What are the first five terms, a1, a2, a3, a4, a5, of the sequence defined by a Subscript n = StartFraction n squared minus 9 Over n cubed + 3 EndFraction, and how can the sequence be described?
PLEASEEE HELP !!
Answer:
Step-by-step explanation:
So if you look at the numerator the degree is 2, and if you look at the numerator of the denominator, it's 3. This means that the value of the denominator will grow faster than the numerator, so it will diverge.
To find the first 5 terms simply plug in 1, 2, 3, 4, and 5 as n
[tex]a_1=\frac{1^2-9}{1^3+3} = \frac{-8}{4} = -2}\\a_2 = \frac{2^2-9}{2^3+3} = \frac{-5}{11} = -\frac{5}{11}\\a_3 = \frac{3^2-9}{3^3+3} = \frac{0}{30} = 0\\a_4 = \frac{4^2-9}{4^64+3} = \frac{7}{67} = \frac{7}{67}\\a_5 = \frac{5^2-9}{5^3+3} = \frac{16}{128} = \frac{1}{8}[/tex]
It should converge to a limit of 0, since the denominator is growing faster than the numerator
Answer:
C
Step-by-step explanation:
Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
Answer: A translation 1 unit to the left
Step-by-step explanation:
See attached image.
In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What is your estimated probability for P(H)?
The estimated probability for P(H) is 0.17.
What is Probability ?Probability is the stream in mathematics that studies about the likeliness of an event to happen.
It is given that
Total number of times coin is flipped = 30
Total number of times the coin gave heads = 5
Total number of times the coin gave tails=25
The P(H) = Total no. of Heads / Total outcomes
P(H) = 5 / 30
= 1/6
= 0.1666
≈ 0.17
Therefore the estimated probability for P(H) is 0.17.
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Based on the family the graph below belongs to, which equation could represent the graph?
Answer:
the first option I believe
what is the formula for finding the area of a sphere
Answer: [tex]4\pi r^{2}[/tex]
Step-by-step explanation:
Area of a circle is pi r squared
Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are
common catches. The mean length of a bluefish is 267 millimeters with a standard deviation of
39 mm. For pompano, the mean is 155 mm with a standard deviation of 28 mm.
Using the normal distribution, it is found that due to the greater z-score, Stewart caught the longer fish relative to the same specie.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.To find who caught the longer fish relative to the same specie, we need to find out who had the higher z-score.
Stewart caught a bluefish with a length of 322 mm, hence the parameters are as follows:
[tex]X = 322, \mu = 267, \sigma = 39[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{322 - 267}{39}[/tex]
Z = 1.41
Gina caught a pompano with a length of 176 mm, hence the parameters are as follows:
[tex]X = 176, \mu = 155, \sigma = 28[/tex]
The z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{176 - 155}{28}[/tex]
Z = 0.75.
Hence Stewart caught the longer fish relative to the same specie.
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If f(a) = 2a ^ 3 + 3a ^ 2 + 5 , find f(- 2)
Step-by-step explanation:
Just plug in -2 anywhere you see an a
[tex]f(a)=2a^3+3a^2+5\\f(-2)=2(-2)^3+3(-2)^2+5\\f(-2)=2(-8)+12+5\\f(-2)=-16+12+5\\f(-2)=1[/tex]
⊰________________________________________________________⊱
Answer [tex]\curvearrowright[/tex] [tex]\\[/tex]
f(-2)=1
Step-by-step explanation [tex]\curvearrowright[/tex]
Given,
Original Expression = [tex]\sf{f(a)=2a^3+3a^2+5}[/tex]To find,
f(-2) = ??All work is shown here. :))
[tex]\Large\begin{gathered} \boldsymbol{\sf{Plug \ in \ the \ number \ for \ a, \ which \ is \ -2 (it's \ given \ to \ us). Then}}\\ \boldsymbol{\sf{evaluate,}} \\ \curvearrowright\\\boldsymbol{\sf{Now \ substitute \ -2}} \\\curvearrowright\\\sf{2(-2)^3+3(-2)^2+5}\\\sf{2*(-8)+3*4+5}\\\sf{}-16+12+5=-4+5}\\\underline{\boxed{\sf{f(-2)=1}}}\end{gathered}[/tex]
Done !!
