What is the mean of the data set: 17,13,18,20,17,15,12

By definitions of line segment and midpoint, we find that \(\overline{TU} \cong \overline {UV}\).

In this problem we find a line segments partitioned in four parts by using midpoints, each of them are listed below:

A point within a line segment is a midpoint if and only if it partitions the line segment into two parts of equal length. If point U is the midpoint of line segment SW, then SU = UW. If point T is the midpoint of SU, then ST = TU and if point V is the midpoint of UW, then UV = VW. Finally, we get the following result by algebraic handling:

SU = UW

ST + TU = UV + VW

2 · TU = 2 · UV

TU = UV

\(\overline{TU} \cong \overline {UV}\)

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Answer:

Step-by-step explanation:

30  30 x 3 = 90

x 3

90  

first  multiply 4 x 5 = 20 bring down 0 then multiply 4 x 2 = 8 then add+2= 10

25 x 4 = 100

12 x 15 = 180

x is 8 units,the length of a side of the hexagon or square, where the perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon.

The concept of a six-sided shape is derived from the Greek word hexágnon, where the word gonia means "angle." This makes sense since a hexagon includes not only six sides, but also six angles, or vertices.

Hexagons are six-sided polygons in geometry. The term "regular hexagon" refers to a hexagon whose side lengths and angle measurements are all equal. In other words, a regular hexagon's sides are congruent.

In order to solve this problem, where we are given that a square and a regular hexagon have sides of the same length.

The perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon.

So  we use the formula for the perimeter of a square which is:  

P = 4x,

and the formula for the perimeter of a regular hexagon is  P = 6x.

Compare this two equation and get -

4x + 32 = 6x,

so x = 8.

Therefore, the length of each side of the square and hexagon is 8 units.

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We have to solve this quotient with factorials:

Answer: the simplified expression is 2/7.

Answer: 11+23i

Step-by-step explanation:

(i+5)(3+4i)

First foil

3i+4i^2 +15+20i

Then combine like terms

23i+15+4i^2

i^2 = -1 so,

23i+15+4(-1)

11+23i

Answer:

x = 36

Step-by-step explanation:

x + y = 2x

y = x

x + 2(x) + 2(x) = 180

x + 2x + 2x = 180

5x = 180

x = 36

Answer:

383.5

Step-by-step explanation:

We want to round 383.52 to the nearest tenth.

The tenth would be the 5.

To round we look at the number after the one we want to round ( so 2 )

If the number is greater than 4 so ( 5, 6, 7, 8 or 9 ) then we raise the number that we want to round but if its less than 5 ( 4, 3, 2, 1 , 0 ) we keep the number as it is.

2 is less than 5 so we keep 5 as it is to get 383.5

1. Carter invested her money for approximately 4.78 years.2.  the annual interest rate charged to Winnie with compound interest compounded semi-annually is approximately 92.4%.

1. To find the duration of Carter's investment, we can use the simple interest formula:

Interest = Principal * Rate * Time

Given:

Principal (P) = $5300

Rate (R) = 7.2% = 0.072 (as a decimal)

Interest (I) = $1200

Substituting the values into the formula, we have:

$1200 = $5300 * 0.072 * Time

Simplifying the equation:

Time = $1200 / ($5300 * 0.072)

Time ≈ 4.78 years

Therefore, Carter invested her money for approximately 4.78 years.

2. To find the annual interest rate charged to Winnie with compound interest compounded semi-annually, we can use the compound interest formula:

A = P(1 + r/n)^(n*t)

Given:

Principal (P) = $2112

Amount (A) = $1879

Number of compounding periods per year (n) = 2 (semi-annually)

Time (t) = 1.5 years

Substituting the values into the formula, we have:

$1879 = $2112(1 + r/2)^(2 * 1.5)

Simplifying the equation and isolating the variable:

(1 + r/2)^(3) ≈ 0.8888

Taking the cube root of both sides:

1 + r/2 ≈ 0.962

Subtracting 1 and multiplying by 2:

r ≈ 0.924

Therefore, the annual interest rate charged to Winnie with compound interest compounded semi-annually is approximately 92.4%.

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Answer:

\(= \frac{2m^2n^8}{3}\)

Step-by-step explanation:

Given expression is

\((\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}\)

The correct simplified form is shown below:-

From the above equation, we will simplify

we will shift \(m^{-6}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}\)

now we will shift the \(n^{-8}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}\)

here we will solve the above equation which is shown below

\(= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}\)

So,

\(= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}\)

Which gives result

\(= \frac{2m^2n^8}{3}\)

Answer:

12183

Step-by-step explanation:

Answer:

13.2

Step-by-step explanation:

multiply 6.3×4

she swims 6.3 hours per week for 4 weeks. to find the answer you just need to multiply then together

Answer: Ma Lee swims for (4x6.3) which equals 25.2

Step-by-step explanation:

If you write them stacked on top of each other like this

6.3

6.3

6.3

6.3

when you add up the tenths place first you get 12 so regroup the 1 over to the ones place and put 2. Next add up 6's 6x4 equals 24 but dont forget the regrouped 1. Add 24+1=25. So altogether your answer is 25.2.

