The answer is B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.
To solve this problem, we are given a function h(x) and asked to find its antiderivative or indefinite integral, which is denoted by H(x) and is defined as the function whose derivative is h(x). We are also given a specific value of H(x) at x = 6 and asked to use it to find the constant of integration, denoted by C.
The given function is h(x) = 22x - 3x² - 6/x, and we want to find H(x), which is the antiderivative of h(x). Using the power rule of integration, we can integrate each term of h(x) separately:
∫ (22x - 3x² - 6/x) dx = ∫ 22x dx - ∫ 3x² dx - ∫ 6/x dx= 11x² - x³ - 6ln|x| + Cwhere C is the constant of integration. Note that we need to include an absolute value sign around x in the natural logarithm term because the function is not defined for x = 0.
Next, we are given that H(6) = 31, which means that when x = 6, the value of H(x) is 31. Substituting x = 6 and H(x) = 31 into the above equation, we get:
31 = 11(6)² - (6)³ - 6ln|6| + CSimplifying, we get:
31 = 132 - 216 - 6ln(6) + CC = 221/3 - 6ln(6)Therefore, the antiderivative of h(x) is:
H(x) = 11x² - x³ - 6ln|x| + 221/3 - 6ln(6)We can simplify the expression by using the identity ln|a/b| = ln|a| - ln|b|:
H(x) = 11x² - x³ - 6ln(3) - 6ln(x) + 2ln(3) + Cwhere C is the constant of integration. Thus, the final answer is:
B) - (11x² - 6x)ln(3) + 2ln(3) - 6ln(x) + C, where C is the constant of integration.To learn more about integration, here
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Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
71.38 in word form is Seventy-one and thirty-eight hundredths.
What is the decimal number?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.
To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.
For example: 0.25 can be written as "zero and twenty-five hundredths"
Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.
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A sales person in the stereo store is given a choice of two different compensation plans. One plan offers a weekly salary of $250 plus a commission of $25 for each serial sold. The other plan offers no salary will pays $50 commission on each stereo sold her daughter plan offers no celer sales person in the stereo store is given a choice of two different compensation plans
10 stereos must the salesperson sell to make that same amount of money under both plans.
How many stereos must the salesperson sell ?Assume that in order for the salesperson to earn the same amount of money under both schemes, x stereos must be sold.
The salesperson will be paid a salary of $250 + $25 for each stereo sold under the first strategy. So, these are the total earnings:
First plan's total profits are $250 plus $25.
Instead of receiving a salary under the second proposal, the salesperson would be compensated with a $50 commission for each stereo sold. So, these are the total earnings:
Total income under the second plan equals $50x
We can set the two equations for total earnings to be equal in order to determine the value of x:
$250 + $25x = $50x
When we simplify the equation, we obtain:
$250 = $25x
x = 10
The sales person must thus sell 10 stereos in order to.
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4 m - (30cm+40mm)=………………m
Answer:
3.966m
Step-by-step explanation:
4m - (30cm + 40mm)
Converting cm and mm to metre by dividing by 100 and 1000 respectively
=> 4.000m - (30/100 m + 40/1000 m)
=> 4.000m - (0.030m + 0.004m)
=> 4.000m - 0.034m
=> 3.966m
Answer:
3.66m
Step-by-step explanation:
First, we have units measured in meters, centimeters, and millimeters. This means we have to convert everything to the same measurement.
The easiest way is to convert everything to meters, as that's what the unit in the final answer will be.
To convert centimeters to meters, divide by 100
30/100=0.3
To convert millimeters to meters, divide by 1,000
40/1000=0.04
Next, plug the values back into the original equation:
4m-(0.3+0.04)
solve the parenthesis first
4-0.34
3.66
So, this equals 3.66 meters.
Hope this helps! :)
Persevere with Problems Triangle XYZ is reflected across the x-axis to produce triangle X'Y'Z'. Then triangle X'Y'Z' is rotated 90° counterclockwise about the origin to create triangle X''Y''Z''. If triangle X''Y''Z'' has vertices X''(4, 0), Y''(2, –1), and Z''(2, 1), what are the coordinates of the vertices of triangle XYZ? Write your answers as integers.
The vertices of triangle XYZ are (-4, 0), (1, -2), and (-2, 1).
How to calculate the verticesWe are given that X''(4, 0), Y''(2, -1), and Z''(2, 1). We can use these coordinates to determine the coordinates of the vertices of triangle XYZ.
Starting with X, we have (-y, x) = (4, 0). This implies that y = 0 and x = -4.
Moving on to Y we have (-z, y) = (2, -1). This implies that z = -2 and y = 1.
Finally, for Z, we have (-x, z) = (2, 1). This implies that x = -2 and z = 1.
Therefore, the vertices of triangle XYZ are (-4, 0), (1, -2), and (-2, 1).
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1. A triangle, △DEF, is given. Describe the construction of a circle with center C circumscribed about the triangle. (3-5 sentences)
2. ⊙O and ⊙P are given with centers (−2, 7) and (12, −1) and radii of lengths 5 and 12, respectively. Using similarity transformations on ⊙O, prove that ⊙O and ⊙P are similar
This circle with center C will be circumscribed around triangle △DEF, touching each vertex. The translated and dilated ⊙O will coincide with ⊙P, proving that they are similar.
1. To construct a circle with center C circumscribed about triangle △DEF, first find the perpendicular bisectors of all three sides of the triangle. Next, locate the point where the three perpendicular bisectors intersect, which will be the center C of the circumscribed circle. Finally, draw the circle using the distance from point C to any vertex of the triangle as the radius.
2. To prove that ⊙O and ⊙P are similar using similarity transformations on ⊙O, follow these steps:
a. Translate ⊙O by the vector <-2+12, 7-(-1)> or <10, 8> so that its center coincides with the center of ⊙P. The translated ⊙O will have the center (10, 15).
b. Since the ratio of the radii of ⊙O and ⊙P is 5:12, perform a dilation of ⊙O with a scale factor of 12/5 and center (10, 15). The dilated ⊙O will have a radius of 12, which is equal to the radius of ⊙P.
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What type of triangle would be represented by the vertices (1, 3), (4, -1), and (5, 6)?
Brenton invested an average of $250 per month since age 39 in various securities for his retirement savings. His investments averaged a 6% annual rate of return unitl he retired at age 66. Given the same monthly investment and rate of return, how much more would Brenton have in his retirement savings had he started investing at age 25? Assume monthly compounding.
44,520. 00
79,500. 00
292,795. 72
330,027. 55
Brenton would have $330,027.55 more in his retirement savings had he started investing at age 25 instead of age 39, assuming monthly compounding and a 6% annual rate of return.
Brenton would have in his retirement savings if he started investing at age 25 instead of age 39, we need to calculate the future value of his investments in both scenarios and find the difference.
We'll use the formula for the future value of a series of equal payments (annuity) compounded monthly:
[tex]FV = P * (((1 + r)^nt - 1) / r)[/tex]
Where FV is the future value, P is the monthly payment ($250), r is the monthly interest rate (0.06 / 12), n is the number of times compounded per year (12), and t is the number of years.
Scenario 1 (investing since age 39):
t = 66 - 39 = 27 years
[tex]FV1 = 250 * (((1 + 0.06/12)^(12*27) - 1) / (0.06/12))[/tex]
FV1 ≈ $292,795.72
Scenario 2 (investing since age 25):
t = 66 - 25 = 41 years
[tex]FV2 = 250 * (((1 + 0.06/12)^(12*41) - 1) / (0.06/12))[/tex]
FV2 ≈ $622,823.27
Now, find the difference between the two scenarios:
Difference = FV2 - FV1
Difference ≈ $622,823.27 - $292,795.72
Difference ≈ $330,027.55
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In building a brick staircase, we need 200 bricks for the bottom step and 84 bricks for the top step. If, beginning with the bottom step, each successive step requires four fewer bricks, how many bricks will be required to build the staircase?
The number of bricks that will be required to build the staircase is: 30 bricks
How to find the nth term of an arithmetic sequence?An arithmetic sequence is defined as one where you get the next term by adding a constant, called the common difference, to the previous term. A lot of formulas come from this simple fact. and they allow us to solve for any term in the sequence and even the sum of the first few terms.
The formula for the nth term of an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where:
a₁ is first term
d is common difference
n is nth term
We are given:
a₁ = 200
d = -4
aₙ = 84
Thus:
84 = 200 + (n - 1)(-4)
84 - 200 = -4n + 4
-4n = -120
n = 30
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9. castle black camping is twice as risky as the average stock. the market should earn 11% and the risk free rate is 2%. what is a fair return for cbc? (20%)
10. harlan county safety co. has a beta of 1.2. form a portfolio that is half hcsc and half cbc (from number 9). what is a fair return? (16.4%)
The fair return for Castle Black Camping (CBC) is 20%.
This is calculated by subtracting the risk-free rate (2%) from the market's expected return (11%), and then multiplying the result by 2 (since CBC is twice as risky as the average stock).
To form a portfolio that is half Harlan County Safety Co. (HCSC) and half CBC, we need to calculate the portfolio's beta. This is done by multiplying each stock's beta by its weight in the portfolio, and then adding the results. In this case, the portfolio's beta would be 0.6 (1.2 x 0.5 + 2 x 0.5).
The fair return for the portfolio is then calculated by adding the risk-free rate to the product of the portfolio's beta and the market's expected return. This gives us a fair return of 16.4% for the HCSC and CBC portfolio.
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Help me please!
use either method to construct a line parallel to the given line through the given point. gl 3.1)
a lab 1 question 1
To construct a line parallel to a given line through a given point, there are two methods that can be used: the ruler and compass method or the parallel line equation method.
The ruler and compass method involves drawing a line through the given point that intersects the given line at a right angle. Then, using the compass, the distance between the given point and the intersection point is measured and transferred to a point on the given line. Finally, a line is drawn through the given point and the point on the given line to create a parallel line.
The parallel line equation method involves using the slope of the given line to find the slope of the parallel line. This is done by recognizing that parallel lines have the same slope. Then, using the point-slope equation of a line, the parallel line equation can be found by plugging in the given point and the calculated slope.
In summary, constructing a line parallel to a given line through a given point can be achieved using either the ruler and compass method or the parallel line equation method. Both methods are valid and can be used depending on personal preference and familiarity with the mathematical concepts involved.
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If P = (1,1), Find:
Rx=5 (P)
([?], []
The coordinate of the image point is (9,1).
There are eight types of rules for the transformation of a point. When the takes place across a line, then the point (x,y) is changed to the point (y,x).
Given that the rule for the transformation of a point P(1,1) is [tex]R_{x=5} (P)[/tex], which defines the reflection of a point about a line, that is parallel to the y-axis. The line [tex]x=5[/tex] is like a mirror. So, the distance between the line and the image point is equal to the distance between the line and the original point.
Using the point-line distance formula, the distance between the line [tex]x=5[/tex] and a point (1,1) is given by [tex]|5-1|=4[/tex].
Similarly, by the above statement, the distance between the line [tex]x=5[/tex] and the image point will also be 4.
Therefore, the coordinate of the image point is (9,1).
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The complete question is -
If P = (1,1), then find the reflection [tex]R_{x=5} (P)[/tex].
A waiter had five tables he was waiting on, with three women and three men at each table. How many customers total did the waiter have?
The total number of customers that the waiter had would be = 30 customers.
How to calculate the total number of customers?The total number of tables the waiter had = 5 tables
The total number of women at each table = 3
The total number of men at each table = 3
The total number of people one each table = 6
Therefore the total number of customers that the waiter attended to would be = 5×6 = 30
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After 16 years in an account with a 6.2% annual interest rate compounded continuously, an investment is worth a total of $58,226.31. What is the value of the principal investment? Round the answer to the nearest penny.
$21,737.59
$21,592.31
$36634.00
$36488.72
Answer:
Principal = $21,592.31
Step-by-step explanation:
The formula for continuous compound interest is
[tex]A = Pe^r^t[/tex], where A is the amount (aka investment worth), r is the interest rate, and t is the time in years (the number e simply shows us that we're dealing with continuous compound interest)
Since we're already given that have A = $58,226.31, r = 0.062 (we must convert the percentage to a decimal by simply moving the decimal two places to the left, which is the same as dividing by 100), and t = 16 years, we can simply solve for P:
[tex]58226.31=Pe^(^0^.^0^6^2^*^1^6^)\\58226.31=Pe^0^.^9^9^2\\58226.31/(e^0^.^9^9^2)=P\\21592.31176=P\\21592.31=P[/tex]
Almost all employees working for financial companies in New York City receive large bonuses at the end of the year. A sample of employees selected from financial companies in New York City showed that they received an average bonus of last year with a standard deviation of. Construct a confidence interval for the average bonus that all employees working for financial companies in New York City received last year.
Round your answers to cents.
$________ to _______ $
To construct a confidence interval for the average bonus that all employees working for financial companies in New York City received last year, we need to know the sample size and the level of confidence. Without this information, we cannot calculate the confidence interval. Please provide the sample size and the level of confidence to proceed with the solution.
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Jenny is planning an extended trip to russia.the table below shows a list of cities which she would like to visit during her stay, along with the amount of money she anticipates needing to spend on travel, lodging, and similar expenses in each city. all costs are given in russian rubles (rub). city cost (rub) izhevsk 4,721 novosibirsk 4,870 nizhny novgorod 6,920 moscow 5,485 chelyabinsk 5,217 saint petersburg 5,960 tolyatti 5,598 yaroslavl 4,901 even though jenny wants to go to each of these cities, her budget is only rub 33,000, so she recognizes that she must change her itinerary and choose not to visit some cities. which of the following pairs of cities will not put jenny back under budget if she drops them? a. moscow and chelyabinsk b. izhevsk and nizhny novgorod c. novosibirsk and saint petersburg d. yaroslavl and tolyatti
The pairs of cities that will not put Jenny back under budget if she drops them are:
a. Moscow and Chelyabinsk
b. Izhevsk and Nizhny Novgorod
To determine which pair of cities Jenny can drop without going over budget, we need to find the total cost of each pair and see if it exceeds her budget of rub 33,000.
a. Moscow and Chelyabinsk:
Total cost = 5,485 + 5,217 = 10,702 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Moscow and Chelyabinsk.
b. Izhevsk and Nizhny Novgorod:
Total cost = 4,721 + 6,920 = 11,641 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Izhevsk and Nizhny Novgorod.
c. Novosibirsk and Saint Petersburg:
Total cost = 4,870 + 5,960 = 10,830 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
d. Yaroslavl and Tolyatti:
Total cost = 4,901 + 5,598 = 10,499 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
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A triangle as a base of 20 ft and a height of 3 yd. What is its area?
(DOES NOT HAVE A PICTURE)
(PLS HELP!!!)
Answer: 90 feet squared
Step-by-step explanation:
The formula for finding the area of a triangle is
(bxh)/2
In this problem, you need to convert 3 yards to feet. The conversion is as follows:
1 yard = 3 feet
Therefore, 3 yards = 9 feet.
You can then plug everything in and solve as follows:
20x9= 180
Then divide 180 by 2.
180/2=90
Answer:[tex]90ft^{2}[/tex]
Step-by-step explanation:
Area of a triangle: A=(bh)/2
b = 20 ft
h = 3 yds = 9ft
Plug in
A=[(20ft)(9ft)]/2
A=180ft/2
A=90ft^2
Amelie has 385 muffins that she must package into boxes. Each box must hold 9 muffins. Amelie divides 385 by 9 and gets an answer of 42 R 7. What is the correct interpretation of R 7 for this situation?
In Amelie's situation, the remainder of 7 indicates that she has 7 muffins left over that cannot be packed into a full box of 9.
When Amelie divides the total number of muffins (385) by the number of muffins per box (9), she obtains a quotient of 42 and a remainder of 7. The quotient represents the number of complete boxes that Amelie can fill with 9 muffins each, while the remainder represents the number of muffins that cannot be put into a full box.
In other words, the quotient tells us how many full boxes Amelie can pack, and the remainder tells us how many muffins are left over after packing all the full boxes. In this case, Amelie can pack 42 full boxes, each with 9 muffins, which totals to 378 muffins. The remaining 7 muffins cannot fill a full box, and they are left over after all the full boxes are packed.
The "R 7" notation is commonly used to indicate the remainder in long division problems. The letter "R" stands for "remainder," and the number following it (in this case, 7) represents the actual remainder. The remainder is important because it indicates how many items are left over after dividing them into equal-sized groups.
In Amelie's situation, the remainder of 7 indicates that she has 7 muffins left over that cannot be packed into a full box of 9.
Overall, interpreting the "R 7" in this problem helps us understand how many full boxes of muffins Amelie can pack and how many muffins are left over after packing the full boxes.
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Find the absolute maximum value on (0, [infinity]) forf(x)=4x−2xlnx.
The absolute maximum value on (0, ∞) for f(x) = 4x - 2x ln x is approximately 2e (5.436), which occurs at x = e.
To find the absolute maximum value on (0, ∞) for the function f(x) = 4x - 2x ln x, we need to follow these steps:
1. Determine the critical points of the function by finding its first derivative and setting it equal to zero.
2. Check the critical points for the maximum value.
3. Verify the behavior at the boundary of the interval (0, ∞).
Step 1: Find the first derivative of f(x).
f(x) = 4x - 2x ln x
f'(x) = d/dx (4x) - d/dx (2x ln x)
Using the product and constant rules, we get:
f'(x) = 4 - 2(ln x + 1)
Step 2: Set the first derivative equal to zero to find the critical points.
4 - 2(ln x + 1) = 0
2(ln x + 1) = 4
ln x + 1 = 2
ln x = 1
Solving for x:
x = e^1
x = e (approximately 2.718)
Step 3: Check the behavior at the boundaries.
As x approaches 0 from the right, ln x approaches negative infinity, making the term -2x ln x approach infinity. Since the interval is (0, ∞), we only need to consider the behavior as x approaches ∞. As x goes to infinity, both 4x and -2x ln x will also go to infinity. However, -2x ln x will increase at a slower rate compared to 4x, so f(x) will approach infinity.
Now, we need to check the value of f(x) at the critical point x = e:
f(e) = 4e - 2e ln e
f(e) = 4e - 2e(1)
f(e) = 2e (approximately 5.436)
Thus, the absolute maximum value on (0, ∞) for f(x) = 4x - 2x ln x is approximately 5.436, which occurs at x = e.
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If I lose 20 cents an hour, and I make 10. 50 an hour. How much money do I lose every 10 dollars?
This is the simplest way I could figure out how to put it, sorry
You lose 515 dollars every time you lose 10 dollars.
Now that we know it takes 50 hours to lose 10 dollars, we can calculate how much money you lose every 10 dollars by
the hourly rate of 10.50 dollars by 50 hours and subtracting that amount from 10 dollars:
Money lost = (10.50 dollars/hour) x 50 hours - 10 dollars
Money lost = 525 dollars - 10 dollars
Money lost = 515 dollars
Therefore, you lose 515 dollars every time you lose 10 dollars.
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Wesley makes spherical fish tanks with a diameter of 30cm. Kate requests a smaller tank with half the volume of the tank that Wesley usually makes. Kate tried to figure out the approximate diameter of the smaller tank, but she made a mistake. In which step did Kate first make her mistake?
Kate's mistake was in Step 2: "Divide the volume of Wesley's tank by 2." Since she wants a tank with half the volume of Wesley's tank, she should have divided the volume of Wesley's tank by 2, not the radius.
How to determine which step did Kate first make her mistakeThe correct approach would be to use the formula for the volume of a sphere:
V = (4/3)πr^3
Since Wesley's tank has a diameter of 30 cm, its radius is 15 cm. Substituting this value into the formula gives:
V = (4/3)π(15)^3
V ≈ 14,137 cm^3
To find the radius of the smaller tank with half the volume, Kate should have solved for the radius using the formula for the volume of a sphere:
(4/3)πr^3 = (1/2)(4/3)π(15)^3
Simplifying this equation gives:
r^3 = (1/2)(15)^3
r ≈ 10.8 cm
Therefore, the approximate diameter of the smaller tank should be 21.6 cm (twice the radius), not 10.8 cm.
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Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum
The common ratio for the geometric series 1, 1/2, 1/4, 1/8, ... is 1/2 and the sum of series is 2 which is finite.
To determine whether the series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is:
S = a/(1-r),
where a is the first term and r is the common ratio.
In this case, a = 1 and r = 1/2, so
S = 1/(1 - 1/2) = 2.
Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
The common ratio of a geometric series is the ratio between consecutive terms. For example, in the series 1, 2, 4, 8, 16, ..., the common ratio is 2 because each term is obtained by multiplying the previous term by 2.
To determine whether a geometric series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is S = a/(1-r), where a is the first term and r is the common ratio.
If the value of r is between -1 and 1 (excluding -1), then the series has a finite sum. If the value of r is greater than 1 or less than -1, then the series has an infinite sum.
In the given series 1, 1/2, 1/4, 1/8, ..., the common ratio is 1/2. To find the sum of the series, we can use the formula S = a/(1-r) with a=1 and r=1/2, which gives S=2. Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
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complete question:
Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum 1,1/2,1/4,1/8....
question in picture
Answer:
Trapezoid--------------------
First, plot the points and connect together in the given order.
See attached.
As we can see all sides are of different length but two sides seem to be parallel.
Let's find the slopes of segments BC and AD and compare:
m(BC) = (3 - 5)/(5- 1) = - 2/4 = - 1/2m(AD) = (- 8 - (-4))/(5 - (-3)) = - 4 / 8 = - 1/2As se see the slopes are same, so BC and AD are parallel.
Since we have a pair of parallel sides, the quadrilateral is a trapezoid.
Mark and Diane pay a rate of 43. 7 mills in property tax. The assessed value of the home is $74,000. What is their property tax?
Mark and Diane's property tax is $3,231.80.
To calculate the property tax for Mark and Diane, we need to multiply the assessed value of their home by the tax rate.
First, we need to convert the tax rate from mills to a decimal. One mill is equal to one-tenth of one cent or 0.001 dollars. Therefore, 43.7 mills is equal to 0.0437 dollars.
Next, we can calculate the property tax as follows:
Property tax = Assessed value × Tax rate
Property tax = $74,000 × 0.0437
Property tax = $3,231.80
Therefore, Mark and Diane's property tax is $3,231.80.
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A charity donates 40% of its proceeds to a local food bank. If the charity raised £1000, how much money did the food bank receive?
Answer:
£400
Step-by-step explanation:
first find 40% of £1000
40\100*1000
=400
Therefore answer is £400
Raj tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Find the present ages of Raj and his daughter. Also, verify the present age of Raj and his daughter graphically
The present ages of Raj and his daughter are respectively: 42 years and 12 years.
How to solve Algebra Word Problems?Present Age of Raj =y years
Present Age of daughter =x years
According to Question :
7 Years ago,
y − 7 = 7(x − 7)
⇒ 7x − y − 42 = 0.............(1)
And 3 Years from now
y + 3 = 3(x + 3)
⇒ 3x − y + 6 = 0............(2)
From eq (1) and eq (2)
Subtract eq 2 from eq 1 to get:
7x − 3x − y + y − 42 − 6 = 0
⇒ 4x = 48
⇒ x = 12
Putting x = 12 in Equation (2). we get,
(3 × 12) − y + 6 = 0
⇒ y = 42
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Traffic Jam
There are 8 cans of strawberry jam, 7 raspberry jam,
and 5 cherry jam in the cellar. You're trying to sneak
some out, but don't want to attract attention or take
too many. It's dark, so you can't tell what kind of jam
you're taking.
How many cans can you sneak out of the
cellar in the dark with the certainty that there
will still be at least 4 cans of one kind of jam
and 3 cans of another left over?
Answer:
Hey!
You could obviously count how many you're taking, so that's 7 left behind. My guess is that you could taste the jam... but that's the best I've got.
The requreid we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
What is arithmetic?It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Let's first find the minimum number of cans that need to be left in the cellar to meet the given criteria. We want at least 4 cans of one kind of jam and 3 cans of another leftover. This means we can take a maximum of:
8 - 4 = 4 cans of strawberry jam
7 - 3 = 4 cans of raspberry jam
5 - 3 = 2 cans of cherry jam
So, we can take a maximum of 4 + 4 + 2 = 10 cans in total.
To have certainty that we meet the criteria, we need to take one less than the maximum number of cans, which is 9 cans. So, we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
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if integrate f(x) dx = 1/3 * x ^ 3 - 2x ^ 2 + 3x - 5 then the value of f(-2) = ...
A. -9
B. -1
C. 7
D. 15
E. 23
please
pleasee
The value of f(-2) is 15.
Hence option D is correct.
The given expression is
[tex]\int\limits {f(x)} \, dx[/tex] = (1/3)x³ - 2x² +3x - 5
To find expression of f(x)
Differentiate it with respect to x
f(x) = x² - 4x + 3
Now put x = -2
f(-2) = (-2)² - 4(-2) + 3
= 4 + 8 + 3
= 15
Hence,
f(-2) = 15
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Sarah is saving for a vacation. she kept track of how much she saved each month over the last six months in the following table. what did sarah save per month on average? sep oct nov dec jan feb $135.00 $144.00 $104.00 $80.00 $90.00 $160.00 a. $118.80 b. $119.50 c. $713.00 d. $118.83
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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A ninja star, or shuriken, is usually constructed using four congruent isosceles triangles that are placed along the sides of a square. What is the value of x?
a.) 46
b.) 56
c.) 62
d.) 118
The measure of angle x of the ninja star is given by x = 56°
Given data ,
Let the ninja star be represented as an isosceles triangle
Now , it is constructed using four congruent isosceles triangles that are placed along the sides of a square
And , the vertex angle of the triangle is x
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
So , the measure of x = 180° - ( 62° + 62° )
On simplifying , we get
x = 56°
Hence , the angle of triangle is x = 56°
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find the value of x.
Answer:
x ~= 61.0°
Step-by-step explanation:
This is a trig question. The marked angle is unknown so we will use an inverse trig function to find a missing angle. On your calculator you may need to use the 2nd button or shift to get not just "cos" but the inverse cos. It might look like cos with a -1 exponent or "arccos" or "acos"
So the triangle is a right triangle. The angle is next to one of the given sides. "Next to" is called "adjacent" these mean the same thing. One side is adjacent to the angle. The other given side is the hypotenuse.
The trig function that puts together Adjacent and Hypotenuse is cosine.
cos (angle) = adj/hyp
We know the two sides. Fill them in.
cos (angle) = 31/64
We are looking for the angle.
cos x = 31/64
Use the inverse cos to find the angle.
cos^-1 (31/64) = x
This is a calculator activity. Unless your teacher has given you tables of values (this is how it was done before calculators) you have to use a calculator.
x = 61.0284677763
round to the nearest tenth.
x ~= 61.0
