consider the experiment of rolling ten dice. assume the event we look for is rolling an odd number (success), while x is the amount of times we roll an odd number. then p(x > 5) =
Answers
the probability of rolling an odd number more than 5 times when rolling ten dice is approximately 0.377, or 37.7%.
To calculate the probability of rolling an odd number more than 5 times when rolling ten dice, we can use the binomial distribution. Let p be the probability of rolling an odd number on any given die, which is 1/2 since there are three odd numbers (1, 3, and 5) and three even numbers (2, 4, and 6) on each die. Let n be the number of trials, which is 10 in this case. Let X be the random variable representing the number of successes (i.e., the number of times an odd number is rolled).
Then, X follows a binomial distribution with parameters n and p. The probability of rolling an odd number exactly k times out of 10 is given by the binomial probability mass function:
\(P(X = k) = (n choose k) * p^k * (1-p)^(n-k)\)
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k objects from a set of n distinct objects.
To find the probability of rolling an odd number more than 5 times, we need to sum the probabilities of rolling an odd number 6, 7, 8, 9, or 10 times:
P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
\(= (10 choose 6) * (1/2)^6 * (1/2)^4 + (10 choose 7) * (1/2)^7 * (1/2)^3\)
\(+ (10 choose 8) * (1/2)^8 * (1/2)^2 + (10 choose 9) * (1/2)^9 * (1/2)^1\)
\(+ (10 choose 10) * (1/2)^10 * (1/2)^0\)
≈ 0.377
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Related Questions
A salesman has a car for sale for $5000. He decides to increase the price by 40%. When no one buys the car, he decreases the new price by 10%.
What is the final price of the car?
Answers
Answer:
$6300
Step-by-step explanation:
original price: $5000
increase price by 40%: $5000×1.4=$7000
decrease new price by 10%: %7000×0.9=$6300
Complete the factorization of 3x ^ 2 - 10x + 8 3x^ 2 -10x+8=(x- Box x-4)
Answers
Answer:
\(3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})\)
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
\(ax^2+bx+c\) (1)
You have the following polynomial:
\(3x^2-10x+8\) (2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
\(x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\) (3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
\(x_{1,2}=\frac{-(-10)\pm \sqrt{(-10)^2-4(3)(8)}}{2(3)}\\\\x_{1,2}=\frac{10\pm2}{6}\\\\x_1=2\\\\x_2=\frac{4}{3}\)
Then, the factorization of the polynomial is:
\(3x^2-10x+8=(x-x_1)(x-x_2)=(x-2)(x-\frac{4}{3})\)
calls for dial-in connections to a computer center arrive at an average rate of four per minute. the calls follow a poisson distribution. if a call arrives at the beginning of a one-minute interval, what is the probability that a second call will not arrive in the next 20 seconds?
Answers
The probability that a second call will not arrive in the next 20 seconds is approximately 0.2636 or 26.36%.
What is Poisson probability?Poisson probability is a mathematical concept that describes the probability of a certain number of events occurring in a fixed interval of time or space, given a known average rate of occurrence. The Poisson probability distribution is named after French mathematician Siméon Denis Poisson, who introduced it in the early 19th century to model the occurrence of rare events, such as errors in counting or measurement, accidents, or phone calls.
The Poisson probability distribution is a discrete probability distribution that gives the probability of a certain number of events (x) occurring in a fixed interval (t), when the average rate of occurrence (λ) is known. The Poisson probability distribution assumes that the events occur independently and at a constant average rate over time or space. The formula for Poisson probability is:
P(x; λ) = (\(e^{-\lambda}\)) * λˣ) / x!
where:
P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ
e = a mathematical constant e (approximately 2.71828)
λ = it is the average rate of occurrence in the given interval
x = it is number of occurrences in the given interval
Given that calls for dial-in connections arrive at an average rate of four per minute and follow a Poisson distribution, we can use the Poisson probability formula to solve this problem. The Poisson probability formula is:
P(x; λ) = (\(e^{-\lambda}\)) * λˣ) / x!
