mean and median of 11, 41, 36, 4, 7

Answer:

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $100, r = 9% = 0.09, n = 1 (compounded annually), and t = 16. We want to find A.

A = 100(1 + 0.09/1)^(1*16)

A = $397.42

Therefore, Javae will have $397.42 in his account on his 30th birthday. The answer is option D.

Answer:

To calculate the volume of soil needed, we first convert the dimensions of the backyard to feet:

Length = 70 ft

Width = 60 ft

Depth = 4 in = 4/12 ft = 1/3 ft

Volume = Length x Width x Depth

Volume = 70 ft x 60 ft x (1/3) ft

Volume = 1400 ft³

Option 1: Bags of topsoil

Each bag of topsoil contains 3 ft³ of soil, so the number of bags needed is:

Number of bags = Volume / Bag size

Number of bags = 1400 ft³ / 3 ft³ per bag

Number of bags = 467 bags

The total cost of bags of topsoil is:

Cost = Number of bags x Cost per bag

Cost = 467 bags x $2.50 per bag

Cost = $1167.50

Option 2: Bulk topsoil

The volume of topsoil needed is 1400 ft³, which is equivalent to:

Volume = 1400 ft³ / 27 ft³ per yd³

Volume = 51.85 yd³ (rounded to two decimal places)

The cost of bulk topsoil is:

Cost = Volume x Cost per yd³ + Delivery fee

Cost = 51.85 yd³ x $22.00 per yd³ + $20.00 delivery fee

Cost = $1153.70

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil. The cost of bulk topsoil is $1153.70, while the cost of bags of topsoil is $1167.50

Answer:

Bulk is less expensive

Step-by-step explanation:

First convert inches to feet:  4 in x 1 ft/12 in =0.333 ft

Volume of topsoil needed = 70 x 60 x 0.333 = 1400 ft³

Bagged topsoil:   1400 ft³ x $2.50/3 ft³ = $1166.67

Bulk: 1400 ft³ x 1 yd³/27 ft³ x $22.00/yd³ + $20 = $1160.74

Bulk is just a little cheaper

Answer:

[tex]f(x) = (x + 2)(x - 12)[/tex]

[tex]f(x) = {x}^{2} - 10x - 24[/tex]

The Median and IQR are most appropriate to describe the measures of center and variability of distribution. The histogram depicts the distribution of time is positively skewed. So, option(b) is right one.

We have a graph present in above figure, which showes the amount of time in hours spent on homework per week for a sample of students. We have to select correct measures of center and variability. The graph is a histogram. From the graph we can see that the data is positively skewed. Now for skewed distribution we prefer median over mean as mean is more sensitive to the outliers. As the data(time) is in ratio scale we can use any of the measures of dispersion; but for skewed distribution IQR is preferred because of its robustness. In a word both median and IQR can handle outliers. Thus the appropriate answer is Median and IQR, option (c).

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Complete question :

The above figure complete the question

the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution? group of answer choices

a) mean and standard deviation

b) mean and iqr

c) median and standard deviation

d) median and iqr

e) median and range

The amount it will cost to recarpet the the whole room is $891.12

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

For example, the area of a circle is given as: A = πr², where r is the radius and π is constant.

The room takes the shape of a rectangle, therefore,

Area of the room = l× w, where l is the length and w is the width.

Area = 3×8 = 24 m²

The cost of 1m² = $33.38

therefore the cost for 24m²

= 24× 33.8

= $801.12

therefore the cost to recarpet the room is $801.12

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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Answer:

x = 18°

Step-by-step explanation:

7x - 6° = 120°

7x = 126°

x = 18°

So, the answer is x = 18°

Answer: s = p - 0.25p; $30

Step-by-step explanation:

      First, we need to know that a percent divided by 100 becomes a decimal.

          25% / 100 = 0.25.

      Next, we will use this equation because it takes 25% off of the original price (p) by subtracting 0.25p from p.

          s = p - 0.25p

      Lastly, we will substitute 40 in for 0 and solve.

          s = ($40) - 0.25($40)

          s = $30

The simple interest earned after 3 years on $500 at an interest rate of 6% is $90.

Simple interest is a type of interest that is calculated based only on the initial amount borrowed or invested, called the principal amount, and does not take into account any additional interest earned on the interest over time.

To find the simple interest earned on $500 at an interest rate of 6% after 3 years, we can use the formula:

Simple Interest = Principal x Rate x Time

Where

Principal = $500

Rate = 6% = 0.06 (in decimal form)

Time = 3 years

Plugging these values into the formula, we get

Simple Interest = $500 x 0.06 x 3

= $90

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Find the simple interest earned after 3 years on $500 at an interest rate of 6%.

We have (0, 1) and (3, 5) as two points on the line y = 4/3x + 1.

The equation y = 4/3x + 1 represents a line in slope-intercept form, where the coefficient of x (4/3) represents the slope of the line and the constant term (1) represents the y-intercept.

To select two points on the line, we can choose any values for x and use the equation to find the corresponding values of y.

For example, let's choose x = 0:

y = 4/3x + 1

y = 4/3(0) + 1

y = 1

So one point on the line is (0, 1).

Now let's choose x = 3:

y = 4/3x + 1

y = 4/3(3) + 1

y = 5

So another point on the line is (3, 5).

Since both equations hold true, we can conclude that (0, 1) and (3, 5) are two points on the line y = 4/3x + 1.

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It looks like you did a great job solving the equation, and your final answer is correct. Here is a brief summary of the steps you took:
your final answer is correct[tex]: x = 1 - (pm - pn) / 4t[/tex]

Mathematics has been classified into many branches. Arithmetic is the branch that handles numbers and their operations. Arithmetic taught us addition, subtraction, multiplication and divisions of two or more numbers. Geometry is all about shapes and their construction using different tools like a compass, ruler and pencil. Algebra is another interesting branch where we express our daily life situations in numbers and letters (variables).
1. Expanded the equation: [tex]12 - tx^2 - pn = 12 - t(2 - x)^2 - pm[/tex]
2. Simplified: [tex]12 - tx^2 - pn = 12 - 4t + 4tx - tx^2 - pm[/tex]
3. Eliminated the 12 and tx^2 terms: -pn = -4t + 4tx - pm
4. Rearranged the equation:[tex]-4tx = -4t + pn - pm[/tex]
5. Divided both sides by [tex]-4t: x = 1 - (pm - pn) / 4t[/tex]
So, your final answer is correct[tex]: x = 1 - (pm - pn) / 4t[/tex]

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Answer:

A correct option is option (b).

Given,

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

Now, calculate the angles.

Again,

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Step-by-step explanation:

a) The depreciation expenses for Year 1 to Year 4 using the straight-line method are $2,632, $5,263, $4,211, and $2,632, respectively.

b) Using the units-of-activity method, the depreciation expenses are $7,000, $14,000, $11,900, and $7,000, respectively.

c) Using the double-declining-balance method, the depreciation expenses are $4,658, $11,172, $7,302, and $2,640, respectively.

a) To calculate the depreciation expense for each year using the straight-line method, the company needs to first determine the depreciable cost of the equipment. This is the cost of the equipment minus its estimated residual value.

The depreciable cost is $41,550 - $1,650 = $39,900.

To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment, which is three years.

Year 1: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

Year 2: ($39,900 ÷ 3) × (2,000 ÷ 5,700) = $5,263

Year 3: ($39,900 ÷ 3) × (1,700 ÷ 5,700) = $4,211

Year 4: ($39,900 ÷ 3) × (1,000 ÷ 5,700) = $2,632

b) To calculate the depreciation expense using the units-of-activity method, the company needs to first determine the depreciation rate per unit of activity. This is the depreciable cost of the equipment divided by its total estimated hours of use.

The depreciation rate per unit of activity is $39,900 ÷ 5,700 hours = $7 per hour.

Year 1: $7 × 1,000 hours = $7,000

Year 2: $7 × 2,000 hours = $14,000

Year 3: $7 × 1,700 hours = $11,900

Year 4: $7 × 1,000 hours = $7,000

c) To calculate the depreciation expense using the double-declining-balance method, the company needs to first determine the straight-line depreciation rate. This is the depreciable cost of the equipment divided by its useful life.

The straight-line depreciation rate is $39,900 ÷ 3 years = $13,300 per year.

The double-declining-balance depreciation rate is twice the straight-line rate, or $13,300 × 2 = $26,600.

Year 1: $26,600 × (1,000 ÷ 5,700) = $4,658

Year 2: ($39,900 - $4,658) × (2,000 ÷ 5,700) = $11,172

Year 3: ($39,900 - $4,658 - $11,172) × (1,700 ÷ 5,700) = $7,302

Year 4: ($39,900 - $4,658 - $11,172 - $7,302) × (1,000 ÷ 5,700) = $2,640

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The power of -1 to a function, or [tex]((f^{-1})(x)),[/tex]represents the inverse function of f. In other words, if f(x) produces a certain output y, then the inverse function[tex]f^{-1}(y)[/tex]will produce the input x. It is important to note that not all functions have an inverse, and if they do, they may only be valid for certain inputs and outputs.

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f1. The inverse of f exists if and only if f is bijective.

[tex]((f^{-1})(x)),[/tex]

The inverse function of f is denoted by. For a function, its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y1.

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John will be able to fill 8 glasses with iced tea.

To convert quarts to cups, we need to multiply the number of quarts by 4, since 1 quart is equal to 4 cups. So, 3 quarts of iced tea is equivalent to 3 x 4 = 12 cups of iced tea.

Since each glass holds 1½ cups of iced tea, John will need to divide the total cups of iced tea by the capacity of each glass: 12 cups / 1.5 cups/glass = 8 glasses.

Therefore, John will fill 8 glasses with iced tea.

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Answer:

Quotient=23 and remainder=14

Answer: 12 units

Step-by-step explanation: see both shapes are the same just one is flipped and its small meaning the first shape without numbers is only double of the shape with numbers so you answer would be 12 units

small shape x 2 gives all your answers to the big shape

TOO

EASY

BYE

Answer: The answer is 84

The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.

The maximum number of mail swaps that Bagelbot can perform between officials from A and officials from B can be 150 .

It can be determined by calculating the maximum number of edges possible for a bipartite graph between A and B. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.

In this case, the officials from A and officials from B represent the two disjoint sets.

The maximum number of edges in a bipartite graph between A and B can be calculated as the product of the number of officials in A and the number of officials in B. Therefore, if there are n officials in A and m officials in B, the maximum number of mail swaps that Bagelbot can perform is n x m.

For example, if there are 10 officials in A and 15 officials in B, the maximum number of mail swaps that Bagelbot can perform is 10 x 15 = 150.

This means that Bagelbot can potentially redirect up to 150 pieces of mail between officials from A and officials from B.

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The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum").

For the case of -

A total of 100 distinct gummy vitamins that are offered worldwide were counted for their milligrammes of vitamin C content.

The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

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Answer:

True

hope it helps :) !!!

Answer:

the answer is true, it's the objects net is the same as the surface area.

The probability that at least one visitor views another page on the site is very high, close to 1. This suggests that the website is engaging and visitors are likely to navigate beyond the home page.

Assuming that 200 visitors come to the home page of the website, we can use the binomial distribution to calculate the probability that at least one visitor views another page on the site.

Let X be the number of visitors who view another page. Then X follows a binomial distribution with n = 200 and p = 0.2.

P(X ≥ 1) = 1 - P(X = 0)

[tex]= 1 - (0.2)^0 * (0.8)^200= 1 - 0.8^200[/tex]

≈ 1

Therefore, the probability that at least one visitor views another page on the site is very high, close to 1. This suggests that the website is engaging and visitors are likely to navigate beyond the home page.

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40 out of 200 visitors to the homepage are expected to view another page on the site.

The probability that a visitor to a website's homepage views another page on the site and how it relates to 200

visitors.

The probability is 0.2.

To find out how many visitors out of 200 are likely to view another page on the site, you can follow these steps:

Identify the given probability, which is 0.2 in this case.

Multiply the probability by the total number of visitors (200).

So, the calculation would be:

0.2 × 200 = 40

Based on the given probability, approximately 40 out of 200 visitors to the homepage are expected to view another

page on the site.

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After Jenny invested the $1900 in a 5-year CD,

A) Given principal money (P) = $1900

Rate of interest (r) = 1.47% / 100 = 0.047

number of times interest compounded per year (n) = 4

number of years (t) = 5

Amount Jenny will have after 5-years (A) = [tex]p(1+r/n)^{nt}[/tex]

A = [tex]1900(1+0.047/4)^{4*5}[/tex]

A = [tex]1900(1 + 0.01175)^{20}[/tex]

A = [tex]1900(1.01175)^{20}[/tex]

A = 1900(1.2631) ≅ $2400

B) Interest earned after 5 years = $2400 - $1900 = $500.

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The conditional probability of A given B (P(A|B)) is 1/6, or approximately 0.167.

Conditional probability is the probability of an event occurring given that another event has already occurred.

It is denoted by P(A|B), where A and B are events, and P(A|B) represents the probability of event A occurring given that event B has already occurred

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

To find the conditional probability of A given B (P(A|B)), we can use the formula
P(A|B) = P(A ∩ B) / P(B)
We are given:
P(A) = 0.5 (probability of event A occurring)
P(B) = 0.6 (probability of event B occurring)
P(A ∩ B) = 0.1 (probability of both A and B occurring)
Now, we can plug in the given values into the formula:
P(A|B) = 0.1 / 0.6
P(A|B) = 1/6.

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option B is correct: [tex](x+2)^2+(y+7)^2=36[/tex]

The general equation of the circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]              

where,

(h, k) is the center of the circle and r is the radius of the circle.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

[tex]\implies (h, k) = (-2, -7)[/tex] and [tex]r = 6[/tex] units

Substitute these we have:

[tex](x-(-2))^2+(y-(-7))^2=6^2[/tex]

[tex]\implies(x+2)^2+(y+7)^2=36[/tex]

Therefore, the equation of circle is, [tex]\bold{(x+2)^2+(y+7)^2=36}[/tex]

Answer:

(i) Calculation:

1 GB = 1000 MB

Number of videos that could be stored = (1 GB / 100 MB) = 10

Therefore, William can store 10 videos on his computer if each video is 100MB in size.

(ii) Algorithm using pseudocode:

Ask the user to input the file size in megabytes.

Multiply the file size by 1,000,000 to convert it to bytes.

Print the result in a user-friendly format by dividing the bytes by 1,048,576 and rounding to two decimal places, and adding "MB" and "bytes" to the output.

Pseudocode:

Input file_size_in_mb

Set bytes = file_size_in_mb * 1000000

Set result = round((bytes / 1048576), 2)

Output "There are " + result + " MB " + bytes + " bytes".

The volume of the cylinder is 90π cubic units.

To calculate the volume of a cylinder with a radius of 3 and a height of 10, you can use the following formula:

Volume = π × r² × h

Where:

- Volume represents the volume of the cylinder,

- π (pi) is a mathematical constant approximately equal to 3.14159,

- r is the radius of the cylinder (in this case, 3), and

- h is the height of the cylinder (in this case, 10).

Now, plug in the given values:

Volume = π × (3)² × 10

Simplify the expression:

Volume = π × 9 × 10

Volume = 90π

So, the volume of the cylinder is 90π cubic units.

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Step-by-step explanation:

[tex] - 3 = \frac{3}{4} (2) + b[/tex]

[tex] - \frac{6}{2} = \frac{3}{2} + b[/tex]

[tex]b = - \frac{9}{2} [/tex]

[tex]y = \frac{3}{4} x - \frac{9}{2} [/tex]

Alternately, starting at (2, -3), go up 3 units, then right 4 units, to (6, 0). Draw a line that goes through these points.

The solution of the given problem of percentage comes out to be Karin's future account value would therefore be about $313,425.67 after 20 years.

In statistics, a figure or metric that may be presented as a percentage or 100 is denoted by the abbreviation "a%". Other unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this.

Here,

Using the compound interest calculation, we can determine Karin's account worth in 20 years:

=> A = P(1 + r)ⁿ

P =$83,555 (current balance), as given.

(Annual interest rate) r = 9.8% = 0.098

20 years, n

Let's use the following formula to determine the future account worth for each year:

Year 1: P = $83,555 (balance as of now)

(Annual interest rate) r = 9.8% = 0.098

Given that this is the first year, n equals 1.

=> A = $83,555(1 + 0.098)¹

=> A = $83,555(1.098)

=>A = $91,785.09

Year 2: P = $6,225 (current balance after deposit) = $3,000 + $3,225.

(Annual interest rate) r = 9.8% = 0.098

n = 1 year

=> A = $6,225(1 + 0.098)¹

=> A = $6,225(1.098)

=> A = $6,834.44

After 20 years, the current balance is

=>  P = $12,873.51 + (20 - 1)($3,000 + 7.5% of $3,000)

= $12,873.51 + $71,132.10 = $83,005.61.

The yearly interest rate is 9.8%, or 0.098.

20 years, n

=>  A = $83,005.61(1 + 0.098)²⁰

=>   A = $83,005.61(3.778)

=>  A = $313,425.67

Karin's future account value would therefore be about $313,425.67 after 20 years.

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