Assume that in a given year the mean mathematics SAT score was
605
, and the standard deviation was
136
. A sample of
76
scores is chosen. Use the TI-84 Plus calculator.
Part 1 of 5
(a) What is the probability that the sample mean score is less than
589
? Round the answer to at least four decimal places.
The probability that the sample mean score is less than
589
is . Part 2 of 5
(b) What is the probability that the sample mean score is between
575
and
610
? Round the answer to at least four decimal places.
The probability that the sample mean score is between
575
and
610
is . Part 3 of 5
(c) Find the
85
th percentile of the sample mean. Round the answer to at least two decimal places.
The
85
th percentile of the sample mean is . Part 4 of 5
(d) Would it be unusual if the the sample mean were greater than
620
? Round answer to at least four decimal places.
It ▼(Choose one) be unusual if the the sample mean were greater than
620
, since the probability is . Part 5 of 5
(e) Do you think it would be unusual for an individual to get a score greater than
620
? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.
▼(Choose one), because the probability that an individual gets a score greater than
620
is
.

To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).

Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.

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Answer:

6 and -2

Step-by-step explanation:

In the 1984 domestic violence study conducted by Sherman and Berk, the ethical concern was that they potentially withheld a beneficial treatment.

The domestic violence study conducted by Sherman and Berk in 1984 raised an ethical concern in that they financially profited from the research. This raises the question of whether their motives were purely altruistic or whether they were driven by financial gain. Additionally, the study did not adhere to special protections for vulnerable populations such as women and children who may have been victims of domestic violence. This raises concerns about the validity and generalizability of the study's findings. Furthermore, the study potentially withheld a beneficial treatment, which raises questions about the ethical responsibility of researchers to ensure that their subjects receive the best possible care. Finally, there are also concerns that the researchers may have deceived their subjects, which raises questions about the integrity and transparency of the research process. In conclusion, the ethical concerns raised by this study highlight the need for researchers to carefully consider the impact of their research on vulnerable populations and to ensure that they adhere to the highest ethical standards.
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Answer:

b = \(\frac{g}{(d^{2}+4) }\)

Step-by-step explanation:

(\(d^{2}\) + 4)b = g  Divide both sides by (\(d^{2}\) + 4)

b = \(\frac{g}{(d^{2}+4) }\)

Answer:

7/4a + 1/3

1 3/4a + 1/3

Step-by-step explanation:

Answer:

1 3/4AN + 1/3

Step-by-step explanation:

Answer:   \(\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right]\)

Step-by-step explanation:

A magic cube is something like:

\(\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]\)

Where the numbers that we must use are:

1, 3, 5, 7, 9, 11, 13, 15, 17

If we take the addition of those 9 numbers, we get 81.

Now, we divide it by 3 (the number of numbers in each row or column) and get:

81/3 = 27

so the sum in each row, column and diagonal must be 27.

1 + 9 + 17 = 27

13 + 11 + 3 = 27

5 + 7 + 15 = 27

9 + 13 + 5 = 27

You can keep playing with this, and then start forming our number cube, some of the hints tat we can use is that the median of the group is 9, so it must be in the middle of the cuve, and the extremes, 1 and 17, must be in the same column or row as 9.

so we start with:

\(\left[\begin{array}{ccc}x&x&x\\1&9&17\\x&x&x\end{array}\right]\)

and start to fill the empty spaces, now we can use that

1 + 11 + 15 = 27 and get:

\(\left[\begin{array}{ccc}11&x&x\\1&9&17\\15&x&x\end{array}\right]\)

now for the diagonals:

11 + 9 + 7 = 27

15 + 9 + 3 = 27

\(\left[\begin{array}{ccc}11&x&3\\1&9&17\\15&x&7\end{array}\right]\)

and for the last one:

11 + 3 + 13 = 27

15 + 7 + 5 = 27

\(\left[\begin{array}{ccc}11&13&3\\1&9&17\\15&5&7\end{array}\right]\)

Answer:

No

Step-by-step explanation:

Use the formula, difference/original. The difference is 8%. The original is 72%.

