uppose that the walking step lengths of adult males are normally distributed with a mean of 2.8 feet and a standard deviation of 0.2 feet. A sample of 76 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]n=\frac{58}{31}[/tex]

Step-by-step explanation:

[tex]124n=232\\\frac{124n}{124}=\frac{232}{124}\\n=\frac{232}{124}=\frac{58}{31}[/tex]

The value of n is 18.75. To find the value of n, we need to solve the equation: 124n = 232 five

Let's first convert "232 five" into a numerical value:

"232 five" means 2325 (since five is in the units place).

Now, the equation becomes:

124n = 2325

To solve for n, divide both sides of the equation by 124:

n = 2325 / 124

Now, perform the division:

n = 18.75

So, the value of n is 18.75.

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Answer:

B) 1 unit to the left

Step-by-step explanation:

Answer:

0.85714285714286 x 100 = 85.7143%.

Step-by-step explanation:

Answer:

t=7.27 years

Step-by-step explanation:

Let the money be p and t will be the number of years that will be needed for the money to get double.

ATQ, 2p=p*(1+0.1)^t

2=(1.1)^t

log(2)/log(1.1)=t, t=7.27

Answer:

4 scoops of ice cream

Step-by-step explanation:

Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:

C = 0.50s + 0.35n + 0.25t

3.55 = 0.50s + 0.35(3) + 0.25(2)

3.55 = 0.50s + 1.05 + 0.5

3.55 = 0.50s + 1.55

2 = 0.50s

4 = s

So, the sundae had 4 scoops of ice cream.

Answer:

D) y = 2x + 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

1500(1.055)^7= 2182.02

Answer:

26 cm

Step-by-step explanation:

P = 2a + 2b

a = side

b = base

Answer:

The area=base×height

=10×4

=40cm^2

perimeter=2(length+breadth)

I think to find the height Dc you use the pythagoras theorem of

Dc^2=de^2+ce^2

=√16+9

=5

therefore the perimeter will be

p=2(5+10)

=20cm

I hope this helps and sorry if it's wrong

Answer:

1/4 cup each

Step-by-step explanation:

Take the amount of ice cream and divide by 3

3/4÷ 3

Copy dot flip

3/4 * 1/3

Rewriting

3/3 * 1/4

1/4 cup each

Let W be the random variable representing your winnings from playing the game. Then

[tex]P(W=w)=\begin{cases}\text{prob. of rolling an even number}=\frac12&\text{if }w=\$0.50-\$1=-\$0.50\\\text{prob. of rolling a 1}=\frac16&\text{if }w=\$2-\$1=\$1\\\text{prob. of rolling 3 or 5}=\frac13&\text{if }w=\$1-\$1=\$0\\0&\text{otherwise}\end{cases}[/tex]

In short, you have a 1/6 chance of profiting from the game, and a 5/6 chance of losing money. So the odds of winning are (1/6)/(5/6) = 1/5 or 1 to 5.

The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The mean and the variance are:

[tex]\mu = \frac{nk}{N}[/tex]

[tex]\sigma^2 = \frac{nk(N-k)(N-n)}{N^2(N-1)}[/tex]

We have that:

5 + 7 = 12 rocks, which means that [tex]N = 12[/tex]

9 are chosen, which means that [tex]n = 9[/tex]

7 are granite, which means that [tex]k = 7[/tex]

Question a:

[tex]E(X) = \mu = \frac{9\times7}{12} = 5.25[/tex]

[tex]Var(X) = \sigma^2 = \frac{9\times7(12-7)(12-9)}{12^2(12-1)} = 0.5966[/tex]

Thus:

[tex]E(X) = 5.25, Var(X) = 0.5966[/tex]

Question b:

Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:

[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 4) = h(4,12,9,7) = \frac{C_{7,4}*C_{5,5}}{C_{12,9}} = 0.1591[/tex]

[tex]P(X = 5) = h(5,12,9,7) = \frac{C_{7,5}*C_{5,4}}{C_{12,9}} = 0.4773[/tex]

[tex]P(X = 6) = h(6,12,9,7) = \frac{C_{7,6}*C_{5,3}}{C_{12,9}} = 0.3181[/tex]

Thus

[tex]P(X < 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.1591 + 0.4773 + 0.3181 = 0.9545[/tex]

So P(X < 6) = 0.9545.

Question c:

5 of basaltic and 4 of granite: 0.1591 probability.

7 of granite is P(X = 7), in which

[tex]P(X = 7) = h(7,12,9,7) = \frac{C_{7,7}*C_{5,2}}{C_{12,9}} = 0.0455[/tex]

0.1591 + 0.0455 = 0.2046, thus:

P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.

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Answer:

145

Step-by-step explanation:

Angles in a straight line = 180

So,

Let unkown angle be x,

x+35=180

x=180-35

x=145

Answer:

i have attached pic of the graph

i hope this helps you

Answer:

A

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan12° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{BC}[/tex] = [tex]\frac{AC}{44}[/tex] ( multiply both sides by 44 )

44 × tan12° = AC , then

AC ≈ 9.35 ( to 2 dec. places )

9514 1404 393

Answer:

  (a)  C = 92/n

Step-by-step explanation:

The "inversely proportional" relation is represented by the equation ...

  C = k/n

The value of k can be found from the given values of C and n.

  23 = k/4

  23×4 = k = 92

Then the relationship is ...

  C = 92/n

Answer:

Step-by-step explanation:

(ii) right angle becuase perpendicular

iv) congruent because <b=<a (opp ang in isc.tria. is equal)

since ΔADC ≅ Δ BDC, AB=BD

Answer:

x = 74.74 m

Step-by-step explanation:

you need simple trigonometry to solve it

cosine of an angle is the ratio of the adjacent side to the hypotenuse

cos(42.2) is about 0.74

so X / Hypotenuse = 0.74

we know hypotenuse is 101 m

X / 101 = 0.74

x = 74.74 m

hope this helped!

9514 1404 393

Answer:

  (f·g)(x) = 2x^3 +6x^2 -4x -12

Step-by-step explanation:

The distributive property is used to find the expanded form of the product.

  (f·g)(x) = f(x)·g(x) = (x +3)(2x^2 -4) = x(2x^2 -4) +3(2x^2 -4)

  = 2x^3 -4x +6x^2 -12

  (f·g)(x) = 2x^3 +6x^2 -4x -12

Answer:

-6

Step-by-step explanation:

27-3/2x=36

53-3x=72

3x=-18

x=-6

Answer: No, there isn't equal opportunity

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

Explanation:

Let's define the two events

From the table, we see that

P(B) = 340/500 = 0.68

meaning that there's a 68% chance of picking someone who got the class they wanted (i.e. 68% of the people got the class they wanted)

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

Now let's assume that the person is on the honor roll. This means we only focus on the "honor roll" column. There are 125 people here that got the class they wanted out of 205 honor roll students total.

So,

P(B given A) = 125/205 = 0.609756

which rounds to 0.61

This says that if a person is on the honor roll, then they have roughly a 61% chance of getting the class they want.

The chances have gone down from 68% to 61% roughly.

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

It appears that being on the honor roll does affect your chances of getting into the class you want.

Therefore, all students do not have the same equal opportunity.

We would need to have P(B) and P(A given B) to be the same exact value for true equal opportunity to happen.

All students do not have equal opportunity.

From the table, we have the following parameters:

The above means that:

The probability that a person is on honor roll call is:

p1 = 205/500

p1 = 0.41

The probability that a person got the math class requested

p2 = 340/500

p2 = 0.68

Both probabilities are not equal.

Hence, it is true that all students do not have equal opportunity.

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Answer:

27.756

Step-by-step explanation:

1) Move all the decimal points to the right and do the multiplication

  18 * 1524 = 27756

1.8 to 19 = one move

15.42 to 1542 = two moves

total three decimal point shifts

2) count the number (total) that you moved the decimal points

3) starting from the right move the decimal point that many times to the LEFT in for the answer

27.756

Answer:

Step-by-step explanation:

The steps and their reasons for the equation 8(y - 3) = - 40 are given below.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

8(y - 3) = - 40

            Steps                                               Reason

       8(y - 3) = - 40                                          Given

       8y - 24 = - 40                                Distributive property

8y - 24 + 24 = - 24 + 24                 Addition Property of Equality

               8y = - 16                                      Simplifying

          8y / 8 = - 16/8                       Division property of equality

                  y = - 2                                       Simplifying

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Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.

[tex]A(t) = A(0)e^{-kt}[/tex]

[tex]0.7278A(0) = A(0)e^{-10k}[/tex]

[tex]e^{-10k} = 0.7278[/tex]

[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]

[tex]-10k = \ln{0.7278}[/tex]

[tex]k = -\frac{\ln{0.7278}}{10}[/tex]

[tex]k = 0.03177289938 [/tex]

Then

[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]

[tex]A(5) = 0.8531[/tex]

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Answer:

1

Step-by-step explanation:

First, find the inverse of the original function.

x = 2y + 2

x-2/2

Second, substitute x with 4 and solve.

4-2/2

2/2

1

Best of Luck!

If f(x) = 2x + 2 is invertible, then its inverse is another function f ⁻¹(x) such that

f(f ⁻¹(x)) = 2 f ⁻¹(x) + 2 = x

Solve for f ⁻¹(x) :

2 f ⁻¹(x) + 2 = x

2 f ⁻¹(x) = x - 2

f ⁻¹(x) = (x - 2)/2 = x/2 - 1

Then when x = 4, we have f ⁻¹ (4) = 4/2 - 1 = 2 - 1 = 1.

Answer:

D ) none of these .. i think this help you