Mathematics is a field that involves primarily abstract reasoning and mental calculations, but there are still several types of equipment that mathematicians may use to aid in their work.
What are different equipments use in mathematics?
1.) Calculator: A calculator is an electronic device that performs arithmetic operations quickly and accurately. It is often used by mathematicians to check their calculations, solve equations, and perform more complex calculations.
2.) Protractor: A protractor is a tool used to measure and draw angles. It is commonly used in geometry and trigonometry to draw and measure angles of various shapes.
3.) Compass: A compass is a tool used to draw circles and arcs. It is commonly used in geometry to draw circles, bisect angles, and construct various geometric shapes.
4.) Ruler: A ruler is a straightedge tool used to measure lengths and draw straight lines. It is commonly used in geometry and algebra to draw graphs, construct figures, and measure distances.
5.) Graph paper: Graph paper is a type of paper that has a grid of small squares printed on it. It is often used in algebra and geometry to draw graphs, plot data, and make calculations.
The question doesn't contain any table and is incomplete, below is the complete question -
Fill in the table with equipment measurements.
Equipment Code: The required field for the primary key.
Standard for equipment: The kind of equipment. confirmed by the listing of equipment standards.
Use of Equipment: Describe how the piece of equipment is used in this field.
categorization: Select a categorization for this piece of equipment using the field provided. The Condition Assessment programme organises and categorises your data using this classification.
Equipment state: To characterise the equipment's condition, select one of the values from the list box: new, good, fair, or poor.
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If x is so small that its fourth and higher powers may be neglected show that ∜((1+x) )+∜((1-x) )=a-bx^2 and find the numbers a and b.Hence by putting x=1/16 show that the sum of the fourth roots of 17 and of 15 is 3⋅9985 approximately
Using binomial expansion, the sum of the fourth roots of 17 and 15 is approximately 3.9985.
We are given that x is so small that its fourth and higher powers may be neglected. Therefore, we can use the binomial expansion to approximate the fourth roots of (1+x) and (1-x) as follows:
∜((1+x)) ≈ 1 + (1/4)x - (1/32)x² + O(x³)
∜((1-x)) ≈ 1 - (1/4)x - (1/32)x² + O(x³)
where O(x³) represents the neglected terms of x³ and higher powers.
Adding these approximations, we get:
∜((1+x)) + ∜((1-x)) ≈ 2 + (1/16)(-2x²) + O(x³)
Simplifying:
∜((1+x)) + ∜((1-x)) ≈ 2 - (1/8)x²
Comparing this with the given equation a - bx², we see that a = 2 and b = 1/8.
Now, we can substitute x=1/16 into the approximate expression we obtained for the sum of the fourth roots:
∜((1+(1/16))) + ∜((1-(1/16))) ≈ 2 - (1/8)(1/16)²
Simplifying:
∜(17/16) + ∜(15/16) ≈ 3.9985
Therefore, the sum of the fourth roots of 17 and 15 is approximately 3.9985.
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Choose the list that shows the investment with the least risk to the one with the highest risk.
A. Mutual Funds, Savings Bonds, Stock Market
B. Savings Bonds, Mutual Funds, Stock Market
C. Savings Bonds, Stock Market, Mutual Funds
D. Stock Market, Mutual Funds, Savings Bonds
The best choice is B. Saving Bonds, Stock Market, Mutual
Why do you use the word "investment"?Investments are defined as assets bought or invested in with the goal of increasing wealth and setting aside funds from salary or capital gains. The main goal of an investment is to generate extra income or to make money on an investment over a certain amount of time.
Generally speaking, the following is the order of investments from the lowest risk to the greatest risk:
Bonds for savings, mutual funds, and the stock market
As a result, list B is the one that runs from investment with the lowest risk to investment with the greatest risk. Stock market, mutual funds, and savings bonds.
The sequence of mutual fund investments, Savings Bonds, and Stock Market in Option A is not in decreasing order of danger.
Savings Bonds, the stock market, and mutual funds are listed in Option C's order, and this is also not from lowest to greatest risk.
Stock markets, mutual funds, and savings bonds are listed in Option D's order of greatest to lowest risk.
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Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices. If Ahmed likes chocolate four times as much as vanilla, what is the dollar value that Ahmed places on a chocolate slice?
Ahmed placed a chocolate slice is $1.75.
What is arithmetic?Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: Ahmed and Tiana buy a cake for $14 that is half chocolate and half vanilla. They cut the cake into 8 slices.
Denoting the value of the slice of chocolate as C and V as the vanilla slice then
4 slices × C + 4 slices *V = $14
if Ahmed likes 4 times more the chocolate than the vanilla slice, then he finds C four times more valuable than V, thus
C = 4*V
4 slices × 4V + 4 slices ×V = $24
20 slices × P = $14
P = $0.7/slice
V = 4 × P = 4 × $0.7/slice = $2.8/slice
for a slice that is half chocolate and half vanilla
value= 1/2 slice × C + 1/2 slice × V = 1/2 slice ($0.7 /slice + $2.8/slice) = $1.75
Hence, Ahmed placed a chocolate slice is $1.75.
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Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.
a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree?
b. What is the probability that exactly seven of the college graduates plan to pursue a graduate degree?
c. What is the probability that at least six but no more than nine of the college graduates plan to pursue a graduate degree?
For A (15) (0.4) (0.6) (15-i) For B. Consequently, there is a 0.196 percent chance For C. As a result, there is a roughly 0.382 percent chance
Binomial distribution: what is it?The number of successes in a certain number of independent trials with the same chance of success are described by the binomial distribution, which is a probability distribution. The two parameters n and p define the binomial distribution. The parameters n and p represent the number of trials and the probability of success in each trial, respectively.
Let's say that 40 percent of recent college grads want to earn a graduate degree. We choose fifteen recent college grads at random.
a. Using the binomial distribution formula, we can determine the likelihood that no more than four of the college grads intend to pursue a graduate degree:
P(X ≤ 4) = Σ(i=0 to 4) Choose (15) (0.4) (0.6) (15-i)
where X represents the proportion of recent college graduates who intend to pursue a graduate degree. We can determine that using a calculator or software that:
P(X ≤ 4) ≈ 0.0001
As a result, there is a roughly 0.0001 chance that no more than four of the college graduates will go on to get a graduate degree.
b. We can once more use the data to determine the likelihood that precisely seven of the college grads intend to pursue a graduate degree.
use the formula for the binomial distribution:
P(X = 7) = (15 choose 7) (15 choose 7) (0.4)⁷ (0.6⁸
We can determine that using a calculator or software that:
P(X = 7) ≈ 0.196
C . The cumulative binomial distribution function can be used to calculate the likelihood that at least six but no more than nine of the college graduates intend to pursue a graduate degree:
P(6 X 9) = (i=6 to 9) (15 choose I (0.4)i (0.6) (15-i)
We can determine that using a calculator or software that:
P(6 ≤ X ≤ 9) ≈ 0.382
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On your graph paper, plot points A(-5, -2), B(-3, -2), and D(-5, -4). Mark point C to make a square in the third quadrant. Name the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3).
After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).
Define graphs?Simply said, the graph is a structured representation of the data. Because of this, it is simpler for us to understand the facts. Data is the term used to describe the numerical information obtained through observation.
The word data is derived from the Latin word datum, which meaning "something delivered."
After developing a research question, data are progressively obtained through observation. The information is then organised, categorised, and visually shown.
Here in the question,
After plotting the points A (-5, -2), B (-3, -2), and D (-5, -4) in the 4th quadrant as shown in the attached graph, we can see that to make the square we have to plot point C, at (-3, -4).
And the coordinate rule that will rotate the rectangle to the fourth quadrant, with vertex C’ at point (4, -3) is known as reflection.
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The graph represents a function.
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a
function?
O(-5,2) O (-2,5) O (2, -1) (2,-5)
Answer:
b
Step-by-step explanation:
Ron and Jim are making sandwiches for a party. Ron make 2 times as many sandwiches as Jim. Together they make a total of 42 sandwiches.
14 because 14+28=42.
A study found that the mean migration distance of the green turtle was 2200 kilometers and the standard deviation was 625 kilometers. Assuming that the distances are normally distributed, find the probability that a randomly selected green turtle migrates a distance of
(a) less than 1900 kilometers.
(b) between 2000 kilometers and 2500 kilometers.
(c) greater than 2450 kilometers.
a. the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers is approximately 0.3156 or 31.56%.
b. the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers is approximately 0.3556 or 35.56%.
c. the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers is approximately 0.3446 or 34.46%.
India uses kilometres because?As the decimal system uses kilometres as the unit of measurement, distance is expressed in kilometres instead of miles. Using a unit with decimals improves accuracy and convenience. Miles are not decimal system units.
Which nation doesn't utilise kilometres?Just three nations—the United States, Liberia, and Myanmar—continue to use the imperial measurements, which relies on measurements of length, weight, height, or area that ultimately refer to human parts or commonplace objects.
We can use the standard normal distribution to solve this problem, by transforming the distances into z-scores using the formula:
z = (x - μ) / σ
Where:
x is the distance we want to find the probability forμ is the mean migration distanceσ is the standard deviation(a) To find the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers, we need to find the z-score for 1900 using the formula:
z = (1900 - 2200) / 625 = -0.48
We can then use a standard normal table or calculator to find the probability corresponding to this z-score, which is approximately 0.3156.
Therefore, the probability that a randomly selected green turtle migrates a distance of less than 1900 kilometers is approximately 0.3156 or 31.56%.
(b) To find the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers, we need to find the z-scores for both distances:
z₁ = (2000 - 2200) / 625 = -0.32
z₂ = (2500 - 2200) / 625 = 0.48
We can then use a standard normal table or calculator to find the probability corresponding to each z-score and subtract them to find the probability in between, which is approximately 0.3556.
Therefore, the probability that a randomly selected green turtle migrates a distance between 2000 kilometers and 2500 kilometers is approximately 0.3556 or 35.56%.
(c) To find the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers, we need to find the z-score for 2450 using the formula:
z = (2450 - 2200) / 625 = 0.4
We can then use a standard normal table or calculator to find the probability corresponding to this z-score and subtract it from 1 to find the probability of a distance greater than 2450, which is approximately 0.3446.
Therefore, the probability that a randomly selected green turtle migrates a distance greater than 2450 kilometers is approximately 0.3446 or 34.46%.
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In Exploration 5.3.2 Question 3, you found multiple average rates of change with different intervals and discussed in Question 6, the limiting value that your average rates are approaching. In Question 7, what was the significance of the numerical sign of the limiting value you found in 6?
The numerical sign of the limiting value is significant because it indicates the general direction of the function's behavior (increasing or decreasing) within the given interval,
Hi there! In Exploration 5.3.2, Question 3 required finding multiple average rates of change for different intervals, and in Question 6, you discussed the limiting value that those average rates are approaching. The significance of the numerical sign of the limiting value found in Question 6, addressed in Question 7, is as follows:
The sign of the limiting value (positive or negative) indicates the general direction of the function's behavior during the given interval. A positive limiting value means that the function is generally increasing, while a negative limiting value suggests that the function is generally decreasing.
Understanding the sign of the limiting value is essential as it provides insight into the overall trend of the function in the specified range. This information can be useful in various applications, including predicting future behavior and identifying potential maximum or minimum points of the function.
In summary, providing valuable information about the function's characteristics and trends.
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Determine the point estimate of the population mean and the margin of error for the given confidence interval. Lower bound: 12 Upper bound: 20
Determine the point estimate of the population mean and the margin of error for the given confidence interval. Lower bound: 12 Upper bound: 20To determine the point estimate of the population mean, we simply take the average of the lower and upper bounds of the confidence interval: Point estimate = (Lower bound + Upper bound) / 2 = (12 + 20) / 2 = 16 Therefore, the point estimate of the population mean is 16. To calculate the margin of error, we need to determine the distance between the point estimate and either the lower or upper bound of the confidence interval. We can do this by subtracting the point estimate from the upper bound (or vice versa): Margin of error = (Upper bound - Point estimate) / 2 = (20 - 16) / 2 = 2 Therefore, the margin of error for this confidence interval is 2.
Answer: its 16 I think
Step-by-step explanation:
I’m stuck I need you to do it
Answer: The length of the prism is 8 yards
Step-by-step explanation:
First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)
How many solutions does this equation have?
-12g + 9 = 2q - 6-15q
no solution
one solution
or
infinitely many solutions
Answer:
One solution---------------------------
Given equation:
- 12q + 9 = 2q - 6 - 15qSolve it in below steps:
- 12q + 9 = 2q - 6 - 15q-12q + 9 = - 13q - 613q - 12q = - 6 - 9q = - 15This equation has one solution.
convert to slope intercept (y=mx+b)
find the minors of the matrix A 1*3
Answer:
A 1x3 matrix only has one entry, so there is only one minor, which is the determinant of the matrix itself.
For example, if A = [a, b, c], then the minor of A is simply:
|A| = det(A) = a
Since the determinant of a 1x1 matrix is just its single entry.
Step-by-step explanation:
a
3. Woody and Buzz each bought a pink bear for
$50.
• Woody sold his bear for 10% more than the
original price.
• Buzz sold his bear for 30% more than the original
price.
Enter how much more money, in dollars, Buzz
earned for his pink bear than Woody received for his
bear.
Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
How to calculate earnings?
Woody sold his bear for $50 + 10% of $50 = $55.
Buzz sold his bear for $50 + 30% of $50 = $65.
Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
To determine how much more money Buzz earned than Woody for their pink bears, we first needed to calculate the selling price for each of them.
We know that both of them bought their bears for $50. Woody sold his bear for 10% more, which means his selling price was $50 + 10% of $50 = $55. Buzz sold his bear for 30% more, which means his selling price was $50 + 30% of $50 = $65. Therefore, Buzz earned $65 - $55 = $10 more than Woody for his pink bear.
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pls help asap!
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths cm2
The surface area of the prism from the net is 260.5 cm².
Calculating the surface areaThe rectangular prism has dimensions of length, width, and height given by 5 and three-fourths cm, 4 cm, and 11 and three-fourths cm respectively.
To find the surface area of the prism, we need to find the area of each of its six faces and then add them up.
So, we have
Area = 2 * (5 3/4 * 4 + 5 3/4 * 11 + 4 * 11)
Evaluate
Area = 260.5
Therefore, the surface area of the prism is 260.5 cm².
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A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 7m and a diameter of 8m. The container will be made from steel (including its top and bottom). If the steel costs 29$ for each square meter, how much will the steel cost in total? Use 3.14 for pi, and do not round your answer.
Step-by-step explanation:
Two ends' area = 2 * pi r^2 r is radius = 1/2 diameter = 4m
2 * 3.14 * (4^2) = 100.48 m^2
Sidewall is cicumfernce ( = pi *d) times the height ( =7m)
3.14 * 8 *7=175.84 m^2
Cost = (100.48 +175.84) m^2 * $ 29 /m^2 = $ 8013.28
A breakfast special consists of choosing one item from each category in the following menu. Juice: Apple, Orange, Grapefruit Toast: White, Brown Eggs: Scrambled, Fried, Poached Beverage: Coffee, Tea, Milk
According to the question there are 54 different breakfast specials that can be ordered from this menu.
What is multiplication?Multiplication in mathematics is the addition of equal groups. As we proliferate, the multitude of issues in the group increases. The product as well as the two elements are part of a multiplication issue. 6 and 9 are factors in the multiplication equation 6 9 = 54, and 54 is the result.
Given,
It seems like the breakfast special menu consists of four categories, with different options for each category.
Juice: Apple, Orange, Grapefruit
Toast: White, Brown
Eggs: Scrambled, Fried, Poached
Beverage: Coffee, Tea, Milk
To order the breakfast special, a customer must choose one option from each category. For example, a customer might choose Orange juice, Brown toast, Scrambled eggs, and Coffee for their breakfast special.
The total number of different breakfast specials that can be ordered is the product of the number of options in each category. So, in this case, the total number of breakfast specials is:
3 (options for juice) x 2 (options for toast) x 3 (options for eggs) x 3 (options for beverage) = 54
Therefore, there are 54 different breakfast specials that can be ordered from this menu.
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Sales of portable MP3 players grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. Predict the sales of MP3 players in 2008
the sales of portable MP3 players in 2008 will be approximately $3.50 billion. To predict the sales of MP3 players in 2008, we need to first understand the exponential growth pattern of sales from 2001 to 2005.
