The table shows the results of a survey of male and female students about whether their school should adopt a dress code. What is the probability that a randomly selected male student says that the school should adopt a dress code? Give your answer as a decimal rounded to the nearest thousandths

Using the normal distribution, the percentages are given as follows:

a) 9.18%.

b) 97.72%.

c) 50%.

d) 4.27%.

e) 0.13%.

f) 59.29%.

g) 2.46%.

h) 50%.

i) 50%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the mean and the standard deviation are given as follows:

[tex]\mu = 247, \sigma = 60[/tex]

For item a, the proportion is the p-value of Z when Z = 167, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (167 - 247)/60

Z = -1.33.

Z = -1.33 has a p-value of 0.0918.

Hence the percentage is of 9.18%.

For item b, the proportion is the p-value of Z when Z = 367, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (367 - 247)/60

Z = 2.

Z = 2 has a p-value of 0.9772.

Hence the percentage is of 97.72%.

For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (247 - 247)/60

Z = 0

Z = 0 has a p-value of 0.5.

Hence the percentage is of 50%.

For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (350 - 247)/60

Z = 1.72

Z = 1.72 has a p-value of 0.9573.

1 - 0.9573 = 0.0427.

Hence the percentage is of 4.27%.

For item e, the proportion is the p-value of Z when Z = 67, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (67 - 247)/60

Z = -3.

Z = -3 has a p-value of 0.0013.

Hence the percentage is of 0.13%.

For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:

X = 300:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (300 - 247)/60

Z = 0.88.

Z = 0.88 has a p-value of 0.8106.

X = 200:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (200 - 247)/60

Z = -0.78.

Z = -0.78 has a p-value of 0.2177.

0.8106 - 0.2177 = 0.5929.

Hence the percentage is 59.29%.

For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:

X = 400:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (400 - 247)/60

Z = 2.55.

Z = 2.55 has a p-value of 0.9946.

X = 360:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (360 - 247)/60

Z = 1.88.

Z = 1.88 has a p-value of 0.97.

0.9946 - 0.97 = 0.0246

Hence the percentage is 2.46%.

For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.

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The remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54

Expressions are mathematical statements that are represented by variables, coefficients and operators

The quotient expression is given as

(2x^(3) + 2x^(2) - 9x + 9) -:- (x+3)

Set the divisor of the expression to 0

So, we have

x + 3 = 0

Evaluate the value of x

So, we have

x = -3

Substitute 3 for x in 2x^(3) + 2x^(2) - 9x + 9

So, we have

2(3)^(3) + 2(3)^(2) - 9(3) + 9

Evaluate the expression

So, we have

54

Hence, the remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54

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Answer:

[tex]32000( {1.07}^{x} ) > 75000[/tex]

The required inequality represents the worth of the car more than $75,000 is 32000[1.07]ˣ > 75000.

Given that,
A vintage car costs $32,000 when purchased. The car increases in value by approximately 7% at the end of each year, x, after it is purchased.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
According to the question,
The relationship of the cost of the car after x year,
= 32000[1 + 0.07]ˣ
= 32000[1.07]ˣ
Now, this cost should be more than $75000
So,
32000[1.07]ˣ > $75000

Thus, the required inequality represents the worth of the car more than $75,000 is 32000[1.07]ˣ > 75000.

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After riding their bikes, Larry and Jason will be 3.5 miles apart after 10 minutes of their start.

We have Larry and Jason riding their bikes at the speed of 12 miles/hr and 9 miles/hr respectively in opposite directions.

We have to determine how far apart, in miles, will Larry and Jason be after riding their bikes for 10 minutes.

The distance travelled can be calculated using the formula -

distance = speed x time

According to the question -

Average speed of Larry = 12 miles/hr

The distance covered by Larry in 10 minutes = d [1] = 12 x 10/60 =

2 miles.

Average speed of Jason = 9 miles/hr

The distance covered by Jason in 10 minutes = d [2] = 9 x 10/60 =

1.5 miles.

Distance between Jason and Larry after 10 minutes -

d[1] + d[2] = 2 + 1.5 = 3.5 miles.

Hence, Larry and Jason will be 3.5 miles apart after 10 min of riding in the opposite directions.

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Answer:

The answer is 5

Step-by-step explanation:

From every side

Answer:

Jade would need to walk 16 more dogs to earn $100 total.

Step-by-step explanation:

20 divided by 4 equals 5, so that means Jade is earnings $5 per dog. Just multiply 5 for each dog Jade walks, and you have your answer! If she already walked 4 dogs and made $20, then do 5 times 16 for your answer.

Answer:

Step-by-step explanation:

20

Answer:

93750 is the answer!!!!!

The answer to the given question is Option B.

At no point can we distinguish between diamonds and hearts, as we are only interested in finding red cards. as a result,

The wrong statement is:

For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.  

Therefore, the ultimate answer to the given question is Option B.

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The question is incorrect, The correct question is

Joseph selects a card from a standard deck of 52 cards and then replaces it afterwards. He decides to record the total number of red cards that he selects and calculates the proportion of red cards that he has selected so far after each pick. He then constructs a graph to visualize his results. Which of the following statements is FALSE?

A. The theoretical probability for selecting a red card in each pick is 0.5.

B. For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far.

C. This is an example of the law of large numbers.

D. The relative frequency of selecting a red card changes with the increase in number of selections.

Answer: 33

Step-by-step explanation:

3*33=99

Answer: 33

Step-by-step explanation:

9/3 = 3

90/3 = 30

99/3 = 33

The distance that the light travels on 36 seconds is 6696000 miles.

From the information, it was illustrated that light travels about 186,000 mi/s and the function d(t) = 186,000t gives the distance.

Therefore, the distance in 36 seconds will be:

d(t) = 186,000t

= 186000 × 36

= 6696000 miles.

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According to the solving the perimeter of the tringle  = 12 cm.

Add the lengths of the triangle's sides to find its perimeter. For instance, if a triangle comprises sides a, b, as well as c, the perimeter of the that triangle is P = a + b + c.

2D objects have two dimensions, for example, width and height. A rectangle or even a circle are two-dimensional shapes. Because they have without depth, 2D forms are absolutely flat and can not be physically handled.

Points of the tringles:

A (−3,−1),

B (1,−1),

C (1,2)

we know that the:

Perimeter of the triangle = sum of all the side of the triangle

                                         = AB + BC + CA

So

Length of the AB  :

A (−3,−1),

B (1,−1),

AB =√((x2 – x1)² + (y2 – y1)²).

AB =  √((1 – (-3))² + (-1 – (-1))²).

AB = √((4) + (0))

     = √(16)

     = 4

Length of the BC :

B (1,−1),

C (1,2)

BC =√((x2 – x1)² + (y2 – y1)²).

BC =√((1 – 1)² + (2 – (-1))²).

BC =√(0)² + (3)²).

BC = √(9)

    = 3

Length of the CA:

A (−3,−1),

C (1,2)

CA =√((x2 – x1)² + (y2 – y1)²).

CA =√((1 – (-3))² + (2 – (-1))²).

CA =√((4))² + (3)²).

CA =√(16 + 9)

CA =√(25)

      = 5

The perimeter of the triangle asked  = AB + BC + CA

                                                            = 4 + 3 + 5

                                                            = 12 cm

According to the solving the perimeter of the tringle  = 12 cm.

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Answer:

  m = -4

Step-by-step explanation:

You want the solution to the "two step" equation m -4 = 2m.

A "two-step" linear equation is one that can be solved in two steps. The steps in general are ...

The "inverse" properties of addition and multiplication are used to identify the quantities added or multiplied.

There are two forms a two-step equation might take:

  ax +b = c

  ax +b = cx

You will notice that one side of the equal sign has a sum of two terms: a term with the variable, and a constant term without the variable. The other side of the equation will have one term, which may be either a constant term or a variable term.

The idea of the first step is to make sure the variable term ends up on one side of the equal sign, and the constant term ends up on the other side.

The parts of the first step are ...

For the given equation ...

  m - 4 = 2m

The term by itself is a variable term. The variable term on the other side of the equation is "m". The first step will be to add "-m" to both sides of the equation.

  m -4 -m = 2m -m . . . . . . -m added to both sides

  -4 = m . . . . . . . . . . . . . simplify

Now, we have a variable term (m) on one side of the equal sign, and a constant term (-4) on the other side. This is the desired result of the first step.

The idea of the second step is to make the coefficient of the variable be 1. We do that by multiplying both sides of the equation by the reciprocal (inverse) of the coefficient of the variable.

For the equation ...

  ax = b

we multiply by the reciprocal of 'a', which is 1/a.

  (ax)(1/a) = b(1/a)

  x = b/a . . . . . . . . . . . effectively, we're dividing by 'a'

In the given equation, we have ...

  -4 = m

which already has a coefficient of 1 on the variable m. This means we're done, and no additional step is actually needed.

The solution is m = -4.

__

Additional comment

There is another form of 2-step equation you may see occasionally:

  a(x +b) = c

Solving this can be done by reversing the order of the steps: first divide by the coefficient of x, then subtract the constant.

  x +b = c/a

  x = (c/a) -b

If the variable term inside parentheses has a coefficient other than 1, it may be useful to eliminate parentheses using the distributive property, then solve like a regular 2-step equation.

The m∠POS would be - 65° by the angle addition postulate and substitution postulate.

Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°

Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.

Substitution postulate states that a quantity may be substituted for its equality in any expression.

Then substitute the angle  measurements into the resulting equation to find, m∠POS:

m∠POQ + m∠QOR = m∠POR (by angle addition)

m∠POR + m∠ROS = m∠POS (by substitution)

m∠POS = m∠POQ + m∠QOR + m∠ROS

= 19° + 31° + 15°

= 65°

Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.

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Answer:

2200

Step-by-step explanation:

1/10 of 2000 is 200. add it on top of 2000

The original price of the camera is $220.00 based on the fact that discount of 44% is $96.80

What portion of the original price is the discount?

The discount of $96.80 in dollar terms, represents 44% of the original of the camera, in other words, we can determine the 1%  of the original price of the camera by dividing the discount of $96.80 by 44

1% of the original price of the camera=$96.80/44

1% of the original price of the camera=$2.20

100% of the original price=1% of the original price of the camera*100

100% of the original price=$2.20*100

100% of the original price=$220.00

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Answer:

hahah thats funny

Step-by-step explanation:

Answer:  20 steaks

Step-by-step explanation: 12x0.6= 20

Answer: 334.600

Step-by-step explanation:

I should be that, you have to look at the line

Answer:

The right answer would be 1

Step-by-step explanation:

The description in the table is that for every second, there are 20 wing flaps.

It should be noted that the constant of proportionality is a term that used to show the proportional relationship between different values.

In the table, at 1 second, the number was 20 while at 2 seconds, the number of wing flaps is 40.

Therefore, the constant of proportionality will be:

= 20/1

= 20

Therefore, the description in the table is that for every second, there are 20 wing flaps.

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The value of the expression m • s will be 10 after evaluating it for m = 2 and s = 5.

We are given an expression:

m • s

We need to evaluate the expression for m = 2 and s = 5

So, after substituting the values in the expression, we get that:

m • s

= ( 2 ) • ( 5 )

Multiplying the values, we get that:

= 10

Therefore, the value of the expression m • s will be 10 after evaluating it for m = 2 and s = 5.

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By evaluating the functions we get:

Here we have the two functions:

f(x) = -2x - 5

g(x)= 3x^2 - 3x - 13

And we want to evaluate them in some values of x, first let's do the ones for f(x).

We just replace the variable x by the numbers.

f(3)= -2*3 - 5 = -10 - 5 = -15

f(-2) = -2*(-2) - 5 = 4 - 5 = -1

The ones for the function g(x) are:

g(4) = 3*4^2 -3*4 -13 = 23

g(-5) = 3*(-5)^2 - 3*(-5) - 13 = 77

g(a) = 3*a^2 - 3*a - 13

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Answer: 66.66%

Step-by-step explanation:

1=100%

2/3=

1*2/3=

100%*2/3=

200%/3=66.66%

Answer:

6

Step-by-step explanation:

Answer:

6 pages per day

Step-by-step explanation:

The constant of proportionality is 0.3.

From the information, Damian can make 3 free-throw shots in 10 seconds and 18 free-throw shots in 1 minute.

Therefore, we can choose any of the figures to solve the question since it is constant.

The constant of proportionality will be:

= Number of throes / Time taken

= 3/10

= 0.3

The constant of proportionality is 0.3.

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The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].

As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.

We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".

To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as

[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].

Here, if we consider (x = 0) at 1990, c(x) = 94.

And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].

Thus, we can consider (x₁, y₁) as (0, 94).

Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,

We can consider as (x₂, y₂) as (14, 290).

Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,

[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].

Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is  [tex][c(x) = 14x+94][/tex].

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The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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