How do I do part 2 and 3?? Please show all steps of working. I have no clue how to do this!
Answers
The vector b is [10, 5, 10] and the general solution for [A|b] is [1, 5, -3] + [-3, 2, -1]s
Calculating the vector bTo find the vector b, we need to multiply the matrix A by the vector x and solve for b in the equation Ax = b.
So, we have:
[tex]\left[\begin{array}{ccc}1&3&-3&0&1&-2&3&5&-1\end{array}\right]\left[\begin{array}{c}1&1&-2\end{array}\right] &= \left[\begin{array}{c}10&5&10\end{array}\right][/tex]
Therefore, the vector b is [10, 5, 10].
Calculating the general solution for [A|b]To find the general solution of [A | b], we need to perform row reduction on the augmented matrix [A | b] and express the pivot variables in terms of the free variables.
[tex]\left[\begin{array}{ccc|c}1&3&-3&10&0&1&-2&5&3&5&-1&10\end{array}\right] &\rightarrow \left[\begin{array}{ccc|c}1&0&3&1&0&1&-2&5&0&0&0&0\end{array}\right][/tex]
The third column does not have a pivot variable, so we can express x3 in terms of the free variables.
Let s be the free variable, then we have:
x3 = -s - 3
We can now express the pivot variables in terms of s:
x1 = 1 - 3s
x2 = 5 + 2s
Thus, the general solution of [A | b] is:
[tex]\left[\begin{array}{c}x_1&x_2&x_3\end{array}\right] &= \left[\begin{array}{c}1 - 3s&5 + 2s&-s - 3\end{array}\right] \&= \left[\begin{array}{c}1&5&-3\end{array}\right] + s\left[\begin{array}{c}-3&2&-1\end{array}\right][/tex]
Therefore, the general solution of [A | b] is [1, 5, -3] + [-3, 2, -1]s
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Related Questions
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?
Answers
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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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
Answers
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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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
Answers
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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I’m stuck I need you to do it
Answers
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)
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.
Answers
(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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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?
Answers
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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please help !!
Determine the length of side FE
18
20
21
26
Answers
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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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'.
Answers
Dividends per share of preferred stock = Total dividends on preferred stock / Number of outstanding shares of preferred stock
Dividends per share of common stock = Total dividends on common stock / Number of outstanding shares of common stock
First, we need to calculate the total dividends on preferred and common stock for each year:
Year 20Y1:
Total dividends on preferred stock = 25,000 shares x $50 par x 2% = $25,000
Total dividends on common stock = $37,500
Year 20Y2:
Total dividends on preferred stock = $25,000 (cumulative preferred stock) + $20,000 x 2% = $25,400
Total dividends on common stock = $20,000
Year 20Y3:
Total dividends on preferred stock = $25,000 (cumulative preferred stock) + $20,000 (cumulative preferred stock) + $30,000 x 2% = $26,600
Total dividends on common stock = $75,000
Using the formulas above, we can calculate the dividends per share for each year:
Year 20Y1:
Dividends per share of preferred stock = $25,000 / 25,000 shares = $1.00
Dividends per share of common stock = $37,500 / 50,000 shares = $0.75
Year 20Y2:
Dividends per share of preferred stock = $25,400 / 25,000 shares = $1.02
Dividends per share of common stock = $20,000 / 50,000 shares = $0.40
Year 20Y3:
Dividends per share of preferred stock = $26,600 / 25,000 shares = $1.06
Dividends per share of common stock = $75,000 / 50,000 shares = $1.50
Therefore, the dividends per share for preferred and common stock for each year are as follows:
Year 20Y1: Preferred stock = $1.00, Common stock = $0.75
Year 20Y2: Preferred stock = $1.02, Common stock = $0.40
Year 20Y3: Preferred stock = $1.06, Common stock = $1.50
find the minors of the matrix A 1*3
Answers
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:
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.
Answers
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.
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
Answers
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.
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
Answers
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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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.
Answers
14 because 14+28=42.
Suppose that a cliff diver's height (in feet) after t seconds is given by the model
H(t)=-16t^2+32t+20 find the height after 1.25 seconds pls help me
Answers
The height of the cliff diver after 1.25 seconds is 35 feet.
Calculating Height :
The concept used is evaluating a function at a given input or value. In this case, we are evaluating the height function H(t) at t = 1.25 to find the height of the cliff diver after 1.25 seconds. The formula for the height function is given as H(t) = -16t^2 + 32t + 20.
Here we have
A cliff diver's height (in feet) after t seconds is given by the model
H(t)=-16t² +32t +20
Given time t = 1.25 seconds
To find the height after 1.25 seconds, we simply need to evaluate H(1.25) using the given formula:
H(1.25) = -16(1.25)² + 32(1.25) + 20
On Simplifying the expression we get:
H(1.25) = -16(1.5625) + 40 + 20
H(1.25) = -25 + 60
H(1.25) = 35
Therefore,
The height of the cliff diver after 1.25 seconds is 35 feet.
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Help with math problems
Answers
(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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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.
Answers
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
Determine the point estimate of the population mean and the margin of error for the given confidence interval. Lower bound: 12 Upper bound: 20
Answers
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:
Solve the problems.
