's hourly pay will be $10.42 in two years.

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Answer:

Step-by-step explanation:

Impossible. Using simple logic skills, the only possible outcomes from rolling a dice are 1,2,3,4,5,6. Hence, rolling a 9 is an impossible outcome.