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Zigmanuir [339]
3 years ago
5

Find the sum of the first 40 terms of a geometric sequence where the first term is 16 and the common ratio is 1.1. 704 7,081.480

89 7,805.62898 6,423.16445
Mathematics
1 answer:
Lilit [14]3 years ago
8 0

Step-by-step explanation:

The nth term of a geometric progression can be determined by using the formula:

Tn=arn−1

where: a = first term and r = common ratio

Substitute the given values of first term and common ratio into the formula:

Tn=arn−1

T5=(40)(0.5)5−1

T5=(40)(0.5)4

T5=(40)(0.0625)

T5=2.5

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Determine the values of the unlabeled parts of the triangle.
____ [38]

Answer:

∠Q = 63.4º, PQ = 2, QO = 4.47

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as the equilateral triangle, isosceles triangle, scalene triangle, right angled triangle.

Triangle POQ is a right angled triangle because ∠P = 90°. Also, ∠O = 26.6°.

Therefore in ΔPOQ: ∠P + ∠O + ∠Q = 180° (sum of angles in a triangle).

90 + 26.6 + ∠Q = 180

∠Q + 116.6 = 180

∠Q = 180 - 116

∠Q = 63.4°

We can find PQ and QO using sine rule. Sine rule for ΔPOQ is given as:

\frac{PO}{sin Q}= \frac{PQ}{sinO}= \frac{QO}{sin P}\\\\Finding\ PQ  :\\\\\frac{PO}{sin Q}= \frac{PQ}{sinO}\\\\\frac{4}{sin(63.4)} =\frac{PQ}{sin(26.6)}\\\\PQ= \frac{4}{sin(63.4)} *sin(26.6)\\\\PQ = 2\\\\Also\ finding\ QO:\\\\\frac{PO}{sin Q}= \frac{QO}{sinP}\\\\\frac{4}{sin(63.4)} =\frac{QO}{sin(90)}\\\\QO=\frac{4}{sin(63.4)} *sin(90)\\\\QO = 4.47

4 0
2 years ago
The percentage of students in school that attended the talent show for the years 2008 to 2013 are shown. This year, the school h
Elodia [21]

Answer:

352 students

Step-by-step explanation:

Given

See attachment for table

n = 400

Required

Attendance of students in this year's show

First, we calculate the mean of the table

Mean= \frac{\sum x}{n}

So, we have:

Mean= \frac{85\% + 91\% + 92\% + 87\% +84\% + 89\%}{6}

Mean= \frac{528\%}{6}

Mean= 88\%}

Multiply the mean by the total students

Expected = Mean * n

Expected = 88\% * 400

Expected = 352

7 0
2 years ago
Which statement is correct?
HACTEHA [7]

Answer:

1.09 x104

Step-by-step explanation

3 0
2 years ago
I am a square. One of my side is 9 feet long. What is my area?
Stella [2.4K]

Hello from MrBillDoesMath!

Answer:

81 ft^2

Discussion:

The area of a square is (length of a side)^2.  In this case,

Area = 9^2 = 81


Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!


8 0
3 years ago
Solve for y 16y^2-25=0
Pepsi [2]

Answer:

\large\boxed{x=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}

Step-by-step explanation:

16y^2-25=0\\\\METHOD\ 1:\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\16=4^2\ \text{and}\ 25=5^2\ \text{therefore we have}\\\\4^2y^2-5^2=0\\\\(4y)^2-5^2=0\\\\(4y-5)(4y+5)+0\iff4y-5=0\ \vee\ 4y+5=0\\\\4y-5=0\qquad\text{add 5 to both sides}\\4y=5\qquad\text{divide both sides by 4}\\\boxed{y=\dfrac{5}{4}}\\\\4y+5=0\qquad\text{subtract 5 from both sides}\\4y=-5\qquad\text{divide both sides by 4}\\\boxed{x=-\dfrac{5}{4}}

METHOD\ 2:\\\\16y^2-25=0\qquad\text{add 25 to both sides}\\\\16y^2=25\qquad\text{divide both sides by 16}\\\\y^2=\dfrac{25}{16}\to y=\pm\sqrt{\dfrac{25}{26}}\\\\y=-\dfrac{\sqrt{25}}{\sqrt{16}}\ \vee\ x=\dfrac{\sqrt{25}}{\sqrt{16}}\\\\\boxed{y=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}

7 0
3 years ago
Read 2 more answers
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