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Complete Question

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in.If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 50% of most averages for the breadths of male heads in the sample

Answer:

The range is  from   [tex] \=x_1   = 6.312 [/tex]  to  [tex] \=x_2  = 6.488  [/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\mu = 6.4 \ in[/tex]

   The standard deviation  [tex]\sigma =  0.9 \  in[/tex]

    The sample  size is  n  =  47  

Generally the standard error is mathematically represented as

               [tex]\sigma_{\= x} =  \frac{0.9}{\sqrt{47} }[/tex]

=>             [tex]\sigma_{\= x} =   0.13128 [/tex]

Generally the proportion where the middle 50% of most average for the breaths of male heads in the sample is mathematically evaluated as

 [tex]P(\= x_1 <  \= X  <  \= x_2 ) =  P(\frac{\=x_1 - \mu }{\sigma_{\= x} } < \frac{\= X - \mu }{\sigma_{\= x} }   <  \frac{\=x_2 - \mu }{\sigma_{\= x} } ) =  0.5[/tex]

Generally  [tex]\frac{\= X - \mu }{\sigma_{\= x} }  =  Z(The \  standardized \  value  \  of  \  \= X )[/tex]

So

 [tex]P(\= x_1 <  \= X  <  \= x_2 ) =  P(\frac{\=x_1 - 6.4}{ 0.13128 } <Z  <  \frac{\=x_2 - 6.4 }{0.13128} ) =  0.5[/tex]  

From the z table  the z-score of  0.5 is

  [tex]z-score =   \pm 0.674[/tex]

So

      [tex]\frac{\=x_1 - 6.4}{ 0.13128 } = -0.674[/tex]

       [tex] \=x_1   = 6.312 [/tex]

and

        [tex]\frac{\=x_2 - 6.4}{ 0.13128 } = 0.674[/tex]

          [tex] \=x_2  = 6.488  [/tex]

Answer:

1. if its (5+2^3)/4-2 then its 6.5

2. if its just 5+2^3/4-2 then its 5

Step-by-step explanation:

1. (5+2^3)/4-2

   (5+8)/4-2

   (13)/4-2

    (13)/2

    6.5

2. 5+2^3/4-2

   5+8/4-2

  5+2-2

 7-2

 5

Answer:

the same

Step-by-step explanation:

because the binomial and trinomial is the same

Answer:

false

Step-by-step explanation:-3 in the () means -3 x -3 which is positive 9, where as without () it's -3x3 which is -9. Positive 9 is bigger than -9.

Answer:

False

Step-by-step explanation:

-3^2 = -(3^2) = -(3 × 3) = -9

(-3)^2 = -3 × -3 = 9

-9 < 9

Answer:

x = -1/2

Step-by-step explanation:

50x + 54 = 34x + 46

Subtract 34x from each side

50x-34x + 54 = 34x-34x + 46

16x +54 = 46

Subtract 54 from each side

16x+54-54 = 46-54

16x = -8

Divide by 16

16x/16 = -8/16

x = -1/2

Answer:

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

Step-by-step explanation:

So we are given an equation and we are asked to solve for x.

50x + 54 = 34x + 46

Subtract 54 from both sides.

50x = 34x - 8

Subtract 34x from both sides.

16x = -8

Divide both sides by 16.

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

So now we have solved for x. We have found that [tex]x=-\frac{1}{2}[/tex].

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

58 ≤ x ≤ 126

Step-by-step explanation:

hopefully i understood that

Answer:

If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.  The Zero-Product Property states that for all real numbers a and b, if [tex]ab=0[/tex], then a=0 or b=0.

We can The Zero-Product Property to solve a quadratic equation when we can factor the standard form of the equation. Because when we apply The Zero-Product Property to a factored quadratic equation we can find the x-intercepts of the graph of the related functions. Respectively we can find the solutions to the quadratic equation.

Answer:

No

Step-by-step explanation:

Given that:

Amount earned when a student does comminty service = $5

Number of students in club = 12

Amount earned E, is a function of number of members (n) who does community service.

Hence,

E = n * amount earned per member

Is 24 a possible output?

To test, then E = 24

24 = n * 5

24 = 5n

24/5 = 5n/5

4.8 = 5

Hence, 24 is not a possible output, be use number of membwra cannot be a decimal

Answer:

11.

[tex]1 \times \frac{3}{8} [/tex]

12.

[tex]2 \times \frac{5}{6} [/tex]

Answer:

The function is Speed, f(t) = x/t

Step-by-step explanation:

The given information are;

The distance the man drove = 40 miles

The duration of time the man drove = 2-hours

Given that a function maps each item of the input domain to a single item of the output domain, we can have the following relation for the above parameters;

Speed = (Distance travelled)/(Time taken)

Where, speed f(t), is a function of the time taken, t, to travel a distance x

The function is therefore;

Speed, s = f(t) = x/t

Speed = 40/2 = 20 mile per hour.

Answer:

The function is Speed, f(t) = x/t

Step-by-step explanation:

its late but i hope it helps

Answer:

(x + 10, y + 0)

Step-by-step explanation:

in the graph, all points of the triangle (a, b, and c) are translated 10 units to the right. when things are translated to the right, the x is the number being affected.

Answer:

1 degrees and 60 degrees

Step-by-step explanation:

Answer:

Slope: 5/3, y-intercept (0,-3)

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Absolute value of |-32| = 32

Answer: |-32|

Step-by-step explanation:

Answer:

1km per minute

Step-by-step explanation:

Given the table in the picture :

The average rate of change over the interval from 8 to 15 minutes will be :

Change in distance / change in time

Change in distance between 8 and 15 minutes :

Distance d1 at 8 minutes t1 = 7km

Distance d2 at 15 minutes t2 = 14km

Average rate of change = (d2 - d1) / (t2 - t1)

Average rate of change = (14 - 7)km / (15 - 8)min

Average rate of change = 7km / 7minutes

Average rate of change = 1km per minute

Answer:

The rate of change is 1 kilometer per minute

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Given

17 ≤ - 3x + 2 ≤ 26 ( subtract 2 from each of the 3 intervals )

15 ≤ - 3x ≤ 24

Divide the 3 intervals by - 3, reversing the symbols as a result of dividing by a negative quantity.

- 5 ≥ x ≥ - 8 , that is

- 8 ≤ x ≤ - 5 → D

[tex]17 \leqslant - 3x + 2 \leqslant 26[/tex]

Subtract sides -2

[tex]17 - 2 \leqslant - 3x + 2 - 2 \leqslant 26 - 2 \\ [/tex]

[tex]15 \leqslant - 3x \leqslant 24[/tex]

Divided sides by -3

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

Point :

When the sides of a inequality multiply or divided by an negative number It changes direction and returns them.

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

Thus ;

[tex] \frac{15}{ - 3} \geqslant \frac{ - 3}{ - 3}x \geqslant \frac{24}{ - 3} \\ [/tex]

[tex] - 5 \geqslant x \geqslant - 8[/tex]

[tex] - 8 \leqslant x \leqslant - 5[/tex]

Thus the correct answer is (( D )) .

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Answer:

3x - 12 = -15

x = -1

Step-by-step explanation:

3x - 12 = -15

3x = -3

x = -1

Lmk if this helped if not im sorry

Answer:

47°

Step-by-step explanation:

a staight angle equals 180 degrees

180=6x+29+3x+124

x=3

18+29=boc

boc=47

btw, if u know how to do my question could u plz help

thx

Answer:  angle BOC is 47°

Step-by-step explanation:

Supplementary angles add to 180°

6x + 29 + 3x + 124 = 180

6x + 3x + 29 + 124 = 180

9x + 153 = 180

9x = 180 -153

9x = 27

x = 3

Substitute 3 for x in   ∠BOC = 6x +29

6(3) + 29 = ∠BOC

18 + 29

47° =m∠BOC

Answer:

3x+2x=95

5x=95

X=19

Step-by-step explanation:

it may help you to understand

Answer:

The reason is because there is a constant rate of change. notice how the rise over run stay the same even though they dont fall on the exact point's.

Use rise over run to find the first part of your answer, then use the slope formula to find out the rest. the slope formula is m = rise over run.

Step-by-step explanation:

where m= slope, and rise over run will help you find the slope.

Answer:

second one pretty sure

Step-by-step explanation:

Answer:

nope sorryyyyyy

Step-by-step explanation:

Answer:

152.4 centimeters

Step-by-step explanation:

Answer: y=3x-3

Step-by-step explanation: First plot your point then use the slope to plot another one and get a line. then use slope-intercept formula y=mx+b. M= slope which is 3 and B= the y-intercept.

Answer:

       y=3x-3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1 + (-1) - (-3)

when adding a negative number to a positive number remove the addition sign.

1 - 1 - (-3)

0 - (-3) Make addition sign

0 + 3 = 3

Answer:

2(-2)2=0

Step-by-step explanation:

if you meant to put it a different way tell me and i can do the correct one, just because this one seems weird lol

The value of the function when x = -2 then g(-2) = 4.

A function is defined as a relation between the set of inputs having exactly one output each. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can be represented by mathematical symbol.

WE have been given an function as g(x) = 2x² - 4

Now plug the value x = -2 in the given function;

g(-2) = 2(-2)² - 4

g(-2) = 2 x 4 - 4

g(-2) = 8 - 4

g(-2) = 4

Therefore, the value of the function when x = -2 then g(-2) = 4.

Learn more about function here:

https://brainly.com/question/2253924

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