A rectangle is to be inscribed in a semicircle of radius r cm. If the height of the rectangle is h, write an expression in terms of r and h for the Area and Perimeter of the rectangle. What dimensions of the rectangle yield the maximum Area?

Answer:

£4.80

Step-by-step explanation:

We know

A shop advertises 15% off

100% - 15% = 85%

So, £4.08 is the price at 85%

Find 1% by taking

4.08 divided by 85 = £0.048

Now find the price before the reduction by taking

0.048 times 100 = £4.80

So, it was £4.80 before the price reduction.

An equation to represent how long it would take them working together to paint 20 rooms is m/15 + m/10 = 20.

In order to determine the amount of time it would take them working together to paint 20 rooms, we would have to assign variables to the amount of time taken by Maria to paint a room and the amount of time taken by Miek to paint a room, and then translate the word problem into an algebraic equation as follows;

Next, we would write an algebraic equation that models the combined work rate;

Combined work rate = 1/x + 1/y

(1 room/15 minutes) × m + (1 room/10 minutes) × m = 20 rooms

Substituting the given parameters into the algebraic equation, we have;

m/15 + m/10 = 20

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The most convenient type of loan Jane should consider obtaining based on her situation is an FHA loan.

FHA stands for Federal Housing Administration loan. This type of loan different from other loans allows those wanting to buy a house to request the loan with a very low down payment (about 3%). This makes it more accessible to people with limited incomes or who have not saved a lot of money to buy a house.

This is the best option for Janet because due to the low requirements, she can request the loan.

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The system of linear inequalities to represent the constraints of this situation is x + y ≥ 200, x ≤ 220, y ≥ 50.

This means that the total number of computers (desktop plus laptops) must be at least 200 (x + y ≥ 200). The company needs no more than 220 desktops (x ≤ 220), and at least 50 laptops (y ≥ 50).

The inequality x + y ≥ 200 represents the total number of computers needed, x ≤ 220 represents the maximum number of desktops needed, and y ≥ 50 represents the minimum number of laptops needed. Together, these inequalities represent the constraints of the situation.

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The stem-and-leaf plot of the given data is attached. The correct options regarding percentage distribution, the distribution skewness, and gaps within the data are A, E, and F.

A stem and leaf plot refers to a technique used to to present and organize quantitative data (discrete or continuous) in a graphical format. It is displayed as table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). A stem and leaf plot can be used to visualize the shape of a distribution. The stem and leaf plot of the given data regarding the percentage loss of wetlands in the lower states is attached.

Based on the plot, it can be seen that:

Note: The question is incomplete. The complete question probably is: Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is given. i) Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) ii). How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) A) The percentages are concentrated from 20% to 60%. B) ii. The percentages are concentrated from 60% to 90%. C) There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. D) These data are strongly skewed left. E) These data are fairly symmetric, perhaps slightly skewed right. F) There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. G) There are no gaps in the data.

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Answer:43%

Step-by-step explanation:

Time taken to complete 10.3 half lives is 10.3 × 122 s = 1257 s which is equal to for the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴of the initial value.

Now, According to the question:

Radioactive Decay:

The rate of decay of nuclei of a radioactive element is directly proportional to the number of radioactive nuclei present at that moment in the sample.

The equation which determines the disintegration of atoms is,

N = N₀ e⁻(λt)

where, N is the number of atoms undergoing decay

N₀ is the initial number of atoms present

λ is the rate constant

t is the time

For the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴ of the initial value, the number of half-lives decay took place be n which is given by,

2⁻ⁿ = 8 × 10⁻⁴

Taking log on both sides we have,

- n ln 2 = ln(8 × 10⁻⁴)

n = 10.3

Time taken to complete 10.3 half lives is 10.3 × 122 s = 1257 s which is equal to for the number of 15 8 O nuclei in a given sample to decrease to a factor of 8 × 10⁻⁴ of the initial value.

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5 yards are equal to 15 feet. The solution has been obtained by using the unit conversion.

What is unit conversion?

The same feature is expressed in a different unit of measurement by using a unit conversion. For example, you may represent time in minutes rather than hours or distance in feet rather than miles. It is usual for measures to be given in one set of units, like feet, but to be requested in another set, like chains.

We are given 5 yards which are to be converted into feet.

We know that 1 yard = 3 feet

So,

⇒5 yards = 5 * 3

⇒5 yards = 15 feet

Hence, 5 yards are equal to 15 feet.

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Answer:

C

Step-by-step explanation:

3/4s=1(3/4f and 6/4s=2(3/4)f

Answer:

41

Step-by-step explanation:

x - 23 = 18  Add 23 to both sides

x - 23 + 23 = 18 +23

x = 41

The solution to the system is (13,4) and not (20,7.5). The following statements are true

1. The point (20,7.5) is not the solution to the system

2. The point (20,7.5 ) only satisfies equation 1

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

to solve;

x- 2y = 5 equation 1

4x + 2y = 60 equation 2

add equation 1 and 2

5x = 65

x = 65/5

x = 13

substitute 13 for x in equation 1

13-2y = 5

-2y =5-13

-2y = -8

divide both sides by -2

y = 4

therefore the solution is( x,y) = (13,4). Therefore the following statements are true

1. The point (20,7.5) is not the solution to the system

2. The point (20,7.5 ) only satisfies equation 1

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For the differential equation dy/dx = (x - 2)e^-2y having initial condition y(2) = ln(2), the solution is e^2y = x² - 4x + 8.

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

The given differential equation is dy/dx = (x - 2)e^-2y.

The initial condition is y(2) = ln(2).

Then the integration of the equation will be -

1/(e^-2y) dy = (x - 2) dx

e^2y dy = (x - 2) dx

(e^2y)/2 = (x²/2) - 2x + C

The value of C at x = 2, y(2) = ln (2).

Then it is obtained that -

[e^(2 ln 2)]/2 = [(2)²/2] - 2(2) +C

e^(ln 2²)/2 = 4/2 - 4 + C

Simplifying the equation further -

2²/2 = (4 - 8)/2 + C

2 = -4/2 + C

C = 2 + 4/2

C = 4

Then the equation will be -

(e^2y)/2 = (x²/2) - 2x + C

(e^2y)/2 = (x²/2) - 2x + 4

e^2y = x² - 4x + 8

Therefore, the solution is e^2y = x² - 4x + 8.

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The equation of the line that passes through (-2,1) and is perpendicular to y = -5x² is y = -10x + 21

The equation of a line is a mathematical representation of the relationship between its x and y values.

In this case, we are given a line that passes through the point (-2,1) and is perpendicular to y = -5x².

To find the equation of this line, we first need to find the slope of the line that is perpendicular to y = -5x².

The slope of a line can be found by finding the derivative of the original equation.

In this case, the derivative of

=> y = -5x² is -10x,

which gives us the slope of -10x.

Since we know that the line passing through (-2,1) is perpendicular to

y = -5x²,

we can use the point-slope form of the equation of a line.

The point-slope form of the equation is given by

=> y - y1 = m(x - x1),

where m is the slope and (x1, y1) is a point on the line.

Plugging in the values, we have

=> y - 1 = -10(x + 2).

We can simplify this equation further by distributing the -10 and combining like terms.

This gives us

=> y - 1 = -10x - 20,

which we can then rearrange to get

=> y = -10x + 21.

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Answer:

3

Step-by-step explanation:

12x-4x+8x = 16+x

Answer:

x = 7 and x = 16

Step-by-step explanation:

the measure of a secant- secant angle is half the difference of the measures of the intercepted arcs.

11

39 = [tex]\frac{1}{2}[/tex] (17x + 6 - (7x - 2) ) ← multiply both sides by 2 to clear the fraction

78 = 17x + 6 - 7x + 2

78 = 10x + 8 ( subtract 8 from both sides )

70 = 10x ( divide both sides by 10 )

7 = x

12

54 = [tex]\frac{1}{2}[/tex] (13x - 6 - (5x + 14) ) ← multiply both sides by 2 to clear the fraction

108 = 13x - 6 - 5x - 14

108 = 8x - 20 ( add 20 to both sides )

128 = 8x ( divide both sides by 8 )

16 = x

Answer:

x 7 x16

is the answer

Step-by-step explanation:

is the answer

Answer:

B

Step-by-step explanation:

8 weeks, 2 sessions per week =16 sessions

45mins each = 16*45=720 mins = 12 hours

52 /12 =4.33 / hour

B: $4.33/hour is the closest to the charge per hour for the courses. Hence, the correct option is (B)

The total charge for the 8-week course is $52, which means each 45-minute session costs $52 / (2 sessions/week * 8 weeks) = $1.67.

To convert this to an hourly rate, we divide by 45 minutes to get an hourly rate of $1.67 / (45 minutes/hour) = $3.93/hour.

Therefore, the answer closest to this is $4.00/hour, which is not one of the options, but we can see that $3.93/hour is closest to option B: $4.33/hour.

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The bug's acceleration at any given time, t, is 0 when the location of a large traveling down the x axis is given by x(t)=at+b.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

f(t)=at+b

f'(t)=a

f''(t)=0

The acceleration of the bug at any given time, t is 0 when position of a big moving along the x axis is given by x(t)=at+b.

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The time required to paint the new cone is 2.9 minutes.

Let the radius of the original cone be r.

∴ the area of the base is :

πr² = 49 π in²

so r² = 49.

Hence, the radius, r = 7 in.

∵ the lateral height of the cone is 8 inches, the slant height can be calculated using the Pythagorean Theorem: a² = b² + c²

i.e., s² = r² + h²

s² = 7²+ 8² = 49 + 64 = 113

s = √(113) in.

Let the area of the base of the new cone be, A

∴ A = 2 × 49 π in² = 98 π in².

Then, the radius of the new cone is √(98) in = 7 in × √(2).

The slant height of the new cone can be calculated in a similar manner:

s² = r² + h²

s² = (7 × √(2))² + 8² = 49 × 2 + 64 = 162

s = √(162) in.

The new cone will require more time to paint because its radius and height are bigger. Since the rate of painting is constant, the time needed to paint a fresh cone is inversely related to its surface area. Since the new cone's surface area is related to its slant height, the amount of time needed to paint it is equal to the new cone's slant height divided by the original cone's slant height. This means that it will take time to paint the new cone:

Time = 2.5 × √(162) ÷ √(113)

Time = 2.96 minutes

The time required to paint the new cone, rounded to the nearest tenth, is 2.9 minutes.

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The original number was 4 is the correct answer.

Let's call the original number "x".

According to the problem, "a number is decreased by seven" which means x - 7.

And then, the new number is multiplied by 3 to get an answer of -9. That means (x - 7) * 3 = -9.

We can simplify the equation to 3x - 21 = -9 and then add 21 to both sides to isolate the variable: 3x = 12.

Finally, we can divide both sides by 3 to find x: x = 4.

So, the original number was 4.

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A program is created that questions the user however many cookies they want to make and then displays how many cups of every ingredient are required to make that many cookies.

Writing code to support certain activities in a computer, application, or software program and giving them instructions on how to do is known as computer programming.

The given data for ingredients used in making cookie recipe.

user_cookies_input = float(input('Enter number of cookies: '))

cups_of_sugar = 1.5

cups_of_butter = 1.0

cups_of_flour = 2.75

number_of_cookies = 48

sugar_output = (user_cookies_input * cups_of_sugar) / number_of_cookies

butter_output = (user_cookies_input * cups_of_butter) / number_of_cookies

flour_output = (user_cookies_input * cups_of_flour) / number_of_cookies

print("You need" + int(sugar_output, '.2f') + "cups of sugar," + int(butter_output, '.2f') +

   "cups of butter, and" + int(flour_output, '.2f') + "cups of flour.")

Thus, a program is created that questions the user number of  cookies they want to make and then displays how many cups of every ingredient are required to make that many cookies.

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Step-by-step explanation:

If Sandra works for 42 hours per week and her weekly wage is £389.76, her hourly wage can be calculated as follows:

£389.76 / 42 hours = £9.28 per hour

When she receives a pay increase of 35p per hour, her hourly wage becomes:

£9.28 + 0.35 = £9.63 per hour

Her new weekly wage can then be calculated as:

£9.63 per hour * 42 hours = £404.66

So Sandra's new weekly wage is £404.66 after receiving a pay increase of 35p per hour.

The promotion rate distribution of employees can be either unimodal or bimodal, depending on the company's policies and the type of employees. Understanding the distribution is important for employees as it provides insight into the likelihood of being promoted and the time it may take to reach the desired promotion.

Promotion Rates for Employees: Promotion is a common goal for employees as it is often associated with career advancement, higher salaries, and increased responsibility. The rate at which employees are promoted can vary from company to company, depending on various factors such as the size of the organization, the industry, and the company's policies.

In this context, it is important to understand the distribution of the promotion rates, which can be either unimodal or bimodal. Unimodal Distribution: A unimodal distribution is a type of distribution that has a single peak or mode. This means that the majority of the employees are promoted at a certain rate, and the frequency of promotions decreases as the rate moves away from the mode.

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b) An approximate value for e is 2.71828,

c) The natural exponential function is eˣ

The number e is a mathematical constant that is closely related to the exponential function. It is one of the most important and widely used numbers in mathematics and science.

The number e is defined as the limit of the sequence of numbers

=> (1 + 1/n)ⁿ

as n approaches infinity.

In other words, it is the unique number that satisfies the equation

=> eˣ = lim(n→∞) (1 + x/n)ⁿ.

This equation states that as n increases, the value of the exponential function of x approaches eˣ.

The approximate value of e is 2.71828, but it can be calculated to an infinite number of decimal places.

The natural exponential function is a mathematical function that is defined by

=> eˣ

It is used to model real-world situations that involve exponential growth or decay, such as the growth of a population or the decay of a radioactive substance.

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Option(c) is the correct answer.

The image is attached below.

According to the question,

Create an inequality from the given details:

( 2x ≥ 28, where x denotes the number of weeks)

Then divide both sides of the inequality by 2, resulting in x ≥ 14, or all values greater than or equal to 14.

Now, choose the number line that shows all numbers greater than or equal to 14 (all the numbers to the right of 14 and including 14, which is indicated by a shaded circle).

Hence, [C} is the correct answer.

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Option C has an x larger than or equal to 5 domain and a y less than or equal to 3 range. y = negative Start Root x minus 5 End Root + 3.

What is Domain and Range of Functions?

Let's consider a function y=f(x) where x is a set of values such as f exists. All the values of x are called the domain of f. Similarly, f takes a set of values when x takes values in its domain. All the values f could take is its range. We know the domain and range of f are, respectively x≥5,y≤3. Since all the options contain a square root, we already know the domain will be restricted by the argument of a square root, that is, it must be non-negative. From the given domain, we construct the argument of the square root x≥5 x-5≥0. It corresponds to the argument of a square root that must be non-negative. So our function must contain √x-5. Now about the range, the square root is assumed as positive or zero, and the range is restricted as less or equal to zero, so we operate the inequality for y

y≤3=>0≤3-y=>3-y≥0

Now we can safely say

3-y=√x-5

Or equivalently

y=3√x-5

This corresponds to the option C. written as

y= negative start root x minus 5 end root + 3

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If Stephanie recorded the time, in minutes, she took to walk from home to work {15,16,18,20,21} and the time, in minutes, she took to walk from work to home {14,21,21,25,27} the best conclusion Stephanie can make is:

D. Stephanie’s walk times are more spread out going to work than coming home.

The data Stephanie collected shows that the range of times for walking to work is greater than for walking home. The range for walking to work is 15-21 minutes, while the range for walking home is 14-27 minutes. This indicates that Stephanie’s walk times are more spread out going to work than coming home.

This suggests also that Stephanie may be taking a more direct or efficient route when walking home, while she may be taking a more leisurely or meandering route when walking to work. It is possible that this could be due to a variety of factors, such as traffic, terrain, or the presence of stops along the way.

The data also reveals that the average time for walking to work is 18.4 minutes, while the average time for walking home is 20.6 minutes. This indicates that, on average, Stephanie takes slightly longer to walk home than to work.

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Not true about scanner data is a. scanner data is considered primary data .

Scanner panel data are just data that are recorded through checkout scanners that track purchases of the panel participants. So the panel is made up of different consumers who agree to have their purchase behavior tracked.

The scanner converts the light energy into electrical energy, which is then converted into data by the decoder and forwarded to a computer

scanner panel data allows us to make comparisons between different consumers

So, scanner panel data is a rich source of information that can be very helpful in guiding us and in designing and implementing our marketing strategy.

Not true about scanner data is a. scanner data is considered primary data

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Not true about scanner data is a. scanner data is considered primary data .

Scanner panel data are just data that are recorded through checkout scanners that track purchases of the panel participants. So the panel is made up of different consumers who agree to have their purchase behavior tracked.

The scanner converts the light energy into electrical energy, which is then converted into data by the decoder and forwarded to a computer

scanner panel data allows us to make comparisons between different consumers

So, scanner panel data is a rich source of information that can be very helpful in guiding us and in designing and implementing our marketing strategy.

Not true about scanner data is a. scanner data is considered primary data

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Based on the definition of the geometric mean, the value of x is: 64.

The geometric mean of two numbers is the square root of the product of the two numbers.

In other words, if x and y are two numbers, the geometric mean of x and y is represented as √(xy).

If 16 is the geometric mean between 4 and x, then we have the following relationship:

√(4x) = 16

Squaring both sides:

4x = 256

Dividing both sides by 4:

x = 64

So the value of x is 64.

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