Answer:
see explanation
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₁ = 3 and r = - 2 , then
3 × - 2 = - 6
- 6 × -2 = 12
12 × - 2 = - 24
- 24 × - 2 = 48
48 × - 2 = - 96
- 96 × - 2 = 192
The positive terms are in a geometric progression
3, 12, 48, 192, ....
with a₁ = 3 and r = 12 ÷ 3 = 48 ÷ 12 = 4 , then
S₈ = [tex]\frac{3(4^{8}-1) }{4-1}[/tex] = [tex]\frac{3(65536-1)}{3}[/tex] = 65536 - 1 = 65535
The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.
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➯Question:The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.Answer:Both numbers are 25 and 400.Step By Step Explanation:Given that:The product of two numbers is 10000.One number is 16 times the other number.To Find:Both numbers?Solution:Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.According to the Question :[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]
Hence,1st number = n = 252nd number = 16n = 16 × 25 = 400∴ Hence, both numbers are 25 and 400.▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
Answer:
(25, 400) or (-25, - 400)Step-by-step explanation:
Let the numbers be x and y.
We have:
y = 16xxy = 10000Substitute y and solve for x:
x(16x) = 1000016x² = 10000x² = 10000/16x² = 625x = √625x = ± 25Then y is:
y = ± 25*16 = ± 400The numbers are:
25 and 400 or -25 and - 400Seventy-two books were to be divided up among 18 children. Which of the following
expressions is equivalent to this fraction?
a. 8/3 divided by 6/9
b. 8/3 times 2/3
c. 2/9 divided by 8/9
d. 2 times 8/2
Answer:
a
Step-by-step explanation:
cause if 72 book were divided by 18 kids they would hav all gotten 4 books each
so a is the answer cause it gives youthe answer 4
Answer: a. 8/3 divided by 6/9
Step-by-step explanation: I got this question on my test
Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height
pls help
Answer:
8% out of 175 = ( 8 ÷ 100 ) × 175 = 14
175 cm - 14 = 161 cm
...............
On a recent math test. Samantha scored 3 points for each of the 18 multiple choice que non se
answered correctly and 5 points for each of the 6 short response questions she answered correctly
She scored an additional 4 points for the bonus question. Write an expression for her total score on
the test and then find her score.
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points :
From the question given, we are told that Samantha scored 3 points for each of 18multiple questions his means that the total points made here is expressed as:
(3 × 18) ...1
If she got 5 points for each of the 6 short responsmultiple choice questione questions she answered
correctly, the total point made will be expressed as;
(5×6) ... 2
Total score for an additional 4 points for the bonus question will be "4"
Expression for her total score will be the sum of all the expression above as thus:
(3×18) + (5×6) + 4
Taking the sum, her score will be:
= (3×18) + (5×6) + 4
= 54 + 30 + 4
= 84 + 4
= 88 points
The required expression will therefore be:
(3×18) + (5×6) + 4
Her total score is 88points
Learn more about sum here: brainly.com/question/16397188
Fill in the table to explore the graph.
Miles Walked by Alonso
" Time (hours) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Miles Walked
6
V
16
12
Miles
8
4
X
1
4
3
Time (hours)
time
Answer:
Step-by-step explanation:
so you have divide ok by my and divide 5x1
[tex]\sqrt[3]{x+1} =2x+2[/tex]
. If a = 120°, find the measure of angles b, c and d.
Explain your reasoning.
Find the distance between the two points.
(5,5)
(2.2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
Answer:
[tex]{18}[/tex]
Step-by-step explanation:
[tex] \sqrt{(2 - 5) {}^{2} + ( 2 - 5) {}^{2} } [/tex]
[tex] = \sqrt{( - 3) {}^{2} + ( - 3) {}^{2} } [/tex]
[tex] = \sqrt{9 + 9} [/tex]
[tex] = \sqrt{18}[/tex]
Answered by GAUTHMATH
How do I do question 2?
