The limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] means that the term [tex]a_n[/tex] becomes large as n becomes large
The limit of a function describes the behavior of such function as the independent variable approaches a certain value
Infinity [tex]\infty[/tex] represents a very large number
In the limit, both n and [tex]a_n[/tex] tend to infinity
The given limit is:
[tex]\lim_{n \to \infty} a_n = \infty[/tex]
The limit above describes the behavior of [tex]a_n[/tex] as n approaches infinity
As n approaches infinity [tex]a_n[/tex] also approaches infinity
Therefore, the description of the limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] is that the term [tex]a_n[/tex] becomes large as n becomes large
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The statement 'lim n → ∞ an = ∞' means that the terms an become large as n becomes large.
Explanation:The statement lim n → ∞ an = ∞ means that the terms an become large as n becomes large.
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Given the following triangle, if c = 17 and a = 15, find the measure of A. 28° 41° 62°
A biker traveled 20 miles in 4 hours. A unit rate to describe this would be 5 miles per hour. What is another unit rate in this situation?
If the CPI (consumer price index) of 141 increased 8.3 % this year. What was the end of year CPI?
If the CPI increased by 8.3%, therefore this means that there was a fractional increase of 0.083. So amount increased is:
CPI increase = 141 * 0.083 = 11.703
Therefore the end of year CPI is the sum of the original and the increase:
end of year CPI = 141 + 11.703 = 152.703
Answer:
152.703
Rick works off commission. He earns 10 percent of all manufacturing equipment he sells. If he made a sale of $9,000, how much was his commission?
commission would be 9000 * 0.10 = 900
he would make $900
A shirt company has 3 designs that can be made with short or long sleeves. there are 6 color patterns available. how many different types of shirts are available from this company?
Answer: 36 Types
Step-by-step explanation:
3 designs and 6 color options so that would be
3 x 6 = 18
they also have the option of either long or short sleeve so that would be
18 x 2 = 36
Which represents the first three terms of the sequence: a1 = 2 and an = 4(an-1)2? 2, 16, 1024
4, 16, 1024
2, 16, 32
4, 16, 32
The formula for glue says to add 50ML
of hardener to each container of resin. How much hardener should be added to 15 containers of resin?
Final answer:
To find out the total hardener needed for 15 containers of resin, multiply 15 by the amount per container, 50ML, which equals 750ML of hardener in total.
Explanation:
To calculate the total amount of hardener needed for 15 containers of resin, we use a simple multiplication. We have been given that each container requires 50ML of hardener. Therefore, we multiply the number of containers by the amount of hardener needed per container.
Calculation:
Number of containers × Amount of hardener per container = Total amount of hardener
15 containers × 50ML/container = 750ML
Thus, for 15 containers of resin, you would need to add a total of 750ML of hardener.
what is 5/6 - (2/3) = ?
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
The function to find the number of rides Jay went on is [tex]\( 10.50 + 4.50x = 46.50 \)[/tex]
Let x be the number of rides Jay went on.
The cost of the entrance fee is $10.50, and the cost per ride is $4.50. The total amount Jay spent is $46.50. The equation representing this scenario is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
To find the number of rides, you can solve for x:
1. Subtract the entrance fee from the total amount:
[tex]\[ 46.50 - 10.50 = 36.00 \][/tex]
2. Divide by the cost per ride:
[tex]\[ \frac{36.00}{4.50} = 8 \][/tex]
So, Jay went on 8 rides.
The function to find the number of rides x is:
[tex]\[f(x) = 10.50 + 4.50x\][/tex]
Setting this equal to the total expenditure ($46.50), the function to find x is:
[tex]\[10.50 + 4.50x = 46.50\][/tex]
Evaluate the expression. [6(22 + 4)2 − 2(19 + 3)2]0
Answer:
the anwser is 1 so B)Step-by-step explanation:i just gottt it right on usa test prep
solve the system by graphing or using a table 3x+y=5 x-y=7
A golf-course architect has six linden trees, four white birch trees, and three bald cypress trees to plant in a row along a fairway. in how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced? the trees can be planted in nothing different ways.
Answer:
the trees can be planted 4200 ways
Step-by-step explanation:
The landscaper can plant the trees in a row in 864 different ways.
