The limit of the expression as x approaches 1 is 5.
Explain limit
A limit is a value that a function or sequence approaches as the input or index approaches a specific value or infinity. It is used to describe the behaviour of a function or sequence as it approaches a certain point or as the input values become infinitely large or small. The limit is an essential concept in calculus and is used to solve problems involving derivatives, integrals, and infinite series.
According to the given information
Here we use algebraic manipulation and direct substitution to find the limit:
lim x→1 [(x² + 1)/(x + 1) + x² + 3]
= lim x→1 [(x² + 1)/(x + 1)] + lim x→1 (x² + 3) (by the limit laws of algebra)
= [(1² + 1)/(1 + 1)] + (1² + 3) (by direct substitution)
= (2/2) + 4
= 1 + 4
= 5
Therefore, the limit of the expression as x approaches 1 is 5.
To know more about limit visit
brainly.com/question/12211820
#SPJ1
The angle measures for 2 supplementary angles are 3x and 2x +40.
What is the value of x?
Answer:
28°
Step-by-step explanation:
If the angles are supplementary, they add up to 180°.
(3x) + (2x + 40) = 180
5x + 40 = 180
- 40 - 40
5x = 140
x = 28°
x=10 3x+5y=20 in the system of equations, what is the value of x
4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
Read more about trasnformation at
https://brainly.com/question/1548871
#SPJ1
Workout 461÷4 give your answer as a whole number and a reminder
Step-by-step explanation:
the answer is 115 remainder 1
On January 1, Year 2, Kincaid Company's Accounts Receivable and the Allowance for Doubtful Accounts carried balances of $74,600 and $3,700, respectively. During Year 2, Kincaid reported $208,000 of credit sales, wrote off $2,000 of receivables as uncollectible, and collected cash from receivables amounting to $258,900. Kincaid estimates that it will be unable to collect one percent (1%) of credit sales.
What effect will recognizing the uncollectible accounts expense for Year 2 have on the elements of the financial statements?
Multiple Choice
Decrease total assets and net income
Decrease total assets and increase retained earnings
Increase total assets and decrease net income
Increase total assets and retained earnings
The correct answer is: Decrease total assets and net income.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.
When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.
Therefore, the correct answer is: Decrease total assets and net income.
To learn more about statistics from the given link:
https://brainly.com/question/28053564
#SPJ1
You have a jar of marbles, each marble is numbered 1-35. 10 Marbles are Blue, 12 Marbles are Green, and 13 Marbles are Red. You draw a random marble.What is the probability that you pull out a marble that is Green or an even number.
The probability of drawing a marble that is green or even-numbered is 28/35
Calculating the probabilityThe total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.
We need to find the probability of drawing a marble that is green or an even number.
First, let's find the number of even-numbered marbles.
Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).
There are 12 green marbles, and 17 even-numbered marbles,
Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.
The probability of drawing a marble that is green or even-numbered is
28/35
So the probability of drawing a marble that is green or even-numbered is 28/35
Read more about probability at
https://brainly.com/question/251701
#SPJ1
Is the graph increasing, decreasing, or constant?
-8 -6 4
A. Decreasing
B. Increasing
C. Constant
-2
4-
2
-2
AY
2
4
6
8
SUBMIT
Is the graph increasing, decreasing, or constant: C. Constant.
What is a graph?In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.
In conclusion, the above is constant, rather than increasing or decreasing.
Read more on a graph here: brainly.com/question/4546414
#SPJ1
Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Know more about the quadratic function in vertex form:
https://brainly.com/question/28201865
#SPJ1
Alex scored 7/20 of the points in a basketball game. How many of the team's 120 points did Alex score?
Answer:
Step-by-step explanation:
I think its 42 because 7/20ths of 120 is 42
7/20 x 120 =42
Solve by using matrices.
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
X
= -66, y = [?], z =
Enter
Solving the system of equations using matrices is : = -66, y = 163, and z = 11.
Solving the system of equations using matrices ?To solve this system of equations using matrices, we can write it in the form AX = B, where:
A = coefficient matrix
X = variable matrix (containing x, y, and z)
B = constant matrix (containing the constants on the right-hand side of each equation)
So, we have:
| 2 -1 3 | | x | | 180 |
| -4 2 3 | x | y | = | 225 |
| 3 -4 0 | | z | | 270 |
We can solve for X by multiplying both sides of the equation by the inverse of A:
X = A^-1 * B
First, we need to find the inverse of A. We can do this by using the formula:
A^-1 = (1 / det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
The cofactor matrix is:
| 2 9 6 |
| 12 0 -2 |
| 13 -9 8 |
Taking the transpose of the cofactor matrix gives us the adjugate of A:
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
So, we have:
A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
Multiplying A^-1 by B gives us:
| x | | -66 |
| y | = | 163 |
| z | | 11 |
Therefore, x = -66, y = 163, and z = 11.
Learn more about matrix here:https://brainly.com/question/94574
#SPJ1
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Construct the confidence interval for the population mean
A 90% confidence interval for µ is (8.92, 9.28).
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
The formula for a confidence interval for the population mean is:
CI = x ± z * (σ / sqrt(n))
where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.
Given the values provided:
c = 0.90
x = 9.1
σ = 0.6
n = 45
First, we need to find the z-score associated with a 90% confidence level. We can use a standard normal distribution table or a calculator to find that z = 1.645.
Then, we can plug in the values and calculate the confidence interval:
CI = 9.1 ± 1.645 * (0.6 / sqrt(45))
= 9.1 ± 0.176
= (8.92, 9.28)
Therefore, a 90% confidence interval for µ is (8.92, 9.28).
To learn more about statistics from the given link:
https://brainly.com/question/28053564
#SPJ1
pls help :)
Angie is really fit and wants to test her endurance by competing in a swimming competition over four days. On the first day, she covers 25 per cent of the distance. On the second day, she covers one third of the remaining distance, on the third day, 25 per cent of the remaining distance and, on the final day, she swims half of the remaining distance. She still has 15km to swim to complete the competition. Form a linear equation and find the total distance of the swimming competition. (Use x as the total distance of the swimming competition).
Answer: Total distance of the swimming competition is 55.56 km.
Step-by-step explanation:
Let x be the total distance of the swimming competition.
On the first day, Angie covered 25% of the total distance, which means she swam 0.25x km.
On the second day, she covered one-third of the remaining distance, which is (1 - 0.25)x = 0.75x km.
So, she swam (1/3) * 0.75x = 0.25x km on the second day.
On the third day, she covered 25% of the remaining distance, which is (1 - 0.25 - 1/3)x = 0.42x km.
So, she swam 0.25 * 0.42x = 0.105x km on the third day.
On the final day, she swam half of the remaining distance,
which is (1 - 0.25 - 1/3 - 0.5)x = 0.125x km.
The total distance she swam is the sum of the distances swum on each day:
0.25x + 0.25x + 0.105x + 0.125x = 0.73x
We know that the total distance of the competition is x - 15 km (since she still has 15 km left to swim).
So we can set up the equation:
0.73x = x - 15
Solving for x, we get:
x-0.73x = 15
0.27x = 15
x = 55.56
Therefore, the total distance of the swimming competition is 55.56 km.
A principal of $1500 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
Which is the largest of the followin fractions? 7/12, 2/3,5/6,3/4, 5/8, (a) 2/3 (b) 3/4 (c) 5/ 5
Answer:
Step-by-step explanation:it is 5/5 because it is a whole number and all the others aren’t
PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
$14,000 was invested at 5% and $49,500 was invested at 9%.
what is system of equations?
A system of equations is a collection of two or more equations that are to be solved simultaneously. In other words, it is a set of equations that must be satisfied by a common set of variables. These equations can be linear or nonlinear, and they can have one or more variables.
The goal of solving a system of equations is to find the values of the variables that satisfy all the equations in the system. This can be done by using various methods, such as substitution, elimination, or matrix methods. The number of equations in a system can be greater than or equal to the number of variables in the system.
Systems of equations are used in various fields such as engineering, physics, economics, and many more. They are also an essential part of algebra and mathematics education, as they provide a powerful tool for solving real-world problems that involve multiple variables and relationships.
Let's assume that x is the amount invested at 5% and y is the amount invested at 9%. We can write two equations based on the given information:
x + y = 63,500 (the total amount invested)
0.05x + 0.09y = 5155 (the total annual income)
We can use these equations to solve for x and y.
First, we can rearrange equation 1 to solve for one of the variables in terms of the other:
x = 63,500 - y
Then, we can substitute this expression for x into equation 2:
0.05(63,500 - y) + 0.09y = 5155
Simplifying this equation:
3175 - 0.05y + 0.09y = 5155
0.04y = 1980
y = 49,500
So we now know that $49,500 was invested at 9%. We can substitute this value into equation 1 to solve for x:
x + 49,500 = 63,500
x = 14,000
Therefore, $14,000 was invested at 5% and $49,500 was invested at 9%.
To learn more about system of equations from the given link
https://brainly.com/question/12895249
#SPJ1
You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each
month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money
toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the
credit card each month and make the payments at the beginning of the month?
Be sure to include in your response:
the answer to the original question
• the mathematical steps for solving the problem demonstrating mathematical reasoning
a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.
Define APR?APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.
a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:
PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)
where:
PV is the present value of the debt
PMT is the payment amount per period
r is the monthly interest rate
n is the number of periods
Substituting the values, we get:
754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV ×r / PMT)) / log(1 + r)
= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)
= 6.18
Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.
b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.
754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV × r / PMT)) / log(1 + r)
= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)
= 3.43
Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.
To know more about APR, visit:
https://brainly.com/question/13597527
#SPJ1
Help me thank you
click the screenshot for more info
Answer: The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?
Step-by-step explanation:
To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.
Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.
The actual difference between the numbers is:
87.71 - 5.8 = 81.91
Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.
Answer:
Yasmine estimated the difference to be 82. The actual difference is 81.91.
Step-by-step explanation:
The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.
So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be
(88 - 6) = 82.
The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.
Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.
Al has a goal to read 2,000 pages over
summer break. He has read 1,248 pages.
How many more pages does Al need to
read to reach his goal?
Al needs to read 752 more pages to reach his goal of 2,000 pages.
What is subtraction?The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign.
To find out how many more pages Al needs to read to reach his goal of 2,000 pages, we can subtract the number of pages he has already read from his goal:
Number of pages Al needs to read = Goal - Pages already read
Number of pages Al needs to read = 2,000 - 1,248
Number of pages Al needs to read = 752
Therefore, Al needs to read 752 more pages to reach his goal of 2,000 pages.
Learn more about subtraction on:
https://brainly.com/question/1927340
#SPJ1
if the pink lines are parallel, solve for n
The option that is true about the equations for these two lines iis that they represent the same lines.
How to explain the informationThe trick to questions like this is to get both equations into the slope-intercept form. That is done for our first equation (y = 3x + 5). However, for the second, some rearranging must be done:
5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5
Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.
Learn more about equations on;
https://brainly.com/question/22688504
#SPJ1
Two lines are described by the equations:
y = 3x + 5 and 5y – 25 = 15x
Which of the following is true about the equations for these two lines?They represent perpendicular lines.
None of the other answers
They represent non-perpendicular, intersecting lines.
They represent the same lines.
They represent parallel lines.
The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
To learn more about the mean and standard deviation visit:
brainly.com/question/475676
#SPJ1
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
Your first job is to figure out the price of your candy selection. You have a goal to sell $250 per week of candy. You can buy a case of assorted candy snacks for $15.50 a case. Write an equation to show how many cases c you can buy.
The equation which shows how many cases c you can buy is $250 = $15.50 * c.
What is an equation?An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation represents a relationship between quantities, and it is often used to describe or model real-world situations or problems.
According to the given information:
Let's denote the number of cases of assorted candy snacks as "c". The price of one case of assorted candy snacks is $15.50. The goal is to sell $250 worth of candy per week.
The total cost of buying "c" cases of assorted candy snacks can be calculated by multiplying the price per case ($15.50) by the number of cases (c):
Total Cost = Price per case * Number of cases = $15.50 * c
The goal is to sell $250 worth of candy per week. So, we can set up an equation to represent this goal:
$250 = $15.50 * c
This equation shows the relationship between the number of cases of candy snacks (c) that you can buy and the total cost of buying those cases, which is equal to $250, your goal for weekly candy sales.
To know more about equation visit: https://brainly.com/question/27996921
#SPJ1
Work out sheet below please
Using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
What is division?The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.
Multiplication, addition, and subtraction make up the remaining operations.
We may examine the quotient and the division's remainder using the division formula Dividend = (Divisor Quotient) + Remainder.
We can multiply our quotient by the divisor to check its accuracy if the remainder is 0.
If the product and dividend are equal, the quotient is correct.
So, the price per gram when pre-packed:
1.49/120 = £0.012
Now, the price per gram when the product is loose:
0.89/100 = £0.0089
Now, we know that per pound the loose sweets are better.