The radius of the cylinder is 14 meters (diameter of 28 meters divided by 2). Using the formula for the volume of a cylinder, V = πr²h, where π is approximately 22/7, r = 14 meters, and h = 4.5 meters, we get:

V = (22/7) x 14² x 4.5

V = (22/7) x 196 x 4.5

V = 11,088 cubic meters (rounded to the nearest whole number)

Therefore, the volume of the cylinder is approximately 11,088 cubic meters. The answer is (A) 11,088 cubic meters.

A group of nine people can now be seated in a row in 40320 different ways.

The two people who insist on sitting next to one other can be situated in one of two ways. The remaining seven people can be seated in seven different ways.

As a result, the total number of ways in which the nine persons can be seated in a row is 1 x 7! = 40320.

In this situation, the two people who dislike each other can be seated in

(7-1)! different ways.

The remaining seven people can be seated in seven different ways.

As a result, the total number of possible combinations for seating 9 individuals in a row is (7-1)! x 7! = 40320.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

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Answer:

Future amount = 100(1.9)^5 ;

2476

Step-by-step explanation:

P(t) = P0 * (1 + r)^t

P(t) = 100 * (1 + 90/100)^t#

P(t) = 100 * (1 + 0.9)^t

Therefore, the number of bacteria in 5 years :

P(5) = 100 * (1 + 0.9)^5

P(5) = 100 * (1.9)^5

P(5) = 100 * 24.76099

P(5) = 2476.099

P(5) = 2476 bacteria

P(10%

Answer:

No, they are not parallel

Step-by-step explanation:

Parallel means two lines that will never touch, but if you look at B and D, you can see that they will eventually touch if you make an imaginary line going off the screen.

Answer:

Your correct answer is going to be the third option

Step-by-step explanation:

Graph D shows the relationship between the number of side dishes and the total cost of the special.

Since we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

In Graph D, the y coordinate, or we can say that the number of boxes is 25 for the x coordinate, or the time (in days).

As we follow the graph, we can say that there is 21 boxes for 3 days, 19 boxes for 4 days, and 13 boxes for 7 days.

Therefore, Graph D shows the relationship given in the table.

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Answer: 222.78

Step-by-step explanation:

The probability that they end up with four boys on the left and two girls on the right is 1/15.

To solve this problem, we need to calculate the probability of the desired seating arrangement occurring. Let's break it down step by step:

Step 1: Calculate the total number of ways the 6 friends can be seated in a row with no restrictions.

Since there are 6 seats, the first friend can choose any of the 6 seats, the second friend can choose any of the remaining 5 seats, the third friend can choose any of the remaining 4 seats, and so on. Therefore, the total number of ways they can be seated is:

Total ways = 6 x 5 x 4 x 3 x 2 x 1 = 720

Step 2: Calculate the number of ways the four boys can be seated on the left and two girls on the right.

Since there are 4 boys, the first boy can choose any of the 4 seats on the left, the second boy can choose any of the remaining 3 seats, and so on. Similarly, the first girl can choose any of the 2 seats on the right, and the second girl can choose the remaining seat. Therefore, the total number of ways they can be seated according to the desired arrangement is:

Desired ways = 4 x 3 x 2 x 1 x 2 x 1 = 48

Step 3: Calculate the probability by dividing the desired ways by the total ways.

Probability = Desired ways / Total ways = 48 / 720 = 1 / 15

Therefore, the probability that they end up with four boys on the left and two girls on the right is 1/15.

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The number of bacteria  After 3 hours, in the petri dish would be approximately 823,542,481.

To calculate the number of bacteria in the petri dish after a certain number of hours, you can use the formula:

Number of bacteria = Initial number of bacteria × (growth factor)^(number of hours)

In this case, the initial number of bacteria is 500,500,500 and the growth factor is 1.21.21, point, 2.

Let's calculate the number of bacteria after 1 hour:

Number of bacteria after 1 hour = 500,500,500 × (1.21.21, point, 2)^1

Number of bacteria after 1 hour ≈ 500,500,500 × 1.21.21, point, 2 ≈ 605,662,605

After 1 hour, the number of bacteria in the petri dish would be approximately 605,662,605.

If you want to calculate the number of bacteria after multiple hours, you can simply raise the growth factor to the power of the number of hours. For example, to calculate the number of bacteria after 3 hours:

Number of bacteria after 3 hours = 500,500,500 × (1.21.21, point, 2)^3 ≈ 500,500,500 × 1.21.21, point, 2 × 1.21.21, point, 2 × 1.21.21, point, 2 ≈ 500,500,500 × 1.64642042 ≈ 823,542,481

After 3 hours, the number of bacteria in the petri dish would be approximately 823,542,481.

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Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Gets Narrow, and opens opposite direction

The function in Excel that is used to compute the statistics required to create a histogram is the FREQUENCY function.

The FREQUENCY function is used to calculate how often values occur within a specified range or bin.

The output of the function is an array of values that represents the frequency distribution of the data, which can then be plotted to create a histogram.

To use the FREQUENCY function, we first need to define the bins or intervals that we want to use for our histogram.

These bins should cover the range of the data and should be of equal width.

Once we have defined our bins, we can use the FREQUENCY function to calculate the frequency of values that fall within each bin.

The syntax of the FREQUENCY function is as follows:

=FREQUENCY(data_array, bins_array)

The data_array argument is the array or range of data that we want to analyze, and the bins_array argument is the array or range of bins that we have defined.

The function returns an array of values that represents the frequency of values that fall within each bin.

Once we have the frequency distribution of our data, we can create a histogram by plotting the frequency values against the bin intervals.

Excel has built-in tools for creating histograms, which can be found under the "Data Analysis" menu.

By defining our bins and using the FREQUENCY function, we can quickly and easily analyze the distribution of our data and visualize it in a histogram.

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Answer: 13/25

Step-by-step explanation: it is equal to 52% which is greater than 50%

50% is greater than 13/25. To compare these two values, you can convert both of them to a common denominator, such as 50%. 50% is equal to 1/2, so 13/25 is equal to 52/50, which is less than 1/2 or 50%. Alternatively, you can also express both fractions as decimals and compare the two values that way. 50% is equal to 0.5, and 13/25 is equal to 0.52, so 50% is still greater than 13/25.

The probability that a quarter lands on tail and a rolling die land on 2 is 1/12

A probability is a number that reflects the likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space /total outcome

A quarter has two faces, the head and the tail. Therefore the probability for a quarter to land on tail = 1/2

A die has 6 faces , labelled 1, 2,3,4, 5,6.

The probability for a die to land on 2 = 1/6

Therefore the probability for a quarter to land on tail and a die to land on 2 = 1/2 × 1/6 = 1/12

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One possible value of ∠U is 80° (to the nearest degree).

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

To find the possible values of ∠U, we can use the Law of Cosines:

c² = a² + b² - 2ab cos(C)

Where c is the side opposite the angle we want to find (∠U), a and b are the other two sides, and C is the angle opposite side c.

In this case, we want to find ∠U, so we'll use side u as c and sides t and s (which we don't know yet) as a and b, respectively:

u² = t² + s² - 2ts cos(U)

Substituting the given values, we get:

340² = 620² + s² - 2(620)(s)cos(U)

Simplifying:

115600 = 384400 + s² - 1240s cos(U)

Subtracting 384400 and rearranging:

s² - 1240s cos(U) + 268800 = 0

Now we can use the quadratic formula to solve for s:

s = [1240 cos(U) ± √(1240² cos²(U) - 4(1)(268800))]/(2)

Simplifying under the square root:

s = [1240 cos(U) ± √(1537600 cos²(U) - 1075200)]/(2)

s = [1240 cos(U) ± √(409600 cos²(U) + 1742400)]/(2)

s = [620 cos(U) ± √(102400 cos²(U) + 435600)]

Since s must be positive, we can discard the negative solution, and we have:

s = 620 cos(U) + √(102400 cos²(U) + 435600)

Now we can use the fact that the sum of angles in a triangle is 180° to find ∠U:

∠U = 180° - ∠T - ∠S

Since we know ∠T = 110°, we just need to find ∠S. We can use the Law of Sines to do this:

sin(S)/s = sin(T)/t

sin(S) = (s/t)sin(T)

Substituting the values we know:

sin(S) = (620 cos(U) + √(102400 cos²(U) + 435600))/620 * sin(110°)

sin(S) ≈ (1.481 cos(U) + 2.225)/6.959

Now we can use a calculator to find the arcsin of both sides to get ∠S:

∠S ≈ arcsin((1.481 cos(U) + 2.225)/6.959)

Finally, we can substitute the values we found for ∠S and ∠T into the equation we found earlier for ∠U:

∠U = 180° - 110° - arcsin((1.481 cos(U) + 2.225)/6.959)

Simplifying:

∠U = 70° - arcsin((1.481 cos(U) + 2.225)/6.959)

Now we can use trial and error or a graphing calculator to find the values of ∠U that satisfy this equation. One possible solution is:

∠U ≈ 80°

Therefore, one possible value of ∠U is 80° (to the nearest degree).

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Answer:

i)

ii)

iii)

Imagine parallel line through vertex of angle x.

iv)

Same as above:

Answer:

Step-by-step explanation:

As,

Landslide, also called landslip, the movement downslope of a mass of rock, debris, earth, or soil (soil being a mixture of earth and debris).

Landslides occur when gravitational and other types of shear stresses within a slope exceed the shear strength (resistance to shearing) of the materials that form the slope.

Answer:

Landslide                              

Hope this helps. Plz give brainliest

Answer:

Step-by-step explanation:

The roots are:

The equation is: