find the mean of the set of data 3,5,4,4,5,7,7

Conversion models can be used to express numbers of different bases to base-2 and base-5. To convert a number from base-10 to base-2, we use division-by-2, and for base-5, we divide by 5. To convert between bases, we convert to base-10 first and then to the desired base. for example 25 in binary is 11001, 45 in base-5 is 104, 89 to base-2 is 1011001.

In computer science and mathematics, binary (base-2) and quinary (base-5) numbering systems are commonly used to represent numbers. However, it is often necessary to express numbers in other bases as well. This is where conversion models come into play.

To convert a number from base-10 to base-2, we can use the division-by-2 method.

The process involves repeatedly dividing the decimal number by 2 and keeping track of the remainders until the quotient becomes 0. We then write the remainders in reverse order to get the binary representation of the number.

For example, to convert the number 25 to binary

25 / 2 = 12 R1

12 / 2 = 6 R0

6 / 2 = 3 R0

3 / 2 = 1 R1

1 / 2 = 0 R1

Therefore, 25 in binary is 11001.

To convert a number from base-10 to base-5, we can use a similar method. Instead of dividing by 2, we divide by 5 and keep track of the remainders. For example, to convert the number 45 to base-5

45 / 5 = 9 R0

9 / 5 = 1 R4

1 / 5 = 0 R1

Therefore, 45 in base-5 is 104.

We can also convert a number from base-2 to base-5 or vice versa. To convert a number from base-2 to base-5, we can first convert it to base-10 and then to base-5. For example, to convert the binary number 101110 to base-5

1*2⁵ + 0*2⁴ + 1*2³ + 1*2² + 1*2¹ + 0*2⁰ = 46

46 to base-5 is 141

To convert a number from base-5 to base-2, we can first convert it to base-10 and then to base-2. For example, to convert the quinary number 324 to base-2

3*5² + 2*5¹ + 4*5⁰ = 89

89 to base-2 is 1011001

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A symbolic representation of the contrapositive is

letter D

Answer:

b

Step-by-step explanation:

The opposite side of the right triangle is determined as 10.6 cm.

The value of x is calculated by applying trigonometry ratio as shown below;

we will use the short form; SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.

sin (62) = x/12

x = 12 sin (62)

x = 10.6 cm

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The number of days it would take for the investment to be valued at £3,800 is 4.4 days

From the question, we have the following parameters that can be used in our computation:

A = 1200 × 1.3^n

For the investment to be valued at £3,800, the value of A would be

A = 3800

Substitute the known values in the above equation, so, we have the following representation

1200 × 1.3^n = 3800

Divide both sides by 1200

1.3^n = 3800/1200

So, we have

n = ln(3800/1200)/ln(1.3)

Evaluate the quotient

n = 4.4

Hence, it would take 4.4 days

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Answer:

π(5^2)(8) + (1/2)(4/3)π(5^3)

= 200π + 250π/3 = 850π/3 cubic meters

= about 889.67 cubic meters

Answer:

B

Step-by-step explanation:

Answer:

I think It's b or a

Step-by-step explanation:

did this like 4 weeks ago.

The exact volume of the soup can is 18.375 π cubic inches. So, correct option is C.

The volume of a cylinder can be found by multiplying the area of the base (circle) by the height of the cylinder. In this case, the diameter of the base is 3.5 inches, which means the radius is 1.75 inches (since radius = diameter/2).

So the area of the base can be calculated as:

π × (1.75 in)² = π × 3.0625 in²

The height of the cylinder is given as 6 inches.

Therefore, the exact volume of the soup can would be:

π × (1.75 in)² × 6 in = π × 3.0625 in² × 6 in = 18.375 π cubic inches (rounded to two decimal places)

So, correct option is C.

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The volume of this rectangular prism include the following: 84.375 cubic meters.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 5 × 4 1/2 ×  3 3/4

Volume of rectangular prism = 5 × 4.5 ×  3.75

Volume of rectangular prism = 84.375 cubic meters.

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If Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

Mark bought 55 lbs of clay for his art projects

He used 12.4 lbs to make a sculpture

The left over clay is 55-12.4 = 42.6

We know that 0.75 lbs for each mug

We have to find the number of mugs he can make from left over clay

To find this we have to divide 42.6 by 0.75

Number of mugs = 42.6/0.75

=56.8

=57

Hence, if Mark  used 12.4 lbs to make a sculpture, and 0.75 lbs for each mug then the number of mugs he can make is 57.

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Answer:

The function that is a translation one unit right of the function f(x) = log x is k(x) = log(x - 1).

When we shift a function f(x) one unit right, we replace x with (x - a) where "a" is the amount of the shift. In this case, "a" is equal to 1. Therefore, the function becomes:

f(x - 1) = log(x - 1)

This means that the function k(x) = log(x - 1) is obtained by shifting the function f(x) one unit to the right.

The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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Answer: 2.35619

Step-by-step explanation: Hope this helps! :)

The probability that a person surveyed is 40 or older and gets the news by reading the paper is 60%. The Option C is correct.

We must find the probability of a person getting their news by reading the paper and are given with a condition that the person must be 40 or older.

Data

The survey is conducted among 80 people.

Number of people aged 40 or older = 40

No of people aged 40 or older and read paper = 24

The probability of a person aged 40 or older reads a paper will be:

= (No. of People aged 40 or older and read paper)/(No. of people aged 40 or older)

= 24/40

= 0.6

= 60%

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The number of malaria cases in 2017 is 2700.

Let the dependent variable, y is malaria cases in thousands and the independent variable, x is the year.

Here, x is the number of years starting in the year 2000.

The required model is obtained as [tex]y = 299e^{0.1295x}[/tex]

Now, the predicted number of malaria cases in the year 2017, that is, x = 17 years can be computed as,

[tex]y = 299e^{0.1295(17)}\\\\= 299(9.020\\\\= 2700[/tex]

Hence, the number of malaria cases in 2017 is 2700.

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Answer:

The correct option that compares the end behavior of the functions f and g is D.

For function f, as x → ∞, f(x) → -∞, which means that the function approaches negative infinity as x approaches infinity. This is because the leading term of the function is -17x, which approaches negative infinity as x approaches infinity.

For function g, as x → ∞, g(x) → -∞, which means that the function also approaches negative infinity as x approaches infinity. This is because the leading term of the function is -78/87x, which approaches negative infinity as x approaches infinity.

Therefore, both functions have the same end behavior, which is approaching negative infinity as x approaches infinity.

An inequality to find the least number of bananas your character slipped on: -3x ≤ -27

And  the least amount of race time character took to slip on bananas = 18 seconds.

Let us assume that x represents the number of bananas your character slipped on.

Here, based on the informtaion we get an inequality to find the least number of bananas your character slipped on -3x ≤ -27

We solve this inequality to find  the least number of seconds of race time.

-3x ≤ -27

⇒ x ≥ 9

When the character slips, it takes 2 seconds for him to resume the race.

Therefore, the least amount of race time your character took to slip on bananas would be,

9 × 2 = 18 seconds

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The complete question is:

In an online game, you receive -3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most -27. When the character slips, it takes 2 seconds for him to resume the race. Write and solve an inequality to find the least number of bananas your character slipped on. At least how many seconds of race time

The limit as a definite integral is  given as   lim (n → ∞) Σ(8i²)/n³ = 8/3n³

The area under the curve f(x) from x= a to x  = b is represented by the definite integral of f(x  )

There are 2 kinds of    integrals

To express the limit as a definite integral, we can use the following formul

lim(n → ∞  ) Σf(i)/n = ∫  a^bf(x)dx

where....

a and b are the lower and upper limts of the definite integral

f (x) is the function being integrated

In this case, we have

lim(n → ∞) Σ(8i²)/n³

Let f  (x) = x ²

So, f(i/n) = (i/n) ²

And, the sum can be written as

Σ(8i^2)/n³ = 8/n³ Σi²

= 8/n³ Σ(i/n)²

= 8/n³ Σ[f(i/n)]

= 8/n³ ∫0¹ f(x) dx (using the formula above)

Therefore, the limit can be   expressed as

lim(n → ∞) Σ(8i²)/n³ = 8/n³ ∫0¹ x² dx

Simplifying the integral, we get....

8/n³  ∫0¹ x₂ dx = 8/n^3 [x³/3] from 0 to 1

= 8/3n ³

Se we can say here that  the limit as a definite integral is lim(n → ∞) Σ(8i ₂)/n^3 = 8/3n ₃

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The monthly payments and total cost of interest depend on the interest rate and the length of the loan. Generally, a lower interest rate or a shorter loan term results in lower total interest costs.

To calculate the monthly payments, we can use the formula for the present value of an annuity:

[tex]PV = P * (1 - (1 + r)^{-n}) / r[/tex]

where PV is the present value of the loan, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments.

(a) 30 years, 5%:

PV = 0.9 * $90,000 = $81,000 (since she puts 10% down)

r = 0.05 / 12 = 0.0125(monthly interest rate)

n = 30 * 12 = 360 (number of monthly payments)

Using the formula, we get:

PV = $81,000

Monthly payment = $436.82

Total cost of interest = $57,255.85

(b) 30 years, 5.12%:

r = 0.0512 / 12 = 0.00427 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $439.88

Total cost of interest = $59,956.19

(c) 30 years, 6%:

r = 0.06 / 12 = 0.005 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $485.24

Total cost of interest = $95,687.34

(d) 15 years, 3.78%:

n = 15 * 12 = 180 (number of monthly payments)

r = 0.0378 / 12 = 0.00315 (monthly interest rate)

Using the formula, we get:

PV = $81,000

Monthly payment = $591.93

Total cost of interest = $34,147.07

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Compare the data by observing the shape, center, and spread of the data in both representations.

1. Understand the data: Before comparing two representations of data, it is important to understand what the data represents and its context.

2. Identify the type of data: Identify the type of data represented in each representation to ensure the data is comparable.

3. Plot the data: Plot the data in each representation, such as a line plot, box plot, or histogram.

4. Compare the data: Compare the data by looking at the shape, center, and spread of the data in both representations.

Example: To compare data in two-line plots, plot the data as two lines on the same graph. Observe the difference in the shape of the two lines, the difference in center (the average value of the data), and the difference in spread (the range of the data).

Example: To compare data displayed in a box plot, plot the data as two box plots side by side. Observe the difference in the shape of the two box plots, the difference in center (the median value of the data), and the difference in spread (the interquartile range of the data).

Example: To compare data displayed in histograms, plot the data as two histograms side by side. Observe the difference in the shape of the two histograms, the difference in center (the mean value of the data), and the difference in spread (the standard deviation of the data).

List the steps to create a back-to-back stem-and-leaf plot:

1. Organize the data: Organize the data into two sets of numerical data.

2. Create stems: Create a stem for each set of data by dividing the values by a common multiple.

3. Create leaves: Create leaves for each set of data by recording the remainder of the original values after dividing them by the common multiple.

4. Plot the data: Arrange the stems and leaves into a back-to-back stem-and-leaf plot.

5. Compare the data: Compare the data by observing the shape, center, and spread of the data in both representations.

Therefore, compare the data by observing the shape, center, and spread of the data in both representations.

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The following equation denotes the correlation between the duration and output of an activity: A = kT

It should be noted that A represents the amount of production, T is the period of working on the task, and k consists of a constant ratio.

Therefore, it can be conclusively stated that the culminating yield is in direct correlation to the amount of effort contributed, as denoted by the factor of proportionality k, thus producing a linear relationship when displayed upon a graph.

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The value of the variable x;

1. x = -4, BC = 4x + 3 = -13

2. x = 72 degrees

3. x = 5/2, SV = 6.5, ZU = 6.4

4. x = 4

5. x = 5

6. x = 3

Tangent are simply described as any straight line that is drawn from the curve at a point but never reaches the center of the circle.

It is also important to note that tangent segments of a circle are equal.

From the information given, we have that;

1. The tangents are;

4x + 1 = 5x - 3

collect the like terms

-x = 4

x = -4

Then BC = 4x + 3 = -13

2. 2x - 1 = 143

collect the like terms

2x = 143 + 1

2x = 144

x = 72 degrees

3. 3x - 1 = 5x - 6

collect the like terms

-2x = -5

x = 5/2

Then,

SZ = ZU =  3(5/2) - 1 = 15/2 - 1 = 6.5

4. 5x² + 10 = x² + 74

collect the like terms

4x² = 64

x² = 16

x = 4

5. 2x + 7 = 5x - 8

collect the like terms

-3x = -15

divide the values

x = 5

6. 3x - 1.2 = 2x + 1.8

x = 3

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well, if the hemisphere has a diameter of 8, that means its radius is half that or 4, hmm let's find the volume of a Sphere with such a radius, then let's halve it.

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3} \\\\\\ \stackrel{\textit{now let's get half of that for the hemisphere}}{V=\cfrac{1}{2}\cdot \cfrac{4\pi (4)^3}{3}\implies V=\cfrac{128\pi }{3}}\implies \boxed{V\approx 134.0}[/tex]

The correct statement regarding the graph is given as follows:

C. The graph is non-proportional and has the equation y = -2x + 18.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope and the intercept of the line in this problem are given as follows:

Thus the equation is:

y = -2x + 18.

The equation is non-proportional, as it has an intercept which is different of zero.

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The graph of the function f(x) = 4(2/3)^x is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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Answer:

Step-by-step explanation:

your supposed to learn things in class pay attetion

[tex]-37 < -12v+1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ v=-11\hspace{5em}-37 < -12(-11)+1\implies -37 < 133 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-9\hspace{5em}-37 < -12(-9)+1\implies -37 < 109~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=-5\hspace{5em}-37 < -12(-5)+1\implies -37 < 61~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ v=6\hspace{5em}-37 < -12(6)+1\implies -37 < -71 ~~ \bigotimes[/tex]