where:
P(x; λ) = the probability of x occurrences in a given interval, when the average rate is λ
e = a mathematical constant e (approximately 2.71828)
λ = the average rate of occurrence in the given interval
x = it is the number of occurrences in the given interval
In this problem, we are interested in finding the probability that a second call will not arrive in the next 20 seconds, given that a call has already arrived at the beginning of a one-minute interval. Since we are given the average rate of calls per minute, we need to adjust the interval to 20 seconds, which is 1/3 of a minute. Therefore, the average rate of calls per 20 seconds is:
λ = (4 calls/minute) * (1/3 minute) = 4/3 calls/20 seconds
Using the Poisson probability formula, we can calculate the probability of no calls arriving in the next 20 seconds:
P(0; 4/3) = ( \(e^{-4/3}\)* (4/3)⁰) / 0! = \(e^{-4/3}\) ≈ 0.2636
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The rylander sold 150 tickets to a movie some of the tickets were student tickets the rest were adult tickets a student ticket cost 7.00 dollars and an adult ticket cost 10.00 dollars the the ticket sales totaled 1419 dollars determine the number of student tickets and the number of adult tickets
Answers
Answer:dont knon
Step-by-step explanation:sorry
will a numbers prime factorization always be the smae, regardless of which factor pair you start with? Explain.
Answers
A planet rotates through one complete revolution every 17 hours. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. Find the angular velocity of a person standing on the equator.
Answers
The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s
What is angular velocity?Angular velocity is the number of revolution per second of an object.
How to find the angular velocity of a person standing on the equator?Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.
The angular velocity is given by ω = 2π/T where T = period of revolution
Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s
So, substituting the period into the equation for the angular velocity, we have
ω = 2π/T
ω = 2π/61200 s
ω = π/30600 s
ω = 0.0001026 rad/s
ω = 1.026 × 10⁻⁴ rad/s
So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s
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find the surface area of a rectangle prism that has the following deminsions.
length : 2ft
width : 14in
height : 11in
surface area : in 2
Answers
Answer:
SA(surface area) of the rectangular prism is 1,510 in inches
Step-by-step explanation:
SA=2(lh+lw+hw)
2inch=24ft
lh=264
lw=336
wh=154
755*2=1,510
2 ft
3 ft
1 ft
1 ft
3 ft
What is the total area, in square feet, of the top of the desk? Enter the answer in the box.
I square fe
Answers
You invested $1200 into an account that earned interest that was compounded semiannually. After 10 years, the amount in the account is now $4034.22. What was the interest rate of the investment?
Answers
the interest rate of investment is r = 6.25 %.
Principal amount = $ 1200
Time = 10 years
Since the interest is compounded semi annually, the time period will become:
n = 2 × 10 = 20
Amount after 10 years = $ 4034.22
Using the formula for compound interest, we get that:
A = P (1 + r)ⁿ
Substitute the values, we get that:
4034.22 = 1200 ( 1 + r)²⁰
3.36185 = ( 1 + r)²⁰
( 1 + r)²⁰ = 3.36185
( 1 + r) = 1.06245
r = 0.0625
Interest Rate will be:
r = 6.25 %
Therefore, we get that the interest rate of investment is r = 6.25 %.
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For the following systems, draw a direction field and plot some representative trajectories. Using your graph, give the type and stability of the origin as a critical point. You may need to look at the eigenvalues to be sure. 3 5 3 -2 4 2 2 -2 1 x, b. X'= X, X 5 3 1 -5 4 1 4 2 2 a. X' c. X'= -63) — —
Answers
Plot direction fields and trajectories. Analyze eigenvalues to determine stability and type of critical point.
For system (a):
The direction field and trajectories should be plotted based on the given matrix:
[3 5] [x]
[3 -2] * [y]
To determine the type and stability of the origin as a critical point, we can analyze the eigenvalues of the matrix. The eigenvalues are found by solving the characteristic equation:
det(A - λI) = 0,
where A is the given matrix and λ is the eigenvalue.
For system (b):
The direction field and trajectories should be plotted based on the given matrix:
[1 -5] [x]
[4 1] * [y]
To determine the type and stability of the origin as a critical point, we can again analyze the eigenvalues of the matrix.
For system (c):
The direction field and trajectories should be plotted based on the given matrix:
[-6 3] [x]
[ -4 -2] * [y]
To determine the type and stability of the origin as a critical point, we once again analyze the eigenvalues of the matrix.
Analyzing the eigenvalues will allow us to determine if the critical point is a stable node, unstable node, saddle point, or any other type of critical point.
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WILL MARK BRANLIEST AND GIVE 70 POINTS
Alex paid $6 for renting a movie for 3 days. Which graph shows the relationship between the costs of renting a movie for different days? (3 points) a A graph is shown with title Movie Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars. Points are plotted on the ordered pairs 1, 1, and 2, 2, and 3, 3. b A graph is shown with title Movie Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of rental in dollars. Points are plotted on the ordered pairs 1, 3 and 2, 5, and 3, 7. c A graph is shown with title Movie Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of rental in dollars. Points are plotted on the ordered pairs 1, 2 and 2, 4, and 3, 6 d A graph is shown with title Movie Rentals. The horizontal axis label is Days, and the vertical axis label is Cost of Rental in dollars. Points are plotted on the ordered pairs 2, 1 and 4, 2, and 6, 3.
Answers
Answer:
This is clearly a linear relationship. If Alex rented the movie for 0 days, he'd owe nothing. If he paid $6 for a 3-day rental, the slope of this line would be m = rise / run = $6/(3 days) = $2/day, which is positive.
Answer:
c
Step-by-step explanation:
Which equation could define the function below?
y= (x+1)(x+ .5) (x+ 3.5)
y= (x+1) (X - .5) (x-3.5)
y = (x-1) (X-.5) (x-3.5)
y= (x+1) (X- .5) (x +3.5)
Answers
Answer:
y= (x+1)(x+ .5) (x+ 3.5)
y= (x+1) (X - .5) (x-3.5)
y = (x-1) (X-.5) (x-3.5)
y= (x+1) (X- .5) (x +3.5)
Step-by-step explanation:
10. If the coefficient of x*4 is equal to that of x*6 in (1+x² + ax³)*4 what is the value of a
Answers
Answer: We can expand the given expression using the binomial theorem:
(1 + x² + ax³)^4 =
C(4,0) + C(4,1)x² + C(4,2)(ax³)^2 + C(4,3)x^6 + C(4,4)(ax³)^4
where C(n,k) denotes the binomial coefficient "n choose k", which is equal to n! / (k!(n-k)!).
The coefficient of x^4 is the coefficient of the second term, which is C(4,1) = 4. The coefficient of x^6 is the coefficient of the fourth term, which is C(4,3) = 4.
Since the coefficient of x^4 is equal to that of x^6, we have:
4 = C(4,1) = 4a C(4,3) = 4a
Solving for a, we get:
a = 1/4
Therefore, the value of a is 1/4.
Step-by-step explanation:
a = 1/4
Step-by-step explanation:
We can use the binomial theorem to expand (1 + x² + ax³)^4:
(1 + x² + ax³)^4 = (1)^4 + 4(1)^3(x²)(a) + 6(1)^2(x²)^2(a^2) + 4(1)(x²)^3(a^3) + (x²)^4(a^4)
Simplifying the terms with x^4 and x^6, we get:
x^4: 4a(x^2)^1 + (x^2)^4(a^4) = 4ax^2 + a^4x^8
x^6: 4(x^2)^2(a^2) + 4(x^2)^3(a^3) = 4a^2x^4 + 4a^3x^6
Since the coefficient of x^4 is equal to that of x^6, we can set their respective expressions equal to each other:
4ax^2 + a^4x^8 = 4a^2x^4 + 4a^3x^6
Dividing both sides by x^2, we get:
4a + a^4x^6 = 4a^2x^2 + 4a^3x^4
Since this must hold for all values of x, we can equate the coefficients of the powers of x on both sides:
For the coefficient of x^2: 4a = 4a^2
Simplifying, we get: a = 1/4
Therefore, the value of a is 1/4.
Could someone help with 9 and 10?
I’m lost :,)
Answers
Answer:
9.) -32 thousand ft per hour
10.) 9/4° per hour
Step-by-step explanation:
9.) To solve this problem, we first need to know the time that the plane landed, which is after 5 hours. Now, we need to find the altitude of the plane a four hours and thirty minutes, which is 16 thousand ft. Lastly, we need to know the formula for rate of change, which is change in y over change in x. Below is the work for how to solve the problem:
change in y / change in x = \(\frac{16-0}{4.5-5}\)
[Note: four hours and thirty minutes is equal to 4.5 hours.]
\(\frac{16-0}{4.5-5} = \frac{16}{-0.5} =32\)
So, the rate of change from four hours and thirty minutes to when the plane landed is -32 thousand ft per hour.
10.) You did number 10 for the most part, except that the denominator is 8 not 9-0. The reason for this is that is is 8 hours between 6am and 2pm, not 9. This means our final answer is 18/8, or 9/4° per hour.
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Have a GREAT day!!!
I need somebodys help quickly please!
(look at the attachment it shows the math equation).
Answers
After answering the provided question, we can conclude that As a result, square one side of the square is 9 metre long.
what is a square?According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.
We know that the formula \(A = s^2\) gives the area of a square, where A is the area and s is the length of each side of the square.
\(81 = s^2\)
s = √81
s = 9
As a result, one side of the square is 9 metre long.
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How many line segments are shown in the drawing
Answers
Answer:
i cant see the drawing :(
Step-by-step explanation:
i wish i could help tho
Answer: 1
Step-by-step explanation:
it is correct
It is of interest to verify that the content of coke-filled bottles is the prescribed 13 ounces. Assuming that the content is a random variable having a normal distribution N(μ,0.04), a random sample of size n=25 is taken and it is found that the sample mean is 12.9. Test the null hypothesis H 0
:μ=13 vs H 1
:μ<13
at the 5% level of significance. The value of the test statistic and the decision are −2.5, reject the null hypothesis 0 , do not reject the null hypothesis −0.5, do not reject the null hypothesis −12.5, reject the null hypothesis
Answers
To test the null hypothesis H0: μ = 13 against the alternative hypothesis H1: μ < 13, we can perform a one-sample t-test with a significance level of 5%. The decision is to reject the null hypothesis H0: μ = 13
To test the null hypothesis H0: μ = 13 against the alternative hypothesis H1: μ < 13, we can perform a one-sample t-test with a significance level of 5%. Given that the sample size is n = 25, the sample mean is 12.9, and the population standard deviation is 0.04, we can calculate the test statistic.
The test statistic for a one-sample t-test is given by:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the values, we have:
t = (12.9 - 13) / (0.04 / sqrt(25))
t = -0.1 / (0.04 / 5)
t = -0.1 / 0.008
t = -12.5
The calculated test statistic is -12.5. To make a decision, we compare this value to the critical value from the t-distribution with (n - 1) degrees of freedom at a significance level of 5%. Since -12.5 is smaller than the critical value, we reject the null hypothesis.
Therefore, the decision is to reject the null hypothesis H0: μ = 13.
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A normal distribution has μ = 30 and Ï = 5.
(a) Find the z score corresponding to x = 25.
(b) Find the z score corresponding to x = 42.
(c) Find the raw score corresponding to z = â3.
(d) Find the raw score corresponding to z = 1.5.
Answers
(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d) The raw score corresponding to z = 1.5 is 37.5.
For a normal distribution with mean μ = 30 and standard deviation σ = 5:
(a) To find the z-score corresponding to x = 25, we use the formula:
z = (x - μ) / σ
Substituting the values, we get:
z = (25 - 30) / 5 = -1
Therefore, the z-score corresponding to x = 25 is -1.
(b) To find the z-score corresponding to x = 42, we again use the formula:
z = (x - μ) / σ
Substituting the values, we get:
z = (42 - 30) / 5 = 2.4
Therefore, the z-score corresponding to x = 42 is 2.4.
(c) To find the raw score (x) corresponding to z = -3, we use the formula:
z = (x - μ) / σ
Rearranging the formula, we get:
x = μ + zσ
Substituting the values, we get:
x = 30 + (-3) x 5 = 15
Therefore, the raw score corresponding to z = -3 is 15.
(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:
x = μ + zσ
Substituting the values, we get:
x = 30 + 1.5 x 5 = 37.5
Therefore, the raw score corresponding to z = 1.5 is 37.5.
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A cylinder with a base diameter of x units has a volume
of cx cubic units.
Which statements about the cylinder are true? Select
two options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is xx2 square units.
The area of the cylinder's base is
rxsquare units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Mark this and return
Save and Exit
Submit
ity.com/ContentViewers/AssessmentViewer/Activit
Answers
Answer:
use symbolab
Step-by-step explanation:
thank you for your help>>>>>>>>>>+++++++
Answers
Answer:
A
Step-by-step explanation:
can someone help pls 16=3x-7/2
Answers
Answer: To solve the equation 16=3x-7/2, you can follow these steps:
Multiply both sides of the equation by 2 to get rid of the fraction:
16 * 2 = (3x - 7/2) * 2
32 = 6x - 7
Add 7 to both sides of the equation to isolate the term with x:
32 + 7 = 6x
39 = 6x
Divide both sides of the equation by 6 to solve for x:
39 / 6 = x
6.5 = x
Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.
Step-by-step explanation:
Answer:
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ㅤㅤ \(\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}\)
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Step-by-step explanation:
ㅤ
\(\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{39 = 6x}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}\)
ㅤ
\(\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}\)
ㅤ
━━━━━━━━━━━
ㅤ
\(\large{\underline{\underline{\sf{Verification:-}}}}\)
ㅤ
• Substituting the value of (x) in the given equation,
ㅤ
\(\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}\)
ㅤ
\(\large{\pmb{\tt{\leadsto{16 = 16}}}}\)
ㅤ
As LHS = RHS,
Hence Verified
The total amount of calories in a personal pan pizza from Pizza Hut is 1500. It contains 90g of fat and 100 g of carbs
Calculate:
What is the amount of calories provided from fat and carbohydrates?
How many calories are left over? Which macronutrient do these Calories come from?
How many grams of protein are in this meal?
Answers
The amount of calories provided from fat and carbohydrates is 1210 calories.
The number of calories left over is 290 calories.
These calories come from proteins.
The amount of protein in this meal is not specified, so we cannot calculate it.
The amount of calories provided from fat and carbohydrates: Fat provides 9 calories per gram, so 90g of fat would provide 9 x 90 = 810 calories. Carbohydrates provide 4 calories per gram, so 100g of carbs would provide 4 x 100 = 400 calories. So, the total amount of calories provided from fat and carbohydrates is 810 + 400 = 1210 calories.
The number of calories left over: 1500 calories - 1210 calories = 290 calories. These calories come from proteins.
The amount of protein in this meal: The amount of protein in this meal is not specified, so we cannot calculate it.
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Need help asap! What is x and y?
Answers
Answer:
C
Step-by-step explanation:
I THINK THAT IS THE ANSWER.
A straw is placed inside a rectangular box that is 4 inches by 3 inches by 6 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
The length οf the straw is 8 inches.
What is a cubοid?A cubοid is 3- d structure which has length, breadth and height.It is made up οf six rectangles.
What is equation?An equatiοn is a fοrmula in mathematics that expresses the equality οf twο expressiοns by cοnnecting them with the equals sign (=). The wοrd equatiοn and its cοgnates in οther languages may have subtly different meanings; fοr example, in French, an équatiοn is defined as cοntaining οne οr mοre variables, whereas in English, an equatiοn is any well-fοrmed fοrmula cοnsisting οf twο expressiοns linked by an equals sign.
The length οf bοx is 4 inches, breadth is 3 inches and the height is 6 inches.
The straw is fits diagοnally.
Length of the diagonal \(\sqrt{4^2+3^2+6^2}=\sqrt{64}=8\) inches.
Hence, the length of the straw is 8 inches.
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find dy/dx by implicit differentiation. y sin(x2) = x sin(y2)
Answers
The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).
In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.
Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.
Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.
Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.
Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.
By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.
Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).
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how did you solve it??
Answers
Step by step
Perimeter is the sum of all sides
Add
4a + 5a -7 + 7a + 2 + 4a + 3
Combine like terms
(4a + 5a + 7a + 4a) + (-7 +2 +3)
B) 20a -2 is your answer
Prove that, if x and y are odd positive integers, then x2+y2 is even but not divisible by ... If n is an odd integer then show that n2−1 is divisible by 8.
Answers
If x and y are odd positive integers then x² + y² is even but not divisible by 4 and if n is an odd integer then n² - 1 is divisible by 8.
To prove x² + y² is even but not divisible by 4. Let's assume that x and y are odd positive integers. x = 2m + 1 and y = 2n + 1 where m and n are some positive integers.x² + y² = (2m + 1)² + (2n + 1)²= 4m² + 4m + 1 + 4n² + 4n + 1= 4(m² + n² + m + n) + 2. This is an even number but not divisible by 4. Hence proved.
To prove: n² - 1 is divisible by 8 when n is an odd integer. Let's assume that n is an odd integer.n = 2m + 1 where m is some integer.n² - 1 = (2m + 1)² - 1= 4m² + 4m + 1 - 1= 4m² + 4m= 4m(m + 1)This is an even number. To check if it's divisible by 8, let's simplify it further.4m(m + 1) = 8 × m(m + 1)/2. We know that at least one of m or (m + 1) is even.
Hence it will contain at least one 2 factor. So we can take a common 2 from numerator to make it divisible by 8.8 divides n² - 1, thus n² - 1 is divisible by 8. Hence proved.
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Willl mark you brainlieestttt
Answers
Answer:
7/12
Step-by-step explanation:
y = 12
x = 7
y = Kx
K = y/x
K = 7/12
The mean age of 15 students in a class is 6 years. If the age of
their teacher is included, mean becomes 9 years. Which is the age of
the teacher?
Answers
Answer:
might be wrong but 54
Step-by-step explanation:
15 × 6 = 90
90 + 54 = 144
144 ÷ 16 = 9
hope this helps
slop intercept trouble need some help!! preparing for
exam
12. Find the equation of the line (in slope-intercept form) and graph the resulting line. (a.) Line with slope \( m=-3 \) and \( y \)-intercept \( (0,2) \). (b.) Line through the points \( (-3,4) \) a
Answers
The equation for the line in slope-intercept form is:
y = -3x + 2.
The equation of the line that passes through the points \((-3,4)\) and \((a,b)\) in slope-intercept form is y = 4
(a) The slope-intercept equation for a line is given as: y = mx + b
Where "m" is the slope of the line and "b" is the y-intercept. We are given the slope \(m = -3\) and y-intercept \((0,2)\).
Therefore, the equation for the line in slope-intercept form is:
y = -3x + 2. The graph of the line is shown below:
b) We are given that the line passes through the points \((-3,4)\) and \((a,b)\).Let the slope of the line be "m". Therefore, the equation of the line can be expressed in the point-slope form as:
y - b = m(x - a)
We have the values of the point (a, b) which is (-3,4). Substituting the values of a, b, and x, y in the equation, we get:
y - 4 = m(x + 3). We need to find the value of "m" in order to get the equation of the line.
To find "m", we will use the fact that the line passes through the point (-3,4). ``Substituting the values of x and y of the given point (-3,4) in the above equation, we get:
4 - 4 = m(-3 + 3)0
= m(0)0
= 0.
Therefore, the value of "m" is zero. Substituting the value of "m" in the equation of the line in point-slope form, we get:
y - 4 = 0(x + 3)
y = 4.
The equation of the line can also be written in slope-intercept form as:
y = 0x + 4
y = 4.
The graph of the line is shown below:
Conclusion: (a) The equation of the line with slope \(m = -3\) and y-intercept \((0,2)\) in slope-intercept form is
y = -3x + 2.
The graph of the line is shown below:
(b) The equation of the line that passes through the points \((-3,4)\) and \((a,b)\) in slope-intercept form is y = 4. The graph of the line is shown below:
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