Suppose the heights of the members of a population follow a normal
distribution. If the mean height of the population is 72 inches and the
standard deviation is 3 inches, 99.7% of the population will have a height
within which range?
A. 63 inches to 81 inches
B. 66 inches to 78 inches
C. 60 inches to 84 inches
D. 69 inches to 75 inches

Answer:

Ok I can walk you through if you comment the questions ok?

Step-by-step explanation:

Trust me :-)

Answer:

1. obtuse

2.straight

3.right

4. acute

5. <EAF

6. <DAF

7. <BAF

8. They are perpendicular to each other

Answer:

E empty set

Step-by-step explanation:

The answer is empty at

Answer:

the vertex is (-3 , -3)

Step-by-step explanation:

[tex]\frac{1}{2} x^{2}+3x+\frac{3}{2}[/tex]

[tex]=\frac{1}{2} \left( x^{2}+6x+3\right)[/tex]

[tex]=\frac{1}{2} \left[ \left( x+3\right)^{2} -9+3\right][/tex]

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

then the vertex is (-3 , -3)

Step-by-step explanation:

1)

SOLUTION

5(x+5) = 6. (6 +9)

90 = 5x + 25

13 = x

2)

SOLUTION

x (3) = (4) (6)

3x = 24

x= 8

3)

SOLUTION

3 (3 + x + 2) = (x+1)(x + 1 + x – 1) Use Theorem

3x + 15=2x²+2x

0 = 2x² – x – 15

0 = (x – 3) (2x + 5) Solve for x

3 = x Use positivesolution

Answer:

56.31 degrees

Step-by-step explanation:

6 = opposite and 4 = adjacent

Tan = opposite over adjacent

Tan(theta)=6/4

=56.30993247

Answer:

The value of the rational expression when x = -3 is undefined.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Rational Functions

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{x}{x^2 - 9} ,\ x = -3[/tex]

Step 2: Find Value

∴ since we can't divide by 0, our rational expression when x = -3 will have to be undefined.

___

Topic: Algebra II

Answer: Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation: Given :  a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the  sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean  and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

Step-by-step explanation:

since there are answer options we don't need to formally solve the system of equations, we only need to try the first point of every option, and see, where the equations are true.

if we cannot find it for the first point, then we would need to try the same thing for the serving points.

let's put (0, 6) into the first equation :

-2×0² + 6 = 6

6 = 6 true

let's put it into the second equation ;

4×0² + 3×6 = 28

18 = 28 false

that eliminates the first 2 answers.

let's put (-1, 4) into the first equation :

-2×(-1)² + 4 = 6

-2×1 + 4 = 6

-2 + 4 = 6

2 = 6 false

that eliminates the third answer.

let's put (-1, 8) into the first equation :

-2×(-1)² + 8 = 6

-2 + 8 = 6

6 = 6 true

let's put it into the second equation :

4×(-1)² + 3×8 = 28

4 + 24 = 28

28 = 28 true

and because the square function delivers the same result for -1 and +1, it is also true for the second point.

and the 4th answer is therefore correct.

The distance that would be covered after t seconds = 1.5t meters

The speed of the race=distance/time =1.5m/s

The time given = t seconds

The distance (d) = ?

From the formula of speed = distance/time, make distance the subject of formula,

distance (d) = speed×time

= 1.5×t

= 1.5t meters

Therefore, the distance covered is 1.5t meters after t seconds.

Learn more about distance here:

https://brainly.com/question/7243416

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The best approximation of the factor by which the population increases over a ten years period will be 6.19.

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

A certain buffalo population increases by a factor of 1.2 each year.

Then the best approximation of the factor by which the population increases over a ten years period will be

→ 1.2¹⁰

→ 6.1917

→ 6.19

More about the exponent link is given below.

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Answer:

angle A = 112 degrees

Step-by-step explanation:

Angle ADC is bisected (given)  ...so angle 1 = angle 2  

    then angle D = 68 degrees

now you have to remember that adjacent corners (angles on the same LEG) of a trapezoid sum to 180 (they are 'supplementary' )

  angle A = 180 - 68 = 112 degrees

Answer: 160 seconds

Step-by-step explanation:

First let us find the number of seconds per rotation

52 second/65 rotations

52/65

0.8 seconds/1 rotation

0.8 seconds per rotation

Now let us multiply 0.8 by 200 to get our answer

0.8 * 200

160

It takes 160 seconds to do 200 rotations

Answer:

160 seconds

Step-by-step explanation:

We have 65 rotations in 52 seconds, let's represent it like this:

[tex]\frac{52 seconds}{65 rotations}[/tex]

Now, let's multiply this by 200 rotations, and cancel out the rotations on the bottom:

[tex]\frac{52 seconds}{65 rotations} * 200 rotations[/tex]

See how there is rotations on both the top and bottom? This cancels both of them and leaves seconds!

Multiply the above equation and we get:

160 seconds or 2 minutes 40 seconds.

Hope this helps! Good luck and if you have questions please leave them in the comments!

25÷5=5 if five dot is throw in the air the probability of five seeing on the dot will be slim

Answer:

4/11

Step-by-step explanation:

a ratio is a fraction:

a:b or a to b

= a/b

so 12:33

= 12/33, which can be reduced to 4/11 when dividing the numerator and denominator by 3

Answer:

2x + 2y + 3y

Step-by-step explanation:

The others are equations ( containing the = sign).

