Answer:
The rate at which the radius is increasing
dr/dt = 1.91 cm/s
Step-by-step explanation:
The circumference C of a circle can be written as;
C = 2πr .....1
Where;
r = radius
The rate at which the circumference of the circle
is increasing can be written as dC/dt;
Differentiating equation 1, we have;
dC/dt = 2π dr/dt
Making dr/dt the subject of formula;
dr/dt = (dC/dt)/2π
Given;
dC/dt = 12cm/s
Substituting the value of dC/dt;
dr/dt = 12/2π
dr/dt = 1.909859317102 = 1.91 cm/s
The rate at which the radius is increasing dr/dt is 1.91 cm/s
For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.
a. Sample from the mixed joint pmf/pdf:
f(p, n) = p(1 - p)^-1, 0
Answer:
Step-by-step explanation:
The number of hours of daylight measured in one year in Ellenville can be modeled by a sinusoidal function. During 2006, (not a leap year), the longest day occurred on June 21 with 15.7 hours of daylight. The shortest day of the year occurred on December 21 with 8.3 hours of daylight. Write a sinusoidal equation to model the hours of daylight in Ellenville.
Answer:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
Step-by-step explanation:
Solution:-
- We are to model a sinusoidal function for the number of hours of daylight measured in one year in Ellenville.
- We will express a general form of a sinusoidal function [ f ( t ) ] as follows:
[tex]f ( t ) = A*sin ( w*t ) + c[/tex]
Where,
A: The amplitude of the hours of daylight
w: The angular frequency of occurring event
c: The mean hours of daylight
t: The time taken from reference ( days )
- We are given that the longest day [ [tex]f ( t_m_a_x )[/tex] ] occurred on June 21st and the shortest day [ [tex]f ( t_m_i_n )[/tex] ] on December 21st.
- The mean hours of daylight ( c ) is the average of the maximum and minimum hours of daylight as follows:
[tex]c = \frac{f(t_m_a_x ) +f(t_m_i_n ) }{2} \\\\c = \frac{15.7 + 8.3}{2} = \frac{24}{2} \\\\c = 12[/tex]
- The amplitude ( A ) of the sinusoidal function is given by the difference of either maximum or minimum value of the function from the mean value ( c ):
[tex]A = f ( t_m_a_x ) - c\\\\A = 15.7 - 12\\\\A = 3.7[/tex]
- The frequency of occurrence ( w ) is defined by the periodicity of the function. In other words how frequently does two maximum hours of daylight occur or how frequently does two minimum hours of daylight occur.
- The time period ( T ) is the time taken between two successive maximum duration of daylight hours. We were given the longest day occurred on June 21st and the shortest day occurred on December 21st. The number of days between the longest and shortest day will correspond to half of the time period ( 0.5*T ):
[tex]0.5*T = 7 + 31 + 31 + 30 +31 +30 +21\\\\T = 2* [ 181 ] \\\\T = 362 days[/tex]
- The angular frequency ( w ) is then defined as:
[tex]w = \frac{2\pi }{T} = \frac{2\pi }{362} \\\\w = 0.01736[/tex]
- We will now express the model for the duration of daylight each day as function of each day:
[tex]f ( t ) = 3.7*sin ( 0.01736*t ) + 12[/tex]
In the diagram provided line L is parallel to line M. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose More than one correct answer
Answer:
1 and 4 are alternate interior angles.
m5 + m1 = 180
m5 = m3 + m2
Question:
The complete version of your question as found in other site is stated below:
In the diagram provided, line l is parallel to line m. Select which of the following statements could be used to prove that the interior angles of a triangle have a sum of 180°. You may choose more than one correct answer.
1 and 4 are alternate interior angles.
m4 + m5 + m6 = 180.
m5 + m1 = 180.
m5 = m3 + m2
Step-by-step explanation:
Given: line l is parallel to line m
We need prove that the interior angles of a triangle have a sum of 180°. In order to do that, the angles in the triangle = 180°
∠1 + ∠2 + ∠3 = 180°
Alternate angles:
∠1 = ∠4
∠6 = ∠2
∠5 = ∠3 + ∠6
Checking the options and inserting the values above in them:
a) 1 and 4 are alternate interior angles
∠1 = ∠4
This gives one of the side of the interior angles. The alternate angles enables us to find the sum of the interior angles. It is correct
b) m4 + m5 + m6 = 180
∠4 + ∠5 + ∠6 = 180°
∠1 + (∠3 + ∠6) + ∠2 = 180°
The above option wont give ∠1 + ∠2 + ∠3 = 180°. Hence it is wrong.
c) m5 + m1 = 180
(∠3 + ∠6) + ∠1 = 180°
∠5 = (∠3 + ∠6) = ∠3 + ∠2
∠3 + ∠2 + ∠1 = 180°
This option is correct
d) m5 = m3 + m2
∠5 = ∠3 + ∠2
From the diagram, ∠5 + ∠1 = 180° (angles on a straight line)
∠5 = ∠3 + ∠2
This option can be used to get sum of interior angles.
a number,x, rounded to 1 significant figure is 40 write down the error interval for x
Answer:
Error interval is [tex]35\leq x< 45[/tex]
Step-by-step explanation:
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
Solution:
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
orly uses 2 cups of raisins for every 12 cups of trail mix she makes. How many cups of trail mix will she make if she uses 8cups of raisins
Answer:
Step-by-step explanation:
48 cups of trail mix
Staples sells boxes of pens ($10) and rubber bands ($5). Leona ordered a total of 24 cartons for $200. How many boxes of each did Leona order? Hint: Let P = Pens.
Answer:
number of box of pen = 16
number of box of ribbon bands = 8
Step-by-step explanation:
Let
number of boxes of pen = p
number of boxes of rubber bands = r
He ordered 24 boxes of both items. Therefore,
p + r = 24...............(i)
The total cost of what he ordered is $200 . Therefore,
10p + 5r = 200.......(ii)
combine the equations
p + r = 24...............(i)
10p + 5r = 200.......(ii)
from equation (i)
p = 24 - r
insert the value of p in equation (ii)
10(24 - r) + 5r = 200
240 - 10r + 5r = 200
240 - 200 = 5r
40 = 5r
divide both sides by 5
r = 40/5
r = 8
insert the value of r in equation(i)
p + 8 = 24
p = 24 - 8
p = 16
number of box of pen = 16
number of box of ribbon bands = 8
The value of homes in Baltimore, Maryland is dropping by 2.5% each month. If a house
costs $215,000 now, how much is it expected to be worth in 6 months
Answer:
The house will be worth $184,699.6847 in 6 months.
Step-by-step explanation:
Since the cost of the houses is dropping by 2.5 % per month, then it is decreasing exponentially and can be modeled by the following formula:
[tex]cost(x) = 215000*(1 - \frac{2.5}{100})^t\\cost(x) = 215000*(1 - 0.025)^t\\cost(x) = 215000*(0.975)^t\\[/tex]
After 6 months:
[tex]cost(6) = 215000*(0.975)^6\\cost(6) = 184699.6847[/tex]
The house will be worth $184,699.6847 in 6 months.
Please answer this correctly
Answer:
13 2/3 cm
Step-by-step explanation:
To find the perimeter, add up all the sides
2 1/2 + 3 1/3+ 4 1/2 + 3 1/3
Add up the whole numbers
2+3+4+3 = 12
Add up the fractions
1/2+1/3+1/2+1/3
2/2 + 2/3
1 +2/3
Put them together
12+1+2/3
13 2/3
Answer: 13 2/3 cm
Step-by-step explanation:
1. Turn mixed fractions into improper fractions:
2 1/2 = 5/2
3 1/3 = 10/3
3 1/3 = 10/3
4 1/2 = 9/2
2. Formula for perimeter: left side + right side + upper base + lower base
3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2
4. Solve: 41/3
5. Simplify into mixed fraction: 41/3 = 13 2/3
6. Don't forget to add the unit!
Find the perimeter of the figure when l = 15 m, w = 9 m, x = 3 m, and y = 6 m
Answer:
54
Step-by-step explanation:15+15+9+9+3+3=54
The general form of a circle is given as x^2+y^2+4x-10y-7=0.
What are the coordinates of the center of the circle?
What is the length of the radius of the circle?
Answer:
center: (-2, 5)radius: 6Step-by-step explanation:
We can complete the squares of the x- and y-terms by adding the square of half the linear term coefficient.
(x^2 +4x) +(y^2 -10y) = 7
(x^2 +4x +4) +(y^2 -10x +25) = 7 + 4 + 25
(x +2)^2 +(y -5)^2 = 6^2
Compare to ...
(x -h)^2 +(y -k)^2 = r^2 . . . . . standard form equation of a circle
We see that the center is ...
(h, k) = (-2, 5)
and the radius is ...
r = 6
The zeros of the function p(x) = x2 – 2x– 24 are
1) -8 and 3
3) -4 and 6
2) -6 and 4
4) -3 and 8
Can u show work too
Answer:
3) -4 and 6
Step-by-step explanation:
I find it easiest to solve these by factoring. Here, you're looking for factors of the constant (-24) that have a sum equal to the coefficient of the linear term (-2). You know the divisors of 24 are ...
-24 = 1(-24) = 2(-12) = 3(-8) = 4(-6)
The sums of these factors are, respectively, -23, -10, -5, -2. So, the last pair of factors are the ones we're looking for. These are the constants that go into the binomial factors of the function:
p(x) = x^2 -2x -24
p(x) = (x +4)(x -6)
Then the zeros are the values of x that make these factors zero:
x +4 = 0 ⇒ x = -4
x -6 = 0 ⇒ x = 6
The zeros of the function are -4 and 6.
____
The graph of the function confirms these values.
I need this asap
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle:
A(2,-3) B(4, -3) C(4, 5) D(2,5)
What is the perimeter of the rectangle ABCD?
Answer:
20
Step-by-step explanation:
The rectangle is 2 x 8.
2 + 2 + 8 + 8 = 20
Perimeter=8+8+2+2
=20
daryl hit a home run 8 out of 32 times.if he is at bat 224 times how many home runs will he hit
Answer:
56 out of 224 times
Step-by-step explanation:
8 out of 32 = 1 out of 4
56 out of 224 = 1/4
Answer:56
Step-by-step explanation:
Four expressions are shown below which expression are equivalent A:10 (10 +5y) B:5(20x + 25y) C:5 (2x + y) D: 0.25(400x + 500y)
Answer:
Step-by-step explanation:
remove parentheses by multiplying factors.
use exponent rules to remove parentheses in terms with exponents.
combine like terms by adding coefficients.
combine the constants.
(3x+12)+x=180 Find the value of x.
Answer:
x =42
Step-by-step explanation:
(3x+12)+x=180
Combine like terms
4x +12 = 180
Subtract 12 from each side
4x +12-12=180-12
4x = 168
Divide by 4
4x/4 =168/4
x =42
Answer:
x=42
Step-by-step explanation:
180-12=168
168 divided by 4 = 42
x=42
Lucy obtains a 1-year payday loan for $5000.00 at 12% interest compounded monthly. To get the loan, she
also pays an origination fee of $125.00. What is the total cost of the loan to Lucy? Enter your answer as a
dollar amount, such as: 1400.68.
Answer:
$5759.12
Step-by-step explanation:
$5759.12
At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.
Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x+24y−185=07x2+24xy−34x+24y−185=0
Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]
A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservations. She records whether they were made by a man or a woman, and also records how the reservation was made. She gets the following data: Phone 28 Men Women Fax 9 12 Email 37 29 45 Perform a chi-square significance test of association with a = .05. Be sure to include your null and alternative hypotheses, a justification for the use of this test, your test statistic calculations, your P-value, and your conclusion.
Answer:
Step-by-step explanation:
Here,
H_o: The way of reservation is independent of gender.
H_a: The way of reservation is not independent of gender.
We use a chi square test because we can calculate the expected frequencies for this chart.
Doing an Expected Value Chart,
33.7625 9.7125 30.525
39.2375 11.2875 35.475
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 4.482385929
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 3
b = 2
df = 2
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 5.991464547
Also, the p value is
P = 0.106331579
Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]
Step-by-step explanation:
The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.
Please help ;-; what is the answer?
Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
The radius of a circle is 1 meter. What is the area of a sector bounded by a 135º arc?
