20) Which of the following is in ascending order?
2
f)
3
3
0.8, , 0.67, 70%
,
70%, Ž, 0.67, 0.8
h) Ž, 0.67, 70%, 0.8
,
j) 0.67,0.8,, 70%
2
3
3

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

Yes

Step-by-step explanation:

The velocity components of a particle moving in a parabolic path given by y² = 4fx are determined in rectangular and plane polar coordinates. The equation of the parabola in plane polar coordinates is shown to be r = (1 - cos(2θ))/2f or rcos²(2θ) = f.

When a particle moves in a parabolic path defined by the equation y² = 4fx, we can determine its velocity and acceleration components in rectangular and plane polar coordinates.

In rectangular coordinates, we can differentiate the equation of the parabola with respect to time to find the x and y components of velocity. By using the chain rule, we find that the x-component of velocity (Vx) is constant and equal to v, while the y-component of velocity (Vy) is given by Vy = 2fx'(t), where x'(t) is the derivative of x with respect to time.

In plane polar coordinates, we can express the position of the particle as (r, θ), where r represents the radial distance from the origin and θ represents the angle with respect to a reference axis. We can rewrite the equation of the parabola in terms of polar coordinates, resulting in r = (1 - cos(2θ))/2f. By differentiating this equation with respect to time, we can find the radial and angular components of velocity.

To determine the acceleration components, we can differentiate the velocity components obtained in both rectangular and polar coordinates with respect to time.

The derived equation r = (1 - cos(2θ))/2f or rcos²(2θ) = f represents the parabolic path in polar coordinates, providing an alternative representation of the given parabola equation.

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The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.

Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.

To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.

Your answer: a. 1%

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Answer:

36.9

Step-by-step explanation:

1. The average time it takes a customer from when they arrive at the truck until they receive their taco is 141.67 seconds.

2. The average utilization of the truck 141.67 seconds.

3. On average, there is 1 person waiting in line.

4. In order to achieve a delay probability of under 10%, a minimum of 1 server is required.

1 The arrival rate is 1 customer every 2 minutes, which is equivalent to 0.5 customers per minute. The service rate is 1 customer per 50 seconds, which is equivalent to 1.2 customers per minute (since there are 60 seconds in a minute).

2 Average Number of Customers = (0.5 / 1.2) + 1 = 1.4167.

Average Waiting Time = 1.4167 * (50 + 50)

= 141.67 seconds.

3 The average utilization of the truck is given by the formula: Utilization = Arrival Rate / Service Rate.

Utilization = 0.5 / 1.2

= 0.4167 (or 41.67%).

The average number of people waiting in line can be calculated using the formula: Average Number of Customers - Average Utilization.

Average Number of Customers - Average Utilization = 1.4167 - 0.4167

= 1.

4 Given that the desired delay probability is 10% (or 0.1), we can rearrange the formula to solve for the utilization:

Utilization = Delay Probability / (1 + Delay Probability).

=

Utilization = 0.1 / (1 + 0.1) = 0.0909 (or 9.09%).

The utilization we calculated represents the maximum utilization to achieve a delay probability of 10%. In conclusion, to achieve a delay probability of under 10%, a minimum of 1 server is required.

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Answer:

5/6

Step-by-step explanation:

Divide it

The equivalent expression can be used to solve the quotient 2/3 divided by 4/5 is 5/6.

Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.

The equivalent expression that can be used to solve the quotient 2/3 divided by 4/5 is;

\(= \dfrac{\dfrac{2}{3}}{\dfrac{4}{5}}\\\\=\dfrac{2}{3} \times \dfrac{5}{4}\\\\=\dfrac{1}{3} \times \dfrac{5}{2}\\\\=\dfrac{5}{6}\)

Hence, the equivalent expression can be used to solve the quotient 2/3 divided by 4/5 is 5/6.

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The interval estimate of the population mean when a random sample is taken of the speed on highway is 59.5<h<64.1. Option C is correct.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The interval estimate of the population mean can be found out using the following formula:

\(\overline X\pm MOE\)

Here, \(\overline X\) is the average mean, and the MOE is the margin of error.

On a highway, a random sample is taken of the speed, in mph, of 50 cars.

Put the values in the above formula as,

\(61.8\pm 2.3\\59.5,641\)

Thus, the interval estimate of the population mean

\(59.5 < h < 61.8\)

Hence, the interval estimate of the population mean when a random sample is taken of the speed on highway is 59.5<h<64.1. Option C is correct.

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Answer:

Marty = 50  Taylor = 35

Step-by-step explanation:

50 x 2 = 100

35 x 3 = 105

100 + 105 = 205

The payoffs for choosing a low price include the subsidy amount, resulting in higher profits for both Mutale and John if they choose the low price strategy.

To redraw the payoff matrix under the government subsidy system, we need to incorporate the subsidy of K200 for individuals who choose to set a low price for their beds. The original payoff matrix is as follows:

      | High Price | Low Price

-------+------------+----------

Mutale | (20, 10)   | (15, 12)

John   | (18, 11)   | (14, 13)

Under the government subsidy system, we need to adjust the payoffs for choosing a low price by adding the subsidy amount of K200. The new payoff matrix considering the subsidy is:

      | High Price   | Low Price + Subsidy

-------+--------------+-------------------

Mutale | (20, 10)     | (15, 12 + 200)

John   | (18, 11)     | (14, 13 + 200)

Simplifying the payoffs, the redrawn payoff matrix under the government subsidy system is:

      | High Price   | Low Price + Subsidy

-------+--------------+-------------------

Mutale | (20, 10)     | (15, 212)

John   | (18, 11)     | (14, 213)

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False, the zip codes of a sample of 345 customers at pet shop are not an example of qualitative variables

The zip codes of a sample of 345 customers at a pet shop are an example of quantitative variables because they are numerical values that can be measured and compared. Qualitative variables, on the other hand, are categorical variables that describe a characteristic or attribute of a person, place, or thing, such as gender, color, or nationality. They cannot be measured numerically and are often described using words or labels.

Qualitative Variables: Qualitative variables are variables that are not numerical or quantifiable. Examples of qualitative variables include gender, race, eye color, ethnicity, nationality, marital status, and religious preference.

Quantitative Variables: Quantitative variables are variables that are numerical or quantifiable. Examples of quantitative variables include height, weight, age, income, income level, GPA, number of children, and number of hours worked.

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Answer:

15. 2m

17. 1.5m

Step-by-step explanation:

just square root it

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

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These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

These scatterplots show that model type A is best suited to summarize the relationship between year and stock price. The scatterplot of the processed data is nearly linear, so a linear model is suitable.

A linear model is applicable if we can create a linear equation based on the connection between the independent and dependent variables (because there is no constant rate of change).

Otherwise, we can simulate the relationship using an exponential model.

An exponential model is:When the rate of increase representing the relationship between the year and stock price is proportional or constant, we utilize the exponential model.

By determining whether the ratio of the dependent values is the same, one can choose to describe the connection as an exponential equation.

As a result, even though the time and price scatterplot is curved, a linear model is adequate.

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What is the question, is their answer options or...?

Answer:

See attached

Step-by-step explanation:

Based on Chebyshev's theorem, we can conclude that approximately 75% of the club members' ages are between 27 and 67.

Based on Chebyshev's theorem, we can conclude that at least (1 - 1/k^2) of the data falls within k standard deviations of the mean, where k is any positive number greater than 1.

In this case, the mean age of the club members is 47 years and the standard deviation is 10 years. To find the percentage of club members aged between 27 and 67, we need to calculate the number of standard deviations between these ages and the mean.

For the lower limit, (27 - 47) / 10 = -2 standard deviations from the mean.
For the upper limit, (67 - 47) / 10 = 2 standard deviations from the mean.

Since k is any positive number greater than 1, we can choose k = 2. Therefore, according to Chebyshev's theorem, at least (1 - 1/2^2) = 1 - 1/4 = 3/4 or 75% of the club members' ages fall between 27 and 67.

In summary, based on Chebyshev's theorem, we can conclude that approximately 75% of the club members' ages are between 27 and 67.

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Answer:

I guess Letter B. One Larger, More stable nucleus

It produces nearly all the elements that are heavier than helium..

Answer:

Answer A

Step-by-step explanation:

Edge 2021

The derivation of the surface area of the cuboid,

A  =  2(ab² + bc² + ca²)

The surface area is a total outer layer of the three-dimensional figure. It is defined only for three dimensional shapes.

Suppose,

The length of  sides of the cuboid  are

a,

b,

c

Cuboid has 6 faces, and each face is like a rectangle,

So, If area of each face is calculated,

Then, the sum of area of each face will be equal to surface area of cuboid.

Surface Area =  A₁ + A₂ + A₃ + A₄ + A₅ + A₆

                      =  ab + bc + ca + ab + bc + ca

                      = 2( ab + bc + ca )

Hence, the surface of a cuboid is 2( ab + bc + ca )

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Step-by-step explanation:

This may help you

Thank you

Answer:

36 monkeys where sleeping

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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By the end of week 52, Westway Company deducted $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

To calculate the deductions made by Westway Company, we'll need to consider the Social Security and Medicare taxes.

Social Security tax:

The Social Security tax rate is 6.2% on income up to $142,800.

Since Suzle Chan earns $3,220 per week, their annual income is $3,220 * 52 = $167,440.

However, the maximum taxable income for Social Security is $142,800.

Therefore, the Social Security tax deduction is $142,800 * 0.062 = $8,857.60.

Medicare tax:

The Medicare tax rate is 1.45% on all income.

The Medicare tax deduction is $167,440 * 0.0145 = $2,426.48.

By the end of week 52, Westway Company would have deducted a total of $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

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The scale that Wyatt used is 1 inch represents 0.36 yards

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale provides information on the proportional relationship between the scale of the drawing and the original image.

Scale of the drawing = original length / length of the drawing

84 / 231 = 0.36 yards

This means that 1 inch is represented by 0.36 yards

Alternatively, it can be written as 1 : 0.36 yards

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The residue from $0 to $82 is 44 ≡ x(mod83)

17−1≡x(mod83)

17∗17−1≡17x(mod83)      

5∗1≡5∗17=85(mod83)

5≡2x(mod83)

42∗5=210≡2∗42x=84x≡x(mod83)

44 ≡ x(mod83).

A mathematical operations that performs a calculation on two numbers is known as an arithmetic provider. They are used in everyday arithmetic, and most computer languages include a set of such operators that can be used within equations to perform a variety of sequential calculations. The following are examples of basic arithmetic operations are:

(+) Addition

Subtraction (-) (-)

() Multiplication            

() division

In programming, computers use different symbols to represent multiplication (*) and division (/). More complex operators, such as

Let's look at an ice cream multiplication example.              

There are two  groups, each has its own ice cream.

The total number of ice creams is 2x3=6    

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The dimensions are 156m and 65 m

The perimeter of the field is 442 m.

The perimeter of the rectangle is the product of length to its breadth.

i.e., Perimeter= 2( l + b)

As, the diagonal of every rectangle makes right angled triangle with respect of length and width.

Diagonal² = length² + width²

Let the common ration be x

then, length = 12x and breadth = 5x

Diagonal² = length² + width²

                = (12x)²+ (5x)²

                 = 144 x² + 25 x²

                 = 169 x²

169² = 169 x²

x²= 169

x= 13

Hence, length = 12x = 12 * 13 = 156 m

width = 5x = 5*13 = 65 m

(ii) Perimeter,

= 2 ( l+ b)

= 2 ( 156 + 65 )

=2( 221)

= 442 m

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The descriptive statistics for the above data is given as follows:
X = 12.5

A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.

For X (mean) = \({\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}\)

= 300/24

= 12.5

For sample variance = \(s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr]\)

= (1/(24-1) (4,900 - (300²/24)

= 50

Standard deviation s = √s²

= √50

= 7.0711

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