Evaluate the limit, or state that the limit does not exist.(6n^2-2n)/(n^2+8)
Answers
Assuming the limit is taken as n approaches infinity, we have
\(\displaystyle\lim_{n\to\infty}\frac{6n^2-2n}{n^2+8}=\lim_{n\to\infty}\frac{6-\frac2n}{1+\frac8{n^2}}=\boxed6\)
because the rational terms in the numerator and denominator will vanish.
Related Questions
A cookie recipe calls for ¾ cups of sugar. The recipe makes 20 cookies. How much sugar is required to make 80 cookies
Answers
Answer:
So based on the given problem above, it says that, for one batch with 3/4 cup of brown sugar can make 6 dozen big cookies. If we are to make 15 dozen cookies, what we need to do is to divide 3/4 cup of brown sugar by 6 dozen, and we get 0.125. This means that per dozen, it is equivalent to 0.125 cup of brown sugar. If we multiply it by 15 dozens, we get 1.875 cup or 1 and 7/8 cup of brown sugar.
Answer:
3 cups of sugar.
Step-by-step explanation:
80/20 = 4 batches
3/4 cups x 4 = 3 cups of sugar
A student created this table to represent a linear relationship between x and y. X. Y-2. 10.0-1. 7.50. 5.01. 2.52. 0Write an equation of the line represented by the relationship between x and y shown in the table.
Answers
The equation of a line can be written using the slope-intercept form given as
\(y=mx+c\)For that equation, we need to find m (rate of change) and c (y-intercept).
To find m, we can use the formula
\(m=\frac{y_2-y_1}{x_2-x_1}\)Let us pick any two points on the graph such that
\(\begin{gathered} (x_1,y_1)\Rightarrow(-2,10.0) \\ \text{and} \\ (x_2,y_2)\Rightarrow(1,2.5) \end{gathered}\)Substituting these into the equation, we have
\(\begin{gathered} m=\frac{2.5-10.0}{1-(-2)} \\ m=-\frac{5}{2} \end{gathered}\)The intercept, c, can be calculated by substituting the rate of change, m, and any point coordinates to the equation of a line.
Let us pick the point
\((x,y)=(0,5.0)\)Substituting, we have
\(\begin{gathered} 5=(-\frac{5}{2}\times0)+c \\ \therefore \\ c=5 \end{gathered}\)Therefore, we have the equation of the line to be
\(y=-\frac{5}{2}x+5\)Multiplying all terms by 2 to clear out the fraction, we get the equation to be
\(2y=-5x+10\)the minimum requirements for a class i aluminum main lightning conductor are ? strand size, 95 pounds/1,000 feet weight per length, and a cross-sectional area of 98,600 circular mils.
Answers
The minimum requirements for a class i aluminum main lightning conductor are a strand size, 95 pounds/1,000 feet weight per length, and a cross-sectional area of 98,600 circular mils.
These requirements are set by industry standards and regulations to ensure the safety and effectiveness of the lightning protection system. The strand size refers to the diameter of the individual wires that make up the conductor, which must meet a minimum size to withstand the forces of a lightning strike. The weight per length is a measure of the conductor's strength and durability, with a higher weight indicating a more robust design. Finally, the cross-sectional area is the total area of the conductor's circular shape, which impacts its ability to conduct electrical current and dissipate the energy from a lightning strike.
Overall, meeting these minimum requirements is essential for ensuring that a lightning protection system is capable of effectively capturing and directing the energy from a lightning strike to the ground, protecting the building and its occupants from potential harm.
To know more about conductor visit :-
https://brainly.com/question/14405035
#SPJ11
i thought of a number. four times the number increased by 30 equals 70 decreased by the number. what was my number?
Answers
Answer:
number is 8
Step-by-step explanation:
let n be the number then 4 times the number is 4n and increased by 30 means adding 30 to it , that is 4n + 30
70 decreased by the number means subtracting n fro 70 , 70 - n
then
4n + 30 = 70 - n ( add n to both sides )
5n + 30 = 70 ( subtract 30 from both sides )
5n = 40 ( divide both sides by 5 )
n = 8
what is the value of r of the geometric series?
Answers
Value of r is different for every series
let
a , b , c , d ..... be geometric series then
r = b/a or d/c and so on
where r is common ratio
Grace wants to buy a jump rope that costs $7, a board game that costs $10, and a playground ball that costs $4. She has saved $10 from her allowance, and her uncle gave her $3. How much more money does Grace need to buy the jump rope, the game, and the ball?
Answers
Grace need to buy the jump rope, the game, and the ball $8.
$7 will get you a jump rope.
$10 will get you a board game.
$4 will get you a playground ball.
total amount to be spent: $7 + $10 + $4 = $21
She has ten dollars.
$3 was all her uncle gave her.
13 dollars are all she has.
She needed $8, therefore 21 - 13 = $8.
a sum of money awarded as compensation, a bounty, or to cover costs. a wage that comes with a cost-of-living supplement. especially: a regular amount set aside for household or personal costs.
To know more about cost-of-living, click the below link
https://brainly.com/question/22665912
#SPJ4
xercise 4(1) Christopher takes (x1, x2) to be at least as good as (y1, y2) if and only if x1 ≥ y1and x2 ≥ y2. Show which condition his preferences violate.(2) Explain how it would be possible to cheat someone who had intransitive pref- erences. Be explicit about what you would offer him, and what he would do in response.(3) A household formed by Mom (M), Dad (D), and Child (C) is deciding what to do on Friday evening. The alternatives are attending an opera (O), a rock concert (R), or an ice-skating show (I). The three members of the household have individual preferences: O≻M R≻M I,I≻D O≻D R,R≻C I≻C O. Thehouseholdmakes decisions by majority voting: An option is chosen if and only if at least two people vote for it. Show which condition the majority rule violates
Answers
1. Christopher's preferences violate the transitivity condition.
2. One way to cheat someone who has intransitive preferences is to offer them a series of choices that are designed to lead them to make inconsistent choices.
3. The majority rule violates the Pareto efficiency condition.
1.
According to the principle of transitivity, if A is chosen over B and B over C, then A must also be preferred over C. Yet, it is feasible to identify three options—x, y, and z—in Christopher's preferences such that x is preferred to y, y is preferred to z, but z is preferred to x. Christopher could prefer x to y, y to z, but z to x if, for instance, x represents a huge quantity of food, y represents a smaller quantity of tastier food, and z represents an even smaller quantity of even sweeter food.2.
As an illustration, consider the case when someone has intransitive preferences among three possibilities, A, B, and C, So that A B C A. If you gave them the option between A and B, they may pick A. If you gave them the option between B and C, they may pick B. When given the option to select between C and A, they could pick C. As a result, you may have tricked them into making decisions that are inconsistent.3.
According to Pareto efficiency, a group should select the choice that everyone in the group prefers over the other options. A choice that is desired by every household member but is not selected by the majority rule can be found in the preferences of the household. For instance, even though everyone in the house agrees that the opera is preferable than both the rock concert and the ice skating event, if everyone only votes once, the rock concert wins since it obtains two votes. Due to the lack of selection of the group's favourite alternative, this breaks the Pareto efficiency criterion.For more questions on Pareto efficiency criterion
https://brainly.com/question/29990566
#SPJ4
If a SOC has a goal of 99.99% uptime, how many minutes of downtime a year would be considered within its goal
Answers
To achieve a goal of 99.99% uptime, the SOC would allow approximately 52.56 minutes of downtime per year.
To calculate the number of minutes of downtime allowed within a goal of 99.99% uptime, we first need to determine the allowable downtime percentage.
Uptime percentage can be calculated as follows:
Uptime percentage = 100% - Downtime percentage
For a goal of 99.99% uptime, the downtime percentage would be:
Downtime percentage = 100% - 99.99% = 0.01%
To calculate the number of minutes of downtime, we need to convert the downtime percentage to minutes in a year:
Minutes of downtime = (Downtime percentage / 100) × Minutes in a year
Assuming there are 365 days in a year and 24 hours in a day (ignoring leap years), the number of minutes in a year would be:
Minutes in a year = 365 × 24 × 60 = 525,600 minutes
Now we can calculate the allowable minutes of downtime:
Minutes of downtime = (0.01% / 100) × 525,600 minutes
Minutes of downtime ≈ 0.0001 × 525,600 ≈ 52.56 minutes
Therefore, to achieve a goal of 99.99% uptime, the SOC would allow approximately 52.56 minutes of downtime per year.
Learn more about percentage here:
https://brainly.com/question/14319057
#SPJ11
Find the value of x.
Answers
Answer:
x = -7
Step-by-step explanation:
Make an equation:
3x + 33 = 12
3x = -21
x = -7
Answer:
x = -7
Step-by-step explanation:
form an equation.
14 + x + 2x + 19 = 12
like terms together;
x + 2x = 12 - 14 - 19
simplify;
3x = -21
divide both sides by 3;
x = -7
After listing her expenses and income, sara realizes that her actual expenses exceed her actual income. what can sara do to eliminate the negative difference between her expenses and income? use complete sentences in your response
Answers
She has to work more harder or she needs to cut her expenses are the only two choices for her.
Define expense.The price one must pay to acquire anything is referred to as an expense.
Difference between cost and expense.An expense is a recurring expense, such as the salary of an employee or the rent for a retail location, whereas a cost normally refers to the amount paid to purchase an item.
She has two options: she either work harder to earn more money or she may spend less money. Increasing the value being added (income) or decreasing the value being subtracted (expenses) will make the difference less negative/positive because income - expense is negative.
To learn more about expense visit the link:
https://brainly.com/question/25530648
#SPJ4
Which segment represents a radius of the circle below?
Answers
Answer: Choose A my smart self just knew
The average water consumption per day is 48 ounces with a standard deviation of 12.8 ounces.
5. P(x ≤ 12 ounces)
6. P(x > 64 ounces)
7. P(24 ounces < x ≤ 36 ounces)
8. P(x > 90 ounces)
9. Find the z-score that corresponds with:
a) 82.12% b) 28.43%
10. If salaries of teachers In the United States are normally distributed with a mean of $42,000 and a standard deviation of $5500,
a) What is the highest salary for those teachers in the bottom 20%?
b) What is the range of salarles of 68% of the teachers according to the Empirical Rule?
c) The teachers in the top 5% are making at least what salary amount?
Answers
5. P(x ≤ 12 ounces) is approximately 0.0025.
6. P(x > 64 ounces) is approximately 0.1056.
7. P(24 ounces < x ≤ 36 ounces) is approximately 0.1432.
8. P(x > 90 ounces) is approximately 0.0006.
9. The cumulative probability for a z-score of 3.28125 is approximately 0.9994.
a) The z-score corresponding to a cumulative probability of 0.1788, which is approximately 0.92.
b) The z-score corresponding to a cumulative probability of 0.95 is approximately 1.645.
c) The teachers in the top 5% are making at least $51,972.50 in salary
5. P(x ≤ 12 ounces):
To find this probability, we need to calculate the z-score corresponding to 12 ounces and then find the cumulative probability up to that z-score.
Z-score = (x - μ) / σ
where x is the value (12 ounces), μ is the mean (48 ounces), and σ is the standard deviation (12.8 ounces).
Z-score = (12 - 48) / 12.8 = -2.8125
Using a standard normal distribution table or a calculator, we can find that the cumulative probability for a z-score of -2.8125 is approximately 0.0025.
