Determine whether the sequence converges or diverges. If it converges, find the limit. [Hint:
consider limit laws, the Squeeze Theorem, behavior of related real-valued functions, etc.]
(a) an = 2 + (0.86)^n
(b) an =(4^n)/(1+9^n)
(c) an = arctan(ln n)
(a) converges; consider the function f(x) = a ˣ, which converges to 0 as x gets large for |a | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As n gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(n ) → ∞ and arctan(n ) → π/2 as n → ∞. So the limit is π/2.
In ΔVWX, w = 680 cm, ∠X=80° and ∠V=32°. Find the area of ΔVWX, to the nearest 10th of a square centimeter
Answer:
56
Step-by-step explanation:
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
The area of the triangle.
= 1/2 x base x height
The area of the triangle is 105760 cm².
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
In ΔVWX.
w = 680 cm
∠X=80°
∠V=32°
This means,
∠W + ∠X + ∠V = 180
∠W = 180 - 112
∠W = 68°
This means,
68° = 680
1° = 10
Now,
∠X=80°
x = 800 cm
∠V=32°
v = 320 cm
Now,
V
/ | \
(x) / | \ (w)
/ | \
W M X
(v)
680² = VM² + (320/2)²
462400 = VM² + 25600
VM² = 436800
VM = 661 cm
Thus,
The area of the triangle.
= 1/2 x base x height
= 1/2 x 320 x 661
= 160 x 661
= 105760 cm²
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ2
https://cantonschools.instructure.com/courses/1278/discussion_topics/14354
A small liberal arts college in the Northeast has 350freshmen. One hundred five of the freshmen are female. Suppose sixty freshmen are randomly selected (without replacement).Step 2 of 2:Find the standard deviation of the number of females in the sample. Round your answer to two decimal places, if necessary.
Answer:
The standard deviation of the number of females in the sample is 3.21.
Step-by-step explanation:
For each freshmen, there are only two possible outcomes. Either it is a female, or it is not. Sixty freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.
Standard deviation of the hypergeometric distribution:
We have that:
N is the population size.
n is the sample size.
s is the number of successes in the sample.
The standard deviation is given by:
[tex]\sigma = \sqrt{n(\frac{s}{N})(1 - \frac{s}{N})(\frac{N - n}{N-1})}[/tex]
A small liberal arts college in the Northeast has 350freshmen.
This means that [tex]N = 350[/tex]
One hundred five of the freshmen are female.
This means that [tex]s = 105[/tex]
Suppose sixty freshmen are randomly selected
This means that [tex]n = 60[/tex]
Find the standard deviation of the number of females in the sample.
[tex]\sigma = \sqrt{60(\frac{105}{350})(1 - \frac{105}{350})(\frac{350 - 60}{350 -1})} = 3.21[/tex]
The standard deviation of the number of females in the sample is 3.21.
Enter an algebraic expression for the word expression.
The quotient of -5 and y
The expression is
9514 1404 393
Answer:
-5/y
Step-by-step explanation:
The wording "the quotient of A and B" is used to signify A/B.
Here, we want the quotient of -5 and y:
-5/y
does this graph show a function? explain how you know.
What is 1+1 I need help
Answer:
2
Step-by-step explanation:
1 + 1 = 2
Number Order: 1 2 3 4 5 6...
1 plus an additional value of 1 gives us the next number which is 2
please help MATHEMATICS
Answer:
area is 26.75 units^2
Step-by-step explanation:
Top Triangle area is (3.5*9)/2=15.75
Square area is 2*2=4
Left bottom triangle is (2*2)/2=2
bottom right triangle is (2*5)/2=5
15.75+4+2+5=26.75
A group of friends really love to go bowling together. Here are a set of final scores from a recent bowling trip: 147, 160, 80, 110, 121, 164, 62, 90, 76, 83, 110 What is the median
Answer:
110
Step-by-step explanation:
The first step is to rearrange the number from smallest to the biggest
62, 76, 80, 83, 90, 110, 110, 121, 147, 160, 164
Median is described as the middle number
Hence the median is 110
I WILL GIVE YOU 100 points and Braine at Math Properties of Equality, Part 2
For each expression, write an equivalent expression to show the
mathematical properties of equality.
Distributive Property:
6(m +4) = ?
Associative Property:
2 + (m + x) = ?
Commutative Property:
x + 3 = ?
Distributive Property:
3(2y - 6) = ?
Distributive Property:
m(y + 5) = ?
Answer:
1. 6(m + 4) = 6m + 24
2. 2 + (m + x) = (2 + m) + x
3. x + 3 = 3 + x
4. 3(2y - 6) = 6y - 18
5. m(y + 5) = my +5m
Step-by-step explanation:
1. Distributive property "distributes"/multiplies the 6 outside the parentheses to each term inside the parentheses.
2. Associative property deals with how terms and numbers are grouped into parentheses. The terms/numbers stay in the same order.
3. The commutative property means terms can change in order, and you will still get the same result.
4, 5. See #1 above. Distribute/multiply the number/term outside the parentheses to the numbers/terms inside.
Let me know if you have questions.
Which of the points labeled shows the solution to the system of equations? (A, B, C, D, or E)
Answer:
E
Step-by-step explanation:
When is comes to a system of equations, the point where the lines intercept is the answer.
Someone help I don’t understand
Answer:
2052
Step-by-step explanation:
19 times 18=342
342 times 6=2052
Need help asap
Question 6
Answer:
AC=30
BD=30
BE=15
AB=27
Answer:
AC = 30, BD = 30, BE = 15, AB = 27, BC = 13.1
Step-by-step explanation:
AC = AE * 2
BD = BE * 2
BE = AE
AB = CD
BC = [tex]\sqrt{30^{2}-27^{2} }[/tex] (Pythagorean theorem)
2[tex]\sqrt{64[/tex]
PLEASE!! trigonometry
A= 61 degrees a=5 cm b=12 cm
Answer:
problem is undefined meaning there is no triangle
5th grade math. Correct answer will be marked brainliest.
Zander found these coins in his Couch
Answer:
91 cents
Step-by-step explanation:
3 quarters+3 nickel+1 penny=91 cents
Answer:
91 cents
Step-by-step explanation:
3 quarters=75c
3 nickels=15c
1 penny=1c
75c+15c+1c=91 cents
40 points! Please help me
Answer:
x = 8
y = 14
Step-by-step explanation:
2x + 6 = 4x - 10 (Corresponding angles so they're equal)
2x - 4x = -10 - 6
-2x = -16
x = 8
2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)
2(8) + 6 + 13y - 24 = 180
16 + 6 + 13y - 24 = 180
13y - 2 = 180
13y = 182
y = 14
Answer:
2x+6=4x-10[corresponding angle]
16=2x
x=8
again
2×8+6+13y-24=180°[linear pair]
13y=180+2
y=182/13
y=14
Don't we just love geometry! Speaking of that, I need some help!
Please only answer if you know the answer, the comment section is right below. Please don't waste my points!
Also, please show all of your work, you are trying to help me better understand the concept, not just give me the answer.
The image is down below. Show work! Thanks!
Answer:
23.3 milesStep-by-step explanation:
Use the law of sines:
a / sin A = b / sin B = c / sin CApply to the given triangle:
AC / sin 39 = 32 / sin 60AC / 0.629 = 32 / 0.866AC = 0.6293*32/0.866AC = 23.3 (rounded)PLSS HELP THIS IS DUE TODAY
Answer:[tex]\frac{1}{42}[/tex]
Step-by-step explanation:
1 out of 7 times 1 out of 6
[tex]\frac{1}{7} *\frac{1}{6} = \frac{1}{42}[/tex]
find the measure of angle P
Answer:
i dont see the picture clearly
Step-by-step explanation:
an aquarium has 4 plants for every 3 fish there are 36 pants in the aquarium. How many fish are there?
A. 27 C. 32
B 48 D. 42
Answer:
A. 27 fish
Step-by-step explanation:
4/3 = 36/f
4f = 108
f = 27
Justin is going to invest $31,000 and leave it in an account for 7 years.
Assuming the interest is compounded quarterly, what interest rate, to the
nearest tenth of a percent, would be required in order for Justin to end up
with $45,000?
Answer:
5.4 percent
Step-by-step explanation:
Which function is best represented by this graph?
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
the -2 in the answer is the y intercept. 1/4 is the slop. rise over run, so up one and over four
A baker is experimenting with a new brand of yeast. He bakes his first batch of bread using the old brand of yeast that he usually uses and a second batch using the new brand of yeast. After baking both batches of bread, he compares the height, texture, and taste of each batch.
Answer:
control group: second batch
explanatory variable: new brand of yeast
response variable: height, texture, and taste
Step-by-step explanation:
Answer:
Explanatory variable = new brand of yeast
Response variable = height, texture, and taste
Control group = first batch
**See screenshot of graded answer
Simplify the following fraction: 6/9
What value of k makes the equation below true 33k=1,716
Answer:
Given:
33k=1,716
k=1716/33
k=52
7/3 =q+2/3 what is q?
Answer: q=5/3
Step-by-step explanation:
Let's take our equation
7/3=q+2/3
-2/3 -2/3
5/3=q
q=5/3
Answer: q = 5/3
Step-by-step explanation: Step 1: Flip the equation.
q + 2/3 = 7/3
Step 2: Subtract 2/3 from both sides.
q + 2/3 - 2/3 = 7/3 - 2/3
Juice is on sale with the rule "buy one, get one half-off.” Write an expression two different ways to represent the cost of buying two containers of juice, j, on sale. Enter the correct answers in the boxes.
Answer:
34
24
Step-by-step explanation:
divide 25 by 3
What are the solutions of x2 - 7x + 13 = 0 ? Imaginary numbers
Answer:
Step-by-step explanation:
I know what your thinking YOU DIDNT ANSWER!!!!! but think again i did, it is just an imaginary answer. dad jokeCRINGE!!!!!
Answer:
2 imaginary numbers
Step-by-step explanation:
x^2-7x+13=0
C=(-7)^2-4x1x13
D=-3
2 imaginary numbers