What is the measure of an exterior angle of a regular hexagon?

Empirical rule is defined for normal distributions. The percentage of the parts the lengths between 3.8 inches and 4.2 inches lie is: Option B: 68%

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]

where we had  

[tex]X \sim N(\mu, \sigma)[/tex]

where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex]

For the given case, as it is given that the lengths of a lawn mower part are approximately normally distributed, let its lengths be tracked by a random variable X

Then, [tex]X \sim N(\mu =4, \sigma = 0.2)[/tex]

The needed percentage is

[tex]P(3.8 < X < 4.2)[/tex]

We can rewrite it as:

[tex]P(4-0.2 < X < 4 + 0.2)[/tex]

This is the percent of values lying under one standard deviation about the mean of X. Using the empirical rule, we get the percentage as:

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%[/tex]

Thus,

[tex]P(4-0.2 < X < 4 + 0.2) = 68\%[/tex]

Thus, The percentage of the parts the lengths between 3.8 inches and 4.2 inches lie is: Option B: 68%

Learn more about empirical rule here:

https://brainly.com/question/13676793

Answer:

[tex]y - 6 = 5[/tex]

equation are màthematical statements containing two algebraic expression on both sides of an "equal to (=)" sign.

Answer:

the answer is C/3

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    v/5-4-(v/4)=0

                 v

Simplify   —

                 4

  v          v

 (— -  4) -  —  = 0

  5          4

STEP 2:

                v

Simplify   —

                 5

Equation at the end of step

2

:

  v          v

 (— -  4) -  —  = 0

  5          4

STEP 3:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        4     4 • 5

   4 =  —  =  —————

        1       5  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

v - (4 • 5)     v - 20

———————————  =  ——————

     5            5  

Equation at the end of step 3:

 (v - 20)    v

 ———————— -  —  = 0

    5        4

STEP 4:

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple

     The left denominator is :       5

     The right denominator is :       4

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

5 1 0 1

2 0 2 2

Product of all

Prime Factors  5 4 20

     Least Common Multiple:

     20

Calculating Multipliers :

4.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 4

  Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      (v-20) • 4

  ——————————————————  =   ——————————

        L.C.M                 20    

  R. Mult. • R. Num.      v • 5

  ——————————————————  =   —————

        L.C.M              20  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions

(v-20) • 4 - (v • 5)     -v - 80

————————————————————  =  ———————

         20                20  

STEP 5:

Pulling out like terms :

5.1     Pull out like factors :

  -v - 80  =   -1 • (v + 80)

Equation at the end of step 5:

 -v - 80

 ———————  = 0

   20  

STEP 6:

When a fraction equals zero :

6.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 -v-80

 ————— • 20 = 0 • 20

  20  

Now, on the left hand side, the  20  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -v-80  = 0

Solving a Single Variable Equation:

6.2      Solve  :    -v-80 = 0

Add  80  to both sides of the equation :

                     -v = 80

Multiply both sides of the equation by (-1) :  v = -80

The product of (x + 3)² demonstrates the closure property of multiplication. [tex]\rm x^{2} + 6x + 9[/tex] is a polynomial. Option D is correct.

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

A set is closed under an operation when we do that operation on the member of the set and we always get a set member.

Given

An expression is (x + 3)²

On simplifying, we have

[tex]\rm (x + 3)(x + 3)\\\\x (x + 3) + 3 (x + 3)\\\\x^{2} +3x +3x +3^2\\\\x^{2} +6x + 9[/tex]

Thus, [tex]\rm x^{2} + 6x + 9[/tex] is a polynomial.

More about the polynomial link is given below.

https://brainly.com/question/17822016

Answer:

Option D

Step-by-step explanation:

180°

sum of angles of triangle = 180°

Answer:

∠A + ∠B + ∠C = 180⁰

Step-by-step explanation:

The sum of the angles in a triangle is 180. This sum is a semicircle or a straight angle. The angle of the semicircle is × 360⁰.

________________

Answer:

I think that the selected answer is correct

Step-by-step explanation:

Answer:

Its step 3 which needs correction.

