17 students are present in a class. in how many ways ,they can be made to stand in 2 circles of 8 and 9 students

The amount of medication needed for 30 days is approximately 59.84 tablets of carprofen.

To calculate the amount of carprofen medication needed for 30 days, we need to consider the prescribed dosage, the weight of the patient, and the concentration of the tablets.

The prescribed dosage is 2.2 mg/kg BID x 30d. This means that the patient should take 2.2 milligrams of carprofen per kilogram of body weight, twice a day, for 30 days.

The weight of the patient is 34 kilograms. So, we need to calculate the total amount of carprofen needed for the entire treatment period.

First, we calculate the daily dosage by multiplying the weight of the patient (34 kg) by the prescribed dosage (2.2 mg/kg).

Daily dosage = 34 kg * 2.2 mg/kg = 74.8 mg/day.

Since the medication is prescribed twice a day, we multiply the daily dosage by 2 to get the total dosage per day.

Total dosage per day = 74.8 mg/day * 2 = 149.6 mg/day.

Finally, to find the total amount of medication needed for 30 days, we multiply the total dosage per day by the number of days.

Total medication needed = 149.6 mg/day * 30 days = 4488 mg.

Since the concentration of the tablets is 75 mg, we divide the total medication needed by the tablet concentration to find the number of tablets required.

Number of tablets needed = 4488 mg / 75 mg = 59.84.

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Answer:

? = 220°

Step-by-step explanation:

the measure of the inscribed angle QRS is half the measure of its intercepted arc QS , then

QS = ? = 2 × QRS = 2 × 110° = 220°

1a. Sum of interior angles of a heptagon:

[tex]\displaystyle \sf \text{Sum of interior angles} = (7 - 2) \times 180^\circ = 900^\circ[/tex]

1b. Sum of interior angles of a 13-gon:

[tex]\displaystyle \sf \text{Sum of interior angles} = (13 - 2) \times 180^\circ = 1980^\circ[/tex]

2. Number of sides for a polygon with a sum of interior angles of 1260°:

[tex]\displaystyle \sf (n - 2) \times 180^\circ = 1260^\circ[/tex]

[tex]\displaystyle \sf n - 2 = \frac{1260^\circ}{180^\circ}[/tex]

[tex]\displaystyle \sf n - 2 = 7[/tex]

[tex]\displaystyle \sf n = 7 + 2 = 9[/tex]

Therefore, the sum of the measures of the interior angles of a heptagon is 900°, the sum of the measures of the interior angles of a 13-gon is 1980°, and the polygon with a sum of interior angles of 1260° is a nonagon (9-gon).

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

1. a. 900°       b. 1980°

2. Nonagon

Step-by-step explanation:

In order to find the interior angles of a polygon, use the formula,

Sum of interior angles = (n-2)*180°

For

a. Heptagon

no of side =7

The sum of the interior angles of a heptagon:

(7-2)*180 = 900°

b. 13-gon

no. of side =13

The sum of the interior angles of a 13-gon:
(13-2)*180 = 1980°

2.

The sum of the interior angles of a convex polygon is 1260°,

where n is the number of sides.

In this case, we have

1260 = (n-2)*180

1260/180=n-2

n-2=7

n=7+2

n=9

Therefore, the polygon has 9 sides and is classified as a nonagon.

The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.

Counterexample:

Consider the following counterexample:

[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:

[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]

The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.

In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.

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The sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.

To add the given time durations, we start by adding the seconds:

12 sec + 25 sec = 37 sec.

Since 60 seconds make a minute, we carry over any excess seconds to the minutes place, which gives us a total of 37 seconds. Moving on to the minutes, we add 30 min + 16 min = 46 min.

Again, we carry over any excess minutes to the hours place, resulting in a total of 46 minutes.

Finally, we add the hours: 5 hr + 2 hr = 7 hr.

Thus, the sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.

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The money raised by Lucas for the fundraiser is $30.

The bars sold on Saturday are 12 bars. Each bar costs $1.50.

So, the amount will be:  12 * 1.50 = 18

The bars sold on Sunday are  8 bars.

So, the amount will be:  8 * 1.50 = 12

Hence, the total amount: is 18+12= 30

Answer:

We have to multiply everything to find the amount of different possible outcomes so 3*7*8*4 = 672 unique outfits

Step-by-step explanation:

Hope this helps!

