HELP!
What is the solution set of |2x + 1| > 5?

A {x|1 < x < –3}

B {x|–1 < x < 3}

C {x|x > 2 or x < –3}

D {x|x < 2 or x > –3}

Answer:

Because it's an odd function, the "tails" go off in different directions.  Also, because it's a negative function, the left starts from the upper left and the right goes down into negative infinity.  If it was a positive, the tails would be going in the other directions, meaning that the left would come up from negative infinity and the right would go up into positive infinity.

Step-by-step explanation:

Answer:

C on Edge: As x--> -∞, y-->+∞ and as x-->+∞, y-->-∞

:) Have a good day / night Everyone and stay safe!

Answer:

ASA

Step-by-step explanation:

Answer: the ASA Postulate

Step-by-step explanation:

In the given picture , we have two triangles ∆LKM and ∆JKM , in which we have

[tex]\angle{LKM}\cong\angle{JKM}\\\\\angle{LMK}\cong\angle{JMK}[/tex]

[tex]\overline{KM}\cong\overline{KM}[/tex] [common]

By using ASA congruence postulate , we have

∆LKM and ∆JKM

ASA  congruence postulate tells that if two angles and the included side of a triangle are congruent to two angles and the included side of other triangle then the triangles are congruent.

Answer:

87 gift bags

Step-by-step explanation:

Answer:

6 pens

2 pencils

1 eraser in each gift bag

Most number of Gift Bags = 27.

Step-by-step explanation:

There will be some bags left over. The limiting factor is the erasers. At most, you can have 27 erasers and therefore 27 gift bags.

171 pens: 171/27 = 6 (you have to round down). The number of pens left over is 9.

(27*6 = 162)    

171 - 162 = 9

63 Pencils: 63/27 = 2 pencils per gift bag. There will be

63 - 2*27

63 - 54

9 pencils will be left over.

Answer:

Step-by-step explanation:

1. The multiplier for the first equation can be found by the ratio ...

  -(second equation x-coefficient)/(first equation x-coefficient)

  = (-2/3)/(1/5) = -10/3

This tells you that multiplying the first equation by -10 and the second equation by 3 will make the x-terms cancel. Matches selection A.

__

2. Adding the two equations shown gives ...

  (-2x -8y) +(2x +y) = (-60) +(-45)

  -7y = -105

  y = -105/-7 = 15 . . . . matches selection C.

__

3. Using the rule shown in question 1, the multiplier for the first equation will be ...

  -(second equation y-coefficient)/(first equation y-coefficient)

  -12/(3/4) = -16

Multiplying the first equation by -16 gives ...

  -16(-5x +3/4y) = -16(12)

  80x -12y = -192 . . . . no matching answer choice

(Sometimes, the problems have errors in their answers. This is one of those times. Choice A will probably be graded as correct, even though it is not.)

Answer:

△ABC ~ △DEF

Step-by-step explanation:

the AA (angle angle) postulate is a postulate that says two triangles can be similar if they have two congruent angles. using this postulate with how each triangle has a 90° angle and ∠F is congruent to ∠C, we can determine that △ABC ~ △DEF.

The correct answer is C. OBC DE because of the definition of similarity in terms of similarity transformations.

A similarity transformation is a transformation that maps a figure onto a similar figure. A similar figure is a figure that has the same shape as the original figure, but may be a different size and orientation.

A rigid transformation is a transformation that maps a figure onto a congruent figure. A congruent figure is a figure that has the same size and shape as the original figure.

Since a series of rigid transformations maps F onto C where F is congruent to C, then the rigid transformations must have preserved the shape and size of F. This means that the rigid transformations must have been similarity transformations.

Therefore, the statement "OBC DE because of the definition of similarity in terms of similarity transformations" is true.

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Answer:

[tex]y-1=3(x-4)[/tex] -----> equation into point slope form

[tex]y=3x-11[/tex]  -----> equation into slope intercept form

[tex]3x-y=11[/tex] -----> equation in standard form

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are the same

step 1

Find the slope of the line passing through ( 7 , 11 ) and ( 10 , 20 )

The slope m is equal to

[tex]m=(20-11)/(10-7)=3[/tex]

step 2

Find the equation of the line with m=3 that passes through (4,1)

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

substitute

[tex]y-1=3(x-4)[/tex] -----> equation into point slope form

Convert to slope intercept form

[tex]y=mx+b[/tex]

isolate the variable y

[tex]y=3x-12+1[/tex]

[tex]y=3x-11[/tex]  -----> equation into slope intercept form

Convert to standard form

[tex]Ax+By=C[/tex]

[tex]3x-y=11[/tex] -----> equation in standard form

The slope of the given line passing through (7, 11) and (10, 20) is 3. Since parallel lines have equal slopes, the line passing through (4, 1) will also have a slope of 3. Plugging in the slope and point into the slope-intercept form, we find the equation of the line to be y = 3x - 11.

To find the equation of the line that passes through the point (4, 1) and is parallel to another line, we first need to determine the slope of the given line that passes through (7, 11) and (10, 20).

The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates between two points on the line, which is often expressed as Δy/Δx or (y2-y1)/(x2-x1).

The slope of the line passing through (7, 11) and (10, 20) is calculated as follows:
Δy = 20 - 11 = 9

Δx = 10 - 7 = 3

Slope (m) = Δy/Δx = 9/3 = 3

Since parallel lines have the same slope, the line passing through (4, 1) will also have a slope of 3.

The equation of a line in slope-intercept form (y = mx + b) can then be used, where 'm' is the slope and 'b' is the y-intercept.

As we have the slope and a point on the line, we can substitute them into the equation to solve for 'b'.

The equation will look like this:
y = mx + b

1 = 3(4) + b

1 = 12 + b

b = 1 - 12

b = -11

The equation of the line that goes through (4, 1) and is parallel to the line through (7, 11) and (10, 20) is therefore y = 3x - 11.

Answer:

GCF -The greatest real number shared between two integers. On the other hand, the Lowest Common Multiple (or LCM) is the integer shared by two numbers that can be divided by both number.

Step-by-step explanation:

The 60% of adults who like pizza was found by dividing the adults who like pizza ( 0.36) by the total adults ( 0.60): 0.36 / 0.6 = 0.6 = 60%

To find the percent of children that like pizza divide 0.29 by 0.40:

0.29 / 0.40 = 0.725 = 72.5%, which is about 70%

The answer would be C. A greater percentage of children (about 70%) prefer pizza.

The percentage of children that prefer pizza are about 70%, which is Option(c) .

A relative figure reflecting hundredth parts of any quantity is called a percentage.

Children who like pizza = 0.29

Total No. of children = 0.40

Percentage of children who like pizza = (0.29 / 0.40) * 100

Percentage = 72.5% (about 70%)

The percentage of children who like pizza are about 70%(Option - c)

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Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

cosC = cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]

sinA = sin60° = cos30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Hence

cosC × sinA = [tex]\frac{\sqrt{3} }{2}[/tex]  × [tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Since,

[tex]\sin \theta=\frac{Opposite leg of }\theta}{\text{Hypotenuse}}[/tex]

[tex]\cos \theta=\frac{Adjacent leg of }\theta}{\text{Hypotenuse}}[/tex]

Given,

In triangle ABC,

AB = 1 unit, AC = 2 unit, and BC = √3 unit

Thus, by the above formule,

[tex]\cos C = \frac{\sqrt{3}}{2}[/tex]

[tex]\sin A=\frac{\sqrt{3}}{2}[/tex]

[tex]\implies \cos C\times \sin A =  \frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}= \frac{3}{4}[/tex]

Just fun I'm going to add something above the below.

You can write an equation for this without the parameter.

You have y=t+5 and x=2t.  If you multiply both sides of y=t+5 by 2 you should get 2y=2t+10 and guess what you can replace 2t with x since you have x=2t.  So you can write 2y=x+10 as your equation to represent the parametric version they have here.

This is a linear equation as our graph appears to be below.   Solve for y by dividing both sides by 2 gives you y=x/2  +5.  The slope is 1/2 and the y-intercept is 5.  If t is between -2 and 3 then x is between -4 and 6 since x is doubled t (inclusive here since we have those equal signs along with those inequalities).

So you could have just graph the line y=x/2+5 on the interval [tex]-4 \le x \le 6 [/tex]/

Anyways, I'm also going to look at this without the rewrite:

I'm going to make a table with 4 columns.  The first column is t.  The second is x(t), the third is y(t), and the fourth will be a list of points (x,y) our relation will go through).

t    |     x(t)        |     y(t)           |   (x,y)

------------------------------------------------------

-2       2(-2)=-4      -2+5=3          (-4,3)

-1        2(-1)=-2       -1+5=4           (-2,4)

0        2(0)=0         0+5=5           (0,5)

1         2(1)=2           1+5=6           (2,6)

2        2(2)=4          2+5=7          (4,7)

3        2(3)=6          3+5=8           (6,8)

Now I'm going to graph the points in the last column on a coordinate-plane.

The horizontal axis is your x-axis and the vertical axis is your y-axis. I did the x-axis going up or down by two's while the y-axis is going up and down only by one's.

Answer:

its answer is -x^3+x^2+3x-1

Step-by-step explanation:

f(x) +g(x)

= 8-4x-x^3+x^2+7x-9

= -x^3+x^2+3x-1

Answer:

The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Step-by-step explanation:

The given functions are

[tex]f(x)=8-4x-x^3[/tex]

[tex]g(x)=x^2+7x-9[/tex]

We have to find the value of f(x)+g(x).

[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]

[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]

On combining like terms we get

[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]

On simplification we get

[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]

Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].

Answer:

  C.  (-2, -8)

Step-by-step explanation:

The function reduces to ...

  f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2

At x=-2, the function would evaluate to ...

  f(-2) = -2 -6 = -8

but cannot, because there is a hole in the function definition at that point.

There is a hole at (-2, -8).

Answer:

[tex]P (X = 140) = 0[/tex]

Step-by-step explanation:

We know that the heron wingspan follow a normal distribution with an mean of 125 cm.

In this case we seek to find

[tex]P (X = 140)[/tex]

If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.

Then by definition of continuous random variable we have to:

[tex]P (X = a) = 0[/tex] where a is a constant.

That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.

Finally we can conclude that

[tex]P (X = 140) = 0[/tex]

To find the proportion of herons with a wingspan of exactly 140cm, calculate the z-score using the given mean and standard deviation. Use the z-score to find the area under the normal curve and determine the proportion. The resulting area is approximately 0.8944 or 89.44%.

To find the proportion of herons with a wingspan of exactly 140cm, we need to calculate the z-score for 140cm using the formula:

z = (x - μ) / σ

where x is the value being analyzed, μ is the mean, and σ is the standard deviation. Plugging in the values:

z = (140 - 125) / 12 = 1.25

To find the proportion, we can use the z-table or calculator to find the area under the normal curve to the left of z = 1.25. The resulting area is approximately 0.8944 or 89.44%.

Answer:

the three options i chose:

A. n and k are on plane A and s

C. p is the inteersection of n and g

D. those 3 lines are noncollinear

Answer:

The correct options are A, C and D.

Step-by-step explanation:

From the given figure it is clear that points N and K lie on the line f, and line f is the intersection line of plane A and S.

So, points N and K are on plane A and S. Option A is correct.

Points P and M lie on the line n, and line n is not the intersection line of plane B and S.

We clearly see that point M is not on the plane S.

So, option B is incorrect.

Point P is the intersection of line n and line g.

So, option C is correct.

Point M and P lie on line n and point P and Q lie on line g.

Three points are collinear if they are lie on a straight line.

Since points M, P and Q are not collinear, therefore they are noncollinear.

So, option D is correct.

Line d intersects plane A at point L.

So, option E is incorrect.

Answer:

The dimensions of enclosed area are 200 and 400/3 feet

Step-by-step explanation:

* Lets explain how to solve the problem

- There are 800 feet of fencing

- We will but it around a rectangular field

- We will divided the field into 2 identical smaller rectangular plots

 by placing a fence parallel to one of the field's shorter sides

- Assume that the long side of the rectangular field is a and the

 shorter side is b

∵ The length of the fence is the perimeter of the field

∵ We will fence 2 longer sides and 3 shorter sides

∴ 2a + 3b = 800

- Lets find b in terms of a

∵ 2a + 3b = 800 ⇒ subtract 2a from both sides

∴ 3b = 800 - 2a ⇒ divide both sides by 3

∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)

- Lets find the area of the field

∵ The area of the rectangle = length × width

∴ A = a × b

∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]

- To find the dimensions of maximum area differentiate the area with

  respect to a and equate it by 0

∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]

∵ [tex]\frac{dA}{da}=0[/tex]

∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides

∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3

∴ 800 = 4a ⇒ divide both sides by 4

∴ 200 = a

- Substitute the value of a in equation (1)

∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]

* The dimensions of enclosed area are 200 and 400/3 feet

Answer:

 =57.89%

Step-by-step explanation:

The total number of golf ball is 4+8+7 = 19

P (red or yellow) = number of red or yellow

                              ------------------------------------

                                total number of golf balls

                           = 4+7

                              -----

                              19

                         =11/19

Changing this to a percent means changing it to a decimal and multiplying by 100%

                        = .578947368 * 100%

                         =57.8947368%

Rounding to two decimal places

                         =57.89%

The probability of drawing a red or yellow golf ball from the box can be calculated by dividing the total number of red and yellow balls (11) by the total number of balls in the box (19), resulting in a probability of 11/19 or approximately 57.89%.

To calculate the probability of drawing a red or yellow golf ball from the box, we first need to figure out the total number of balls in the box. This is found by adding up the number of each color of balls: 4 red balls + 8 green balls + 7 yellow balls = 19 total balls.

Next, we consider the total number of red and yellow balls, which is 4 red + 7 yellow = 11.

To find the probability, we divide the number of desired outcomes (red or yellow balls) by the total number of outcomes (total balls). So, the probability is 11/19.

To express this as a percentage rounded to two decimal places, we can multiply the result by 100, which gives us approximately 57.89%. So, there is a 57.89% chance of drawing a red or yellow ball from the box.

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Answer:

(14.7 , 16.9)

Step-by-step explanation:

it is given that [tex]\bar{x}=15.8[/tex] tons

σ=3.8 tons

n=49

at 95% confidence level α=1-.95=0.05

[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]

=1.96 ( from the standard table)

at 95% confidence level the coefficient interval for μ is

[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]

[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]

[tex]15.8\pm 1.1[/tex]

(14.7, 16.9)

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

f(x) = -3 sin (x-pi) +2

Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value

sin has a maximum of 1

f (min) = -3(1) +2 = -1

g(x) has a minimum at x =3  

g(minimum) = -1

h(x) = (x+7)^2 -1

        The smallest a squared value can be is zero

     = 0 -1

h(min) =-1

Answer:

D. All three functions have the same minimum value

Step-by-step explanation:

Just did this :)

Answer:

  C.  y = Ae^(-(x-b)²/c)

Step-by-step explanation:

A is a model of exponential growth.

B is a model of exponential decay.

D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.

The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.

The model that the graph represent is C that is y = Ae^(-(x-b)²/c).

A is an exponential growth model.

B is an exponential decay model.

D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.

The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.

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Answer:

Step-by-step explanation:

Answer:

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Step-by-step explanation:

[tex]\sin(\theta)+1=\cos(2\theta)[/tex]

Applying double angle identity:

[tex]\cos(2\theta)=1-2\sin^2(\theta)[/tex]

Doing so would give:

[tex]\sin(\theta)+1=1-2\sin^2(\theta)[/tex]

We need to get everything to one side so we have 0 on one side.

Subtract 1 on both sides:

[tex]\sin(\theta)=-2\sin^2(\theta)[/tex]

Add [tex]2\sin^2(theta)[/tex] on both sides:

[tex]\sin(\theta)+2\sin^2(\theta)=0[/tex]

Let's factor the left-hand side.

The two terms on the left-hand side have a common factor of [tex]\sin(\theta)[/tex].

[tex]\sin(\theta)[1+2\sin(\theta)]=0[/tex].

This implies we have:

[tex]\sin(\theta)=0 \text{ or } 1+2\sin(\theta)=0[/tex].

We need to solve both equations.

You are asking they be solved in the interval [tex][0,2\pi)[/tex].

[tex]\sin(\theta)=0[/tex]

This means look at your unit circle and find when you have your y-coordinates is 0.

You this at 0 and [tex]\pi[/tex]. (I didn't include [tex]2\pi[/tex] because you don't have a equal sign at the endpoint of [tex]2\pi[/tex].

Now let's solve [tex]1+2\sin(\theta)=0[/tex]

Subtract 1 on both sides:

[tex]2\sin(\theta)=-1[/tex]

Divide both sides by 2:

[tex]\sin(\theta)=\frac{-1}{2}[/tex]

Now we are going to go and look for when the y-coordinates are -1/2.

This happens at [tex]\frac{7\pi}{6}[/tex] and [tex]\frac{11\pi}{6}[/tex].

The solution set given the restrictions is

[tex]\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}[/tex]

Answer:

  (D)  t^4

Step-by-step explanation:

You have defined ...

  a3 = a2·a1

  a4 = a3·(a2·a1) = a3²

  a5 = a4·(a3·a2·a1) = a4² = (a3²)² = a3⁴

Then if a3 = t, a5 = t⁴

Let's begin by understanding the given sequence and the pattern it follows.
We are given the initial terms:
a1 = 3
a2 = 5
For n > 2, the next term is defined as the product of all preceding terms. Therefore,
a3 = a1 * a2
a4 = a1 * a2 * a3
and so on.
Now, let's generalize this for any term an where n > 2. According to the problem, an = t.
The term immediately after an would be an+1, which equals the product of all preceding terms:
an+1 = a1 * a2 * a3 * ... * an-1 * an
Since an = t, and every term before it has been multiplied to give t (by definition of the sequence), we have:
an+1 = t * t
an+1 = t^2
Now, let's find an+2. This term is the product of all preceding terms, which now includes an+1:
an+2 = a1 * a2 * a3 * ... * an-1 * an * an+1
From above, we know an = t and an+1 = t^2. Hence:
an+2 = t * t^2
an+2 = t^3
Therefore, the value of an+2 in terms of t is t^3. The correct answer is (C) t^3.

This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).

11x11 rectangle = 165cm^2 area.

2 circles of 2cm radius = 2*4pi = 8pi = 25.13

165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)

Answer:

139.9

Step-by-step explanation:

First find the area of the circles.

A = pi*r^2

So pi*2^2

2^2 = 4

4*pi = 12.57

Then divide 12.57 by 2 because its only half a circle.

12.57/2 = 6.285

Then multiply 6.285 by 4 since there are 4 half circles.

6.285*4 = 25.14

Now find the area of the square.

A = lw

A= 15*11

A = 165

Now subtract 165 and 25.14.

165 - 25.14 = 139.86

Now round 139.86 to the nearest tenth

So 139.9

Answer:

Step-by-step explanation:

Income less expenses

Answer:

15

Step-by-step explanation:

i got it right pls mark brainliest

Below is the formula for the circumference of a circle

C = 2πr

This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...

16.4/ 2  = 8.2

Plug what you know into the formula and solve...

π = 3.14

r = 8.2

C = 2(3.14)(8.2)

C = 6.28(8.2)

C = 51.496

In the question it asks to round to the nearest tenth like so...

51.5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

51.496 rounded to the nearest tenth is 51.5

Check the picture below.

Answer:

15

Step-by-step explanation:

70 = 4 x (a + 2.5)

70 = 4a + 10

70-10 = 4a

60 ÷ 4 = a

15= a

Answer:

D. 70 degrees.

Step-by-step explanation:

Because the 2 triangles are similar corresponding angles are congruent.

So m < P = m< X = 66 degrees.

And since there are 180 degrees in a triangle:

m < W = 180 - (m < V + m < X)

= 180 - (44 + 66)

= 70 degrees.

The measure of the angle ∠W is 70°.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that two sides of a triangle measure 7 feet and 19 feet.

Since the triangles VWX and triangle NOP are similar, we can say that the corresponding angles of both triangles is same.

∠W = ∠O

Also -

∠O + ∠N + ∠P = 180

∠O = 180 - 110

∠O = 70°

∠W = ∠O = 70°

Therefore, the measure of the angle ∠W is 70°.

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Answer:

65

Step-by-step explanation:

Jake measured the height of the Great Sphinx of Giza by using a mirror and the Law of Reflection. Doubling the height of the mirror gives us an approximation of the statue's height.

In order to measure the height of the Great Sphinx of Giza, Jake used the concept of the Law of Reflection.

He placed a mirror on the ground and walked backwards until he could see the top of the statue in the mirror.

If his eyes were 5.5 feet above the ground, the mirror's height would be equal to half the height of the statue.

Since Jake's eyes are at a height of 5.5 feet, the distance from the ground to the top of the mirror should also be 5.5 feet.

Therefore, the height of the Great Sphinx of Giza can be calculated by doubling the height of the mirror, which gives us 11 feet.

So, the approximate height of the statue is 11 feet.

Answer:

95% of students are between 14 and 18 years old

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=16[/tex]

The standard deviation is:

[tex]\sigma=1[/tex]

The z-score formula is:

[tex]Z = \frac{x-\mu}{\sigma}[/tex]

For x=14 the Z-score is:

[tex]Z_{14}=\frac{14-16}{1}=-2[/tex]

For x=18 the Z-score is:

[tex]Z_{18}=\frac{18-16}{1}=2[/tex]

Then we look for the percentage of the data that is between [tex]-2 <Z <2[/tex] deviations from the mean.

According to the empirical rule 95% of the data is less than 2 standard deviations of the mean.  This means that 95% of students are between 14 and 18 years old