The equation would be: 8/72

Which is 1/9

1/9 = 11.1%

So he made a mistake of 11%

Answer:

8.9 Feet

Step-by-step explanation:

a^2+b^2 = c^2

Answer: Mila is climbing 28 feet per hour faster than Malik.

Step-by-step explanation:

Mila is climbing 721 feet per hour.

hope this helps :)

Answer:

JWJEJEJENDJDIDLLLENDKENDHDJD

Step-by-step explanation:

JEJENSNSKNSNEKZJEBE

The forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5 is $32935.

It should be noted that the forecasted cost is simply used to know the expected cost for a give data.

In this case, the forecasted cost for a liberal arts college, which has no religious affiliation, a size of 1,500 students and a reputation level of 4.5 is $32935.

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The probability of a random patient being alcoholic with elevated cholesterol levels is 55/80, or 0.6875. The probability of a random patient being nonalcoholic is 320/400, or 0.8. Lastly, the probability of a random patient being nonalcoholic with Non elevated cholesterol levels is 248/400, or 0.62.

To calculate the probability of a random patient being alcoholic with elevated cholesterol levels, we must first determine the total number of patients with elevated cholesterol levels. This can be done by adding the number of alcoholic patients (55) with elevated cholesterol levels to the number of nonalcoholic patients (72) with elevated cholesterol levels.

The result is a total of 127 patients with elevated cholesterol levels. This means that out of 400 patients, 55 of them were alcoholic and had elevated cholesterol levels. Therefore, the probability of a random patient being alcoholic with elevated cholesterol levels is 55/400, or 0.6875.

The probability of a random patient being nonalcoholic is equal to the total number of nonalcoholic patients (320) divided by the total number of patients (400). This yields a probability of 0.8.

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Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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What question do you need to get or is it all?

Answer:

32 years old.

Step-by-step explanation:

Do the math.

1(first year)+32(last year)=33

33/2=16.5(average)

16.5*32=528

Answer:

32

Step-by-step explanation:

The solution of the equation x^ay! + 5xy + (4 + x)y = 0, where x > 0, can be represented as a power series of the form y = ΣCnx^n, where C0 = 1 and Cn = 0 for n = 1, 2, 3, ...

To find the solution of the equation x^ay! + 5xy + (4 + x)y = 0, we can represent the solution as a power series expansion of the form y = ΣCnx^n, where Cn is the coefficient of x^n and n ranges from 0 to infinity. Plugging the power series into the equation, we get:

x^a*(ΣCnx^nn!) + 5x*(ΣCnx^n) + (4 + x)(ΣCn*x^n) = 0

We can then collect the terms with the same powers of x:

ΣCnx^(n+a)n! + Σ5Cnx^(n+1) + Σ(4 + x)Cnx^n = 0

For the equation to hold true for all powers of x, each term with the same power of x must be zero. Therefore, we can determine the coefficients Cn for each power of x. For n = 0, the term ΣCnx^a0! simplifies to C0x^a0! = C0*x^a. Since the equation must hold for all x > 0, the coefficient C0 must be non-zero. Therefore, C0 = 1. For n = 1, the term Σ5Cnx^2 simplifies to 5C1x^2 = 0. Therefore, C1 = 0. Similarly, for n = 2, 3, 4, ... , the terms involving Cn will also be zero, as they are multiplied by powers of x. Hence, the solution of the equation x^ay! + 5xy + (4 + x)y = 0 can be represented as y = C0x^a = x^a, where a is a positive real number, and the coefficients Cn are zero for n = 1, 2, 3, ....

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Answer:

ypotenuse squared = adjacent squared + opposite squared

Step-by-step explanation:

sin θ =opposite/hypotenuse

tan θ = opp/adjacent

cos θ = adj/hyp

Pythagoras Theorem states that hypotenuse squared = adjacent squared + opposite squared

The missing entries for f(x) are 20, 30, and 40, and the missing entries for g(x) are 40, 80, and 160.

The missing entries for f(x) can be found by knowing that f is a linear function and using the values given. A linear function has the form f(x) = ax + b, where a is the slope and b is the y-intercept. Since f(0) = 10 and f(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

f(0) = 10 = a(0) + b

Putting x = 1 in the equation, we get:

f(1) = 20 = a(1) + b

Solving these two equations simultaneously, we find:

a = 10

b = 0

So, the equation for f is:

f(x) = 10x + 0 = 10x

Using this equation, we can find the missing entries for f(x) in the table:

f(2) = 10x = 10(2) = 20

f(3) = 10x = 10(3) = 30

f(4) = 10x = 10(4) = 40

So the missing entries for f(x) are 20, 30, and 40.

To find the missing entries for g(x), we need to know the form of the exponential function g. A common form for exponential functions is g(x) = ab^x, where a is the y-intercept and b is the growth factor. Since g(0) = 10 and g(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

g(0) = 10 = a(1)^0 = a

So, a = 10.

Putting x = 1 in the equation, we get:

g(1) = 20 = 10b

Solving for b, we find:

b = 2

So, the equation for g is:

g(x) = 10(2^x)

Using this equation, we can find the missing entries for g(x) in the table:

g(2) = 10(2^2) = 10(4) = 40

g(3) = 10(2^3) = 10(8) = 80

g(4) = 10(2^4) = 10(16) = 160

So the missing entries for g(x) are 40, 80, and 160.

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--The given question is incomplete; the complete question is

"The table below shows some values of a linear function f and an exponential function g. find exact values (not decimal approximations) for each of the missing entries.                                                                                    x      0  1  2  3 4                                                                                                                                             f(x)  10 _ 20 _ _                                                                                                                                 g(x) 10 _ 20 _ _"--

Yes, the function f(x) = x / (x + 2) satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. This is because f is continuous on [1, 4] and differentiable on (1, 4).

Given f(x) = x/ x + 2

We are asked to check whether the function satisfies the hypotheses of the mean value theorem on the given interval [1, 4].

Mean Value Theorem: If f(x) is continuous on the closed interval [a, b] and is differentiable on the open interval (a, b), then there exists a number c in (a, b) such that: f(b) − f(a) / b − a = f'(c)

For the given function, we have the interval [1, 4]. The function is continuous on [1,4].

Also, the function is differentiable on (1,4).

Therefore, the given function satisfies the hypotheses of the mean value theorem on the given interval [1, 4]. Hence, the correct option is Yes, f is continuous on [1,4] and differentiable on (1,4).

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Given DC is tangent to circle N at point C: m∠DCN < m∠BAN and BE is tangent to Circle N at point A, is True

(1) From the diagram, we can see that angles ∠DCN and ∠BAN are vertical angles, so they are equal in measure. Since DC is tangent to Circle N at point C, we know that m∠DCN is a right angle. Therefore, m∠DCN = 90° and m∠BAN = 90° - m∠DCN. Since m∠DCN is positive, we have m∠BAN < 90°, which implies that m∠DCN < m∠BAN. So, statement (1) is true.

(2) Since DC is tangent to Circle N at point C, we know that angle ∠CBE is a right angle, and hence BE is perpendicular to CE. Also, we know that CE is the radius of Circle N, so it is perpendicular to NB. Therefore, BE is tangent to Circle N at point A. So, statement (2) is true.

(3) The length of NB cannot be determined from the given information. We only know that CE = 6, but we do not know the radius of Circle N or the position of point B along the circle. Therefore, we cannot determine the length of NB. So, statement (3) cannot be determined.

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Complete question:

Given DC is tangent to circle N at point C, which statements are true?

- m∠DCN < m∠BAN

- BE is tangent to Circle N at point A.

- NB ≈ 6.1

Answer:

  (ii) (x, y, z) = (110°, 30°, 30°)

  (iii) (x, y, z) = (110°, 70°, 70°)

Step-by-step explanation:

The things you need to know and use are ...

  Opposite angles of a parallelogram are congruent.

  Adjacent angles of a parallelogram are supplementary.

  Alternate interior angles between a transversal and parallel lines are congruent.

  Corresponding angles where a transversal crosses parallel lines are congruent.

__

(ii) Angles B and D are opposite, so congruent:

  x = 110°

Angle DAB is supplementary to angle B, so is 70°. That means z is ...

  z = 70° -40° = 30°

Angle y is "alternate interior" relative to z, so is congruent to z:

  y = 30°

__

(iii) Angle x is adjacent to angle N, so is supplementary to 70°.

  x = 180° -70° = 110°

Angle y is opposite angle N, so is congruent.

  y = 70°

Angle z is corresponding to angle N, so is congruent. (It is also "alternate interior" with respect to angle y, so is congruent to y.)

  z = 70°

Answer:

D. im answering for the purpose of the first person getting brainliest

Step-by-step explanation:

Answer:

Explained below.

Step-by-step explanation:

Complementary angles are angles that sum up to 90°.

Here,

Then,

Angle P + Angle Q = 90°

2x + 7x = 90°

9x = 90°

x = 90/9

x = 10°

Therefore,

\(\rule{150pt}{2pt}\)

To determine how the decreasing price will affect the demand and revenue, we can use the concept of related rates. We are given that the price is currently $25 each and it is decreasing at a rate of $1.50 per unit per month. We need to find the related change in demand with time (dq/dt) and the related change in revenue with time (dR/dt).

Given:

p = 25 (price in dollars)

dp/dt = -1.50 (rate of change of price in dollars per unit time)

We are asked to find:

dq/dt (related change in demand with time)

dR/dt (related change in revenue with time)

First, let's calculate dq/dt:

q = 2p² - 135p + 2400

Taking the derivative with respect to time (t) on both sides:

dq/dt = d(2p² - 135p + 2400)/dt

Substituting the given values:

dq/dt = -150 - (-202.50)

dq/dt = 52.50

So, the demand (q) will increase by 52.5 units per month.

Next, let's calculate dR/dt:

R = pq (revenue)

R = (2p³ - 135p² + 2400p)

Taking the derivative with respect to time (t) on both sides:

dR/dt = d((2p³ - 135p² + 2400p))/dt

Substituting the given values:

dR/dt = 900 - (-10125) + (-3600)

dR/dt = 900 + 10125 - 3600

dR/dt = 9000

So, the revenue (R) will increase by $9000 per month.

In summary, the demand will increase by 52.5 units per month and the revenue will increase by $9000 per month.

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the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

The given partial differential equation is:

au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)

a) BCs (Boundary Conditions):

We have u(0, t) = 0 and u(π, t) = 0.

IC (Initial Condition):

We have u(x, 0) = x.

To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.

The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:

X(x) * T'(t) = 4 * X''(x) * T(t) / a

Dividing both sides by X(x) * T(t) gives:

T'(t) / T(t) = 4 * X''(x) / (a * X(x))

Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².

T'(t) / T(t) = -λ²

X''(x) / X(x) = -λ² * (a / 4)

Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.

Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.

Now, applying the boundary conditions:

1) u(0, t) = 0:

Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.

2) u(π, t) = 0:

Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.

Now, let's find the expression for u(x, t) using the initial condition:

u(x, 0) = X(x) * T(0) = x

Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:

C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x

This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.

Therefore, the solution for the initial value problem is:

u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)

where λ = ± sqrt(-4n² / a), and n is a non-zero integer.

Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.

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Answer:

I think it's B, the range is 70 in the mid-range is 50

The simplified expression is given by (x² - 3x - 3) / ((x + 3)(x - 2)(x - 4)).

To simplify this expression, we need to find a common denominator for the two fractions and then combine them. To do this, we need to factor the denominators of both fractions.

Let's start with the first fraction's denominator:

x² + x - 6

We need to find two numbers that multiply to -6 and add to +1. These numbers are +3 and -2. Therefore, we can write:

x² + x - 6 = (x + 3)(x - 2)

Now let's factor the second fraction's denominator:

x² - 6x + 8

We need to find two numbers that multiply to 8 and add to -6. These numbers are -2 and -4. Therefore, we can write:

x² - 6x + 8 = (x - 2)(x - 4)

Now we can rewrite the original expression with a common denominator:

(x(x - 2) - (1)(x + 3)) / ((x + 3)(x - 2)(x - 4))

Next, we can simplify the numerator:

(x² - 2x - x - 3) / ((x + 3)(x - 2)(x - 4))

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

Finally, we can't simplify this expression any further. Therefore, the simplified expression is:

(x² - 3x - 3) / ((x + 3)(x - 2)(x - 4))

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