The mean for the data set is 2. 5.
What is the mean absolute deviation (MAD)? Round to the nearest tenths ​

Answers

Answer 1

Given:

The mean of the data set is 2.5.

We are asked to calculate the mean absolute deviation (MAD) of the data set.

Formula for MAD:

MAD = ∑ | xi - μ | / n

Where:

μ = Mean of the data set

xi = Data points

n = Number of data points

Calculation for MAD:

Data set: 1, 2, 3, 4, 5

Step 1: Find the deviations of each data point from the mean.

Data point Deviation from mean

1 -1.5

2 -0.5

3 -0.5

4 -1.5

5 -2.5

Step 2: Find the total deviation (absolute value).

Total deviation (absolute value): 1.5 + 0.5 + 0.5 + 1.5 + 2.5 = 6

Step 3: Calculate the mean absolute deviation (MAD).

MAD = Total deviation / Number of data points = 6 / 5 = 1.2

Rounded to the nearest tenth:

MAD ≈ 1.2

Therefore, the mean absolute deviation (MAD) of the given data set is 1.2 (rounded to the nearest tenth).

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Related Questions

A compound inequality is shown below.

x ≤ 3 and x ≥ 0

Which graph represents the solution of the inequality?​

Answers

Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

Write an equation to represent the following statement.
51 divided by 3 is k


Solve for k.

Answers

Answer:

K = 17

Based on the given conditions, formulate: 

51 / 3 = k

Swap the sides : k = 51 / 3

Cross out the common factor: k = 17

Jagrit is looking at two computer repair stores.


Store 1: Data-Fix

The total cost charged by Data-Fix is represented by the graph

as shown.

a) Write an equation to model the relation of total cost, C, and

number of hours, n as shown in the graph.

b) One of the points on the graph is (3, 60). Explain the

meaning of this point, in the context of this scenario.


Store 2: Comput-Repair

It charges a fixed cost of $10 plus $15 per hour for repair

services.

c) Write an equation to model the relation of total cost, C, and

number of hours, n, in Comput-Repair.

d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.

e) What are the coordinates of the point of intersection?

f) What does it mean in this scenario?

g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two

computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME

Answers

See below for the solution of each question

The equation of the model

The points are given as:

(3,60) and (5, 80)

The equation is calculated as:

[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]

This gives

[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]

Evaluate the quotient

C(n) = 10 * (n - 3) + 60

Expand

C(n) = 10n - 30 + 60

Evaluate

C(n) = 10n + 30

Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30

Explain the points on (3, 60)

The point (3, 60) means he paid $60 for 3 hours

The equation of the model for Comput-Repair

Here, we have:
Fixed = $10

Hourly rate = $15

The equation is calculated as:

C(n) = Fixed + Rate * Number of hours

This gives

C(n) = 10 + 15n

Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n

The graph of the fee structure for Compu-Repair

The equation is represented as:

C(n) = 10 + 15n

See attachment for the graph

The coordinates of the point of intersection

This is the point where the two lines intersect.

From the graph, we have the point of intersection to be:

(n, C(n)) = (4, 70)

The meaning in this scenario

This means that the charges for Comput-Repair and Data-Fix are the same after 4 hours

Advice Jargit

Based on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate

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Can anyone help me solve this
I need it left in terms of pi and pls show work

Answers

Circumference = 10π in, Area = 25π in²

Circumference = 19 π in, Area = 90. 25 π in²

Area = 225 π in²

Circumference = 16π

How to determine the circumference and area

It is important to note that the formula for area and circumference are;

Area = πr^2

Circumference = 2πr

For the first column, we have

radius = 5in

Substitute the values of the radius into the formula

Circumference = 2 × π × 5

Circumference = 10π in

The area;

Area = π × 5 × 5

Area = 25π in²

For the second column,

radius = 9. 5 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 9. 5

Circumference = 19 π in

Area = π × 9. 5 × 9. 5

Area = 90. 25 π in²

For the third column

radius = 15in

Substitute the values of the radius into the formula

Area = π × 15 × 15

Area = 225 π in²

For the fourth column

radius = 8 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 8

Circumference = 16π

From the solved solution, we can see that the shape is a circle.

