Answer:
Your question is Incomplete....
Use the Chain Rule to find dw/dt.
w = ln
sqrt2a.gif x2 + y2 + z2
, x = 4 sin t, y = 7 cos t, z = 9 tan t
Using the Chain Rule to dw/dt. w = ln [tex]\sqrt{2a}.gifx^{2} + y^{2} + z^{2}[/tex], x = 4 sin t, y = 7 cos t, z = 9 tan t the expression will give us the final result for dw/dt.
To find dw/dt using the Chain Rule,
we'll start by expressing w as a composition of functions and then differentiate it step by step.
Given:
w = ln[tex](\sqrt{} (x^2 + y^2 + z^2))[/tex], where x = 4 sin(t), y = 7 cos(t), and z = 9 tan(t).
We'll first substitute the values of x, y, and z into the expression for w:
w = ln[tex](\sqrt{} ((4 sin(t))^2[/tex] + [tex](7 cos(t))^2[/tex] + [tex](9 tan(t))^2))[/tex]
Next, we'll differentiate w with respect to t using the Chain Rule.
The Chain Rule states that if we have a composite function f(g(t)),
its derivative is given by f'(g(t)) ×g'(t).
In our case, f(u) = ln[tex](\sqrt{u}[/tex] and g(t) represents the expressions within the square root.
Applying the Chain Rule, we have:
dw/dt = [tex](1/\sqrt{} (x^2 + y^2 + z^2))[/tex] × (2xdx/dt + 2ydy/dt + 2z×dz/dt)
Substituting the expressions for x, y, and z, we get:
dw/dt = (1/[tex]\sqrt{} ((4 sin(t))^2 + (7 cos(t))^2[/tex]+[tex](9 tan(t))^2))[/tex] ×(2(4 sin(t))(cos(t)) + 2(7 cos(t))(-sin(t)) + [tex]2(9 tan(t))(sec^2(t)))[/tex]
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Fill in the blank. -6_-1*
>
<
=
Answer:
<
Step-by-step explanation:
-6 is lower than -1. you can make a little line and count backwards from 0. -1 is closer to 0 than -6 is, therefore -1 being bigger and the sign being <
CAN SOMEONE HELP AND EXPLAIN WHAT TO DO PLEASEEEEEEEEEEEEEE
Answer:
a. 19 Questions
b. No, Collins grade was 81%, or B-minus :(
Step-by-step explanation:
There are 21 questions in total on the test. Collin wants a 90 percent at least. If you multiply 21 by 90 percent (as below), you will get 18.9
[tex]21 * .9\\=18.9[/tex]
Of course, you can't get 18.9 questions right (unless you're teacher gives .9 extra points lol, So we need to round UP to a whole number (don't round down because it'll give you a number lower than what 90 percent would equate to.
And, Collin got 17 questions right. That's equivalent to 81 percent of 21 (as below).
[tex]17 / 21\\=.8095[/tex]
This rounds to about 81%, meaning Collin did not reach his goal :(. Oh well, he'll just have to try harder next time!
Have a nice day, fam.
{A,B,C,D,E,F,G,H}
how many 4-element subsets are there in the set ?? and please
solve step by step
After considering the given data we conclude that the total number of 4-element subsets that can be generated is 70.
To evaluate the number of 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}, we can apply the combination formula:
[tex]nCr = n! / r!(n-r)![/tex]
Here,
n = maximum count of elements in the set
r = total count of elements we want to choose.
For the given case, n = 8 (since there are 8 elements in the set) and r = 4 (since we want to choose 4-element subsets).
Placing in these values, we get:
[tex]nCr = 8! / 4!(8-4)! = 8! / 4!4![/tex]
[tex]= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70[/tex]
Hence, creation of 70, 4-element subsets that can be formed from the set {A,B,C,D,E,F,G,H}.
