(1 point) The weight of a lake trout as a function of age satisfies the formula W(t) = 25.5(1 - -0.181)3, where W is in kg and t is in years. a. Differentiate this weight function. W'(t) = Find its second derivative. W"(t) = Give both the t and W values for any points of inflection (t > 0). t = yr. W(t) = kg. The trout is gaining weight most rapidly at this point of inflection. Find this most rapid rate of growth. W'(t) = kg/yr.

π/32 is the area enclosed by the curve r= sin(8θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(8θ) =0

=> sin(8θ) =0

=> 8θ = 0,π

=> θ = 0, π/8

so a=0 , b= π/8

now  

   A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)    ------(i)

 so   \(r^2\) = (sin(8θ))^2

=>  \(sin^2\) ( 8θ )

ans we know that

cos(2α) = 1 -  2\(sin^2\) α

so   \(r^2\)  = (1- cos(16θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha\)

=> 1/4* \(\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha\)

here a=0 and b=π/8

after putting the value and solving the integral

A = π/32

so A is the area enclosed by r=sin(8θ) is π/32

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Answer: See explanation

Step-by-step explanation:

You didn't say what you would like to calculate but based on tbe information given in the question, I guess that you want to calculate the percentage of readers who use an e-reader. This will be:

Number of readers surveyed = 3,000

Number of readers reading on e-reader = 1,954

Percentage of e-readers would then be:

= (1954 / 3000) × 100

= 65.13%

The Pythagorean Theorem states the following:

Where "c" represents the hypotenuse of the Right triangle (which is a triangle that has an angle that measures 90 degrees), and "b" and "c" are the legs of the triangle.

To rewrite the formula solving for "b", you can follow the steps shown below:

1. Apply the Subtraction property of Equality by subtracting a^2 from both sides of the equation:

2. Now you must apply square root to both sides of the equation:

Because remember that:

Therefore, the formula solved for "b", is:

Answer:

------------------

Use circumference formula:

Find the radius by rearranging the formula and substituting 32 for C:

Answer:

5.09 in

Step-by-step explanation:

We know that the formula to find the circumference of a circle is:

C = 2πr

Here,

C → Circumference → 32 in

r → radius

Let us find the radius of the circle by substituting the given values.

\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)

After answering the given query, we can state that So, -6 is the figure equation we're searching for.

Using the equals sign (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical formulas through a mathematical assertion. The equal symbol, for example, puts a space between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two lines that are printed on opposite sides of a letter. Most of the time, the emblem and the particular program match. e.g., 2x - 4 = 2 is an example.

"x + 5" can be used to represent "five more than a particular number."

It is possible to express "four less than half that number" as "0.5x - 4".

Thus, the solution is:

x + 5 = 0.5x - 4

We can now determine x:

x + 5 = 0.5x - 4

Take 0.5x away from both sides:

0.5x + x + 5 = -4

combining similar words

1.5x + 5 = -4

Take 5 away from both ends.

1.5x = -9

1.5 divided by both sides gives x = -6.

So, -6 is the figure we're searching for.

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Answer: Greater than 10.

Answer:

X = 5

Y = 7

Step-by-step explanation:

First we will find x

4x + 2 = 3x + 7

x + 2 = + 7

x = 5

Next we will find y

2y + 9 = 4y - 5

-2y + 9 = -5

-2y = -14

y = 7

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.

If the process is discrete, then the function is a sequence of values at discrete points in time.

A stochastic process is one that evolves over time and the outcomes are uncertain.

The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.

To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.

The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

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Barbara is converting 78°F to degrees Celsius. First, she subtracts 32 from 78. The next step for Barbara is to multiply 46 by 5/9, as given by option A. The correct option (A) multiply 46 by 5/9

To convert Fahrenheit (°F) to Celsius (°C), Barbara has already subtracted 32 from 78. The next step is to multiply the result by the appropriate conversion factor.