⊱______________________________________________________⊰
[tex]\tiny\pmb{CALLIGRAPHY}[/tex]
THE QUESTION IS DOWN BELOW.
major points when given branliest
The ratios are Surface area ⇒ 4 : 25 Height ⇒ 2 : 5 and Volume ⇒ 8 : 125
How to determine the ratios?The scale factor is given as:
m : n = 2 : 5
For the area, we take the square of the ratios.
i.e.
Area = 2^2 : 5^2
Evaluate
Area = 4 : 25
For the volume, we take the cube of the ratios.
i.e.
Volume = 2^3 : 5^3
Evaluate
Volume = 8 : 125
The given scale factor can be used for the height of the model and the original bicycle
Hence, the ratios are
Surface area ⇒ 4 : 25
Height ⇒ 2 : 5
Volume ⇒ 8 : 125
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what statement is true
Answer:
D. Both graphs are exponential functions.
Step-by-step explanation:
Hope it helps :)
Ethel is in town for the day making several purchases on her credit card. She spends $154.18 on groceries and $122.79 on tops at a sale at the local dress shop. Then she goes by to pay the utility bill, which is $219.54. How much did she charge to the nearest dollar?
Answer:
$497
Step-by-step explanation:
Added all three purchases (154.18 + 122.79 + 219.54) will give you $496.51. Rounded to the nearest dollar, you get $497.
How does an earthquake with a magnitude of 7 on the Richter scale compare to one with a magnitude of 5?
50 times stronger
100 times stronger
20 times stronger
2 times stronger
Answer:
100 times stronger
Step-by-step explanation:
The Richter scale is a measurement system for the strength of Earthquakes. The most powerful Earthquakes are at 5-10, while the least powerful ones stay from 1-4.
This is how the Richter scale works:
An earthquake with a magnitude of 2 is 10 times more powerful than an earthquake with a magnitude of 1. Each number is 10 times more powerful than the last.
So, simple math tells us that Magnitude six is 10 times more powerful than magnitude five, and magnitude seven is 100 times more powerful than magnitude 5..
In analyzing hits by certain bombs in a war, an area was partitioned into regions, each with an area of km2. A total of bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.
x is 3 that is the number of hits
e = 2.71828 is the Euler number
μ is the mean in the given interval = 0.967
There is 5.72% probability that a randomly selected region had exactly three hits.
Let X be the random variable denoting the number of bombs hitting the selected sample.
The following formula determines the likelihood that x in a Poisson distribution corresponds to the number of successes of a random variable.
P(X = x) = e^₋μ × μˣ / (x)!
Here, X is the random variable denoting the number of bombs hitting the selected sample.
μ is the mean number of hits per region.
e is the constant value.
Since 535 bombs struck a total of 553 regions, the ratio of strikes per region to the total number of regions is 535 to 553.
μ = 535 / 553
μ = 0.967
Assume that we want to find the probability that a randomly selected region had exactly 3 hits.
which means, P(X = 3)
P(X = x) = e^₋μ × μˣ / (x)!
P(X = 3) = e^₋0.967 × (0.967)³/ (3)!
= 0.057
There is approximately 5.72% probability that a randomly selected region had exactly three hits.
Your question was incomplete. Please find the missing content here.
In analyzing hits by certain bombs in a war, an area was partitioned into 553 regions, each with an area of 0.95 km². A total of 535 bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.In applying the Poisson probability distribution formula, P(X) = e^₋μ × μˣ / (x)!, identify the values of μ, x and e. Also , briefly describe what each of those symbols represent.
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Martina runs 3/1/2 miles every day for 7 days . How many miles does she run altogether
Answer:
24.5
Step-by-step explanation:
All you have to is Multiply 3 1/2 by 7
3 1/2 x 7= 24.5
One hundred riders from several countries participated in a bicycle race. Only eighty riders, including Juan and Charlie, finished the race. Juan finished 5th and Charlie was the winner. All the riders' countries of origin and finishing times were recorded on the race register. No two riders who finished had the same time and those who did not finish were recorded as DNF.