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a youth basketball has a diameter of about 8.75 inches. what is the volume of air, in cubic inches, that can fill the basketball? round your answer to the nearest hundredths place.
answer(s);
1.) 1,052.31 in^3
2.) 350.77 in^3
3.) 240.41 in^3
4.) 2,805.16 in^3
Answer:
this took hella long to do but it's B
Use the method of undetermined coefficients to solve the initial value problem below. y'' + 7y=7 sin (√7t), y(0) = 8, y'(0)=√7 19 2 y =
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
To solve the initial value problem using the method of undetermined coefficients, we assume a particular solution of the form:
y_p(t) = A sin(√7t) + B cos(√7t)
where A and B are constants to be determined.
Taking the first and second derivatives of y_p(t), we have:
y'_p(t) = A√7 cos(√7t) - B√7 sin(√7t)
y''_p(t) = -A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)
Substituting these derivatives back into the differential equation, we get:
(-A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)) + 7(A sin(√7t) + B cos(√7t)) = 7 sin(√7t)
Simplifying, we have:
(-A(√7)^2 + 7A) sin(√7t) + (-B(√7)^2 + 7B) cos(√7t) = 7 sin(√7t)
To satisfy this equation for all t, the coefficients of sin(√7t) and cos(√7t) must be equal to the corresponding coefficients on the right side.
Therefore, we have the following system of equations:
-A(√7)^2 + 7A = 0 (coefficient of sin(√7t))
-B(√7)^2 + 7B = 7 (coefficient of cos(√7t))
Solving these equations, we find:
A = 0
B = 1
So, the particular solution is:
y_p(t) = cos(√7t)
To find the general solution, we need to find the complementary solution by solving the homogeneous equation:
y'' + 7y = 0
The characteristic equation is:
r^2 + 7 = 0
Solving this quadratic equation, we find two complex roots:
r₁ = √7i
r₂ = -√7i
The complementary solution is then:
y_c(t) = C₁ cos(√7t) + C₂ sin(√7t)
where C₁ and C₂ are constants to be determined.
Using the initial conditions y(0) = 8 and y'(0) = √7, we can substitute these values into the general solution and solve for C₁ and C₂.
y(0) = C₁ cos(0) + C₂ sin(0) = C₁ = 8
y'(0) = -C₁√7 sin(0) + C₂√7 cos(0) = C₂√7 = √7
Therefore, C₁ = 8 and C₂ = 1.
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
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me needs a hug and help
Answer: C
Step-by-step explanation:
How do I find degrees of monomials?
Two fifths of a number is 24.
what is the number?
Answer:
60
Step-by-step explanation:
half of 2/5 is 1/5 so half of 24 is 12.
since 12 is 1/5 of the number multiply 12 by 5 and you get 60.
The whole number will be 60 whose two fifths will be 24.
Given, Two fifths of a number is 24.
Writing in form of equation,
Let the whole number be x.
So, two fifth of x is 24.
[tex]\frac{2}{5} of x = 24[/tex]
[tex]\frac{2}{5} \times x = 24[/tex]
Apply cross multiplication,
[tex]x = \frac{24 \times 5}{2}[/tex]
x = 60.
Therefore the whole number is 60.
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A hawk is flying 130 meters up in the sky and spots a rodent on the ground at a 20
degree angle of depression. To the nearest meter, what is the horizontal distance
between the hawk and the rodent?
Answer:
arc length d = ∫ √(1 + (dy/dx)²) dx
y = 228 - x²/57
dy/dx = -2x / 57
(dy/dx)² = (2x/57)²
Upper limit for integration:
y = 0 = 228 - x²/57
yields x = 114
d = ∫ √(1 + (2x/57)²) dx for 0 ≤ x ≤ 114 = 264.9 m
Step-by-step explanation:
The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
(a) Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.
(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
a)Using the chi-square distribution table, the critical value is 12.592 using Hypothesis.
b)The value of chi-square statistic for the sample is 16.042, given that
(a)Chi-square test
The Null Hypothesis H₀ : Myers-Briggs preference type is independent of area of study.
Alternative Hypothesis H₁ : Myers-Briggs preference type is dependent of area of study.
Test statistic is χ² = ∑ ((Oi - Ei)² / Ei)
Expected frequencies:To compute the expected frequencies of the data we use the formula:
Eij = (row total i * column total j) / n where
i is the row number and j is the column number.
To find the value of chi-square statistic, the following table is necessary:
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 66 11 19 96
EN 80 42 32 154
IS 54 30 31 115
ES 71 40 43 154
Column total 271 123 125 519
We obtain the expected frequencies by the above formula, and these are listed in the table below.
Myers-Briggs Preference Arts and Science Business Allied Health Row Total
IN 51.55 23.43 21.03 96
EN 86.71 39.56 27.73 154
IS 50.14 22.88 20.97 115
ES 82.61 37.13 32.27 154
Column total 271 123 125 519
The expected frequencies are computed by multiplying the row total and column total and dividing by the grand total, n.
Here, we have four rows and three columns.
Thus, the degrees of freedom are df = (4 - 1)(3 - 1) = 6 at the 0.05 level of significance.
Since we have four rows and three columns, the number of degrees of freedom will be 6.
Using the chi-square distribution table, the critical value is 12.592.
Since 16.04 > 12.592,
we reject the null hypothesis and conclude that Myers-Briggs preference type is dependent of area of study.
(b) Value of chi-square statisticThe formula to compute the chi-square statistic is
χ² = ∑ ((Oi - Ei)² / Ei) where Oi is the observed frequency and Ei is the expected frequency.
Calculating the chi-square statistic, we have
χ² = ((66 - 51.55)² / 51.55) + ((11 - 23.43)² / 23.43) + ... + ((43 - 32.27)² / 32.27)
= 16.042 (rounded to three decimal places).
The value of chi-square statistic for the sample is 16.042.
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A biweekly compounding will generate a higher annual percentage yield ( APY )
than a monthly compounding .
True
False
True. A biweekly compounding will generate a higher annual percentage yield (APY) than a monthly compounding.
True. A biweekly compounding frequency will generate a higher annual percentage yield (APY) compared to a monthly compounding frequency. The APY takes into account the effect of compounding on the total return of an investment over a year.
Biweekly compounding means that interest is calculated and added to the account balance every two weeks, resulting in more frequent compounding periods throughout the year. This more frequent compounding leads to the accumulation of interest on a larger balance, thus generating a higher APY.
On the other hand, monthly compounding occurs once a month, resulting in fewer compounding periods and a lower overall APY. Therefore, for the same nominal interest rate, a biweekly compounding schedule will yield a higher APY compared to a monthly compounding schedule.
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A random sample of students were surveyed as to how much non-school screen time
they had each week (for purposes of the survey, screen time was defined as: time
spent online, on social media, watching TV, or playing video games) and if their grade
average was above or below 80.
Screen Time
less than 4 hours
4-8 hours
8-12 hours
more than 12 hours
above below
6
15
9
13
17
17
11
20
How many total students who spend more than 12 hours a week on screens were
surveyed?
The correct answer is that 13 students who spend more than 12 hours a week on screens were surveyed.
The provided data represents the number of students based on their screen time and whether their grade average is above or below 80.
To find the total number of students who spend more than 12 hours a week on screens, we need to look at the "Screen Time" category that corresponds to "more than 12 hours" and sum up the corresponding counts.
Looking at the data:
Screen Time:
less than 4 hours: 6 students
4-8 hours: 15 students
8-12 hours: 9 students
more than 12 hours: 13 students
If we consider only the "more than 12 hours" category, we find that there were 13 students.
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Does anyone know this one?
Answer:
-3
Step-by-step explanation:
(-5) - (-2) = (-3)
hope it helps
Answer:
there is a three degree difference between san Diego and Los Angeles
There are 244 seventh grade students. The number of students enrolled in P.E. Is 8 fewer than three times the number of students enrolled in health
Answer:
No. of students enrolled in Health = 63
No. of students enrolled in P.E. = 181
Step-by-step explanation:
Given,
Total students in grade seven = 244 students
A.T.Q.
Let the number of students enrolled in Health be x
so, The number of students enrolled in P.E. = 3x - 8
As we know,
x + (3x - 8) = 244
4x = 244 + 8
x = 252/4
x = 63
Thus, the number of students enrolled in Health = 63
The number of students enrolled in P.E. = 3x - 8
= 3 * 63 - 8
= 189 - 8
= 181 students
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answer:
it does not form a triangle
Step-by-step explanation:
brainliest give me pls pls pls
Answer:
It forms a obtuse triangle
Step-by-step explanation:
Because two sides are the same.
(6/-7)/(3/11)
6/-7 divided by 3/11
Answer:
-22/7
Step-by-step explanation:
To divide fractions, we multiply by the reciprocal:
(6/-7)/(3/11)
(6/-7)(11/3)
66/-21
22/-7
-22/7
Therefore, your simplifed answer is -22/7
Answer:
36/49
Step-by-step explanation:
108/49/3
=108/147
=36/49
Which of the following answers matches “The quotient of 9 and the sum of the quantities 5 and product of 8 and x.”
Answer:
I believe this is the answer 9/(5 + 8x)
Here is a graph of a quadratic function f(x). What is the minimum value (y-value only) of f(x)?
Answer:
Zero.
Step-by-step explanation:
The minimum value is where the function touches the x axis , at y = 0.
The dot plots below show the test scores of some mathematics students and some science students:
Based on visual inspection of the dot plots, which group of students appears to have the larger average score?
The mathematics students
The science students
Both groups are similar.
Not enough information is available to draw a conclusion.
Answer:
Science students
Step-by-step explanation:
_______1. What is 22% of 10?
_______2. 16% of 30 is ______.
_______3. 25 percent of 50 is ______.
_______4. What is 65% of 300
_______5. Find 10% of 450
A. 195
B. 45
C. 4.8
D. 12.5
E. 2.2
Pa sagot po pls
Answer:
1. 22% of 10 = 2.2
2. 16% of 30 = 4.8
3. 25% of 50 is 12.5
4. 65% of 300 = 195
5. 10% of 450 = 45
HAHA, I KNEW IT!!!
HOPE THIS HELPS!!!!
MARK AS BRAINLIEST (probably)
GIVE 5 STARS PLEASE
Answer:
E - 2.2C - 4.8D - 12.5A - 195B - 45Step-by-step explanation:
For each questions, multiply the whole number by the percentage.
Or, change each percentage by getting rid of the percentage sign and dividing by 100.
EX : 65% = .65 or 22% = .22
10 x .22 = 2.2
help asap please i need to get thru this
Answer:
The Scale Factor is 1/4.
Step-by-step explanation:
if you multiply each side (of figure A) by 1/4, the product matches with figure B's corresponding sides. for example, 56 to 14, 28 to 7, and 64 to 16.
the scale factor is just how much a chosen shape is multiplied by to get the next shape.
to get bigger shapes into a smaller shape, multiply the sides by fractions like we did this problem.
A cylindrical soup can has a radius of 1.9 in. and is 5.9 in. tall. Find the volume of the can.
Answer:
66.93 in^3
Step-by-step explanation:
Volume = πr^2h
=> V = 22/7*(1.9)^2*5.9 = 66.93 in^3
Hila found the data at the left that shows the number of ways that each sum can be obtained when rolling three dice. a) Determine the mean and the standard deviation. b) Draw a frequency polygon to show the data. c) Does the data have a normal distribution? Explain. Rolling 3 Dice Sum Frequency 3 1 4 3 5 0 6 6 10 7 15 8 21 9 25 10 27 11 27 12 25 13 21 14 15 15 10 16 6 17 3 18 1
a) The mean and standard deviation need to be determined for the given data on the number of ways each sum can be obtained when rolling three dice.
b) A frequency polygon can be drawn to represent the data.
c) Whether the data has a normal distribution or not needs to be determined, and an explanation is required.
a) Mean and Standard Deviation: The mean can be calculated by summing up the products of each value and its corresponding frequency, then dividing by the total frequency. The standard deviation can be calculated by finding the square root of the variance, where the variance is the sum of the squared differences between each value and the mean, divided by the total frequency.
b) Frequency Polygon: A frequency polygon can be plotted by taking the sum values on the x-axis and the corresponding frequencies on the y-axis. Points are plotted for each sum value, and then lines are drawn to connect these points to form the polygon.
c) Normal Distribution: To determine if the data follows a normal distribution, one can visually analyze the frequency polygon. If the polygon displays a symmetric, bell-shaped curve, it suggests a normal distribution. However, if the polygon is skewed or does not exhibit a bell shape, the data is unlikely to have a normal distribution.
