In a list of 200 numbers,each number after the first is 4 more then the number that comes before it.What is the difference betwe
1 answer:
Let a₁ = the first number.
Because each number is 4 more than the number before it, the list of numbers forms an arithmetic sequence with a common difference of d = 4.
The n-th term is
The 200-th term is
a₂₀₀ = a₁ + (200 - 1)*4
= a₁ + 796
a₂₀₀ - a₁ = 796
Because a₂₀₀ is the last number on the list, the difference between the first and the last number on the list is 796.
Answer: The difference is 796.
Because each number is 4 more than the number before it, the list of numbers forms an arithmetic sequence with a common difference of d = 4.
The n-th term is
The 200-th term is
a₂₀₀ = a₁ + (200 - 1)*4
= a₁ + 796
a₂₀₀ - a₁ = 796
Because a₂₀₀ is the last number on the list, the difference between the first and the last number on the list is 796.
Answer: The difference is 796.
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Answer:
The volume of the new crate is exactly 174.4% of the old crate.
Step-by-step explanation:
Volume of a rectangular prism:
The volume of a rectangular prism of dimensions x, y and z is given by:
She decided that the dimensions of the new crate needs to be increased by 40% of the original length.
Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So
Percentage:
The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.
The volume of the new crate is exactly 174.4% of the old crate.
Answer:
Step-by-step explanation:
The opposite angles in a quadrilateral theorem states that when a quadrilateral is inscribed in a circle, the angles that are opposite each other are supplementary, their degree measures add up to 180 degrees. One can apply this here by using the sum of (<C) and (<A) to find the measure of the parameter (z). Then one can substitute in the value of (z) to find the measure of (<B). Finally, one can use the opposite angles in a quadrilateral theorem to find the measure of angle (<D) by using the sum of (<B) and (D).
Use the opposite angles in an inscribed quadrialteral theorem,
<A + <C = 180
Substitute,
14x - 7 + 8z = 180
Simplify,
22z - 7 = 180
Inverse operations,
22z = 187
z =
Simplify,
z =
Now substitute the value of (z) into the expression given for the measure of angle (<B)
<B = 10z
<B = 10()
Simplify,
<B = 85
Use the opposite angles in an inscribed quadrilateral theorem to find the measure of (<D)
<B + <D = 180
Substitute,
85 + <D = 180
Inverse operations,
<D = 95