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Angelina_Jolie [31]
3 years ago
15

The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170. what is the first term of the series?

Mathematics
1 answer:
azamat3 years ago
7 0

Answer:

128

Step-by-step explanation:

The sum of the first n terms of a geometric sequence is:

S = a₁ (1 − r^n) / (1 − r)

170 = a₁ (1 − ¼^4) / (1 − ¼)

a₁ = 128

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guapka [62]

The total surface area of the remaining solid is 48(4+✓3) centimeters square.

<h3>How to calculate the surface area?</h3>

Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.

The formula for the total surface area will be:

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Parameter of base=12(2) = 24

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The surface area of the remaining solid will be:

= 2(64✓3/4) + 24 × 8

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With the hole is a rhombus prism with the following parameters:

diagonal 1 = 6, diagonal 2 = 8, height = 12

The volume is:

V1 =0.5 × d1 × d2 × h

V1 = 0.5 × 6 × 8 × 12

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The dimensions of the hexagonal prism are:

Base edge (a) = 8

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The volume is

V2 = (3✓(3)/2)a²h

V2 = (3✓3)/2) × 8² × 12

V2 = 1152✓3

The remaining volume is

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4 0
2 years ago
Use the graphing tool to create a histogram of Gretchen’s data. Use eight bins for your histogram.
lozanna [386]

The number of bins in the histogram determines the width of the bins and

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  • Please find attached the graph of the histogram of Gretchen's data created with MS Excel.
<h3 /><h3>Method used to create the histogram of Gretchen's data</h3>

Given:

The table from  Gretchen's data is presented as follows;

\begin{tabular}{|c|c|} \underline{ Member}& \underline{Number of Days}\\x_1&2\\x_2&4\\x_3&7\\x_4&8\\x_5&12\\x_6&15\\x_7&10\\x_8&7\\x_9&9\\x_{10}&6\\x_{11}&13\\x_{12}&3\\x_{13}&8\\x_{14}&10\\x_{15}&10\end{array}\right]

The required number of bins = 8 bins

The steps to create the histogram using MS Excel;

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Answer:

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Step-by-step explanation:


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The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A it is true.

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