(z+1/z)

**Answer: **[tex]\frac{(\sqrt{10} +3)^{2}+1 }{\sqrt{10}+3 }[/tex]

**Step-by-step explanation： **

A) A researcher believes that a particular study exhibits large sampling error. What does the researcher mean by sampling error? B) How can sampling error be diminished? C) Discuss why one of the following methods of sample selection might yield sampling error: convenience, snowball, or judgmental.

**Sampling error** refers to the discrepancy between sample characteristics and population characteristics. It can be diminished by increasing the sample size, using random sampling techniques, and improving response rates.

A) **Sampling error** refers to the difference between the characteristics of a sample and the characteristics of the population from which it was drawn.

In other words, sampling error refers to the degree to which the sample statistics **deviate** from the population parameters.

B) Sampling error can be diminished by **increasing** the sample size, using random sampling techniques to ensure that the sample is representative of the population, and minimizing sources of bias in the sampling process.

C) Convenience sampling, snowball sampling, and judgmental sampling are all methods of **non-probability sampling**, which means that they do not involve random selection of participants.

As a result, these methods are more likely to yield** sampling error **than probability sampling methods.

**Convenience sampling **involves selecting participants who are readily available, which may not be representative of the population of interest.

**Snowball sampling** involves using referrals from existing participants, which may create biases in the sample.

**Judgmental sampling **involves selecting participants based on the researcher's judgment of who is most relevant to the study, which may not be representative of the population of interest.

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Calculate the area of the following parallelogram: parallelogram with a 4 inch side, a 10 inch side, and 3 inches tall 26 in2 30 in2 40 in2 28 in2

The **area** of the parallelogram is** 21 in².**

**Area **is the region bounded by a plan shape.

To calculate the **area** of the **parallelogram, **we use the formula below

Formula:

A = h(a+b)/2...................... Equation 1Where:

A = Area of the parallelogramh = Height of the parallelograma, b = The two parallel sides of the parallelogramFrom the question,

Given:

h = 3 incha = 4 inchb = 10 inchSubstitute these values into equation 1

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8. Max is remodeling his house and is trying to come up with dimensions for his

bedroom. The length of the room will be 5 feet longer than his bed, and the

width of his room will be 7 feet longer than his bed. The area of his bed and the

room together is given by the function:

A(x) = (x + 5) (x + 7)

Part A: Find the standard form of the function A(x) and the y-intercept. Interpret

the y-intercept in the context.

Standard Form: A(x)

y- intercept:

Interpret the y-intercept:

=

The y-**intercept **represents the area of the bed and room together when the length and width of the bed are both zero and the **function **is given by the relation A(x) = x² + 12x + 35

Given data ,

To find the **standard **form of the **function **A(x), we first expand the expression:

A(x) = (x + 5) (x + 7)

A(x) = x² + 7x + 5x + 35

A(x) = x² + 12x + 35

So the standard form of the **function **A(x) is:

A(x) = x² + 12x + 35

To find the y-**intercept**, we set x = 0 in the function:

A(0) = 0² + 12(0) + 35

A(0) = 35

So the y-intercept is 35. In the context of the problem, the y-**intercept **represents the area of the bed and room together when the length and width of the bed are both zero.

Hence , the **function **is solved

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A segment that connects two points on a circle is called a

A. circumference

B. chord

C. radius

D. diameter

A segment that connects two points on a **circle** is called a **chord**, which makes the option B correct.

In the context of **circles**, a chord refers to a line segment that connects two points on the circumference of the circle. It can also be defined as the longest possible segment that can be drawn between two points on a circle. Every **chord** in a circle creates two arcs, one on each side of the chord.

Note that **diameter** is a special type of chord that passes through the center of the circle. It is the longest possible chord in a circle, and it divides the circle into two congruent semicircles.

Therefore, a segment that connects two points on a **circle** is called a **chord**.

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The singular points of the differential equation xy''+y'+y(x+2)/(x-4)=0 are Select the correct answer. 0 none 0, -2 0, -2, 4 0, 4

The singular point(s) of the differential** equation** are x = 4.