Therefore, P(x ≤ 12 ounces) is approximately 0.0025.
6. P(x > 64 ounces):
Similarly, we calculate the z-score corresponding to 64 ounces and find the cumulative probability beyond that z-score.
Z-score = (x - μ) / σ
Z-score = (64 - 48) / 12.8 = 1.25
Using a standard normal distribution table or a calculator, we can find that the cumulative probability for a z-score of 1.25 is approximately 0.8944.
Since we want the probability of x being greater than 64 ounces, we subtract the cumulative probability from 1:
P(x > 64 ounces) ≈ 1 - 0.8944 = 0.1056.
7. P(24 ounces < x ≤ 36 ounces):
We need to calculate the z-scores corresponding to 24 ounces and 36 ounces and find the difference in cumulative probabilities between those z-scores.
Z-score for 24 ounces = (24 - 48) / 12.8 = -1.875
Z-score for 36 ounces = (36 - 48) / 12.8 = -0.9375
Using a standard normal distribution table or a calculator, we can find the cumulative probabilities for these z-scores:
P(Z ≤ -1.875) ≈ 0.0304
P(Z ≤ -0.9375) ≈ 0.1736
To find P(24 ounces < x ≤ 36 ounces), we subtract the cumulative probability for 24 ounces from the cumulative probability for 36 ounces:
P(24 ounces < x ≤ 36 ounces) ≈ 0.1736 - 0.0304 = 0.1432.
8. P(x > 90 ounces):
We calculate the z-score corresponding to 90 ounces and find the cumulative probability beyond that z-score.
Z-score = (x - μ) / σ
Z-score = (90 - 48) / 12.8 = 3.28125
Using a standard normal distribution table or a calculator, we can find that the cumulative probability for a z-score of 3.28125 is approximately 0.9994.
Since we want the probability of x being greater than 90 ounces, we subtract the cumulative probability from 1:
P(x > 90 ounces) ≈ 1 - 0.9994 = 0.0006.
Find the z-score that corresponds with:
a) 82.12%:
To find the z-score corresponding to 82.12%, we subtract the cumulative probability from 1 (since we need the z-score on the right side of the distribution curve).
P(Z ≤ z) = 1 - 0.8212 = 0.1788
Using a standard normal distribution table or a calculator, we can find the z-score corresponding to a cumulative probability of 0.1788, which is approximately 0.92.
b) The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
In this case, the mean salary is $42,000 and the standard deviation is $5,500.
To find the range of salaries for 68% of the teachers, we can calculate the lower and upper limits.
Lower limit: Mean - 1 standard deviation
Lower limit = $42,000 - $5,500 = $36,500
Upper limit: Mean + 1 standard deviation
Upper limit = $42,000 + $5,500 = $47,500
Therefore, the range of salaries for 68% of the teachers according to the Empirical Rule is $36,500 to $47,500.
c) The top 5% of salaries corresponds to the area under the curve that lies beyond approximately two standard deviations above the mean.
To find the salary amount for the top 5%, we can calculate the z-score corresponding to a cumulative probability of 0.95 (1 - 0.05).
P(Z ≤ z) = 0.95
Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to a cumulative probability of 0.95 is approximately 1.645.
Now we can calculate the salary amount:
Salary amount = Mean + (z-score × standard deviation)
Salary amount = $42,000 + (1.645 × $5,500) = $51,972.50
Therefore, the teachers in the top 5% are making at least $51,972.50 in salary
for such more question on probability
https://brainly.com/question/13604758
#SPJ11
The circumstances of the base of the cone is 6π cm. If the volume of the cone is 12π. what is the height?
Answers
Answer: 4
Step-by-step explanation:
\(\frac{1}{3} \pi 3^{2} h=12\pi \\3h=12\\h=4\)
Add. = -6+ (-2) = 3+ (-6) =
Answers
Answer:
its a false equation they arent equal to each other srry
Step-by-step explanation:
Answer:
ans is -5 is the currect ans
Which phrase represents this expression?
