The integral using integration by parts with the indicated choices of u and dv is equal to, [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c
Basic Power Rule:
f(x) = cxⁿ
f’(x) = c· n xⁿ⁻¹
Integration
Integrals
[Indefinite Integrals] Integration Constant C
Integration Property [Multiplied Constant]:
[tex]\int\limits cf(x)dx[/tex] = c [tex]\int\limitsf(x) dx[/tex]
Integration Rule [Reverse Power Rule]:
[tex]\int\limits x^{n} dx[/tex] = [tex]\frac{x^{n+1} }{n+1}[/tex] + c
Integration by Parts:
[tex]\int\limits u dv[/tex] = uv - [tex]\int\limits v du[/tex]
Given that,
= [tex]\int\limits 5x^{2} lnx dx[/tex]
Rewrite [Integration Property - Multiplied Constant]:
[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]\int\limits x^{2} lnx dx[/tex]
Set u:
u = [tex]lnx[/tex]
[u] Logarithmic Differentiation:
du = [tex]\frac{1}{x}[/tex] dx
Set dv:
dv = [tex]x^{2}[/tex]
[dv] Integration Rule [Reverse Power Rule]:
v = [tex]\frac{x^{3} }{3}[/tex]
Integration by Parts:
[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]( \frac{x^{3}ln(x) }{3} - \int\limits \frac{x^{2} }{3} dx )[/tex]
Rewrite [Integration Property - Multiplied Constant]:
[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex](\frac{x^{3}ln(x) }{3} -\frac{1}{3} \int\limits x^{2} dx )[/tex]
Factor:
[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \int\limits x^{2} dx )[/tex]
Integration Rule [Reverse Power Rule]:
[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \frac{x^{3} }{3} )[/tex] + c
Factor:
[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c
Therefore,
The integral using integration by parts with the indicated choices of u and dv is equal to, [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c
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suppose we had a room filled with 400 people. will there be at least two people who have the same birthday? explain why or why not.
The two people who have same birthday is 1.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.Assuming no leap year
P (two people in a room and they are sharing a birthday) = 1-(364/365)
P (3 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex]×[tex]\frac{363}{365} )[/tex]
P (4 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex] ×[tex]\frac{363}{365}[/tex] ×[tex]\frac{362}{365} )[/tex]
and so on, let n people in a room.
P (n people in a room and at least two of them are sharing birthday = 1-[tex]\frac{365!}{365^n(365-n)!}[/tex] )
we find out the nearly after n = 60 this becomes equals to 1.
Therefore, the two people who have same birthday is 1.
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calculer les produit suivant en ecritures scientifiques puis les classer dans l'ordre croissant:
a) 25 000 x 280 b) 30 000 x 850
c) 72 000 x 90 d) 330 x 850 000
Answer:
c < a < b < d
Step-by-step explanation:
a) 25000 x 280, c'est 7000000
ou 7 * 10^6
b) 30000 x 850, c'est 25500000
ou 25.5 * 10^6
c) 72000 x 90, c'est 6480000
ou 6.48 * 10^6
d) 330 x 850,000, c'est 280500000
ou 280.5 * 10^6
On peut dire que l'ordre croissant est:
6.48 * 10^6 < 7 * 10^6 < 25.5 * 10^6 < 280.5 * 10^6
∴ c < a < b < d
Voilà
when a substrate concentration is much greater than km, the rate of catalysis is almost equal to:
When a substrate concentration is much greater than km, the rate of catalysis approaches Vmax.
Km is the Michaelis-Menten constant and represents the substrate concentration at which the reaction rate is half of its maximum rate, Vmax. When the substrate concentration is much greater than km, the rate of catalysis is almost equal to Vmax because the enzymes are saturated with substrate and the reaction rate is limited only by the rate of the catalytic reaction itself, not by the availability of substrate.
In other words, when the substrate concentration is high, there are enough substrate molecules to occupy all of the active sites on the enzymes, so the reaction rate is not limited by the availability of substrate. The reaction rate can only be limited by the rate of the catalytic reaction itself, which is maximum at Vmax.
Therefore, when the substrate concentration is much greater than km, the rate of catalysis approaches Vmax.
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a biologist is studying the depths of plants growing near the surface of the ocean he uses negeitive numbers to represent the depths of the plants he finds below sea level.the table shows the depths of four plants order the number from least to greatest
a) The data in ascending Order; -83/4 < -67/4 < -62/4 < -1/4.
b) Sea Grass is the furthest the Surface of water.
What is Ascending Order?Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.
Given that -20 3/4, -15 1/2, -14 3/4, -1/4
Now, the above fraction into Normal fraction;
-83/4, -31/2, -67/4, -1/4.
Now, Arranging the data in ascending Order;
-83/4 < -67/4 < -62/4 < -1/4.
b) Since Sea Grass is the furthest below the Surface of water.
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Annabelle and Eric made 17ounce of pizza dough they ue 5/8 of the pizza dough to make pizza and ue the ret to make roll what i the difference between the amount of dough they ue to make pizza and the amount of dirty ue to make roll?
The difference between the amount of dough they use to make pizza and the amount of dirty use to make roll is 4.25 ounce. The result is obtained by using calculations in fractions.
How to count a set of objects using fractions?Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.
For example:
1/4 (one-fourth)2/5 (two-fifth)It means one of four parts and two of five parts.
Annabelle and Eric made 17 ounce of pizza dough.
5/8 of the pizza dough is used to make pizza.The rest is used to make roll.Find the difference between the amount of dough they use to make pizza and the amount of dirty use to make roll!
To make pizza, the pizza dough they use is
= 5/8 × 17 ounce
= 85/8 ounce
= 10.625 ounce
To make roll, the pizza dough they use is
= 17 - 10.625 ounce
= 6.375 ounce
The difference amount of the usage is
= dough to make pizza - dough to make roll
= 10.625 ounce - 6.375 ounce
= 4.25 ounce
Hence, the difference amount of dough to make pizza and dough to make roll is 4.25 ounce.
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8. What is the equation of a polynomial function R with rational
coefficients that has a zero of 2 + √3 and -5i?
Sums of terms with the pattern k.[tex]x^{n}[/tex]—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5.
What is polynomial?A polynomial is a mathematical expression made up of coefficients multiplied by the sum of powers in one or more variables.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses solely the operations addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial of a single indeterminate x. A polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1. A polynomial is described as an expression made up of variables, constants, and exponents that are joined using mathematical operations like addition, subtraction, and multiplication.To learn more about polynomial refer to:
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Julio is buying a car. He makes a down payment of 20% and he makes arrangements to finance the remaining $14,000. What is the dollar amount of Julio's down payment?
well, we know the downpayment is 20%, so 100% - 20% = 80%, that's the remaining amount, which we know is 14000 bucks, let's say the 20% is really "x" bucks, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 14000 & 80\\ x& 20 \end{array} \implies \cfrac{14000}{x}~~=~~\cfrac{80}{20} \\\\\\ \cfrac{ 14000 }{ x } ~~=~~ 4\implies 14000=4x\implies \cfrac{14000}{4}=x\implies 3500=x[/tex]
Brandon is playing a game which he has to pull two chips from a bag without looking The bag contains 5 chips. the chips are red, green, purple, and 2 blue. what are the possible outcomes that Brandon can chose
llllllllylylylltyllylltlylltl ok bye
18
18°
χ
Find the missing side. Round to the nearest tenth.
The missing side of Right triangle will be 9.8.
What is meant by Trigonometric angles?Angles in trigonometry are those determined by the ratios of the trigonometric functions. In trigonometry, the relationship between a triangle's angles and sides is studied. The angle value is between 0 and 360 degrees. Angles 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360° are significant in trigonometry.
A subfield of mathematics called trigonometry is concerned with the study of triangles. It is sometimes known by the colloquial term "trig." In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.
We have,
Hypotenuse = 18 cm
Perpendicular = x cm
One of the angle = 33°
Using the Trigonometric angles,
[tex]$${Sin 33^{\circ}=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$[/tex]
substitute the values in the above equation, we get
So, [tex]$${Sin} 33^0=\frac{x}{18}$[/tex]
simplifying the equation, we get
[tex]$$x=18 Sin 33^0$[/tex]
x = 9.8
The missing side is 9.8.
Therefore, the missing side of Right triangle will be 9.8.
The complete question is:
Find the missing side. Round to the nearest tenth.
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Someone help fast please
Find the value of sin
W rounded to the nearest hundredth, if necessary.
Answer:
30 i believe
Step-by-step explanation:
i record the age, paint color, engine size and cost of 243 used cars in an online car dealership. the number of variables i have recorded is ?
The number of variables you have recorded for each of the 243 used cars in an online car dealership is 4.
A variable is a characteristic or attribute of an object or a set of objects that can be measured or recorded. In this case, you have recorded the age, paint color, engine size, and cost of each of the 243 used cars. Each of these characteristics represents a separate variable.
For example, the age of a car is a variable that can be measured or recorded, and it provides information about the car's history and how long it has been in use. The paint color, engine size, and cost of each car are also variables that can be recorded, and they provide additional information about each car's unique characteristics.
In total, you have recorded 4 different variables for each of the 243 used cars, so the number of variables is 4.
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in a survey, the planning value for the population proportion is p=*0.25. how large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.1? round your answer to next whole number.
Sample size of 385 should be taken. Rounding up to the next whole number, the required sample size would be 385. So, in order to provide a 95% confidence interval with a margin of error of 0.1 for the population proportion of 0.25, a sample size of 385 should be taken.
We can use the formula:
n = (Z^2 * p * (1-p)) / E^2
where:
Z is the z-score corresponding to the desired confidence level (for 95% confidence, Z = 1.96)
p is the estimated population proportion (p = 0.25)
E is the desired margin of error (E = 0.1)
Plugging in the values:
n = (1.96^2 * 0.25 * (1 - 0.25)) / 0.1^2
n = 384.16
we are attempting to gauge the populace extent with a room for mistakes of 0.1 and a certainty level of 95%.
To find the example size we want, we utilize an equation that considers the assessed populace extent (0.25), the ideal safety buffer (0.1), and the certainty level (95%). The recipe gives us a number that we gather together to the closest entire number. For this situation, the recipe lets us know that we want to test 385 individuals.
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If:
x = 4 and y = 6 , evaluate the following expression:
3 ( x + y )
show that the given argument is invalid by giving values for the predicates p and q over the domain {a, b}. (a) ∀x (p(x) → q(x)) ∃x ¬p(x) ∴ ∃x ¬q(x) (b) ∃x (p(x) ∨ q(x)) ∃x ¬q(x) ∴ ∃x p(x)
The given argument is invalid by giving values for the predicates p and q over the domain = But both P(a) = p(b) = f There doesn’t exist any x, such that p(x) is true
What is Values?
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.
Given,
fx( p(x) – a(x))
f.(p(x))
fx (a(x))
Let p(a)=T
P(b) = F
And a(a) = T
A(b) = T
So, p(a)=a(a)
=T
P(a) – a(b)
= T
And p(b)=T
So, f.(p(x)-a(x))
Fx(p(x))are T
But we have a (a) + A(b) =T
So, there doesn’t exist any x, such that (x) is true
Hence fX (a(x)) Doesn’t follow from the given statement.
This argument is include
b) fx(p(x) v a(x))
fx (a(x))
fx p(x)
Let P(a) = F
P(b) = F
And a(a) = F
A(b) = T
So, p(b) v a(b) = T
A(a) = F
= ft((x))
But both P(a) = p(b)
= f There doesn’t exist any x, such that p(x) is true
Hence fx p(x)) Dose’t follow from the given statements.
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A rectangular building ha a bae that i 255ft long, 255 feet wide, and the building i 42 ft tall. Find the unit for the volume of the building
The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.
The volume of the building will be calculated by the formula -
Volume = length × breadth × height
Thus, keeping the value of each component of building in the formula to find the volume of the building.
Volume of building = 255 × 255 × 42
Performing multiplication on Right Hand Side of the equation to find the value of volume
Volume of building = 2,731,050 feet³
Therefore, the volume of the building is 2,731,050 feet³.
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Solving systems by elimination
4x - 6y = 16
-4x+8y=-8
P=(prime numbers less than 20) and Q=(odd numbers less than 10) find PnQ
The solutions are, P= 2,3,5,7,11,13,17,19 & Q= 1,3,5,7,9
when, P=(prime numbers less than 20) and Q=(odd numbers less than 10)
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
P=(prime numbers less than 20)
and Q=(odd numbers less than 10)
so, P= 2,3,5,7,11,13,17,19
as, A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.
now,
Q= 1,3,5,7,9
as, Odd numbers are whole numbers that cannot be divided exactly into pairs. Odd numbers, when divided by 2, leave a remainder of 1. 1, 3, 5, 7, 9, 11, 13, 15 … are sequential odd numbers.
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In ΔRST, r = 71 cm, � m∠T=48° and � m∠R=37°. Find the length of t, to the nearest 10th of a centimeter.
Answer:
t/sin T = r/sin R
where T and R are the measures of the opposite angles of t and r, respectively.
First, we need to find the measures of T and R in radians:
T = 48° * pi/180 = pi/4
R = 37° * pi/180 = 37 * pi/180
Next, we can use these values in the formula:
t/sin T = r/sin R
t = r * sin T / sin R
t = 71 * sin(pi/4) / sin(37 * pi/180)
Using a calculator, we can estimate t to the nearest 10th of a centimeter:
t ≈ 107.9 cm
So the length of t is approximately 107.9 cm to the nearest 10th of a centimeter.
Answer:87.7
Step-by-step explanation:
The weight of a number of sheet varies directly as the number of sheets. If
12 sheets of paper weigh 90g, how many sheets of paper will weigh 360 g?
Answer:
13.5 sheets of paper have a mass of 300g
Step-by-step explanation:
Since there is a direct correlation between mass and number of sheets, we can find the correlation and then use it as a conversion factor.
We are told that 12 sheets have a mass of 90g.
Make this into a conversion factor: 90g/(12 sheets) = 6.7777 g/sheet
Now use this conversion factor to answer the question of how many sheets are in 360g.
Let x be the number of sheets required for a mass of 360 g.
Mass is the product of x times the conversion factor (6.7777 g/sheet):
x*(6.7777 g/sheet) = 90g
x = (90g)/(6.7777 g/sheet)
The units of the right reduce to sheets, since grams cancel and sheets comes to the top.
X = 13.5 SHEETS
how to determine density of a liquid with cubes, a meterstick and stopwatch
The formula to determine the density of a liquid with cubes, a meterstick and stopwatch is density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)
Density is a measure of how much mass is contained in a given volume of a material. In order to determine the density of a liquid, you will need three things: cubes, a meterstick, and a stopwatch.
First, gather your materials and select a cube of known dimensions. Place the cube on the surface of the liquid and start the stopwatch. Observe how long it takes for the cube to sink to the bottom of the container. Let's call this time t.
Next, use the meterstick to measure the height of the liquid in the container
With these two pieces of information, you can calculate the density of the liquid using the formula:
=> density = mass / volume
The mass of the cube can be calculated as:
=> mass = volume * density of the cube
where the volume of the cube is given by
=> volume = s³, where s is the length of one side.
Since we know the length of one side (s = 1 cm), the volume of the cube is 1 cm³.
The density of the cube can be assumed to be a constant value (for example, if the cube is made of aluminum, the density is approximately 2.7 g/cm³).
So,
=> mass = volume * density of the cube = 1 cm³ * 2.7 g/cm³ = 2.7 g.
The volume of the liquid displaced by the cube can be calculated as:
volume = mass / density of the liquid = mass / (h/t²)
where h/t² is the acceleration due to gravity.
Finally,
density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)
Complete Question:
Determine the density of an unknown liquid with only a meterstick, stopwatch, and cubes that sink.
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After 10 days, 95% of a radioactive material has decayed
a) What is the half-life of the material?
b) How long will it take for there to be 15% of the original material left?
how can do braily app use
Answer:
Below
Step-by-step explanation:
a) 1/2^n will show how much remains after 'n' halflives
95 % = .95
.95 = 1/2^n log both sides to find n = .07400058
so 10 days is .07400058 half lives
10 / .0740058 = half life = 135.1 days
b) .15 = 1/2^n shows n = 2.736 halflives
2.736 halflives * 135.1 days/halflife = 369.8 days
3 (4-x) = 18 What is X?
[tex]3(4-x)=18[/tex]
Distribute everything outside of parentheses:
[tex](3)(4)+(3)(-x)=18[/tex]
[tex]-3x+12=18[/tex]
Subtract 12 from both sides:
[tex]-3x+12-12=18-12[/tex]
[tex]-3x=6[/tex]
Divide both sides by -3:
[tex]\dfrac{-3x}{-3} =\dfrac{6}{-3}[/tex]
[tex]\fbox{x = -2}[/tex]
Answer:
[tex] \sf \: x = - 2[/tex]
Step-by-step explanation:
Given equation,
→ 3(4 - x) = 18
Now the value of x will be,
→ 3(4 - x) = 18
→ 12 - 3x = 18
→ -3x = 18 - 12
→ -3x = 6
→ x = 6 ÷ (-3)
→ [ x = -2 ]
Hence, the value of x is -2.
The formula for measuring sound intensity in decibels is defined by the equation D = 10 log(I/I0), where I is the intensity of the sound in watts per square meter and I0 = 10-12 is the lowest level of sound that the average person can hear. How many decibels are emitted from a jet plane with a sound intensity of 8.3 x 102 watts per square meter?
149.190781 decibels are emitted from a jet plane with a sound intensity of 8.3 x 102 watts per square meter.
The given formula is:
D = 10 log ([tex]I[/tex] / [tex]I_{0}[/tex])
The intensity of the sound emitted by the jet plane is (I) :
8.3 x 102 watts per square meter
The lowest level of sound that the average person can hear [tex]I_{0}[/tex] :
[tex]10^{-12}[/tex]
Therefore, the intensity of the sound emitted from the given jet plane:
D = 10 log (8.3 x [tex]10^{2}[/tex] / [tex]10^{-12}[/tex])
= 10 log (8.3 x [tex]10^{2}[/tex] x [tex]10^{12}[/tex] )
= 10 log (8.3 x [tex]10^{14}[/tex])
= 10 (log 8.3 + log [tex]10^{14}[/tex]) (since log (a x b) = log a + log b)
= 10 (0.9190781 + 14 log 10) (log 10 = 1)
= 10 (0.9190781 + 14)
= 149.9190781
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a fireman leaned a 36- foot ladder against a building. if he placed the ladder 7 feet from the base of the building, what angle is formed between the ladder and the ground
The angle between the ladder and the ground is 78.78
What is ladder?
Ladder is a structure for climbing up or down that consists essentially of two long sidepieces joined at intervals by crosspieces on which one may step.
It is given that the length of the ladder is 36 foot and the distance between the base and the ladder is 7 feet.
Here we can see that the hypotenuse is 36 foot and the base is 7 feet.
To find the angle between the ladder and the ground we take the cos inverse of 7÷36
Let the angle between the ladder and the ground is ‘x’.
We know, cosx = base
hypotenuse
⇒ cosx 7
36
⇒x = cos (-1) 7
36
⇒ x = 78.78
Therefore, The angle between the ladder and the ground is 78.78
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Calculate the size of angle DAB.
Answer:
25
Step-by-step explanation:
DAB＝180-CBA
＝180-155
＝25
pls give brainliest if correct
Answer:
[tex]\angle DAB=25 \textdegree[/tex]
Step-by-step explanation:
We can use the Sum of Interior Angles formula to help us evaluate the size of angle DAB.
The formula for the Sum of Interior Angles is
[tex](n-2)*180[/tex]
where [tex]n[/tex] is the number of sides.
In this example we have 4 sides.
[tex](4-2)*180\textdegree\\2*180\textdegree=360\textdegree[/tex]
So the sum of all the interior angles in this shape must add up to 360°.
We are given 2 right angles and 1 additional angle. There are 4 angles total. Since we are given 3 we can evaluate the value of the 4th angle.
[tex]\angle A +\angle B +\angle C+\angle D=360 \textdegree[/tex]
[tex]360 \textdegree-\angle B -\angle C-\angle D=\angle A[/tex]
[tex]360\textdegree-90\textdegree-90\textdegree-155\textdegree=25\textdegree[/tex]
The data below are the monthly average high temperatures for New York City. What is the median temperature?
40, 40, 48, 61, 72, 78, 84, 84, 76, 65, 54, 42
Based on the information above, the average temperature for New York City would be 61 or 65.
How to find the average temperature of New York?To find the average temperature of New York we must find the average of the temperatures recorded in each month. Here is the mathematical procedure:
To find the median we must organize the data from the smallest to the largest and identify the value or values that are located in the middle, then the median would be: 61 or 65.
40, 40, 42, 48, 54, 61, 65, 72, 76, 78, 84, 84.According to the above, the average temperature would be 61° or 65°.
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A donkey suffers an attack of hiccups and the first hiccup happens at 4:00 one afternoon. Suppose that the donkey hiccups regularly every 5 seconds. At what time does the donkey’s 700th hiccup occur?15 seconds after 4:5820 seconds after 4:5825 seconds after 4:5830 seconds after 4:5835 seconds after 4:58
Answer:
At 4:58.
Step-by-step explanation:
The time for the 700th hiccup is 5 * 7000
= 3500 seconds.
= 3500/60
= 58.33 minutes,
Three angles of a triangle have measures of 63.5°, 76.5°, and 2x°. Ariette, Bertrand, and Carly each wrote an equation describing the relationship among the three angles. Touch the student who wrote the correct equation.
Answer:
Either 63.5 + 76.5 + 2x = 180 or some variation of it.
Step-by-step explanation:
The sum of all the angles in a triangle equals 180 so any answer would have to add up the three angles given and set them equal to 180.
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a player rolls two fair six sided dice until the player rolls doubles. the probability of rolling doubles with one roll of two fair dice is 1/6, what is the probability that it takes 3 rolls until the player rolls doubles
The probability that it takes three rolls until the player rolls doubles is 25/216.
The probability of rolling doubles with one roll of two fair six-sided dice is 1/6.
The probability of an event is nothing but a number between 0 and 1, where zero shows the impossibility, and one shows the certainty.
First, determine the probability of rolls to obtain doubles in each roll.
Fails in the first roll:
P = 1 - 1/6 = 5/6
Fails in the second roll:
P = 1 - 1/6 = 5/6
In the third roll, the player rolls doubles, that is,
p = 1/6
Now, the probability of requiring 3 rolls until getting doubles will be:
= 5/6 × 5/6 × 1/6
= 25/216
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A community is laid out as a rectangular grid in relation to two main streets that intersect at the city center. Each point in the community has coordinates (x,y) in this grid, for
−10 ≤ x ≤ 10 − 10 ≤ x ≤ 10, −8 ≤ y ≤ 8 − 8 ≤ y ≤ 8, with x measured in miles east of city center and y in miles north of city center. Suppose the value of the land located at the point (x,y) is V thousand dollars per square mile, where: V(x,y) =(150+5x)e^(-0.04x-0.04y).
Compute Vx(3,-2).
The partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.
The value of the land located at the point (x,y) is calculated by the equation V(x,y) = (150+5x)e^(-0.04x-0.04y). Here, x is measured in miles east of city center and y is measured in miles north of city center. To calculate the value of the land at the point (3,-2), we substitute in the equation x = 3 and y = -2. This gives us V(3,-2) = (150+5*3)e^(-0.04*3-0.04*(-2)) = 181.95. Therefore, the value of the land located at the point (3,-2) is 181.95 thousand dollars per square mile. To calculate the partial derivative of this equation with respect to x, we take the derivative of the equation with respect to x while keeping y constant. This gives us Vx(3,-2) = 5e^(-0.04*3-0.04*(-2)) = 5.07. Therefore, the partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.
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