To calculate the cost of each tile, we need to first determine the volume of each tile. The length and width of the tile are given as 16 inches, and the thickness is given as 1/4 inches, which can be converted to 0.25 inches. Therefore, the volume of each tile is 16 x 16 x 0.25 = 64 cubic inches.
Next, we need to determine the weight of gold in each tile. Since the density of gold is 11.17 ounces per cubic inch, the weight of gold in each tile is 64 x 11.17 = 715.68 ounces.
Finally, we can calculate the cost of each tile by multiplying the weight of gold by the price of gold per ounce. The price of gold is given as $1,303.80 per ounce, so the cost of each tile is 715.68 x $1,303.80 = $933,526.78. Rounded to the nearest dollar, each tile will cost $933,527.
In summary, each square tile made of solid gold and measuring 16 inches long and 1/4 inches thick will cost approximately $933,527. This cost is based on the density of gold, which is 11.17 ounces per cubic inch, and the price of gold, which is $1,303.80 per ounce.
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Select the best real-world situation that can be represented by 12 + c = 13. 50
Adding 12 apples to a basket initially containing c apples results in a total of 13.50 apples.
How can a real-world situation be represented by the equation 12 + c = 13.50?
The equation 12 + c = 13.50 can represent a real-world situation of purchasing items at a store and calculating the total cost. In this scenario, let's assume that 12 represents the price of a particular item, and c represents the additional cost, such as taxes or fees.
The equation states that when the additional cost is added to the base price of 12, the total cost becomes 13.50. This can occur when there is a sales tax or an additional charge applied to the base price. By solving the equation for c, we find that the additional cost is 1.50.
Therefore, in this situation, the real-world interpretation is that the item costs 12 dollars, and the additional cost, such as taxes, is 1.50 dollars, resulting in a total cost of 13.50 dollars.
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How to find the area of a tier
_________________________________
A = L × B × H = 22ft × 4ft × 6ft = 528ft²_________________________________
Can someone how to use a TI-84 Plus to do the following:
Normal Distribution: Finding Values
Normal Distribution: Finding Probibilities
Sampling Distributions and the Central Limit Theorem
!!!!I have a test on this tmr please help!!!!
Normal Distribution: Finding Values
Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "Normalcdf" and press enter.
Enter the lower bound, upper bound, mean, and standard deviation. For example, if you want to find the probability that X is between 60 and 70, given that the mean is 65 and the standard deviation is 5, you would enter "60, 70, 65, 5".
Press enter to get the result. The calculator will give you the probability that X falls between the two values you entered.
Normal Distribution: Finding ProbabilitiesPress the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "InvNorm" and press enter.
Enter the probability you want to find. For example, if you want to find the z-score that corresponds to the 90th percentile, you would enter "0.9".
Enter the mean and standard deviation. For example, if the mean is 65 and the standard deviation is 5, you would enter "65, 5".
Press enter to get the result. The calculator will give you the z-score that corresponds to the probability you entered.
Sampling Distributions and the Central Limit Theorem: Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "1-PropZTest" or "2-PropZTest" and press enter, depending on the type of test you want to perform.
Enter the sample statistics and the population parameters, if known. The calculator will use these values to calculate the test statistic and p-value.
Press enter to get the result. The calculator will give you the test statistic and the p-value, which you can use to make inferences about the population.
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Show that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f.
To show that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f, we can use the Comparison Test. Let's choose a series that is easier to compare to, such as Σ(1/2n^3).
First, note that 0 ≤ f(n) ≤ 1 for all n, since f is a function that is not negative and bounded by 1. Thus, we have: 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3, Now, we can compare the given series to the series Σ(1/2n^3) using the Comparison Test. Since 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3 for all n, we know that: 0 ≤ Σα) f(n)/2n^3 - 1 n ≤ Σ(1/2n^3), The series Σ(1/2n^3) is a convergent p-series with p = 3 > 1, so by the Comparison Test, the given series Σα) f(n)/2n^3 - 1 n also converges. Therefore, we have shown that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f.
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Term 1: 1 + 1×4 = 5 Term 2: 1 + 2x4 = 9 Term 3: 1 + 3x4 = 13 1.4.1. Term 4: 144x4 = 17 1.4.2. Term 5: 1 +5XL = 21 1.4.3. Term 10:+10X4=4/ 1.4.4. Term 50: 1450 xy = 201 1.5. What stays the same in the pattern in (1.4.1. - 1.4.4.) and what varies? (2)
The polynomial x²+xy+y² has 3 terms. Option C is correct.
We have,
A polynomial is an algebraic statement made up of variables and coefficients.
Variables are sometimes known as unknowns. We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.
Given polynomial;
⇒x²+xy+y²
The three terms are as follows;
x²
xy
y²
The polynomial x²+xy+y² has 3 terms.
Hence, option C is correct.
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complete question:
How many terms does the polynomial x² + xy y2 have?
1 term
2 terms
3 terms
4 terms
Line m is represented by the equation
y +2=
3/2(x + 4). select all equations that represent lines perpendicular to
line m.
oa.
y= -3/2x + 4
oь.
y= -2/3x + 4
oc.
y= 2/3x + 4
od.
y= 3/2x + 4
oe.
y+1= -4/6(x+5)
of.
y + 1= 3/2(x+5)
The equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.
The equation of line m is given as y + 2 = (3/2)(x + 4). To determine the equations that represent lines perpendicular to line m, we need to find the negative reciprocal of the slope of line m and use it as the slope in the perpendicular lines.
The slope of line m is (3/2), so the negative reciprocal is -2/3. We can eliminate options oa, oб, and of because they do not have a slope of -2/3.
Now, let's check the remaining options:
oc: y = (2/3)x + 4
This equation has a slope of 2/3, which is not the negative reciprocal of -2/3. Therefore, it is not perpendicular to line m.
od: y = (3/2)x + 4
This equation has the same slope as line m, which means it is not perpendicular to line m.
oe: y + 1 = (-4/6)(x + 5)
Simplifying the equation, we get y + 1 = (-2/3)(x + 5), which has a slope of -2/3. Therefore, this equation represents a line that is perpendicular to line m.
Therefore, the equation oe: y + 1 = -4/6(x + 5) represents a line perpendicular to line m.
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The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the interval on which the distribution is defined. true or false
True. In a continuous uniform distribution, all values within a specified interval are equally likely to occur. The mean or expected value of this distribution can be found by taking the average of the upper and lower limits of the interval.
This can be represented mathematically as (a+b)/2, where a and b are the lower and upper limits of the interval. For example, if we have a continuous uniform distribution on the interval [0,10], the mean value would be (0+10)/2 = 5.
This means that on average, we would expect a randomly selected value from this distribution to be around 5. It's important to note that the mean of a continuous uniform distribution is not affected by the shape or spread of the distribution, as all values have an equal chance of occurring.
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SPEEDBOAT RACE Speedboats race around four buoys in the lake on a rectangular course. If the total length of the course is 2.4
kilometers and the ratio of the length to the width is 2:1, what are the length and width of the course?
length:
width:
Let's represent the width of the rectangular course as $w$. Then the length of the rectangular course can be represented as $2w$, since the ratio of the length to the width is given as 2:1.
We know that the total length of the course is 2.4 kilometers, so we can write an equation:
$\sf\implies\:2w + 2(2w) = 2.4$
Simplifying the equation:
$\sf\implies\:6w = 2.4$
$\sf\implies\:w = \frac{2.4}{6}$
$\bigstar\implies\sf{\textbf{\boxed{w = 0.4}}}$
Therefore, the width of the course is 0.4 kilometers.
The length of the course is $\sf\:2w = 2(0.4)=$
${\boxed{\sf{0.8 kilometers.}}}$
Hence, the length of the course is 0.8 kilometers and the width of the course is 0.4 kilometers.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
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When estimating population parameters, a point estimate is: group of answer choices the population mean a statistic that estimates a population parameter a range of possible values for a population parameter always equal to a population value
When estimating population parameters, a point estimate is: a population parameter
What is a point estimatePoint estimates are statistical estimates used to approximate population parameters such as mean, proportion or variance that remain unknown.
They provide one value as an approximation for unknown parameters in a population sample that may or may not match up exactly with true population value; nevertheless they serve as reasonable approximations.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex] Thus, option D is correct.
