To find the average amount that Sarah saved per month over the last six months, we need to add up the total amount saved and divide by the number of months.
Total amount saved = $135.00 + $144.00 + $104.00 + $80.00 + $90.00 + $160.00 = $713.00
Number of months = 6
Average amount saved per month = Total amount saved / Number of months = $713.00 / 6 = $118.83
Therefore, the correct answer is d. $118.83.
It is important to note that when working with numbers and calculations, accuracy is crucial. In this case, rounding off the answer to the nearest cent would result in a different answer.
Additionally, checking the calculations multiple times to ensure accuracy is always recommended.
Overall, tracking and analyzing expenses and savings is important for financial planning and achieving financial goals. By keeping track of how much she saved each month,
Sarah can make informed decisions about her spending and saving habits and adjust accordingly to reach her vacation savings goal.
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How many non-identical triangles can be made using
these side lengths: 4 cm, 8 cm, and 14 cm?
With side lengths of 4, 8, and 14 cm, only one non-identical triangle can be formed.
This is due towards the triangle inequality theorem, which stipulates that the total of any two triangle sides must be bigger than the third side. In this instance, 4 cm plus 8 cm equals 12 cm, that is smaller than 14 cm.
A triangle cannot be formed with these side lengths since they do not meet the triangle inequality theorem. To elaborate, a triangle is created by joining three line segments to create a closed form with three angles.
These line segments' lengths are referred to as the triangle's sides. The total of both sides must be higher than the length of the third one to qualify for a triangle to be present. The triangle inequality hypothesis is what this states.
It is impossible to build a triangle with the side lengths of 4 cm, 8 cm, and 14 cm since the sum of the two shorter sides (4 cm + 8 cm = 12 cm) is less than the length of the longest side (14 cm). Hence, One non-identical triangle can be made.
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Last season joao scored a goal in 3/5 or 60% of the soccer games. use this experimental probability to determine the number of games he will score a goal this season, if he plays in 10 games
If Joao scored a goal in 60% of the soccer games last season, then we can expect him to score a goal in about 60% of the games he plays this season.
So, if Joao plays in 10 games this season, we can estimate that he will score a goal in approximately 60% of those games.
To calculate the actual number of games he is expected to score a goal in, we can use the formula:
Expected number of goals = Total number of games x Probability of scoring a goal
Plugging in the numbers, we get:
Expected number of goals = 10 x 0.6 = 6
Therefore, based on the experimental probability from last season, we can estimate that Joao will score a goal in around 6 games out of the 10 he plays this season.
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You pick a card at random.
What is P(even or prime)?
Write your answer as a percentage
Probability of picking an even or prime card at random is approximately 88.89%.
To find the probability of picking an even or prime card at random, we first need to identify the possible cards that meet these conditions.
In a standard deck of cards, there are 52 cards, but we only consider the numerical values, which are 2-10 for each of the four suits (hearts, clubs, spades, and diamonds).
Even numbers: 2, 4, 6, 8, 10
Prime numbers: 2, 3, 5, 7
Combining the even and prime numbers, we have: 2, 3, 4, 5, 6, 7, 8, 10. Note that 2 appears only once in the combined list.
Now we find the probability by dividing the number of favorable outcomes (even or prime numbers) by the total number of possible outcomes (cards numbered 2-10).
P(even or prime) = (Number of even or prime cards) / (Total number of cards from 2-10)
P(even or prime) = 8 / 9
To express the probability as a percentage, multiply by 100:
P(even or prime) = (8 / 9) × 100 ≈ 88.89%
So, the probability of picking an even or prime card at random is approximately 88.89%.
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The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
number of meals dispensed. n. 1. 3. 6. 7. amount of pet food remaining . f of n. cups. 21. 15. 6. 3.
based on the table, which function models this situation?
The function that models this situation is f(n) = -3n + 24.
To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).
1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.
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I need help I have no idea how to do this
Answer:
x=6
Step-by-step explanation:
5x+150=180
-150 -150 (subtract 150 from both sides)
5x=30
x=6
Answer:
x = 6
Step-by-step explanation:
Supplementary angles add up to 180 degrees, and lines A and B are parallel, so:
180 - 150 = 30
30/5 = x
6 = x
please help with question 9
The value of the function g(x) = 4x⁴ - 4x³ - 10x - 51
What are functions?Functions are defined as those expressions or equations showing the relationship between two variables.
From the information given, we have the functions;
f(x) = 4x³ + 3x² - 12x - 32
h(x) = 4x⁴ - 3x² + 2x - 19
(f + g(x) = h(x)
To determine the function, let us follow the expression
f(x) + g(x) = h(x)
Make g(x), the subject of formula
g(x) = h(x) - f(x)
Substitute the expressions
g(x) = 4x⁴ - 3x² + 2x - 19 - 4x³ + 3x² - 12x - 32
Now, collect the like terms, we get;
g(x) = 4x⁴ - 4x³ - 3x² + 3x² + 2x - 12x - 19 - 32
Add or subtract the values
g(x) = 4x⁴ - 4x³ - 10x - 51
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Joyner Company’s income statement for Year 2 follows:
Sales $ 703,000
Cost of goods sold 109,000
Gross margin 594,000
Selling and administrative expenses 151,700
Net operating income 442,300
Nonoperating items:
Gain on sale of equipment 9,000
Income before taxes 451,300
Income taxes 135,390
Net income $ 315,910
Its balance sheet amounts at the end of Years 1 and 2 are as follows:
Year 2 Year 1
Assets
Cash and cash equivalents $ 294,410 $ 55,900
Accounts receivable 228,000 141,000
Inventory 318,000 289,000
Prepaid expenses 10,000 20,000
Total current assets 850,410 505,900
Property, plant, and equipment 639,000 508,000
Less accumulated depreciation 165,300 130,200
Net property, plant, and equipment 473,700 377,800
Loan to Hymans Company 46,000 0
Total assets $ 1,370,110 $ 883,700
Liabilities and Stockholders' Equity
Accounts payable $ 311,000 $ 262,000
Accrued liabilities 49,000 57,000
Income taxes payable 84,200 80,700
Total current liabilities 444,200 399,700
Bonds payable 209,000 105,000
Total liabilities 653,200 504,700
Common stock 340,000 287,000
Retained earnings 376,910 92,000
Total stockholders' equity 716,910 379,000
Total liabilities and stockholders' equity $ 1,370,110 $ 883,700
Equipment that had cost $31,500 and on which there was accumulated depreciation of $10,400 was sold during Year 2 for $30,100. The company declared and paid a cash dividend during Year 2. It did not retire any bonds or repurchase any of its own stock.
Required:
1. Using the indirect method, compute the net cash provided by/used in operating activities for Year 2.
2. Prepare a statement of cash flows for Year 2.
3. Compute the free cash flow for Year 2
the free cash flow for Joyner Company in Year 2, we need to follow these steps:
Step 1: Calculate operating cash flow (OCF).
Operating cash flow is calculated by taking the company's net income, adding back non-cash expenses (depreciation and amortization), and adjusting for changes in working capital.
Step 2: Calculate capital expenditures (CapEx).
Capital expenditures are the funds used by the company to acquire, upgrade, and maintain physical assets, such as equipment or buildings. In this case, we need to find the net change in equipment and accumulated depreciation.
Step 3: Subtract the cash dividend.
The cash dividend paid by the company during Year 2 should be subtracted from the operating cash flow.
Step 4: Calculate the free cash flow.
Free cash flow is the remaining cash after deducting capital expenditures and cash dividends. It represents the cash available for the company to repay debt, reinvest in the business, or distribute to shareholders.
Unfortunately, the provided information is not sufficient to compute the free cash flow for Year 2. Specifically, the net income, changes in working capital, and complete equipment transactions are needed to perform these calculations. Please provide the missing information so that a detailed step-by-step explanation can be given to compute the free cash flow for Joyner Company in Year 2.
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Use the following bond listing for Pacific Bell to answer the following: Bonds Cur. Yia. Vol Close Net. Chg. 5 6. 55 5 1 1 Pac Bell 6– 34 99- 4 8 What is the coupon rate and maturity date for this bond? 5 The coupon rate is 62, the maturity date is 2034. A. B 1 The coupon rate is 8 the maturity date is 2034. 5 The coupon rate is 6. The maturity date is 2099. D. The coupon rate is 6. 55; the maturity date is in 5 years.
The coupon rate for this Pacific Bell bond is 6%, and the maturity date is in 2034. So, the correct option is B: The coupon rate is 6%, and the maturity date is 2034.