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I can't figure out the equivalent fraction. Whoever gets it first gets brainliest, and please do explaination

Answers

Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.

[tex]\dfrac{28}{48} = \dfrac{4\times7}{4\times12} = \dfrac7{12} = \dfrac{3\times7}{3\times12} = \boxed{\dfrac{21}{36}}[/tex]

The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches

Answers

The surface area of a rectangular prism is found as 150 square inches.

What is rectangular prism?

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.

Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.

Calculation for the surface area of rectangular prism-

Height of a rectangular prism => H = 4 inches

Width of a rectangular prism => B = 9 inches

Length of a rectangular prism => L = 3 inches

Surface area of a rectangular prism = 2(LB + BH + HL)

                                                           = 2(9×3 + 9×4 + 4×3)

                                                           = 150

Therefore, the surface area of a rectangular prism is found as  150 square inches.

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Please please answer following question and show work

Answers

The y-intercept of the function f(x) is (0, 10/3)

The limits of the function

The function is given as:

[tex]f\left(x\right)=\frac{30}{1+2^{3-x}}[/tex]

As x approaches infinity, we have:

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-x}}[/tex]

This gives

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-\infty}}[/tex]

[tex]\lim_{x \to \infty} \frac{30}{1+2^{-\infty}}[/tex]

Evaluate

[tex]\lim_{x \to \infty} \frac{30}{1}[/tex]

[tex]\lim_{x \to \infty} 30[/tex]

As x approaches negative infinity, we have:

[tex]\lim_{x \to -\infty} \frac{30}{1+2^{3+x}}[/tex]

This gives

[tex]\lim_{x \to -\infty} \frac{30}{\infty}[/tex]

Evaluate

[tex]\lim_{x \to -\infty} 0[/tex]

Hence, the limits of the function are [tex]\lim_{x \to \infty} 30[/tex] and [tex]\lim_{x \to -\infty} 0[/tex]

The horizontal asymptote

Remove the denominator

f(x) = 30

Also, set the numerator to 0

f(x) = 0

Hence, the horizontal asymptotes are y = 30 and y = 0

The y-intercept

Set x = 0

[tex]f\left(0\right)=\frac{30}{1+2^{3-0}}[/tex]

Evaluate

[tex]f\left(0\right)=\frac{30}{9}[/tex]

Divide

[tex]f\left(0\right)=\frac{10}3[/tex]

Hence, the y-intercept is (0, 10/3)

How the numerator is related to (b)

The numerator of f(x) is 30.

In (b), we have

The horizontal asymptotes are y = 30 and y = 0

This means that the horizontal asymptotes and the numerator are the same

The graph

See attachment for the graph of f(x)

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A population of protozoa develops with a constant relative growth rate of 0.469 per member per day. On day zero the population consists of five members. Find the population size after eight days.

Answers

If the growth rate is 0.469 per member per day and in the beginnning there are 5 members then the population size after eight days is 108.42.

Given growth of population of protozoa 0.469 per member per day and population in beginninng is 5 members.

We have to find the population afte eight days.

First of all we have to find the function or equation showing sum of population after t days.

Because it is given that the rate is 0.469 per member per day it means it is like compounding.

The equation which shows the sum after compounding is P[tex](1+r)^{n}[/tex]

where P is the amount in beginning, r is the rate and n is the number of years.

In this problem the equation will be 5[tex](1+0.469)^{t}[/tex] where t is number of days.

We have to put the value of t=8 to find the population after 8 days=

=5[tex](1.469)^{8}[/tex]

=5*21.68

=108.42

Hence the population of protozoa after 8 days is 108.42.

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According to a survey, 15% of city workers take the bus to work. Donatella randomly surveys 10 workers. What is the probability that exactly 6 workers take the bus to work

Answers

By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.

What is Binomial Distribution?

When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.

The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.

The formula for binomial distribution is-

[tex]P(X=x)={ }^{n} C_{k} p^{k}(1-p)^{n-k}[/tex]

'p' is the probability of success,

(1-p) is probability of failure,

'n' is the number of workers,

'k' is number of given workers.

According to the question,

Calculate the probability of success as;

[tex]p=\frac{15}{100}=0.15[/tex]

The, the probability of the failure becomes;

[tex](1-p)=1-0.15=0.85[/tex]

Put above two value in formula of binomial theorem to get the value.

[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]

Therefore, the probability that exactly 6 workers take the bus to work is 0.001.

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Sally's balance on her credit card is $75.00 on the first day of august. she makes a payment of $18.00 on august 17 and
a new purchase of $41.00 on august 29. the annual interest rate is 21.25%. what is sally's average daily balance and
finance charge for the month of august?

Answers

The average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

Averages

Given that Sally's balance on her credit card is $75.00 on the first day of August, and she makes a payment of $18.00 on August 17 and a new purchase of $41.00 on August 29, and the annual interest rate is 21.25%, to determine what is Sally's average daily balance and finance charge for the month of August, the following calculation must be made:

75 x ((21.15/12 x 16) / 100) + 75 = A = 86.8957 x ((21.15/12 x 13) / 100) + 57 = B = 70.0698 x ((21.15/12 x 3) / 100) + 98 = C = 103.18(86.89 x 16 + 70.06 x 13 + 103.18 x 3) / 31 = X84.21 = X86.89 + 70.06 + 103.18 - 75 - 57 - 98 = Y30.13 = Y

Therefore, the average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

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For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.
(fog)(x) =
Domain of fog:

Answers

Find fog

fog(x)f(g(x))f(√x-5)2√(x-5)+3

For real range the domain

x-5≥0x≥5

Domain is [5,oo)

Choose the equation that satisfies the data in the table.

Answers

Answer:

Option A.

Step-by-step explanation:

Demonstration

[tex]y=\frac{7}{4} x+7[/tex]

for x = -4

[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]

for x= 0

[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]

for x= 4

[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]

Hope this helps

a total of $7000 is invested: part at 6% and the remainder at 10%. How much is invested at each rate if the annual interest is $470?

Answers

Answer:

680

Step-by-step explanation:

PLEASE HELP QUICK!!!!
Bernie borrowed b books from his friend Grant's collection of 29 books. What does the expression 29 - b represent?

Answers

answer:
the amount of books grant has left

explanation:
if you take away b books, he is left with 29-b books

A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data

Answers

The central tendency researcher use to describe these data is "mode".

What is mode?

The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.

Calculation of mode is done by-

The number that appears the most frequently in a piece of data is its mode. Put the numbers in ascending order by least to greatest, then count the occurrences of each number to quickly determine the mode. The most frequent number is the mode.Simply counting how many times each number appears in the data set can help you identify the mode, which is the number that appears the most frequently in the data set. The figure with the largest total is the mode.Example: Since it happens most frequently, the mode for the data set [5, 7, 8, 2, 1, 5, 6, 7, 5] is 5.

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What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

Answers

The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).

How to calculate the minimum value?

To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:

Step 1: Identify the system of inequalities in the given constraints

Step 2: Graph those inequalities

Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities

Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.

Calculation:

The given equation is C = 7x + 8y, and the constraints list is

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Graphing these inequalities and shading the region that satisfies the given inequalities.

So, from the graph,

the x-values that satisfy all the given inequalities are [6, ∞]

the y-values that satisfy all the given inequalities are [0, ∞]

So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y

Then,

C = 7(6) + 8(0) = 42 + 0 = 42

Thus, the minimum value of the given equation is 42.

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Disclaimer: The given question is incomplete. Here is the complete question.

Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Please HELP!!!!
will give brainliest!!