The number a is less than the number b by (1)/(5) of b. By what part of a is b greater than a ?
Answers
Answer:
B is greater than A by 1/4 of A
Step-by-step explanation:
Let's use the information given in the problem to write expressions for the values of a and b:
a = b - (1/5)b = (4/5)b
b is greater than a by the difference:
b - a = b - (4/5)b = (1/5)b
To express this difference as a fraction of a, we divide by a:
(b - a)/a = ((1/5)b)/((4/5)b) = 1/4
Therefore, b is greater than a by 1/4 of a.
A soccer team is planning to sell candy bars to spectators at their games. They will buy two-pound bags of candy. The number of candy bars per bag has mean 12 and standard deviation 2. They will sell each candy bar for $1.25. (Assume that all of the candy in a bag will be sold.)
1. What is the expected value and the standard deviation for the amount of money that would be made selling all of the candy in one bag of candy?
Answers
The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.
What exactly is a standard deviation?The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.
The expected value for the amount of money made selling all of the candy in one bag can be found by;
Expected value = mean number of candy bars per bag x price per candy bar
Expected value = 12 x $1.25 = $15
Formula for the standard deviation of a product of random variables:
[tex]SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}[/tex]
where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.
X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:
E(Y²) = $1.25² = $1.5625
E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148
Cov (X,Y) = 0 (because X and Y are independent)
Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:
[tex]SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))[/tex]
SD = √(592)
SD ≈ $24.33
Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.
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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
Answers
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 point at (-5,7) is reflected across the x-axis. The new point is then reflected across the y-axis. What ordered pair names the third point?explain.
Answers
Answer:
Step-by-step explanation:
Reflecting a point across the x-axis negates the y-coordinate, so the point (-5, 7) reflected across the x-axis becomes (-5, -7).
Reflecting a point across the y-axis negates the x-coordinate, so the point (-5, -7) reflected across the y-axis becomes (5, -7).
Therefore, the third point is (5, -7).
Similarly, above the x-axis, y-values are positive, and below the x-axis, y-values are negative.
Starting with (-5,7), this point is located to the left of the y-axis and above the x-axis.
Reflected over the x-axis, the sign of the y-value changes from positive to negative:
7 becomes -7 so the second point is (-5,-7).
Reflect the second point over the y-axis, and the x-value changes from negative to positive:
-5 becomes 5, so the third point is (5,-7)
The third point is (5,-7).
Hope this helps!
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.
Answers
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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[tex]\sqrt[4]{-81}[/tex]
Answers
The fourth root of -81 is not a real number is 3√i.
What is imaginary number?A number that can be represented in the form a + bi is an imaginary number. In this case, a and b are real numbers, while I is the imaginary unit, which is equal to the square root of -1. In mathematics, imaginary numbers are used to expand on the real number system and to describe values that cannot be stated using real numbers.
Complex numbers, which are numbers of the type a + bi, where a and b are real numbers, are one of the principal applications for imaginary numbers. Several mathematical and scientific disciplines, such as electrical engineering, signal processing, and quantum physics, require complex numbers.
The value of -81 can be written as i²(3)⁴.
Taking the fourth root of the number we get 3√.
Hence, the fourth root of -81 is not a real number is 3√i.
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A company makes steel rods shaped like cylinders. Each rod has a diameter of 6 centimeters and a height of 20 centimeters. If the company used 30520.8cm3 of steel, how many rods did it make?
Answers
As a result, the company produced number of rods are **56** rods.
What exactly is radius?
A radius is a section of a straight line in geometry that connects a circle's or sphere's center to its edge or surface Its length is divided by the circle's diameter by two.
Each rod has a diameter of 6 centimeters, hence the radius is 3 centimeters. Each rod has a 20-centimeter height.
The following formula can be used to determine a cylinder's volume:
V = πr²h
where V stands for volume, r for radius, which is equal to half of the diameter, and h for height.
Adding these values to the formula yields the following results:
V = π(3)²(20) (20)
V = 180π
The volume of each rod is therefore 180 cubic centimeters.
30520.8 cubic centimeters of steel were used to make how many rods?
To find out,
divide the total volume of steel by the volume of each rod:
30520.8 / (180π) ≈ **56** rods
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Hall deposited $920 into a savings account. The account earns 8%
interest, compounded annually. What is the balance of his account
after 11 years? Answer in dollars and round to the nearest cent.
Answers
The required balance of Hall's account after 11 years is [tex]$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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(2x^3 -3x^2 +4x -1) /(x+2)
Answers
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]
What is the solution to the equation below?
√x-1=x-13
OA. 14
OB. 15
O C. 17
D. 16
Answers
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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convert to slope intercept (y=mx+b)
Answers
x - 2y = -6
move the x value to the other side of the equation:
-2y = -x - 6
now divide the right side by -2 (isolate y):
y = (-x/-2) - (6/-2)
Simplify:
y = x/2 + 3
or
y = (1/2)x + 3
Hope this helps!
Someome help! (identify the solid figures in number order like 1. rectangle 2. square, etc. ) HELP!!!!!
Answers
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.
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).
Answers
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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