Answer:
r = 2
Step-by-step explanation:
nth term of a geometric sequence = [tex] ar^{n - 1} [/tex].
Where,
a = first term, r = common ratio,
We are given that, the 11th term is 32 times larger than the 6th term of the geometric sequence. Thus:
the 6th term can be expressed as [tex] ar^{n - 1} = ar^{6 - 1} [/tex]
[tex] a_6 = ar^{5} [/tex]
The 11th term is expressed as [tex] a_11 = ar^{10} [/tex]
Since the 11th term is 32 times larger than the 6th term, therefore, the following equation can be derived to find the common ratio, r, of the sequence:
[tex] a_11 = 32*a_6 [/tex]
[tex] a_11 = ar^{10} [/tex]
[tex] a_6 = ar^{5} [/tex], therefore:
[tex] ar^{10} = 32*ar^{5} [/tex]
Divide both sides by ar⁵
[tex] \frac{ar^{10}}{ar^5} = \frac{32*ar^{5}}{ar^5} [/tex]
[tex] r^5 = 32 [/tex]
[tex] r^5 = 2^5 [/tex]
[tex] r = 2 [/tex]
Common ratio = 2
I need help I got this wrong
y = -2|x +1|
→ |x + 1| = -y/2
→ x+1 = y/2
and
x + 1 = -y/2
→ x + 1 belongs to R
→ x belongs to R
Domain = R
Range = y = -2(R)
→( -∞ , 0)
Solve for x. 4(2x−3)=11x
Answer: x=-4
Step-by-step explanation:
Answer:
The correct answer is x = -4.
Step-by-step explanation:
To solve this problem, we should first use the distributive property to get rid of the parentheses on the left side of the equation. This is modeled below:
4(2x - 3) = 11x
8x - 12 = 11x
Then, we should subtract 8x from both sides to move all of the variable terms to the right side of the equation.
-12 = 3x
Finally, we can divide both sides by 3 to get the variable x completely alone on the right side of the equation.
-4 = x
Therefore, the answer to your question is x = -4.
Hope this helps!
ethan made a rectangular prism that has a volume of 16 cubic inches. What is one set of possible dimensions for ethans rectangular prism?
Answer:
0.5 inches by 0.5 inches by 64 inches
Step-by-step explanation:
Any three positive dimensions that have a product of 16 will be a set of possible dimensions. There are an infinite number of them. One such is listed above.
(If you have a list of answer choices, you can multiply them out to see which have a product of 16. We cannot guess what your choices might be.)
A town built a scale model of the ancient construction of Stonehenge based on the original construction
found in Wiltshire, England. The scale of the model to the original is 5 to 9. The Altar Stone of the original
construction is 49 meters tall. Find the height of the model of the Altar Stone. Round your answer to the
nearest hundredth.
Answer:
27.22 m
Step-by-step explanation:
The scale factor is:
9/5= 1.8Height of the model according to scale factor:
49/1.8 = 27.22 mZandra went into a candy store to buy jelly beans. She wanted to choose 3 flavors from 12 flavors they sold. How many combinations of 3 flavors could she make
Answer:
220 ways
Step-by-step explanation:
Total number of flavors (n) = 12
Number of flavors to combine (r) = 3
Recall:
nCr = n! ÷(n-r)! r!
nCr = 12! ÷ (12 - 3)!3!
nCr = 12! ÷ 9!3!
nCr = (12 * 11 * 10) / (3 * 2 * 1)
nCr = 1320 / 6
= 220 ways
Use calculator to evaluate each expression. sin²36° + cos² 36°
Answer:
1 because sin2theta + cos2theta is equal to 1
Step-by-step explanation:
what is the square root of 35
Answer:
Step-by-step explanation:
the square root of of 35 is
5.916079783099616
5.9160797831
Step-by-step explanation:
You can round this to 6 as a whole number or 5.9 to 1dp.
Simplify nine square root of two minus three square root of seven-plus square root of eight minus the square root of twenty-eight.