Answer:

To evaluate the expression when a = 5 and b = 1, we substitute the values into the expression:

12 + 2(4(5)²) ÷ 7 + 8

= 12 + 2(4 * 25) ÷ 7 + 8 (Note: 5² means 5 raised to the power of 2)

= 12 + 2(100) ÷ 7 + 8 (Note: 4 * 25 = 100)

= 12 + 200 ÷ 7 + 8

= 12 + 28.57 + 8 (Note: ÷ means divide)

= 48.57

To plot the resulting value on the provided number line , we would need to know the scale and range of the number line. Without this information, we cannot accurately plot the value.

Step-by-step explanation:

The exponential decay function that satisfies the given conditions is:

[tex]f(x) = 4 * (1/2)^x[/tex].

In this equation, the y-intercept is 4, which means that when x = 0, the function value is 4. As x increases by 1, the function decreases by a factor of one-half. This behavior is captured by raising 1/2 to the power of x in the equation.

The base of the exponent, 1/2, ensures that the function decreases exponentially. When x = 1, the exponent becomes 1, and[tex]1/2^1[/tex] equals 1/2. This means that the function value decreases to half of its previous value. Similarly, when x = 2, the exponent becomes 2, and[tex]1/2^2[/tex] equals 1/4. The function value decreases to one-fourth of its previous value, and so on.

By multiplying the exponential term by 4, we ensure that the y-intercept is 4. This scaling factor allows us to control the initial value of the function and match the given condition.

The exponential decay function[tex]f(x) = 4 * (1/2)^x[/tex] represents a decaying process where the y-values decrease exponentially as x increases, while starting at a y-intercept of 4.

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Answer:

27

Step-by-step explanation:

The strength of the correlation as shown in the scatter plot can be concluded to be: b) no correlation.

To estimate the strength of the correlation in a scatter plot, visually assess the clustering and linearity of the data points. If the points cluster tightly around a linear trend, it indicates a strong correlation, whereas dispersed and non-linear points suggest a weak correlation.

However, if the points on a scatter plot do not exhibit a discernible pattern (as shown in the image given above), it can be concluded that there is no correlation between the variables being plotted.

Therefore, the answer is: b. no correlation.

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Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= [tex]\frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = [tex]\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}[/tex]

=[tex]\frac{-10-+\sqrt{100-92} }{2}[/tex]

=[tex]\frac{-10-+\sqrt{8} }{2}[/tex]

then we form two equations according to negative and positive symbols

x=[tex]\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}[/tex]

therefore x = [tex]-5+\sqrt{2}[/tex]   or x=[tex]-5-\sqrt{2}[/tex]

Answer:

Third option

Step-by-step explanation:

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x <-- Third option

15 < 10 + x

5 < x

x > 5

There only appears to be one option. The solution to the inequality is x>5, not x<5.

The fraction of the container needed to fill up the gas tank of the lawn mower four times is 6/12. Option D.

The shaded part of the circle represents the fraction of gas needed to fill up the gas tank of the lawn mower once. To determine the fraction needed to fill it up four times, we can simply multiply the fraction by 4.

Let's assume that the shaded part of the circle represents x part of the whole container. Therefore, the fraction needed to fill up the gas tank of the lawn mower once is x.

To fill up the gas tank four times, we need to multiply x by 4. Therefore, the fraction needed to fill up the gas tank four times is 4x.

Now, we can compare this to the answer choices given:

8/48: This can be simplified to 1/6, which is not equal to 4x.

8/12: This can be simplified to 2/3, which is not equal to 4x.

6/16: This can be simplified to 3/8, which is not equal to 4x.

6/12: This can be simplified to 1/2, which is equal to 4x.

Therefore, the correct answer is 6/12, which represents the fraction of the container needed to fill up the gas tank of the lawn mower four times. so Option D is correct.

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Note the complete question is

A "⊂-maximal element" in set theory refers to an element in a set that cannot be strictly contained within any other element of the set, indicating a maximum extent or boundary within that set.

In the context of set theory and Tarski's notion of finiteness, a "⊂-maximal element" refers to an element within a set that cannot be strictly contained within any other element of the set. Let's break down the meaning of this term.

Consider a set S and a partial order relation ⊆ (subset relation) defined on the power set P(S) of S. A "⊂-maximal element" u of a set A ⊆ S is an element that is not strictly contained within any other element of A with respect to the subset relation. In other words, there is no element v in A such that u is a proper subset of v.

Formally, for any u ∈ A, if there is no v ∈ A such that u ⊂ v, then u is a ⊂-maximal element of A. This means that u is as large as possible within A and cannot be extended by including additional elements.

In the context of T-finite sets, the existence of a ⊂-maximal element in every nonempty subset of the set guarantees that the set has a well-defined structure and does not continue indefinitely without boundaries.

