Plz help me with this

Plz Help Me With This

Answers

Answer 1

Answer:  C) the variance

Step-by-step explanation:

Variance is the "average" of the squared differences from the Mean.


Related Questions

URGENT, literally will give 40 points and dub thee brainliest


Given the coordinates of the triangle, determine the coordinates of its image after a dilation with the given scale factor centered at the origin.

A(-1, 3), B(1, 1), C(-4, 1); scale factor: 2



A.
A' (negative 1 half,3 over 2)

B' (1 half,1 half)

C' (0, negative 3 over 2)



B.
A' (1,5)

B' (3,3)

C' (2, -1)



C.
A' (-2, 6)

B' (2,2)

C' (0, -6)

D.
A' (-3, 1)

B' (-1, -1)

C' (-2, -5)



Answers

Answer:

D

Step-by-step explanation:

What is the following quotient? Sqr root 6+ sqr root 11/sqr root 5 + sqr root of 3

Answers

Answer:4.31

Step-by-step explanation:

Which number is the same as (4-^1)(2^3÷4-^2)

A. -2
B. 1/8
C. 2
D. 32
E. 512

Answers

The answer is letter C. 2

Answer:

The answer to this problem is down below

Step-by-step explanation:

C

30 points + brainliest for correct answer! If a triangle has sides X, 4.0, and 8.0, what is the range of possible sizes for side x?

Answers

Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

Answer:

4.0 is less than x is less than 12.0

Step-by-step explanation:

Please Help Me =)
----------------------------

Answers

Steps:

6(1)+1= 7

6(2)+1= 13

6(3)+1=19

6(4)+1= 25

7,13,19,25

Answer is third choice

ANSWER

7,13,19,25

EXPLANATION

The given rule is:

6n+1

When n=1,

We obtain 6(1)+1=6+1=7...This is the first term.

When n=2,

6(2)+1=13

When n=3, we obtain,

6(3)+1=19

When n=4:

We have :

6(4)+1=25

The third choice is correct.

a man is hiking in Death Valley he start at an elevation of 65 feet above sea level and descends to an elevation 30 feet below sea level. How far did the hiker travel

Answers

Answer:95

Step-by-step explanation: i added 65 and 30

Answer:

Well lets think of this as a number line.

And 0 is equal to the sea level.

And anything above the sea level is a positive number and anything below it is a negative number.

So our starting place is 65 feet above sea level.

And we know that he hikes 30 feet below sea level.

So he hikes down 65 feet (reaches sea level) & continues another 30 feet

So we have to add.

30 + 65 = 95

And the question is asking how many feet the hiker traveled.

Step-by-step explanation:

ya ik im late but i thought i could help other people so good luck!

a particular toddler has an average nap of about two hours and sleep for 13 hours at night. nap time and night time sleep can each vary by about 15 minutes. what are the possible time legnths for the child's total nap and night time sleep?​

Answers

Answer:

14 h. 30min - 15h. 30

Step-by-step explanation:

Becuase the time varies by 15 minutes each, just find the difference after  adding and subtracting and then add the nap and sleep time.

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

What is the maximum and minimum value of the number?

The first number mentioned is the least because it is the smallest, and the final number listed is the greatest because it is the biggest.

A specific little child has a typical rest of around two hours and rest for 13 hours around evening time. rest time and evening rest can each differ by around 15 minutes.

The minimum amount of the time is calculated as,

⇒ 2 - (15/60) + 13 - (15/60)

⇒ 15 - 0.5

⇒ 14.5 hours

The maximum amount of the time is calculated as,

⇒ 2 + (15/60) + 13 + (15/60)

⇒ 15 + 0.5

⇒ 15.5 hours

The possible time lengths for the child's total nap and nighttime sleep will be 14.5 hours and 15.5 hours.

More about the maximum and minimum link is given below.

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Which are solutions of x2=-11+4?

Answers

For this case we have a quadratic equation of the form:

[tex]ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0[/tex]

Where:

[tex]a = 1\\b = 11\\c = -4[/tex]

We find the roots:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}[/tex]

The roots are:

[tex]x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}[/tex]

ANSWER

[tex]x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i[/tex]

EXPLANATION

The given expression is

[tex] {x}^{2} = - 11 + 4[/tex]

Simplify the left hand side to get:

[tex] {x}^{2} = - 7[/tex]

Take square root

[tex]x = \pm \sqrt{ - 7} [/tex]

[tex]x = \pm \sqrt{ 7} \times \sqrt{ - 1} [/tex]

Note that:

[tex] {i}^{2} = - 1 \implies \sqrt{ - 1} = i[/tex]

[tex]x = \pm \sqrt{ 7}i[/tex]

Split the plus or minus sign

[tex]x = - \sqrt{ 7}i \: \: or \: \: x = + \sqrt{ 7}i[/tex]

The shaded octagon is transformed to the unshaded octagon in the coordinate plane below.


Which statement about the transformation is true?


A. The unshaded octagon is a reflection because it is a flip over a diagonal line.


B. The unshaded octagon is a dilation because it is smaller than the shaded octagon.


C. The unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon.


D. The unshaded octagon is a vertical translation because it is directly under the shaded octagon.

Answers

Answer:

The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Lets solve the problem

- Look to the answer

# Answer D is wrong because the un-shaded octagon is not a vertical

  translation because it is not directly under the shaded octagon.

# Answer C is wrong because the un-shaded octagon is not a

  horizontal translation because it is not directly to the left of

  the shaded octagon

# Answer B is wrong because the un-shaded octagon is not a dilation

  because it is not smaller or bigger than the shaded octagon it has

  the same size

# The answer A is the right because:

∵ The shaded octagon in the first quadrant and the un-shaded

   octagon in the third quadrant

∵ The vertex of (2 , 1.5) has image (-1.5 , -2)

- The coordinates are replaced by each other the their signs are

 changed

∴ The shaded is reflected across the line y = -x

* The un-shaded octagon is a reflection because it is a flip over a

  diagonal line (y = -x)

Answer:A

Step-by-step explanation:

If you deposit $540 in an account that pays 6% interest compounded annually how much would be in the account after three years

Answers

Answer:

A=$643.15

Step-by-step explanation:

We can use the formula

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Now we can plug the information in the problem into the formula

[tex]A=540(1+\frac{0.06}{1} )^{(1)(3)}\\\\A=643.15[/tex]

Answer:

The amount after 3 year = $ 643.15

Step-by-step explanation:

Compound interest  formula:

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t - number of times compounded yearly

n  number of years

To find the amount after 3 years

Here P = $540, R = 6%, t = 1 and n = 3 years

A = P[1 +R/n]^nt

 = 650[1 + 0.06/1]^(3*1)

 = 540[1.06]^3

 = $ 643.15

A Young sumo wrestlers decided to go on a special diet to gain weight rapidly w (t)=80+5.4t how much weight does the wrestler gain every 2 months

Answers

The rate is 5.4 per month so in two months gains 10.8

Answer:

10.8 kg

Step-by-step explanation:

We are given that weight of young Sumo wrestler is given by

[tex]w(t)=80+5.4t[/tex]

We have to find the weight of wrestler gain in every months.

In order to find the weight gain in 2 month we will find out w(2)

Then, we get

[tex]w(2)=80+5.4(2)[/tex]

[tex]w(2)=80+10.8[/tex]

[tex]w(2)=90.8[/tex]

Weight gain in 2 month=90.8-80=10.8 kg

Hence,the wrestler gain 10.8 kg in every 2 months.

what is the volume of a cylinder with the base radius of 10 units and a height of nine units?

Answers

Answer:

[tex]V = 2827.43\ units^3[/tex]  or [tex]V = 900\pi\ units^3[/tex]

Step-by-step explanation:

The volume of a cylinder is calculated by the following formula

[tex]V = \pi r^2 *h[/tex]

Where r is the radius of the cylinder and h is the height

In this case we know that the radius r of the base is:

[tex]r=10\ units[/tex]

and

[tex]h=9\ units[/tex]

So the Volume is:

[tex]V = \pi (10)^2 *9[/tex]

[tex]V = 900\pi\ units^3[/tex]

[tex]V = 2827.43\ units^3[/tex]

Answer:

The volume is [tex]2827.4units^3[/tex] to the nearest tenth

Step-by-step explanation:

The volume of cylinder is : [tex]V=\pi r^2h[/tex]

The base radius of the cylinder is r=10 units.

The height of the cylinder is h=9 units.

Substitute the values into the formula to get;

[tex]V=\pi \times 10^2\times 9[/tex]

[tex]V=900\pi units^3[/tex]

[tex]V=2827.4units^3[/tex] to the nearest tenth

The graph of Fx), shown below, has the same shape as the graph of G(x) x2, but it is shifted up 4 units and to the right 3 units. What is its equation?

Answers

Using translation concepts, it is found that the equation of function F(x) is given by:

D. F(x) = (x - 3)² + 4.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is given by:

G(x) = x².

Then, these following translations happen:

Shift up 4 units, hence F(x) = x + 4.Shift right 3 units, hence x -> x - 3.

Thus, the equation of function F(x) is given by:

D. F(x) = (x - 3)² + 4.

More can be learned about translation concepts at https://brainly.com/question/4521517

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Estimate the area of the circle using 22/7

Answers

Answer: [tex]A_{circle}=616cm^2[/tex]

Step-by-step explanation:

You can observe in the figure that the value of the diameter of the circle is

[tex]d=28cm[/tex]

Then, since you know the diameter , you can use this formula for calculate the area of the circle:

[tex]A_{circle}=\frac{\pi d^2}{4}[/tex]

Where "d" is the diameter.

Then, substituting  [tex]d=28cm[/tex] and  [tex]\pi =\frac{22}{7}[/tex] into the formula, you can estimate the area of the circle. This is:

[tex]A_{circle}=\frac{(\frac{22}{7})(28cm)^2}{4}[/tex]

[tex]A_{circle}=616cm^2[/tex]

PLEASE HELP THANK YOU SO MUCH

Answers

Answer:

Step-by-step explanation:

Just add up all of the numbers basic math 38

Answer:

74 cm^2

Step-by-step explanation:

Divide this figure into two rectangles whose areas are easy to calculate:

First area would be on top, with a width of 4 and a length of 6 cm.  Its area is (4 cm)(6 cm) = 24 cm^2.

Second area would be the lower rectangle, with a length of 10 cm and width of 5 cm.  Its area is (10 cm)(5 cm) = 50 cm^2.

The total area of the given figure is thus 24 cm^2 + 50 cm^2, or 74 cm^2.

Quick geometry question please help ASAP!!!

For #3

Answers

Answer:

The volume of the composite figure is equal to [tex]400\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the area of the rectangular prism plus the volume of the rectangular pyramid

step 1

Find the volume of the rectangular prism

The volume is equal to

[tex]V=LWH[/tex]

we have

[tex]L=12\ in[/tex]

[tex]W=4\ in[/tex]

[tex]H=5\ in[/tex] ----> height of the rectangular prism

substitute

[tex]V=12*4*5=240\ in^{3}[/tex]

step 2

Find the volume of the rectangular pyramid

The volume is equal to

[tex]V=\frac{1}{3}LWh[/tex]

we have

[tex]L=12\ in[/tex]

[tex]W=4\ in[/tex]

[tex]h=10\ in[/tex] ----> height of the rectangular pyramid

substitute

[tex]V=\frac{1}{3}(12)(4)(10)=160\ in^{3}[/tex]

step 3

Adds the volumes

[tex]240\ in^{3}+160\ in^{3}=400\ in^{3}[/tex]

how do you simplify this expression.

Answers

4 + √16-(4)(5)  / 2

Simplify the numerator:

4 + √16 -20   = 4 +√-4

Now you have 4 + √-4 / 2

Rewrite the -4 as -1 *4

4 + √ -1*4  / 2

Rewrite √-1*4 as √-1 * √4

√-1 = i

Now you have 4 + i * √4 / 2

√4 = 2

Now you have 4 + i * 2 /2

Divide the numerator by the denominator to get the final answer: 2 + i

Find f(-3) if f(x) = x 2.

Answers

Answer:

f(-3) = 9

Step-by-step explanation:

Lets define f(a) first where a is any integer,

f(a) is found out by putting the integer in the function in place of the variable

So for the given question

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

In order to find f(-3) we will put -3 in place of x

So putting -3,

[tex]f(-3) = (-3)^{2}[/tex]

[tex]f(-3) = 9[/tex]

So, the value of function at -3 is 9 ..

Answer:  [tex]f(-3)=9[/tex]

Step-by-step explanation:

Given the quadratic function [tex]f(x)=x^2[/tex], you can find [tex]f(-3)[/tex] by substituting the input value [tex]x=-3[/tex] into this function, with this procedure you will get the corresponding output value.

Therefore, when [tex]x=-3[/tex], you get that the output value is the following:

[tex]f(x)=x^2\\\f(-3)=(-3)^2[/tex]

NOTE: Since the exponent is an even number, the result will be positive, because:

[tex](-3)(-3)=3[/tex]

Therefore, knowing this, you get that [tex]f(-3)[/tex] of the function [tex]f(x)=x^{2}[/tex] is:

[tex]f(-3)=9[/tex]

99% confidence interval for the mean

Answers

Answer:

16.3 ± 0.8391

Step-by-step explanation:

The confidence interval is:

CI = x ± SE * CV

where x is the sample mean, SE is the standard error, and CV is the critical value (either t score or z score).

Here, x = 16.3.

The standard error for a sample mean is:

SE = σ / √n

SE = 1.5 / √25

SE = 0.3

The critical value is looked up in a table or found with a calculator.  But first, we must find the alpha level, the critical probability, and the degrees of freedom.

α = 1 - 0.99 = 0.01

p* = 1 - (α/2) = 1 - (0.01/2) = 0.995

df = n - 1 = 25 - 1 = 24

Since df < 30, we use a t-score.  Looking up in a t-table, we find the critical value is CV = 2.797.

Therefore:

CI = 16.3 ± (0.3 * 2.797)

CI = 16.3 ± 0.8391

use a graphing calculator to find an equation of the line of best fit for the data. Identify and Interpret the correlation coefficient.​) I don't have a caculator btw

Answers

Answer:

Go to desmos.com/calculator

Step-by-step explanation:

It has a graphing calculator and it super easy to plug in.

The equation of the line of the best fit  for the data will be,y=2.07x-7.5.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The equation of the line is;

y=mx+c

y=2.07x-7.5

Hence, the equation of the line of the best fit will be,y=2.07x-7.5

Learn more about the line of best fit here:

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HELP ASAP MARKING BRAINLEST

use the diagram to write the standard equation of the circle.

Answers

Answer:

your answer is:

(x-2)^2 +(y-2)^2=16

Hope this helps.

Brainliest plz :)

The standard equation of the given circle is (x-2)²+(y-2)²=16. This can be obtained by using the general equation of the circle.

What is the general equation of the circle?

The general equation of the circle is,

(x-h)²+(y-k)²=r² , where (h,k) is the center and r is the radius

From the figure we say that (2,2) is the circle and 4 is the radiusBy using the general equation of the circle we can write the standard equation,

                   (x-2)²+(y-2)²=4² ⇒ (x-2)²+(y-2)²=16

Hence the standard equation of the given circle is (x-2)²+(y-2)²=16.

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Label all of the parts of the circle

Answers

Answer:

The dot is the center

the long line is the diameter

the circle is the circumference

the half way line is the radius

Final answer:

The parts of a circle include the center, radius, diameter, chord, arc, sector, segment, and circumference.

Explanation:The circle is divided into several parts: center, radius, diameter, chord, arc, sector, segment, and circumference.The center is the point in the middle of the circle, denoted by the letter C.A radius is the distance from the center of the circle to any point on its circumference. It is denoted by the letter r.The diameter is a chord that passes through the center of the circle and is twice the length of the radius. It is denoted by the letter d.A chord is a line segment that connects two points on the circumference of the circle. It does not necessarily pass through the center.An arc is a part of the circumference of the circle.A sector is the region between an arc and two radii.A segment is the region between an arc and a chord.The circumference is the distance around the circle. It can be calculated using the formula C = 2πr, where π is approximately 3.14.

Find the median of the following set of data:
48, 65, 57, 54, 61, 57, 52, 61, 57

a.) 54
b.)57
c.)61
d.)65

Answers

Answer:

b

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle value then it is the average of the values either side of the middle.

Arrange the data in ascending order

48, 52, 54, 57, 57, 57, 61, 61, 65

                          ↑

The median of the data set is 57 → b

Which expression is equivalent to (-4y-x)-(3y-9x)

A.-7y-8x
B.-7y+8x
C.-y-10x
D.y+10x

Answers

Answer:

B. -7y + 8x.

Step-by-step explanation:

(-4y - x) - (3y - 9x)

Distributing the negative over the second parentheses we get:

-4y - x - 3y + 9x

= -7y + 8x.

the probability of event a is 0.56 and the probability of event b is 0.34

Answers

Answer:

Since A and B are independent:

P(A and B) = P(A) * P(B)

P(A and B) = 0.34 * 0.56 = 0.1904

* Hopefully this helps:)!!

Mark me the brainliest:)!!

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A certain car depreciates about 15% each year.

Write a function to model the depreciation in value for a car valued at $20,000.

Answers

A certain car depreciates about 15% each year that car valued at $20,000 in 2005 will be worth $10,000 in approximately 4.96 years later, which is around the end of 2009.

To model the depreciation in value of a car that depreciates about 15% each year, we can use the formula:

[tex]V(t) = V(0) * (1 - r)^t[/tex]

where V(0) is the initial value of the car, r is the annual depreciation rate, t is the time in years, and V(t) is the value of the car after t years.

Using this formula, we can model the depreciation of a car valued at $20,000 as:

[tex]V(t) = 20000 * (1 - 0.15)^{t}[/tex]

To predict when this car will be worth $10,000, we can set V(t) to 10000 and solve for t:

[tex]10000 = 20000 * (1 - 0.15)^{t}[/tex]

Taking the natural logarithm of both sides, we get:

ln(0.5) = -0.15t * ln(e)

Simplifying this expression, we get:

t = ln(0.5) / (-0.15 * ln(e))

Using a calculator, we find that t is approximately 4.96 years.

Therefore, a car valued at $20,000 in 2005 will be worth $10,000 approximately 4.96 years later, which is around the end of 2009.

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Complete Question

A certain car depreciates about 15% each year. Write a function to model the depreciation in value for a car valued at $20,000. Predict when a car valued at $20,000 in 2005 will be worth $10,000.

Which equation could be used to calculate the sum of the geometric series?

1/3 + 2/9 + 4/27 + 8/81 + 16/243

Answers

[tex]\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{27}+\dfrac{8}{81}+\dfrac{16}{243} = \\ \\\\ = \sum\limits_{k=1}^{5}\dfrac{2^{k-1}}{3^k} = \sum\limits_{k=1}^{5}\dfrac{2^{k}}{2\cdot 3^k} = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\dfrac{2^{k}}{3^k} = \\ \\\\ = \dfrac{1}{2}\cdot \sum\limits_{k=1}^{5}\Big(\dfrac{2}{3}\Big)^k = \dfrac{1}{2}\cdot \left[\Big(\dfrac{2}{3}\Big)^1+\Big(\dfrac{2}{3}\Big)^2+...+\Big(\dfrac{2}{3}\Big)^5\right] =[/tex]

[tex]= \dfrac{1}{2}\cdot \dfrac{\dfrac{2}{3}\cdot\left[\Big(\dfrac{2}{3}\Big)^5-1\right]}{\dfrac{2}{3}-1} =-\Big(\dfrac{2}{3}\Big)^{5}+1 = \dfrac{-2^5+3^5}{3^5} = \boxed{\dfrac{211}{243}}[/tex]

[tex]\text{I used the geometric series formula for sum: }S_n = \dfrac{b_1\cdot (q^n - 1)}{q-1}[/tex]

Answer:

C

Step-by-step explanation:

Megan drove from her house to work at an average speed of 45 miles per hour. The drive took her
20 minutes. If the drive home took her 30 minutes and she used the same route in reverse, what was her average speed going home?

Answers

Answer:

30

Step-by-step explanation:

Since the question says that it took her 45 minutes per hour, you can use that to find the distance of the route she took.  

45 miles: 60 minutes  

15 miles: 20 minutes ----------------cross multiply (20x45 and then divide by 60)  

Therefore, if she is going to use the same route in reverse, the distance would be 15 miles.  

Use the formula for speed:  

speed= distance/time  

= 15/0.5 ---------- 0.5 hours is the same as 30 minutes  

= 30

Answer:

First option: 30 miles per hour

Step-by-step explanation:

For the first scenario, we will convert the minutes into hours first to get all the quantities in same unit

So,

20 minutes = 1/3 hours = 0.33 hours

Now using the speed, distance and time formula

Speed = distance/time

[tex]Speed = \frac{distance}{time}[/tex]

[tex]45 = \frac{distance}{\frac{1}{3} }[/tex]

[tex]45 = 3 * distance[/tex][tex]\frac{45}{3} = Distance[/tex]

So the distance is 15 miles.

For returning through the same route

Time = 30 minutes = 0.5 hour

Distance = 15 miles

So,

[tex]speed = \frac{distance}{time}[/tex]

[tex]Speed = \frac{15}{0.5}[/tex]

Speed = 30 miles per hour

So first option is correct..

The table below shows the probability distribution of the number of credit cards people own. What is the probability (as a percentage) that a person will have at least three credit cards

Answers

Answer:

28%

Step-by-step explanation:

From the table, the probability that the person will have

0 credit cards - 0.16;1 credit card - 0.12;2 credit cards - X;3 credit cards - Y;4 credit cards - 0.72

The sum of all probabilities must equal to 1, so

[tex]0.16+0.12+X+Y+0.72=1\\ \\X+Y=1-0.16-0.12-0.72\\ \\X+Y=0[/tex]

The probability that a person will have at most 3 credit cards is

[tex]Pr(\text{at most 3 credit cards})=Pr(\text{0 credit cards})+Pr(\text{1 credit card})+Pr(\text{2 credit cards})+Pr(\text{ 3 credit cards})=0.16+0.12+X+Y=0.28+0=0.28[/tex]

and as a percentage 28%

Ten people at a party decide to compare ages. Five people are 30 years old, three are 32, one is 31, and one is 65.

Given the ages of the ten people, to the nearest tenth, determine the average of their ages and the standard deviation.

A. The mean age of the ten people at a party is

B. The standard deviation is:

Answers

Answer:

A. The mean age of the ten people at a party is 34.2 years

B. The standard deviation is 10.30 years

Step-by-step explanation:

The average of the ages of the people is defined as:

[tex]{\displaystyle {\overline {x}}} =\frac{\sum^n_i x_i}{n}[/tex]

Where [tex]x_1, x_2\ ,...,\ x_n[/tex] are the ages of the people and n is the number of people

Then

[tex]n=10[/tex]

[tex]{\overline {x}}} =\frac{5*30 + 3*32 + 31 + 65}{10}\\\\{\overline {x}}}=34.2\ years[/tex]

To calculate the standard deviation we calculate the squared differences between the mean and [tex]x_i[/tex]

[tex]5*(34.2 - 30)^2 = 88.2\\\\3*(34.2-32)^2 = 14.52\\\\(34.2-31)^2 = 10.24\\\\(34.2 - 65)^2 = 948.64[/tex]

Now we add the differences and divide them by the total number of people and we get the variance

[tex]\sigma^2=\frac{88.2+14.52+10.54+948.64}{10}=106.19[/tex]

Finally the standard deviation is

[tex]\sigma=\sqrt{\sigma^2}[/tex]

[tex]\sigma= \sqrt{106.19}[/tex]

[tex]\sigma=10.30\ years[/tex]

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