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Convert 13,000,000,000,000,000,000,000,000 to scientific notation.
Answer:
1.3 times 10 to the 25th power
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
Hi! The answer to your question is 1.3 x [tex]10^{25}[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
PLSS HELP I WILL GIVE YOU BRAINLYEST!!
Students were surveyed about their
favorite sports to play in physed. The
results are represented in this arcle graph
If 48 students were surveyed, how many
chose soccer?
Part/total=%/100
A. 15
B. 12
C. 13
D. 10
Answer: C
So I was right, I guess.
3333 divided by 77. i really need help
Answer:
43.2857142857
plz mark me as brainliest
Answer:
476.142857143
Step-by-step explanation:
The number of claims follows a negative binomial distribution with parameters β and r, where β is unknown and r is known. You wish to estimate β based on n observations, where xˉ is the mean of those observations. Determine the maximum likelihood estimate of β.
(a) xˉ/r2
(b) xˉ/r
(c) xˉ
(d) rxˉ
(e) r2xˉ
Since s = Σ(xi - x) / n is the sample variance therefore,
Option (a) x/r is correct.
To find the maximum likelihood estimate of β,
We need to maximize the likelihood function L(β) with respect to β.
The likelihood function for a negative binomial distribution with parameters β and r, given n observations with mean x, is,
⇒ L(β) = (Γ(r+n)/Γ(r)n!) (β^r / (β+x)^r+n) ∏([tex]x_i[/tex]+x)/(([tex]x_i[/tex]+β)^r+1
where Γ is the function and ∏ denotes the product over all n observations xi.
Taking the natural logarithm of the likelihood function, we get,
⇒ ln L(β) = ln(Γ(r+n)) - ln(Γ(r)) - ln(n!) + r ln(β) - (r+n) ln(β+x) + Σ ln(xi+x) - Σ ln(xi+β) - (r+1)Σ ln(xi+x)
To find the maximum likelihood estimate of β,
we take the derivative of ln L(β) with respect to β,
set it equal to zero, and solve for β,
⇒ d/dβ ln L(β) = r/β - (r+n)/(β+x) + Σ 1/(xi+β) - (r+1)Σ 1/(xi+x) = 0
We can solve this equation numerically using iterative methods, but we can also simplify it by using the fact that when the derivative of a function equals zero, the function is at a maximum or minimum.
Multiplying both sides of the equation by β(β+x), we get.
⇒ r(β+x) - (r+n)β + β(β+x)Σ 1/(xi+β) - (β+x)(r+1)Σ 1/(xi+x) = 0
Simplifying and solving for β, we get,
⇒ β = x(r+n-1) / (Σ 1/(xi+β) - (r+1)Σ 1/(xi+x))
We can use an iterative method to solve for β, starting with an initial estimate of β and updating it until convergence.
One common method is to use the Newton-Raphson algorithm.
After some algebraic manipulations,
we can show that the maximum likelihood estimate of β is,
⇒ B = x(r / s - 1)
Here s = Σ( - x) / n is the sample variance of the n observations. Therefore, the correct option is (a) x/r.
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Help please multiple choice interval. 20 Points. Thanks very much!
Answer:
D
Step-by-step explanation:
A study was run to determine if more than 30% of Cal State East Bay students work full-time. A random sample of 100 Cal State East Bay students had 36 work full-time. The p-value was found to be 0.0952. Group of answer choices There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time if exactly 30% of Cal State East Bay students work full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have the same as our sample's 36 working full-time if exactly 30% of Cal State East Bay students work full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.
The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time
A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.
The sample of Cal State East Bay students selected was random.
Out of 100 students, 36 were found to be working full-time.
The p-value was calculated to be 0.0952.
The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.
Therefore, it is concluded that the null hypothesis cannot be rejected.
The p-value is greater than 0.05 which shows the significance level.
Hence, we accept the null hypothesis.
The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.
The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.
The test is a right-tailed test.
The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.
Since the p-value is less than 0.05, we can reject the null hypothesis.
Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.
Hence, option D is the correct answer.
There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.
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