What is the quadratic equation?the quadratic equation [tex]2x^2+12x-3=0$ is \ $x = \frac{-6 \pm \sqrt{42}}{2}[/tex], which simplifies to [tex]$x = -3 \pm \frac{\sqrt{42}}{2}$.[/tex]
However, the three options listed are the steps that Inga could use to solve the quadratic equation, and only three of them are correct. The correct options are:
[tex]$2\left(x^2+6 x\right)=-3$[/tex]
[tex]$2\left(x^2+6 x\right)=3$[/tex]
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
Option 1 is the result of dividing both sides of the original equation by 2, which simplifies the coefficients.
Option 2 is the result of adding $\frac{3}{2}$ to both sides of the equation to isolate the quadratic terms. Option 3 is the final step, where the equation is solved for $x$ by completing the square and taking the square root of both sides.
Therefore, it is not one of the three steps that Inga could use to solve the quadratic equation. [tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
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Inga is solving [tex]$2 x^2+12 x-3=0$.[/tex] Which steps could she use to solve the quadratic equation? Select three options.
[tex]$2\left(x^2+6 x+9\right)=3+18$[/tex]
[tex]$2\left(x^2+6 x\right)=-3$[/tex]
[tex]$2\left(x^2+6 x\right)=3$[/tex]
[tex]$x+3= \pm \sqrt{\frac{21}{2}}$[/tex]
You put $4500 into an account earning 6% interest compounded annually.
Write an equation to model the situation
The equation of this model situation with $4500 into an account earning 6% interest compounded annually is 4500(1.06)ᵗ.
The equation to model the situation would be:
A = P(1 + r/n)ⁿᵗ
where A is the amount of money in the account after t years, P is the initial investment (which is $4500), r is the interest rate (which is 6% or 0.06 as a decimal), n is the number of times the interest is compounded per year (in this case, annually), and t is the number of years.
Plugging in the values, the equation becomes:
A = 4500(1 + 0.06/1)ⁿᵗ
Simplifying further, it becomes:
A = 4500(1.06)ᵗ
This equation can be used to find the amount of money in the account after any number of years.
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You should always measure your following distance in.
You should always measure your following distance in seconds. The correct answer for measuring following distance is A.
It is important to keep a safe distance between vehicles on the road, which is known as following distance. Measuring following distance in seconds is a more reliable method than measuring it in car lengths or feet.
The recommended following distance is typically two to three seconds. This means that when the vehicle in front of you passes a fixed point on the road, you should not reach that same point before two to three seconds have elapsed.
Measuring in seconds is more effective as it takes into account the speed at which both vehicles are traveling. If you measure in car lengths or feet, it may not be accurate as the length of the cars may differ, and it does not account for the speed of the vehicles. By measuring in seconds, you can maintain a safe distance and reduce the risk of accidents or collisions.
The correct answer for measuring following distance is A.
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Complete question is:
You should always measure your following distance in __________
A. seconds. B. car lengths. C. feet.
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting. How much will Nicole make after babysitting for 8 hours?
Answer:
Sure. Here is the equation for the cost, C, after h hours of babysitting:
```
C = 3 + 5h
```
This equation can be found by combining the flat fee of $3 with the hourly rate of $5. For example, if Nicole babysits for 2 hours, she will make $3 + (2 * $5) = $13.
To find how much Nicole will make after babysitting for 8 hours, we can simply substitute h = 8 into the equation. This gives us:
```
C = 3 + 5(8) = 3 + 40 = $43
```
Therefore, Nicole will make $43 after babysitting for 8 hours.
Answer:c= 3 + 5(8)
Step-by-step explanation:
3 is flat fee, and then plus $5 and hour. you know she's going for 8 hours, so you multiply hourly rate by the number of hours plus flat fee and you get your answer
A funnel is in the shape of a cone with a radius of 4 inches and a height of 10 inches.
a. Find the volume of the funnel. Round your answer to the nearest tenth.
b. The funnel is filled with oil. How many quarts of oil are in the funnel? (1 qt ≈ 58 in. ³) Round your answer to the nearest tenth
a. The volume of the funnel is 167.6 in³.
b. The amount in quarts of oil are there in the funnel is approximately 2.9 quarts.
a. To find the volume of a cone, you can use the formula V = (1/3)πr²h, where r is the radius and h is the height. Substituting in the values given, we get V = (1/3)π(4 in)²(10 in) ≈ 167.6 in³. Rounded to the nearest tenth, the volume of the funnel is 167.6 in³.
b. To convert cubic inches to quarts, we need to divide by the conversion factor of 58 in³/qt. So, V = 167.6 in³ ÷ 58 in³/qt ≈ 2.9 qt. Rounded to the nearest tenth, there are approximately 2.9 quarts of oil in the funnel.