35÷(12−5)
Select each correct answer.
(1) 5 less than the quotient of 35 and 12
(2) 35 divided by the difference of 12 and 5
(3) the quotient of 35 and the difference of 12 and 5
(4) the total of 35 and 12 is subtracted by 5
Answers
Answer:
answer 2(35 divided by the difference of 12 and 5
Answer:
2 and3
Step-by-step explanation:
Describe the likelihood of the situation. Use likely, unlikely, neither likely nor unlikely, certain, or impossible.
The next baby born at a hospital is a girl.
What best describes thelikelihood of the statement?
Please hurry
Giving BRAINLYest
Answers
It cannot be predicted, theres a 50/50 chance.
Please Help me - You will get 60 points for the rapid reply- Use isosceles trapezoid ABCD to determine the following measurements-
Answers
Answer:
1) AD = 9 in
2) DE = 9.25 in
3) ∠EDC = 36°
4) ∠AEB = 108°
5) 11.5 in
Step-by-step explanation:
1) AD = BC = 9in
2) AC = BD (diagonals are equal)
⇒ BD = 14.25
⇒ BE + DE = 14.25
⇒ 5 + DE = 14.25
DE = 9.25
3) Since AB ║CD,
∠ABE = ∠EDC = 36°
4) ∠ABE = ∠BAE = 36°
Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)
⇒ 36 + 36 + ∠AEB = 180
∠AEB = 108
5) midsegment = (AB + CD)/2
= (8 + 15)/2
11.5
Explain how to find the value of the digit 7 in the number 3,684,591.74.
Answers
Step-by-step explanation:
every position in a number stands for a different power of 10, which is then multiplied by the digit in that position.
and the value of the whole number is the sum of these little individual calculations.
left of the decimal point we start with 10⁰ = 1 as basic value.
then the second position left of the decimal point stands for 10¹ = 10.
the third position left of the decimal point stands for 10² = 100.
and so on.
now, right of the decimal point we go in the other direction. the first position right of the decimal point stands for 10^-1 = 1/10.
the second position stands for 10^-2 = 1/100.
and so on.
so, the 7 in this number has the value of 7/10 or 7 tenths.
the given number would be fully written
3×10⁶ + 6×10⁵ + 8×10⁴ + 4×10³ + 5×10² + 9×10¹ + 1×10⁰ + 7×10^-1 + 4×10^-2
the decimal point tells us for a number where to begin counting with 10⁰ and 10^-1.
PLEASE HELP WILL MARK BRAINLIESTTTT
Answers
Answer:
470 \(cm^{3}\)
Step-by-step explanation:
8x9x10 = 720
5x5x10 = 250
720-420 = 470
Nine less then a number is four
Answers
Answer: 13 (simplified)
Step-by-step explanation: 9 + 4= 13, minus 9 equals 4
Answer: Question: x-9=4
Step-by-step explanation: X is 13
John has a 20 oz. water bottle. He drinks 8 ounces. What is the percentage of ounces he has left of his water?
Answers
Answer: 60%
Step-by-step explanation:
There are 20 ounces of water in John's water bottle, and 20-8=12 after consumption. Since we want to find the percentages of ounces, we can divide 12 by 20, which can be represented by the fraction 12/20. Simplify, we get 6/10 which is equal to 60%.
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of x. V = cm^3 (b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.) = ? (c) Find the length L , width W, and height H of the resulting box that maximizes the volume. (Assume that W < or = to L ) L= ?cm W= ?cm H= ? cm (d) The maximum volume of the box is ? cm^3.
Answers
(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x
(b) The domain of V in interval notation is 0<x<5,
(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773
(d) The maximum volume of the box is 192.421 cm^2.
In the given question,
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.
(a) We have to express the volume V of the box as a function of x.
If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.
So V = x(10-2x) (20-2x)
V = x(10(20-2x)-2x(20-2x))
V = x(200-20x-40x+4x^2)
V = x ( 200 - 60 x + 4x^2)
V = 4x^3-60x^2+200x
(b) Now we have to give the domain of V in interval notation.
Since the lengths must all be positive,
10-2x > 0 ≥ x < 5 and x> 0
So 0 < x < 5
(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.
We take the derivative of V:
V'(x) = 12x^2-120x+200
Taking V'(x)=0
0 = 4 (3x^2-30x+50)
3x^2-30x+50=0
Now using the quadratic formula:
x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
From the equationl a=3, b=-30, c=50
Putting the value
x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)
x= \(\frac{30\pm\sqrt{900-600}}{6}\)
x= \(\frac{30\pm\sqrt{300}}{6}\)
x= \(\frac{30\pm17.321}{6}\)
Since x<5,
So x= \(\frac{30-17.321}{6}\)
x= 2.113
So H = 2.113, W = 5.773, L= 15.773.
d) Now we have to find the maximum volume of the box.
V = HWL
V= 2.113*5.773*15.773
V = 192.421 cm^3
To learn more about volume of rectangle link is here
brainly.com/question/13798973
#SPJ4
Think of a matrix A and B which are both 3X3 matrices. Do not use all zeros or all
1’s!
3. Multiply A X B and record the result.
4. Multiply B X A and record the result
Answers
Answer:
9
Step-by-step explanation:
3x3 =9 hope this helps bbs
3x-1=2(x+34) in inches=feet. inches
Answers
Answer:
-69
Step-by-step explanation:
inches:-69
-5 9/12 (-5 3/4 clearer) feet
Explanation in detail:
Write the equation down and distribute it.
3x - 1 = 2(x + 34)
3x - 1 = 2x + 68
Remove the variable on one side first (it makes solving the equation less complicated.)
3x - 1 = 2x + 68
-3x -3x
-1 = -x + 68
On all sides, subtract 68.
-1 = -x + 68
-68 -68
-69 = x
I'm guessing the answer in feet and inches is...
inches:-69
-5 9/12 (-5 3/4 simplified) feet
Committee: The Student Council at a certain school has nine members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer. Part 1 of 4 In how many ways can these four positions be filled? There are 3024 ways to fill the four positions. Part: 1/4 = Part 2 of 4 In how many ways an four people be chosen for the executive committee if it does not matter who gets which position? There are ways to choose four people for the executive committee if it does not matter who gets which position
Answers
Part 1: The four positions in the executive committee can be filled in 3024 ways. Part 2: If it does not matter who gets which position, there are several ways to choose four people for the executive committee.
Part 1:
To determine the number of ways to fill the four positions in the executive committee, we need to consider that each position can be filled by a different member from the nine-member Student Council. We can use the concept of permutations to calculate this.
The first position can be filled by any of the nine members. Once the first position is filled, there are eight remaining members to choose from for the second position. Similarly, there are seven members left for the third position and six members for the fourth position.
Therefore, the total number of ways to fill the four positions is calculated as:
9 * 8 * 7 * 6 = 3024 ways.
Part 2:
If it does not matter who gets which position, we are essentially choosing a group of four members from the nine-member Student Council. In this case, we can use the concept of combinations.
The number of ways to choose four people from a group of nine can be calculated using the combination formula:
C(9, 4) = 9! / (4! * (9-4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126 ways.
Therefore, if it does not matter who gets which position, there are 126 ways to choose four people for the executive committee.
To know more about concept of permutations, click here: brainly.com/question/1216161
#SPJ11
WILL GIVE BRAINLYNESS
Suppose a publishing company estimates that its monthly cost is
C(x) = 600x2 + 300x and its monthly revenue is
R(x) = -0.4x3 + 700x2 – 600x + 500, where x is in thousands of
books sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?
