Given: r(x) = x3 - 7, k(x) = 5 ln (2x) Find: (k ○ r) (x)

Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.

To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.

For Brett:

APR = 12.6%

MPR = 12.6% / 12 = 1.05%

For Andy:

APR = 16.2%

MPR = 16.2% / 12 = 1.35%

Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.

For Brett:

Finance charge = $7,980 * 1.05% = $83.79

For Andy:

Finance charge = $7,980 * 1.35% = $107.73

To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:

Difference = $107.73 - $83.79 = $23.94

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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To solve:

On simplification we get,

Hence, the answer is x=4.

Answer:

Step-by-step explanation:

You want a transformation that maps figure P in the 3rd quadrant to figure Q in the second quadrant.

The figures have the same orientation (sequence of angles and side lengths), so reflection is not needed as part of the transformation.

The shorter mid-length side in Figure P has a slope of -1, and the corresponding side in Figure Q has a slope of +1. This can be the result of a 90° clockwise rotation about the origin.

Rotation 90° CW about the origin will map the right-angle corner from (-7, -7) to (-7, 7).

The right-angle corner in Figure Q is at (-7, 12), so a translation upward after the rotation is required. The amount of that translation is 12-7 = 5 units.

Translation upward by 5 units will map the right angle corner from its rotated position at (-7, 7) to its position in Figure Q at (-7, 12).

The series of transformations could be ...

__

Additional comment

The required transformation can be accomplished in one step by rotation 90° CW about the point (2.5, 2.5).

If Figure P is rotated 90° CW about its right-angle corner, then translation up by 19 units will map it to Figure Q. That is, there are many combinations of rotation and translation that will do the job.

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

From the question, we were told that if the parent function is y = 2^x. We are to determine which is the function of the graph.

The parent function is in this form:

y = ab^x

Where:

a = the y-intercept, when x = 0

In the graph, we can see that the y-intercept is at:

y = 1/2

y = 0.5

Therefore, y = 0.5(2)^x

So, the correct option i

Yes, there are several ways to understand the concept of a limit in calculus without going into the details of a formal proof. One way to understand the concept of a limit is to think of it as a way to measure how close a function gets to a particular value as the input to the function gets closer and closer to a certain number. For example, if we have a function f(x) and we want to find the limit of the function as x approaches 2, we can think of this as asking "how close does f(x) get to a certain number as x gets closer and closer to 2?"

Another way to understand the concept of a limit is to think of it as a way to describe the behavior of a function as the input gets very large or very small. For example, if we have a function f(x) and we want to find the limit of the function as x approaches infinity, we can think of this as asking "how does f(x) behave as x gets very large?"

Overall, the concept of a limit is a fundamental concept in calculus that allows us to describe and analyze the behavior of functions as the input to the function changes. While a formal proof of the limit can be quite complex, there are several intuitive ways to understand the concept without going into the details of the proof.

Answer:

4 miles

Step-by-step explanation:

In order to find how many miles the car will travel in 0.5 hours, we can set up a proportion.

\(\frac{32}{4} = \frac{x}{0.5}\)

We can now cross multiply to find the value of x.

\(32 \cdot 0.5 = 16\\\\16\div4 = 4\)

So the car can travel 4 miles in 0.5 hours.

Hope this helped!

Answer:

4 miles

Step-by-step explanation:

32 divided by 4=8

8 divided by 2= 4

since 0.5 is half of one hour

B because it is the only one were the 'y-coordinate' is not the same for 2 different 'x-coordinates'

hope this helps!!

The true statements are:

Fractions are numbers that are represented as the quotient of two integers

From the table, we have the following measurements

39/50 inch, 4/5 inch, 76/99 inch, 1/2 inch, 26/33 inch, 9/10 inch, 2/3 inch and 7/9 inch

Convert the fractions to decimal

0.78 inch, 0.80 inch, 0.77 inch, 0.50 inch, 0.78 inch, 0.90 inch, 0.67 inch and 0.78 inch

From the list of measurements,

3 lengths are less than 0.78 inch wide

This is less than half the number of rulers (i.e 4)

Hence, the supervisor does not need to call someone

When the fractions are converted to decimal, we have:

\(\frac{39}{50} = 0.78\)

This means that:

0.78 as a simplified fraction is 39/50

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She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car

The total amount of the car loan = 13456.44

Number of instalments = 36 monthly payments

Affordable installment per month = $350

EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.

Total payment that can be made using the instalments = Monthly instalments * Number of instalments

= 350*36

Total payment that can be made using the instalments = 12600

The amount remaining after paying instalments = 13456.44 - 12600

= 856.44

Downpayment required = $856.44

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The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

?

Step-by-step explanation:

Answer:

13. 3.5

14. 21.5

Step-by-step explanation:

For each one, divide the real size by what 1 unit measures. For the first question, the real size is 10.5 and 1 unit (in this case an inch) represents 3 feet. So do 10.5/3 to get the number of inches uses to represent the total width. 10.5/3 = 3.5

For the second one, the real size is 186 meters. And 1 unit (this time it's a centimeter) represents 4 meters. So do 186/4 and you get 21.5, which is the number of centimeters used to represent the total height.

a. This situation would be a binomial experiment if the following conditions are met:

The trials are independent: The selection of one part does not affect the selection of the other.

Each trial has two possible outcomes: In this case, defective or non-defective.

The probability of success (finding a defective part) remains constant for each trial: In this case, the probability is 3% or 0.03.

The number of trials is fixed: We are selecting two parts, so the number of trials is predetermined.

b. Here is a tree diagram representing the two-trial experiment:

          D                ND

        /   \            /   \

       D     ND         D     ND

The branches represent the two trials, with D representing a defective part and ND representing a non-defective part.

c. To find the number of experimental outcomes resulting in exactly one defect, we can observe that there are two outcomes that meet this criterion: D-ND and ND-D. Both represent one defective part and one non-defective part.

d. The probabilities associated with finding no defects, exactly one defect, and two defects can be calculated as follows:

Probability of finding no defects: (1 - probability of finding a defective part) * (1 - probability of finding a defective part) = (1 - 0.03) * (1 - 0.03) = 0.97 * 0.97 = 0.9409.

Probability of finding exactly one defect: (probability of finding a defective part) * (probability of finding a non-defective part) + (probability of finding a non-defective part) * (probability of finding a defective part) = 0.03 * 0.97 + 0.97 * 0.03 = 0.0582.

Probability of finding two defects: (probability of finding a defective part) * (probability of finding a defective part) = 0.03 * 0.03 = 0.0009.

Therefore, the probabilities associated with finding no defects, exactly one defect, and two defects are approximately 0.9409, 0.0582, and 0.0009, respectively.

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Answer:

28

Step-by-step explanation:

35% × 80 =

(35 ÷ 100) × 80 =

(35 × 80) ÷ 100 =

2,800 ÷ 100 =

28

I hope this helps :)

Answer:

You would have to add two different percents to get to 35. You would need to add 25% and 10%. So, I would divided 80 by 4, which gets me 20, and divided 80 by 10, which gets me 8. If you add 20 and 8 together, that gets you 28. Your answer is 28.

Not sample answer, but correct

Answer:

\(\text {CI} = (60.54, \: 81.46)\\\\\)

Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)

Step-by-step explanation:

Let us find out the mean savings for a televisit to the doctor from the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be

\(\bar{x} = \$71\)  

Let us find out the standard deviation of savings for a televisit to the doctor from the given data.

Using Excel,

=STDEV(number1, number2,....)

The standard deviation is found to be

 \(s = \$ 22.35\)

The confidence interval is given by

\(\text {confidence interval} = \bar{x} \pm MoE\\\\\)

Where the margin of error is given by

\($ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\\)

Where n is the sample of 20 online doctor visits, s is the sample standard deviation and \(t_{\alpha/2}\) is the t-score corresponding to a 95% confidence level.

The t-score is given by is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 20 - 1 = 19

From the t-table at α = 0.025 and DoF = 19

t-score = 2.093

So, the margin of error is

\(MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 2.093\cdot \frac{22.35}{\sqrt{20} } \\\\MoE = 2.093\cdot 4.997\\\\MoE = 10.46\\\\\)

So the required 95% confidence interval is

\(\text {CI} = \bar{x} \pm MoE\\\\\text {CI} = 71 \pm 10.46\\\\\text {CI} = 71 - 10.46, \: 71 + 10.46\\\\\text {CI} = (60.54, \: 81.46)\\\\\)

Therefore, we are 95% confident that actual mean savings for a televisit to the doctor is within the interval of ($60.54 to $81.46)

The total cost of the new outfits for all the members is $264. So, the correct answer is option A.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, the shirts are $21, the pants are $26, the hats are $6 and the canes are $13.

