Mr. thomas is going to climb on his roof to clean the gutters. he has an 8 foot extension ladder that can extend to 16 feet. if the roof is 12 feet off the ground and the ladder needs to be 3 feet away from the house, does mr. thomas have a tall enough ladder?

Answer:

2:1

Step-by-step explanation:

2/3 of the class is girls, so that means 1/3 of the class is boys. Make the number of people in the class x. The equasion would be (2/3x)/(1/3x) This simplifies to 2:1

Answer:

Your answer would be 2:1

Step-by-step explanation:

1. 2/3 of the class is girls, so that means 1/3 of the class is boys.

2. Make the number of people in class x.

3. The equasion would be (2/3x) (1/3x)

4. 2:1

a. Using the smallest possible number of items, is not generally a way to enhance reliability.

b. Measuring something that is minimally important, does not necessarily enhance reliability.

c. Aggregating measurements, is the generally useful way to enhance reliability.

d. Maximizing error variance, is not a way to enhance reliability.

Among the options provided, the generally useful way to enhance reliability is option c: to aggregate your measurements.

Aggregating measurements refers to combining multiple measurements or observations to improve the overall reliability of the data. By taking multiple measurements, you can reduce the impact of random errors and obtain a more accurate estimate of the true value or attribute you are measuring.

Option a, using the smallest possible number of items, is not generally a way to enhance reliability. In fact, having a larger sample size or more data points often improves reliability by reducing the effects of random variations.

Option b, measuring something that is minimally important, does not necessarily enhance reliability. The importance of what is being measured is not directly related to the reliability of the measurements. Reliability focuses on the consistency and accuracy of the measurements themselves.

Option d, maximizing error variance, is not a way to enhance reliability. Error variance refers to the variability or spread of errors in measurement. Maximizing error variance would lead to less reliable measurements as it increases the uncertainty and inconsistency of the data.

In summary, option c, aggregating measurements, is the generally useful way to enhance reliability.

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Answer:

The anwer is A

Step-by-step explanation:

If it is a right angle triangle we use paythagoras theorem

a ×a + b× b= c × c

1. 15× 15( square of 15) + b× b(square of b) = 17 ×17 (square of 17)

;2. 225 + b×b(square of b ) = 289

3. b×b(square of b) = 289-225

4. b × b( square of b )= 64

\( \sqrt{b \times b} = \sqrt{64} \)

b = 8

I hope it is helpful

Answer:

f(2r) 6r - 5

Step-by-step explanation:

Substitute x = 2r into f(x) , that is

f(2r) = 3(2r) - 5 = 6r - 5

Answer:

false

Step-by-step explanation:

bc i said so

The power series representation of f(x) =x²/(x⁴ + 16) is given by:

f(x) = (1/4i) × ∑[(-1)ⁿ ×(x²/4i)ⁿ  + (-x²/4i)ⁿ ] and the interval of convergence for this series is -2 < x < 2.

To find the power series representation of the function f(x) = x²/(x⁴ + 16), we can start by decomposing the denominator as a difference of squares:

x⁴ + 16 = (x²)² + 4²= (x² + 4i)(x²- 4i),

where i is the imaginary unit.

Next, we can rewrite the function f(x) as a partial fraction:

f(x) = x²/[(x² + 4i)(x² - 4i)].

We can express the function f(x) as a sum of two fractions:

f(x) = A/(x² + 4i) + B/(x² - 4i),

where A and B are constants to be determined.

To find the values of A and B, we can multiply both sides of the equation by (x² + 4i)(x² - 4i) and then simplify:

x²= A(x² - 4i) + B(x² + 4i).

Expanding the right side, we get:

x² = (A + B)x² + (4B - 4Ai).

From this equation, we can equate the coefficients of the like terms:

1 = A + B,

0 = 4B - 4Ai.

Solving these equations simultaneously, we find A = 1/8 and B = 7/8.

Now, we can rewrite the function f(x) as:

f(x) = (1/8)/(x² + 4i) + (7/8)/(x² - 4i).

Next, we can expand each term using the geometric series:

1/(x² + 4i) = 1/(4i) × 1/(1 - (-x²/4i)) = (1/4i) × ∑((-x²/4i)ⁿ),

and

1/(x² - 4i) = 1/(-4i)×1/(1 - (x²/4i)) = (-1/4i) × ∑((x²/4i)ⁿ).

Substituting these series expansions into f(x), we get:

f(x) = (1/4i) × ∑((-x²/4i)ⁿ) + (-1/4i) × ∑((x²/4i)ⁿ).

f(x) = (1/4i) × ∑((-1)ⁿ × (x²/4i)ⁿ) + (-1/4i) × ∑((x²/4i)ⁿ).

Now, we can combine the two series into one and simplify the expression:

f(x) = (1/4i) × ∑[(-1)ⁿ ×(x²/4i)ⁿ  + (-x²/4i)ⁿ ].

To find the interval of convergence, we need to consider the convergence of each term separately.

Let's examine the absolute value of the common ratio, r, for each term:

|r| = |x²/(4i)| = |x²|/|4i| = |x²|/4.

For convergence, we require |r| < 1:

|x²|/4 < 1.

Simplifying this inequality, we find:

|x²| < 4.

Taking the square root of both sides:

-2 < x < 2.

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Answer:

For any value

Step-by-step explanation:

Answer:

Anything substituted for p should be correct

Step-by-step explanation:

Answer:

29 years

Step-by-step explanation:

In 29 years the grandson will be 40 and the grandfather will be 80. 80 is twice as much as 40.

Answer: 29 years

Step-by-step explanation: if the grandfather is 51 when the grandson is 11 then the grandfather was 40 when his grandson was born. This mean the grandfather will be 80 when the grandson is 40. 40-11=29

Answer:

7 2/3

Step-by-step explanation:

Answer:

23/4 + 23/12

Step-by-step explanation:

Multipy 5 by 4 and then add it to 3/4

Add 12 to 11/12

The equation of a line that passes through points (0, 2) and (-2,0) is y=1x+2

x^2 - 5 this will be the equation formed.

An exponent is the number of times a number is multiplied by itself. For example, 2 to the third (written as 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of one is itself.

let the number be x

x^2 - 5 this will be the equation formed

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The pairing is not a function, as the input 2 is mapped to two different outputs.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

From the table, the mappings are given as follows:

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Answer:

x=-1 y=0

(-1,0)

Step-by-step explanation:

Answer: x= -1, y= 0

Step-by-step explanation: hope this helps

The radical form of the number √ ( - 27 ) is given by the equation A = 3i√3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

The value of n = √( -27 )

Now , the value -1 can be represented as the complex number i

where i² = 1

So , the number n can be written as

A = √ ( 3i )² 3

A = √9i² (3)

A = √27i²

A = √-27

On simplifying the equation , we get

A = 3i√3

Therefore , the value of A is A = 3i√3

Hence , the equation is A = 3i√3

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The first 4-terms of sequence {aₙ} defined by recurrence-relation : aₙ₊₁ = 2aₙ²-1;  a₁ = 0 are 0, -1, 1 and 1.

To find the first four terms of the sequence {aₙ} defined by the recurrence relation aₙ₊₁ = 2aₙ² - 1, with the initial-condition a₁ = 0, we apply the recurrence relation,

Starting with a₁ = 0, we can find the subsequent terms as follows:

⇒ a₂ = 2a₁² - 1 = 2(0)² - 1 = -1

⇒ a₃ = 2a₂² - 1 = 2(-1)² - 1 = 1

⇒ a₄ = 2a₃² - 1 = 2(1)² - 1 = 1

Therefore, the first four terms of the sequence are : a₁ = 0, a₂ = -1, a₃ = 1

and a₄ = 1.

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The given question is incomplete, the complete question is

Write the first four terms of the sequence {aₙ} defined by the following recurrence relation.

aₙ₊₁ = 2aₙ²-1;  a₁ = 0.

There would be 56 exchange relationships if eight bakeries each tried to sell their products directly to seven supermarkets.

To calculate the total number of exchange relationships that would be established, we can multiply the number of bakeries by the number of supermarkets.

In this case, there are eight bakeries and seven supermarkets.

Total number of exchange relationships = Number of bakeries × Number of supermarkets

Total number of exchange relationships = 8 × 7 = 56

Therefore, there would be 56 exchange relationships established between the bakeries and the supermarkets.

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Answer:

39 investors contributed $6,000, and 21 investors contributed $12,000.

Step-by-step explanation:

Let's say that x investors contributed $6,000, and y investors contributed $12,000.

x + y = 60

6,000x + 12,000y = 486,000

x + 2y = 81

x + y = 60

y = 21

x + 21 = 60

x = 39

So, 39 investors contributed $6,000, and 21 investors contributed $12,000.

Hope this helps!

Answer:

n = 15

Step-by-step explanation:

360 ÷ 24 = 15.

good luck, i hope this helps :)

Answer:

N = 15

Step-by-step explanation:

Answer:

x + 1

Step-by-step explanation:

Step-by-step explanation:6x^3 + 6 = 6 ^ 3+ 1 = 6(x+1) (x^2 - x + 1)

Answer:

y = -2

Step-by-step explanation:

Put x as -19 and solve for y.

2(-19) - 5y = -28

Multiply.

-38 - 5y = -28

Add 38 on both sides of the equation.

-5y = -28 + 38

-5y = 10

Divide both sides by -5.

y = 10/-5

y = -2

Answer:

2x - 5y = -28

when x = - 19

Substitute the value of x into the equation

That's

2(-19) - 5y = -28

-38 - 5y = -28

-5y = -28 + 38

-5y = 10

Divide both sides by - 5

We get

y = 10/-5

y = -2

Hope this helps

Answer:

160km^2

Step-by-step explanation:

The length of the sider labelled f in the right triangle, found using Pythagorean Theorem expressed in simplest radical form is 2·√2 centimeters

Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the legs of the right triangle. The side f is the hypotenuse side of the triangle.

The rectangle angle mark indicates that the figure is a right triangle.

The measures of the interior angles of the right triangle are; 45° and 45°

The 45° right triangle is an isosceles triangle.

Therefore, the lengths of the legs of the right triangle are congruent

The length of one of the legs is 2 centimeters, therefore

The length of the other leg is also 2 centimeters

The side labelled f in the right triangle is the hypotenuse side and the Pythagorean Theorem, indicates therefore, that we get;

f² = 2² + 2² = 8

f = √8 = √(4 × 2) = 2·√2

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Answer: 8.4261

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Salma and Jared each threw 5 darts at the target shown. Salma scored 19 points by landing 2 darts in A and 3 in B. Jared scored 17 points by landing 1 dart in A and 4 in B. How many points are given for a dart landing in A?

this can be solved using simultaneous equation. Two equations can be formed from the question

2a + 3b = 19  equation 1

1a + 4b = 17    equation 2

Multiply equation 2 by 2

2a + 8b = 34  equation 3

Subtract equation 1 from 3

5b = 15

divide both sides of the equation by 5

b = 3

Substitute for b in equation 1

2a + 3(3) = 19

2a = 9 = 19

collect like terms

2a = 10

divide both sides of the equation by 2

a = 5

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

Step-by-step explanation:

you can divide 11/30 and get 0.37

0.37%/ 100*11 =

Multiply:

0.37*11 =

add the 100 to the product you multiplied and divide them together:

4.07/100=

your quotient:

0.0407

round by 2 decimals:

0.04

your final answer is :

0.04