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The rate at which the top of the ladder is slipping down at the instant when the bottom of the ladder is 15 feet from the base of the building is -75/8 feet per second

The length of the ladder = 17

Consider the length of the base as x and the height is h

The rate at which the ladder is sliding = 5 feet per second

dx/dt = 5

Apply the Pythagorean theorem

x^2 + h^2 = 17^2

h^2 = 289 - x^2

h = \(\sqrt{289-x^2}\)

The rate of change of height with respect to x is

dh/dx = - x / (289 - x^2)^(1/2)

dh/dt = dh/dx × dx/dt

Substitute the values in the equation

= - 15 / (289 - 15^2)^(1/2) × 5

= -15/8 × 5

= -75/8 feet per second

Therefore, the rate of change of height when x = 15 is -75/8 feet per second

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Answer:

A

Step-by-step explanation:

n is the number.

So n*6=26

Hey there!

Guide:

• Difference = Subtract

• Is = Equal to

• Product = Multiply

• Quotient = Divide

• Sum = Add

• Unknown number = a number that’s isn’t known yet

Question reads….

“ A [PRODUCT] of [a NUMBER] & 6 [is] 26”

RANDOM:

• Product is multiply/multiplication

• A number is unknown so we will label it as “n”

• 6 stays the same because nothing happened to it

• 26 is BEHIND the equal sign but nothing happens to it because nothing is being compared to it

ANSWER:

“n * 6 = 26”

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

cluldnt get the answer for one

Answer:

B

Step-by-step explanation:

Mark as Brainliest

Answer:

8.5

Step-by-step explanation:

ABCD is a rectangle meaning, AD = BC AND AB = DC. Since BC = PQ, we need to solve for PQ.

We know that QR = 10 cm, and the area of a rectangle is the length times the width. We know the area is 45 cm^2, so:

a = l * w

45 = 10 * PQ

PQ = 4.5

Since PQ = BC, then BC = 4.5. We know that the perimeter of the rectangle is 26 cm, we can solve for AB:

2(AB) + 2(BC) = 26

2(AB) + 2(4.5) = 26

2(AB) = 17

AB = 8.5

The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.

The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:

1. Random Sampling:

The samples should be selected randomly from the population to ensure that they are representative of the entire population.

2. Independence:

Each sample should be independent of the others.

This means that the outcome of one sample should not influence the outcome of another sample.

3. Sample Size:

The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.

In general, a sample size greater than 30 is considered sufficient.

Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.

Independence is necessary to avoid any potential confounding factors that may influence the results.

Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

These conditions are important to ensure the validity and reliability of the statistical analysis.

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If per capita energy consumption is approximately 3.5 × 108 BTU for US population of 325 million people , the energy the entire population consume is 1.14 × 1016 BTU. The correct answer is (d).

The United States has a population of approximately 325 million people. To estimate the total energy consumption for the entire population, we need to multiply the per capita energy consumption by the total number of people.

The per capita energy consumption is given as 3.5 × 108 BTU, which means that on average, each person in the US consumes 3.5 × 108 BTU of energy. By multiplying this value by the total population, we can estimate the total energy consumption for the entire population.

The calculation can be done by multiplying the per capita energy consumption by the population:

Per capita energy consumption (E): 3.5 × 108 BTU

Population (P): 325 million

Total energy consumption (T) = E × P

To calculate T, we need to multiply E and P:

3.5 × 108 BTU × 325 million = 1.14 × 1016 BTU

The total energy consumption for the entire population is 1.14 × 1016 BTU

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To compare the greater pay between a salary of $74,000 per year and an hourly rate of $40 for 80 hours every fortnight, we need to calculate the total earnings for each option.

Salary per year:

To calculate the total earnings for the salary option, we simply take the annual salary of $74,000.

Total earnings = $74,000 per year

Hourly rate:

To calculate the total earnings for the hourly rate option, we need to determine the total number of hours worked in a year. Since there are 26 fortnights in a year, and the lawyer works 80 hours per fortnight, the total number of hours worked in a year would be:

Total hours worked per year = 26 fortnights * 80 hours/fortnight = 2,080 hours

Now we can calculate the total earnings:

Total earnings = Hourly rate * Total hours worked per year

= $40/hour * 2,080 hours

= $83,200

Comparing the two options, we find that the greater pay is $83,200 from the hourly rate, which exceeds the $74,000 salary per year.

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The length of the side marked x is 15, and the scale factor is 1.5, Similar figures have the same shape, but they may be different sizes. The ratio of the corresponding side lengths of two similar figures is called the scale factor.

In the problem, we are given that the two hexagons are similar. We are also given that the side length of the smaller hexagon is 10. We can use this information to find the scale factor and the length of the side marked x.

The scale factor is the ratio of the corresponding side lengths of the two similar figures. In this case, the scale factor is 10/15 = 2/3. This means that every side of the larger hexagon is 2/3 times as long as the corresponding side of the smaller hexagon.

The side marked x is a side of the larger hexagon, so its length is 10 * 2/3 = 15.

Therefore, the length of the side marked x is 15, and the scale factor is 2/3.

