Find the particular solution to the differential equation subject to the given initial condition. dB/dt +0.3B – 30 = 0, B(3) = 6 NOTE: Round your value for the integration constant to the nearest integer. B = 100 - 94 e-0.3t+0.9

Prove that a || b

What is Angles?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given,

c || d

<1 = <7

We have to prove a || b

∠1 = ∠5         corresponding angles of lines a and b

∠1 = ∠4          are alternate interior angles of lines a and b

∠5 = ∠7         corresponding angles of lines a and b

∠3 = ∠7         corresponding angles of lines a and b

Therefore, a || b by converse corresponding angle theorem

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Answer:

3/10

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

Answer:

semoga jawapan ini dapat membantu

The equation of the line in standard form is 2x - y = 4

The equation of a line in standard form is expressed as Ax + By  = C

Get the slope of the line passing through (2, 0) and (0, -4)

Slope = -4/-2
Slope = 2

GThe y intercept of the line is -4

Get the equation

y = 2x - 4

y - 2x = -4
-2x + y = -4
2x - y = 4

Hence the equation of the line in standard form is 2x - y = 4

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Apply the Binomial Probability Distribution, The Answer is 0.044.

The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.

The required formula is:

\(P(x)= C(n,x) p^{x}q^{n-x}\)

n=10

x=8

p(8)= \(C(10,8) * 0.5 ^ {8} *0.5 ^{2}\)

=0.044

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Step-by-step explanation:

A bunny seller began their business with only 2 bunnies. The seller noticed that the number of bunnies the farm expanding after t days can be modeled by the equation

\(P=2(3)^t\)

we know that the exponential equation is in the form of

\(y=a(b)^x\)

Where 'a' is the initial value

y is the final value

b is the rate factor

x is the time period

P=2(3)^t

\(3^3\) represent the value of t is 3

we know that 't' represents the number of days

\(3^3\) represent the farm expanding after 3 days

In total, the fibonacci() function is called 9 times (excluding the initial function call).

To determine the number of times the fibonacci() function is called when given the input 4, we need to analyze the recursive nature of the Fibonacci sequence and count the number of function calls.

When fibonacci(4) is called, it will recursively call the fibonacci() function for the inputs 3 and 2. The call for input 3 will further call the function for inputs 2 and 1, and the call for input 2 will call the function for inputs 1 and 0. The Fibonacci function stops recursive calls when reaching the base cases of 1 and 0.

Let's break it down step by step:

fibonacci(4)

-> fibonacci(3) + fibonacci(2)

-> fibonacci(2) + fibonacci(1) + fibonacci(1) + fibonacci(0)

-> fibonacci(1) + fibonacci(0)

-> base case reached (1 and 0)

-> base case reached (1)

-> fibonacci(2) + fibonacci(1)

-> fibonacci(1) + fibonacci(0)

-> base case reached (1 and 0)

-> base case reached (1)

In total, the fibonacci() function is called 9 times (excluding the initial function call).

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Step-by-step explanation:

Hey there!

Given;

f ( x ) = x² + 2x - 1

g ( x ) = 3x - 2

To verify:

\(( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} \)

LHS:

\( (\frac{f}{g} )(x) = \frac{ {x}^{2} + 2x - 1}{3x - 2} \)

~ Insert "2" instead of "x".

\( (\frac{f}{g} )(2) = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} \)

Simplify it;

\( \frac{f}{g} (2) = \frac{4 + 4 - 1}{6 - 2} \)

Therefore; (f/g)(2) = 7/4.

RHS:

\( \frac{f(x)}{g(x)} = \frac{ {x}^{2} + 2x - 1}{3x - 2} \)

~Insert "2" instead of"x".

\( \frac{f(2)}{g(2)} = \frac{ {2}^{2} + 2 \times 2 - 1 }{3 \times 2 - 2} \)

Simplify it.

\( \frac{f(2)}{g(2)} = \frac{4 + 4 - 1}{6 - 2} \)

Therefore, f(2)/g(2) = 7/4.

Since (f/g)(2) = f(2)/g(2) = 7/4.

Proved!

Hope it helps!

Step-by-step explanation:

Soo :

\( \tt( \frac{f}{g} )(2) = \frac{f(2)}{g(2)} \)

\( \tt( \frac{ {x}^{2} + 2x - 1 }{3x - 2} )(2) = \frac{ {2}^{2} + 2(2) - 1 }{3(2) - 2} \)

\( \tt( \frac{ {2}^{2} + 2(2) - 1}{3(2) - 2} )= \frac{7}{4} \)

\( \boxed{ \tt \frac{7}{4} = \frac{7}{4} }\)

Soo true.

Answer:

73

Step-by-step explanation:

The explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1)

We can easily determine the value of any term in the sequence using the formula once you have those values.

where:

The sequence's nth word is a n.

The first term in the series is a 1.

The frequency of successive terms is expressed as r.

The sequence's length, n, is given.

The values of a 1, r, and n must be known in order to use this algorithm as a geometric sequence calculator. You can easily determine the value of any term in the sequence using the formula once you have those values.

Therefore, the explicit formula for geometric sequence calculator is  n = a 1 + r^(n-1) (n-1).

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The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

a =-13/24 b = 5/3

Step-by-step explanation:

From given

8a + 5b = 4 (1)

3b = 5 (2)

Using (2)

b = 5/3

Putting the value of b into (1) gives

8a + 5(5/3) =4

8a + 25/3 = 4

8a = 4 - 25/3

8a = -13/3

a = -13/(3*8)

a = -13/24

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Answer:

x = -5

Step-by-step explanation:

Start by combining terms.

8x-2 = 12x +18

8x -12x = 18+2

-4x = 20

*Divide both sides by -4

x = -5

First, we order the numbers from least to greatest: -12.5, -4.5, and 10.5.

Observe that the first two are negative because they are below sea level.

Having said that, we can place the numbers on the number line.

The graph of this function would be a straight line passing through the point (0, c) with a slope of m.

What is the function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

If the function increases at a constant rate of m and has a y-intercept of (0, c), then its equation can be written as:

f(x) = mx + c

The graph of this function would be a straight line passing through the point (0, c) with a slope of m.

Here's an example of the graph of f(x) = 2x + 3:

Attachment

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Answer:

Move each point 2 left then 3 up then connect the dots

Step-by-step explanation:

Answer:

65°

Step-by-step explanation:

The sum of the angles of a triangle is always 180°. Meaning, ∠P + ∠Q + ∠R = 180.

(2x-9) + (2x+4) + x = 180

Combine like terms:

5x-5 = 180

5x = 185

x = 37

P = (2x - 9) = 2(37) - 9 = 74 - 9 = 65

Answer:

50 bags

Step-by-step explanation:

1 kg = 1000 grams

10 kg * 1000g/ 1kg = 10000 g

Divide 10000 grams by 200 g

10000g / 200g = 50

The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of  Permutation and Combination.

If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.

To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.

To get the total number of ways, we can multiply these numbers:

495 x 1,365 = 7,425.

To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.

To get the total number of ways, we can add these numbers:

495 x 5,005 + 2,190 x 3,003 = 58,275.

To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.

To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.

Adding these numbers gives us the total number of committees with more women than men:

15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700

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Answer:

(a) 494₁₀ = 111101110₂

(b) 494₁₀ = 13232₄

(c) 494₁₀ = 3434₅

(d) 494₁₀ = 756₈

(e) 494₁₀ = 608₁₀

Step-by-step explanation:

494₁₀ means the number is to the base 10 and therefore a decimal number which we interpret in everyday terms as just 494

To convert a number from base 10 to another base, say b, we continuously divide by that base, noting the remainder at each operation. Then we read the remainders from the last to the first and that will give you the number in terms of that other base

This is a tedious operation and best done by a base conversion calculator.

I will demonstrate using base 9 as an example

494₁₀ = what in base 9

Keep dividing by 9 until you can divide no more. Keep track of the remainder at each division

operation        quotient    remainder

494 ÷  9             54                8
54  ÷  9               6                0
   6  ÷ 9               0                6

Read the remainders from the last to the first: 6 0 8
So 494₁₀ = 608₉

The others can be done in a similar manner

However this is tedious and a computer program is easy to write for this conversion

Search for number base conversion calculator - you will find several online.

I have provided the answers for you to verify

Answer:

x = 10

Step-by-step explanation:

Both cosine and sine functions are defined for all angles, so none of the functions are undefined for -2π.

When we consider the unit circle, angles are measured in radians. The angle -2π represents a full revolution around the unit circle in the clockwise direction. In other words, it is equivalent to an angle of 0 radians or 360 degrees.

Since the point (-1, 0) corresponds to an angle of 0 radians on the unit circle, it also corresponds to an angle of -2π radians. Therefore, the point on the unit circle that corresponds to -2π is (-1, 0).

Now let's find cos(-2π) and sin(-2π):

cos(-2π) = cos(0) = 1

sin(-2π) = sin(0) = 0

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Answer:

I think the answer is 792

Answer:

SA = 696cm^2

Step-by-step explanation:

First we need to identify the shapes

There are 3 rectangles and 2 triangles

Now the individual surface area for each shape

20 x 10 = 200 (1 rectangle)

1/2(12 x 8) = 48 (1 triangle)

Now we add them together

(200 x 3) + (48 x 2) = 696

Answer:

The answer is A.

Step-by-step explanation:

First, you have to add 2 to both sides, to get rid of the -2 on the left side :

\(9x - 2 = 2x + 12\)

\(9x - 2 + 2 = 2x + 12 + 2\)

\(9x = 2x + 14\)

Next, you have to subtract 2x to both sides, to make all the x terms to one side and then, solve it :

\(9x - 2x = 2x + 14 - 2x\)

\(7x = 14\)

\(x = 14 \div 7\)

\(x = 2\)

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The slope of the line segment that represents the period of time during which the speed decreases is: C: The slope is -10.

The parameters given are:

Starting speed of the car = 55 km/hr

Let us suppose when t=0 , the speed of car was 55 km/hr.

Then car broke down.

The following Data are given regarding car's speed versus the amount of time elapsed from the moment that it began to brake.

Elapsed Time (sec) Speed (mph) → 1 :45 ,2 :35, 3 :25, 4 :15, 5 :15 ,6 :15

Slope of line passing through two points (a, b) and (p, q) is given by the formula:

Slope = (q - b)/(p - a)

Thus, Slope of line passing through two points (1,45) and (2,35) is:

Slope = (35 - 45)/(2 - 1)

Slope = -10

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Answer:

21x+14u-7

Step-by-step explanation:

Just distribute the -7 into the numbers in the parentheses.

Answer:

x=5, y=3

Step-by-step explanation: