The derivative of the given function is,
dy/dx = 3y(1-lnx)/x²
The given expression,
y = \(x^{(3/x)\)
We have to differentiate it by using logarithmic
So take log both sides we get,
⇒ ln y = ln \(x^{(3/x)\)
⇒ ln y = (3/x) ln x
Now differentiate it with respect to x
⇒ (d/dx)(lny) = (d/dx)[(3/x) ln x]
Use rule of differentiation of product of two functions,
⇒ (1/y) dy/dx = (3/x)(d/dx) lnx + ln x (d/dx)(3/x)
= 3/x² - ln x (3/x²)
= 3(1-lnx)/x²
⇒ (1/y) dy/dx = 3(1-lnx)/x²
⇒ dy/dx = 3y(1-lnx)/x²
Hence, derivative be,
dy/dx = 3y(1-lnx)/x²
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A recipe uses 5 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can be made from three quarts?
Answer: 24 servings
Step-by-step explanation:
First and foremost, we should note that:
4 cups = 1 quart
Therefore, 3 quarts = 3 × 4 cups = 12 cups
Since she uses 5 cups of milk to make 10 servings, it means that 1 cup of milk is used to make 2 servings. Therefore, 12 cups would be used to make:
= 12 × 2
= 24 servings.
Use the algebra tiles tool to model the equation
5x + (–6) = 6x + 4. What is needed to model the equation? Check all that apply.
- 5 negative x-tiles on the left
- 6 positive x-tiles on the right
- 4 positive unit tiles on the right
- 6 negative x-tiles on the right
- 6 negative unit tiles on the left
Answer:b,c,e
Step-by-step explanation:
I got it on edg 2020
Answer:
B C D
Step-by-step explanation:
Kai has 4 bags of marbles .there are 3 red,5 green,2 yellow,and 6 black marbles in each bag. How many marbles does kai have? Show how you found the answer
Answer:
The correct answer is 64 marbles.
Step-by-step explanation:
Let's analyze the information we have:
Jill has 4 bags of marbles.
In each bag she has 16 marbles (in each one she has 3red, 5green, 2 yellow, and 6black)
If each bag has 16 marbles, and she has 4 bags, then we must multiply the contents of each bag by 4.
And we do it as follows:
16 x 4 = 64
Therefore, we can say that Jill has 64 marbles.
Answer:
There is 16 in each bag so there is 64 marbles in total.
Step-by-step explanation:
3 + 2 = 5
5 + 5 = 10
10 + 6 = 16
16 x 4 (16 + 16+ 16+ 16) = 64
Shanika purchased 5 nail polishes for $21.25. At this rate, how much would she pay for 1 bottle?
tubes of oil paint are on sale for $0.50 off. cody bought 6 tubes of paint on sale and paid a total of $25.80. write and solve an equation to find r, the regular price in dollars of each tube of oil paint.
0.50 off of each
6 tubes bought
So, saved
0.50 * 6 = $3
Paid 25.80 total for 6 of them (after sale). Saved $3. So, regularly it costed:
25.8 + 3 = $28.80
6 cost 28.80, so 1 cost:
28.80/6 = $4.80
Regular Price of each tube = $4.80 (r)
Note: Equation >>>
\(25.80+6\mleft(0.5\mright)=6r\)A triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. What is the length of the third side?
If a triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. The length of the third side is 16.
How to find the length?Let x km represent the length of the third side
Let Length of other two sides is 12 km and 20 km.
Hence,
Perimeter of triangle = Sum of all sides = 48 km
12 + 20 + x = 48
32 +x = 48
x = 48 - 32
x = 16
Therefore we can conclude that the length of the third side is 16.
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Additive area
What is the total area
A.70 square feet
B.27 square feet
C.30 square feet
D.35 square feet
I will mark you as brainliest if you get it correct
B, 27 ft²
2*3 + 7*3 = 27
but for this one you could just actually count the tiles
PLZ HURRY will give BRAIN-LY-EST and 20 points if correct
Answer:
\({ \boxed{ \tt{4x + 4x \: → \: 8x}}} \\ \\ { \boxed{ \tt{3x + 5x + 8 \:→ \: 8x + 8 }}} \\ \\ { \boxed{ \tt{ - 7x + 4 + 3x \: → \: - 4x + 4}}} \\ \\ { \boxed{ \tt{4x + 4x + 4x + 4x \: → \: 16x}}}\)
Answer:
4x + 4x → 8x
3x + 5x + 8 → 8x + 8
-7x + 4 + 3x → -4x + 4
4x + 4x + 4x + 4x → 16x
Step-by-step explanation:
The left side consists of a series of expressions and the right side is the list of choices to match to. This is simple math if you already know how to combine like terms. Combining like terms is combining numbers that represent the same value. Take a look at 4x + 4x for example, 4x and 4x are two numbers with the same value. Not that they both have the number 4, but that they have the same special variable. If there are two or more numbers with the same variable like x for example, combine the two, meaning you add the numbers. Just don't add the variables because clearly, the variable is an unknown number so you can't add variables. Instead, you can apply the same variable to the sum of two or more numbers. So 4x + 4x equals 8x. Do the same process again to the other 3 expressions. Also, you can't add a number with a variable to a number alone. They don't represent the same value.
3x and 5x are the same value so combine them. Now you only have 8x + 8 left as the simplified version of the expression.
-7x and 3x are the same value so combine them. Don't forget that the 7 is negative. Use a calculator if needed. Now you only have -4x + 4 as the simplified version of the expression.
Similar to 4x + 4x in the first expression, just add all of the numbers up. There isn't a number alone in this expression. 16x should be your final answer.
I hope this helps! Let me know if I am wrong. :D
Write the following as a number: minus one thousand, eight hundred and five point nine six.
The final number is a decimal number which is equal to -1805.96.
It is given to us that the set of expression is given by -
minus one thousand, eight hundred and five point nine six.
We have to write the given expression as a number.
According to the given information we see that there is a "point" word in the expression. This implies that the final number will be a decimal number.
So, from the given information, we can represent the number as -
-1805.96
Thus, the final number is a decimal number which is equal to -1805.96.
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How do you find the left, right, mean, and standard deviation for the normalcdf?
To find the left, right, mean, and standard deviation for the normalcdf, you can follow these two steps:
Find the mean and standard deviation of the normal distribution. Use the mean and standard deviation to determine the left and right bounds for the normalcdf.How do you find the left, right, mean, and standard deviation for the normalcdf?Finding the mean and standard deviation of the normal distribution.The mean of the normal distribution is denoted by μ (mu), and the standard deviation is denoted by σ (sigma). If you have been given the mean and standard deviation, you can skip this step. If not, you need to calculate these values.
For example, let's say you are given the following normal distribution:
X ~ N(50, 10)
Here, the mean is 50, and the standard deviation is 10.
Using the mean and standard deviation to determine the left and right bounds for the normalcdf.Once you have the mean and standard deviation, you can use them to determine the left and right bounds for the normalcdf.
The left bound is the smallest value in the range of values that you are interested in. The right bound is the largest value in the range of values that you are interested in.
For example, let's say you want to find the area under the normal distribution between x = 40 and x = 60. To do this, you need to find the left and right bounds.
Using the mean and standard deviation from Step 1:
μ = 50
σ = 10
To find the left bound, you subtract the mean from the left endpoint
left bound = 40 - μ = 40 - 50 = -10
To find the right bound, you subtract the mean from the right endpoint:
right bound = 60 - μ = 60 - 50 = 10
So the left and right bounds for the normalcdf are -10 and 10, respectively. You can then use these values to find the area under the normal distribution using a calculator or statistical software.
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Each turn in a game, you randomly draw a card from a deck and replace it.
The table shows the number of times you draw each type of card. How
many times can you expect to not draw a point card in 25 turns?
Answer:
20
Step-by-step explanation:
3 is 20% of 15
5 is 20% of 25
so 25 - 5 is 20
for each group in the following list, find the order of the group and the order of each element in the group. what relation do you see between the orders of the elements of a group and the order of the group?
The relation which we see between the orders of the elements of a group and the order of the group is smallest positive power.
G = U(20), order of each element of G = ?
The smallest positive power of an element that gives you your identity is the order of the element in a group. Three instances are covered: complex numbers, a 2x2 rotation matrix, and real number elements of finite order.