Answer:
= 11√2 - 5√7
Step-by-step explanation:
9√2 - 3√7 + √8 - √28
= 9√2 - 3√7 + 2√2 - 2√7
add similar elements
= 11√2 - 3√7 - 2√7
= 11√2 - 5√7
Answer:
11[tex]\sqrt{2}[/tex] - 5√7
Step-by-step explanation:
= 9[tex]\sqrt{2}[/tex] - 3[tex]\sqrt{7}[/tex] + 2√2 - 2[tex]\sqrt{7}[/tex]
= 11[tex]\sqrt{2}[/tex] - 3[tex]\sqrt{7}[/tex] - 2[tex]\sqrt{7}[/tex] add similar elements
= 11[tex]\sqrt{2}[/tex] - 5[tex]\sqrt{7}[/tex]
raise 3 to the 2nd power, then add c to the result
Answer:
Below
Step-by-step explanation:
● 3
● 3^2
● 9
● 9 + c
======================================================
Explanation:
3 to the 2nd power is the same as writing 3^2 in shorthand
3^2 = 3 squared
When we square a number, we're multiplying it by itself (having 2 copies total of the number). Think of a square with side length 3 units. Its area is 3^2 = 3*3 = 9 square units.
From here, we add on c to get our answer 9+c. We don't know the value of c, so we cannot evaluate further. Also, 9 and c are not like terms so we cannot combine them.
evaluate 70 divided by root 10 +root 20 +root 40 - root 80 , if root 10= 3.16 and root 5 =2.24
Answer:
18.0397079611
Step-by-step explanation:
Ok please help i might put 50 for this one
Your question has been heard loud and clear.
a)
Initial velocity , U=50km/h = 250/18 m/s
Final velocity , V = 0 (this is because the car finally comes to rest)
From 3rd equation of motion , V^2-U^2=2AS.
Now , for a car that goes 50km/h , it has been proven that miniumum brake distance is 6 metres.
so , S = 6 metres.
Using this , we can find the distance stopped by car , and then we can find time.
0-(250/18)^2=2*A*6
0= 2*A*6+(250/18)^2
0 = -12A + 192.90 ( minus sign because car is deccelerating)
So , A = 16.07 m/s^2
V^2-U^2 = 2AS
0 - 192.90 = 2* 16.07*S
So , S (distance) = 24 metres.
Now , we know time = distance / speed
so , time = 24 / 253 = 0.094 seconds
Thank you
A cylindrical well has a radius of 10 feet and a height of 12 feet. How many cubic feet of water will it take to fill the well?
Assume that π = 3.14 and round to the nearest tenth when necessary.
Answer:
3769.91
Step-by-step explanation:
volume = π[tex]r^{2}[/tex]h
volume = 3.14(10 * 10) (12)
volume = 3769.91
Find the value of 2(1 + 4i) – (-2 + i)
Answer:
4+7i
Step-by-step explanation:
Solve for x.
4 + 3 x / 2 = 5
x = [?]
Answer: 2/3 I got this question on my test to and I got it correct!
Combine the like terms to create an equivalent expression:-12-6p-(-2)
Answer:
-10-6p
Step-by-step explanation:
-12-(-2)-6p = -12+2-6p= -10-6p
Answer:
-10-6p
Step-by-step explanation:
-12-6p-(-2)
-12-6p+2
-12+2-6p
-10-6p
Hope this helps ;) ❤❤❤
Amy regularly works 20 hours per week at Pook's Dry Cleaners from Monday through Friday. She earns $15.50 per hour and receives double-time pay for working Sundays. Next week she will work her regular 20 weekday hours, and an additional eight hours on Sunday. What will her total pay be for the week
Total amount she earn is $558
Multiply based problem:Given that;
Payment per hour on weekdays = $15.50
Payment per hour on Sunday = 2($15.50) = $31
Hour work on Sunday = 8 hour
Hour work on weekdays = 20 hour
Find:
Total amount she earn
Computation:
Total amount she earn = (20)(15.50) + (8)(31)
Total amount she earn = $310 + 248
Total amount she earn = $558
Find out more information about 'Total earning'.
https://brainly.com/question/25788016?referrer=searchResults
Type a simplified fraction as an answer. PLEASE ANSWER I AM BEGGING!!!!!!
Answer:
0.06944444444 as a fraction equals 6944444444/100000000000
In an effort to prepare for retirement, Zeus decided to sell off some of his powers to Poseidon. Each box of powers contained 4 specific powers. Each box cost Zeus $250. If Zeus wanted to make a profit $900 per box, how much would have to charge Poseidon for each power?
Answer:
$287.50Step-by-step explanation:
From the problem statement the cost price per box is
$250.
And the box contains 4 specific powers, since Zeus plans to make $900 per box which contains 4 powers
we need to find the selling price
profit= selling price-cost price
let the selling price be x
900=x- 250
x=900+250
x= 1150
Selling price = $1150
Hence the unit cost of a specific power in a box that will see a profit of $900 per box is 1150/4= $287.50
What is the slope of the graph of y = 12x - 197
Answer:
Slope = 12Step-by-step explanation:
Since the equation above is a linear graph
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question the equation is
y = 12x - 197
Comparing the equation with the general equation above
Slope / m = 12Hope this helps you
A fisherman positions his net to -8 relative to the surface of the water. how far does he need to raise the net to bring it to the surface of the water?
