2.


(03. 02 MC)


Kayla was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:



−9, which represents the depth of water in the swimming pool


+10, which represents the height of the slide at the pool



Part A: What does 0 represent in this situation? (3 points)



Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)



Part C: Kayla held a pole in the swimming pool. The bottom of the pole was at a depth of 3 feet. How should Kayla mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)

Assuming that the sequence converges, its limit must be one of the two possible values of L, i.e., L = (-3 + sqrt(13)) / 2 or L = (-3 - sqrt(13)) / 2.

Given the recursive formula for the sequence, we can use the hint provided in the question to find the limit of the sequence.

Hint: If lim an = L, then lim an+1 = L as well.

Assuming that the sequence converges, i.e., lim an = L, we can apply the above hint to find the value of L. Using the recursive formula, we have:

an+1 = 1/(3+an)

Taking the limit of both sides as n approaches infinity, we get:

lim an+1 = lim 1/(3+an)

Since lim an = L, we can substitute L in place of an in the above equation, and we get:

lim an+1 = lim 1/(3+an) = 1/(3+L)

We know that lim an+1 = L as well, so we can equate the two expressions for lim an+1 to get:

L = 1/(3+L)

Solving for L, we have:

3L + L^2 = 1

L^2 + 3L - 1 = 0

Using the quadratic formula, we get:

L = (-3 ± sqrt(3^2 - 4(1)(-1))) / 2(1)

L = (-3 ± sqrt(13)) / 2

Therefore, assuming that the sequence converges, its limit must be one of the two possible values of L, i.e., L = (-3 + sqrt(13)) / 2 or L = (-3 - sqrt(13)) / 2.

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Answer:

$3.45

Step-by-step explanation:

15% of 23 is 3.45

There are 15 different outcomes possible when rolling four identical dice.

Since each die has six possible outcomes (numbers 1 to 6), the number of different outcomes for a single die is 6.

The total number of different outcomes when rolling four dice, we need to calculate the number of combinations of four elements taken from a set of six elements (one for each die).

This can be calculated using the formula for combinations, given by:

C(n, r) = n! / (r!(n - r)!)

Where, n is the total number of elements (6 in this case) r is the number of elements to be chosen (4 in this case) ! represents the factorial operation

Using this formula, we can calculate the number of different outcomes

C(6, 4) = 6! / (4!(6 - 4)!)

C(6, 4) = 6! / (4!2!)

C(6, 4) = 30 / 2

C(6, 4) = 15

Therefore, there are 15 different outcomes possible when rolling four identical dice.

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1)The pdf of U is f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

2)U follows a gamma-distribution with parameter a = 3/2 or a = 1/2.

3)x = (y²/2) and dx = y dy using exponential distribution

We can rewrite the integral as:

I(1/2) = ∫₀^∞ y exp(-y²) dy

       = 1/2 ∫₀^∞ exp(-u/2) du

This is the same as the integral for f(u) when u = 1/2.

Therefore, we have:

I(1/2) = V1

(1) For U = Z², we can use the method of transformations.

Let g(z) be the transformation function such that

U = g(Z)

   = Z².

Then, the inverse function of g is given by h(u) = ±√u.

Thus, we can apply the transformation theorem as follows:

f(u) = |h'(u)| g(h(u)) f(u)

     = |1/(2√u)| exp(-u/2) for u > 0 f(u) = 0 otherwise

Therefore, the pdf of U is given by:

f(u) = (1/(2√u)) exp(-u/2) for u > 0 and f(u) = 0 otherwise.

(2) We are given that f(1/2) = VT, where V is a constant.

We can substitute u = 1/2 in the pdf of U and equate it to VT.

Then, we get:VT = (1/(2√(1/2))) exp(-1/4)VT

                            = √2 exp(-1/4)

This gives us the value of V.

Now, we can use the pdf of the gamma distribution to find the parameter a such that the gamma distribution matches the pdf of U.

The pdf of the gamma distribution is given by:

f(u) = (u^(a-1) exp(-u)/Γ(a)) for u > 0 where Γ(a) is the gamma function.

We can use the following relation between the gamma and the factorial function to simplify the expression for the gamma function:

Γ(a) = (a-1)!

Thus, we can rewrite the pdf of the gamma distribution as:

f(u) = (u^(a-1) exp(-u)/(a-1)!) for u > 0

We can now equate the pdf of U to the pdf of the gamma distribution and solve for a.

Then, we get:

(1/(2√u)) exp(-u/2) = (u^(a-1) exp(-u)/(a-1)!) for u > 0 a = 3/2

Therefore, U follows a gamma distribution with parameter

a = 3/2 or equivalently,

a = 1/2.

(3) We need to show that I(1/2) = V1.

Here, I(1) = ∫₀^∞ exp(-x) dx is the integral of the exponential distribution with rate parameter 1 and V is a constant.

We can use the change of variables y = √(2x) to simplify the expression for I(1/2) as follows:

I(1/2) = ∫₀^∞ exp(-√(2x)) dx

Now, we can substitute y²/2 = x to obtain:

x = (y²/2) and

dx = y dy

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what is the question your trying to find, if you could repile to this so I can try to figure it out. (I'll be heading off soon)

Answer:

b

Step-by-step explanation:

They are used for tissue repair and growth

Answer: 0.4

Step-by-step explanation: Simplify the expression

One drink of an alcoholic beverage contains approximately 100 to 150Kcal. That is option D

An alcoholic beverage is a type of beverage that contains ethanol which is also a type of alcohol.

The three main types of alcoholic beverage are beer, wine and spirits.

Alcoholic drinks contain a lot of kilojoules and have no nutritional benefits

One drink of an alcoholic beverage contains approximately 100 to 150Kcal.

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Answer:

without a value under the square root there are no I tercepts because you can't graph xsqrt

Answer:

30x + 28

Step-by-step explanation:

To evaluate (f ￮ g)(x), substitute x = g(x) into f(x) , that is

f(g(x))

= f(- 6x - 6)

= - 5(- 6x - 6) - 2 ← distribute parenthesis and simplify

= 30x + 30 - 2

= 30x + 28

Answer: 5 2/4

Step-by-step explanation: you do not add the bottom numbers. You add 2+3=5 and then you add 1+1 that is 5 2/4

Answer:

5 1/2

Step-by-step explanation:

You have a common denominator so just add the fractions together. Then,add you whole numbers.

Answer:

$51.20

Step-by-step explanation:

36% of 80 is 28.8

80 - 28.8 = 51.2

Formatted properly, the answer is $51.20

Answer:

Step-by-step explanation:

The answer is $51.20!

Hope this helps!

It is both antisymmetric and transitive.

{2, 4, 6, 8} is one of the equivalence classes.

The relation R, defined as {(n, m) | n, m ∈ Z, n < m}, is both antisymmetric and transitive.

To show antisymmetry, we need to demonstrate that if (a, b) and (b, a) are both in R, then a = b. In this case, if we have n < m and m < n, it implies that n = m, satisfying the antisymmetric property.

Regarding transitivity, we need to show that if (a, b) and (b, c) are in R, then (a, c) is also in R. Since n < m and m < c, it follows that n < c, satisfying the transitive property.

The equivalence classes of the relation R, defined as {(n, m) | n, m ∈ Z, [n/4] = [m/4]}, are sets that group elements with the same integer quotient when divided by 4. One of the equivalence classes is {2, 4, 6, 8}, where all elements have a quotient of 0 when divided by 4.

Equivalence classes group elements that have an equivalent relationship according to the defined relation. In this case, the relation compares the integer quotients of the elements when divided by 4. Elements within the same equivalence class share this common characteristic, while elements in different equivalence classes have different quotients.

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public class acre calculator {

   public static void main(String[]  args) {

       double square feet = 389767;

       double acres = square feet / 43560;

       system.out.println("The parcel of land with " + square feet + " square feet is equivalent to " + acres + " acres.");

   }

}

In this program, we declare a double variable square feet with the value of 389,767, which represents the area of the parcel of land in square feet.

We then calculate the number of acres by dividing square feet by the constant value 43,560, which is the number of square feet in one acre. The result is stored in a double variable acres.

Finally, we output the result using the system.out.println() method, which prints a message to the console indicating the area of the land in acres.

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Answer:

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

Find each area and then find their difference.

The difference is:

Answer:

E=mc2 ................

E=mc2 is Energy equals mass times the speed of light squared.

Mind-BLOWN lol

(a) The interval on which f is increasing: (0, ∞)

The interval on which f is decreasing: (0, 1)

(b) Local minimum: At x = 1, f(x) has a local minimum value of -1.

There is no local maximum value.

(c) Inflection point: At x ≈ 0.293, f(x) has an inflection point.

The function f(x) = x^2 - x - ln(x) is a quadratic function combined with a logarithmic function.

To find the interval on which f is increasing, we need to determine where the derivative of f(x) is positive. Taking the derivative of f(x), we get f'(x) = 2x - 1 - 1/x. Setting f'(x) > 0, we solve the inequality 2x - 1 - 1/x > 0. Simplifying it further, we obtain x > 1. Therefore, the interval on which f is increasing is (0, ∞).