Answer:
518
Step-by-step explanation:
solution:
=8^2^×1^+1+6^2^×1^-1
=8^3+6^1
=8^3+6
=8×8×8+6
=512+6
=518
Please help! Geometry 9th grade
Answer:
69.3
Step-by-step explanation:
if you put it into 2D, you get a right triangle with leg lengths 62 (vertical height) and 31 (1/2 the base's length). Using Pythagorean's Theorem you get sqrt((62^2)+(31^2))= 69.318. Rounding to the nearest tenth you get 69.3
please help! will give brainliest if the answer is correct:) need the answers in order to move on in the lesson!
Answer:
Just use a calculator and wite the square root value in it
Step-by-step explanation:
Atempt this method with all options at last u will have ur answer
What is the domain of the function shown below?
[tex]y = log_{3}(x + 2) [/tex]
A. All real numbers greater than -2
B. All real numbers less than 2
C. All real numbers
D. All real numbers greater than 0
Answer:
A
Step-by-step explanation:
A logarithmic function, log(x) has a domain x>0. For this logarithmic equation x+2>0, x>-2.
describe the rule that describes the relationship between the numbers in the top row (x) and the bottom row (y) in the following table
Answer:
y(x) = 2x+3
Step-by-step explanation:
the rule is y(x) = 2x+3
Zoe walks at a speed of 10 miles/h and jogs at a speed of 20 miles/h. She goes to the park to walk 2 miles on a Monday. How long will she take to walk 2 miles?
Answer:
12 minutes
Step-by-step explanation:
Given
[tex]s_1 = 10mi/h[/tex] --- walk speed
[tex]s_2 = 20mi/h[/tex] --- jog speed
[tex]d = 2\ miles[/tex] --- distance
Required
The time to walk the given distance
Time is calculated as:
[tex]Time = \frac{distance}{speed}[/tex]
In this case, the speed is the speed at which she walks.
So, we have:
[tex]Time = \frac{d}{s_1}[/tex]
Substitute known values
[tex]Time = \frac{2mi}{10mi/h}[/tex]
[tex]Time = 0.2hr[/tex]
Convert to minutes
[tex]Time = 0.2 * 60mins[/tex]
[tex]Time =12mins[/tex]
please help i’ll mark brainliest
Answer:
x=0
x=6
x=-1
Step-by-step explanation:
x(x^2-5x-6)
x(x-6)(x+1)
x=0
x=6
x=-1
Alex has collected apples. It has 40 boxes of 8.5 kg each and 6 sacks of 90kg each. Pack the apples in bags of 2.5 kg each. how many bags do you get?
Answer:
40*8.5=340
6*90=540
total=880/2.5=352bags
8w + 19 - 4w = -5? What is the value of w?
Answer:
4w = -5-19
4w=-24
w=-6
hope that answers your question
good luck
How do I solve this problem?
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Short answer: to solve this problem, follow directions.
a. Write the inequalitiesLet c and p represent numbers of cakes and pies produced daily. Then the constraints are ...
2c +3p ≤ 108 . . . . . . . . available hours of preparation time
1c +0.5p ≤ 20 . . . . . . . available hours of decoration time
p ≥ 0, c ≥ 0 . . . . . . . . . negative numbers of cakes or pies cannot be produced
__
b. Sketch the feasible regionIt works well to let a graphing calculator do this.
The feasible region is the doubly-shaded area with vertices ...
(0, 0), (0, 36), (3, 34), (20, 0)
__
c. Write the profit functionProfit is $25 per cake and $12 per pie, so is ...
p = 25c +12p
__
d. Determine maximum profitThe attached table shows the profit for the various mixes of cakes and pies in the feasible region. The most profit is had by production of cakes only.
The maximum profit is $500 per day for production of 20 cakes.
_____
Additional comment
We have used x for cakes and y for pies in the attachment, because those are variables that the Desmos calculator prefers.