The conversion formula from Fahrenheit to Celsius is given by:

°C = (°F - 32) * (5/9)

In this case, Barbara subtracted 32 from 78, yielding 46. To complete the conversion, she needs to multiply 46 by the fraction 5/9.

Therefore, the next step for Barbara is to multiply 46 by 5/9, as given by option A.

A.) multiply 46 by 5/9

This step will provide the value of 46°C, which represents the equivalent temperature in Celsius for 78°F.

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Step-by-step explanation:

Using absolute value to tell wether the sum of two integers is positive or negative.

Suppose we have a positive integer,

x and a negative interger, -x and we want to find their sum, we take the absolute values of each of the integers, that is |x| and |-x|. Then we subtract these values: |x| - |-x|. If the larger integer is positive, the result of the difference is positive, but if the larger number is negative, the result of the difference is negative.

For any integer x, x + (-x) = 0

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

2x+1/3 = 9 - 6

2x+1/3 = 3

2x + 1 = 3 × 3

2x + 1 = 9

2x = 9 - 1

2x = 8

x = 8/2

x = 4

Good luck :)

If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .

In the question ,

it is given that ,

the number of residents in the local apartment complex is = 71

the mean electric bill for the 71 residents = $62 ;

we know that the sample mean is itself called as the best point estimate ;

So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of  local apartment complex which is given as $62 .

Therefore , the best point estimate is $62 .

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The area of circle calculated form the circumference of circle is 6.25π cm².

The circumference of circle is represented by the formula -

Circumference = 2πr, where r is the radius of the circle.

Keep the value of circumference to find the radius of circle.

5π = 2πr

Cancelling π on each side of the equation

2r = 5

r = 5/2 cm

Now, we know the area of circle is given by the formula -

Area = πr²

Keep the values of radius in the formula -

Area = π× (5/2)²

Taking square on Right Hand Side of the equation

Area = 25π/4

Performing division on Right Hand Side of the equation

Area = 6.25π cm²

Thus, the area is 6.25π cm².

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Answer: 10+12x=58

Step-by-step explanation:

The equation would be 10+12x=58, where x is the amount of additional hours babysitting besides the first hour.

To solve: move terms to one side (subtract 10) so you'd get 12x=48

The answer to this equation would be x=4 (you divide by 12)

To check if correct: plug in 4, to get 10+12(4)=58 which is 10+48=58 which gets 58=58

So the time worked was a total of 5 hours since you have to add on the first hour, but the solution to your equation represents just the amount of additional hours worked besides the first hour.

Answer:

5x

Step-by-step explanation:

The area of the domain enclosed by the curve with parametric equations x = tsin t, y = cost, t ∈ [0, 2π] is 2π + 2.

The parametric equations given are:

x = t sin t
y = cos t

To find the area of the domain enclosed by the curve, we can use the formula for the area of a region bounded by a curve given in parametric form:

A = ∫[a,b] y dx

where a and b are the limits of the parameter t that describe the domain of the curve.

In this case, we have:

a = 0
b = 2π

So, we need to compute:

A = ∫[0,2π] cos(t) (t sin(t)) dt

Using integration by parts with u = t and dv = sin(t) dt, we get:

A = [t cos(t)]|[0,2π] - ∫[0,2π] cos(t) dt + ∫[0,2π] sin(t) dt

The first integral evaluates to:

[t cos(t)]|[0,2π] = 2π

The second integral evaluates to:

∫[0,2π] cos(t) dt = [sin(t)]|[0,2π] = 0

The third integral evaluates to:

∫[0,2π] sin(t) dt = [-cos(t)]|[0,2π] = 2

Therefore, the area of the domain enclosed by the curve is:

A = 2π - 0 + 2 = 2π + 2

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Answer:

So for the table , .3 + .1 + .25 + .35= 1.

and 10 green pins. read my explanation please cause i worked a lot on this.