Here are some additional details about the problem:

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To factor completely, we can follow the below given steps:

Step 1: Split the middle term. Multiply the coefficient of the first term and the constant term: 35 × (-48) = -1680

Find two factors of -1680 that add up to the coefficient of the second term (2). -1680 can be written as -42 × 40, and -42 + 40 = -2, which matches the coefficient of the middle term.35r² - 42r + 40r - 48 (splitting the middle term)

Step 2: Group the first two terms and the last two terms.5r(7r - 8) + 6(7r - 8) (grouping terms)

Step 3: Factor out the common binomial. (7r - 8)(5r + 6) (factoring out the common binomial)

Therefore, the factorization of the given expression is:\[ 35 r^{2}+2 r-48 = \boxed{(7r - 8)(5r + 6)} \]

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Answer:

100% increase

Step-by-step explanation:

Answer:

100% increase

Step-by-step explanation:

1.6 plus 100% = 3.2 :)))

Answer:

There is one solution

Step-by-step explanation:

The solution is \(x=8\)

Explanation:

\(7(x-5)=x+13\)

\(7x-35=x+13\)

\(6x=48\)

\(x=8\)

Answer:

c

Step-by-step explanation:

Answer:

you have chosen the correct answer

Step-by-step explanation:

the answer is 9.45

3/6.30=4.5/x

4.5*6.30=28.35

28.35/3= 9.45

Answer:

Step-by-step explanation:

Answer:

20/6

Step-by-step explanation:

16/6 is 2 4/6

6/6 is 1

3 is well 3

and 20/6 is 3 1/2

The values are k = -1 and k = 0 ,  Option D , E is the right answer.

The missing options are

Select two options. k = –10 k = –7 k = –5 k = –1 k = 0

The statement formed when two algebraic expressions are equated by an inequality operator is called an Inequality.

The inequality given that

\(\rm \dfrac{k-3}{4} > -2\)

k > - 8 + 3

k > -5

As k is greater than -5 so k = -1 and k = 0

Therefore Option D , E is the right answer.

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Answer:

Step-by-step explanation: 0 because it is not considered a natural number.

Answer:

50/50

Step-by-step explanation:

The total amount of cards are 20 10 being red, 10 being black

Answer:

$3 for every pound....

Answer:it would be b $3.00 for every pound

explanation:A unit price is something for each not multiple

Given In a =2, In b = 3, and in c = 5, we need to evaluate the following and give the answer as an Integer, fraction, or decimal rounded to at least 4 places.a. In (a³/b⁻² c³) = In (8/b⁻²*5³) = In (8b²/125)B² = 3² = 9.

Putting the value in the expression we get; In (8b²/125) = In(8*9/125)≈ 0.4671b. In √(b²c⁻⁴a²) = In (b²c⁻⁴a²)¹/²= In(ba/c²) = In (3*2/5²)≈ -0.8630c. In (a²b⁻²)/ ln ((bc)²) = In (2²/3²)/In (5²*3)²= In(4/9)/In(225) = In(4/9)/5.4161 = -1.4546/5.4161≈ -0.2685

Therefore, the answer to the given question is; a. In (a³/b⁻² c³) = In(8b²/125) ≈ 0.4671b. In √(b²c⁻⁴a²) = In (3*2/5²)≈ -0.8630c. In (a²b⁻²)/ ln ((bc)²) = -0.2685.

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The inequality 4(x – 3) + 4 < 10 + 6x is solved as x > -9. Then the variable x is greater than the negative 9. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign.

The inequality equation is given below.

4(x – 3) + 4 < 10 + 6x

Then the steps of solving are given below.

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: x > –9

Then x is greater than the negative 9.

Then the correct option is B.

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If sentence 6 states that ¬C is true, and sentence 7 presents a conditional statement with C as the antecedent and Q as the consequent, we can use modus ponens to infer that Q is false.

Modus ponens is a deductive reasoning rule that allows us to derive a conclusion from a conditional statement and its antecedent. Therefore, we can apply modus ponens to sentence 7 given that we know ¬C from sentence 6.
Since from sentence 6 we know ¬C, we can apply modus ponens to sentence 7. To do this, follow these steps:
1. Identify the premises: One premise is sentence 6, which states ¬C. The other premise should be a conditional statement, such as "If ¬C, then P" (replace P with the relevant proposition).
2. Apply modus ponens: Modus ponens is a rule of inference that allows us to deduce a conclusion from the given premises. If we have the premises "If ¬C, then P" and "¬C", we can conclude "P" using modus ponens.
3. State the conclusion: After applying modus ponens, we can conclude "P" based on the given premises, which include sentence 6 (¬C) and the conditional statement.

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Answer:

The mean  absolute deviation is 2

Answer:

M A D is 2

Step-by-step explanation:

Examining the given graph the number of computers infected in

The graph shows that the function is an exponential function

represented as

The starting term of the function  f(x) = 4^t is 1, and base is 4

f(x) = number of computer infected

t = time in hours

90 minutes in hours

90 / 60 = 1.5 hours

for t = 1.5 hours

f(x) = 4^1.5

f(x) = 8

for t = 6 hours

f(x) = 4^6

f(x) = 4096

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The amount of Protein intake is 900 kilocalorie.

We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.

Wе have to find out the amount of protein intake.

Percentage of students affected are -  \(\frac{x}{n} \times 100\)

In the question given -

Let the amount of Protein intake be y.

Then -

45 = y % of 2000

45 = \(\frac{y}{2000} \times100\)

y = \(\frac{45\times2000}{100}\)

y = 900 Kilocalorie

Hence, the amount of Protein intake is 900 kilocalorie.

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The part of the function over the interval (-2,2) is nonlinear and decreasing.

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