The average score for games played in the NFL is 21.9 and the standard deviation is 9.1 points. 48 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of x
ˉ
? x
ˉ
−N( b. What is the distribution of ∑x ? ∑x−N( c. P( x
ˉ
>22.4298)= d. Find the 79th percentile for the mean score for this sample size. e. P(22.1298< x
ˉ
<22.6568)= f. Q3 for the x
ˉ
distribution = B. P(∑x<1062.2304)=

Isolating for a variable: rearranging an equation so that a variable is on its own. This is done by performing inverse operations until a variable is isolated.

\(P-9=-3w+9-9\)

\(p-9=-3w\)

\(\frac{p-9}{-3}=\frac{-3w}{-3}\)

\(-\frac{P-9}{3} =w\)

Answer:DE = 4

AB = 30

Step-by-step explanation:

Answer:

30cm²

Step-by-step explanation:

AE/BD = CE/CD

9/6 = CE/8

CE = 9/6 x 8

CE = 12cm

DE = CE - CD

DE = 12 - 8 = 4 cm

½(6 + 9)4 = 30cm²

Answer:

520 are kids and 280 are adults

Step-by-step explanation:

Answer:

\(\huge\mathtt{{\colorbox{silver}{ANSWER~~~↴}}}\)

if 800 people visit zoo

64% were children

so = 65/100 ×800

65×8=520

no of children =280

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Social scientists gather data from samples instead of populations because c. populations are often too large to test.

Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.

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Answer:

D: U= 2.5

Step-by-step explanation:

The value of u in the equation is approximately 2.5

where

(u – 2) = the number of hours sledding down the hill

The value of u can be found as follows:

9(u – 2) + 1.5u = 8.25

9u - 18 + 1.5u = 8.25

combine like terms

9u + 1.5u - 18 = 8.28

add 18 to both sides

10.5u = 8.28 + 18

10.5u = 26.28

divide both sides by 10.5

u = 26.28 / 10.5

u = 2.50285714286

u = 2.5

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The value of g(x) in f(x) formula we get (f ∘ g)(x) = 8x − 120 √x + 640.

The given problem is solved using composite function formula. The composite function is a function of one variable that is formed by the combination of two functions where the output of the inside function becomes the input of the outside function. The formula of composite function is given as (f ∘ g)(x) = f(g(x)).

Using the given functions f(x) = 8x³ + 5 and g(x) = ³√x − 5,

we can find the composite function (f ∘ g)(x) by replacing g(x) in f(x).

Therefore, (f ∘ g)(x) = f(g(x)) = f(³√x − 5).

Now, replace ³√x − 5 in f(x) to get the answer.

(f ∘ g)(x) = f(³√x − 5) = 8(³√x − 5)³ + 5 = 8(³√x)³ − 8 × 3(³√x)² × 5 + 8 × 3(³√x) × 5² − 125 + 5 = 8x − 120 √x + 640.

Therefore, the composite function (f ∘ g)(x) = 8x − 120 √x + 640.

In conclusion, the function of f(x) = 8x³ + 5 and g(x) = ³√x − 5 is used to find the composite function (f ∘ g)(x) using the formula (f ∘ g)(x) = f(g(x)).

Replacing the value of g(x) in f(x) formula we get (f ∘ g)(x) = 8x − 120 √x + 640.

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Answer:

55%

Step-by-step explanation:

1.  You add all the candy together to show that all the candies added together equals 20.

11+6+3=20

2. You divide 11 by 20 to get the decimal

11/20=.55

3.  To get the percentage you just have to multiply .55 by 100.

4.  The final answer should be 55 %

Answer:

50+50

75+25

60+40

90+10

45+55

Step-by-step explanation:

you didn't show the figure..

Answer: i don't see

Step-by-step explanation:

a figure

The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

The speed of the motorboat is given as -3.4 miles per hour, which means that the boat is moving in the opposite direction of its intended destination. If we assume that the boat is moving at a constant speed of -3.4 miles per hour for 0.75 hours, we can use the formula:

distance = speed x time

where distance is the distance traveled, speed is the speed of the boat, and time is the time for which the boat travels at that speed.

Plugging in the given values, we get:

distance = -3.4 miles/hour x 0.75 hour

distance = -2.55 miles

The negative sign indicates that the boat traveled in the opposite direction of its intended destination, and it traveled a distance of 2.55 miles.

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a motorboat travels -3.4 miles per hour for o.75 hours how far did it go?

Answer:

0.3 of the x = y is the square of Uranus

Step-by-step explanation:

Answer:

113°

Step-by-step explanation:

because supplementary angles add up to 180°

thus if a is 67° then we subtract 67° from 180° and b will be 113°

the total price you would pay for the $860 stereo in Philadelphia, including the sales tax, would be $911.60.

