Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.7 feet and a standard deviation of 0.4 feet. A sample of 74 men’s step lengths is taken. Step 1 of 2 : Find the probability that an individual man’s step length is less than 2.5 feet. Round your answer to 4 decimal places, if necessary.

Answer:

[tex]x-2y=3[/tex]

Step-by-step explanation:

[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]

[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]

Answer:

That is Arithmetic

Step-by-step explanation:

Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity. Which is -5 in this case.

Hope this helps

Answer:

The correct answer is:

(a) 0.54

(b) 0.0385

Step-by-step explanation:

Given:

Restaurant tax,

p = 0.54

Sample size,

n = 168

Now,

(a)

The mean will be:

⇒ μ [tex]\hat{p}= p[/tex]

         [tex]=0.54[/tex]

(b)

The standard error will be:

[tex]\sigma \hat{p}[/tex] = [tex]\sqrt{[\frac{p(1-p)}{n} ]}[/tex]

    = [tex]\sqrt{[\frac{(0.54\times 0.46)}{168} ]}[/tex]

    = [tex]\sqrt{[\frac{(0.2484)}{168} ]}[/tex]

    = [tex]0.0385[/tex]

Answer:

c

Step-by-step explanation:

There are three types of variations.

1. Direct

2. Inverse

3. Joint

There is positive proportionality is two variables are positively related to each other.

The equation for direct proportionality =

y = bx

where y = dependent variable

b = constant

x = independent variable

if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable

the equation that represents inverse proportion :

 where b = constant of proportionality

Joint variation occurs when the dependent variables value is determined by two or more values

For example, the volume of a cylinder is dependent on the value of the radius and height

Answer:

x = 21, y = 40

Step-by-step explanation:

The angle above (7x - 13) is (2x + 4 ) ← alternate angle

(7x - 13) and (2x + 4) are adjacent angles and sum to 180° , then

7x - 13 + 2x + 4 = 180

9x - 9 = 180 ( add 9 to both sides )

9x = 189 ( divide both sides by 9 )

x = 21

Then

2x + 4 = 2(21) + 4 = 42 + 4 = 46

(2x + 4) and (3y + 14) are adjacent angles and sum to 180° , so

46 + 3y + 14 = 180

60 + 3y = 180 ( subtract 60 from both sides )

3y = 120 ( divide both sides by 3 )

y = 40

Answer: 12

Step-by-step explanation: Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

Answer:

Step-by-step explanation:

Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.

A surveyor is estimating the distance across a river. The actual distance is 284.5 m. The surveyor's estimate is 300 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.

(i) Absolute error = 15.5m

(ii) Percent error = 5.5%

Given:

Actual measurement of the distance = 284.5 m

Estimated measurement of the distance by the surveyor = 300 m

(i) The absolute error is the magnitude of the difference between the estimated value measured by the surveyor and the actual value of the distance across the river.

i.e

Absolute error = | estimated value - actual value |

Absolute error = | 300m - 284.5m | = 15.5m

(ii) The percent error (% error) is given by the ratio of the absolute error to the actual value then multiplied by 100%. i.e

% error = [tex]\frac{absoluteError}{actualValue}[/tex] x 100%

% error = [tex]\frac{15.5}{284.5}[/tex] x 100%

% error = 0.05448 x 100%

% error = 5.448%

% error = 5.5%  [to the nearest tenth]

Answer:

Volume = h * w * l (height, width, length)

Volume = 4* 6 * 3

Volume = 72 cube meters

Surface area is finding the are of every 2D plane on the solid.

2(w * h) + 2(l*h) + 2(w * l)

Surface are = 108 square meters

Answer:

Step-by-step explanation:

[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]

The length of B'C' is 0 units.

It is the movement of the shape in left, right, up, and down direction.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The length of AD = 5 units.

Since the rectangle translates down by 4 units,

The length of A'D' =5 units.

The width of the original rectangle is AB, which is 3 units.

Since the rectangle translates to the right by 2 units,

The width of the new rectangle = 3 units.

Now,

The length of B'C' is the same as the length of AD', which is 5 units.

Subtracting 5 units from 5 units gives us a length of 0 units.

Thus,

The length of B'C' is 0 units.

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Answer:

f(5) = 75

Step-by-step explanation:

The function is f(x) = 2x^2 + x(100 - 15x).

Evaluate this function at x = 5:  replace each instance of x with 5:

f(5) = 2(5)^2 + 5(100 - 15·5)

Order of operations rules require evaluating the expression enclosed in parentheses first.  We get:

f(5) = 2(5)^2 + 5(100 - 15·5)

      = 50       + (100 - 75), so that:

f(5) = 50 + 25 = 75

f(5) = 75

Answer:

175?

Step-by-step explanation:

Answer:

thiếu giữ liệu không thể trả lời được

Step-by-step explanation:

Answer:

option : b, c

Step-by-step explanation:

1 meter = 100 centimeters

45 meters = 4500 centimeters

1000 meter = 1 kilometer

 [tex]45 \ meters = \ \frac{45}{1000} = 0.045 \ kilometers[/tex]

1 meter = 1000 millimeters

45 meters = 45, 000 millimeters

Answer:

2x^2 + 4

Step-by-step explanation:

f(g(x)) just means to first solved g(x) and put the solution into f(x).

Therefore, it becomes f(x)=(10x^2+5)/5 + 3, and you can simplify that into

2x^2 + 4.

Answer:

good point I don't know that either

Answer:  [tex]19x+11y \ge 4500[/tex]

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

Explanation:

x = number of adults

y = number of students

The expression 19x represents the money from all the adults while 11y represents the money from all the students (since we get $19 per adult and $11 per student).

In total, the money collected is 19x+11y dollars.

We want this total to be $4500 or larger.

So that's how we get the final answer of [tex]19x+11y \ge 4500[/tex]

Answer:

2cm

Step-by-step explanation:

vbjufdxcvhjjkknvxzdhjkbcxdf

Answer:

The answer to this question is dilating the figure by a scale factor of one half.

Answer:

Adult ticket = 38

Student ticket = 17

Step-by-step explanation:

Let :

Adult ticket = x

Student ticket = y

x + y = 55 - - - - (1)

Cost per x = 3.75

Cost per y = 2

3.75x + 2y = 176.50 - - - (2)

From (1):

x = 55 - y

Put in (2)

3.75(55 - y) + 2y = 176.50

206.25 - 3.75y + 2y = 176.50

-1.75y = - 29.75

y = - 29.75 / - 1.75

y = 17

From :

x = 55 - y

x = 55 - 17

x = 38

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

Work Shown:

S = sum of all interior angles of a polygon

S = 180(n-2)

2700 = 180(n-2)

180(n-2) = 2700

n-2 = 2700/180

n-2 = 15

n = 15+2

n = 17

There are 17 sides to this polygon.

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

Extra info (optional section):

We call this a 17-gon. Simply start with "n-gon" and replace n with 17.

You could also call it a heptadecagon

hepta = 7

deca = 10

so heptadeca means 17. Personally, I prefer 17-gon as the better name since it's easier to remember.

Answer:

20 minutes

Step-by-step explanation:

20 minutes after 3:15 is 3:35, then 5 more minutes is 3:40. Therefore Sten has 20 minutes left until 4pm.

Answer:

(a) The sample variance is 16.51

(a) The sample standard deviation is 4.06

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}[/tex]

Solving (a); The sample variance.

First, calculate the class midpoints.

This is the mean of the intervals.

i.e.

[tex]x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13[/tex]

[tex]x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88[/tex]

[tex]x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63[/tex]

[tex]x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38[/tex]

[tex]x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13[/tex]

So, the table becomes:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}[/tex]

Next, calculate the mean

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}[/tex]

[tex]\bar x = \frac{1845.73}{146}[/tex]

[tex]\bar x = 12.64[/tex]

Next, the sample variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}[/tex]

[tex]\sigma^2 = \frac{2393.6875}{145}[/tex]

[tex]\sigma^2 = 16.51[/tex]

The sample standard deviation is:

[tex]\sigma = \sqrt{\sigma^2}[/tex]

[tex]\sigma = \sqrt{16.51}[/tex]

[tex]\sigma = 4.06[/tex]

Answer:

0.16

Step-by-step explanation:

As it is stated that the card having the label of a dog has a probability of 0.4. Hence, the probability that they both choose a card labeled dog is 0.16.

The probability that a marble chosen at random is shaded or is labeled with a multiple of 3 is 6/11.

We have given that options

Two-elevenths

Three-elevenths

Five-elevenths

Six-elevenths

We have to determine the probability that a marble chosen at random is shaded or is labeled with a multiple of 3.

Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Therefore the probability that a marble chosen at random is shaded or is labeled with a multiple of 3 is 6/11.

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6/11

Step-by-step explanation:

Answer:

Value of 7.34 centimeter into meter is 0.0734

Step-by-step explanation:

Given value;

7.34 centimeter

Find:

Value of 7.34 centimeter into meter

Computation:

We know that

⇒ 1 centimeter = 0.01 meter

So,

⇒ 7.34 centimeter = 7.34 x 0.01

⇒ 7.34 centimeter = 7.34 x 1/100

⇒ 7.34 centimeter = 7.34 / 100

⇒ 7.34 centimeter = 0.0734 meter

Value of 7.34 centimeter into meter is 0.0734

Explanation:

x is the number of years since 1988

x = 0 represents the year 1988

x = 1 is the year 1988+1 = 1989

x = 2 is the year 1988+2 = 1990

etc

x = 32 is the year 1988+32 = 2020

Answer:

4 StartRoot 3 EndRoot units

Hope this answer is right!!

Step-by-step explanation:

Since AD is perpendicular to BC, so ΔABD will be aright-angled triangle. Thus, the length of the altitude is 4√3 units.

The length of the altitude of the equilateral triangle is 4√3  units.

The given parameters;

The half length of the base of the triangle is calculated as follow;

[tex]x = \frac{8 \ units}{2} \\\\x = 4 \ units[/tex]

The height of the triangle is calculated by applying Pythagoras theorem as follows;

[tex]h^2 = L^2 - x^2\\\\h = \sqrt{(8^2) - (4^2)} \\\\h = \sqrt{48} \\\\h = \sqrt{16 \times 3} \\\\h = 4\sqrt{3} \ \ units[/tex]

Thus, the length of the altitude of the equilateral triangle is 4√3  units.

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Given:

The graphs of the function f(x) and g(x).

To find:

The correct statement for the given graph.

Solution:

From the given graph it is clear that, the function f(x) passes through the points (0,4) and (2,0). So,

[tex]f(0)=4[/tex]

[tex]f(2)=0[/tex]

[tex]f(-2)\neq 0[/tex]

The graph of the function g(x) passes through the point (-2,0). So,

[tex]g(-2)=0[/tex]

Since [tex]f(2)=0[/tex] and [tex]g(-2)=0[/tex], therefore the correct option is C.

The graphs of the given functions, f(x), and g(x), bounces off the x-axis.

Correct response:

The true statement regarding the graphed function is the option;

The properties of the graph of f(x) and g(x) are;

When x = 0, the value of f(x) is; f(0) = 4

Therefore;

f(0) = 4

When x = 2, the value of f(x), which is the point on the graph corresponding to a x-value of 2 is; [tex]\underline{f(2) = 0}[/tex]

When x = 0, g(x) value is g(0) = 4

When x = -2, g(x) is; g(-2) = 0

The correct option is therefore;

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Let's focus on f(x) = |x| for now.

Recall that the absolute value of any number is never negative.

Some examples: |-7| = 7 and |5| = 5

So as x gets bigger in the positive direction, so does y. That explains the notation [tex]x \to \infty, \ f(x) \to \infty[/tex]. Informally, we can say "the graph rises to the right".

Similarly, we have [tex]x \to -\infty, \ f(x) \to \infty[/tex] which means it "rises to the left". Both endpoints rise to positive infinity. The left side of the graph goes up forever because again the result of any absolute value function is never negative. So if we plug in say negative a million, then the result is positive a million. In a sense, the V shape absolute value function is almost like a parabola. Both have the exact same end behavior on both sides.

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

Now let's move onto g(x) = 2x^2+4

The only thing that matters when determining the end behavior is the leading term. The leading term here is 2x^2

The even exponent means the endpoints either A) go up together or B) go down together. We go with case A because the leading coefficient is positive. Like I mentioned earlier, this parabola mimics the V shaped absolute value graph in terms of the end behaviors being the same.

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

Lastly, let's focus on h(y) = 3y^4-2

I'm not sure why your teacher is using y when the others were using x. I'll just swap y for x to get h(x) = 3x^4-2

Like the g(x) function, the largest exponent is even, so the left and right end behaviors go in the same direction. The positive leading coefficient means we have the endpoints going upward toward positive infinity.

Answer:

8 miles

Step-by-step explanation:

I'm going to assume the question said that she "couldn't" repair the tire and was forced to walk back home, that makes more sense.

With that in mind:

She rode her bike 2 miles.

She walked 4 miles on the way there, and 6 miles on the way back.

You can deduce that it was a 6 mile walk back because of the 2 mile bike ride, then the 4 mile walk that it took to get there.

All in all that rounds out to 10 mile walking, and 2 mile biking. That is 8 miles more walking than biking.

Answer:

[tex]M = (0,0)[/tex]

Step-by-step explanation:

Given

[tex](4,-5)[/tex] and [tex](-4,5)[/tex]

Required

The midpoint (M)

This is calculated as:

[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]

So, we have:

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

[tex]M = \frac{1}{2}(0,0)[/tex]

[tex]M = (0,0)[/tex]