To find the** singular points** of the differential equation xy'' + y' + y(x + 2)/(x - 4) = 0, we need to find the values of x at which the coefficient of y'' or y' becomes infinite or undefined, since these are the points where the equation may behave differently.

The coefficient of y'' is x, which is never zero or undefined, so there are no singular points due to this term.

The coefficient of y' is 1, which is also never zero or **undefined, **so there are no singular points due to this term.

The coefficient of y is (x + 2)/(x - 4), which becomes infinite or undefined when x = 4, so 4 is a singular point of the **differential** equation.

Therefore, the singular point(s) of the differential equation are x = 4.

Note that this** analysis **does not consider any initial or boundary conditions, which may affect the behavior of the solution near the singular point(s).

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determine and from the given parameters of the population and sample size. u=83. =14, n=49

The population **mean**, denoted by u, is 83, and the standard deviation of the population, denoted by sigma, is 14. The sample size, denoted by n, is 49.

Hi! I'd be happy to help you with your question. Based on the given parameters of the **population** and sample size, we need to determine µ (mean) and σ (standard deviation).

From the information provided, we have the following parameters:

1. Population mean (µ) = 83

2. Population standard **deviation** (σ) = 14

3. Sample size (n) = 49

Using these parameters, we can determine the mean and **standard** deviation for the sample. Since the population mean is given, the sample mean will also be 83.

To find the standard error (SE), which is the standard deviation for the sample, use the formula:

SE = σ / √n

Plugging in the **values**, we get:

SE = 14 / √49

SE = 14 / 7

SE = 2

So, the sample mean (µ) is 83, and the **sample** standard deviation (SE) is 2.

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find a cubic function that has a local maximum value of 4 at 1 and a local minimum value of –1,184 at 7.

The **cubic function** that has a **local maximum value** of 4 at 1 and a **local minimum value** of –1,184 at 7 is:

[tex]f(x) = (-28/15)x^3 + (59/15)x^2 - 23x - 149/3[/tex]

We can start by writing the **cubic function **in the general form:

[tex]f(x) = ax^3 + bx^2 + cx + d[/tex]

To find the **coefficients of the function,** we can use the given information about the local maximum and minimum values.

First, we know that the function has a **local maximum value **of 4 at x = 1. This means that the derivative of the function is equal to zero at x = 1, and the **second derivative** is **negative** at that point. So, we have:

f'(1) = 0

f''(1) < 0

Taking the **derivative of the function**, we get:

[tex]f'(x) = 3ax^2 + 2bx + c[/tex]

Since f'(1) = 0, we have:

3a + 2b + c = 0 (Equation 1)

Taking the **second derivative of the function**, we get:

f''(x) = 6ax + 2b

Since f''(1) < 0, we have:

6a + 2b < 0 (Equation 2)

Next, we know that the function has a local minimum value of -1,184 at x = 7. This means that the derivative of the function is equal to zero at x = 7, and the second derivative is **positive **at that point. So, we have:

f'(7) = 0

f''(7) > 0

Using the same process as before, we can get two more **equations:**

21a + 14b + c = 0 (Equation 3)

42a + 2b > 0 (Equation 4)

Now we have four equations (Equations 1-4) with four unknowns (a, b, c, d), which we can **solve simultaneously** to get the values of the coefficients.

To solve the equations, we can** eliminate c and d **by subtracting Equation 3 from Equation 1 and Equation 4 from Equation 2. This gives us:

a = -28/15

b = 59/15

Substituting these values into Equation 1, we can solve for c:

**c = -23**

Finally, we can substitute all the values into the **general form** of the function to get:

[tex]f(x) = (-28/15)x^3 + (59/15)x^2 - 23x + d[/tex]

To find the value of d, we can use the fact that the function has a** local maximum value **of 4 at x = 1. Substituting x = 1 and y = 4 into the function, we get:

4 = (-28/15) + (59/15) - 23 + d

**Solving for d**, we get:

**d = -149/3**

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5.2 in

7 in

9 in

4.7 in

There is no question :(

write dissociation reactions for the following ionic compounds (example: bai2(s) ba2 (aq) 2 i−(aq) ): a) kcl(s) b) cabr2(s) c) fe2(so4)3(s)

**Potassium chloride **(KCl) is a binary **ionic compound **consisting of potassium cations (K+) and chloride anions (Cl-). a) KCl(s) → K+(aq) + Cl-(aq). b) CaBr2(s) → Ca2+(aq) + 2Br-(aq). c) Fe2(SO4)3(s) → 2Fe3+(aq) + 3SO42-(aq).

a) KCl(s) → K+(aq) + Cl-(aq)

**Potassium chloride **(KCl) is a binary ionic compound consisting of potassium cations (K+) and chloride anions (Cl-). When KCl is dissolved in water, it dissociates into its constituent ions, i.e., K+ and Cl-. This process is represented by the above chemical equation.

b) CaBr2(s) → Ca2+(aq) + 2Br-(aq)

**Calcium bromide **(CaBr2) is also a binary **ionic compound **consisting of calcium cations (Ca2+) and bromide anions (Br-). When CaBr2 is dissolved in water, it dissociates into its **constituent ions**, i.e., Ca2+ and 2Br-. This process is represented by the above chemical equation.

c) Fe2(SO4)3(s) → 2Fe3+(aq) + 3SO42-(aq)

Iron(III) sulfate (Fe2(SO4)3) is a complex ionic compound consisting of two iron cations (Fe3+) and three sulfate anions (SO42-). When Fe2(SO4)3 is dissolved in **water**, it dissociates into its constituent ions, i.e., 2Fe3+ and 3SO42-. This process is represented by the above chemical equation.

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Let f and g be functions such that, f(0)=2, g(0)=3, f'(0)=-10, g'(0)=-3. Find h'(0) for the function h(x)=g(x)f(x). h'(0)=??

If f and g be **functions** such that, f(0)=2, g(0)=3, f'(0)=-10, g'(0)=-3, then :

h'(0) = -36.

To find h'(0), we can use the** product rule** for **derivatives**. The product rule states that if h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x).

Applying this to our function h(x) = g(x)f(x), we get:

h'(x) = g'(x)f(x) + g(x)f'(x)

Now we can evaluate this **expression** at x = 0, since we are looking for h'(0). Plugging in the given values, we get:

h'(0) = g'(0)f(0) + g(0)f'(0)

= (-3)(2) + (3)(-10)

= -6 - 30

= -36

Therefore, we can state that the value of h'(0) = -36.

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The length of life, in hours, of a drill bit in a mechanical operation has a Weibull distribution with a = 2 and B = 50. Find the probability that the bit will fail before 10 hours of usage. The probability is approximately: O 1 O 0 O 0.5 O 0.8

The** probability **that the bit will fail before 10 hours of usage is:

P(X < 10) = F(10) = 1 - e^(-(10/50)^2) ≈ 0.3935

The Weibull distribution is given by the probability **density function**:

f(x) = (a/B) * (x/B)^(a-1) * e^(-(x/B)^a)

where a and B are the shape and** scale parameters**, respectively.

In this case, a = 2 and B = 50. We want to find the probability that the bit will fail before 10 hours of usage, i.e., P(X < 10), where X is the random variable representing the length of life of the drill bit.

Using the cumulative distribution function (CDF) of the Weibull distribution, we have:

F(x) = 1 - e^(-(x/B)^a)

Substituting the values of a and B, we get:

F(x) = 1 - e^(-(x/50)^2)

So the answer is approximately 0.4.

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Consider a city X where the probability that it will rain on any given day is 1%. You have a weather prediction algorithm that predicts the weather at the start of each day and obeys two rules: a. Before a rainy day, it'll predict rain with probability 90% b. Before a dry (no rain) day, it'll predict rain with probability 1%. Find the probability that 1. The probability that it won't rain given that your algorithm predicted a rainy day. 0.01 X 0.01 2. The probability that it will rain given that your algorithm predicted a dry day. 0.1 X 0.1

The **probability **that it won't rain given that your algorithm predicted a rainy day is approximately 9.1%. The probability that it will rain given that your algorithm predicted a dry day is approximately 0.01%.