It ensures that there is a definitive maximum element within each subset, which is a key characteristic of finiteness.

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The statistical questions for this problem are given as follows:

A question is classified as statistical if it can receive answers of data that vary, that is, questions that do not have an exact answer.

When the answer is exact, it must be composed by a set of data, such as the number of students that like football in each school, the number will vary for each school.

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Answer:

[tex]\displaystyle \pi\biggr(1-\frac{1}{e}\biggr)[/tex]

Step-by-step explanation:

Shell Method (Vertical Axis)

[tex]\displaystyle V=2\pi\int^b_ar(x)h(x)\,dx[/tex]

Radius: [tex]r(x)=x[/tex]

Height: [tex]h(x)=e^{-x^2}[/tex]

Bounds: [tex][a,b]=[0,1][/tex]

Set up and evaluate integral

[tex]\displaystyle V=2\pi\int^1_0xe^{-x^2}\,dx[/tex]

[tex]\displaystyle V= -\frac{1}{2}\cdot2\pi\int^{-1}_0e^u\,du\\\\V= -\pi\int^{-1}_0e^u\,du\\\\V=\pi\int^0_{-1}e^u\,du\\\\V=\pi e^u\biggr|^0_{-1}\\\\V=\pi e^0-\pi e^{-1}\\\\V=\pi-\frac{\pi}{e}\\\\V=\pi\biggr(1-\frac{1}{e}\biggr)[/tex]

The correct answer is an option (d): Impossible.

Both the geometric mean and harmonic mean require positive values. However, in the given set of values, we have negative values (-11 and -14), which makes it impossible to calculate the geometric mean and harmonic mean. Therefore, the correct answer is that it is impossible to calculate the geometric mean and harmonic mean for the given values.

The table that shows the same function as the given graph is: A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

To determine which table shows the same function as the given graph, we need to find the values of y corresponding to the given values of x on the graph.

Point A: (0, 4)

Point B: (2, 5)

Let's check each table:

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries negative 8, negative 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 0, 4, 0, 4.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 5, 6, 7.

A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 2, 4, 6. Column 2 is labeled y with entries 4, 8, 12, 16.

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Answer:

Part A: Answer: D.

Part B:

true

false

true

Step-by-step explanation:

Part A:

Use a tree.

Round 1                 Round 2                   Round 3

W                               W                                W

W                               W                                L

W                               L                                 W

W                                L                                 L

L                                 W                               W

L                                 W                               L

L                                 L                                W

L                                 L                                L

All possibilities are:

WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL

Answer: d.

Part B:

Winning 3 games is WWW.

WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL

Out of the 8 possible outcomes shown above, only 1 of them is WWW.

p(WWW) = 1/8

Answer: true

Winning exactly 2 games happens when there are exactly 2 W's:

WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL

p(exactly 2 wins) = 3/8

Answer: false

Wining at least 2 games means winning exactly 2 or exactly 3 times.

WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL

p(winning at least 2 games) = 4/8 = 1/2

Answer: true

The journal entries for the given transactions are as follows:

Cash A/c Dr. 40,000

Furniture A/c Dr. 5,000

Motor Car A/c Dr. 12,000

Stock A/c Dr. 20,000

To Capital A/c 77,000

Bank A/c Dr. 15,000

To Cash A/c 15,000

Purchase A/c Dr. 9,000

To Sen's A/c 9,000

Basu's A/c Dr. 6,000

To Sales A/c 6,000

Stationery A/c Dr. 200

To Cash A/c 200

Cash A/c Dr. 2,000

To Dalal's A/c 2,000

Travelling Expenses A/c Dr. 600

To Cash A/c 600

Drawings A/c Dr. 1,000

To Bank A/c 1,000

Cash A/c Dr. 3,000

To Bank A/c 3,000

Sen's A/c Dr. 8,800

To Bank A/c 8,800

Freight and Clearing A/c Dr. 400

To Cash A/c 400

Bank A/c Dr. 6,000

To Basu's A/c 6,000

Journal entries for the given transactions are as follows:

Pater commenced business with 40,000 cash and also brought into business furniture worth ₹5,000; Motor car valued for ₹12,000 and stock worth ₹20,000.

Cash A/c Dr. 40,000

Furniture A/c Dr. 5,000

Motor Car A/c Dr. 12,000

Stock A/c Dr. 20,000

To Capital A/c 77,000

Deposited ₹15,000 into State Bank of India.

Bank A/c Dr. 15,000

To Cash A/c 15,000

Bought goods on credit from Sen for ₹9,000.