To find the interval on which f is decreasing, we need to determine where the derivative of f(x) is negative. Solving the inequality 2x - 1 - 1/x < 0, we get 0 < x < 1. Thus, the interval on which f is decreasing is (0, 1).

The local minimum is found by locating the critical point where f'(x) changes from negative to positive. In this case, it occurs at x = 1. Evaluating f(1), we find that the local minimum value is -1.

There is no local maximum in this function since the derivative does not change from positive to negative.

The inflection point is the point where the concavity of the function changes. To find it, we need to determine where the second derivative of f(x) changes sign. Taking the second derivative, we get f''(x) = 2 + 1/x^2. Setting f''(x) = 0, we find x = 0. Taking the sign of f''(x) for values less than and greater than x = 0, we observe that the concavity changes at x ≈ 0.293. Therefore, this is the inflection point of the function.

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The plan with the smallest one-time membership fee is Plan D.

The point-slope formula will be used to determine the equation that models the cost of each plans.

(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)

where (x₁, y₁) is the coordinates of point 1

(x₂, y₂) is the coordinates of point 2.

For the equation y = mx + b,

let x = number of discs rented

y = total cost

m = rental rate per disc

b = one-time membership fee

Plan A

(y - 14) = [(17 - 14)/(2 - 1)](x - 1)

y - 14 = 3x - 3

y = 3x + 11

Plan B

(y - 12) = [(16 - 12)/(2 - 1)](x - 1)

y - 12 = 4x - 4

y = 4x + 8

Plan C

(y - 10) = [(15 - 10)/(2 - 1)](x - 1)

y - 10 = 5x - 5

y = 5x + 5

Plan D

(y - 12) = [(21 - 12)/(2 - 1)](x - 1)

y - 12 = 9x - 9

y = 9x + 3

Hence, the plan with the smallest one-time membership fee, b, is Plan D.

Your question is incomplete, but most probably you are asking

"...Which plan has the smallest one-time membership fee?"

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Answer: The exact distance between the 2 points is √2, but the approximate distance is 1.41421356 (repeating decimal)

Hope this helped :D

Step-by-step explanation:

Let width of the rectangle be y

Length of rectangle = 3y + 12.1

Perimeter = 2(L + y) = 122.6

2 (4y + 12.1 ) = 122.6

8y + 24.2 = 122.6

y = 98.4 / 8

y (width) = 12.3

Length = 49

In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal, Option B states two lines are equal and two angles are equal, Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal. All of these provide the proof that ΔCAM≅ΔCOM.

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In order for ΔCAM≅ΔCOM to be proved, all three sides and all three angles must be equal. Option E does not provide proof of this as it only states that two angles are equal. So the correct answer is E. ΔCAM≅ΔCOM.

Corresponding sides are two sides in a polygon that are directly across from each other. This can be seen when two sides are connected by a line that is perpendicular to the other two sides.

ΔCAM≅ΔCOM can be proved when the two triangles have three corresponding sides and three corresponding angles that are equal.

However, option E does not provide proof of this as it only states that two angles are equal.

The other four options provide such proof.

Option A states that two angles are equal,

Option B states two lines are equal and two angles are equal,

Option C states two lines are equal and two angles are equal, and Option D states two lines are equal and two lines are equal.

All of these provide the proof that ΔCAM≅ΔCOM.

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Answer:

The number of sweets in the 10th bag is 53

Step-by-step explanation:

Given

Let the Number of sweets in a bag  be represented by x and frequency be represented by f

The table is as follows

x   F

39 1

40 2

41 5

42 0

43 1

Mean = 42

Required

How many sweets are in the 10th bag?​

Represent the number of sweets in the 10th bag by y;

The table becomes

x   F

39 1

40 2

41 5

42 0

43 1

y   1

The mean of observation is calculated using the following formula;

Mean = ∑fx/∑f

Where ∑ means summation

fx means f * x; i.e. product of frequency and number of sweets

f represents frequency;

Calculating ∑fx

∑fx = 39 * 1 + 40 * 2 + 41 * 5 + 42 * 0 + 43 * 1 + y * 1

∑fx = 39 + 80+ 205 + 0 + 43 + y

∑fx = 367 + y

Calcuating ∑f

∑f = 1 + 2 + 5 + 0 + 1 + 1

∑f =  10

Recall that

Mean = ∑fx/∑f and Mean = 42;

So, Mean = ∑fx/∑f becomes

\(42 = \frac{367 + y}{10}\)

Multiply both sides by 10

\(42 * 10 = \frac{367 + y}{10} * 10\)

\(420 = 367 + y\)

Subtract 367 from both sides

\(420 - 367= 367 -367 + y\)

\(53 = y\)

\(y = 53\)

Hence, the number of sweets in the 10th bag is 53

The total number of sweets in the 10th bag is 53 and this can be determined by using the formula of the mean.

Given :

The following steps can be used in order to determine the total number of sweets in the 10th bag:

Step 1 - The formula of the mean can be used in order to determine the total number of sweets in the 10th bag.

Step 2 - The formula of mean is given below:

\({\rm Mean}= \dfrac{\sum f \times x}{\sum f}\)

Step 3 - Now, substitute the values of the known terms from the given table in the above expression.

\({\rm Mean}= \dfrac{39 \times 1+40 \times 2+41 \times 5+42 \times 0+43 \times 1+y \times 1}{1+2+5+0+1+1}\)

Step 4 - Simplify the above expression.

\(\begin{aligned}\\42&= \dfrac{367+y }{10}\\y &=53 \\\end{aligned}\)

So, the total number of sweets in the 10th bag is 53.

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Using the logarithm quotient rule, it can be simplified to log1 - logA. Since log1 = 0 for any base, this simplifies further to -logA.

We simplify and solve the given expressions using the mentioned terms. Here are the step-by-step explanations for each expression:

1. logA: This expression represents the logarithm of a number A to a specified base. Without any base provided, it cannot be simplified further.

2. 1logAA: Since the coefficient of the logarithm is 1, this simplifies to logAA, which represents the logarithm of A to the base A. By definition, logAA = 1.

3. logA x Blog (a/b): This expression seems to have formatting issues, so I'll break it down into two separate expressions: - logA x B: This represents the logarithm of the product AB to a specified base. Using the logarithm product rule, it can be simplified to logA + logB. - log (a/b): This represents the logarithm of the quotient a/b to a specified base. Using the logarithm quotient rule, it can be simplified to loga - logb.

4. log A ^ B: This expression represents the logarithm of A raised to the power of B to a specified base. Using the logarithm power rule, it can be simplified to B * logA. 5. log 1/A: This expression represents the logarithm of the reciprocal of A (1/A) to a specified base.

Using the logarithm quotient rule, it can be simplified to log1 - logA. Since log1 = 0 for any base, this simplifies further to -logA.

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The element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

An atom consists of protons, neutrons, and electrons. The atomic number of an element corresponds to the number of protons present in the nucleus of an atom. Hence, the atomic number (p) of the given element is 17. A neutral atom contains an equal number of protons and electrons.

Therefore, the number of electrons (e-) of the given element is 17 as well. The number of neutrons (n°) can be calculated as the difference between the atomic mass number (A) and the atomic number (p).

In the case of the given element, the atomic number is 17, and the atomic mass number is 37 (as chlorine has two stable isotopes of mass numbers 35 and 37). Hence, n° = 37 - 17 = 20. Therefore, the element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

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Answer: x=7

               ab=21

               bc=14

Step-by-step explanation:

ab=3x

bc=2x±7

ac=42

3x±2x±7=42

5x±7=42

5x=42-7

5x=35

to get the value of x you divide 35 by 5x

35÷5x=7

so the value of x is 7

ab=3x

x=7

3x=7×3x

7×3=21

x=7

2x=7×2x

2×7=14

Answer:

a x=1

explanation:

i got it right on my test today

Answer:

The number will be 15

Hope you have a great day!

Answer:

15 is the correct answer

Given:

it is given that the four people took part in two conditions of a study and their data is given as

Person A: 2, 3 Person B: 6, 4 Person C: 2, 5 Person D: 3, 6

Find:

we have to find the Standard Deviation of their

You should remember the formula: Interest = P * R * T /100

Apply it in every part.

A) I = 624 * 5 * 3 / 100

I = 9360/100

I = 93.60

So, Total amount = 93.60 + 624 = $717.60

B) I = 4120 * 7 * 3 / 2*100

I = 86520 / 200

I = 432.60

So, Total amount = 432.60 + 4120 = $4552.60

C) I = 900 * 3.1 * 1 / 2 * 100

I = 2790 / 200

I = 13.95

So, Total Amount = 13.95 + 900 = $913.95

D) I = 275 * 4.8 * 8 /100

I = 10560 / 100

I = 105.60

So, Total amount = 105.60 + 275 = $380.60

Hope this helps