As is sometimes the case, the production point giving maximum profit leaves one of the resources (preparation time) only partially utilized.
A construction crew is completing about 40 yards of a new highway each day. At this rate, how long will it take them to complete a stretch of 1.6 miles? Round your answer to the nearest tenth if necessary
Answer:
70 days
Step-by-step explanation:
that is the procedure above
Two thirds of the students in a class have pets. There are
36 students in the class. How many of the students have pets?
what is the ordered pair to (-4,2)
Answer:
(1,2) is ordered pair to (-4,2).
Step-by-step explanation:
(1,2)
hora khoi thaha vayena hai
Simplify : -2a(a-d)+2a(2a-3D) pls help.
-2a(a - d) + 2a(2a - 3d)
(-2a * a) + (-d * -2a) + (2a * 2a) + (2a * -3d)
-2a^2 + 2ad + 4a^2 - 6ad
(4a^2 - 2a^2) + (2ad - 6ad)
2a^2 - 4ad
---The above expression is simplified, though not fully. The below expression is fully simplified.
2a(a - 2d)
Hope this helps!
Help me pls
Find the missing segment in the image below
Answer:
The answer is 12
Step-by-step explanation:
You see its because.
Answer:
?=12
Step-by-step explanation:
Using the Thalès's theorem:
[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]
10-7+12 dived (2^3-6) hope you can answer
Answer:
The answer is 7.5
The baseball team has a double-header on Saturday. The probability that they will win both games is 34%. The probability that they will win the first game is 75%, What is the probability that the team will win the second game given that they have already won the first game?
A. 45%
B. 74%
C. 90%
D. 26%
Answer:
A. 45%
Step-by-step explanation:
34/75=45 = 45%
The length of a room is two times its breadth and three times its height . if the cost of white wash on the 4 wall at Rs. 50 per m² is Rs. 7200, find the cost of carpeting its floor at Rs. 325 per m²
Answer:
Step-by-step explanation:
let the height of the room(h) = x
Length(l) = 3*x = 3x
length = 2 * breadth
breadth(b) = length /2 = 3x/2
Cost of whitewashing the 4 walls = ₹ 7200
Area of 4 walls = 7200 ÷ 50 = 144 m² ------(I)
Area of walls = 2lh + 2bh
= 2*3x*x + 2 *[tex]\frac{3x}{2}[/tex] * x
= 6x² + 3x²
= 9x²
9x² = 144 {From (I)}
x² = 144/9
x² = 16
x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]
x = 4 m
height = 4 m
length = 3*4 = 12m
Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]
Area of floor = l*b
= 12 * 6
= 72 m²
Cost of carpeting the floor = 72 * 325 = ₹ 23400
Hi!! Can you please help with this question and explain how to solve it??
Find the height in centimeters of a square pyramid with a volume of 144 cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.
9514 1404 393
Answer:
7.56 cm
Step-by-step explanation:
The volume is given by the formula ...
V = 1/3b²h . . . . where b is the base edge length, and h is the height.
Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...
144 cm³ = 1/3h³
432 cm³ = h³
h = ∛432 cm ≈ 7.55953 cm
The height of the pyramid is about 7.56 cm.
Answer:
[tex]7.56cm[/tex]
Step-by-step explanation:
Given that,
base length = Height
so,
[tex]volume = \frac{1}{3} {b}^{2} h \\ [/tex]
We can also write this as( according to this question)
[tex]v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} [/tex]
let's solve
[tex]v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55[/tex]
[tex]base = height = 7.55cm \\ [/tex]
= 7.56cm
A motorboat travels 81 miles in 3 hours going upstream. It travels 135 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Answer:
27, 18
Step-by-step explanation:
Here's why
Write each decimal as a fraction or mixed number in simplest form -0.4
Answer:
-2/5
Step-by-step explanation:
what is 15 out of 24 as a percent?