What is a tax rate?

A tax rate is the percentage of a price that is charged as a tax. It is the ratio of the tax to the price of an item, expressed as a percentage.

To find the tax and the total price for an $860 stereo in Philadelphia, where the sales tax is 6%, we first find 6% of the price:

6% of $860 = (6/100) * $860 = $51.60

So the tax for the stereo is $51.60.

To find the total price, we add the tax to the price of the stereo:

$860 + $51.60 = $911.60

Hence, the total price you would pay for the $860 stereo in Philadelphia, including the sales tax, would be $911.60.

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Answer:

x = 45

Step-by-step explanation:

x + 135 = 180  {Linear pair}

        x = 180 - 135          {Subtract 135 from both sides}

        x = 45

SOLUTION

The shape is a parallelogram

The consecutive angle of a parallelogram is supplementary that is added up to 180 degree

Hence we have

Therefore the right option is D

Using the divergence theorem we can compute that the outward flux of the vector field is 16π .

The outward flux of F over the solid cylinder and z = 0 is

∫∫F·ds  = ∫∫∫ DivF dv

F = 2xy² i   +  2x²y j + 2xy k

Div F  =  D/dx (2xy²)  +   D/dy (2x²y )

Div F  =  2y²  +  2x²

In cylindrical coordinates   dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ

Using the parametric form of the surface equation

x = rcosθ        y =  r sinθ      and z = z

Div F  = 2r² sin²θ  + 2r²cos²θ

∫∫∫ DivF dv  =  ∫∫ [2r²sin²θ  + 2r²cos²θ] × rdrdθ

∫∫ 2r² [sin²θ  + cos²θ] × rdrdθdz   ⇒  ∫∫ 2r³ drdθ

Integration limits

0 < r < 2          0 < θ < 2π

2∫₀² r³ ∫dθ

(2/4) × (2)⁴ × 2π

The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.

In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.

Therefore the flux is 16π .

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Answer:

4.25+8=17/4+32/4=49/4 or 12.25

Answer:

1. 343^2/3 = 49

2. (2197^1/3)² = 169

3. 729^2/3 = 81

4. (1000²)^1/3 = 100

5. (³√9261)² = 441

6. ³√216² = 36

Hope this helps.

The morbidity rate is 500 cases per 100,000 people.

The morbidity rate is a measure of the number of cases of a particular disease within a specific population. In this scenario, out of 100,000 individuals exposed to the bacterial pathogen, 500 individuals develop the disease. Therefore, the morbidity rate is calculated by dividing the number of cases (500) by the total population (100,000) and multiplying by 100,000 to express it per 100,000 people.

Morbidity rate = (Number of cases / Total population) x 100,000

In this case, the calculation would be:

Morbidity rate = (500 / 100,000) x 100,000 = 500 cases per 100,000 people.

This means that for every 100,000 individuals exposed to the bacterial pathogen, there are 500 cases of the disease. The morbidity rate provides an important measure of the impact and prevalence of a disease within a population, allowing for comparisons and assessments of public health.

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Answer:

I'm notsure what you mean

The logistic model, which is a special type of growth model, is appropriate for analyzing population growth. The logistic model includes environmental and social constraints in its interpretation, which help to make population growth more realistic.

We can model the population growth of deer in a forest using the logistic model as follows:f(0) = 200 f(n) = f(n-1) + [0.02 * f(n-1) * (1 – f(n-1) / 800)]The first value of the sequence is f(0) = 200, representing the initial population of deer in the forest. The second value is f(1) = f(0) + [0.02 * f(0) * (1 – f(0) / 800)] = 200 + [0.02 * 200 * (1 – 200 / 800)] = 202.The third value is f(2) = f(1) + [0.02 * f(1) * (1 – f(1) / 800)] = 202 + [0.02 * 202 * (1 – 202 / 800)] = 204.04. We can continue this process for any value of n, but we can also generalize the sequence:f(n) = f(n-1) + [0.02 * f(n-1) * (1 – f(n-1) / 800)]We can interpret the formula above as follows: the population at time n, f(n), is equal to the population at time n-1, f(n-1), plus the change in population due to birth and death rates.

The rate of change in population is given by [0.02 * f(n-1) * (1 – f(n-1) / 800)]. This formula assumes that the rate of population growth is proportional to the population size and that there is a maximum carrying capacity of 800 deer for the forest.

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Tripling the linear size of an object multiplies its area by a factor of nine.

When the linear size of an object is tripled, the area of the object is multiplied by 9.

This can be understood by considering the relationship between the linear size and the area of an object. If we assume that the object has a regular shape and the linear size refers to the length of its sides, then the area is directly proportional to the square of the linear size.