Answer:
d=2
Step-by-step explanation:
Shape: Circle
Solved for diameter
Radius: 1
Formula: d=2r
Formula: Radius
Answer: 2
Hope this helps.
What is imaginary 34
Answer:
raising a number to the 34th power
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
[tex] \frac{11}{24} [/tex]
Answer:
D. 11/24
Step-by-step explanation:
Total students' reading preferences = 240
Using electronic device = 110
Probability of having electronic device = 110/240
= 11/24
plifying a Radical
Find the values for a, b, and c that complete the simplificatio
12.95
Y Z
12
y8 .y . z. z = x y z Syz
a =
I
b =
Answer: answer is D
Step-by-step explanation:
Answer: The correct answer is 6,4,2
Step-by-step explanation: Doing a 100 point giveaway stay tuned!
A firm can produce only 2500 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x − 1 100 x2 dollars, how many items, x, should the firm produce for maximum profit?
Answer:
2500
Step-by-step explanation:
Monthly total cost, C(x) = 400 + 200x dollars
Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars
Profit = Revenue - Cost
[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]
To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.
[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]
Next, we check if the point x=7500 is a maxima or a minima.
To do this, we find the second derivative of P(x).
[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]
Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.
Therefore, the company needs to produce 2500 units to maximize profit.
A teacher needs to cut pieces of yarn, each 3/4 yards in length. How many
pieces can he cut from a string of yarn that is 6 yards long?
Answer:
8 pieces
Step-by-step explanation:
Take 6 yds and divide by the length of each piece
6 ÷ 3/4
Copy dot flip
6 * 4/3
24/3
8
We can get 8 peices
A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________.
Answer:
the standard error of the proportion is 0.0272
Step-by-step explanation:
We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :
fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]
We know that N = 250 n = 91, replacing:
fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]
fpc = 0.799
Now, the formula would then be:
SE = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc
Now replacing, knowing that p = 0.12
SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799
SE = 0.0272
So the standard error of the proportion is 0.0272
A piece of wire is 290 cm long.
Dawid cuts three 25 cm lengths off the wire.
He then cuts the rest of the wire into as many 30 cm lengths as possible.
Work out how many 30 cm lengths of wire Dawid cuts.
Answer:
8
Step-by-step explanation:
(290-25)/30
265/30
8 and 5/6
so how many full 30 cm lengths?
8
Answer:
7
Step-by-step explanation:
3 × 25 = 75cm
He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm
→ He then cuts the rest of the wire into as many 30 cm lengths as possible.
215 ÷ 30 = 7.17
A linear function has a slope of -7 /9 and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = -7/9 (x minus 18)?
Answer:
both functions have the same graph
Step-by-step explanation:
The first function is described in terms of its slope and y-intercept, so can be written in slope-intercept form as ...
y = mx + b . . . . m = slope (-7/9); b = y-intercept (3)
y = -7/9x +3
__
The second function is written in point-slope form:
y -k = m(x -h) . . . . m = slope (-7/9), point = (h, k) = (18, -11)
y +11 = -7/9(x -18)
If we rearrange the second equation to the form of the first, we get ...
y = -7/9x +14 -11 . . . . eliminate parentheses, subtract 11
y = -7/9x +3 . . . . . . . matches the equation of the first function
__
Both functions describe the same relation.
At 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start a text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start a text, space, p, point, m, point, end text
What coordinates represent the temperature at 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text?
Answer:
(5,2)
Step-by-step explanation:
From the graph attached below:
The coordinate for the temperature (in degree Celsius) at 2 p.m. is (2,7) The coordinate for the temperature (in degree Celsius) at 8 p.m. is (8,-3)Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7) and (8,-3).
For two coordinate points [tex]A(x_1,y_1)$ and B(x_2,y_2)[/tex]
[tex]\text{Midpoint of AB }=\dfrac{1}{2} \left( x_1+x_2,y_1+y_2 \right)[/tex]
Therefore, the coordinates for 5p.m.
[tex]=\dfrac{1}{2} \left( 2+8,7+(-3) \right) \\=\dfrac{1}{2} \left( 10,4 \right)\\\\=(5,2)[/tex]