Answers

Answer:

Original equation:

y = a sin(b(θ -c)) + d

a = vertical dilation (stretch) of the amplitude

b = horizontal compression (shrink) of the period

c = horizontal shift (left/right)

d = vertical shift (up/down)

Your function is:

y = 3 sin(3θ + π) - 2

First, put it into the general from by factoring out the three in the argument of the sine:

y = 3 sin(3(θ + π/3)) - 2

a = vertical (amplitude) dilation = 3

b = horizontal (period) compression = 2π/period = 3

c = horizontal shift = π/3 to the left

d = vertical shift = -2

solve these linear equation
x + 4y = 16
3x + 5y = 27​

Answers

Use elimination

x+4y=16--(1)3x+5y=27--(2)

(1)×5 and (2)×4

5x+20y=80--(3)12x+20y=108--(4)

(3)-(4)

-7x=-28x=4

Putting in eq(1)

4y=16-44y=12y=3

x + 4y = 16 __(1)

3x + 5y = 27 __(2)

Multiply the 1st equation by 3

3x + 12y = 48 __(3)

Solving (2) and (3)

3x + 12y = 48

3x + 5y = 27

__________

(-) (-) (-)

7y = 21

So, y = 3

By, putting the value of y = 3 in equation 1

x + 4(3) = 16

x + 12 = 16

x = 16 - 12

x = 4

We got -

The value of x = 4 and y = 3

Hope it helps you any confusions you may ask!

Select the correct answer. Find the solution(s) for x in the equation below. x^2 -25 =0

Answers

Answer:

Step-by-step explanation:

Find the roots of x^2-25=0 by solving for x.

Add 25 to both sides

x^2=25

Square root both sides

x=-5

x=5

Answer:

x=5;x=-5

Step-by-step explanation:

It was right for me

prove that if r is a matrix in echelon form, then a basis for row(R) consists of the nonzero rows of R

Answers

Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.

Step 1: We want to show that

R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write

v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]

Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]

So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}

Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

But trivially,

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)

Step 2: We want to show that  [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,

then we can write

[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]

From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.

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Matthew is flying with his jet pack at 100m/min. A strong wind has blown him 10m east of his intended flight path in 2 minutes. By how many degrees is Matthew off his flight path? Include a diagram.

Answers

Mathew's speed of 100 m/min, and the distance of 10 m. east to which he is blown by the wind gives the angle in degrees Mathew is blown off his path as approximately 2.86°.

How can the angle of deflection be found from the given speeds?

The given parameters are;

Speed at which Mathew is flying = 100 m/min

Distance and direction in which the strong wind blows him = 10 m. east

Time it takes the wind to deflect Mathew by 10 m. = 2 minutes

Therefore;

Speed and direction of the wind = 10/2 m/min east

Speed and direction of the wind = 5 m/min east

Mathew's flight path can be represented using a vector diagram (please see attached drawing)

Distance Mathew travels in 2 minutes = 100 m/min × 2 minutes = 200 m.

Tangent of the angle by which Mathew is off his flight path, A, can be found as follows;

tan(A) = 10/200 = 1/20

A = arctan(1/20) ≈ 2.86°

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please answer both asap!!!

Answers

I think for the first one its always occur along plate boundaries, and for the second one its season of the year.

The following two-way table describes student's
after school activities. find the probability that a
randomly selected student either does sports or
works.
grade
sports
music/drama
work
20
7
sophomore
3
junior
20
13
2
25
5
senior
5
p(sports u work) = [?]
round to the nearest hundredth.
lol

Answers

P ( work/ senior ) = 0.14

The attached table

required

P ( work/ senior )

This is calculated using:

P ( work/ senior ) = n ( work/ senior )/ n ( senior ).

n ( work/ senior ) = 5

n ( senior ) = 25 + 5 + = 35

So:

P ( work/ senior ) = 5/35

P ( work/ senior ) = 0.14

Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

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Given a population mean of 56.7, a standard deviation of 4.3, and a sample size of 260, what is the standard error of the mean? round
your answer to the nearest hundredth.
the standard error of the mean is approximately___.

Answers

The standard error of the mean, rounded to the nearest hundredth is 0.27

What is standard error of mean?

The standard error of the mean (SEM) calculates how big of a difference there is between the mean of a sample and the mean of the population.

The square root of the sample size is divided by the standard deviation in order to obtain  the Standard error of mean.

Always, standard error of mean will be smaller than standard deviation.

But a statistical inference based on the sampling distribution is part of the Standard error of mean definition.

According to the question,

Population Mean=56.7

Standard Deviation=4.3

Sample Size=260

Standard Error of mean=4.3/[tex]\sqrt{260}[/tex]

                                       =4.3/16.1245

                                       =0.27

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Answer:

0.27

Step-by-step explanation:

Plato/Edmentum

The line plot (shown in the attached image) shows the prices of sunglasses at a department store.

a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.

