According to a 2014 poll by the American Academy of Ophthalmology, Americans break down like this when it comes to eye color:

• Brown eyes: 45 %

• Blue eyes: 27 %

• Hazel eyes: 18%

• Green eyes: 9%

• Other: 1%

Consider a random group of 20 American people. Let a random variable X be the number of Americans in this group with green eyes.

(a) Argue that this is a binomial experiment.

(b) Find the probability that

i. None have green eyes

ii. Nine have green eyes

iii. At most three have green eyes

iv. At least four have green eyes

v. If four people out of twenty have green eyes. Is it unusual?

(c) What is the mean and standard deviation of this distribution?

Answer:

3 seconds

Step-by-step explanation:

Complete question:

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t)=144-16t2. How many seconds will it take the object to reach the ground? 2 seconds 3 seconds 9 seconds 16 seconds

Given the height of an object modelled by the expression;

h(t)=144-16t²

The object will reach the ground when h(t) = 0

Substitute into the formula

0 = 144 - 16t²

-144 = -16t²

144 = 16t²

Swap

16t² = 144

t² = 144/16

t² = 9

Square root both sides

√t² = ±√9

t = ±3secs

Since the time cannot be negative, hence the object will reach the ground 3 seconds after

Answer:

24 A-(8+8)

Step-by-step explanation:

Answer: 4(6a-4) This is one equivalent expression of 24a-16.

Complete question :

A chef at a restaurant uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? use the conversion factors 16 oz/1 lb and 28.35 grams/1oz

Answer:

5,424 grams

Step-by-step explanation:

To convert using the conversion factor :

Number of pounds of butter * (16 oz/1) * (28.35) /1

Hence,

12 * 16oz/ 1 * 28.35/1

(12 * 16 * 28)

= 5,424 grams

Answer:

11.72sq.m

Step-by-step explanation:

Area of the shaded region = Area o triangle - Area of the semicircle

Area of triangle = 1/2 * base * height

Area of triangle = 1/2 * 6 * 6

Area of triangle = 3 * 6

Area of triangle = 18sq. m

Area of semicircle = πr²/2

r is the radius =  2m

Area of semicircle = π(2)²/2

Area of semicircle = 2(3.14)

Area of semicircle = 6.28sq. m

Area of the shaded region = 18 - 6.28

Area of the shaded region = 11.72sq.m

Answer:

D. 50

Step-by-step explanation:

50-54 is 30

55-59 is 20

Answer:

$5367.54

Step-by-step explanation:

9000 = P(1 + .03/12)^207*

9000 = P×1.676744643

P = 5367.54

*207 = 12 x 17.25

The 2-point backward difference formula for approximating the derivative of a function at a point x0 is graphically represented by the slope of the line connecting the points (x0 - h, f(x0 - h)) and (x0, f(x0)), where h is a positive value.

The 2-point backward difference formula is a numerical method used to approximate the derivative of a function at a specific point. To understand its graphical interpretation, consider a function f and a point x0 on its graph. The formula involves calculating the slope of a line that connects two points on the graph. The first point is (x0 - h, f(x0 - h)), which corresponds to a slightly shifted x-value from x0, denoted as x0 - h, and its corresponding y-value is f(x0 - h). The second point is (x0, f(x0)), representing the original point on the graph. The value of h is chosen to be positive, indicating that the first point is to the left of the second point. By calculating the slope of the line connecting these two points using the familiar slope formula, rise over run, we obtain an approximation of the derivative of the function at x0 using the 2-point backward difference formula.

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Therefore, there are 23,725 different groups of six members that can be selected from the twenty-three members of the Baltimore Mean Green tennis team.

In this scenario, we are interested in determining the number of different groups of members that can be selected from a total of twenty-three members to form a team of six.

Since the order of selection and specific positions within the team are not considered, we are dealing with combinations rather than permutations.

To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating binomial coefficients is:

Where n represents the total number of items or members (in this case, 23), and k represents the number of items or members to be selected (in this case, 6). The exclamation mark denotes the factorial operation.

Applying the formula, we can calculate the number of combinations as follows:

After performing the calculations, we find that the number of different groups of members that can be selected is:

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Step-by-step explanation:

En la vida diaria estamos rodeados de figuras geométricas como los polígonos y las circunferencias;alguno ejemplos son los siguientes:  las ventanas,las puertas,el reloj de pared,un balón,los vasos de cocina,las llantas de una bicicleta,un automóvil,etc.

Si necesitamos pintar la sala de nuestra casa,debemos saber exactamente la cantidad de pintura que vamos a necesitar ,para eso debemos calcular el área exacta  del  tramo de pared.