The information provided in the bond listing can be interpreted as follows:
Bond issuer: Pacific Bell
Coupon rate: 6.55
Maturity date: 2034
Volume: 511
Closing price: 99-4
Net change: 8
Therefore, the correct answer is: The coupon rate is 6.55 and the maturity date is 2034.
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a laundromat has 5 washing machines. a typical machine breaks down once every 5 days. a repairer can repair a machine in an average of 2.5 days. currently, three repairers are on duty. the owner of the laundromat has the option of replacing them with a superworker, who can repair a machine in an average of 5 6 day. the salary of the superworker equals the pay of the three regular employees. breakdown and service times are exponential. should the laundromat replace the three repairers with the superworker?
Replacing three repairers with a superworker would be cost-effective for the laundromat as the expected repair time would increase and lead to more downtime for the machines.
To determine if the laundromat should replace the three repairers with the superworker, we need to compare the expected repair time under each scenario.
With three repairers, the expected time to repair a machine is the sum of the expected time until a machine breaks down and the expected time for a repairer to fix it
E(time with three repairers) = 5 + 2.5/3 = 6.167 days.
With the superworker, the expected time to repair a machine is
E(time with superworker) = 5/6 = 0.833 days.
Therefore, on average, it takes much less time to repair a machine with the superworker than with three repairers. Since the salary of the superworker is equal to that of three repairers, the laundromat should replace the three repairers with the superworker. It is also more cost-effective.
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Of the 90 people who attended BayBridge Middle School Winter formal, 18 are not students at baybridge
Fill in the grid
________________________________
Students Who Don't Attend: = 18 ÷ 90 × 100= 20% Students Who Do Attend: = 100 - 20= 80%80% of The Students Will Attend The Baybridge Academy Winter Formal & 20% Will Not Be Attending.________________________________
17
Type the correct answer in the box. Use numerals instead of words,
Alex is a single taxpayer with $80,000 in taxable income. His investment income consists of $500 of qualified dividends and short-term capital gains
of $2,000
Use the tables to complete the statement.
Single Taxpayers: Income Brackets
Tax Rate Income Bracket
10%
0 to 9,525
1296
9,526 to 38,700
22%
38,701 to 82,500
Single Taxpayers: Qualified
Dividends and Long-Term
Capital Gains
Tax Rate Income Bracket
0%
O to 38,600
15% 38,601 to 425,800
20%
> 425,800
24%
82,501 to 157,500
32%
157,501 to 200,000
35%
200,001 to 500,000
37%
> 500,000
Alex will owe $
in taxes on his investment income.
My
The exact tax owed cannot be determined without knowing the specific income bracket for Alex's taxable income.
We know that,
Based on the provided information, Alex's investment income consists of
$500 of qualified dividends and $2,000 of short-term capital gains.
Here, we have to calculate the taxes owed on his investment income, we
need to determine the applicable tax rate based on his taxable income.
As the specific income bracket for Alex's taxable income is not mentioned, it is not possible to provide an exact amount of taxes owed.
The tax rate and corresponding income brackets should be referenced to calculate the taxes accurately.
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Find the equation of the axis of
symmetry for this function.
f(x) = -4x² + 8x - 28
Hint: To find the axis of symmetry, use the equation: x =
FR
2a
Simplify your answer completely. Enter
the number that belongs in the green box.
x = [?]
Enter
The equation of the axis of symmetry for the given function is x = 1.
To find the equation of the axis of symmetry for the function f(x) = -4x² + 8x - 28, we can use the formula:
x = -b / (2a)
where "a" and "b" are coefficients in the quadratic equation ax² + bx + c.
In this case, a = -4 and b = 8. Plugging these values into the formula, we get:
x = -8 / (2*(-4))
x = -8 / (-8)
x = 1.
The axis of symmetry for a quadratic function in the form of [tex]f(x) = ax^2 + bx + c[/tex] can be found using the formula x = -b / (2a).
In the case of the given quadratic function f(x) = -4x² + 8x - 28, the coefficient of [tex]x^2[/tex] is a = -4 and the coefficient of x is b = 8.
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A spinner is divided into 15 identical sectors and labeled 1 through 15.
how many spins are expected for a multiple of 4 to be spun 7 times?
select from the drop-down menu to correctly complete the sentence.
the spinner is expected to have to spin approximately times for a multiple of 4 to be spun 7 times.