Please help!! show all work

Answers

a. The median is 70, the mode is 60, and the mean is 70.8.

b. Mean best captures the data.

c. When there are outliers, the mean might be a deceptive center measure.

Calculating the Mean, Median, and Mode

Mean: Total number of sunglasses / total quantity of pries

Mean = (20 + 20 + 50 + 50 + 50 + 60 + 60 + 60 + 60 + 60 + 60 + 70 + 70 + 70 + 80 + 80 + 80 + 80 + 90 + 90 + 90 + 90 + 100 + 100 + 130) / 25

Mean = 70.8

Median is equal to the (n/2 + 1)th term.

The number of sunglasses in this case is n.

(25/2 + 1)th term as the median

Median = 13th term

Median is 70

Mode is  the most frequent data

Therefore, mode = 70

Why is mean the most appropriate central measure ?

The mean is often the ideal measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data are normally distributed. So, mean here denotes the typical cost of the sunglasses.

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Answer:

Step-by-step explanation:

Which geometric shape could be used to model the building?


cylinder

pyramid

cone

rectangular prism

Answers

Answer:

Rectangular Prism

Step-by-step explanation:

We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.

Help please!!!
will give brainliest

Answers

The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.

First graph;

a. Amplitude = 0.5

b. The period = 2•π

c. The horizontal shift = 1

d. The vertical shift = π/4

Second graph;

a. Amplitude = 2

b. The period = π

c. The horizontal shift = -π/4

d. The vertical shift = -2

Which method can be used to find the graph parameters?

First graph;

a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.

The coordinate of a peak point in the first graph is (0, -1.5)

The coordinate of a throw point is (π/2, -2.5)

Therefore;

Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5

b. The period is the number of cycles per second, we have;

Period = 1/ff = Frequency

From the graph, we have;

f = 1 cycle per π

Therefore;

The frequency = 1/π cycle per unit length

Period = 1/(1/π) = π

c. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.

Therefore;

The horizontal shift = (-π/2)/2 = -π/4

d. The vertical shift is the distance from the horizontal axis to the midline of the graph.

By observation, the midline is y = -2

Therefore;

The vertical shift = -2

Second Graph;

For the second graph, we have;

a. Amplitude = (3 - (-1))/2 = 2

b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)

Therefore;

Period = 1/(1/(2•π)) = 2•π

c. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.

Therefore;

Horizontal shift = π/4 - 0 = π/4

d. Vertical shift = (3 + (-1))/2 = 1

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The sum of the series below is 10,900. how many numbers, n, are in the series? 19 20.5 22 23.5 ... 181

Answers

There are 109 terms in given series.

According to the statement

we have given that the sum of series is AP series and

This is 19 20.5 22 23.5 ... 181

And the sum of series is 10,900

Now, we have to find the number of terms in the series.

Then we use the summation formula which is

S = n/2 (a + L)

Substitute the all given values in it like

L = 181

A = 19 and S= 10,900

then

10,900= n/2(19+181)

10,900= n/2(200)

After solve the equation for n

10,900= 100n

n = 10,900 / 100

n = 109

There are 109 terms in given series.

So, There are 109 terms in given series.

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Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle of elevation of 61°. Dan is standing on the ground at a point directly west of the base of the tower and must look up at an angle of elevation of 72° in order to see the top. If the CN Tower is 553.3 m tall,how far apart are Vic and Dan to the nearest meter? Include a well-labeled diagram as part of your solution.

Answers

The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

How can the distance between Vic and Dan be calculated?

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]

[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]

[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]

Vic's distance from the tower ≈ 306.7 m

Similarly, we have;

[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]

Dan's distance from the tower ≈ 179.8 m

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;

d = √(306.7² + 179.8²) ≈ 356

Therefore;

Vic is approximately 356 meters from Dan

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Suppose that events E and F are independent, P(E)=0.6, and P(F)=0.7.
What is the P(E and F)?
The probability P(E and F) is
(Type an integer or a decimal.)

Answers

Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

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