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3 years ago

Round to the nearest hundredth (Geometric Series problem)

Mathematics

1 answer:

WITCHER [35]3 years ago

4 0

Answer:

15.98

Step-by-step explanation:

∑₁¹⁰ $8(\frac{1}{4} )^{n-1}$

$=8[1+\frac{1}{4} +\frac{1}{16} + ........ +t_{10}]$

We have to use the formula of sum of a G.P. series with common ratio r < 1.

If the first term is a, the common ratio is r and the number of terms is n then the sum [a + ar + ar² + ar³ + ......... up to n terms] is given by

$[a \times\frac{1-r^{n} }{1-r}]$

$= 8[1 \times \frac{1-\frac{1}{2^{10} } }{1-\frac{1}{2} } ]$

$= 15.98$ (Answer)

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Please help!!!!!!!!!!!!!!!!

aksik [14]

Step-by-step explanation:

< PQS is exterior angle of the triangle

So,

2X = X + 58

X=58

m < P = 58

m <P QR = 180 - ( 58 + 58 ) =, 64

m < P QS = 116

6 0

3 years ago

1. There are 78 sophomores at a school. Each is required to take at least one year of either chemistry or physics, but they may

SVETLANKA909090 [29]

We are given that there are a total of 78 students. If we set the following variables:

$\begin{gathered} C=\text{students only in chemestry} \\ P=\text{students only in physics} \\ PC=\text{students in physics and chemistry} \end{gathered}$

Then, the sum of all of these must be 78, that is:

$C+P+PC=78$

Since there are 15 in chemistry and physics and 47 in chemistry, we may replace that into the equation and we get:

$47+P+15=78$

Simplifying:

$62+P=78$

Now we solve for P by subtracting 62 on both sides:

$\begin{gathered} 62-62+P=78-62 \\ P=16 \end{gathered}$

Therefore, there are 16 students in physics

3 0

2 years ago

What set of reflections would carry rectangle ABCD onto itself?

Dvinal [7]

Answer:

y=x, x-axis, y=x, y-axis

Explanation:

Reflecting the figure across three axes just moves it from one quadrant to another. It does not map the figure to itself.

Reflecting across the line y=x moves it from quadrant II to IV or vice-versa. If it is in quadrant I or III, it stays there. So the sequence of reflections x-axis (moves from I to IV), y=x (moves from IV to II), x-axis (moves from II to III), y=x (stays in III) will not map the figure to itself.

However, the last selection will map the figure to itself. The initial (and final) figure location, and the intermediate reflections are shown in the attached. The figure starts and ends as blue, is reflected across y=x to green, across x-axis to orange, across y=x to red, and finally across y-axis to blue again.