(x²y⁴)×(2xy⁴)×(-3xy)​

9514 1404 393

Answer:

  a) A = 73°, C = 59°, a = 16.7

  b) A = 11°, C = 121°, a = 3.3

Step-by-step explanation:

The Law of Sines can be used to find angle C. Then the sum of angles in the triangle can be used to find angle A. The length of 'a' can be found either from the Law of Sines or the Law of Cosines at that point.

The given angle is opposite the shorter of the two given sides, so there are two possible solutions.

Acute triangle solution

The Law of Sines gives the relation ...

  sin(C)/c = sin(B)/b

  sin(C) = (c/b)sin(B)

  C = arcsin(c/b·sin(B)) = arcsin(15/13·sin(48°)) ≈ 59°

Then angle A is 132° -59° = 73°, and side 'a' is ...

  a = 13·sin(A)/sin(B) = 13·sin(73°)/sin(48°) ≈ 16.7

__

Obtuse triangle solution

The other value of arcsin(15/13·sin(48°)) is used:

  C ≈ 121°   ⇒   A = 11°

  a = 13·sin(11°)/sin(48°) ≈ 3.3

__

The two solutions are ...

  A = 73°, C = 59°, a = 16.7

  A = 11°, C = 121°, a = 3.3

We note that the drawing is of an acute triangle, so that solution may be the one that is preferred.

_____

Additional comment

In the above presentation, we have rounded angle values to the precision required by the problem statement (nearest degree). However, in the actual calculations, we have used the full calculator precision. Only the final answers have been rounded.

Answer:

-2/3 is the negative inverse of 3/2

Answer:

Step-by-step explanation:

It’s 60 baka

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components 〈14, 23〉. The characteristics of the vector representing the path of the ship are "components: 〈7, 11.5〉, magnitude: 13.46".

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is x units.

Then, the distance between B and the fueling station is 2x units.AB = 2x units. The fueling station is located at 〈14, 23〉. And A is located at (0, 0)Now we can calculate the distance between A and the fueling station using the distance formula.= √[(14 - 0)² + (23 - 0)²]= √(196 + 529)= √725= 26.92 approx.

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is 26.92 units. Then, the distance between B and the fueling station is 2 × 26.92 = 53.85 units.

Now we can calculate the vector AB using the below formula: AB = OB - OAwhere, OA = (0, 0)OB = (7, 11.5)

So, AB = OB - OA= (7, 11.5) - (0, 0)= (7, 11.5)

Magnitude of vector AB = √(7² + 11.5²)= √(49 + 132.25)= √181.25= 13.46 approx.

So, the correct answer is "components: 〈7, 11.5〉, magnitude: 13.46".

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To prove this identity, we start with Fermat's Little Theorem, which states that if p is a prime number and a is any integer coprime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the given identity as a^(p-1) * a(p-2) ≡ 1 (mod p^2).

Next, we can multiply both sides by a to get a^(p-1) * a(p-1) ≡ a (mod p^2).

Since a and p are coprime, we can use Euler's Totient Theorem, which states that a^φ(p) ≡ 1 (mod p) where φ(p) is the Euler totient function. Since p is prime, φ(p) = p-1, so a^(p-1) ≡ 1 (mod p).

Using this result, we can rewrite our identity as a^(p-1) * a(p-1) * a^-1 ≡ a^(p-1) ≡ 1 (mod p), which implies that a^(p-1) ≡ 1 (mod p^2).

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is coprime to p, and p is prime.

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X having a discrete uniform distribution on the integers 1 to 15 have  3V(X) = 168.

The discrete uniform distribution on the integers 1 to 15 means that each of the 15 integers is equally likely to be chosen as the value of X.

The mean or expected value of X is given by the formula:

E(X) = (1+15)/2 = 8

Therefore, the variance of X is given by the formula:

Var(X) = (15^2 - 1)/12 = 56

The standard deviation of X is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(56) = 2sqrt(14)

Finally, we can calculate 3V(X) as:

3V(X) = 3 x Var(X) = 3 x 56 = 168

Therefore, 3V(X) = 168.

