Justify each step of the solution by stating the property that was used to get to each step.
Given:
Step 1:
Step 2:
Step 3: 17x = 40
Step 4:

The edge that is skew to edge AD is edge GC

In geometry, skew edges refer to edges that are not in the same plane and do not intersect. They belong to non-coplanar lines or segments, implying that they extend in different directions. Skew lines, and consequently their edges, never meet and remain at a constant distance from each other.

From the figure

line AD and GC are Skew since they can never meet yet they are not parallel to each other.

Skew lines are non-intersecting, non-coplanar lines in three-dimensional space. They neither share common points nor lie in the same plane, demonstrating their distinct orientation and lack of intersection in a three-dimensional geometric context.

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The Maclaurin series for f(n) is 1.

The Maclaurin series for a function can be found using the formula: f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

In this case, f(0) = (0+1)! = 1, f'(0) = d/dx((0+1)!) = d/dx(1) = 0, f''(0) = d^2/dx^2((0+1)!) = d^2/dx^2(1) = 0, and so on.

Using these values, the Maclaurin series for f(n) is: f(n)(x) = 1 + 0x + 0x^2/2! + 0x^3/3! + ... = 1.

After removing 600 litres from a tank that was half full, it became one-third full. By setting up an equation, we determine that every 600 litres represents one-sixth of the tank's full capacity. Multiplying 600 litres by 6, we find the tank's full capacity is 3600 litres.

The question involves determining the total capacity of a tank based on information given about volume reductions and proportions of fullness. Initially, the tank is half full, but after removing 600 litres, it becomes one-third full. We can set up an equation to find out the total capacity of the tank (T).

Since removing 600 litres takes the tank from being half full to one-third full, that means 600 litres correspond to one-sixth of the tank's capacity because one half minus one-third equals one-sixth.

Now we set up our equation: 600 litres = T/6. To solve for T, we multiply both sides of the equation by 6:

Therefore, the full capacity of the tank is 3600 litres.

Factorize the given complex expression first into simpler terms (x-2)^2, (x+5)^2 and (x-2)(x+5). After canceling the matching terms, you simplify to get (x-2)/(x+5)

This mathematical question involves the simplification of a fractional expression. The problem can be solved with factoring and canceling out matching terms found in both the numerator and denominator. Step by step solution would be:
((x2-4x+4) can be factored into (x-2)^2.
(x^2+10x+25) can be factored into (x+5)^2.
(x^2+3x-10) can be factored into (x-2)(x+5).
Thus, the whole equation will be converted into
((x-2)^2 / (x+5)^2) x ((x+5) / (x-2)(x+5)).
Cancel (x+5) and (x-2) from the numerator and denominator, which leaves:
(x-2)/(x+5).

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Answer:

The value of the car is 0.94 times the value of the car the previous year.

Answer:

Option C is correct

The value of the car is 0.94 times the value of the car the previous year.

Step-by-step explanation:

Given the function:

[tex]p(t) = 24,525(0.94)^t[/tex]

where,

p(t) represents the value of a new car

t is the number of years.

We have to find  the value 0.94 represent in this situation.

For t =0 years.

Initial value of car p(0) is 24,525

For t = 1 years

[tex]p(1) =24,525 \cdot 0.94[/tex]

For t = 2 years

[tex]p(2) =24,525 \cdot (0.94)^2[/tex] and so on...

Since;

[tex]\frac{p(2)}{p(1)} = 0.94[/tex]

⇒[tex]p(2) = 0.94 \cdot p(1)[/tex]

In general:

[tex]p(t) = 0.94 \cdot p(t-1)[/tex] where, t is the number of years.

⇒the value of the car is 0.94 times the value of the car the previous year.

Answer:

D.[tex]f(n)=3n+27[/tex]

Step-by-step explanation:

Total number of pages in a book=f(n)

Jason has already read pages=27

He plans to read pages of the book everyday=3

He takes times to complete reading the book=n days

He read pages in n days=3n

We have to find the function which represents the relationship between f(n) and n.

According to question information

[tex]f(n)=3n+27[/tex]

This is required relation between f(n) and n.

Answer:D.[tex]f(n)=3n+27[/tex]

Answer:

8 quarters; 19 dimes trust me i checked

Step-by-step explanation:

The percent error in Mark's estimate to the nearest tenth of a percent is 6.9%.

Percentage is the ratio such that it can be expressed as a fraction of 100. Percentage is calculated by dividing the number with the whole and then multiplying by 100.

The symbol used to denote percentage is '%'.

Percent error is the absolute value calculated by finding the difference of the estimated value and the actual value and then dividing by the actual value followed by multiplication with 100.

Percent Error = [(Estimated value - Actual value) / Actual value] × 100

                      = [(15.5 - 14.5) / 14.5] × 100

                      = (1 / 14.5) × 100

                      = 6.897%

                      ≈ 6.9%

Hence, there is a 6.9% percent error in Mark's estimate if his estimated distance from his house to the school is 15.5 m and the actual distance is 14.5 m.

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The percent error in Mark's estimate is 6.9%.

To calculate the percent error, we use the formula:

[tex]\[ \text{Percent Error} = \left( \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100\% \][/tex]

Given the estimated distance is 15.5 mi and the actual distance is 14.5 mi, we can plug these values into the formula:

[tex]\[ \text{Percent Error} = \left( \frac{15.5 \text{ mi} - 14.5 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} = \left( \frac{1 \text{ mi}}{14.5 \text{ mi}} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx \left( \frac{1}{14.5} \right) \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 0.069 \times 100\% \][/tex]

[tex]\[ \text{Percent Error} \approx 6.9\% \][/tex]

Therefore, the percent error in Mark's estimate is approximately 6.9%.

The value of x to solve the given equation is 16.

The given equation is:

[tex]log_2x=4[/tex]

A logarithm function is a special style to write an exponential function.

For example, If [tex]a^x=b[/tex] then we write it as [tex]log_ab=x[/tex].

So, [tex]log_2x=4[/tex] can be written as:

[tex]2^4=x[/tex]

Or, [tex]x=2^4[/tex]

[tex]x=16[/tex]

So, the value of x =16.

Hence, the value of x to solve the given equation is 16.

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Answer:

12

Step-by-step explanation:

I did the test

Answer:

Option A is correct.

Step-by-step explanation:

Selecting eight members randomly and recording whether each member is wearing a blue shirt.

A binomial experiment is defined as a statistical experiment which consists of n repeated trials. Only two possible outcomes are possible in each trial- either its a success or a failure. Here the probability of success remains the same on every trial.

Here, in 8 members the person wearing blue will be a success others will be a failure outcome.

I think the answer is $216.99 ?

Answer:

The amount of interest on the loan was of $214.57.

Step-by-step explanation:

Slingerland borrowed $8,000 at an 11% interest rate, thus having to pay $880 after a year.

As the loan was due on October 17, and the difference between July 20 and October 17 is of 89 days, using the exact interest method we can affirm that:

880 / 365 x 89 = X

2.41 x 89 = X

$214.57 = X

The amount of interest on the loan was of $214.57.

Answer:

A. (1,-4)

Step-by-step explanation:

L= (-1, 2)

(x,y)>(x+2, y-6)

(x,y)>(-1+2, 2-6)

(x,y)>(1, -4)

D.) Quadrant lll or Quadrant IV

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Answer:

Szymborska's overall opinion of humanity in "A Contribution to Statistics" is overall positive

Step-by-step explanation:

Szymborska is a poet who likes to comment on society with irony and sarcasm.One example of this is when she splits people into categories in her poem “A Contribution to Statistics”. Here Szymborska’s overall opinion of humanity may seem negative due to her bluntness and dry humor. For example, she says in the tenth stanza, “cruel when forced by circumstances -better not to know even ballpark figures.” It’s implied in this line that most people (maybe even all)are cruel or can be. She also says, “taking only things from life -thirty”which comments how lots of people are selfish. However, this seemingly cynical poem takes a sweeter turn near the end with statistics like, “worthy of compassion - ninety-nine” and “mortal- a hundred out of a hundred.” These lines reveal that even though Szymborska believes that humanity is extremely flawed the mass majority of us deserve and are worthy of love. Plus the fact that we’re all mortal may seem dark but the fact remains that both the righteous and the sinners will all end up in the same place. The fact that no one can escape

death gives humans equality in a way. Szymborska’s overall opinion of humanity turned out to be more optimistic after all.

Answer:

commutative property

Step-by-step explanation:

Given equation: [tex]\pi+10=10+\pi[/tex]

The property of real number used in this equation is Commutative property

Commutative property : A binary operation [tex]{\displaystyle *}[/tex] on a set   is commutative if  [tex]a {\displaystyle *}b= b{\displaystyle *}a[/tex]

Following this property  [tex]\pi+10=10+\pi[/tex]