When the algorithm predicts rain, it has a 90% **accuracy **rate, meaning that it correctly predicts rain 90% of the time. However, since the overall probability of rain in city X is only 1%, most of the algorithm's rainy predictions will be false positives. Using conditional probability, we can **calculate **the probability of no rain given a rainy prediction as follows: (0.01 * 0.1) / (0.01 * 0.1 + 0.99 * 0.9) ≈ 0.0091 or 9.1%.

Conversely, when the **algorithm **predicts a dry day, it has a 99% accuracy rate, meaning that it correctly predicts no rain 99% of the time. Since the overall probability of rain is 1%, the algorithm's dry predictions will mostly be true negatives. Using conditional probability again, we can calculate the probability of rain given a dry prediction as follows: (0.99 * 0.01) / (0.99 * 0.01 + 0.01 * 0.9) ≈ 0.0001 or 0.01%.

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Which numbers round to 4.9 when rounded to the nearest tenth? Mark all that apply.

A 4.95

B 4.87

C 4.93

D 5.04

E 4.97

**Answer:**

B, C

**Step-by-step explanation:**

A would round up to 5

B would round up to 4.9

C would round down to 4.9

D would round down to 5

E would round up to 5

Out of all these only B and C round to 4.9

**Answer:**

B and C

**Step-by-step explanation:**

A 4.95 --- this would round to 5.00.

B 4.87 - - - this would round to 4.9

C 4.93 - - - this would round to 4.9

D 5.04 - - - - this would round to 5.0

E 4.97 - - - this would round to 5.0

Which of the following statements about decision analysis is false? a decision situation can be expressed as either a payoff table or a decision tree diagram there is a rollback technique used in decision tree analysis ::: opportunity loss is the difference between what the decision maker's profit for an act is and what the profit could have been had the decision been made Decisions can never be made without the benefit of knowledge gained from sampling

The** statement **"Decisions can never be made without the benefit of knowledge gained from sampling" is false.

Sampling refers to the process of selecting a subset of data from a larger population to make inferences about that** population.** While sampling can be useful in some decision-making contexts, it is not always necessary or appropriate.

In many decision-making situations, there may not be a well-defined population to sample from. For example, a business owner may need to decide whether to invest in a new product line based on market research and other available information, without necessarily having a representative sample of potential customers.

In other cases, the costs and logistics of sampling may make it impractical or impossible.

Additionally, some** decision-making** approaches, such as decision tree analysis, rely on modeling hypothetical scenarios and their potential outcomes without explicitly sampling from real-world data. While sampling can be a valuable tool in decision-making, it is not a requirement and decisions can still be made without it.

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Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Given the argument: K ⊃ Q / Q ⊃ ∼ K // K ≡ Q This argument is:

The given argument "K ⊃ Q / Q ⊃ ∼ K // K ≡ Q" is **valid**.

To determine the validity of the **argument **"K ⊃ Q / Q ⊃ ∼ K // K ≡ Q," we construct an ordinary truth table. The argument consists of two premises and a conclusion. The symbol "⊃" represents the conditional implication, "∼" represents negation, and "≡" represents equivalence.

We assign truth values (T or F) to the **atomic** propositions K and Q and evaluate the truth values of the premises and the conclusion based on the given argument. By systematically filling out the truth table, we can examine all possible combinations of truth values for K and Q.

After constructing the truth table, we observe that in every row where the** premises** K ⊃ Q and Q ⊃ ∼ K are true, the conclusion K ≡ Q is also true. Therefore, the argument is valid.

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Becoming a fine artist can happen overnight.

True

False

trueeeee but like very unlikely

**Answer:**

**Step-by-step explanation:**

True. But there is a very high chance of not happening

P is a function that gives the cost, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces,w

Given that P is a **function** that gives the **cost**, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w.In order to write a function, we must find the rate at which the cost changes with respect to the weight of the letter in ounces.

Let C be the cost of **mailing** a letter from the United States to **Mexico** in 2018 based on the weight of the letter in ounces, w.Let's assume that the cost C is directly proportional to the **weight** of the letter in ounces, w.Let k be the constant of proportionality, then we have C = kwwhere k is a constant of proportionality.Now, if the cost of mailing a letter with weight 2 ounces is $1.50, we can find k as follows:1.50 = k(2)⇒ k = 1.5/2= 0.75 Hence, the cost C of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w is given by:C = 0.75w dollars. Answer: C = 0.75w

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How many more bushels did mr myers pick of golden delicious apples than of red delicious apples

The amount of **golden **delicious apples than **red **delicious apples that Mr. Myers picked would be 14 1/8.

The extra amount of golden delicious apples that **Mr. Myers** picked in comparison to the red delicious apples that Mr. Myers picked would be gotten by subtracting the amount of golden **delicious **apples from red delicious apples as follows:

27 2/8 - 13 1/8

= 14 1/8

So, the amount with which the number of golden delicious apples that Mr. Myers got was greater than the red delicious apples is 14 1/8

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Complete Question:

Mr.Myers picked 13 1/8 bushels of red delicious apples and 27 2/8 bushels of golden delicious apples. How many bushels of golden delicious apples than of red delicious apples did he pick?

find the first three nonzero terms in the taylor polynomial approximation to the de y″ 9y 9y3=6cos(4t) , y(0)=0,y′(0)=1.

The first three nonzero terms in the **Taylor polynomial **approximation to $y(t)$ are $t + \frac{1}{3}t^2 + O(t^3)$.

Using these initial conditions, we can write the first few terms of the **Taylor polynomial** approximation as:

\begin{align*}

y(t) &\approx y(0) + y'(0)t + \frac{y''(0)}{2!}t^2 \

&= t + \frac{1}{2}y''(0)t^2 \

&= t + \frac{1}{2}\left(\frac{6\cos(0)}{9\cdot 0 + 9}\right)t^2 \

**&= t + \frac{1}{3}t^2**

\end{align*}

Therefore, the first three nonzero terms in the Taylor polynomial approximation to $y(t)$ are **$t + \frac{1}{3}t^2 + O(t^3)$.**

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List three different ways to write 511 as the product of two powers. Explain why all three of your expressions are equal to 511.

Three **different **ways to write [tex]5^{11}[/tex] as the product of two powers are:

[tex]5^{1} * 5^{10} \\\\5^{5} * 5^{6} \\\\5^{3} * 5^{8}[/tex]

How to write the powers in different waysTo write the powers in different ways that all translate to 5 raised to the power of 11, we need to first recall that the product of the same bases is gotten by summing up the bases.

In this case, 1 times 10 is 1 plus 10 which is 11. The same applies for 5 and 6 and 3 and 8. So, the above are three ways to rewrite the expression.

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Lincoln invested $2,800 in an account paying an interest rate of 5 3/8 % compounded continuously. Lily invested $2,800 in an account paying an interest rate of 5 7/8 % compounded quarterly. After 15 years, how much more money would Lily have in her

account than Lincoln, to the nearest dollar?

Given, Lincoln invested $2,800 in an account paying an interest rate of 5 3/8 % compounded continuously. Lily invested $2,800 in an account paying an **interest rate** of 5 7/8 % compounded quarterly.

After 15 years, we need to calculate how much more money would Lily have in her account than Lincoln, to the nearest dollar. Calculation of Lincoln's **investment Continuous compounding** formula is A = Pe^rt Where, A is the amount after time t, P is the principal amount, r is the annual interest rate, and e is the base of the natural logarithm.

Lincoln invested $2,800 in an account paying an interest rate of 5 3/8 % compounded continuously .i.e. r = 5.375% = 0.05375 and P = $2,800Thus, A = Pe^rtA = $2,800 e^(0.05375 × 15)A = $2,800 e^0.80625A = $2,800 × 2.24088A = $6,292.44Step 2: Calculation of Lily's investmentThe formula to calculate the amount in an account with quarterly compounding is A = P (1 + r/n)^(nt)Where, A is the amount after time t, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time. Lily invested $2,800 in an account paying an interest rate of 5 7/8 % compounded quarterly.i.e. r = 5.875% = 0.05875, n = 4, P = $2,800Thus, A = P (1 + r/n)^(nt)A = $2,800 (1 + 0.05875/4)^(4 × 15)A = $2,800 (1.0146875)^60A = $2,800 × 1.96494A = $7,425.16Step 3: **Calculation of the difference** in the amount After 15 years, Lily has $7,425.16 and Lincoln has $6,292.44Thus, the difference in the amount would be $7,425.16 - $6,292.44 = $1,132.72Therefore, the amount of money that Lily would have in her account than Lincoln, to the nearest dollar, is $1,133.

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calculate the fundamental vector product: r(u,v)=2ucos(v)i 2usin(v)j 2k

**Step-by-step explanation:**

the answer is 2k(2ucos)2usin(vi)

An object moves on a trajectory given by r(t)-(10 cos 2t, 10 sin 2t) for 0 t ?. How far does it travel?

Thus, the object travels a distance of 10π units along the given** trajectory.**

To find out how far an object travels along a given trajectory, we need to calculate the arc length of the curve. The formula for **arc length** is given by:

L = ∫_a^b √[dx/dt]^2 + [dy/dt]^2 dt

where L is the arc length, a and b are the start and **end points** of the curve, and dx/dt and dy/dt are the derivatives of x and y with respect to time t.

In this case, we have the trajectory r(t) = (10 cos 2t, 10 sin 2t) for 0 ≤ t ≤ π/2. Therefore, we can calculate the derivatives of x and y as follows:

dx/dt = -20 sin 2t

dy/dt = 20 cos 2t

Substituting these values into the formula for arc length, we get:

L = ∫_0^(π/2) √[(-20 sin 2t)^2 + (20 cos 2t)^2] dt

= ∫_0^(π/2) √400 dt

= ∫_0^(π/2) 20 dt

= 20t |_0^(π/2)

= 10π

Therefore, the object travels a distance of 10π units along the given trajectory.

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find a value of c> 1 so that the average value of f(x)=(9pi/x^2)cos(pi/x) on the interval [2, 20]

c = pi/2, and the value of c > 1 such that the **average value** of f(x) on the interval [2, 20] is equal to c is c = pi/2.

The average value of a **function** f(x) on the interval [a, b] is given by:

Avg = 1/(b-a) * ∫[a, b] f(x) dx

We want to find a value of c > 1 such that the average value of the function [tex]f(x) = (9pi/x^2)cos(pi/x)[/tex] on the** interval** [2, 20] is equal to c.

First, we find the integral of f(x) on the interval [2, 20]:

[tex]∫[2, 20] (9pi/x^2)cos(pi/x) dx[/tex]

We can use **u-substitution** with u = pi/x, which gives us:

-9pi * ∫[pi/20, pi/2] cos(u) du

Evaluating this integral gives us:

[tex]-9pi * sin(u) |_pi/20^pi/2 = 9pi[/tex]

Therefore, the average value of f(x) on the interval [2, 20] is:

[tex]Avg = 1/(20-2) * ∫[2, 20] (9pi/x^2)cos(pi/x) dx[/tex]

= 1/18 * 9pi

= pi/2

Now we set c = pi/2 and solve for x:

Avg = c

[tex]pi/2 = 1/(20-2) * ∫[2, 20] (9pi/x^2)cos(pi/x) dx[/tex]

pi/2 = 1/18 * 9pi

pi/2 = pi/2

Therefore, c = pi/2, and the value of c > 1 such that the average value of f(x) on the interval [2, 20] is equal to c is c = pi/2.

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In a recent election Corrine Brown received 13,696 more votes than Bill Randall. If the total numb

Corrine Brown received

votes.

The **number **of **votes **for each candidate would be:

Corrine Brown = 66,617

Bill Randall = 52,920

How to determine the number of votesTo determine the number of votes for each **candidate**, we will make some equations with the values given.

Equation 1 = CB + BR = 119,537

(BR + 13,696) + BR = 119,537

2BR + 13,696 = 119,537

Collect like terms

2BR = 119,537 - 13,696

2BR = 105841

Divide both sides by 2

BR = 52,920

This means that **Corrine Brown** received 52,920 + 13,696 = 66,617

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Complete Question:

In a recent election corrine brown received 13,696 more votes than bill Randall. If the total number of votes was 119,537, find the number of votes for each candidate

!!HELPP PLEASE 30 POINTSSS!!

this for financial mathematics, thank you for your help!

2) a. The **average **daily balance for the billing period, which ends on June 11. May has 31 days is $547.56.

b. $0.71 is the finance charge calculated on **June 11.** The monthly periodic rate is 1.3%.

c. $548.27 is the **Smith's **new credit card balance on June 12.

3) $83.50 money was **saved **by making the payment earlier in the billing cycle.

a. It does matter when you make your payment because the finance charge is based on the balance at the end of the **billing period.**

b. It also matters when you make your purchases because the daily balance is calculated based on the **charges **and payments up to and including **each day**.

2)

a. To find the average daily balance, we need to first **calculate **the balance for each day of the billing period. The balance for each day is the **sum **of charges and **payments **up to and including that day. We can calculate the balances as follows:

May 12: $378.50

May 13: $378.50 + $129.79 = $508.29

May 14-31: $508.29

June 1: $508.29 + $135.85 = $644.14

June 2-7: $644.14

June 8: $644.14 + $37.63 = $681.77

June 9: $681.77 - $50.00 = $631.77

June 10-11: $631.77

Next, we add up the daily balances and divide by the number of days in the **billing **period:

Average daily **balance **= (31 x $508.29 + 6 x $644.14 + 2 x $681.77) / 39

= $21,328.99 / 39

= $547.56

b. To calculate the finance charge, we first need to **calculate **the daily periodic rate, which is the monthly periodic rate divided by the number of days in a **month**:

Daily periodic rate = 1.3% / 30

= 0.04333%

Next, we multiply the average daily balance by the daily **periodic rate **and by the number of days in the billing period:

Finance charge = $547.56 x 0.0004333 x 30

= $0.71

c. The Smith's new **credit card** balance on June 12 is the sum of the **average** daily balance and the finance charge:

**New balance** = $547.56 + $0.71

= $548.27

3) The payment was made on June 9, which is 3 days before the end of **the billing period.** If the payment had been made on June 11, the balance would have been $631.77 instead of $548.27. This means that the **payment **saved the Smiths $83.50 in finance charges.

a) It does matter when you make your payment because the finance **charge **is based on the balance at the end of the billing period. If you make a payment earlier in the **billing cycle**, your balance will be lower at the end of the **period **and you will pay less in finance charges.

b) It also matters when you make your **purchases **because the daily balance is calculated based on the charges and payments up to and including each day. If you make a large purchase early in the billing cycle, your average **daily **balance will be higher and you will pay more in **finance **charges.

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use direct integration to determine the mass moment of inertia of the homogeneous solid of revolution of mass m about the x- and y-axes. ans: ixx = (2/7)mr 2 , iyy = (1/7)mr 2 (2/3)mh2

the mass moment of **inertia **about the x-axis is ixx = (2/7)[tex]mr^{2}[/tex] and about the** y-axis** is iyy = (1/7)[tex]mr^{2}[/tex] + (2/3)[tex]mh^{2}[/tex]

To find the mass moment of **inertia**, we consider the solid of revolution as a collection of infinitesimally thin disks or cylinders stacked together along the axis of revolution. Each disk or cylinder has a mass element dm.

For the **mass moment** of inertia about the x-axis (ixx), we integrate the contribution of each mass element along the axis of revolution:

ixx = ∫ [tex]r^{2}[/tex] dm

Since the solid is **homogeneous**, dm = ρ dV, where ρ is the density and dV is the volume element. For a solid of revolution, dV = πr^2 dh, where h is the height of the solid.