Based on this information, determine if each set is well-defined. Yes or No
The set of riders who finished minutes or more after the winner (Yes or No)
The set of the three least tired riders at the end (Yes or No)
The set of riders with the best-looking bicycles (Yes or No)
The set of riders who finished the race (Yes or No)
The set of countries of origin of the riders that didn't finish (Yes or No)
Answer:
Finished minutes or more: Yes
Three least tired: No
Best looking bikes: No
Finished the race: Yes
Countries of origin of riders who didn't finish: Yes
Step-by-step explanation:
Things displayed on the board: name of rider, country of origin, finishing time
Finished minutes or more: anyone who finished who wasn't in first
Three least tired: subjective information, not on the board
Best looking bikes: subjective information, not on the board
Finished the race: everyone who doesn't have DNF next to their name
Countries of origin of riders who didn't finish: countries of anyone with DNF next to their name
What are the solutions to the equation? 5x² + 20x = 9 Complete the square to solve. 2145 5 -2 √145 5 0-2± 0-4± -4 29 5 145 5
Answer: [tex]x=-2 \pm \sqrt{29/5}[/tex]
Step-by-step explanation:
[tex]5x^2 + 20x=9\\\\5(x^2 + 4x)=9\\\\5\left((x+2)^2 -4 \right)=9\\\\5(x+2)^2 - 20=9\\\\5(x+2)^2 = 29\\\\(x+2)^2 = \frac{29}{5}\\\\x+2 =\pm \sqrt{29/5}\\\\x=-2 \pm \sqrt{29/5}[/tex]
[19. Solve the given radical equation: √3x +31= x+7.
Step-by-step explanation:
√3x+31=x+7
√3x=+7-31
DBS by√3
√3x/√3=7-31/√3
x=−12.12435565298
x=12.1
A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches. If one item is chosen at random, what is the probability that it is less than 11.9 inches long? Round your answer to 4 decimal places.
The probability that it is less than 11.9 inches long will be 0.11304.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches.
If one item is chosen at random.
Then the probability that it is less than 11.9 inches long will be
Then the z-score will be
z = (11.9 – 14.2) / 1.9
z = –1.21
Then the probability will be
P(x < 11.9) = P(z < –1.21)
P(x < 11.9) = 0.11304
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8. In AABC, LA is a right angle and mzB = 45°. Find BC.
11√2 ft
√22 ft
2√11 ft
11 ft
Answer:
BC = 11[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
sin 45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{11}{BC}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
BC = 11[tex]\sqrt{2}[/tex]
1/2oz 3x day for 7 days how many doses will a patient use
The amount of dose is 10.5oz
How to determine the dose?The dosage is given as:
1/2oz 3x day for 7 days
This means that:
The patient will use 1/2 oz 3 times daily for 7 days
So, the dose is
Dose = 1/2 oz * 3 * 7
Evaluate the product
Dose = 10.5oz
Hence, the amount of dose is 10.5oz
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Given w =startroot 2 endroot (cosine (startfraction pi over 4 endfraction) i sine (startfraction pi over 4 endfraction) ) and z = 2 (cosine (startfraction pi over 2 endfraction) i sine (startfraction pi over 2 endfraction) ) , what is w – z expressed in polar form?
w-z can be expressed in ploar form as √2∠(7π/4)
Sometimes the expression A(cos(α)+i·sin(α)) is written as A·cis(α). I prefer the notation A∠α, because it is more compact.
Given: w = √2∠(π/4)
z = 2∠(π/2)
And you are asked to find the difference w-z in polar form.
In rectangular form, ...
w = √2∠(π/4) = √2(1/√2 +i/√2) = 1 +i
z = 2∠(π/2) = 2(0 +i·1) = 2i
Then the difference is ...
w -z = (1 +i) -(2i) = 1 -i
You may notice this is the conjugate of w, so will have the opposite angle:
w - z = w* = √2∠(-π/4) = √2∠(7π/4)
In the terms used by the problem statement, ...
w -z = √2(cos(7π/4) +i·sin(7π/4))
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Evaluate the expression for s = -15. -S=
Answer:
-S = 15
Step-by-step explanation:
You are asked to find the opposite of the given value.
OppositeThe opposite of an integer value is obtained by changing its sign.
S = -15
-S = -(-15) = 15
__
Additional comment
Equivalently, you are multiplying by -1. The product of an even number of minus signs is a plus sign. We usually don't write the plus sign for a numerical value.