Explanation:To find the number of ways the landscaper can plant the trees, we can use the concept of permutations. Since the trees are evenly spaced, the order in which they are planted matters. We have a total of 6+linden+trees, 4 white birch trees, and 3 bald cypress trees. To calculate the number of ways to arrange them in a row, we can multiply the number of available options at each position. So, the number of ways to plant the trees in a row is 6! * 4! * 3! = 864. Therefore, there are 864 different ways the landscaper can plant the trees in a row.
Where e is the region that lies inside the cylinder x2 + y2 = 16 and between the planes z = −4 and z = 1?
Final answer:
The region e refers to the inside of a cylinder defined by x² + y² = 16 and between the planes z = -4 and z = 1. It represents a three-dimensional space bounded both radially, by the cylinder, and vertically, by the planes.
Explanation:
The region described in the question is a cylindrical volume in three-dimensional space. To visualize this region, we remember that the cylinder is defined by the equation x2 + y2 = 16, which is the set of points in the xy-plane that are at a distance of 4 from the origin (since the radius is √16 = 4). This cylinder extends indefinitely in the positive and negative z-directions.
The planes z = -4 and z = 1 act as boundaries in the z-direction, trimming the cylinder down so that we're only considering the portion of the cylinder between these two planes. Thus the region e of interest is the set of points inside the cylinder that lie at a height between z = -4 and z = 1.
This type of region is common in problems involving volume calculations, especially when using integral calculus to determine the volume of the shape or when analyzing physical phenomena like fluid flow or electric fields within prescribed bounds.
You buy a pair of jeans at a department store.
What is the percent of sales tax to the nearest tenth of a percent?
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
The price of the jeans before the discount is $24.99. The sales tax rate is 6.5%. The percent of markup after the discount is 27.7%.
The price of the jeans before the discount can be found by dividing the total cost by the markup percentage plus 100% and then multiplying by 100%.
So, the price of the jeans before the discount is (39.99 / 160) * 100 = 24.994375.
Next, to find the sales tax, multiply the subtotal by the sales tax rate.
The sales tax rate can be found by dividing the sales tax amount by the subtotal and then multiplying by 100%.
So, the sales tax rate is (1.95 / 29.99) * 100 = 6.502167.
To find the percent of markup after the discount, divide the difference between the total cost and the price before the discount by the price before the discount and then multiply by 100%.
So, the percent of markup after the discount is ((31.94 - 24.994375) / 24.994375) * 100 = 27.67322.
The probable question may be:
You buy a pair of jeans at a department store.
What is the percent of sales tax to the nearest tenth of a percent?
The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent?
Department store
Jeans =39.99
Discount =-10.00
Subtotal =29.99
Sales tax=1.95
Total = 31.94
2.1, -2.1, 2 and 2 1/11, -2 from least to greatest show work
A science fair poster is a rectangle
3
feet long and
2
feet wide. What is the area of the poster in square inches?
What is the solution of the proportion 5/x+4=3/x-2
In the last two years, Mari grew 2 1/4 inches, Kim grew 2.4 inches, and Kate grew 2 1/8 inches. Write the amounts they grew in order from least to greatest
Answer:
[tex]\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]
Step-by-step explanation:
We are given the following information in the question:
Growth in Mari =
[tex]2\displaystyle\frac{1}{4}\text{ inches} = \frac{2\times 4 + 1}{4} = \frac{9}{4} = 2.25\text{ inches}[/tex]
Growth in Kim =
2.4 inches
Growth in Kate =
[tex]2\displaystyle\frac{1}{8}\text{ inches}= \frac{2\times 8 + 1}{8} = \frac{17}{8} = 2.125\text{ inches}[/tex]
Growth in order from least to greatest:
[tex]2.125<2.25<2.4\\\text{Growth in Kate}<\text{Growth in Mari}<\text{Growth in Kim}[/tex]
A bag contains 20 red tickets and 12 blue tickets. What is the probability of randomly selecting a blue ticket from the bag? A. 4/5 B. 3/11 C. 3/8 D. 1/2
92 divided by 4 use partial and quotients to divide
Brainleiest What is the unit rate for 692.08 ft in 21.1 s? Enter your answer, as a decimal, in the box. ft/s
Answer:
Unit rate is [tex]32.9561[/tex] feet per second.