G = U(20) = {1,3,7,9,11,13,17,19}
⇒ 3° ≡ 1, 3¹ ≡ 3, 3² ≡ 9, 3³ ≡ 7, 3¹ ≡ 1(20)
∴ order of 3 = 4
7⁴ ≡ 1 (mod 20) → order (7) = 4
9² ≡ 1 (mod 20) → order (9) = 2
11² ≡ 1 (mod 20) → order (11) = 2
13² ≡ 9(mod 20) → 13⁴ ≡ 81(mod 20) → 13⁴ ≡ 1 (mod 20)
⇒ order (13) = 4
order 07 = 4
17 ≡-3(mod 20) ⇒ 17² ≡ yy (mod 20)
⇒ 17⁴ ≡ 81 (mod 20) ≡ 1 (mod 20) ⇒
19 = -1 (mod 20)
19² ≡ 1 (mod 20) ⇒ order (19) = 2
Hence we get the requires answer.
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A movie theater uses five pounds of butter for their popcorn each day. After six days how many pounds of butter would they have used?
On a road trip, John covers 400 miles in 8 hours, including stops. If he maintains the same pace, how far (to the nearest mile) will he be from his starting point after 15 hours of driving?
Answer: 750 miles
Step-by-step explanation:
From the question, we are informed that on a road trip, John covers 400 miles in 8 hours, including stops. This means that John for every hour, John covers 50 miles (400/5).
For 15 hours of driving, John will have covered:
= 15 × 50miles
= 750 miles
A man took a loan of rs 12,000 with simple interest for as many years as the rate of interest per year.If he paid rs 3,000 as interest at the end of loan period,what was the rate of interest?
A man took a loan of rs 12,000 with simple interest for as many years as the rate of interest per year.If he paid rs 3,000 as interest at the end of loan period. The rate of interest is 5%.
Simple interest is the interest charged on a credit taken.
Simple interest is given by S.I=PRT/100
Substituting the values, we get
3000=12000×t×t/100
t²=25
t=5(ignoring negative value)
So the rate of interest is 5%
What is the rate of interest?
The rate of inetrest is the amount charged by the lender to the borrower over the principal amount.It is paid in addition to the principal amount.Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.To learn more about the rate of interest visit:
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Write the equation in slope-intercept form for the line that is perpendicular to the line y = -3x - 8 that passes through the point (-3, 1).
The equation in slope-intercept form for the line that is perpendicular to the line y = -3x-8 that passes through (-3,1) is y = x/3+2.
According to the question,
We have the following information:
The line is y = -3x-8
Points are (-3,1).
Now, we know that the slope, denoted by m, in this equation is -3.
Now, the slope for the perpendicular line is -1/m.
So, the slope is 1/3.
Now, the equation that can be found using the given information is:
(y-y') = m(x-x')
y' = 1 and x' = -3
(y-1) = 1/3 [x-(-3)]
(y-1) = 1/3(x+3)
(y-1) = x/3 +1
y = x/3 + 1 +1
y = x/3+2
Hence, the equation in slope-intercept form is y = x/3+2.
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2. assume you are taking two courses this semester (a and b). the probability that you will pass course a is 0.835, the probability that you will pass both courses is 0.276. the probability that you will pass at least one of the courses is 0.981.2(c). what is the probability that you will pass course b given that you pass course a?
The probability that you will pass course B is 0.422
No, the passing of the two courses independent events P(A) * P(B) = 0.35237.
It's not mutually exclusive events.
Given that,
Let's say you're enrolled in two classes each this semester, A and B.
The probability that you will pass the course a is 0.835, the probability that you will pass both courses is 0.276, the probability that you will pass at least one of the courses is 0.981
Now, we need to solve the following conditions;
(a) What is the probability that you will pass course B?
P(A) = 0.835
P( A ∩ B) = 0.276
P( A ∪ B) = 0.981
P(B) = P(A ∪ B) - P(A) + P(A ∩ B)
= 0.981 - 0.835 + 0.276
= 0.422
(b) Use statistical data to support your conclusion as to whether the passing of the two courses constitutes independent events.