Si necesitamos acabar con la maleza de nuestra jardin ,debemos saber exactamente cual es el área de nuestro jardín ,para aplicar el volumen o la proporción exacta del plaguicida.

Conocer el área de un terreno o lote nos da una idea de lo grande que es y del valor que tiene, por eso es importante saber cómo obtener el área.

The estimated proportion of college students who drive stick shift cars is calculated with 90% confidence using sample data.

To estimate the proportion of college students who drive stick shift cars, we can use the sample data of 121 cars, out of which 22 have stick shifts. We will construct a confidence interval to estimate the true proportion. Using a graphing calculator, we can perform a proportion confidence interval calculation.

The calculator will take into account the sample size, the number of successes (cars with stick shifts), and the desired confidence level (90% in this case).

The resulting confidence interval will provide an estimate of the proportion of college students who drive stick shift cars. The answer should be rounded to at least three decimal places for accuracy.

This interval will represent a range within which we can be 90% confident that the true proportion of college students who drive stick shift cars lies.

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Answer:

B.

3^4 = 81

3^2 = 9

81/9 = 9

Step-by-step explanation:

Answer: B. 9

Step-by-step explanation:

3^4-2=3²

3²=9

The statement "a - c|ab + cd if and only if a - cl ad + bc" is false. It does not hold for all values of a, b, c, and d in the set of integers.

The given statement is not true in general. To prove its falseness, we can provide a counterexample. Consider a = 2, b = 3, c = 1, and d = 4. Using these values, we have a - c = 2 - 1 = 1.

However, ab + cd = (2)(3) + (1)(4) = 10, which is not divisible by 1. On the other hand, a - cl ad + bc = 2 - (1)(2)(4) + (1)(3) = -2 + 3 = 1. Here, a - cl ad + bc equals a - c, but ab + cd does not satisfy the divisibility condition. Hence, the given statement is false.

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Answer:

A slope of 2/3

Step-by-step explanation:

if you look at the line, starting at the y axis, then just count up 2 and over three, in other graphed lines, just start at the y axis and try to find where the line crosses a specific point, then calculate the rise/run.

Answer:

Independent events

Step-by-step explanation:

Given

[tex]P(A) = 0.50[/tex]

[tex]P(B)= 0.70[/tex]

[tex]P(A\ u\ B) = 0.85[/tex]

Required

Determine the relationship between the events

To do this, we simply calculate P(A n B) using:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

So, we have:

[tex]P(A\ n\ B) = P(A) * P(B)[/tex]

[tex]P(A\ n\ B) = 0.50 * 0.70[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

and

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

[tex]P(A\ n\ B) = 0.50 + 0.70 - 0.85[/tex]

[tex]P(A\ n\ B) = 0.35[/tex]

Since: [tex]P(A\ n\ B) = P(A) * P(B)[/tex] [tex]= 0.35[/tex]

Then: the events are independent

The line integral is -165/7.

The given line integral is ∫ ds, where is the line segment from (−1,0,2) to (1,−3,8).

The line integral is given by the following formula:

∫ (,,) ds = ∫_^ ((),(),()) ||'()|| d

Here,() = 2 − 1, () = −3, () = 6 + 2and a = 0 and b = 1.

We know that ds = ||'()|| d.

Let us find '() first.'() = 〈2,−3,6〉,

therefore, ||'()|| = √(2² + (−3)² + 6²) = 7

So, ds = 7dt.

We need to find the value of (,,) at each of the parameterizations, so let us find those next.

(,,) = = (−3)(6 + 2) = −18² − 6

Now we can compute the integral:

∫ ds=∫0^1(−18² − 6)7=−162/7 - 3/7= −(165/7)

Therefore, the value of the line integral is -165/7.

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The 99% confidence interval for the population mean based on the given sample is (61.86, 69.94). This means that we are 99% confident that the true population mean falls within this interval.

To find the 99% confidence interval for a sample with a sample size of 68, a sample mean of 65.9, and a standard deviation of 16.5, we can use the formula for calculating the confidence interval for a population mean when the population standard deviation is known.

The formula is given by:

Confidence Interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))

First, we need to find the critical value corresponding to a 99% confidence level. Since the sample size is large (n = 68), we can use the Z-table or a Z-table calculator to find the critical value. For a 99% confidence level, the critical value is approximately 2.576.

Next, we can substitute the given values into the formula to calculate the confidence interval:

Confidence Interval = 65.9 ± 2.576 * (16.5 / sqrt(68))

Using a calculator or mathematical software, we can calculate the standard error of the mean:

Standard Error = standard deviation / sqrt(sample size) = 16.5 / sqrt(68) ≈ 1.997

Substituting the standard error into the formula, we have:

Confidence Interval = 65.9 ± 2.576 * 1.997

Calculating the values inside the interval, we get:

Confidence Interval = (65.9 - 2.576 * 1.997, 65.9 + 2.576 * 1.997)

Simplifying further, we have:

Confidence Interval = (61.86, 69.94)

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Answer:

x = 26

Step-by-step explanation:

Step-by-step explanation:

(a) The cardinality of A is 37.

The set A is defined as {2, 3, 4, 5, ..., 38}, which is a set of consecutive integers. To find the cardinality of A, we count the number of elements in the set. We can do this by subtracting the smallest element from the largest element and then adding 1:

|A| = 38 - 2 + 1 = 37

Therefore, the cardinality of A is 37.

(b) The cardinality of A is 16.

The set A is defined as the set of all complex numbers of the form a + bi, where a and b are integers such that -1 ≤ a ≤ 2 and -2 ≤ b ≤ 1. To find the cardinality of A, we count the number of elements in the set.

The set of possible values for a is {-1, 0, 1, 2}, and the set of possible values for b is {-2, -1, 0, 1}. Therefore, the set A has 4 × 4 = 16 elements.

Alternatively, we can write out all the elements in the set:

A = {-1 - 2i, -1 - i, -1, -1 + i, 0 - 2i, 0 - i, 0, 0 + i, 1 - 2i, 1 - i, 1, 1 + i, 2 - 2i, 2 - i, 2, 2 + i}

Therefore, the cardinality of A is 16.

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Answer:

4.997

Step-by-step explanation:

Answer:

Scott spent $53.25 on lattes last month.

Step-by-step explanation:

To find how much Scott spent in total, multiply the number of lattes bought by the cost of each latte:

15 × 3.55

53.25

The probability that among the students in the sample no more than 7 are female is approximately 0.982 or 98.2%.

To calculate the probability that no more than 7 students in the sample are female, we need to consider the binomial distribution.

The community college student body consists of 40% males, which means 60% are females.

We have a random sample of 8 students.

To get the probability, we can use the binomial probability formula:

P(X ≤ k) = Σ (n choose x) * p^x * (1-p)^(n-x)

Where:

n is the number of trials (sample size)

k is the number of successes (female students)

p is the probability of success (proportion of females in the population)

(n choose x) is the binomial coefficient

In this case:

n = 8 (sample size)

p = 0.6 (proportion of females in the population)

k can take the values 0, 1, 2, 3, 4, 5, 6, or 7

We need to calculate the sum of probabilities for each value of k:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculating each term using the binomial probability formula and summing them will give us the desired probability.

Note: The binomial probability formula assumes independent and identically distributed (i.i.d.) trials and a fixed probability of success.

The community college student body consists of 40% males, which means 60% are females.

We have a random sample of 8 students.

Let's calculate the probability:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

To calculate each term, we use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

n is the number of trials (sample size) = 8

k is the number of successes (female students)

p is the probability of success (proportion of females in the population) = 0.6

Let's calculate each term and sum them up:

P(X = 0) = (8 choose 0) * (0.6^0) * (0.4^8) = 0.1678

P(X = 1) = (8 choose 1) * (0.6^1) * (0.4^7) = 0.3579

P(X = 2) = (8 choose 2) * (0.6^2) * (0.4^6) = 0.3020

P(X = 3) = (8 choose 3) * (0.6^3) * (0.4^5) = 0.1463

P(X = 4) = (8 choose 4) * (0.6^4) * (0.4^4) = 0.0410

P(X = 5) = (8 choose 5) * (0.6^5) * (0.4^3) = 0.0068

P(X = 6) = (8 choose 6) * (0.6^6) * (0.4^2) = 0.0006

P(X = 7) = (8 choose 7) * (0.6^7) * (0.4^1) = 0.00003

Summing up the probabilities:

P(X ≤ 7) = 0.1678 + 0.3579 + 0.3020 + 0.1463 + 0.0410 + 0.0068 + 0.0006 + 0.00003 ≈ 0.982

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Answer:

no it does not show a fucntion

Answer:

97.6 cm³

Step-by-step explanation:

Volume of plastic object :

Volume of cylinder - volume of cone

From. The diagram. :

Radius, r = diameter /2 = 4/2

Volume of cylinder = pi*r²h

V = 22/7 * 2² * 8 = 100.53096 cm³

Volume of cone = 1/3*pi*r²h

V = 1/3 * 22/7 * 2² * 8

V = 2.9321531 cm³

(100.53096 - 2.9321531) cm³

= 97.598 cm³

= 97.6 cm³

Answer:

I think there are about 16-20 ducks with red marks on them.

Answer:

Around 10 ducks have a red mark

Answer: A is 70 B is 45 and C is 50

Step-by-step explanation:

Answer:

6c for the total