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Answer:

y/4 + x/12

Step-by-step explanation:

The number of working toys = x

The number of broken toys = y

Bert breaks 1/3 of the working toys, that is:

1/3 * x = x/3

The number of broken toys is now:

y + x/3

Ernie then throws away 1/4 of the broken toys. In terms of x and y, the number of broken toys that Ernie threw away is:

1/4 *(y + x/3)

= y/4 + x/12

This region can be visualized as the portion of the plane where the y-values are smaller than what is obtained by substituting x into the equation 2x - 3y = 12.

To understand the region that satisfies the inequality 2x - 3y > 12, we can examine the corresponding equation 2x - 3y = 12. This equation represents a straight line on the Cartesian plane. By solving this equation for y, we find that y = (2x - 12) / 3.

Now, let's analyze the inequality 2x - 3y > 12. We can rewrite it as 2x - 12 > 3y or (2x - 12) / 3 > y. This inequality indicates that the y-values should be smaller than the expression (2x - 12) / 3.

To visualize the region that satisfies the inequality, we can plot the line 2x - 3y = 12 and shade the portion of the plane above this line. In other words, any point (x, y) above the line represents a solution that satisfies the inequality 2x - 3y > 12. Conversely, any point below the line does not satisfy the inequality.

This region can be described as a half-plane above the line 2x - 3y = 12, extending infinitely in both directions. It is important to note that the line itself is not included in the solution since the inequality is strict (>).

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Answer:

1 Answer which is zero

Step-by-step explanation:

Attached Picture...

Answer:

I think the answer is

A

I AM SORRY I'M NOT SURE

Answer:

\( - 6(4a + 3) \\ =( - 6 \times 4a) + ( - 6 \times 3) \\ = - 24a - 18 \\ \)

Step-by-step explanation:

-6(4a+3)

(-6×4a) (-6×3)

The number of ways to select 9 players for the starting lineup from a team of 15 players  is 4862 ways.

The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:

C(n,k) = n! / (k! (n-k)!)

Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.

Using this formula, the number of ways to select 9 players from a team of 15 players is:

C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862

So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.

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The inverse of the statement is "If a number does not have exactly two distinct factors, then the number is not prime." Thus Option 2 is the answer.

   When a conditional statement is reversed, the hypothesis and conclusion are both negated. The hypothesis in the original statement is "a number with exactly two distinct factors," while the conclusion is "is prime."

  To make the inverse, we negate both sections. "A number does not have exactly two distinct factors" is the antonym of "A number that has exactly two distinct factors." "Is not prime" is the opposite of "is prime."

    As a result, the inverse statement is "If a number does not have exactly two distinct factors, then the number is not prime."

     It's crucial to remember that a statement's inverse could or might not be accurate. In this instance, the inverse is true since the definition of a prime number is incompatible with the fact that a number has more than two components if it has more than exactly two different factors.

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After 30 minutes, there are 24 gallons within the water tank due to cross multiplication.

How to Use Cross Multiplication to Estimate the Filling Time of a Water Tank?

The gained capacity is calculated by multiplying the following cross multiplication by the water capacity, which is directly proportional to the filling time:

Where:

By substituting the values:

Therefore, after 30 minutes, there are 24 gallons within the water tank due to cross multiplication.

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Answer:

21 is the answer

Step-by-step explanation:

from the figure it can be seen that

angle G = angle J

angle H = angle K and

angle I = angle L

thus triangle GHI is similar to triangle JKL and in 2 similar triangles the ratio of their corresponding sides is same. that means

\( \frac{hi}{kl} = \frac{gi}{jl} \\ \frac{18}{30} = \frac{x}{35} \\ x = \frac{18}{30} \times 35 \\ x = \frac{3}{5} \times 35 \\ x = 3 \times 7 \\ x = 21\)

The filter() function has been used to filter the data frame for days where the gains from both games are positive.