We are given that sales grew approximately exponentially from $0.07 billion in 2001 to $0.91 billion in 2005. This means that the sales data can be modeled by an exponential function of the form:
[tex]S(t) = a * b^t[/tex]
where S(t) is the sales at year t, a is the initial sales value (in 2001), and b is the growth factor per year. We can find the values of a and b by using the given sales data.
When t = 0 (in 2001), S(t) = $0.07 billion. So, we have:
[tex]0.07 = a * b^0\\a = 0.07[/tex]
When t = 4 (in 2005), S(t) = $0.91 billion. So, we have:
[tex]0.91 = 0.07 * b^4b = (0.91/0.07)^(1/4) = 1.770[/tex]
Therefore, the exponential function that models the sales data is:
[tex]S(t) = 0.07 * (1.770)^t[/tex]
To predict the sales of MP3 players in 2008, we need to find the value of S(7) (since 2008 is 7 years after 2001). We have:
[tex]S(7) = 0.07 * (1.770)^7= $3.50 billion[/tex]
Therefore, we can predict that the sales of portable MP3 players in 2008 will be approximately $3.50 billion.
It is important to note that this is a prediction based on the data we have and the model we have used. The actual sales value in 2008 could be different due to various factors such as market changes, competition, and technological advancements.
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Roy has decided to visit the new ice cream shop around the corner. When he goes in, he sees 14 big buckets full of ice cream behind the counter, each containing a different flavor. There are 5 flavors that contain chocolate.
If he closes his eyes and picks out a bucket at random, what is the probability that the flavor he picks will contain chocolate?
A. 2/7
B. 5/14
C. 4/19
D. 3/7
The correct option is B. 5/14, which is equivalent to approximately 0.357 or 35.7%
The probability of selecting a chocolate ice cream bucket is calculated by dividing the number of chocolate ice cream buckets by the total number of buckets:
P(chocolate) = number of chocolate ice cream buckets / total number of buckets
P(chocolate) = 5 / 14
P(chocolate) = 0.35714285714285715
To simplify the fraction, we can express it as a decimal or a percentage:
P(chocolate) ≈ 0.357 or P(chocolate) ≈ 35.7%
Therefore, the probability of selecting a chocolate ice cream bucket is approximately 0.357 or 35.7%. The probability of selecting a chocolate ice cream bucket can be calculated by dividing the number of chocolate ice cream buckets by the total number of buckets. The number of chocolate ice cream buckets is 5, and the total number of buckets is 14. Therefore, the probability of selecting a chocolate ice cream bucket is: 5/14
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A convenience store collected data on its customers to determine the most popular items purchased. The manager of the convenience store created a table of the data they gathered.
Convenience Store Item Number of Purchases
Candy 75
Snacks 100
Automotive Supplies 200
Beverages 125
Which of the following circle graphs correctly represents the data in the table?
circle graph titled convenience store purchases, with four sections labeled candy 15 percent, snacks 20 percent, auto supplies 40 percent, and beverages 25 percent
circle graph titled convenience store purchases, with four sections labeled candy 30 percent, snacks 40 percent, auto supplies 20 percent, and beverages 10 percent
circle graph titled convenience store purchases, with four sections labeled snacks 20 percent, candy 40 percent, beverages 25 percent, and auto supplies 15 percent
circle graph titled convenience store purchases, with four sections labeled snacks 25 percent, candy 15 percent, beverages 40 percent, and auto supplies 20 percent
Answer:
The answer is the first option
Step-by-step explanation:
The reason why it is the first option is because if we add up the total amount of things sold (candy, snacks, automotive supplies, and beverages) we would see that together the store sold 500 items. Using that we can diving the amount of candy, snacks, automotive supplies, and beverages by the total amount of things sold to get the percentages.
Ex: 75/500 = 0.15*100 = 15%
100/500 = 0.20*100 = 20%
etc.
Answer:
the correct answer is the last one i think
Step-by-step explanation:
Will put in chat if correct or not if i remember to do it.
Help with math problems
(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.
What is inequality?Inequality refers to the state of being unequal or not equal in some respect. It can refer to various forms of disparities or differences, such as differences in income, wealth, education, opportunities, health, or social status, among others. Inequality can occur between individuals, groups, communities, or nations, and it can be caused by various factors, such as discrimination, historical legacies, social structures, policies, or economic systems. Inequality is often considered a social problem because it can lead to social tension, unrest, and injustice, as well as undermine economic growth and human development.