Step-by-step explanation:

step 3 is deeply a mistake, the step 3 correction is correct that the total sum of interior angles which is 180 degrees is equal to the angle of total straight line angle. Step 2 is correct that when angle m plus angle p sums, they mix up to 180 degrees and its adjacent supplementary angles.

Step-by-step explanation:

hello,

simply knowing the formula will lead you to the answer easily.

formula to find the volume of a prism:

v = bh, where b = base area and h = height.

here, in the picture given, the :

h of the prism = 6m

base area = length * width

b = 8 cm × 7 cm

b = 56 cm²

thus, using v = bh,

v = 56 × 6

v = 336 cm³

please try to understand, and let me know if you have any questions,

have an amazing day! au revoir!

Answer:

false

Step-by-step explanation:

ray is a part of a line

hope it helps

Answer:

904.77

Step-by-step explanation:

(4/3) · π · r3 = (4÷3)×π×(6^3) = 904.778684 = 904.77

Answer:

10%

12.5%

13%

19%

Step-by-step explanation:

First write all of the amounts as a percent.

1/8 = 12.5%

13%

.10 = 10%

19%

Then you can order them from least to greatest.

10%, 12.5%, 13%, and then 19%

hope this helps

Answer:

A.

Step-by-step explanation:

On graph A, all 4 points (G, P, R, and S) are all in the correct order. Options B and D are easy to eliminate because we know that none of the nests are actually at the center.

~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let me know if you have any questions! Spread the love.

Answer:

A.

Step-by-step explanation:

Options A and B are the only number lines with the blue point at the right spot (You can see it is 1/2 mile away so it goes in the middle of 1 and 2). Between these 2 only number line A has the red dot in the right spot (it belongs at -0.25 which is 1 spot left of the center 0).

Answer:30, 75, 60.

Step-by-step explanation:

Answer:

190

Step-by-step explanation:

If the ratio is given 1:200

x : 38000 = 190 times the ratio 1:200

1*190 : 200 * 190

190 : 38000

The answer is 190 security personnels

Hope this helps :)

Have an excellent day!

Answer:

b,d

Step-by-step explanation:

80+3= 83 false

0+3=3 true

70+3= 73 false

60+3=63 true

69+3= 72 false

Hope this helps

[tex]\large\text{Hey there!}[/tex]

[tex]\large\textsf{x + 3}<\large\textsf{70}\\\\\huge\textbf{SUBTRACT 3 to BOTH SIDES}\\\\\large\textsf{x + 3 - 3}<\large\textsf{70 - 3}\\\\\huge\textbf{CANCEL out: 3 -3 because it give you 1}\\\\\huge\textbf{KEEP: 70 - 3 because it help what is}\\\huge\textbf{being compared to the x-value}\\\\\large\text{NEW EQUATION: \textsf{x}} < \large\textsf{70 - 3}\\\\\large\text{SIMPLIFY IT!}\\\\\large\textsf{x}< \large\textsf{67}\\\\\huge\textbf{Thus, your answer is: \boxed{\mathsf{x < 67}}}\huge\checkmark[/tex]

[tex]\large\textbf{It is an (O)(P)(E)(N) circle shaded to the LEFT side of the}\\\large\textbf{number starting at point 67.}[/tex]

[tex]\large\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

3, -6, 12, -24, 48

Step-by-step explanation:

Given:

Therefore,

[tex]a_1=3[/tex]

[tex]a_2=-2 \cdot a_1=-2 \cdot 3=-6[/tex]

[tex]a_3=-2 \cdot a_2=-2 \cdot -6=12[/tex]

[tex]a_4=-2 \cdot a_3=-2 \cdot 12=-24[/tex]

[tex]a_5=-2 \cdot a_4=-2 \cdot -24=48[/tex]

Answer:

the answer is 2

im sure of it

Answer: i think 8

Step-by-step explanation: trebled means three times so 8x3=24 then 24-5=19

Answer:

35,887.1 because 38300×93.7 ➗ 100

Answer:

a = 117°

Step-by-step explanation:

The exterior angle of a triangle = the sum of the remote interior angles.

a + 25° = (a - 47°) + (a - 45°)

a + 25° =  (a + a) + (-47 - 45)

a + 25° = 2a - 92°

-2a        =  -2a        

-a  +25   =    -92

      -25  =     -25    

-a            =  -117°

a = 117°

Example of sphere with a volume

[tex]\pi = 6.15[/tex]

Answer:

c²

Step-by-step explanation:

Finding the factors:

7c³=7×c×c×c

8c²=2×2×2×c×c

Here,

c×c is common in both terms

Hence,GCF=c²

Answer:

3/4

Step-by-step explanation:

common denominator is 28

20/28 and 21/28 so 3/4 is greater

5/7 = 0.71

3/4 = 0.75

¾ is greater.

- Toodles!~

Answer:

Step-by-step explanation:

1/9x5/4

5/36

You multiply across

5*1 = 5

9*4 = 36

5/36

Hope this helps!

Answer:

  a = -2/9

Step-by-step explanation:

Locate two points that cross grid intersections and compute the slope of the line between them. I would choose the vertex (4, 4) and the point (-5, 2) as being points where the graph crosses grid intersections.

The slope of the line between those points is given by the slope formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (2 -4)/(-5 -4) = -2/-9 = 2/9

We note that this representation of the absolute value function appears inverted (reflected across the x-axis). That means the coefficient 'a' will be negative. The slope of an unmodified absolute value function is -1 to the left of the vertex. It will only be 2/9 if the function has been multiplied by -2/9.

  a = -2/9

__

Additional comment

The vertex on the graph is at (4, 4), so the values of (h, k) are (4, 4).

Answer:

[tex]-\frac{2}{9}[/tex]

Step-by-step explanation:

Using the points (-5,2) and (4,4), the slope is given as 2/9. This is an absolute value graph, so from this information the slope is either 2/9 or -2/9. The graph faces downwards, so the slope is negative and therefore [tex]-\frac{2}{9}[/tex].

Answer:

y=2x+3

Step-by-step explanation:

Hi there!

We want to write the equation of the line

We are given that the y-intercept of the line is (0,3) and that the line also goes through the point (2,7)
There are many ways to write the equation of the line, but the most common way is slope-intercept form, which is given as y=mx+b, where m is the slope and b is the y intercept

The value of b is actually the value of y in the point making point of the y intercept
In this case, that point would be 3

So the value of b in this case is 3

Substitute 3 as b into the equation:
y=mx+3

Now we need to find m

As the equation passes through the point (2,7), we can use it to help solve for the value of m

Substitute 2 as x and 7 as y into the equation:

7=2m+3

Subtract 3 from both sides

4=2m

Divide both sides by 2

m=2

Substitute 2 as m into the equation:

y=2x+3

Hope this helps!

Take a look here if you wish to have a similar problem for practice (n.b., the solution uses a different method than the one shown here): https://brainly.com/question/7457022

Answer:

[tex]f(x)=-(x+8)(x-2)[/tex]

Step-by-step explanation:

Start by factoring out a -1...

[tex]f(x)=-(x^2+6x-16)[/tex]

Now, we have to find two integers that multiply to get -16 and have a sum of 6:

(-2)*8=-16

-2+8=8-2=6

Using this, we can split 6x into -2x and 8x...

[tex]f(x)=-(x^2-2x+8x+16)[/tex]

Factor  the first and second half separately...

[tex]f(x)=-[(x^2-2x)+(8x-16)]\\f(x)=-[x(x-2)+8(x-2)]\\[/tex]

Since both x and 8 are being multiplied by x-2, we can combine them to get...

[tex]f(x)=-(x+8)(x-2)[/tex]

Answer:

(3x²-3.5x+1)in²

Step-by-step explanation:

area of a triangle = ½(base × height)

= ½(2x-1)(3x-2)

= ½(6x²-4x-3x+2)

= ½(6x²-7x+2)

= 3x²-3.5x+1

A polynomial that represents the area of the triangle is (3x²-3.5x+1)in²