(cot A - tan A)cos A = cosecA-2sinA
Simplify the LHS by using the identities above to get the RHS:
(cot A - tan A)cosA = (cosA/sinA - cosA/sinA)cosA = Identities 2 and 3(cosA/sinA)cosA - (cosA/sinA)cosA = Distributecos²A/sinA - sinA = Simplify/cancel(1 - sin²A)/sinA - sinA = Identity 11/sinA - sin²A/sinA - sinA = Distribute1/sinA - sinA - sinA = Simplify/cancel1/sinA - 2sinA = cosecA - 2sinA Identity 4Proved
If $1 in U.S. Dollars is equivalent to 0.1273 Chinese yuan, convert 13,000 to yuan.
Answer:
1654.9
Step-by-step explanation
1/0.1273 = 13000/x
x=1654.9
find x and y
pls help
Answer:
x = 14
Step-by-step explanation:
110 + 5x = 180
-110 -110
5x = 70
divide by 5 on both sides
x = 14
to find y add 70 + 40 + missing angle = 2y
missing angle is 70 because 70+40+70 = 180
so 2y = 110
y = 55
Answer:
x=14
y=55
Step-by-step explanation:
5x and 110 form a straight line so they add to 180
5x+110 =180
5x = 180-110
5x = 70
Divide by 5
5x/5 = 110/5
x = 14
We know the exterior angle of a triangle is equal to the sum of the two opposite interior angles
40 + 5x = 2y
Substitute in 14 for x
40 +5(14) = 2y
40 + 70 = 2y
110 = 2y
Divide by 2
110/2 =2y/2
55 = y
I need help with number 13 and 14
Answer:
13)x=59 answer is d 14)x=24
Step-by-step explanation:
180-116(angles on a striaght line sum to 180)180-116=64
angle in a triangle sum to 180
64+x=180
64+57=121
180-121=59
x=59
question 14 answer is 24
90+66=156
sum of a triangle is 180
180-156=24
Without actual calculating the cubes, evaluate using identities:
[tex]-11^3+8^3+3^3[/tex]
Answer:
-792
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{-11^3 + 8^3 + 3^3}[/tex]
[tex]\mathsf{= -11\times -11\times -11 + 8\times8\times8 + 3\times3\times3}[/tex]
[tex]\mathsf{= 121\times -11+ 64\times8+9\times3}[/tex]
[tex]\mathsf{= -1,331 + 512 + 27}[/tex]
[tex]\mathsf{= -819 + 27}[/tex]
[tex]\mathsf{= -792}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{-792}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please can you help me
Answer:
92.16Step-by-step explanation:
(-41.8 + 32.2)² =
(-9.6)² =
92.16
Answer:
92.16
Step-by-step explanation:
solving the brackets first, -41..8 + 32..2 equals -9.6 in total. The bracket has a square around it so our answer would be the square of wat ever we get in the bracket meaning (-9.6)^2 which gives us 92.16
Listed below are measured amounts of caffeine obtained in one can from each of 14 brands. Find the variance, for the given sample data and leave the answer to the nearest hundredths.
57, 34, 30, 44, 33, 41, 60, 47, 56, 41, 31, 22, 12, 40.
Answer:
And here's your answer: 39.14
Step-by-step explanation:
First, add all the numbers up
then divide them all by 14
Twice the sum of two consecutive integers is 22. What are the two integers?
The consecutive two integers are 5 and 6
Linear equations
Let the two consecutive integers be (x+1) and (x). If twice the sum of two consecutive integers is 22 then;
2(x+1+x) = 22
x+x+1 = 22/2
2x + 1 = 11
Subtract 1 from both sides
2x = 11 - 1
2x = 10
x = 5
Hence the consecutive two integers are 5 and 6
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Simplify each expression by combining like terms
-5(n-5)+3(n+1)
Answer:
-2n + 28
Step-by-step explanation:
-5(n-5) + 3(n+1)
Let's distribute!
-5n + 25 + 3n + 3
Now we can add the like terms (n's with n's and numbers with numbers)
-2n + 28
Answer: -2n+28
Step-by-step explanation:
We can use the distributive property to solve this problem.
-5n+25+3n+3
-2n+28