Therefore, using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
Know more about division here:
https://brainly.com/question/25289437
#SPJ1
A theater has 31 rows of seats. The first row has 24 seats, the second row has 27 seats, the third row has 30 seats, and so on. How many seats are in the theater?
I neeeed help
Answer:
2,139 seats
Step-by-step explanation:
the seats increase by 3 every row so I'm going to make a chart to show you how much the seats increase to 31 rows then add all off them to find total.
1 : 24
2: 27
3 : 30
4 : 33
5 : 36
6 : 39
7 : 42
8 : 45
9 : 48
10 : 51
11 : 54
12 : 57
13 : 60
14 : 63
15 : 66
16 : 69
17 : 72
18 : 75
19 : 78
20 : 81
21 : 84
22 : 87
23 : 90
24 : 93
25 : 96
26 : 99
27 : 102
28 : 105
29 : 108
30 : 111
31: 114
You can see from the chart that the number of seats increases by 3 for each row, starting from 24 seats in the first row and ending with 114 seats in the 31st row. To find the total number of seats, you can add up all the numbers in the chart:
24 + 27 + 30 + 33 + ... + 111 + 114
This is an arithmetic series with a first term of 24, a common difference of 3, and 31 terms. You can use the formula for the sum of an arithmetic series to find the total:
Sum = n/2 * (a + l)
where n is the number of terms, a is the first term, and l is the last term.
n = 31, a = 24, and l = 114, so you can substitute these values into the formula and simplify:
Sum = 31/2 * (24 + 114)
Sum = 15.5 * 138
Sum = 2139
Therefore, the theater has a total of 2,139 seats, which agrees with the result obtained earlier.
Answer:
2139 seats
Step-by-step explanation:
24,27,30,.......
n = 31
This forms an arithmetic series. Sum of arithmetic series will give the number of seats in the theater.
a = first term = 24
d = difference = second term - first term
= 27 - 24
= 3
[tex]\sf \boxed{S_n=\dfrac{n}{2}[2a+(n-1)*d]}[/tex]
[tex]=\dfrac{31}{2}[2*24+30*3]\\\\=\dfrac{31}{2}[48+90]\\\\=\dfrac{31}{2}*138\\\\=31*69\\\\=2139[/tex]
Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
Know more about the fraction:
https://brainly.com/question/78672
#SPJ1
Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
Need help will give brainliest and 5 stars! (Check Picture)
Give the equation of a rational function which has all of the properties above.
Answer:
One possible rational function that satisfies the given properties is:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
Step-by-step explanation:
x-intercepts at (2,0) and (6,0)
The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:
r(x) = A(x-2)(x-6)
where A is a constant that we need to determine.
A hole at x=1 and vertical asymptotes at x=5 and x=3
A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
where B is another constant that we need to determine.
We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]
End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1
The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:
A/B = 1, so A = B
Putting it all together
We now have enough information to write the equation for the rational function with the given properties:
r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))
Using A = B, we get:
r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]
Canceling out the common factor of (x-1) in the numerator and denominator, we get:
r(x) = (x-2)(x-6) / [(x-3)(x-5)]
which is the equation for the desired rational function.
Rewrite 5x²+35x using distributive property
Answer:
5x (x + 7)
Step-by-step explanation:
5x² + 35x
First, we find the GCF! In this case, the GCF is 5x
Factor out 5x
5x (x + 7)
So, the answer is 5x (x + 7)
The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² -3,500m + 18,000, where mis
the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
To respond to the question, we must identify the m-values for which V(m) equation decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months),
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
We must identify the values of m for which the function V(m) is dropping in order to estimate the time span during which the value of the card was declining.
The function V(m)'s derivative is provided by:
V'(m) = 500m - 3,500
By setting V'(m) = 0 and solving for m, we may determine the crucial point(s):
500m - 3,500 = 0
m = 7
V''(m) = 500
To respond to the question, we must identify the m-values for which V(m) decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months), as we know that V(m) is falling for m 7.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
The ratio of union members to nonunion members working for a company is 4 to 5. If there are 140 nonunion members working for the company,
what is the total number of employees?
The total number of employees is 112.
Explain numbers
Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.
According to the given information
Let's use x to represent the total number of employees.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.
So, we can set up the following proportion:
4/9 = x/(x - 140)
To solve for x, we can cross-multiply and simplify:
4(x - 140) = 9x
4x - 560 = 9x
560 = 5x
x = 112
Therefore, the total number of employees is 112.
To know more about numbers visit
brainly.com/question/17429689
#SPJ1