if four out of every nine trick-or-treaters that came to your house last Halloween were dressed as Snow White, what proportion of trick-or-treaters were not dressed as Snow White?

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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Answer: 33

Step-by-step explanation:

3*33=99

Answer: 33

Step-by-step explanation:

9/3 = 3

90/3 = 30

99/3 = 33

Answer:

Step-by-step explanation:

20

Answer:

[tex]\textsf{b)} \quad -\dfrac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\textsf{If}\; \cos(\theta)=-\dfrac{3}{4} \implies \sf A=3 \; \textsf{and} \; H=4.[/tex]

Use Pythagoras Theorem to calculate the length of the opposite side:

[tex]\sf \implies O^2+A^2=H^2[/tex]

[tex]\implies \sf O=\sqrt{H^2-A^2}[/tex]

[tex]\implies \textsf{O}=\sqrt{4^2-3^2}[/tex]

[tex]\implies \textsf{O}=\sqrt{7}[/tex]

Therefore, substituting the values of O and H into the sine ratio:

[tex]\implies \sin\theta=\dfrac{\sqrt{7}}{4}[/tex]

As the terminal side of the angle is in Quadrant III, and sine is negative in Quadrants III and IV, the exact value of sin(θ) is:

[tex]\implies \implies \sin\theta=-\dfrac{\sqrt{7}}{4}[/tex]

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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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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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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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: to be honest looks kinda hard

Step-by-step explanation:

I think both are 4

Answer:

f'(5) = 1

Step-by-step explanation:

You are right. The derivative of f(x) = f'(x) = 1 a constant

If you plot y =  f'(x) = 1 it will be a vertical line passing through x = 1 (See graph)

This means f'(x) is constant and equal to 1 for all values of y

So whether it is f'(5) or f'(100) the value = 1

f'(5) = 1

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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Step-by-step explanation:

trapezium means especially

AD || BC

AC = BC tells us that ABC is an isoceles triangle (both legs are identically long, which makes also their angles with their baseline AB equal).

therefore, A1 = B = 80°.

and because the sum of all angles in a triangle is always 180°, we get

180 = 80 + 80 + C1

C1 = 20°

(e)(1)

because of the law of a line intersecting parallel lines with the same angles, and AC is intersecting the parallel lines AD and BC, we know that

C1 = A2 = 20°

(e)(2)

because also the sum of all angles around a single point on one side of a line is 180°, we know D1 + D2 = 180°.

we also know that D2 is an angle in an equilateral triangle (that means all 3 sides are equally long, and therefore all 3 angles are equal too = 180/3 = 60°) and therefore

D2 = 60°.

therefore, D1 = 180 - 60 = 120°.

so, for the triangle ACD we have

180 = A2 + D1 + C2 = 20 + 120 + C2

C2 = 40° = 2×20 = 2×C1

(f)(1)

a kite is a quadrilateral, and as such the sum of all angles is 360°.

again remember the symmetry of a kite, so the angles at H and at F must be equal.

H = F = x

so, we have

360 = 110 + 50 + H + F = 110 + 50 + 2x

200 = 2x

x = 100°

(f)(2)

after drawing EG we see that this line splits the kite into 2 equal (ahem, congruent) triangles due to the symmetry of a kite exactly along that line.

and that splits both angles E and G in half for each of the triangles.

again, the sum of all angles in a triangle is 180°, so

180 = 110/2 + 50/2 + x = 55 + 25 + x = 80 + x

x = 100°

The 20% rate the bank borrowed Oliver the loan for 3 months gives an interest of $125.

The amount Oliver borrowed = $2,500

The interest rate applied to the loan = 20%

Required: To calculate the simple interest using the formula, I = P•R•T

Where;

I = The simple interest

P = The principal borrowed = $2,500

T = The time or loan duration = 3 months = 1/4 year

R = The rate at which the loan is applied = 20% = 0.2

Therefore;

I = $2,500 × 0.2/year × 3/12 year = $125

The correct option for the interest paid on the loan is therefore;

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Answer:

125

Step-by-step explanation:

Answer: Yes because it equals 87/100 which in decimal form is 0.87.

Step-by-step explanation:

Answer:-20 238

Step-by-step explanation:

Answer: The answer is not that

Step-by-step explanation:

The answer would be 1.

Answer:  20 steaks

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

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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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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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:

187.5 miles

Step-by-step explanation:

We can use the rationing method to solve for this problem.

2 inches on map = 75 miles actual distance

1 inch on map = (75 ÷ 2) = 37.5 miles actual distance

5.5 inches on map = (37.5 × 5) = 187.5 miles actual distance

The digit that when multiplied, make a cube and a square out of the number is 88.

It should be noted that this has to do with mental reasoning.

It should be noted that 8 × 8 = 64. This is the square of 8.

Also, it should be noted that 4 × 4 × 4 = 64. This gives the cube value.

Therefore, the number is 88.

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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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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:

6

Step-by-step explanation:

Answer:

6 pages per day

Step-by-step explanation:

Answer: 66.66%

Step-by-step explanation:

1=100%

2/3=

1*2/3=

100%*2/3=

200%/3=66.66%

We get that the cost of the battery is $ 8.24 per battery.

We are given that the cost of 88 batteries = $ 724.72

We need to find the cost of one battery.

We will do this by diving the cost of 88 batteries by 88.

Using division, we get that:

cost of one battery = $ 724.72 ÷ 88

Simplifying the expression, we get that:

cost of one battery = $ 8.24 per battery.

Therefore, we get that the cost of the battery is $ 8.24 per battery.

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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: