What is the quotient of (x3 + 8) ÷ (x + 2)? x2 + 2x + 4 x2 – 2x + 4 x2 + 4 x2 – 4

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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Answer:

The positive difference in the 'y' coordinates of where they agreed to meet and where they should actually meet is 4

Step-by-step explanation:

The segement they form is, using the distance formula,

\(d=\sqrt{((x1-x2)^2+(y1-y2)^2)}\)

but since we only need to find the y coordinates,

we do not need it in this case

now ,

in our case, x1 = 5, y1 = -11

x2=-7, y2=13

so,

y1-y2 is the total y difference for the first points,

so d1=-11-13

d1 = -24

but since distance is positive,so,

d1 = 24

and the midpoint of that would be m= d/2,

m1 = 12

if Barbara is at (-5,5), then the distance will be,

since then, x2=-5,y2=5,

d2 = -11-5

d2=-16

or,

d2 = 16

and

m2 = 16/2

m2 = 8

so the positive difference in the 'y' coordinates of where they agreed to meet and where they should actually meet is,

diff = 12-8

diff = 4

so the difference in y coordinates is 4

Answer:

Y-intercept: 3

Step-by-step explanation:

The equation is y = mx + b

m is the slope

b is the y-intercept

In this case, the y-intercept is 3

The ratio of the number of female attendants to the number of male attendants is 21/17

let

900 = 1200x + 800y / (x + y)

900x + 900y = 1200x + 800y

900x + 1200x = 800y + 900y

2100x = 1700y

x : y = 2100 / 1700

x : y = 21 ; 17

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Answer:

6a=42

Step-by-step explanation:

This equation would be used to find a because we don't know how many assists are for each match. And multiplying the a by the 6 games would be equivalent to 42 assists for the entire match.

The Maclaurin series for the given function f(x) = 9 cos(x) * 7 is:
f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...

To obtain the Maclaurin series for the given function f(x) = 9 cos(x) * 7, follow these steps:
STEP 1: First, identify the base function. In this case, it is cos(x).
STEP 2: The Maclaurin series for cos(x) is given by the following formula:
  cos(x) = Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
STEP 3: Now, we need to incorporate the constants 9 and 7 into the series. We do this by multiplying the series by      9 * 7:
  f(x) = 9 * 7 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
STEP 4: Simplify the series:
 f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...
So, the Maclaurin series for the given function f(x) = 9 cos(x) * 7 is:
f(x) = 63 * Σ [(-1)^n * (x^(2n)) / (2n)!] for n = 0, 1, 2, ...

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Answer:

12 ft!!

Step-by-step explanation:

can u pls mark me brainliest?

Answer:

x=12 ft

Step-by-step explanation:

4/5=x/15

Multiply 5 and x to get 5x, then multiply 4 and 15 to get 60, then you're left with the equation 5x=60. Divide both sides of the equation by five to get 12 :D.

According to Baddeley and Hitch's research, the most important factor in determining whether rugby players will remember a particular game is the amount of time that has elapsed since the game was played.

Specifically, players were more likely to remember games that occurred early in the season and those that were particularly important or emotionally charged, while they were less likely to remember games that occurred later in the season or those that were less meaningful or emotionally significant.

This phenomenon is known as the "serial position effect" and has been observed in other contexts as well.

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Answer:

19.8

Step-by-step explanation:

Tan x = 0.36

x =

\( {tan}^{ - 1} {0.36}\)

x = 19.8

i hope this helped

Answer:

x = tan - 0.36

Step-by-step explanation:

\(x = tan - 1(0.36)\)

Number 1 as a factor, does not need to be explicitly written.

In other words: 1A = A

In our example, the above transformation has been applied once.

\(x = tan - 0.36\)

Based on the given statistics, we will shape each correlation to the corresponding scatterplot as follows:

13.True or False: r = 0.49 → (2)

14.True or False: r = -0.48 → (4)

15.True or False: r = -0.03 → (3)

16.True or False: r = -0.85 → (1)

Based on the given records, we need to match each correlation fee to the corresponding scatterplot. Let's analyze every correlation and its corresponding scatterplot in more detail:

13.True or False: r = 0.49 → (2)

A correlation coefficient of 0.49 shows a tremendous correlation among the variables. This means that as one variable will increase, the alternative variable tends to grow as nicely, albeit not flawlessly. In the scatterplot categorized as (2), we'd assume to look at a trendy upward fashion wherein the factors are quite scattered around the road of satisfactory fit.

14.True or False: r = -0.48 → (2)

A correlation coefficient of -0.48 indicates a bad correlation between the variables. This manner that as one variable increases, the opposite variable has a tendency to lower. In the scatterplot labeled as (2), we'd expect to see a standard downward fashion wherein the points are rather scattered around the line of fine match.

15.True or False: r = -0.03 → (4)

A correlation coefficient of -0.03 shows a very weak terrible correlation between the variables. This method that there is almost no relationship between the variables. In the scatterplot categorized as (four), we would count on seeing factors scattered randomly, with no discernible pattern or fashion.

16. True or False: r = -0.85 → (1)

A correlation coefficient of -0.85 shows a sturdy poor correlation between the variables. This method that as one variable increases, the other variable has a tendency to decrease substantially. In the scatterplot labeled as (1), we might count on to peer a clear downward trend in which the factors are tightly clustered around the road of the first-rate match.

By analyzing the strengths and instructions of the correlations, we can suit each correlation value to its corresponding scatterplot as follows:

13. True or False: r = 0.49 → (2)

14.True or False: r = -0.48 → (2)

15.True or False: r = -0.03 → (4)

16.True or False: r = -0.85 → (1)

Please notice that scatterplots provide visible representations of statistics and relationships between variables, and the interpretations might also vary relying on the context and the statistics being analyzed.

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Using Delta y = f'(x) Delta x to find a decimal approximation of the radical expression, we get the value found using Delta y f' (x) Delta x is 124.176.

The Delta y = f’(x) Delta x is the linear approximation formula used in calculus to estimate the value of an unknown function based on its derivative at a particular point.

In order to solve the problem using Delta y = f’(x) Delta x, we first have to rewrite the radical expression in terms of a function.

Let the function f(x) = sqrt(x) represent the radical expression.

Then, we will find the value of f'(x) by differentiating the function f(x) using the Power Rule of differentiation.

f(x) = sqrt(x) f'(x) = 1/2x^(-1/2)

Next, we will substitute the given value of x in the function f(x) and f’(x) to solve for Delta y = f'(x) Delta x.

Given, x = 124

Delta x = 2 Δy = f’(x) Δx = 1/2 * 124^(-1/2) * 2 = 0.1762

Hence, the decimal approximation of the radical expression is 124.176.

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The average speed of the lift is approximately 6.07 miles per hour.

Average speed is expressed mathematically as;

Average Speed = Distance / Time

Given the data in the question;

Plug in the values into the above equation.

Average Speed = Distance / Time

Average Speed = 801/880 miles ÷ 3/20 hr

Average Speed = 801/880 × 20/3

Average Speed = 267/44 mi/hr

Average Speed = 6.07 mi/hr

Therefore, the average speed of the lift is approximately 6.07 miles per hour.

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Answer:

96 cm^3

Step-by-step explanation:

multiply the three dimensions: 4*6*4=96

Answer:

V=l×W×h

=4cm×6cm×4cm

=96cm cubic

The Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

The statement you are referring to is known as the Central Limit Theorem. It states that when sampling from a population with an unknown distribution, if the sample size is sufficiently large (usually n>30), the sample mean will follow an approximately normal distribution regardless of the shape of the population distribution. This is particularly useful in statistics because it allows us to make inferences about the population mean based on the sample mean.

The standard deviation, sigma, plays an important role in the Central Limit Theorem because it determines how spread out the population is. If sigma is small, the sample means will be tightly clustered around the population mean, while if sigma is large, the sample means will be more spread out.

In conclusion, the Central Limit Theorem allows us to use the sample mean to estimate the population mean even when the population distribution is unknown. The standard deviation of the population, sigma, is an important factor in determining the spread of the sample means.

1. When sampling from a population with an unknown distribution, mean mu, and standard deviation sigma,

2. If the sample size (n) is sufficiently large,

3. The sample mean (x bar) will have approximately a normal distribution.

The CLT(central limit theorem) is a vital tool in many areas of statistical analysis, as it provides a foundation for making inferences about populations based on sample data, even when the original population distribution is unknown or non-normal.

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Advanced single-variable quadratic equations and complex numbers are advanced topics studied in high school mathematics curricula in the US. The specific grade at which they are introduced and studied may vary depending on the state, district, or school.

In general, single-variable quadratic equations are usually introduced in the 9th or 10th grade in high school, but some schools may introduce them in earlier grades.

These equations are a type of polynomial equation of degree two that can be written in the form

ax² + bx + c = 0,

where a, b, and c are constants and x is a variable. The study of quadratic equations includes topics such as factoring, completing the square, and the quadratic formula.

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The pair of hypotheses used to test if the mean of the first population is smaller than the mean of the second population, using independent random sampling, is H0: µ1-µ2 ≥ 0 and HA: µ1-µ2 < 0.

The given pair of hypotheses represents a one-tailed test where we are interested in determining if the mean of the first population (µ1) is smaller than the mean of the second population (µ2).

The null hypothesis (H0) states that the difference between the means, represented by (µ1-µ2), is greater than or equal to zero. This means that there is no significant difference between the means or that the mean of the first population is equal to or greater than the mean of the second population.

The alternative hypothesis (HA) states that the difference between the means, represented by (µ1-µ2), is less than zero. This suggests that there is a significant difference between the means and specifically indicates that the mean of the first population is smaller than the mean of the second population.

By conducting a statistical test, such as a t-test or z-test, and analyzing the results, we can evaluate the evidence and make an inference regarding the relationship between the means of the two populations based on the given pair of hypotheses.

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Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same. The given equation is equivalent to the expression one half and one half x.

Given information-

The expression given in the problem is,

\(\dfrac{1}{4} \times x\)

Equivalent expression is the expression of two equation when the way of representation of the two equation is different but the result is same.

For given expression,

\(\dfrac{1}{4} \times x\)

As the above function is the function of x. Thus it can be written as,

\(f(x)=\dfrac{1}{4} \times x\)

The number four is the product of number 2 and number 2. Thus,

\(f(x)=\dfrac{1}{2\times2} \times x\)

\(f(x)=\dfrac{1}{2} \times \dfrac{1}{2}\times x\)

Hence the given equation is equivalent to the expression one half and one half x.

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Answer: \(\dfrac{53}{16}\ \text{or}\ 3\dfrac{5}{16}\)

Step-by-step explanation:

Given

Length of board is \(16\ \frac{3}{4}\)

It is divided into 4 equal pieces i.e. length of each piece is

\(\Rightarrow \dfrac{\frac{64+3}{4}}{4}=\dfrac{67}{16}\ \text{in.}\)

If  \(\frac{7}{8}\) of an inch is removed from one of the pieces then,

\(\Rightarrow \dfrac{67}{16}-\dfrac{7}{8}\\\\\Rightarrow \dfrac{67}{16}-\dfrac{14}{16}=\dfrac{53}{16}\ \text{inch}\)

Answer:

-5+35k+5x

Step-by-step explanation:

There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

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Answer:

x = -1.135 (approx).

Step-by-step explanation:

x^3 = ∛(x - 2)

Cube both sides:

x^9 = x - 2

Subtract x and add 2 to both sides:

x^9 - x + 2 = 0

We could solve this for real roots by drawing a graph.

I did this and got one root  x = -1.135 (approx).

The other 8 roots are complex.

Answer:

A(-4,1), B(3,0), C(-7, - 2)

Step-by-step explanation:

When we reflect on the y-axis, we simply negate the value of the x-axis coordinate

Thus;

(x,y) becomes (-x,y)

So the correct answer is the coordinates that negates the x/axis values

(4,-1) becomes. (-4,-1)

(-3,0) becomes (3,0)

(7,-2) becomes (-7,-2)

Answer:

A- She is incorrect because systems may have only complex solutions which are not visible on the graph

Step-by-step explanation:

Just took the test on edge 2020

She is incorrect because systems may have only complex solutions which are not visible on a graph. Option A is correct.

Given that,
The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Kelly is incorrect since systems might only have complicated solutions that are hidden on a graph.

Thus, she is incorrect because systems may have only complex solutions which are not visible on a graph. Option A is correct.

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The midpoint of AB is M(4,1), If the coordinates of A are (2,8), then the coordinates of B are (6,-6).

The midpoint formula states that the midpoint of a line segment in a coordinate plane is given by the average of the x-coordinates and the average of the y-coordinates.

The midpoint of AB is M(4,1) and the coordinates of A are (2,8).

Therefore, we can write the following equation: x-coordinate of the midpoint = (x-coordinate of A + x-coordinate of B) / 2y-coordinate of the midpoint = (y-coordinate of A + y-coordinate of B) / 2

Substituting the given values into the above equation, we get:4 = (2 + x-coordinate of B) / 2 1 = (8 + y-coordinate of B) / 2

Simplifying the equations above, we get: x-coordinate of B = 6 y-coordinate of B = -6

Therefore, the coordinates of B are (6,-6).

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Answer:

18.84 yd

38.26 yd²

Step-by-step explanation:

cirumferemnce = 6 x 3. 14 = 18.84 yd

area = 3^2 x 3.14 = 38.26 yd²

Answer:

Area of circle bounded by a 135 ° arc is 4.71 m ²

Step-by-step explanation:

Radius of circle, r = 2 m

Angle of the circle , θ = 135 °

Area of circle bounded by a 135 ° arc.

Using Formula

Area of circle = θ/ 360 × π × r ²

substitute the values,

Area of circle = 135 /360 × 3.14 × ( 2 m) ²

solve it

Area = 27 / 72 × 3.14 × 4 m ²

Area = 27 / 18 × 3.14

Area = 1.5 × 3.14

Area = 4.71 m ²

Therefore, Area of circle bounded by a 135 ° arc is 4.71 m ²

Answer:

it's 3/2pi

Step-by-step explanation:

.

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the price of each kind of ticket when 7 adult and 6 student tickets sold for $119, and 4 adult and 5 student tickets sold for $79.

The two sales can be represented by the equations ...

  7a +6s -119 = 0

  4s +5s -79 = 0

We can solve these equations using the "cross multiplication method" as follows:

  D = (7)(5) -(4)(6) = 11

  Da = (6)(-79) -(5)(-119) = 121

  Ds = (-119)(4) -(-79)(7) = 77

a = Da/D = 121/11 = 11

s = Ds/D = 77/11 = 7

Each adult ticket was $11, and each student ticket was $7.

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Answer:

16π or 50.3 units

Step-by-step explanation:

the formula for the surface area of a sphere (as you mentioned) is:

4πr²

So if we plug in the given value (2) for r:

4π×2²=16π

Answer:

16

Step-by-step explanation:

I got it right