Answer: If i am correct the answer should be 9-10 because if it is -8 it takes 8 to bring it to 0 and it takes 9 to bring it to 1 and it takes 10 to bring it to 2.
Hope this helps!
X is a normally distributed random variable with mean 95 and standard deviation 3. What is the probability that X is between 89 and 98? Write your answer as a decimal rounded to the nearest thousandth.
Answer: 0.819
Step-by-step explanation:
Given: X is a normally distributed random variable with mean 95 and standard deviation 3.
Then, the probability that X is between 89 and 98 will be:
[tex]P(89<X<95)=P(\dfrac{89-95}{3}<\dfrac{X-mean}{standard\ deviation}<\dfrac{98-95}{3})\\\\=P(-2<Z<1)\ \ \ [Z=\dfrac{X-mean}{standard\ deviation}]\\\\ =P(Z<1)-(1-P(Z<2))\\\\= 0.8413- (1-0.9772)\ \ \ [\text{By p-value table}]\\\\= 0.8185\approx0.819[/tex]
Hence, the required probability = 0.819
х
f(x)
Analyze the table of values for the continuous function,
f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
-3
-16
-2
-1
-1
2
0
-1
1
-4
N
-1
Answer: the answer is
(-2,0)
(0,2)
Answer:
The answer is
( -2, 0 )
(0, 2 )
Step-by-step explanation:
I just took the test and got it right
Hopefully this helps you
pls mark brainlest
One thousand students atende queen city elementary school 5/1,000 of the students were absent on Monday how can the number of students be written as a decimal
Answer:
Number of absent student in decimal = 0.005
Step-by-step explanation:
Given:
Number of student = 1,000
Number of absent student = 5 / 1,000
Find:
Write number of absent student in decimal
Computation:
Number of absent student = 5 / 1,000
Number of absent student in decimal = 5 / 1,000
Number of absent student in decimal = 0.005
Find the distance between (8,-4) and (4,3)
Answer:
sqrt65
Step-by-step explanation:
I think this is the answer
9 marbles your draw one what is the probability of drawing a red pen? You have 2 yellow 3 black and 4 reds
Answer:
4 / 9
Step-by-step explanation:
There are 4 reds out of 9 so the probability would be 4 out of 9 or 4 / 9.
Answer:
None
Step-by-step explanation:
Notice how it says red pens, not red marbles. There is no red pen
Convert 1month to hrs
Answer:
730.484397 Hours
Step-by-step explanation:
1 day =24 hours
30 days = 720 hours (30*24)
31 days = 744 hours (31*24)
the difference of 7 and a number n
Answer:
7 - n
Step-by-step explanation:
A machine is used to fill each of several bags with 16 ounces of sugar. If the bag
weights 0.3 ounces more or less than the desired weight, the bag is rejected. Write
this equation to find the heaviest and lightest bag the machine will approve.
Answer: 15.7oz < M < 16.3oz
Step-by-step explanation:
The average mass of each bag will be 16oz
If the bag weighs 0.3 oz more or less than 16 oz, then it is rejected.
Then the extremes are:
16oz - 0.3oz = 15.7oz (this mas counts as a rejected one)
So we have that the mass of the bag must be larger than 15.7oz
M > 15.7oz
Now, the other extreme is:
16oz +0.3oz = 16.3oz (again, this a rejected mass)
Then the mass of the bag must be smaller than 16.3oz
M < 16.3oz
Then the range of the accepted mass of the bags is:
15.7oz < M < 16.3oz
Translating verbal expression: the sum of 15 and a number x.
Answer:
x+15 or 15+x
Step-by-step explanation:
it doesn't really matter since the commutative property.
sum = addition
15 = one term
number x = second term
118 - [121 - (11 × 11) - (-4) - 3 - 9 - 2]
Answer:
Step-by-step explanation:
118 - [121 - ( 11 x 11 ) - ( - 4 ) - 3 - 9 - 2]
118 - [121 - 121 + 4 - 3 - 9 - 2]
118 - [4 - 3 - 9 - 2]
118 - [1 - 9 - 2]
118 - [-8 - 2]
118 - (-10) or 118 - 1(-10)
Negative times negative equals to positive.
118 + 10= 128