No,
P(A ∩ B) != P(A) * P(B)
P(A) * P(B) = 0.422* 0.835
= 0.35237
P( A ∩ B) = 0.276
(c)Are the activities required to pass the courses exclusive,
P(A ∩ B) ! =0, it's not mutually exclusive events
Therefore, The probability that you will pass course B is 0.422
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whatis the product of the polynomials below?
Hey there! :)
Answer:
C. \(16x^{4}+ 16x^{3} - 12x^{2} - 32x-16\)
Step-by-step explanation:
Starting with:
(8x² - 4x - 8)(2x² + 3x + 2)
Begin multiplying the first equation by each of the second equation's terms:
2x²(8x² - 4x - 8) + 3x(8x² - 4x - 8) + 2(8x² -4x - 8)
Distribute:
\(16x^{4}- 8x^{3}- 16x^{2} + 24x^{3} - 12x^{2} - 24x + 16x^{2} - 8x -16\)
Simplify by combining like terms:
\(16x^{4}+ 16x^{3} - 12x^{2} - 32x-16\)
Therefore, the correct answer is C.
Answer: C i had a similar question like yours and got it right! :)
Jonathan went for a jog every time he stops to tie his shoelaces, his jog last. 2 1/2 minutes longer . if he stops to tie his shoelaces four times how much longer does his jog take?
Answer:
10 minutes longer
Step-by-step explanation:
2 1/2 (or 2.5) times 4 equals 10.
40% of the instruments in an orchestra of 125 are strings. How many string insruments are there?
The answer is 50.
First, you convert 40% into a decimal. This would be 0.4.
Then, you multiply 0.4*125. That’s when you get your answer
I will mark brainliest
Whats the correct simplification of d^7g^13/d^2g^7
Answer for ten points!
Answer:
4x+y
Step-by-step explanation:
6x-2x=4x
3y-2y=1y
1y can be written as just y
Do all real numbers have a decimal expansion?
Select from the drop-down menus to correctly complete each statement.
Choose...
real numbers have a decimal expansion. The decimal forms of some real numbers, like 1/9,
Choose...
, while the decimal forms of other real numbers, like 2/5,
Choose...
. Still other real numbers, like 13−−√, have decimal forms that
Choose...
.
Yes, all real numbers have a decimal expansion. A decimal expansion is the representation of a real number in the base-10 numeral system.
It involves writing the integer part of the number, followed by a decimal point, and then the decimal part. The decimal part consists of an infinite sequence of digits, which may repeat or terminate. For example, the real number 1/9 has a decimal expansion of 0.111111..., where the digits 1 repeat infinitely. On the other hand, the real number 2/5 has a decimal expansion of 0.4, which terminates after one digit. Even irrational numbers like 13−−√ have decimal expansions, albeit non-repeating and non-terminating. For example, the decimal expansion of 13−−√ is approximately 3.605551275464... It is important to note that every real number has a unique decimal expansion, although some numbers may have more than one way of being expressed in decimal form.
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A sliding puzzle is a grid of 9 squares with 8 tiles. The goal is to get the 8 tiles into order (the target configuration). A move slides a tile into an empty square. Below, we show first a row move, then a column move. Prove that no sequence of moves produces the target configuration. [Hint: The tiles form a sequence going left to right, top to bottom. An inversion is a pair that is out of order. Prove by induction that the number of inversions stays odd.] USE INDUCTION
By using induction, it can be proven that the number of inversions (pairs of tiles out of order) remains odd throughout any sequence of moves in a sliding puzzle. Therefore, it is impossible to reach the target configuration since it has an even number of inversions.
To prove that no sequence of moves produces the target configuration in a sliding puzzle, we can use mathematical induction. The base case is when the puzzle is initially in the target configuration, which has zero inversions. Zero is an even number.
Now, let's assume that at any given state, the number of inversions in the puzzle configuration is odd. We need to show that after any move, the resulting configuration still has an odd number of inversions.
A move in the sliding puzzle consists of sliding a tile into an empty square. This can be done either horizontally (row move) or vertically (column move). In either case, the relative order of the tiles remains the same, and only one pair of tiles swaps their positions.
Considering the two possible moves separately, we can observe that a row move affects the number of inversions in the same row, while a column move affects the number of inversions in the same column. In both cases, the number of inversions changes by an odd number (either -1 or +1).
By induction, if the initial configuration has an odd number of inversions, and each move changes the number of inversions by an odd amount, it follows that every subsequent configuration will also have an odd number of inversions. Since the target configuration has an even number of inversions, it cannot be reached through any sequence of moves in the sliding puzzle.
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If we subtract half of a number from 20, we get 10, then the number equals; a) -20 b) 60 c) 20 d) -60
Answer:
Step-by-step explanation:
let the number be x
20-x/2=10
40-x=20
40-20=x
x=20
A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5? OA) yes: The packs of socks are marked up to $7 and then discounted to $5. OB) yes; The packs of socks are marked up to $9 and then discounted to $5. OC) no: The packs of socks are marked up to $7 and then discounted to $4.20. OD) no, The packs of socks are marked up to $5.20 and then discounted to $4.99.
Answer:
C) no: The packs of socks are marked up to $7 and then discounted to $4.20
Step-by-step explanation:
You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.
Marked-up priceWhen the $5 cost is marked up by 40%, the resulting price is ...
$5 + 0.40×5 = $5 +2 = $7.
The socks are marked up to $7.
Marked-down priceWhen the $7 price is marked down by 40%, the resulting price is ...
$7 - 0.40×7 = $7.00 -2.80 = $4.20
The socks are discounted to $4.20.
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(4, 5) , B (12, 9) ; 3 to 1
The coordinates of P are…?
For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).
As given in the question,
Given:
Line segment AB with coordinates A( 4,5) and B(12, 9)
Line segment AB divided by point P in the ratio AP : PB = 3: 1
Let (x ,y) be the coordinates of point P .
Coordinates of A(4,5) = ( x₁, y₁)
B(12,9) = (x₂ , y₂)
Ratio m : n = 3 : 1
Coordinates of point P is given by:
x = (mx₂ + nx₁)/ ( m+ n)
= [3(12) + 1(4)] / (3+1)
= ( 36 +4)/ 4
= 40 /4
= 10
x = (my₂ + n y₁)/ ( m+ n)
= [3(9) + 1(5)] / (3+1)
= ( 27 +5)/ 4
= 32/4
= 8
P(x ,y) = P(10, 8)
Therefore, For the line segment AB with coordinates A( 4,5) and B(12, 9) divided by point P in the ratio AP : PB = 3 : 1 then coordinates of P are ( 10,8).
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A triangle has side lengths of 34 in., 28 in., and 42 in. Is the triangle acute, obtuse, or right?
The triangle having 34 in, 28 in, and 42 is an obtuse triangle
To determine the type of a triangle, whether it is an acute, obtuse, or right angles triangle, the application of the Pythagorean theorem is required.
The Pythagorean theorem formula is
A²= B²+C²
In an acute triangle, the square of the length of the hypotenuse will be less than the sum of the squares of the other two sides In an obtuse triangle, the square of the length of the hypotenuse side will be greater than the sum of the squares of the other two sides In right-angled triangles, the square of the length of the hypotenuse side will be equal to the sum of the squares of the otherGiven that the 3-side length is 28,34 and 42
substituting it in the formula we get:
34² + 28² = 1856 and then he bought
42² = 1764
Since 1764 is less than 1856, we can conclude that the triangle is obtuse.
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Find k so that x + 2 is a factor of x ^ 3 - k * x ^ 2 + 2x + 7k. (If anyone could help me out with this that would be amazing!!)
Answer:
k = 4
Step-by-step explanation:
If x + 2 is a factor of the polynomial;
By the factor theorem, if we set x + 2 = 0, then make x the subject of the formula; if we substitute the value into the polynomial, the result we should have after calculating should be zero
So, we have it that;
x + 2 = 0
x = -2
Substitute into the polynomial and equate to zero
(-2)^3 - k (-2)^2 + 2(-2) + 7k = 0
-8 -4k -4 + 7k = 0
-12 -4k + 7k = 0
-12 + 3k = 0
-3k = -12
k = -12/-3
k = 4
PLS HELP I NEED ANSWER ASAP!
PPLS BE RIGHT!
Answer:
They used 6 vans and 3 buses
Step-by-step explanation:
x + y= 9
13x + 40y= 198
x= 9 - y
13(9 - y) + 40y= 198
117 - 13y + 40y= 198
27y= 81
y= 3
9-3= 6