Answers
Answer:
P(x) = -0.4\(x^{3}\) + 100\(x^{2}\) - 300\(x\) + 500
Step-by-step explanation:
C(x) = 600\(x^{2}\) + 300\(x\)
R(x) = -0.4\(x^{3}\) + 700\(x^{2}\) - 600\(x\) + 500
P(x) = R(x) - C(x)
(-0.4\(x^{3}\) + 700\(x^{2}\) - 600\(x\) + 500) - (600\(x^{2}\) + 300\(x\))
= -0.4\(x^{3}\) + 100\(x^{2}\) - 300\(x\) + 500
This should be the answer.
Answer:
p(x)= -0.4x³+100x²-900x+500
HELPPPP FASTER MARK BRAINLIEST IF CORRECT
A college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students. Let x = the number of out-of-state students and y = the number in-state students. Write the constraints to represent the incoming students at the college.
x > 0 and y > 0
0 < x ≤ 100 and 0 < y ≤ 400
0 < x ≤ 100 and y > 400
0 < x and y < 100
Answers
The constraints to represent the incoming students at the college is B. 0 < x ≤ 100 and 0 < y ≤ 400
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this situation, the college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students.
Let x = the number of out-of-state students and
y = the number in-state students.
The constraints is 0 < x ≤ 100 and 0 < y ≤ 400.The correct option is B.
Learn more about inequalities on:
brainly.com/question/25275758
#SPJ1
Determine the period
Answers
Answer:
10
Step-by-step explanation:
acellus
The period of the given graph is 10.
Use the concept of a period of function defined as:
One full wave is set up in a medium for the length of time it takes a particle of that medium to complete one vibration or one wave period.
In the given wave,
X-axis represents time
The Y- axis represents the amplitude of the curve
As we can see,
The first peak of this graph is located at x = 1 and the second peak is at,
x = 13
Since the period is the time interval between two consecutive peaks in a graph.
In this case, the time interval is 10.
Hence,
The period of the given graph is 10.
To learn more about period of a graph visit:
https://brainly.com/question/12682398
#SPJ4
What is the slope of the line through the points (-8, 4) and (4,4)?
Answers
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-4)/(4-(-8))
m=0/(4+8)
m=0/12
m=0
You want to find out the height of a tree so you hold a Squarecard board so the edges lineup with the top and bottom of the tree Ash in the diagram but your friend measures the horizontal distance from you to the tree and vertical distance from the ground to your eye what is the high of the tree to the nearest 10th of a foot don’t put units in your answer
Answers
The height of the tree is equal to the vertical distance from the ground to the observer's eye. To the nearest 10th of a foot, the answer is simply the given vertical distance, which is "Ash" in the diagram.
To find the height of the tree, we can use the principle of similar triangles.
Let's call the height of the tree "h", the distance from the observer to the tree "d", and the distance from the ground to the observer's eye "y".
So, we have: h/d = h/1 (since the cardboard is at a distance of 1 from the observer)
Simplifying, we get: h = d x h
Now, let's consider the right triangle formed by the observer, the tree, and the ground. The vertical distance from the ground to the observer's eye is "y", and the horizontal distance from the observer to the tree is "d". The angle formed by the observer's line of sight and the ground is the same as the angle formed by the top edge of the cardboard and the observer's line of sight. Let's call this angle "θ".
Using trigonometry, we can find the height of the tree:
tan(θ) = h/d
h = d x tan(θ)
But we don't know θ directly, so we need to use the vertical distance from the ground to the observer's eye, which we do know. We can find θ using the tangent function again:
tan(θ) = y/d
So, putting it all together, we get:
h = d x tan(arctan(y/d))
h = d x (y/d)
h = y
Therefore, the height of the tree is equal to the vertical distance from the ground to the observer's eye. To the nearest 10th of a foot, the answer is simply the given vertical distance, which is "Ash" in the diagram.
Learn more about right triangle
brainly.com/question/6322314
#SPJ11