Here, the cost of outfits for a person is

(21+26+6+13)=66

The cost of outfits for the four members is

66×4=$264

Therefore, option A is the correct answer.

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Answer: y= 3 times 2 to the power x. Second answer

Step-by-step explanation:

if you plug in 0 for x, y= 3x 1= 3

if you plug in 1 for x y= 3 x 2 = 6

Look at the x values and y values

(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.

Answer: 0.0496

Step-by-step explanation:

If events are said to be independent it means that the probability of one happening does not affect the probability of the other.

In calculating the probability that an employee is both male and a drug user using independent events, multiply the probabilities of the individual events to find the probability of the the events happening together.

P(A) * P(B) = P(A and B)

0.08 * 0.62 = 0.0496

Probabilities are used to determine the chances of events.

The probability that a randomly chosen employee is a male drug user is 0.0496

Represent the two events as A and B, such that:

\(P(A) = 0.08\)

\(P(B) =0.62\)

So, the probability that a randomly chosen employee is a male drug user is calculated as:

\(P(A\ and\ B) =P(A) \times P(B)\)

This gives

\(P(A\ and\ B) =0.08 \times 0.62\)

Multiply

\(P(A\ and\ B) =0.0496\)

Hence, the probability that a randomly chosen employee is a male drug user is 0.0496

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Answer:

0.5 seconds and 1.5 seconds.

Step-by-step explanation:

h(t) = -16t^2 + 32t + 2

14 = -16t^2 + 32t + 2

16t^2 - 32t - 2 + 14 = 0

16t^2 - 32t + 12 = 0

8t^2 - 16t + 6 = 0

4t^2 - 8t + 3 = 0

(2x - 3)(2x - 1) = 0

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

2x - 1 = 0

2x = 1

x = 1/2

x = 0.5

So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.

Hope this helps!

Answer:

Below in bold.

Step-by-step explanation:

f(x) = -0.1x^2 - 0.2x + 20

(a) f'(x) = -0.2x - 0.2

(b)  When 11,000 units are demanded

Rate of change = f' (11) =  -0.2(11) - 0.2

= -2.4 dollars / 1000 lamps.

Unit price at this level of demand =  p

= -0.1(11)^2 - 0.2(11) + 20

= 5.7 dollars.

a. Find f '(x). f '(x)

This means that we should find the marginal value if x and this will be:

f(x) = −0.1x² − 0.2x + 20  = -0.2x - 0.2

b. What is the rate of change of the unit price (in dollars per 1,000 lamps) when the quantity demanded is 11,000 units?

= -0.2x - 0.2

= -0.2(11000/1000) - 0.2

= -2(11) - 0.2

= -2.2 -02.

= -2.4

The unit price will be:

p = -0.1x² − 0.2x + 20  

p = -0.1(11)² - 0.2(11) + 20

p = -12.1 - 2.2 + 20

p = $5.7

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Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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77 is 0.7% of 11000

this number is a lot greater than 77.

Let 77 is 0.7% of m

0.7 percent of m = 77

(0.7/100) * m = 77

m = 77 * (100/0.7)

m = 11000

Therefore, 77 is 0.7% of 11000

this number is a lot greater than 77.

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A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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Answer:

-39a - 16 is not the answer, it's -5/6a - 5/8

Step-by-step explanation:

Took the test and got it incorrect.

Answer:

-5/6a - 5/8

Step-by-step explanation:

There is a massive difference between -2/3a & -23a.

Same goes for 1/8 & 18, -1/6a & -16a, and -3/4 & -34.

My earlier answer, -39a - 16, IS correct for the question you wrote. What was incorrect was the question.

It is important to write the question properly because

−23a+18−16a−34

and

−2/3a+1/8−1/6a−3/4

will have very different answers.

In conclusion, make sure you write your question correctly. It's unfair to others genuinely trying to help who then are blamed for supplying the "wrong answer" by others who also copied and pasted from their school work.

If you had written, −2/3a+1/8−1/6a−3/4, then the answer would be -5/6a - 5/8.

Answer:

C.

Step-by-step explanation:

Since mAB = mCD

So

3x+9 = 11x-71

9+71 = 11x-3x

80 = 8x

So

x = 10

Now

Arc AB = 3x+9

= 3(10)+9

= 39°

Step-by-step explanation:

N~(62, 12^2)

Use Z-score formula (can find in internet)

\( z = \frac{74 - 62}{12} \\ z = \frac{12}{12} \\ z = 1\)

After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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