Step-by-step explanation:

So first we add the probability of purple and gray getting picked.

.35 + .25= .6

And we know that the probability of green is 3 times yellow.

So. yellow can be x. and the equation would look like this.

3x + x +.6= 1

x equals .1, because 3x + x or 3(.1) + .1= .4

So, .3 + .1 + .25 + .35= 1.

This should be enough info to complete the table. Now b.)

So we know 14 purple pins... and the probability of that is .35

so if 14 = .35 what equals .25?

(I'm going to convert these decimals into percents for problem b until we get the answer, and then i'll make it back to a decimal form)

Okay, so

14= 35%

and that means .4 equals 1% or .01 probability

so now we times .4 to 25% to find out how many green pins are there.

.4 * 25= 10

So there are 10 green pins.

it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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Answer:

I think she only needs 4 cups cuz u add 2/3 and 1/3 which is 1 and then add 1 and 2

1. The ratio of shirts Pete pays for to all shirts is 1000.

2. Pete would pay Ana $8.33 for each shirt.

3. Pete would pay Jun $9600 for the shirt.

To determine what Pete would pay Ana for the shirts, we can use the "Buy 5, Get 1 Free" discount. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 (5 shirts paid, and 1 shirt received for free).

To fill in the statements:

1. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is ____.

To find the missing value, we can set up the following equation:

5/6 * 1200 = x

Solving for x, we have:

x = (5/6) * 1200 = 1000

So, the ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is 1000.

2. ___ × $10 = $

Pete pays $10 for each shirt. Since the ratio is 5:6, the missing value can be calculated as follows:

5/6 * $10 = $8.33 (rounded to two decimal places)

Therefore, Pete would pay Ana $8.33 for each shirt.

3. What would Pete pay Jun for the shirt?

Pete would pay Jun $8 for each shirt. Since Pete needs 1200 shirts, we can calculate the total amount he would pay Jun as follows:

1200 x $8 = $9600

Therefore, Pete would pay Jun $9600 for the shirts.

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The quantity of each ingredient that will be needed for 10 people is 250g of butter and 350 g of flour.

Recipe for 6 people:

150g of butter

210g of flour

Equate the ratio of number of people to each recipe

For butter:

6 : 150 = 10 : x

6/150 = 10/x

cross product

6 × x = 150 × 10

6x = 1500

x = 1500/6

x = 250 g

For flour:

Equate the ratio of number of people to each recipe

6 : 210 = 10 : x

6/210 = 10/x

6 × x = 210 × 10

6x = 2100

divide both sides by 6

x = 2100 / 6

x = 350 g

Therefore, 250 g of butter and 350 g of flour is needed.

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What you need to write in each blank is:

1) positive x-axis.

2) negative x-axis.

3) positive y-axis.

To plot a point (R, θ) on the polar plane. First, if R is positive the angle is measured from the positive x-axis, if R is negative, the angle is measured from the negative x-axis.

Because here R is 4, positive, the point will lie on the x-axis. Then, she needs to move it clockwise by an angle of (3/2)pi (a total of 3 quadrants) This means that the point will end up in the positive y-axis.

So what you need to write in each blank is:

1) positive x-axis.

2) negative x-axis.

3) positive y-axis.

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The z-score for a person who received a score of 77 is approximately 1.90 (rounded to two decimal places).

To calculate the z-score for a person who received a score of 77, we need to use the formula:

z = (x - μ) / σ

where:

x is the individual score,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

Given that the class mean (μ) is 73 and the standard deviation (σ) is 2.1, and the individual score (x) is 77, we can substitute these values into the formula:

z = (77 - 73) / 2.1

z = 4 / 2.1

z ≈ 1.90

Therefore, the z-score for a person who received a score of 77 is approximately 1.90 (rounded to two decimal places).

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Answer:

15

Step-by-step explanation:

15-12+4(3)

15-12+12

3+12

15

Answer:

y= -12x + 5000