Let's denote the initial linear size of the object as L and the initial area as A. When the linear size is tripled, it becomes 3L. According to the square proportionality, the new area (A') can be expressed as:

A' = (3L)^2

A' = 9L^2

Comparing A' with the initial area A, we can see that A' is 9 times larger than A. Therefore, tripling the linear size of an object multiplies its area by 9.

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The final polynomial equation after synthetic division is \(x^5-3x^4-81x+243\)

We need to solve;

Put the solution in the appropriate spot on the grid after using synthetic division to divide the following polynomial. Respond with descending powers of x.

The polynomial equation given is;

\(\left(x^4-81\right)\left(x-3\right)\)

By using synthetic division;

⇒ \(x^4x+x^4\left(-3\right)-81x-81\left(-3\right)\)

    \(x^5-3x^4-81x+243\)

→ The required final equation in descending powers of x is \(x^5-3x^4-81x+243\) .

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The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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Answer: b = 1

Step-by-step explanation:

Given

6.8 - 4.2b = 5.6b - 3

Add 4.2b on both sides

6.8 - 4.2b + 4.2b = 5.6b - 3 + 4.2b

6.8 = 9.8b - 3

Add 3 on both sides

6.8 + 3 = 9.8b - 3 + 3

9.8 = 9.8b

Divide 9.8 on both sides

9.8 / 9.8 = 9.8b / 9.8

\(\boxed{b=1}\)

Hope this helps!! :)

Please let me know if you have any questions

The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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Cosine distance is used in the k-means clustering algorithm to remove outliers. It is a metric used to determine the similarity between two documents. In k-means clustering, cosine distance is used to calculate the distance between data points.

Cosine distance is used to normalize the data so that it is not affected by the length of the data vectors or the scale of the data. The cosine distance is calculated as follows:

Cosine distance = 1 - Cosine similarity,

where Cosine similarity = dot product of two vectors/ product of the magnitude of two vectors.

To remove the outliers from the k-means clustering algorithm, we can set a threshold value for the cosine distance. If the cosine distance between two data points is greater than the threshold value, then those data points are considered outliers and they are not included in the cluster. This helps to ensure that the clustering algorithm only groups together data points that are similar and ignores the outliers.

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Step-by-step explanation:

6 - 4s = - 8 - 6s

Bringing like terms on one side

-4s + 6s = - 8 - 6

2s = - 14

S = - 14/2

S = - 7

The required polynomial is,

⇒ sin(x) ≈ \(x - (x^3)/3! + (x^5)/5!\)

To approximate sin(1) to 3 decimal places using the Taylor series expansion,

Find the minimal degree of the Taylor polynomial around x=0.

The Taylor series for sin(x) is given by,

⇒ sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

The error of the nth-degree Taylor polynomial is given by the (n+1)st term multiplied by \((x-c)^{(n+1)}/(n+1)!\),

where c is the center of the series expansion.

To approximate sin(1) to 3 decimal places,

Find the smallest value of n such that the error term is less than 0.0005.

Using the error formula, we can solve for n as follows,

⇒ \(|(1^n)/(n!)|\) ≤0.0005

When n=6, we get,

⇒ \(|(1^6)/(6!)|\) = 0.000025

                   < 0.0005

Therefore, the minimal degree Taylor polynomial required to approximate sin(1) to 3 decimal places is the 6th-degree polynomial,

⇒ sin(x) ≈ \(x - (x^3)/3! + (x^5)/5!\)

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The probability that the alleged father was not the father is: 0.024, or 2.4% and The probability that the alleged father could be the father is: 0.953, or 95.3%.

To calculate the probability that the alleged father was not the father, we first need to calculate the z-score for a pregnancy length of 240 days and for a pregnancy length of 306 days. The z-score formula is:

where x is the pregnancy length, mu is the mean pregnancy length, and sigma is the standard deviation of pregnancy length.

For a pregnancy length of 240 days, the z-score is:

For a pregnancy length of 306 days, the z-score is:

To calculate the probability that the alleged father was not the father, we need to find the area under the normal distribution curve to the left of the z-score for a pregnancy length of 240 days and to the right of the z-score for a pregnancy length of 306 days, and then add these probabilities together. Using a standard normal distribution table or calculator, we find that the probability to the left of z = -3.08 is approximately 0.001, and the probability to the right of z = 2.00 is approximately 0.023. Therefore, the probability that the alleged father was not the father is:

To calculate the probability that the alleged father could be the father, we need to find the area under the normal distribution curve between the z-scores for a pregnancy length of 240 days and a pregnancy length of 306 days. Using a standard normal distribution table or calculator, we find that the probability between z = -3.08 and z = 2.00 is approximately 0.953. Therefore, the probability that the alleged father could be the father is:

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