Answer: 35
Step-by-step explanation: The other person is wrong
Hope this helped :)
Select all of the statements that are true
The [9.7] = -9.7 because the distance from -9.7 to 0 on the number line is 9.7 units.
Numbers with the same absolute value are opposites because they are the same distance from each other.
The [7.1] = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units.
The [-8.4] = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units.
Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line.
The [-12.5] = 12.5 because the distance from 12.5 to 0 on the number line is -12.5 units.
The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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To integrate f(x, y, z) = ~ over the region ? consisting of the points (2, Y, 2)
such that
•0≤o≤1,
•0≤y≤2,and
• 0 ≤ 2 ≤ 3x + 4y.
If we want to use the bounds of integration, what kind of integration would we use?
We first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
To integrate the given function over the region, we would use triple integration with the bounds of integration as follows:
∫ from 0 to 1 ∫ from 0 to 2 ∫ from 2 to (3x + 4y) f(x, y, z) dz dy dx
This is because the region is defined by the inequalities 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, and 0 ≤ z ≤ (3x + 4y).
Therefore, we first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
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The base of a cone has a radius
of 6 centimeters. The cone is
7 centimeters tall. What is the volume
of the cone to the nearest tenth? Use 3. 14 for it.
A. 260 cm
C. 263. 8 cm3
B. 263. 7 cm
D. 264. 0 cm3
The volume of the cone to the nearest tenth is 263.8 cm^3.
What is the volume, rounded to the nearest tenth, of a cone with a radius of 6 centimeters and a height of 7 centimeters?To find the volume of the cone, we first need to use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
We are given that the radius is 6 centimeters and the height is 7 centimeters, so we can substitute these values into the formula.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Using the given values, we can plug them into the formula and solve:
V = (1/3)π(6 cm)^2(7 cm)
V ≈ 263.7 cm^3
Rounding this to the nearest tenth gives us the final answer of 263.8 cm^3, which is option (C).
Since 3 is less than 5, we round down, which means the answer is 263.8 cm^3, as shown in option (C).
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In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 1.39%. Interpretation: we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%.
To calculate the margin of error at the 99% confidence interval, we can use the formula:
Margin of error = z* × √(p × (1 - p) / n)
where z* is the critical value (2.576 for a 99% confidence interval), p is the sample proportion (0.30), and n is the sample size (5000).
Margin of error = 2.576 × √(0.30 × (1 - 0.30) / 5000) ≈ 0.0139 or 1.39%
The interpretation of this result is that we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%. In other words, if we were to conduct the survey multiple times, we would expect the proportion of viewers under 30 to fall within this interval 99 out of 100 times. This information is useful for understanding the level of uncertainty in the survey results and can help guide decision-making based on the findings.
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Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an
average rate of 6. 6 kilometers per hour. The equation that models the distance he
runs for t hours is = 6. 6t
Find the theoretical and practical domains of the equation.
Select ALL correct answers.
The correct answers are:
The theoretical domain is 1 ≤ t ≤ 2.
The practical domain is 1 ≤ t ≤ 2.
Find out the theoretical and practical domain?The equation that models the distance Kellen runs for t hours is given as 6.6t, where t is the time in hours.
The theoretical domain of the equation refers to all the possible values that t can take in the equation without any restrictions. In this case, the only restriction is that Kellen runs for at least 1 hour but for no more than 2 hours. Therefore, the theoretical domain of the equation is:
1 ≤ t ≤ 2
The practical domain of the equation refers to the values of t that make sense in the context of the problem. Since Kellen runs for at least 1 hour, the practical domain should start at 1 hour. Also, since he cannot run for more than 2 hours, the practical domain should end at 2 hours. Therefore, the practical domain of the equation is:
1 ≤ t ≤ 2
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A. Factor out the GCF: 〖3t〗^4-〖6t〗^3-9t+12
B. Use the Distributive Method to factor: g^2-5g-14
C. Factor: r^2-64
D. Factor: 〖9p〗^2-42p+49
E. Use the Box Method to factor: d^2-18d+45
F. Factor Completely: 〖4d〗^3-〖6d〗^2-4d
SHOW ALL YOUR WORK
These are answers of asked question.