Substituting the expressions and performing the **integration**, we get:

ixx = ∫ [tex]r^{2}[/tex] ρπr^2 dh

= ρπ ∫ [tex]r^{4}[/tex] dh

= [tex](1/5)\beta \pi r^{4}[/tex] h

Since the solid is homogeneous, the mass m = [tex]\beta \pi r^{2}[/tex] h. Substituting this in the equation above, we get:

ixx = (1/5)m [tex]r^{2}[/tex]

Similarly, for the mass moment of inertia about the y-axis (iyy), we integrate along the radius r:

iyy = ∫[tex]r^{2}[/tex] dm

= ∫ [tex]r^{2}[/tex] [tex]\beta \pi r^{2}[/tex] dh

= ρπ ∫ [tex]r^{4}[/tex] dh

= (1/5)[tex]\beta \pi r^{4}[/tex] h

Since the height of the solid is h, substituting [tex]\beta \pi r^{2}[/tex] h = m, we get:

iyy = (1/5)m [tex]r^{2}[/tex] + [tex](2/3)mh^{2}[/tex]

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what is the upper sum for f(x)=17−x2 on [3,4] using four subintervals?

the upper sum for f(x) = 17 - [tex]x^{2}[/tex] on the **interval **[3, 4] using four subintervals is **approximately **6.46875.

To calculate the upper sum, we divide the **interval **[3, 4] into four subintervals of equal width. The width of each subinterval is (4 - 3) / 4 = 1/4.

Next, we evaluate the function at the right endpoint of each **subinterval **and multiply it by the width of the subinterval. For this function, we need to find the maximum value within each subinterval. Since the function f(x) = 17 - [tex]x^{2}[/tex] is a downward-opening parabola, the maximum value within each subinterval occurs at the left endpoint.

Using four subintervals, the right endpoints are: 3 + (1/4), 3 + (2/4), 3 + (3/4), and 3 + (4/4), which are 3.25, 3.5, 3.75, and 4 respectively.

Evaluating the function at these right **endpoints**, we get: f(3.25) = 8.5625, f(3.5) = 10.75, f(3.75) = 13.5625, and f(4) = 13.

Finally, we calculate the upper sum by summing the **products **of each **function **value and the subinterval width: (1/4) × (8.5625 + 10.75 + 13.5625 + 13) = 6.46875.

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find the taylor polynomial 2() for the function ()=63 at =0.

The second-degree **Taylor polynomial** for the function ()=63 at =0 is simply 63.

To find the Taylor polynomial 2() for the function ()=63 at =0, we need to use the formula for the nth-degree Taylor **polynomial**:

2() = f(0) + f'(0)() + (1/2!)f''(0)()^2 + (1/3!)f'''(0)()^3 + ... + (1/n!)f^(n)(0)()^n

Since we are only interested in the second-degree Taylor polynomial, we need to calculate f(0), f'(0), and f''(0):

f(0) = 63

f'(x) = 0 (the **derivative **of a constant function is always 0)

f''(x) = 0 (the second derivative of a constant function is always 0)

Substituting these values into the formula, we get:

2() = 63 + 0() + (1/2!)0()^2

2() = 63

Therefore, the second-degree Taylor polynomial for the function ()=63 at =0 is simply 63.

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18. Ten apples, four of which are rotten, are in a refrigerator. Three apples are randomly selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the probability distribution, then find the mean and standard deviation for the random variable x. (Hint: you can use Table A-1 to find the probabilities)

The** standard deviation** of x can be 0.725.

The table describing the **probability **distribution of x is as follows

x P(X=x)

0 10/120

1 48/120

2 42/120

3 20/120

To find the probabilities, we can use the** hypergeometric** distribution formula:

P(X=x) = (C(4,x) * C(6,3-x)) / C(10,3)

where C(n,r) represents the number of combinations of n things taken r at a time.

The mean of x can be found using the formula:

E(X) = Σ(x * P(X=x))

= 0*(10/120) + 1*(48/120) + 2*(42/120) + 3*(20/120)

= 1.4

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