Answer:

2x+2y+3y

Step-by-step explanation:

an expression is not equated to any number but an equation is equated to any number especially zero

Answer:

y = -4

Step-by-step explanation:

8 = 3y - 12 - 8y

Combine like terms

8 = -5y -12

Add 12 to each side

8+12 - 5y-12+12

20 = -5y

Divide each side by -5

20/-5 = -5y/-5

-4 =y

Step-by-step explanation:

the perimeter is the sum of the 4 individual sides.

if the sides are doubled, so is the sum of them.

therefore, the new perimeter is then

12×2 = 24 cm

Answer:

x=48º

Step-by-step explanation:

[tex]y = 3x-2\\\\~~~=3(-5) -2\\\\~~~= -15-2\\\\~~~= -17[/tex]

Answer:

y = -17

Step-by-step explanation:

Given values :

⇒ x = -5

Let's substitute in the expression to find y :

⇒ y = 3(-5) - 2

⇒ y = -15 - 2

⇒ y = -17

Answer:

[tex]\textsf{i)} \quad \text{T} &=2 \pi r^2 + \dfrac{26}{r}[/tex]

ii)  radius = 1.27 cm (3 sf)

   height = 2.55 cm (3 sf)

Step-by-step explanation:

[tex]\text{Volume of a cylinder}=\pi r^2 h \quad \text{(where r is radius and h is height)}[/tex]

Given volume = 13 cm³, rewrite the equation making h the subject:

[tex]\implies 13=\pi r^2 h[/tex]

[tex]\implies h=\dfrac{13}{\pi r^2}[/tex]

Substitute found expression for h into the Surface Area equation to find the expression for the total surface area, T:

[tex]\begin{aligned}\text{Surface Area of a cylinder} & =2 \pi r^2 + 2 \pi r h\\\implies \text{Surface Area} & =2 \pi r^2 + 2 \pi r \left(\dfrac{13}{\pi r^2}\right)\\& =2 \pi r^2 + \dfrac{26 \pi r}{\pi r^2}\\ \implies \text{T} &=2 \pi r^2 + \dfrac{26}{r}\end{aligned}[/tex]

To find the radius of the minimum surface area, differentiate T with respect to r:

[tex]\begin{aligned}\text{T}& =2 \pi r^2 +26r^{-1}\\\implies \dfrac{dT}{dr} & =(2)2 \pi r^{(2-1)}+(-1)26r^{(-1-1)}\\ & =4 \pi r-26r^{-2}\\ & =4 \pi r-\dfrac{26}{r^2}\\ & = \dfrac{4 \pi r^3-26}{r^2} \end{aligned}[/tex]

Set it to zero, and solve for r:

[tex]\begin{aligned}\dfrac{dT}{dr} & = 0 \\\implies \dfrac{4 \pi r^3-26}{r^2} & = 0 \\\impliles 4 \pi r^3-26 & = 0 \\4 \pi r^3 & = 26 \\r^3 & = \dfrac{13}{2 \pi} \\r & = \sqrt[3]{\dfrac{13}{2 \pi}} \end{aligned}[/tex]

To find the height, substitute the found value of r into the equation for height (found previously):

[tex]\begin{aligned}h & =\dfrac{13}{\pi r^2} \\\implies h & =\dfrac{13}{\pi \left(\sqrt[3]{\dfrac{13}{2 \pi}}\right)^2} \\& =2.548499134\end{aligned}[/tex]

Therefore,

Answer:

The answer is D.

Step-by-step explanation:

f(x) = 5x -3

y = 5x - 3

Switch y and x to find the inverse

x = 5y - 3

Solve for y.

x + 3 = 5y

y = (x+3)/5

g(x) = (x+3)/5

Answer:

(x - 1) x - X^2

Hope this helps :)

We can represent this drawing as follows: 1/5÷3

Fraction is a representation of a division between two real integers. A fraction, can be named as a ratio between two natural terms, integers, rational and/or reals. They consist of a numerator and a denominator.

Looking at the image, we can see that it is divided into 5 parts. In one of these parts, there is one that is divided into three ''group''.

- We know that the numerator indicates the amount that was divided and the denominator indicates the total amount. Therefore, the answer will be:

5 parts in total.                                   =  1  ÷ 3

1 whole part - divided into three           5

So, the correct answer is 1/5 ÷ 3

Answer:

4x² + 4y² + 8xy

Step-by-step explanation:

( 2x + 2y ) ( 2x + 2y ) = ( 2x + 2y )²

Formula : -

( a + b )² = a² + b² + 2ab

Here,

a = 2x

b = 2y

( 2x + 2y )²

= ( 2x )² + ( 2y )² + 2 ( 2x ) ( 2y )

= 2²x² + 2²y² + 8xy

= 4x² + 4y² + 8xy

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

The statement that compares the distribution shapes is (b) East Hills HS is positively skewed, and Southview HS is symmetric.

From the question, we have the following highlights:

Hence, the statement that compares the distribution shapes is (b) East Hills HS is positively skewed, and Southview HS is symmetric.

Read more about skewness at:

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Answer:

Step-by-step explanation:

East hills is negative skewed, Southview is symmetric

Explanation-just took the quiz

Hey there!

EQUATION:

6ac^2

ASSUMING:

= 6(2)(3)^2

SOLVING:

= 6(2)(3^2)

= 12(3^2)

= 12(3 * 3)

= 12(9)

= 108

Therefore, the answer should be: 108

Good luck on assignment & enjoy your day!

~Amphitrite1040:)