A builder was building a fence. In the morning, he worked for 2/5 of an hour. In the afternoon, he worked for 9/5 of an hour. How many times as long as in the morning did he work in the afternoon? Write a division equation to represent this situation, then answer the questions. Show your reasoning.

Answer:

69.08

Step-by-step explanation:

diameter = r2 = 11 x 2 = 22

3.14(22) = 69.08

Answer:

see explanation

Step-by-step explanation:

using the tangent ratio in the right triangle

tan A = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AB}\) = \(\frac{5}{11}\) , then

∠ A = \(tan^{-1}\) ( \(\frac{5}{11}\) ) ≈ 24.4° ( to 1 decimal place )

tan C = \(\frac{opposite}{adjacent}\) = \(\frac{AB}{BC}\) = \(\frac{11}{5}\) , then

∠ C = \(tan^{-1}\) ( \(\frac{11}{5}\) ) ≈ 65.6° ( to 1 decimal place )

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

AC² = AB² + BC² = 11² + 5² = 121 + 25 = 146 ( take square root of both sides )

AC = \(\sqrt{146}\) ≈ 12.08 ( to 2 decimal places )

Answer:

7x sqrt(2) - 2 sqrt(2)

Step-by-step explanation:

5x sqrt(2) - 2 sqrt(2) + 2x sqrt(2)

Combine like terms

5x sqrt(2) + 2x sqrt(2)    - 2 sqrt(2)

7x sqrt(2) - 2 sqrt(2)

Answer: the result is 930 minutes.

Step-by-step explanation:

15.5 hours to minutes has been calculated by multiplying 15.5 hours by 60

The drive from Savannah to Milwaukee takes approximately 930 minutes .

To convert the drive time from hours to minutes, we can multiply the number of hours by 60, as there are 60 minutes in an hour .

Given that the drive from Savannah to Milwaukee takes approximately 15.5 hours, we can calculate the drive time in minutes as follow s:

The time in minutes is equal to the time in hours multiplied by 60 .

15.5 hours = 15.5 hours * 60 minutes/hour .

15.5 hours = 930 minutes .

Therefore, the drive from Savannah to Milwaukee takes approximately 930 minutes .

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To solve the problem.

W=m×g

W=28×10

W=280.

The weight of a dog on the surface of earth is 280N.

Answer:

274.68N and 45.36N respectively

Step-by-step explanation:

Weight of any object is the mass in kilograms(kg) multiplied by the gravity in meter per square second(m/s^2). The gravity on earth is 9.81m/s^2 and on moon is 1.62m/s^2...so since the gravity varies the weight of the dog will also vary. The wight on earth would be 28kg multiplied by 9.81m/s^2 which would be 274.68N and the weight on moon would be 28kg multiplied by 1.62m/s^2 which would be 45.36N.

Answer:

70.01 so 70

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

600 - 529.99 = 70.01

70.01 is rounded to 70

Answer is 70

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.

A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.

The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).

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Answer:

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is 202500 swordfishes.

Step-by-step explanation:

Let be \(f(p) = -0.01\cdot p^{2}+9\cdot p\), the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)

First Derivative Test

\(f'(p) = -0.02\cdot p +9\)

Let equalize the resulting expression to zero and solve afterwards:

\(-0.02\cdot p + 9 = 0\)

\(p = 450\)

Second Derivative Test

\(f''(p) = -0.02\)

This means that result on previous part leads to an absolute maximum.

The population that gives the maximum sustainable yield is 45000 swordfishes.

The maximum sustainable yield is:

\(f(450) = -0.01\cdot (450)^{2}+9\cdot (450)\)

\(f(450) =2025\)

The maximum sustainable yield is 202500 swordfishes.

Answer:

-2/9

Step-by-step explanation:

When you multiply a number by its multiplicative inverse, you should get 1. So, the multiplicative inverse (or reciprocal) of -9/2 is 1/(-9/2) which is -2/9. You can get the answer by simply flipping the numerator and denominator.

Answer:

A. Zero

Step-by-step explanation:

In this example, the two lines are parallel. Henceforth, they will never intersect each other. For the system of equations to have any solutions, they would need to intersect.

Answer:

34/18 is greater than 1 5/6.

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

Answer:

greater than

Step-by-step explanation:

1=6/6 and 6+5=11, so 1 5/6= 11/6

Next, you want to find a common denominator, in this case 18

11/6=x/18

x=33

11/6=33/18

34/18 > 33/18

As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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Answer:

x = 4

Step-by-step explanation:

We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)

Big triangle:little triangle

25:5

5:1

So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.

Solve for x:

3x+8 = 4(5) [ratio!!]

3x+8 = 20

(subtract 8 from both sides)

3x = 12

(divide both sides by 3)

x = 4

Thus, we have our answer!

Answer:

B

-twice what Levi has-  so 2(x)

-eight less than... -  so 2(x) - 8

Answer:

B

Step-by-step explanation:

Let \(j =\)number of cards Johnny has

From 'Johnny has 8 less cards than twice what Levi has', you can form the equation below:

\(j = 2x-8\)

\(\therefore\) B is the correct answer.

Hope this helps :)

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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Answer:

Non-Homogeneous Recurrence Relation and Particular Solutions

A recurrence relation is called non-homogeneous if it is in the form. Fn=AFn−1+BFn−2+f(n) where f(n)≠0.

We know this because the property √ (a * b) = √a * √b allows us to simplify expressions under radicals by factoring out perfect squares or perfect cubes. In this case, we were able to factor out a perfect cube of 1 and simplify the expression to 3 * √11.

In geometry, a cube is a three-dimensional solid object with six square faces, where each face meets the others at a right angle. It has 12 edges and 8 vertices. The cube is a regular polyhedron, meaning all of its faces are congruent (equal in size and shape) and its angles are all equal.

A cube can be thought of as a special case of a rectangular parallelepiped, where all sides are equal in length. The volume of a cube is found by taking the cube of the length of one of its sides, and its surface area is found by taking the product of the length of one of its sides by 6. Cubes are used in many applications, such as in building blocks for children, dice, and in architecture.

by the question.

To find an equivalent form of 3√11, we can use the property of radicals that states:

√ (a * b) = √a * √b

We can use this property to simplify the expression under the radical until we can factor out a perfect cube.

3√11 can be written as 3√ (1 * 11)

Using the above property, we can simplify as follows:

3√ (1 * 11) = 3√1 * √11 = 3 * √11

Therefore, an equivalent form of 3√11 is 3 * √11.

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Answer:

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

Step-by-step explanation:

exponential in the form

f(x) = C\(a^{x}\)

to find C and a use points from the graph

using (0, 2 ) , then

2 = C\(a^{0}\) ( \(a^{0}\) = 1 ) , so

C = 2

f(x) = 2\(a^{x}\)

using (2, \(\frac{2}{9}\) )

\(\frac{2}{9}\) = 2a² ( divide both sides by 2 )

\(\frac{1}{9}\) = a² ( take square root of both sides )

\(\sqrt{\frac{1}{9} }\) = a ⇒ a = \(\frac{1}{3}\)

f(x) = 2 \((\frac{1}{3}) ^{x}\) ← exponential function

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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The answer is \((x+9)+(x-2)\) .

We have given two statements one is " number increased by nine "

Let the number be x .

Mathematically , first statement is represented by

  x + 9

Second statement is " number decreased by two "

Mathematically , second statement is represented by

  x - 2

According to the question

Sum of first and second statement = \((x+9)+(x-2)\)

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer:

2.6 2.6 2.8 2.9 2.9

Step-by-step explanation:

used median for the five numbers.

Answer:

Unit price is $0.47

Step-by-step explanation:

4.23÷9= .47

Answer:

46 hours and 42 minutes

Step-by-step explanation:

2100/45 = 46.7

46 hours and 42 minutes

Hopefully this helps you :)

pls mark brainlest ;)

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

True

Step-by-step explanation:

The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4\(\neq\)9, 1\(\neq\)9, 8\(\neq\)9, and 7\(\neq\)9 then 9 is not an element of this set and the statement is true.

The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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