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Milan bought a table for rs 3600 he sells it to kirtim at a profit of rs 205 kritim sells it at rs 4968 to aayush find the percentage profit of kritim
Kritim's percentage profit is 8.5%.
Milan bought the table for Rs 3600 and sold it to Kritim at a profit of Rs 205. Hence, Kritim paid Rs 3600 + Rs 205 = Rs 3805 for the table. Kritim then sold the table to Aayush for Rs 4968.
To find Kritim's profit percentage, we need to calculate the profit percentage on the cost price. The cost price for Kritim is Rs 3805, and the selling price is Rs 4968. Hence, the profit earned by Kritim is Rs 4968 - Rs 3805 = Rs 1163.
Profit percentage = (Profit / Cost price) x 100%
Profit percentage = (1163 / 3805) x 100%
Profit percentage = 0.3055 x 100%
Profit percentage = 30.55%
Therefore, Kritim's profit percentage is 8.5%.
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7) A tree casts a shadow that is 10 feet long. 5 foot woman standing nearby casts a shadow that is 4 feet long. How tall is the tree?
Answer:
12.5 ft
Step-by-step explanation:
x/10=5/4
4x=5(10)
4x=50
x=12.5
a popular TV series is running for 10 seasons. You are buying the seasons from an online DVD service. If each season arrives at random, what is the probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order?
The probability that the first 5 seasons you receive in the mail are the first 5 seasons that were made, in the correct order is given as follows:
p = 1/30240.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
5 seasons are going to be shown from a set of 10, and the order is relevant, hence the permutation formula is used to obtain the total number of outcomes, as follows:
P(10, 5) = 10!/5!
P(10, 5) = 30240.
Only one of the outcomes has the correct seasons and order, hence the probability is given as follows:
p = 1/30240.
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Qn in attachment . ..
Answer:
Step-by-the answer is (a) 16
Roxie plans on purchasing a new desktop computer for $1250. Which loan description would result in the smallest amount of interest she would have to pay?
12 months at 6. 25% annual simple interest rate
18 months at 6. 75% annual simple interest rate
24 months at 6. 5% annual simple interest rate
30 months at 6. 00% annual simple interest rate
For a purchase of a new desktop computer for $1250, loan description that would result in the smallest amount of interest she would have to pay is 12 months at 6. 25% annual simple interest rate. Therefore, the correct option is option 1.
To determine which loan description results in the smallest amount of interest for Roxie, we'll calculate the interest for each option using the simple interest formula:
Interest = Principal × Rate × Time.
1. 12 months at 6.25% annual simple interest rate:
Interest = $1250 × 6.25% × (12/12)
Interest = $1250 × 0.0625 × 1
Interest = $78.13
2. 18 months at 6.75% annual simple interest rate:
Interest = $1250 × 6.75% × (18/12)
Interest = $1250 × 0.0675 × 1.5
Interest = $126.56
3. 24 months at 6.5% annual simple interest rate:
Interest = $1250 × 6.5% × (24/12)
Interest = $1250 × 0.065 × 2
Interest = $162.50
4. 30 months at 6.00% annual simple interest rate:
Interest = $1250 × 6.00% × (30/12)
Interest = $1250 × 0.06 × 2.5
Interest = $187.50
Comparing the interest amounts, the smallest interest is for the first option, 12 months at 6.25% annual simple interest rate, with an interest amount of $78.13.
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Which expression is equivalent to 24+30?
A. 6(4+5)
B. 6(4+6)
C. 8(3+4)
D. 8(3+12)
Please i need an answer to this
Answer:
A
Step-by-step explanation:
6x4 = 24
6x5 = 30
24+30
:)
Answer:
A.) 6(4+5)
Step-by-step explanation:
*Solve the parenthesis first: 4+5 = 9
*Next, multiply 6×9= 54
Which of the following is the graph of y = StartFraction 1 Over x + 2 EndFraction + 1?
Based on the information provided, the one that is the correct graph is "On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2..." (option 2).
How to identify the correct graph?The graph of y = StartFraction 1 Over x + 2 EndFraction + 1 is the second option described: On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrants 1 and 4. It crosses the x-axis at (3, 0). The other curve opens down and to the left and it crosses the y-axis at (0, negative 1.5).
This graph has a vertical asymptote at x = 2 and a horizontal asymptote at y = 1. It is a hyperbola that opens up and to the right in quadrants 1 and 4. The curve crosses the x-axis at x = 3, which means that when y = 0, x = 3. The other curve opens down and to the left and it crosses the y-axis at y = -1.5, which means that when x = 0, y = -1.5.
Note: This question is incomplete; here is the complete question:
Which of the following is the graph of y = StartFraction 1 Over x + 2 EndFraction + 1?
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrant 1. The other curve opens down and to the left and it crosses the x-axis at (1, 0).
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = 2. One curve opens up and to the right in quadrants 1 and 4. It crosses the x-axis at (3, 0). The other curve opens down and to the left and it crosses the y-axis at (0, negative 1.5).
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1 and 2. It crosses the y-axis at (0, 1.5). The other curve opens down and to the left and it crosses the x-axis at (negative 3, 0).
On a coordinate plane, 2 curves are shown. Both curves have an asymptote at x = negative 2. One curve opens up and to the right in quadrants 1, 2, and 4. It crosses the x-axis at (negative 1, 0). The other curve opens down and to the left in quadrant 3.
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Ac is a diameter of d. if mbdc = 150°, what is the measure of ab?
this is due today so if anyone can answer this in the next 5-15 minutes that would be great!
We know that the measure of AB is 240°.
Given that AC is a diameter of D and MBDC = 150°, we know that angle ABC is a right angle (90°) because it is inscribed in a semicircle.
Using the fact that the sum of angles in a triangle is 180°, we can find angle MBC:
MBC + 150° + 90° = 180°
MBC = -60°
Since angle MBC is negative, we know that it must actually be 360° - 60° = 300°.
Finally, using the fact that angles on a straight line add up to 180°, we can find angle ABM:
ABM + MBC = 180°
ABM + 300° = 180°
ABM = -120°
Again, since angle ABM is negative, we know that it must actually be 360° - 120° = 240°.
Therefore, the measure of AB is 240°.
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Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive? Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families. Use Scratchpad to illustrate both studentsâ solutions
This will show that each family gets 5/16 of a pizza.
Sure, I'd be happy to help you with your question!
So, Savannah and Josiah read the following problem in their math class: Five rectangular pizzas were shared equally by 4 families. How much pizza did each family receive?
Savannah and Josiah solve the problem differently. Savannah gives each family 1 whole pizza and then divides the remaining pizza among the 4 families. Josiah divides all of the pizzas into fourths and then shares the fourths equally among the 4 families.
To illustrate both students' solutions, we can use Scratchpad. For Savannah's solution, we can draw 5 rectangular pizzas and then divide them into 4 equal parts each. Then, we can shade in 1 whole pizza and divide the remaining pizza equally among the 4 families. This will show that each family gets 1 whole pizza and a quarter of a pizza.
For Josiah's solution, we can draw 5 rectangular pizzas and then divide each pizza into fourths. Then, we can divide the fourths equally among the 4 families.
This will show that each family gets 5/16 of a pizza.
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Question 2 < Σ Use integration by parts to evaluate the integral: + 10x – 9)e *dx = 4.1 f(x²
The value of integral ∫(x^2+10x-9)e^-4x dx is (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.
To evaluate the integral ∫(x^2+10x-9)e^-4x dx using integration by parts, we need to choose two functions to multiply together, one of which we differentiate and the other we integrate. A common choice is to let u = x^2+10x-9 and dv = e^-4x dx, which gives du = (2x+10) dx and v = (-1/4)e^-4x.
Using the formula for integration by parts, we have:
∫(x^2+10x-9)e^-4x dx = uv - ∫v du
= (-1/4)(x^2+10x-9)e^-4x - ∫(-1/4)(2x+10)e^-4x dx
= (-1/4)(x^2+10x-9)e^-4x + (1/2)∫(x+5)e^-4x dx.
Now we can use integration by substitution to evaluate the second integral on the right-hand side:
(1/2)∫(x+5)e^-4x dx = (-1/8)(x+5)e^-4x - (1/32)e^-4x + C,
where C is the constant of integration.
Substituting this back into our previous equation, we get:
∫(x^2+10x-9)e^-4x dx = (-1/4)(x^2+10x-9)e^-4x - (1/8)(x+5)e^-4x - (1/32)e^-4x + C.
Thus, we have found the antiderivative of the integrand using integration by parts, up to a constant of integration.
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Complete question is:
Use integration by parts to evaluate the integral: ∫(x^2+ 10x – 9)e ^-4x dx
A scale drawing of a famous statue uses a scale factor of 240:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
288 feet
241.2 feet
238.8 feet
200 feet
The height of the statue is 288 feet.
The scale factor is 240:1
Or, the ratio of the height of the statue to the height of the drawing = 240:1.
This means, for 1 unit height of drawing, the height of the statue = 240 units
Or, for 1 feet height of the drawing, the height of the statue = 240 feet.
Let us suppose the actual height of the statue to be x.
The height of the drawing = 1.2 feet (given)
So, the ratio of the height of the statue to the height of the drawing = x/1.2
But, the scale factor = 240:1 = 240/1
∴ 240/1=x/1.2
⇒x=240×1.2
⇒x=288
Hence, the height of the statue is 288 feet.
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√x+3
a.3x^1/2
b.(x+3)^1/2
c.x^1/2+3
d.(3x)^1/2
Answer:
b
Step-by-step explanation:
The expression √x+3 means the square root of x+3. We can rewrite this as (x+3)^(1/2), using the exponent rule that says taking the square root is the same as raising to the power of 1/2.
So the options become:
a. 3x^(1/2)
b. (x+3)^(1/2)
c. x^(1/2) + 3
d. (3x)^(1/2)
None of the other options match the given expression. So the correct answer is (b) (x+3)^(1/2).
7. The Key West Lighthouse is 86 feet tall. What is the height of the lighthouse in meters?
The height of the Key West Lighthouse in meters is approximately 26.21 meters.
Here's how you can calculate it:
- There are 3.28 feet in a meter.
- Divide the height of the lighthouse in feet by the number of feet in a meter: 86 ÷ 3.28 = 26.21 meters (rounded to two decimal places).
- Therefore, the height of the Key West Lighthouse in meters is approximately 26.21 meters.
A bunch of flowers originally cost $32. It goes on sale at 25% off the original price.
Fill in the blanks.
Original percentage:
Percentage off:
Percentage left over:
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = ----------% x $32
Original percentage: 100%
Percentage off: 25%
Percentage left over: 75%
Complete the number sentence to show how to find the sale price of the bunch of flowers:
Sale price = (100% - 25%) x $32 = 75% x $32 = $24
Zachary says that the equation 0 = (x – 4)(x – c) has one unique real number solution. What must be the value of c for his statement to be true?
c = 4
Answer:
c=4
Step-by-step explanation:
as there is only one solution for this quadratic equation which is supposedly have 2 or more answers, c can only be 4 in order to be the same equation as the the first one x-4=0
A group of friends wants to go to the amusement park. They have no more than $
365 to spend on parking and admission. Parking is $16. 25, and tickets cost $38. 75 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.
The group of friends can consist of at most 9 people, given the budget constraint and pricing can go to the amusement park.
The inequality to determine the number of people who can go to the amusement park can be written as: 38.75p + 16.25 ≤ 365.
Where p represents the number of people and the left-hand side of the inequality represents the total cost of admission and parking for p people.
The inequality is set up such that the total cost cannot exceed the given budget of $365.
To solve this inequality, we can first subtract 16.25 from both sides: 38.75p ≤ 348.75. Then, divide both sides by 38.75: p ≤ 9
To determine the maximum number of people who can go to the amusement park with a given budget,
we can write and solve an inequality based on the cost of parking and admission per person.
In this case, the inequality is 38.75p + 16.25 ≤ 365, and the solution is p ≤ 9.
Learn more about inequality here:
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