Purchase A/c Dr. 9,000

To Sen's A/c 9,000

Sold goods to Basu on Credit for ₹6,000.

Basu's A/c Dr. 6,000

To Sales A/c 6,000

Bought stationery from Ram Bros. for Cash ₹200.

Stationery A/c Dr. 200

To Cash A/c 200

Sold goods to Dalal for ₹2,000 for which cash was received.

Cash A/c Dr. 2,000

To Dalal's A/c 2,000

Paid ₹600 as travelling expenses to Mehta in cash.

Travelling Expenses A/c Dr. 600

To Cash A/c 600

Patel withdrew for personal use ₹1,000 from the Bank.

Drawings A/c Dr. 1,000

To Bank A/c 1,000

Withdrew from the Bank ₹3,000 for office use.

Cash A/c Dr. 3,000

To Bank A/c 3,000

Paid to Sen by cheque ₹8,800 in full settlement of his account.

Sen's A/c Dr. 8,800

To Bank A/c 8,800

Paid ₹400 in cash as freight and clearing charges to Gopal.

Freight and Clearing A/c Dr. 400

To Cash A/c 400

Received a cheque for ₹6,000 from Basu.

Bank A/c Dr. 6,000

To Basu's A/c 6,000

These journal entries represent the various transactions and their effects on different accounts in the accounting system.

They serve as the initial records of the financial activities of the business and provide a basis for further accounting processes such as ledger posting and preparation of financial statements.

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(a) The amount for total expenditures in 2015 was about $63.2 billion.

(b) The first full year in which expenditures exceeded $110 billion was 2027.

(a) To find the amount for total expenditures in 2015, we need to substitute x = 20 into the function h(x) = [tex]23.4(1.08)^{(x-5)[/tex].

h(x) = 23.4(1.0[tex]8)^{(20-5)[/tex]

    = 23.4(1.0[tex]8)^{15[/tex]

    ≈ 23.4(2.717)

Rounding to the nearest tenth, the total expenditures in 2015 were about $63.2 billion.

(b) To determine the first full year in which expenditures exceeded $110 billion, we need to find the value of x when h(x) is greater than $110 billion.

110 = 23.4(1.0[tex]8)^{(x-5)[/tex]

Dividing both sides by 23.4:

4.7008547... = (1.0[tex]8)^{(x-5)[/tex]

Taking the logarithm base 1.08 of both sides:

log₁.₀₈(4.7008547...) = x - 5

Using a logarithm calculator or software, we find:

x - 5 ≈ 11.75

Adding 5 to both sides:

x ≈ 16.75

Rounding to the nearest whole number, the first full year in which expenditures exceeded $110 billion was 2027.

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Answer:

B only

Step-by-step explanation:

Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.

Therefore, only B is correct

The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.

The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.

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The correct expression that is equivalent to (f + g) (4) is: f(4) + g(4).

The expression (f + g) (4) represents the sum of two functions, f(x) and g(x), evaluated at x = 4. To find the equivalent expression, we need to simplify it.

In (f + g) (4), the parentheses indicate that the addition operation is performed first, adding the functions f(x) and g(x) together. Then, the resulting sum is evaluated at x = 4. So, the expression simplifies to f(4) + g(4), where we substitute x with 4 in both functions.

The other options provided:

• ¡(4) + g(4): This option is not correct because the negation operator (!) applied to a value does not make sense in this context.

• f(x) + g(4): This option is not correct because it does not evaluate the sum of the functions at x = 4; it keeps the variable x in the expression.

• ¡(4 + g(4)): This option is not correct because it applies the negation operator to the sum of 4 and g(4), which is not equivalent to (f + g) (4).

• 4(f(x) + g(x)): This option is not correct because it introduces a constant factor of 4 to the sum of the functions, which is not equivalent to (f + g) (4).

The correct expression equivalent to (f + g) (4) is f(4) + g(4).

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This option is not equivalent to (f + g)(4).

The expression (f + g)(4) specifically represents the sum of functions f and g evaluated at x = 4.

To determine which expression is equivalent to (f + g)(4), let's break it down step by step.

The expression (f + g)(4) represents the value obtained by evaluating the sum of functions f and g at x = 4.

We substitute x = 4 into both functions and then add the results.

Let's evaluate each option to see which one matches this process:

¡(4) + g(4):

This option involves evaluating the function f at x = 4 and adding it to the value obtained by evaluating function g at x = 4.

It does not represent the sum of the functions f and g evaluated at x = 4.