A. To factor out the Greatest Common Factor (GCF) of the expression 3t^4 - 6t^3 - 9t + 12, we need to identify the highest power of t that can be factored out. In this case, the GCF is 3t. So we can rewrite the expression as follows:
3t^4 - 6t^3 - 9t + 12 = 3t(t^3 - 2t^2 - 3) + 3t(4)
The GCF, 3t, is factored out from the first two terms, leaving us with t^3 - 2t^2 - 3. The last term, 12, is divisible by 3t, so it becomes +3t(4). Therefore, the factored form of the expression is:
3t(t^3 - 2t^2 - 3) + 3t(4)
B. To factor the expression g^2 - 5g - 14 using the Distributive Method, we look for two numbers whose product is -14 and whose sum is -5 (the coefficient of the middle term). In this case, -7 and +2 satisfy these conditions. So we can rewrite the expression as follows:
g^2 - 5g - 14 = (g - 7)(g + 2)
Using the Distributive Property, we multiply (g - 7) by (g + 2) to verify the factoring:
(g - 7)(g + 2) = g(g) + g(2) - 7(g) - 7(2) = g^2 + 2g - 7g - 14 = g^2 - 5g - 14
Therefore, the factored form of the expression is:
(g - 7)(g + 2)
C. To factor the expression r^2 - 64, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = r and b = 8, since 8^2 = 64. So we can rewrite the expression as follows:
r^2 - 64 = (r + 8)(r - 8)
Using the difference of squares formula, we can multiply (r + 8) by (r - 8) to verify the factoring:
(r + 8)(r - 8) = r(r) - r(8) + 8(r) - 8(8) = r^2 - 8r + 8r - 64 = r^2 - 64
Therefore, the factored form of the expression is:
(r + 8)(r - 8)
D. To factor the expression 9p^2 - 42p + 49, we look for two numbers whose product is 49 and whose sum is -42 (the coefficient of the middle term). In this case, -7 and -7 satisfy these conditions. So we can rewrite the expression as follows:
9p^2 - 42p + 49 = (3p - 7)(3p - 7)
Using the Distributive Property, we multiply (3p - 7) by (3p - 7) to verify the factoring:
(3p - 7)(3p - 7) = 3p(3p) - 3p(7) - 7(3p) - 7(7) = 9p^2 - 21p - 21p +
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28 Laney's art teacher, Mr. Brooks, has four different colors of clay. Laney and some of her classmates will be using this clay to make different figures. The following table shows the number of pounds of each color of clay Mr. Brooks has available. Clay Amount Color (pounds) Biue 11 5 Green 8 Yellow 2 Red 15 4. Use this information to help you answer parts A through E of this problem. Part A Laney noticed that one color of clay was exactly twice the amount of clay of another color. Which color of clay weighs exactly twice the number of pounds of another color of clay? A. Blue B. Green C. Yellow D. Red. â
Blue color of clay weighs exactly twice the number of pounds of another color of clay. The correct option is a.
We need to find the color of clay that weighs exactly twice the number of pounds of another color of clay. We can start by comparing the amounts of clay for each color:
- Blue: 11 pounds
- Green: 8 pounds
- Yellow: 2 pounds
- Red: 15 pounds
To find the answer, we need to see if any of these values is exactly twice another value. We can start by dividing each amount by 2:
- Blue: 11 ÷ 2 = 5.5
- Green: 8 ÷ 2 = 4
- Yellow: 2 ÷ 2 = 1
- Red: 15 ÷ 2 = 7.5
From this, we can see that the amount of blue clay (11 pounds) is exactly twice the amount of green clay (5.5 pounds). Therefore, the answer is A. Blue.
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First derive a recurrence relation giving on for na 2 in terms of co or cy (or both). Then apply the given initial conditions to find the values of co and Cq. Next determine cn (in terms of n) and, finally, identify the particular solution in terms of familiar elementary functions. y"' + 4y = 0; y(0) = 0, y'(O) = 1 = The recurrence relation is on +2 for n 20. (Type an expression using n, cn, and Cn+1 as the variables.) and C1 = The constants are co = (Type integers or fractions.) The explicit formula for the coefficients is c2n and C2n + 1 for n 20. The particular solution in terms of elementary functions is y(x) =
The given differential equation is y"' + 4y = 0. To derive a recurrence relation, we assume that the solution has the form y = e^rx.
Substituting this in the differential equation, we get the characteristic equation r^3 + 4 = 0. Solving this, we get three roots r = -2i, 2i, 0.
So, the general solution is y = c1cos(2x) + c2sin(2x) + c3. Using the initial conditions y(0) = 0 and y'(0) = 1, we get c1 = 0 and c2 = 1/2.
Therefore, the solution is y = 1/2sin(2x) + c3.
Now, we can find the recurrence relation by writing c3 in terms of c2 and c1. We have c3 = y(0) - (1/2)sin(0) = 0. So, the recurrence relation is cn+2 = -4cn.
Using the initial conditions, we have c1 = 0 and c2 = 1/2. Therefore, the explicit formula for the coefficients is cn = (1/2)(-4)^n-2 for n ≥ 2.
Finally, the particular solution can be found by adding the general solution to the homogeneous solution. Since the roots are imaginary, the particular solution will have the form y = Acos(2x) + Bsin(2x).
Substituting this in the differential equation, we get A = 0 and B = -1/8.
So, the particular solution is y = -1/8sin(2x).
Therefore, the final solution in terms of familiar elementary functions is y = (1/2)sin(2x) - (1/8)sin(2x) = (3/8)sin(2x).
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7) Compute the derivative of the function m(x) = -5xğ · V(x2 – 9)3. =
The answer for the derivative of m(x) is:
m'(x) = -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)
This is the final result after applying the product rule and the chain rule.
By use the product rule and the chain rule how we find the derivative?We can use the product rule and the chain rule to find the derivative of the function
First, let's break down the function as follows:
[tex]m(x) = -5x^2 · V(x^2 – 9)^3[/tex][tex]= -5x^2 · (x^2 – 9)^3/2[/tex]
Using the product rule, we have:
[tex]m'(x) = [-5x^2]' · (x^2 – 9)^3/2 + (-5x^2) · [(x^2 – 9)^3/2]'[/tex]Taking the derivative of the first term:
[tex][-5x^2]' = -10x[/tex]Taking the derivative of the second term using the chain rule:
[tex][(x^2 – 9)^3/2]' = (3/2)(x^2 – 9)^(3/2-1) · 2x[/tex][tex]= 3x(x^2 – 9)^(1/2)[/tex]
Putting it all together:
[tex]m'(x) = -10x · (x^2 – 9)^(3/2) + (-5x^2) · 3x(x^2 – 9)^(1/2)[/tex][tex]= -10x(x^2 – 9)^(3/2) - 15x^3(x^2 – 9)^(1/2)[/tex]
To compute the derivative of a function, we need to apply the rules of differentiation, which include the product rule and the chain rule. In this case, we have a product of two functions, [tex]-5x^2[/tex] and [tex]V(x^2 – 9)^3[/tex], where V represents the square root. We apply the product rule to differentiate the two functions.
The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product, u(x) · v(x), is given by u'(x) · v(x) + u(x) · v'(x). We use this rule to differentiate the two terms in the product.For the first term, [tex]-5x^2[/tex], the derivative is straightforward and is simply -10x.
For the second term, [tex]V(x^2 – 9)^3[/tex], we need to use the chain rule because the function inside the square root is not a simple polynomial. The chain rule states that if we have a function g(u(x)), where u(x) is a function of x, then the derivative of g(u(x)) is given by g'(u(x)) · u'(x). In this case, we have [tex]g(u(x)) = V(u(x))^3[/tex], where [tex]u(x) = x^2 – 9[/tex]. We need to apply the chain rule with [tex]g(u) = V(u)^3[/tex] and [tex]u(x) = x^2 – 9[/tex].
To apply the chain rule, we first take the derivative of the function [tex]g(u) = V(u)^3[/tex] with respect to u. The derivative of [tex]V(u) = u^(1/2[/tex]) is [tex]1/(2u^(1/2))[/tex].
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A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.
A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.
To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Identify the longest side. In this case, it's the side with length 7 cm.
Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²
Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²
Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²
Compare the results:
49 cm² = 49 cm²
Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.
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Help me find the Equation
The required quadratic function is y = -17/324 (x-12)(x-48)
What is the Graph of a function?The graph of a function is a visual representation of the relationship between the input values (often referred to as the "domain") and the output values (often referred to as the "range") of the function. The graph is typically drawn on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.
The graph of the function is in the image below:
The domain is (12,48)
Range: (0, 17)
The maximum value is 17
Axis of symmetry: x = 30
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Stewart, Oswaldo, Kevin, and Flynn go to a soccer day at the FC Dallas' arena, Toyota Stadium, in Frisco, Texas. The coach has a computer and video system that can track the height and distance of their kicks. All four soccer players are practicing up-field kicks, away from the goal. Stewart goes first and takes a kick starting 12 yards out from the goal. His kick reaches a maximum height of 17 yards and lands 48 yards from the goal. Oswaldo goes next and the computer gives the equation of the path of his kick as y=-= +148 - 24, where y is the height of the ball in yards and x is the horizontal distance of the ball from the goal line in yards. After Kevin takes his kick, the coach gives him a printout of the path of the ball Hegy Kevin's Kick Finally, Flynn takes his kick but the computer has a problem and can only give him a partial table of data points of the ball's trajectory. Flynn's Table: Distance from the 10 11 12 13 14 15 16 17 18 19 20 goal line in yards Height in yards 0 4.7 8.75 12.2 15 17.2 18.75 19.7 20 19.7 18.75 The computer is still not working but Stewart, Oswaldo, Kevin, and Flynn want to know who made the best kick. For each soccer player, • Write an equation to represent the quadratic function. • Create a graph to represent the quadratic functions • Identify the following: Domain o Range Maximum value (height) Axis of Symmetry x-intercepts Which soccer player made the best kick? Whose kick went the highest? Whose kick went the longest? Explain your answer and support with reasoning.
Create a number pattern that follows the rule x + 7. Include 3 terms using the pattern
The number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.
To do this, let's start with an initial value for x, and then generate the next two terms using the given pattern.
Step 1: Choose an initial value for x. Let's say x = 1.
Step 2: Apply the rule x + 7 to find the first term: 1 + 7 = 8.
Step 3: For the second term, use the first term as the new x: 8 + 7 = 15.
Step 4: For the third term, use the second term as the new x: 15 + 7 = 22.
So, the number pattern that follows the rule x + 7, including 3 terms using the pattern, is: 8, 15, 22.
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The probability of spinning an odd number , not flipping heads , then not spinning a 6 is _?
The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40
Multiply the three probabilities in order to get the compound probability:
Probability = favorable outcome / total number of outcome
Probability of getting an odd number
favorable outcome = 5
Total number of outcome = 10
P(odd number)= 5/10 = 1/2
Probability of not getting filling head
Favorable outcome = 1
P( not flipping heads)= 1/2
Probability of not getting a 6
favorable outcome = 9
P(not spinning a 6)= 9/10
= 1/2×1/2×9/10
= 9/40
The probability of spinning an odd number , not flipping heads , then not spinning a 6 is 9/40
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In the following equation, what is the value of c?
8^c = (8^-4)^5
The figure shown is composed of two congruent triangles and a square Measurements are given in inches 6 in 5 in 4 in A 5 in What is the total area of the figure in square inches 5 in 4 in 5 in
Answer:
60 square inches
Step-by-step explanation:
Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up
Solve the right triangle. Round decimal answers to the nearest tenth.
G
14
H
?
J
16
HJ~
m angle G ~
m angle J~
The required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.
What is Right angled triangle?A triangle with two sides that are perpendicular to one another is known as a right triangle, right-angled triangle, or orthogonal triangle. It was previously known as a rectangled triangle. Trigonometry is based on the relationship between the right triangle's sides and other angles.
According to question:Given data
GH = 14 units and GJ = 16 units
Using Pythagorean theorem;
[tex]16^2 = 14^2 + HJ^2[/tex]
[tex]HJ = \sqrt{16^2-14^2}[/tex]
HJ = √60
HJ = 2√15 units
And
Cos(G) = 14/16 = 7/8
∠G = cos⁻¹(7/8)
∠G = 67.5 Degrees
And
Sin(J) = 14/16 = 7/8
∠J = Sin⁻¹(7/8)
∠J = 61.04 degree
Thus, required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.
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Given square ertn, what is the length of nt?
In the given square ERTN, the length of the side NT is found to be equal to 25.
The square ERTN has ER = 5x and RT = 10x - 25. Because it is a square, the sides will be equal in magnitude. So, we can write,
Length of ER = Length of RT
5x = 10x - 25
5x = 25
x = 25/5
x = 5
So, the length of ER will be 5(5) = 25 and the length of RT will be 10(5)-25 = 25.
So, finally the length of NT would also be equal to 25.
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