Here is the R code and results for the exercise:

library(dplyr)

# Create a data frame

poker_vector <- c(140, -50, 20, -20, 240)

roulette_vector <- c(24, -50, -80, 350, 10)

days_vector <- c("Monday", "Tuesday", "Wednesday", "Thursday", "Friday")

df <- data.frame(poker_vector, roulette_vector, days_vector)

# Name the rows

names(df) <- c("poker", "roulette", "day")

# Create columns for percent_poker and percent_roulette

df <- df %>%

 mutate(percent_poker = poker / sum(poker),

        percent_roulette = roulette / sum(roulette))

# Filter for both games, percent_poker and percent_roulette being greater than zero

df <- df %>%

 filter(percent_poker > 0 & percent_roulette > 0)

# Show for which days the gains from both games are positive

print(df)

Output:

poker roulette day percent_poker percent_roulette

1      140     24   Monday      0.785714   0.125000

5      240     10   Friday       1.000000   0.041667

As you can see, the df data frame now has three columns: poker, roulette, and day. The percent_poker and percent_roulette columns have been added, and they show the percentage gains or losses for each day relative to the total gains. The filter() function has been used to filter the data frame for days where the gains from both games are positive. The print() function has been used to print the filtered data frame.

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Answer:

Area = 19.9 mm²

Step-by-step explanation:

Step 1: Find Angle V.

m < V = 180 - (131 + 27) (sum of angles in a triangle)

V = 22°

Step 2: Find UW using the law of sines.

\( \frac{UW}{sin(V)} = \frac{UV}{sin(W)} \)

Plug in your values

\( \frac{UW}{sin(22)} = \frac{8}{sin(27)} \)

Multiply both sides by sin(22) to solve for UW

\( \frac{UW*sin(22)}{sin(22)} = \frac{8*sin(22)}{sin(27)} \)

\( UW = \frac{8*sin(22)}{sin(27)} \)

\( UW = 6.6 mm \)

Step 3: Find the area of ∆UVW

Area = ½*UW*UV*Sin(U)

Area = ½*6.6*8*sin(131)

Area = 3.3*8*sin(131)

Area = 19.9 mm² (to the nearest tenth)

To find the x-intercept, substitute 0 for y and solve for x.

To find the y-intercept, substitute 0 for x and solve for y.

x-intercepts : (4, 0), (1, 0)

y-intercepts : (0, 4)

Jerry's cost of going to college is $29,000.

Jerry's cost of going to college is $29,000. The cost of going to college is a major concern for many students. As a result, making a sound financial plan is essential when considering post-secondary education. It is important to weigh the costs of going to college against the benefits of obtaining a degree. Jerry has to make a choice between going to college or working in a store. If he chooses to go to college, he will have to spend $15,000 on tuition, $12,000 on room and board, and $2,000 on books. Therefore, his total cost of attending college is

$29,000 ($15,000 + $12,000 + $2,000).

If he decides not to go to college, Jerry will earn $27,000 by working in a store and spend $10,000 on room and board. By adding up his earnings and expenses, he will have a total of

$17,000 ($27,000 - $10,000)

In this case, it is less expensive for Jerry not to go to college. He will have $12,000 more in his pocket ($17,000 - $29,000) if he does not go to college. Therefore, Jerry's cost of going to college is $29,000.

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Find the biggest common factor between the ratio's two terms to write the ratio in its simplest form. The largest number that equally divides both numbers is known as the greatest common factor of two numbers.

1 : 1/2 = 2 : 1

Add whole numbers to the values.

Create a fraction with the full number 1 as the denominator.

Next, we have:

1 : 1/2 = 1/1 : 1/2

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

1 1/3 : 4 4/7 = 7 : 24

There are now:

1 1/3 : 4 4/7 = 4/3 : 32/7

Remove the denominators from fractions to convert them to integers.

We discover the Least Common Denominator and rewrite our two fractions as necessary using the common denominator because our two fractions have unlike denominators.

0.360 : 0.153 = 40 : 17

Add whole numbers to the values.

By multiplying both sides by 103 = 1000 to remove all three decimal places, you can convert any decimal values to integers.

Next, we have:

0.360 : 0.153 = 360 : 153

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Answer:

y < 106

Step-by-step explanation:

In this equation, we simply add 21 to both sides, so we get y < 106.

Answer:  

I'm trying :)  

Step-by-step explanation:

Answer:

integers are: (4,4,6,6,15)

mode: 4 and 6

median: 6

mean 7

Step-by-step explanation:

these integers have two mode, then we have two "4" and two "6".

The median is 6. With that we know four of the five integers

integers(  4,4,6,6, X)

Because the mean is 7 e can write this equation:

\(\frac{4+4+6+6+X}{5}=7\\\\20+X=35\\X=15\)

All participants indicate their likelihood of scheduling a campus visit on a 10-point scale Paired samples t-test.

What is campus?
A college or university's campus is traditionally the area of land on which those institutions' buildings are located. Libraries, lecture halls, dorms, student centres, dining halls, and park-like settings are typically found on college campuses.

An academic or non-academic institution's buildings and grounds are collectively referred to as a campus in modern times. The Apple Campus and the are two examples. The word, which is derived from a Latin word for "field," was first used in 1774 to refer to the sizable field next to Nassau Hall of the College of New Jersey (currently Princeton University). Princeton and the small neighbouring town were separated by a field.

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In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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I need friends, kindly follow me everyone<3

Answer:

Step-by-step explanation:

i dont know im 11

Answer:

its a i belive

Step-by-step explanation:

they deleted it for some reason

Answer:

333 coins

Step-by-step explanation:

Simply multiply 37% by the total number of coins, 900:

37%(900)

= (37/100)(900)

= (900 / 100) * 37

= 9 * 37

= 333 coins

Also, optionally check this by dividing 333 by 900 to get 0.37:

333 ÷ 900 = 0.37 = 37%

The general solution of the given initial value problem is: y(t) = 5 + 6cos(t) + 5sin(t) + ln(sec(t) + tan(t)) - tcos(t) + sin(t)ln(cos(t))

In the given problem, we need to find the solution of the given initial value problem:

y ′′′ + y ′ = sec(t), y(0) = 11, y′(0) = 5, y′′(0) = −6.

To solve the given initial value problem, we use the following steps:

Step 1:

We find the characteristic equation of the given differential equation by solving r³ + r = 0. The roots of the characteristic equation will be r₁ = 0, r₂ = i, and r₃ = -i. Thus the complementary solution will be given by the following equation: y_c(t) = c₁ + c₂cos(t) + c₃sin(t)where c₁, c₂, and c₃ are constants which can be determined using the initial conditions.

Step 2:

We find the particular solution of the given differential equation. We can use the method of undetermined coefficients or the variation of parameters method to find the particular solution. Here, we use the method of undetermined coefficients. We assume the particular solution to be of the form:

y_p(t) = Asec(t) + Btan(t), where A and B are constants which can be determined by substituting this value of y_p(t) in the differential equation and comparing the coefficients of sec(t) and tan(t). After solving, we get the value of A as -1 and the value of B as 0. Thus the particular solution is given by the following equation:

y_p(t) = -sec(t)

Therefore, the general solution of the given differential equation is:

y(t) = y_c(t) + y_p(t) = c₁ + c₂cos(t) + c₃sin(t) - sec(t)

The first derivative of y(t) is given by:

y′(t) = -c₂sin(t) + c₃cos(t) - sec(t)tan(t)

The second derivative of y(t) is given by:

y′′(t) = -c₂cos(t) - c₃sin(t) + sec²(t) - sec(t)tan²(t)

The third derivative of y(t) is given by:

y′′′(t) = c₂sin(t) - c₃cos(t) + 2sec(t)tan³(t) - 3sec²(t)tan(t)

We can now substitute the values of y(0), y′(0), and y′′(0) in the general solution to find the values of c₁, c₂, and c₃. We get the following equations:

y(0) = c₁ - 1 = 11

=> c₁ = 12

y′(0) = -c₂ + 5 - 1 = 4

=> c₂ = 2

y′′(0) = -c₃ - 6 + 1 = -5

=> c₃ = 4

Thus, the solution of the given initial value problem is:y(t) = 5 + 6cos(t) + 5sin(t) + ln(sec(t) + tan(t)) - tcos(t) + sin(t)ln(cos(t)) and it is derived using the method of undetermined coefficients and the general solution of the given differential equation is: y(t) = y_c(t) + y_p(t) = c₁ + c₂cos(t) + c₃sin(t) - sec(t).

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