Factor 4x^2-22x+30.

The midpoint is the point that divide a segment into two equal halves, while the distance between points is the number of units between both points.

The distance between

The coordinate of midpoint of:

The distance in a coordinate geometry is calculated using: [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex].

The distance between points is calculated as follows:

(1,-4.6) and (3,7)

[tex]d = \sqrt{(1 - 3)^2 + (-4.6 - 7)^2}[/tex]

[tex]d = \sqrt{138.56}[/tex]

[tex]d = 11.77[/tex]

(-6,-5) and (2,0)

[tex]d = \sqrt{(-6 - 2)^2 + (-5 - 0)^2}[/tex]

[tex]d = \sqrt{89}[/tex]

[tex]d = 9.43[/tex]

(-1, 4) and (1-1)

[tex]d = \sqrt{(-1 - 1)^2 + (4 - -1)^2}[/tex]

[tex]d = \sqrt{29}[/tex]

[tex]d = 5.39[/tex]

(0.-8) and (3,2)

[tex]d = \sqrt{(0 - 3)^2 + (-8 -2)^2}[/tex]

[tex]d = \sqrt{109}[/tex]

[tex]d = 10.44[/tex]

The midpoint (M) is calculated using: [tex]M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]

The coordinate of midpoint is calculated as follows:

(5, 8) and (-1,-4)

[tex]M = (\frac{5-1}{2},\frac{8-4}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{4}{2})[/tex]

[tex]M = (2,2)[/tex]

(-5,9) and (-2,7)

[tex]M = (\frac{-5-2}{2},\frac{9+7}{2})[/tex]

[tex]M = (\frac{-7}{2},\frac{16}{2})[/tex]

[tex]M = (-3.5,9)[/tex]

(-3,-7) and (13.-5)

[tex]M = (\frac{-3+13}{2},\frac{-7-5}{2})[/tex]

[tex]M = (\frac{10}{2},\frac{-12}{2})[/tex]

[tex]M = (5,-6)[/tex]

(12,-6) and (-8,5)

[tex]M = (\frac{12-8}{2},\frac{-6+5}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{-1}{2})[/tex]

[tex]M = (2,-0.5)[/tex]

Read more about distance and midpoints in coordinate geometry at:

https://brainly.com/question/3715220

Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To calculate the equation of the line first find the slope

Slope of the line using points

(0 , 0) and (4 , -2) is

[tex]m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]

Now use the formula

y - y1 = m(x - x1) to find the equation of the line using any of the points

Using point (0,0)

That's

[tex]y - 0 = - \frac{ 1}{2} (x - 0)[/tex]

The final answer is

[tex]y = - \frac{1}{2} x[/tex]

Hope this helps you

Answer:

F

Step-by-step explanation:

Answer:

Last one

Step-by-step explanation:

The function f is:

● f (x)= √(4x+6)

The function g is:

● g(x) = √(4x-6)

Add them together:

● f+g (x)= √(4x+6 )+ √(4x-6)

Answer:

[tex]\large \boxed{{\sqrt{4x+6} + \sqrt{4x-6} }}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{4x+6}[/tex]

[tex]g(x)=\sqrt{4x-6}[/tex]

[tex](f+g)(x)[/tex]

[tex]f(x)+g(x)[/tex]

Add both functions.

[tex](\sqrt{4x+6} )+ (\sqrt{4x-6} )[/tex]

Answer:

3[x + 3(4x – 5)] = (39x-15)

Step-by-step explanation:

The given expression is : 3[x + 3(4x – 5)]

We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,

[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]

Again open the brackets,

[tex]3[x+12x-15]=3x+36x-45[/tex]

Now adding numbers having variables together. So,

[tex]3[x + 3(4x - 5)]=39x-15[/tex]

So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

2

Step-by-step explanation:

2,8 to 4,12 has a rise of 4 and a run of 2.

4/2 = 2

The slope is 2.

Remember rise/run!

Answer:

2

Step-by-step explanation:

We take take two points and use the slope formula

m = (y2-y1)/(x2-x1)

m = (12-8)/(4-2)

   = 4/2

   = 2

Answer:

XD,XE,XF

Step-by-step explanation:

XA,XB,XC,XD,XE,XF

IT IS BECAUSE OF THE ALPHABETICAL ORDER AFTER X

Hey there! I'm happy to help!

We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.

5x-4y=6

+

-5x+4y=-10

0= -4

Since we lost our x and y while solving, there cannot be any solution.

Therefore, the answer is no solution.

Have a wonderful day!

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

Answer:

The  price of the stock is [tex]P_o = \$ 33.9[/tex]

Step-by-step explanation:

From the question we are told that

     The dividend is  [tex]k = \$ 1.20[/tex]

     The expected growth rate is  [tex]r = 13\% = 0.13[/tex]

      The required rate of return is  [tex]K_e = 17 \% = 0.17[/tex]

The new dividend after 12 months is mathematically represented as

          [tex]D_1 = k * (1 + r)[/tex]

substituting values

           [tex]D_1 = 1.20 * (1 + 0.13)[/tex]

           [tex]D_1 = \$ 1.356[/tex]

The  price of the stock the price of stock is mathematically represented as

        [tex]P_o = \frac{D_1}{ K_e - r }[/tex]

substituting values

       [tex]P_o = \frac{ 1.356}{ 0.17 - 0.13 }[/tex]

       [tex]P_o = \$ 33.9[/tex]

Answer:

The correct answer is c

Step-by-step explanation:

Answer:

C.) 3/2

Explanation:

PLATO

Answer: a. paired samples;

Step-by-step explanation:

Paired samples are samples in which each data point in one sample is uniquely paired to a data point in the other sample.

Here, we have a paired sample of fecal boluses for gerbils by characterizing then as "No Drug" and "Drug".

hence, the design of this study is paired samples.

So, option A is correct.

NOTE : Independent samples are opposite of paired samples.

Testing the significance of a correlation require to check relation between two variables.

Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

Answer: 0.129

Step-by-step explanation:

Let [tex]\overline{X}[/tex] denotes a random variable that represents the mean weight of babies born.

Population mean : [tex]\mu= \text{3316 grams,}[/tex]

Standard deviation: [tex]\text{324 grams}[/tex]

Sample size = 83

Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :

[tex]P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}<\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{-54}{\dfrac{324}{\sqrt{83}}})\\\\=1-[P(-1.518<Z<1.518)\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-[P(Z<1.518)-P(z<-1.518)]\\\\=1-[P(Z<1.518)-(1-P(z<1.518))]\\\\=1-[2P(Z<1.518)-1]=2-2P(Z<1.518)\\\\=2-2(0.9355)\ [\text{By z-table}]\\\\=0.129[/tex]

hence, the required probability =  0.129

Answer:

The answer and explanation are below

Step-by-step explanation:

i followed the data that was given in the question.

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

a.)  please refer to the attachment for the scatter diagram. Y was plotted against X.

b. The equation is given as:

Y = b₁ + b₀X

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²

b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)

= 1375-1309.5/275-225

= 65.5/50

= 1.31

b₀ = 87.3/5 - 1.31(15/5)

= 87.3/5 - 1.31x3

= 13.53

the regression line is

Y = 13.53 + 1.31X

please refer to the attachment for the diagram for the regression line.

c. we are required to find r.

r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

inserting these values:

r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29

= 65.5/106.69

= 0.6139

Coefficient of determination = r²

r = 0.6139

r² = 0.3769 = 37.69%

Therefore 37.69% variation in y is explained by variation in x and the least square model.

Answer:

vol = 17,148 cu. in.

Step-by-step explanation:

vol = 4 / 3 * pi * r³

vol = 4 / 3 *3.14 * 16³

vol = 17,148 cu. in.

Answer:

The answer is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius of the sphere

π = 3.14

From the question

r = 16 inches

Volume of the sphere is

[tex]V = \frac{4}{3} (3.14) {16}^{3} [/tex]

V = 17148.586

We have the final answer as

V = 17149 cubic inches to the nearest cubic inch

Hope this helps you

Answer:

q =  5000/x  + 6

Step-by-step explanation:

D´= dq/dx  =  - 5000/x²

dq = -( 5000/x²)*dx

Integrating on both sides of the equation we get:

q = -5000*∫ 1/x²) *dx

q = 5000/x + K   in this equation x is the price per unit and q demanded quantity and K integration constant

If when  1006 units are demanded when the rice is 5 then

x = 5     and   q = 1006

1006  =  5000/5 +K

1006 - 1000 = K

K = 6

Then the demand function is:

q =  5000/x  + 6

Answer:

47% and 62%

Step-by-step explanation:

1. Drink

The probability that a student buys a drink is 0.47

Step-by-step explanation:

The probability that a student buys a drink will be given by;

( the number of students who bought a drink)/(the total number of students)

We are told that;

Of the 100 students who came to the movie, 62 bought popcorn and 47 bought a drink. Therefore, the required probability is;

47/100= 0.47

0.47 = 47%

2. Popcorn

For popcorn probability, it's basically the same.

The probabilty that a student buys popcorn is 0.62

The probability that a student buys popcorn will be given by;

( the number of students who bought popcorn)/(the total number of students)

So therefore,

62/100 = 0.62

0.62 = 62%

Answer:

x = -3±sqrt( 5)

Step-by-step explanation:

(x + 3)^2-5=0

Add 5 to each side

(x + 3)^2-5+5=0+5

(x + 3)^2 = 5

Take the square root of each side

sqrt((x + 3)^2 )=±sqrt( 5)

x+3 = ±sqrt( 5)

Subtract 3 from each side

x+3-3 = -3±sqrt( 5)

x = -3±sqrt( 5)

Answer:

108 : 145

Step-by-step explanation:

253 - 108 = 145

Ratio of those who receive 2 weeks of paid vacation is 108

Ratio of those paid vacation is not 2 weeks is 145

108 : 145

Answer:

Approximately 25 flavored bagels.

Step-by-step explanation:

The scatter plot is a graph on cartesian plane where;

y-axis represents the number of plain bagels sold.

x-axis representing the number of flavored bagels sold.

The equation of the straight line on the graph is;

y = 1.731x + 6.697

The graph formed is as attached below.

The slope of the graph means that for every 1 flavored bagel sold, 1.731 plain bagels are sold within one hour.

When y = 50 ;

50 = 1.731x + 6.697

x = [tex]\frac{50 - 6.697}{1.731}[/tex] = 25.01617562 ≈ 25 flavored bagels.

Answer:

25

Step-by-step explanation:

Answer: x=60°

Step-by-step explanation:

The sum of the angles of a triangle is 180°. With this, we can find x°.

33+87+x=180                         [combine like terms]

120+x=180                               [subtact both sides by 120]

x=60°

Answer:

60 degrees

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

We know two angles, 33 degrees and 87 degrees.

Now we have to find the last one.

So we make an equation to solve this.

33 + 87 + x = 180

120 + x = 180

Subtracting 120 fr0m both sides get us,

120 - 120 + x = 180 -120

x = 60

60 degrees

We can check by adding all three angles by substituting 60 for x,

33 + 87 + 60 = 120 + 60 = 180 degrees

Answer:

a

        The population parameter of interest is the true proportion of Greek who are suffering

    While the point estimate of this parameter is  proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%  

b

   The condition  is met

c

   The  95% confidence interval is   [tex]0.223 < p < 0.277[/tex]

d

      If the confidence level is increased which will in turn reduce the level of significance but increase the critical value([tex]Z_{\frac{\alpha }{2} }[/tex]) and this will increase the margin of error( deduced from  the formula for margin of error i.e  [tex]E \ \alpha \ Z_{\frac{\alpha }{2} }[/tex] ) which will make the confidence interval wider

e

  Looking at the formula for margin of error if the we see that if the  sample size is increased the margin of error will reduce making the  confidence level narrower

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  1000

     The  population proportion is  [tex]\r p = 0.25[/tex]

Considering question a

   The population parameter of interest is the true proportion of Greek who are suffering

    While the point estimate of this parameter is  proportion of those that would rate their lives poorly enough to be considered "suffering". which is 25%  

Considering question b

The condition for constructing a confidence interval is

        [tex]n * \r p > 5\ and \ n(1 - \r p ) >5[/tex]

So  

        [tex]1000 * 0.25 > 5 \ and \ 1000 * (1-0.25 ) > 5[/tex]

         [tex]250 > 5 \ and \ 750> 5[/tex]

Hence the condition  is met

Considering question c

    Given that the confidence level is  95%  then  the level of significance is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]    

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is  

              [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]        

Generally the margin of error is mathematically represented as

         [tex]E = Z_\frac{ \alpha }{2} * \sqrt{ \frac{\r p (1 - \r p ) }{n} }[/tex]

substituting values

         [tex]E = 1.96 * \sqrt{ \frac{ 0.25 (1 - 0.25 ) }{ 1000} }[/tex]

         [tex]E = 0.027[/tex]

The  95% confidence interval is mathematically represented as

            [tex]\r p - E < p < \r p + E[/tex]

substituting values  

           [tex]0.25 - 0.027 < p < 0.25 + 0.027[/tex]

substituting values

           [tex]0.223 < p < 0.277[/tex]

considering d

  If the confidence level is increased which will in turn reduce the level of significance but increase the critical value([tex]Z_{\frac{\alpha }{2} }[/tex]) and this will increase the margin of error( deduced from  the formula for margin of error i.e  [tex]E \ \alpha \ Z_{\frac{\alpha }{2} }[/tex] ) which will make the confidence interval wider

considering e

     Looking at the formula for margin of error if the we see that if the  sample size is increased the margin of error will reduce making the  confidence level narrower

Answer:

seven hundred sixty-eight thousand six hundred seventy-six

hope this answer correct :)

The number two is a function

First rule of function: for each element of A there is one and only one element of B

For example, in the first one -5 is "collegated" to -2 and 3. So this isn't a function.

Naturally,  every element of B can have more element of A

Answer:

a) 20, 21, 28 : acute

b) 3, 6, 4 : obtuse

c) 8, 12, 15 : obtuse

Step-by-step explanation:

You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:

If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.

If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.

If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.

Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):

a) 20, 21, 28

Insert numbers, using 28 as c:

[tex]20^2+21^2[/tex]_[tex]28^2[/tex]

Simplify exponents ([tex]x^2=x*x[/tex]):

[tex]400+441[/tex]_[tex]784[/tex]

Simplify addition:

[tex]841[/tex]_[tex]784[/tex]

Identify relationship:

[tex]841>784[/tex]

The sum of the squares of a and b is greater than the square of c. This triangle is acute.

b) 3, 6, 4

Insert numbers, using 6 as c:

[tex]3^2+4^2[/tex]_[tex]6^2[/tex]

Simplify exponents:

[tex]9+16[/tex]_[tex]36[/tex]

Simplify addition:

[tex]25[/tex]_[tex]36[/tex]

Identify relationship:

[tex]25<36[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

c) 8, 12, 15

Insert numbers, using 15 as c:

[tex]8^2+12^2[/tex]_[tex]15^2[/tex]

Simplify exponents:

[tex]64+144[/tex]_[tex]225[/tex]

Simplify addition:

[tex]208[/tex]_[tex]225[/tex]

Identify relationship:

[tex]208<225[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

:Done.

The correct values are,

a) 20, 21, 28  = Acute

b) 3, 6, 4  = Obtuse

c) 8, 12, 15 = Obtuse

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides are,

a) 20, 21, 28

b) 3, 6, 4

c) 8, 12, 15

Now,

We know that;

If three sides of a triangle are a, b and c.

Then, We get;

If a² + b² = c², then the triangle is right triangle.

If a² + b² > c², then the triangle is acute triangle.

If a² + b² < c², then the triangle is obtuse triangle.

Here, For option a;

⇒ 20, 21, 28

Clearly, a² + b² = 20² + 21²

                       = 400 + 441

                       = 841

And, c² = 28² = 784

Thus, a² + b² > c²

Hence, It shows the acute angle.

For option b;

⇒ 3, 6, 4

Clearly, a² + b² = 3² + 4²

                       = 9 + 16

                       = 25

And, c² = 6² = 36

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

For option c;

⇒ 8, 12, 15

Clearly, a² + b² = 8² + 12²

                       = 64 + 144

                       = 208

And, c² = 15² = 225

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

Learn more about the triangle visit:

https://brainly.com/question/17335144

#SPJ5

Answer:

Step-by-step explanation:

It is possible that after an elastic collision a moving mass (1) strikes a stationary mass (2) and the two objects will have exactly the same final speed.

During an elastic collision, the momentum and kinetic energy are both conserved. Since one of the object is a stationary object, its velocity will be zero hence the other moving object will collide with the stationary object and cause both of them to move with a common velocity. The expression for their common velocity can be derived using the law of conservation of energy.

Law of conservation of energy states that the sum of momentum of bodies before collision is equal to the sum of momentum of the bodies after  collision.

Since momentum = mass*velocity

Before collision

Momentum of body of mass m1 and velocity u1  = m1u1

Momentum of body of mass m2 and velocity u2  = m2u2

Since the second body is stationary, u2 = 0m/s

Momentum of body of mass m2 and velocity u2  = m1(0) = 0kgm/s

Sum of their momentum before collision = m1u1+0 = m1u1 ... 1

After collision

Momentum of body of mass m1 and velocity vf  = m1vf

Momentum of body of mass m2 and velocity vf  = m2vf

vf is their common velocity.

Sum of their momentum before collision = m1vf+m2vf ... 2

Equating 1 and 2 according to the law;

m1u1 = m1vf+m2vf

m1u1 = (m1+m2)vf

vf = m1u1/m1+m2

vf s their common velocity after collision. This shows that there is possibility that they have the same velocity after collision.

Answer:n-6=168

Step-by-step explanation:

The statement starts with the variable first.

Answer:

n - 6 = 168.

Step-by-step explanation:

Let's say that the value of the number is n.

n minus 6 is 168, so n - 6 = 168.

n - 6 = 168

n = 174.

Hope this helps!

Hello, please consider the following.

We know the following, right ?

[tex](\forall a, b \in \mathbb{R}) \left( sin(a+b)=sin(a)sin(b)+cos(a)cos(b) \right)[/tex]

So, here, it gives.

[tex]Asin(\omega t+\phi)=Asin(\phi){\sf \bf sin(\omega t)}+Acos(\phi){\sf \bf cos(\omega t)}\\\\=c_2{\sf \bf sin(\omega t)}+c_1{\sf \bf cos(\omega t)}\\\\\text{ *** where }c_2=Asin(\phi) \text{ and } c_1=Acos(\phi) \text{ ***}[/tex]

Do not hesitate if you need further explanation.

Answer:

Mean age: 48

Standard deviation: 4

Step-by-step explanation:

a) Mean

The formula for Mean = Sum of terms/ Number of terms

Number of terms

= 42 + 54 + 50 + 54 + 50 + 42 + 46 + 46 + 48+ 48/ 10

= 480/10

= 48

The mean age is 48

b) Standard deviation

The formula for Standard deviation =

√(x - Mean)²/n

Where n = number of terms

Standard deviation =

√[(42 - 48)² + (54 - 48)² + (50 - 48)² +(54 - 48)² + (50 - 48)² +(42 - 48)² + (46 - 48)² + (46 - 48)² + (48 - 48)² + (48 - 48)² / 10]

= √-6² + 6² + 2² + 6² + 2² + -6² + -2² + -2² + 0² + 0²/10

=√36 + 36 + 4 + 36 + 4 + 36 + 4 + 4 + 0 + 0/ 10

=√160/10

= √16

= 4

The standard deviation of the ages is 4