Step-by-step explanation:
Unit rate is a number where one quantity is represented so that the other quantity is 1.
So we can give the unit rate of this as number of feet per 1 second.
It has traveled 692.08 ft in 21.1 seconds.
We have to find how many feet it travels in 1 second.
Unit rate = Number of feet / Number of seconds
=[tex]\frac{692.08feet}{21.1seconds}[/tex]
=[tex]32.9561[/tex] feet per second
Answer: 32.8
Step-by-step explanation: ( I'd use my answer if I was you) :)
Lorenzo bought 15 / 16 pounds of ground beef.He wants to make hamburgers that weigh 3 / 16 pounds each.How many hamburgers can he make?
FIrst of all, i recommends you to do a model. Of 15/16 and 3/16 then compare them and take away the same denominators. What would you get? 15 and 3 so you would divide both of them And you will get 5 as your answer, remember to do an explanation on how you got it. :)
In ΔABC, BC = 4 centimeters, m∠B = m∠C, and m∠A = 20°. What is AC to two decimal places?
A.9.32 centimeters
B.10.01 centimeters
C.11.52 centimeters
D.12.09 centimeters
Answer:
C.11.52 centimeters
Step-by-step explanation:
Given,
In triangle ABC,
BC = 4 centimeters, m∠B = m∠C, and m∠A = 20°.
Since, the sum of all interior angles of a triangle is supplementary,
⇒ m∠A + m∠B + m∠C = 180°
⇒ 20° + m∠B + m∠B= 180°
⇒ 2 m∠B = 160°
⇒ m∠B = 80°,
Now, By the law of sines,
[tex]\frac{sin A}{BC}=\frac{sin B}{AC}[/tex]
By cross multiplication,
[tex]sin A\times AC = sin B\times BC[/tex]
[tex]\implies AC = \frac{sin B\times BC}{sin A}[/tex]
By substituting values,
[tex]AC=\frac{sin 80^{\circ}\times 4}{sin 20^{\circ}}=\frac{3.93923101205
}{0.34202014332
}=11.5175409663
\approx 11.52\text{ in}[/tex]
List all the factor pairs in the table factors of 25
in six years, clem kadiddlehopper will be 5 times as old as he was 26 years ago how old is he now?
The question involves setting up an equation to determine Clem Kadiddlehopper's current age based on his age in six years and 26 years ago. By solving the equation x + 6 = 5(x - 26), we find that Clem is currently 34 years old.
Explanation:Explanation:
The question asks us to determine Clem Kadiddlehopper's current age based on information about his age in future and past years. Let's define Clem's current age as x years old.
In six years, he will be x + 6 years old. It is stated that in six years, Clem will be five times as old as he was 26 years ago. Since 26 years ago he was x - 26 years old, we can write the equation: x + 6 = 5(x - 26).
To find Clem's age, we will solve the equation:
x + 6 = 5(x - 26)x + 6 = 5x - 1304x = 136x = 34Therefore, Clem Kadiddlehopper is currently 34 years old.
In a right triangle, he measure of one acute angle is 3 times the sum of the other acute angle and 8, Find the measure of angle 1 and 2
The measure of angles 1 and 2 are 16.5 and 73.5 respectively.
The sum of the two acute angles is complementary.
Let the complementary acute angles be x and y
Since they form a right angle triangle, hence;
x + y = 90 ............................. 1
If the measure of one acute angle is 3 times the sum of the other acute angle and 8, this is expressed as x = 3(y + 8)
Substitute the value of x into the equation 1 as shown:
3(y+8) + y = 90
3y + 24 + y = 90
4y + 24 = 90
4y = 90 - 24
4y = 66
y = 66/4
y = 16.5
Get the other acute angle:
x = 90 - y
x = 90 - 16.5
x = 73.5 degrees
Hence the measure of angles 1 and 2 are 16.5 and 73.5 respectively.
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Which unit would you use to measure the amount of water in a swimming pool mL, kg, L or cm
Solve this expression 5(4x-13).
a person leaves their house to go to the store. it takes 15 minutes at 12 mph to get to the store. They return home at 31 mph. What is the average rate of the speed for the entire trip?
Find the solution of the given initial value problem y'+2/ty=cost/t^2