Determine if the sequence is geometric . If it is , find the common ratio , the explicit formula and the recursive formula .
1. -40 , 20 , -100 , 500
2. 4 , 20 , 100 , 500
3. 4 , 24 , 144, 864
5. 3 , -12 , 48 , -192
Step-by-step explanation:
if it is a geometric sequence, then
sn = sn-1 × r
with r being the common ratio.
1.
s2 = s1 × r
20 = -40 × r
r = 20/-40 = -1/2
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
-100 = 20 × -1/2 = -10
this is wrong, so, it is not geometric.
2.
s2 = s1 × r
20 = 4 × r
r = 20/4 = 5
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
100 = 20 × 5 = 100
s4 = s3 × r
500 = 100 × 5 = 500
this is all correct, so, it is geometric.
sn = sn-1 × 5
sn = s1 × 5^(n-1) = 4 × 5^(n-1)
3.
s2 = s1 × r
24 = 4 × r
r = 24/4 = 6
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
144 = 24 × 6 = 144
s4 = s3 × r
864 = 144 × 6 = 864
this is all correct, so, it is geometric.
sn = sn-1 × 6
sn = s1 × 6^(n-1) = 4 × 6^(n-1)
5.
s2 = s1 × r
-12 = 3 × r
r = -12/3 = -4
but the same r has to apply to all other terms, if it is geometric.
s3 = s2 × r
48 = -12 × -4 = 48
s4 = s3 × r
-192 = 48 × -4 = -192
this is all correct, so, it is geometric.
sn = sn-1 × -4
sn = s1 × (-4)^(n-1) = 3 × (-4)^(n-1)
A recipe for lemonade called for 1 cup of sugar and 5cups of water.How much sugar is used per cup of water
Write a fraction with a denominator of 9 whose equivalent percent is less than 100%. In complete sentences, explain why the fraction is less than 100%.
The fraction is 8/9
Lets find percentage
8/9(100)800/988.89%Done!
12/14 , 15/, 19/24 which one is greater?
Step-by-step explanation:
12/14= 85.7143% 19/24= 79.1667%
A car weighs 3.6 tons. Find its weight in pounds.
10. Andy has trumpet practice 4 times every month. Every practice lasts half an hour. What is the total number of minutes that Andy will practice?
Answer:
480min a month
Step-by-step explanation:
4×30 =120
120×4=480
Which of the following does NOT represents a function?
Solve for X
2/3 x +10/60 =100/60
Answer:
2 1/4
Step-by-step explanation:
subtract 10/60 from each side to get:
2/3x = 90/60
multiply each side by 3/2 to get:
x = 270/120
x = 27/12 or 2 1/4
Can anybody help me with these three problems thank you
Answer:
1) 1/7
2) 1/3
3) 1/4
Step-by-step explanation:
1) Since there are 7 days in a week it can be expressed as the fraction 1/7
2) Since there are 3 feet in a yard it can be expressed as the fraction 1/3
3) Since there are 4 quarts in a gallon it can be expressed as the fraction 1/4
7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.
A vehicle was travelling at a speed of 72km per hour. What distance did it cover in 2 hours? A. 158km B. 148km C. 168km D. 144km
Answer:
D. 144km
Step-by-step explanation:
If the vehicle travels 72km every hour, in two hours, it will drive 144km. (72x2=144)
The weights of adult polar bears, the largest bear species in North America, have a mean of 950 pounds and standard
deviation of 84 pounds. What is the weight of a polar bear that has a z-score for weight of -1.50?
Find the Z-table here.
O 126 pounds
O 824 pounds
948.5 pounds
O 951.5 pounds
O 1,076 pounds
The weight of 824 pounds of a polar bear has a z-score of -1.50.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation[/tex]
Given that μ = 950, σ = 84
For z = -1.50:
[tex]-1.50=\frac{x-950}{84}\\\\x-950=-126\\\\x=824[/tex]
The weight of 824 pounds of a polar bear has a z-score of -1.50.
Find out more on z score at: https://brainly.com/question/25638875
( 4 1 + 4 5 ) ^ 2 + 4 3 =
Answer: 7,439
Step-by-step explanation:
(86)^2 + 43
7396 + 43 = 7,439
I'm pretty sure that the other user has the same answer. (godlike74)
The dimensions of a rectangular garden is 3 m by 10 m. When both dimensions are increased by equal amounts, the area of the garden doubles. What are the dimensions of the new garden?
Answer:
5 by 12 m
Step-by-step explanation:
The area for rectangle is LxW
The original area is 3*10, or 30 meters.
When both dimensions are increased, now the area is 60.
We can now inch up slowly to see what works:
3.5 and 10.5=36.75 X
4 and 11=40 X
5 and 12=60 YES!
The new dimensions of the garden are 5 m by 12 m, increased by 2, and the new area is 60 meters^2.
No links help
Rectangle X is 5 cm long and 3 cm wide. Rectangle Y is similar to Rectangle X. What could be the dimensions of
Rectangle Y?
A)10 cm long and 8 cm wide
B)15 cm long and 9 cm wide
C) 15 cm long and 13 cm wide
D)10 cm long and 3 cm wide
15. Kate plays a card game with two friends. She gives 5 cards to each player. Ten plus what number is equal to the total number of cards Kate gives out? Write an equation to show and solve the problem.
Answer:
i believe it would be 0
Step-by-step explanation:
2*5 = x
2*5 = 10
x = 10
10 + y = x
10 + y = 10
-10 -10
-----------------
y = 0
the number is 0
hope this helps! :D
have a miraculous day!! <3
Which side lengths form a right triangle?
Choose all answers that apply
(Choice A)
A
3
,
27
,
6
3,
27
,63, comma, square root of, 27, end square root, comma, 6
(Choice B)
B
8
,
15
,
17
8,15,178, comma, 15, comma, 17
(Choice C)
C
Answer:
4, 7.5, 8.54,7.5,8.5
Step-by-step explanation:
We can use the Pythagorean Theorem to see if the side lengths will form a right triangle.
The equation for the Pythagorean Theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.
[How can I tell which side is the hypotenuse?]
Hint #22 / 5
Let's check each set of numbers:
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 +\sqrt8^2 &\stackrel{\large?}{=} 24^2 \\\\ 16 + 8&\stackrel{\large?}{=} 576\\\\ 24&\neq 576\\\\ \end{aligned}
a
2
+b
2
4
2
+
8
2
16+8
24
=c
2
=
?
24
2
=
?
576
=576
The side lengths 4, \sqrt8, 244,
8
,244, comma, square root of, 8, end square root, comma, 24 do not form a right triangle.
Hint #33 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 5^2 + 5^2 &\stackrel{\large?}{=} 5^2 \\\\ 25+ 25&\stackrel{\large?}{=} 25\\\\ 50&\neq 25\\\\ \end{aligned}
a
2
+b
2
5
2
+5
2
25+25
50
=c
2
=
?
5
2
=
?
25
=25
The side lengths 5, 5, 55,5,55, comma, 5, comma, 5 do not form a right triangle.
Hint #44 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 + 7.5^2 &\stackrel{\large?}{=} 8.5^2 \\\\ 16+ 56.25&\stackrel{\large?}{=} 72.25\\\\ 72.25&\stackrel{\checkmark}{=} 72.25\\\\ \end{aligned}
a
2
+b
2
4
2
+7.5
2
16+56.25
72.25
=c
2
=
?
8.5
2
=
?
72.25
=
✓
72.25
Answer:
4, 7.5, 8.5
Step-by-step explanation:
I had this question on Khan, and it was right (:
(Brainliest question) Which type of study best describes the following research most likely to be done? A researcher is trying to determine the effects of animal habitats and animal populations after forest fires. So she visits places that have had a naturally occurring Forest fire to study the area.
Experimental study
Observational study
Simulation study
Double blind study
Answer:
Observational study
Step-by-step explanation:
See the researcher visits the forest.She want to experience or observe the forest fire.She want to observe how it affects the animals.Hence it's observational studyTodd drinks 4 liters of water every day. There are approximately 29.6 Milliliters in 1 fluid ounce. Which measurement is closest of to the number of fluid ounces in 4 liters/
A.7 fl oz
B. 34 fl oz
C. 118 fl oz
D. 135 fl oz
Answer:
D is the closest. The exact is 135.256
If your money doubles once every 30 minutes and your start with $12, how much money will you have in 1.5 day?
Answer:
$1728
Step-by-step explanation:
1.5 days is 36 hrs
36 hrs is 2160 mins
2160/30 = 72 (this is the amount of times our money will be doubled)
72*2 = 144
$12*144 = $1728
Y<-3 which is the solution:
A) 5
B) 0
C)-2
D)-5
Y needs to be less than -3 the larger the negative number the further from 0 it is so -5 would be less than -3
Answer: -5
NEED HELP RELATIONSHIP IN TRIANGLES
We have: PT = NT <=> 4x - 17 = x + 10 <=> 3x = 27 <=> x = 9
=> NT = 4x - 17 = 4.9 - 17 = 19
Δ RNT have:
[tex]RT^2 = NT^2 -RN^2 =19^2 -14^2=165\\=>RT=\sqrt{165} [= 12.84523258][/tex]
Ok done. Thank to me :>
please help! will give brainliest:)
Solve the following system:
2x - z=14 a
10
3x - y + 5z = 0
(4x + 2y + 3z = -2
help me please thanks
Answer:
9.25 would be the value of x
Explanation:
Perimeter = 2(l + w)
2(13.25 + 9.25)
= 45
The next number in the arithmetic sequence 15, 22, 29, is:
A) 34
B) 35
C) 36
D) 37
633 divided by 3 rounded to the the 10
Answer: 211
Step-by-step explanation:
633 divided by 3 answers evenly with no decimal
The income elasticity is +2 and income increases by
20%. Sales were 5000 units, what will they be now?
Answer:
Step-by-step explanation:
The income elasticity is +2.5 and income increases by 20%. Sales were 5000 units, what will they be now? If the income elasticity is +2.5, income increases by 20% and sales were 5000 units, then the sales will increase by 20%*2.5 = 50% to 7500 units.
How to solve 22 – 3y > 7
Answer:
y < 5
Step-by-step explanation:
22 – 3y > 7
=> 22 – 7 > 3y
=> 15 > 3y
=> y < 5
Therefore, y < 5 is the solution.
Hoped this helped.
Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
18 divided by StartFraction 2 Over 9 EndFraction = 81
18 times StartFraction 2 Over 9 EndFraction = 4
StartFraction 2 Over 9 EndFraction divided by 18 = StartFraction 1 Over 81 EndFraction
StartFraction 9 Over 2 EndFraction divided by 18 = one-fourth
Answer:
18 times StartFraction 2 Over 9 EndFraction = 4
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
Answer:
IT'S B I CAN CONFIRM BC I JUST FINISHED THE TEST
Step-by-step explanation:
y=1/4x−2y=−2x+3 help solve problem.
Answer:
(x, y) = (2 2/9, -1 4/9)
Step-by-step explanation:
Equate the values of y and solve for x.
1/4x -2 = -2x +3
(2 1/4)x = 5 . . . . . . . . add 2+2x to both sides
x = 20/9 = 2 2/9 . . . multiply by 4/9
y = -2(2 2/9) +3 = -4 4/9 +3 . . . . substitute for x in the second equation
y = -1 4/9
The solution is x = 2 2/9, y = -1 4/9.