This option is not equivalent to (f + g)(4).

f(x) + g(4):

This option involves adding the value of function f at an arbitrary point x to the value obtained by evaluating function g at x = 4.

It does not specifically represent the sum of functions f and g evaluated at x = 4.

This option is not equivalent to (f + g)(4).

¡(4 + g(4)):

This option involves evaluating the function g at x = 4 and adding it to the value obtained by adding 4 to the result.

It does not represent the sum of functions f and g evaluated at x = 4.

This option is not equivalent to (f + g)(4).

4(f(x) + g(x)):

This option involves evaluating the functions f and g at an arbitrary point x, summing the results and then multiplying the sum by 4.

It does not specifically represent the sum of functions f and g evaluated at x = 4.

None of the given options is equivalent to (f + g)(4).

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Given, Juan y Roberto is two brothers who play Rock, Paper, and Scissors to determine who does the cleaning in their room. The total number of possible outcomes is 3. The possible outcomes are rock, paper, and scissors. So, the probability of Juan not doing the cleaning is 1/2 or 50 percent.

The probability that Juan will not do the cleaning is 1/2 or 50 percent. The possible outcomes for playing the game Rock, paper, and Scissors are given as follows. Rock can break scissors, Paper can cover rock, and Scissors can cut paper. Therefore, there are three possible outcomes in this game. The possible outcomes are rock, paper, and scissors.

The probability that Juan will not do the cleaning is 1/2 or 50 percent since there are two possible outcomes where Juan does not do the cleaning. The two possible outcomes are paper and scissors. Juan can pick the paper or scissors to win. Therefore, the probability of Juan not doing the cleaning is 1/2 or 50 percent.

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Answer:

(a)  $556 billion

(b)  $581 billion

(c)  $693 billion

Step-by-step explanation:

The given function is:

[tex]\boxed{A(x)=314e^{0.044x}}[/tex]

where A(x) is the assets (in billions of dollars) for a financial firm .

If x = 7 corresponds to the year 2007 then:

Therefore, to find the assets for each of the given years, substitute the corresponding value of x into the function.

[tex]\begin{aligned}A(13)&=314e^{0.044 \cdot 13}\\&=314e^{0.572}\\&=314(1.77180712...)\\&=556.34743707...\\&=556\; \sf (nearest\;billion)\end{aligned}[/tex]

[tex]\begin{aligned}A(14)&=314e^{0.044 \cdot 14}\\&=314e^{0.616}\\&=314(1.851507181...)\\&=581.3732549...\\&=581\; \sf (nearest\;billion)\end{aligned}[/tex]

[tex]\begin{aligned}A(18)&=314e^{0.044 \cdot 18}\\&=314e^{0.792}\\&=314(2.20780762...\\&=693.2515954...\\&=693\; \sf (nearest\;billion)\end{aligned}[/tex]

To find the experimental probability of rolling a number greater than 10, we need to determine the frequency of rolling a number greater than 10 and divide it by the total number of rolls.

Looking at the table, we can see that the frequency for rolling a number greater than 10 is the sum of the frequencies for rolling 11 and 12.

Frequency for rolling a number greater than 10 = Frequency of 11 + Frequency of 12

Frequency for rolling a number greater than 10 = 15 + 17 = 32

The total number of rolls is given as 200.

Experimental Probability of rolling a number greater than 10 = Frequency for rolling a number greater than 10 / Total number of rolls

Experimental Probability of rolling a number greater than 10 = 32 / 200

Experimental Probability of rolling a number greater than 10 = 0.16 or 16%

Therefore, the experimental probability of rolling a number greater than 10 is 16%.

Hopes this helps you out :)

Answer:

y = π/3

Step-by-step explanation:

To find the value of y, we can use the trigonometric identity for the sum of angles:

sin(x + y) = sin x * cos y + cos x * sin y

Comparing this with the given equation:

sin(x + y) = 1/2(sin x) + √3/2(cos x)

We can equate the corresponding terms:

sin x * cos y = 1/2(sin x) ----(1)

cos x * sin y = √3/2(cos x) ----(2)

From equation (1), we can see that cos y = 1/2.

From equation (2), we can see that sin y = √3/2.

To determine the values of y, we can use the trigonometric values of cosine and sine in the first quadrant of the unit circle.

In the first quadrant, cos y is positive, so cos y = 1/2 corresponds to y = π/3 (60 degrees).

Similarly, sin y is positive, so sin y = √3/2 corresponds to y = π/3 (60 degrees).

Therefore, the value of y is y = π/3 (or 60 degrees).