(D) |k - 7| < - 6 has no solution is not a true statement because an absolute value can never be negative, so the inequality has no solution.
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Someome help! (identify the solid figures in number order like 1. rectangle 2. square, etc. ) HELP!!!!!
Answer:
1. pyramid
2. cylinder
3. sphere
4. cone
5. cube
6. rectangular prism
7. pyramid
8. sphere
9. cylinder
10. pyramid
11. cube
12. cube
13. cone
14. cylinder
15. sphere
16. cylinder
Step-by-step explanation:
Compare each one to the sample diagrams shown on the top of the paper.
What is the solution to the equation below?
√x-1=x-13
OA. 14
OB. 15
O C. 17
D. 16
The solution for the equation √(x-1) = x - 13 is x = 17, the correct option is C.
How to solve this equation?We have the following equation.
√(x-1) = x - 13
If we apply the square exponent in both sides, we will get:
x - 1 = (x - 13)²
x - 1 = x² - 26x + 169
x² - 27x + 170 = 0
Using the quadratic formula we get:
[tex]x = \frac{27 pm \sqrt{(-27)^2 - 4*170*1} }{2} \\\\x = \frac{27 pm 7}{2}[/tex]
We only care for the positive solution, which is:
x = (27 + 7)/2 = 17
The correct option is C.
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The solution to the given equation is 14 by squaring both sides of the equation and simplifying. Therefore, the solution to the equation is option A.
Explanation:To solve the equation √x-1=x-13, we first square both sides to eliminate the square root.
That results in the equation x - 2*x +1 = x - 13. Simplify this to get -x + 14 = 0. Further simplifying, x = 14 is the solution. Therefore, the solution to the equation is 14 (option A).
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Dividends Per Share Seacrest Company has 25,000 shares of cumulative preferred 2% stock, $50 par and 50,000 shares of $25 par common stock. The following amounts were distributed as dividends: 20Y1 $37,500 20Y2 20,000 20Y3 75,000 Determine the dividends per share for preferred and common stock for each year. Round all answers to two decimal places. If an answer is zero, enter '0'.
Given the side length a=9 and the angle B=46∘ on the triangle below, find the lengths of b and c and the measure of angle A. Do not round during your calculations, but round your final answers to one decimal place.
well, since all interior angles in a triangle add up to 180°, by definition A = 44°, since B and A are complementary anyway.
[tex]\cos(46^o )=\cfrac{\stackrel{adjacent}{9}}{\underset{hypotenuse}{c}}\implies c=\cfrac{9}{\cos(46^o)}\implies c\approx 13.0 \\\\[-0.35em] ~\dotfill\\\\ \tan(46^o )=\cfrac{\stackrel{opposite}{b}}{\underset{adjacent}{9}}\implies 9\tan(46^o )=b\implies 9.3\approx b[/tex]
Make sure your calculator is in Degree mode.
Hall deposited $920 into a savings account. The account earns 8%
interest, compounded annually. What is the balance of his account
after 11 years? Answer in dollars and round to the nearest cent.
The required balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].
How to deal with compound interest?The formula to calculate compound interest is:
[tex]$A = P(1 + \frac{r}{n})^{nt}$[/tex]
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Time (in years)
Here, P = 920, r = 0.08, n = 1 (compounded annually), and t = 11 years.
Plugging in the values:
[tex]$A = 920(1 + \frac{0.08}{1})^{1\times 11}$[/tex]
[tex]$A = 920(1.08)^{11}$[/tex]
[tex]$A = 2145.1$[/tex]
Therefore, the balance of Hall's account after 11 years is [tex]$A = 2145.1$[/tex].
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please help !!
Determine the length of side FE
18
20
21
26
the length of EF is 11 units.
How to solve similar triangles?
Since triangles DEF and GHF are both right triangles, we can use the Pythagorean theorem to find the length of EF.
Let's first find the lengths of DE and EF.
DE = DF + FE = 13 + x, where x is the length of FE.
GF = DE - DG = (13 + x) - 4 = 9 + x.
GH = 4.
Now, using the Pythagorean theorem in triangle GHF, we have:
GH² + HF² = GF²
4²+ HF² = (9 + x)²
16 + HF² = 81 + 18x + x²
And in triangle DEF, we have:
DE²+ EF² = DF²
(13 + x)² + EF² = 13²
169 + 26x + x²+ EF² = 169
Simplifying the above equation, we get:
EF²= -26x - x²
Substituting this into the equation we got from the GHF triangle, we have:
16 + HF² = 81 + 18x + x² - EF²
16 + HF² = 81 + 18x + x²+ 26x + x²
HF² = 97 + 44x + 2x²
Now, using the fact that HE + EF = HF, we have:
8 + x = √(97 + 44x + 2x²)
Squaring both sides and simplifying, we get:
4x² + 16x - 225 = 0
Solving this quadratic equation, we get:
x = (-16 ± √(16² - 44(-225)))/(2*4) = (-16 ± 34)/8
Since x has to be positive, we take the positive solution:
x = 3
Therefore, EF = HE + FE = 8 + 3 = 11.
So the length of EF is 11 units.
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help me please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
(A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
What is the rate of change?
The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.
A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.
Using the formula for an annual rate of change (r):
final value = initial value * [tex](1 - r)^t[/tex]
where t is the number of years and r is the annual rate of change expressed as a decimal.
Substituting the given values, we get:
$15,000 = $44,000 * (1 - r)¹⁴
Solving for r, we get:
r = 0.0804
So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.
B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:
r = 0.0804 * 100% = 8.04%
C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.
Substituting the known values, we get:
value in 2009 = $15,000 * (1 - 0.0804)³
value in 2009 = $11,628.40
Rounding to the nearest $50, we get:
value in 2009 = $11,650
Hence, (A) the annual rate of change between 1992 and 2006 was 0.0804
(B) r = 0.0804 * 100% = 8.04%
(C) value in 2009 = $11,650
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(2x^3 -3x^2 +4x -1) /(x+2)
Quotient ➔ 2x² - 7x + 18
Remainder ➔ - 37
━━━━━━━━━━━━━━━━━━━━━━
SolutioN ::
ㅤ
➸ Attachment[tex]\begin{gathered} \\ \\ \qquad{\rule{120pt}{7pt}} \\ \\ \end{gathered}[/tex]
VerificatioN ::
ㅤ
➸ Taking the product of Divisor and Quotient as LHS[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf {x(2x^{2} - 7x + 18) + 2(2x^{2} - 7x + 18) + ( - 37)} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 18x + 4x^{2} - 14x + 36 - 37} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {2x^{3} - 7x^{2} + 4x^{2} + 18x - 14x - 1} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]
➸ Taking Dividend as RHS[tex]\begin{gathered} \\ \\ \; \; :\longmapsto \; \sf \pink{2x^{3} - 3x^{2} + 4x - 1} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \sf {LHS = RHS} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ \; \; :\longmapsto \; \underline{\boxed{\sf{Verified}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \\ {\underline{\rule{150pt}{10pt}}} \end{gathered}[/tex]
[tex]\blue{\huge {\mathrm{DIVIDING \; POLYNOMIALS}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
[tex]\sf \dfrac{(2x^3 -3x^2 +4x -1)}{(x+2)}[/tex][tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
Through the computations performed, we came to the conclusion that the quotient is [tex]\blue{\bold{2x^2 - 7x + 18}}[/tex] and the remainder is [tex]\red{\bold{-37}}[/tex].[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]
[tex]\qquad\begin{aligned}\sf \blue{2x^2 - 7x + 18} \:\:\:\:\:\:\:\:\:\: &\\\sf x + 2 \: \: ) \overline{2x^3 - 3x^2+4x-1} \quad&\\\sf \: \: \underline{ - 2x^3 - 4x^2 \qquad\qquad \: \: \: \: } \\\sf - 7x^2 + 4x \qquad \: \: \: \\\sf \:\:\: \underline{ - 7x^2 + 14x \qquad \: } \\ \sf 18x - 1 \: \: \: \\ \underline{ \sf{ - 18x - 36 \: }} \\ \sf \red{ - 37} \end{aligned}[/tex]
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]