MATHEMATICS COLLEGE

Find the sum of the first six terms of a geometric progression .

Answers

Answer 1

Answer:

Question:

Find the sum of the first six terms of a geometric progression.

1,3,9,....

Answer:

$S_6 = 364$

Step-by-step explanation:

For a geometric progression, the sum of n terms is:

$S_n = (a(r^n - 1))/(r - 1)$

In the given sequence:

$a = 1$

$r = 3/1 =3$

$n = 6$

So:

$S_n = (a(r^n - 1))/(r - 1)$

$S_6 = (1 * (3^6 - 1))/(3 - 1)$

$S_6 = (3^6 - 1)/(2)$

$S_6 = (728)/(2)$

$S_6 = 364$

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The expression cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5 can be rewritten as which of the following? cosine of 7 times pi over 10 cosine of 3 times pi over 10 sine of 7 times pi over 10 sine of 3 times pi over 10 (The clear version of the question is in the picture below)
You originally draw a design for an art contest on a 4 in. x 5 in. card. The second phase of the contest requires the drawing to be transferred to an 8.5 in x 11 in. standard sheet of paper and utilize as much of the space on the paper as possible. You determine that the largest size one of the dimensions of your drawing can be is 10.5 in. What is the length of the other dimension if the two drawings are similar? Type your exact answer in the blank without the units, and round to the nearest tenths.
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To obtain the graph of y = x2 - 6, shift the graph of y = x2
units.

Answers

Answer: down 6 units

Step-by-step explanation:

Edge 20

Answer:

Down 6 Units

Step-by-step explanation:

a 12-foot piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. find the length of both pieces. what is the length of the shorter piece

Answers

The longer piece would be 7.5f and the shorter 4.5

Five times the smaller of two consecutive numbers is added to 3 times the bigger, the result is 579. Find the smaller integer.

Answers

Here, let's represent the unknown integer with the variable "n":
5n + 3(n + 1) = 579
5n + 3n + 3 = 579
8n = 576
n = 72
The smaller integer is 72

Which solution matches both equations ?

Answers

I believe the answer is C I’m really sorry if it’s wrong.

Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.

Answers

Answer:

C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.

Step-by-step explanation:

Volume=576π cubic centimeters

Radius=8 cm

h=?

Her work:

Volume of a cyclinder=πr^2h

Step 1:

576π= π8^2h

Step 2:

576π = 64πh

Step 3:

576π / 64π = 64πh / 64π

Step 4:

h=9π cm

Correct workings:

Step 1:

576π= π8^2h

Step 2:

576π = 64πh

Step 3:

576π / 64π = 64πh / 64π

Step 4:

h= 9 centimeters

Her error is in step 4

C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.

Answer:

the error was made in step 4, should have also been cancelled making the correct answer as 9 cm.

Step-by-step explanation:

Writing on the SAT Exam It has been found that scores on the Writing portion of the SAT (Scholastic Aptitude Test) exam are normally distributed with mean 484 and standard deviation 115. Use the normal distribution to answer the following questions. Required:
a. What is the estimated percentile for a student who scores 425 on Writing?
b. What is the approximate score for a student who is at the 87th percentile for Writing?

Answers

Answer:

a) The estimated percentile for a student who scores 425 on Writing is the 30.5th percentile.

b) The approximate score for a student who is at the 87th percentile for Writing is 613.5.

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 484, \sigma = 115$