Is the square root of 16.45 a rational number or irrational number?

Answer:

x = 24

y = 19

Step-by-step explanation:

The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that recorded sales represent authorized transactions.

This is because shipments of goods are recorded as sales, and shipments of goods are for authorized sales. Therefore, recorded sales were for goods that were shipped.In addition, it is essential to note that FOB (Free On Board) shipping point is a legal term that indicates that the buyer assumes ownership of the goods as soon as they leave the seller's dock. As a result, the buyer is responsible for paying for the transportation of the goods from the seller's location to their destination.

Therefore, when a rich company sells household goods and appropriately records its sales upon shipment, it indicates that the goods are shipped FOB (Free On Board) shipping point. This method is used to ensure that shipments of goods are for authorized sales and that recorded sales were for goods that were shipped.

The external auditor gathers a sample of shipping documents and matches them to entries in the sales journal to provide corroborating evidence that the recorded sales represent authorized transactions.

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To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

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The equation of the tangent line to the graph of f(x) = sin³(x) + 1 at x = π rad is y = 1, which is a horizontal line passing through the point (π, 1).

To find the rate at which the value of the dining set is changing at exactly 10 years after its purchase, we need to calculate the derivative of the value function v(t) with respect to t and evaluate it at t = 10.

Taking the derivative of v(t), we have:

v'(t) = [d/dt (5500)] + [d/dt (6t^3/√(0.002t^2 + 1))].

The first term, [d/dt (5500)], is zero because 5500 is a constant.

For the second term, we can use the chain rule to differentiate 6t^3/√(0.002t^2 + 1):

v'(t) = 6t^3 * [d/dt (√(0.002t^2 + 1))] / √(0.002t^2 + 1)^2.

Simplifying further:

v'(t) = 6t^3 * (0.001t) / (0.002t^2 + 1).

Now we can evaluate v'(t) at t = 10:

v'(10) = 6(10)^3 * (0.001(10)) / (0.002(10)^2 + 1).

Calculating this expression gives us the rate at which the value of the dining set is changing at exactly 10 years after its purchase.

To find the equation of the tangent line to the graph of the function f(x) = sin³(x) + 1 at x = π rad, we need to find the slope of the tangent line and the point of tangency.

First, we find the derivative of f(x) using the chain rule:

f'(x) = 3sin²(x)cos(x).

Evaluating this derivative at x = π, we get:

f'(π) = 3sin²(π)cos(π) = 3(0)(-1) = 0.

The slope of the tangent line at x = π is 0.

To find the y-coordinate of the point of tangency, we substitute x = π into the original function:

f(π) = sin³(π) + 1 = 0³ + 1 = 1.

So, the point of tangency is (π, 1).

Now we have the slope (0) and a point (π, 1) on the tangent line. We can use the point-slope form of a line to find the equation of the tangent line:

y - 1 = 0(x - π).

Simplifying further:

y = 1.

Therefore, the equation of the tangent line to the graph of f(x) = sin³(x) + 1 at x = π rad is y = 1, which is a horizontal line passing through the point (π, 1).

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The probability that a card drawn randomly from a standard deck of 52 cards is a black six is 1/26 in its lowest terms.

A probability is a numerical value that represents the possibility of an event occurring. It's a likelihood or chance of an event happening.

The formula for probability is:

P (A) = number of favorable outcomes/total number of outcomes

The probability of drawing a black six from a standard deck of 52 cards is 1/26. There are 52 cards in a standard deck, which are evenly divided into four suits of 13 cards each: hearts, diamonds, clubs, and spades. Each suit contains cards numbered 2 through 10, as well as four face cards: jack, queen, king, and ace. Only two of these cards, namely the six of clubs and the six of spades, are black sixes.

There are four suits in a standard deck, each with a six. As a result, there are 4 x 1 = 4 ways to select a six card. There are 52 cards in a deck, so the probability of drawing a black six is:

1/52 × 4= 1/13

There is only one black six in each suit, therefore there are two black sixes in a deck. Since there are 52 cards in a deck and two black sixes, the probability of drawing a black six is 2/52, which simplifies to 1/26 in its lowest terms.

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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Answer: A

Step-by-step explanation:

For II,  when the numerator is expanded, it contains terms of ab and a^2 which makes it a quadratic function, not an algebraic function.

For III, tricky one. The a can be cancelled out in the numerator and denominator and the resulting fraction is (b-3)/3. However, this can be further simplified to 1/3b - 1, which makes it not an algebraic fraction anymore.

Evaluating the line integral integrate C 2xds gives 16/3

We can break the given curve into two parts as mentioned in the question: the parabola and the horizontal line segment. Let's integrate over each part separately.

For the parabola, we can parameterize the curve as x = t and y = t^2 where t goes from 0 to 2. Using the formula for line integrals, we get:

integrate (2t)(sqrt(1 + 4t^2)) dt from 0 to 2

This can be solved using u-substitution (u = 1 + 4t^2) and simplifying the resulting integral to get:

(4sqrt(17) + 2sqrt(5))/3

For the horizontal line segment, we can parameterize the curve as x = t and y = 4 where t goes from 2 to 4. Using the formula for line integrals, we get:

integrate 2 dt from 2 to 4

This simplifies to 4.

Adding the results of the two integrals, we get the final answer:

16/3

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We can conclude that those voting early were more likely to vote for Candidate 1 is true . Option A.

Based on the given information, we can draw the following conclusions:

A. Those voting early were more likely than those on election day to vote for Candidate 1.

This conclusion can be drawn from the fact that Candidate 1 earned 40% of the votes cast early, whereas they only received 30% of the votes on election day. Therefore, it is reasonable to assume that a higher percentage of early voters supported Candidate 1 compared to those who voted on election day.

B. If all of those who voted had voted early instead of on election day, Candidate 1 would be the winner of the election.

To determine if this statement is true, we need to calculate the total percentage of votes received by Candidate 1. Since 20% of the votes were cast early, and Candidate 1 earned 40% of those votes, they would have received 20% * 40% = 8% of the total votes from early voting. For the votes cast on election day, Candidate 1 received 30% of those votes.

As 15% of citizens voted, and if we assume all of them voted on election day, Candidate 1 would have received 15% * 30% = 4.5% of the total votes from election day. Therefore, the total votes for Candidate 1 would be 8% + 4.5% = 12.5%.

Since this is less than 50%, Candidate 1 would not be the winner of the election if all voters had voted early instead of on election day.

C. Citizens voting early were more likely to be hourly workers than those voting on election day.

The given information does not provide any evidence or data to support this conclusion. It is not possible to determine the occupation or employment status of citizens based solely on the voting method they chose.

D. If all citizens had voted, Candidate 1 would be the winner.

As explained in conclusion B, if we assume all citizens voted on election day, Candidate 1 would have received 12.5% of the total votes. Since this is less than 50%, Candidate 1 would not be the winner of the election if all citizens had voted.

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The required equivalent expression would be 3¹² y¹⁰ which is the correct option (C).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable.

We have been given that exponential function as

⇒ (3⁶/y⁻⁵)²

= (3⁶/1 / 1/y⁵)²

= (3⁶ × y⁵)²

= 3¹² y¹⁰

Therefore, the required equivalent expression would be 3¹² y¹⁰ which is the correct option (C).

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The question seems to be incomplete the correct question would be

Select the equivalent expression to (3⁶/y⁻⁵)²

(A) 3¹⁰ y¹²

(B) 3⁶ /y¹⁰

(C) 3¹² y¹⁰

The calculation section of the data sheet asks for both experimental and theoretical equations, with Equation 10-3 and Equation 10-4 provided as references. A more detailed explanation and analysis would require additional information and context.

Based on the given information, it seems that the question is related to an experiment involving standing waves on a string. The data sheet mentions the active length of a heavy string, the added mass of a light string, and the mass of a light weight-holder. The calculation section of the data sheet asks for both experimental and theoretical equations, with Equation 10-3 and Equation 10-4 provided as references.
To answer the question, more information is needed about the specific calculation or problem that needs to be solved. However, one possible approach could be to use the provided equations to determine the standing wave patterns on the string based on the given measurements. This could involve using the weight-holder mass, the active length of both the heavy and light strings, and the added mass of the light string to calculate the necessary variables for the equations.

Overall, the answer to the question will depend on the specific details and requirements of the experiment and the calculation being performed. A more detailed explanation and analysis would require additional information and context.

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Answer:

a) Slave labor was needed for the economy.

Step-by-step explanation:

Slave labor was needed for the economy of the southern states during the early 1800’s. Hence, the option (a) is correct.

2:10

because you times it by 2 both numbers and you get 2:10

the answer is 2:10 i ask my sister and she said its 2:10

-2, 2 and for the other 4,5

Answer:

(-2,2) ; (4,5)

Step-by-step explanation:

Answer:

n=1

Step-by-step explanation:

(5 + 4n) + 11 = -5 (3 - 7n)

5+4n+11=−5(3−7n)

simplify

4n+16=−5(3−7n)

expand

4n+16=−15+35n

regroup

4n+16=35n−15

subtract

16=35n−15−4n

simplify

16=31n−15

add

16+15=31n

simplify

31=31n

n=1

Hope this helps :)

(pls mark brainliest)

Answer:

n=22

Step-by-step explanation:

8 (5 + 4n) + 11 = -5 (3 - 7n)

distribute

=> 40+32n+11=-15+45n

add like terms

=> 51+32n=-15+35n

subtract 35n on both sides and subtract 51 on both sides

32n-35n=-15-51

add like terms

-3n=-66

divide both sides by -3

n=22

Answer:

$230

Step-by-step explanation:

Hes paid 200 for his wages but if he works overtime by 12 hours he gets half of the 5 dollars he earns per hour which is 2.5 which then is 2.5 times 12 which is then 30 plus the 200 he earned for the 40 hours.

Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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The difference quotient of the function g(x) = √x is  [√(x+h) -√x]/h

Difference quotient of the function:

Difference quotient of the function means a measure of the average rate of change of the function over an interval.

The difference quotient formula of a function y = f(x) is,

[ f(x + h) - f(x) ] / h

where

f (x + h) is obtained by replacing x by x + h in f(x)

f(x) is the actual function

Given,

Function g(x) = √x where x≥0.

Here we need to find the difference of the quotient of the function.

For that,

First we have to calculate the value of g(x + h),

By simply replacing the value of x as x + h,

So,

g(x + h) = √(x+h)

Now apply the values on the formula in order to solve it,

=> [√(x+h) -√x]/h

We can't simplify it further.

So, the difference quotient of function is,

=> [√(x+h) -√x]/h

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Answer: D

Step-by-step explanation:

took one for the team

Answer:

30 baskets per minute

Step-by-step explanation:

We know

Shaq shot 420 baskets in 14 minutes.

Find his basket rate in baskets per minute.

We take

420 / 14 = 30 baskets per minute

So, the answer is 30 baskets per minute.

Answer:

2/5

Step-by-step explanation:

Total=4+5+1=9+1=10

4/10=2/5

2/5 is the correct answer

Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

Y is equal to 2

Step-by-step explanation:

X equals -8

So,

4(-8) + 9y = -14

-32 + 9y = -14

-32 + 32 + 9y = -14 + 32

9y = 18

1/9 × 9y = 18 × 1/9

y = 2

Answer:

11.25

Step-by-step explanation:

Base on the given we can conclude that:

3.75 + 6 × 1.25

Now solve the following:

3.75 + 6 × 1.25

3.75 + 7.50

=11.25

~lenvy~

Answer:11.25

Step-by-step explanation:

Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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Answer:

2b+9

Step-by-step explanation:

(7-b)+(3b+2) ---> remove parenthesis

7-b+3b+2 ---> combine like terms

2b+9

The length of radius of the circle having center at (2-i) and point on circle at (8+7i) is 10 units .

To find the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i), we can use the distance formula , which is

The formula to find distance between 2 points (x₁, y₁) and (x₂, y₂) is given by:

⇒ d = √[(x₂ - x₁)² + (y₂ - y₁)²] ,

In this case, the center of the circle is (2-i), which means that the x-coordinate of the center is 2 and the y-coordinate is -1.

The point on the circle is (8+7i), which means that the x-coordinate of the point is 8 and the y-coordinate is 7.

By using distance formula, we can find distance between the center and the point on circle ,

⇒ d = √[(8 - 2)² + (7 - (-1))²]

⇒ d = √[6² + 8²]

⇒ d = √[36 + 64]

⇒ d = √100

⇒ d = 10

Therefore, the length of the radius of the circle is 10 units.

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The given question is incomplete , the complete question is

What is the length of the radius of a circle with a center at (2-i) and a point on the circle at (8+7i)?

Answer: B

Step-by-step explanation: A whole number is a number that is not a decimal or a fraction and is over 0.