7. A high school counselor wishes to see if the average number of dropouts in his school is 21. He reviews the last 17 years and finds that the number of dropouts each year is as shown. At a=0.01, is the hypothesis refutable? Explain
12 18 24 16 21 20 18 19
19 22 25 16 18 19 19 20 23

Answer: 18

Step-by-step explanation: 20 - 2 = 18

The triangle with sides 44, 73, and 86 is an obtuse triangle.

The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the lengths of the other two sides, can be used to determine whether the triangle is right, acute, or obtuse.

In an acute triangle, the square of the hypotenuse length is less than the sum of the squares of the other two sides; in an obtuse triangle, the square of the hypotenuse length is greater than the sum of the squares of the other two sides.

Begin by calculating the square of each side:

[tex]44^2 = 1936[/tex]

[tex]73^2 = 5329[/tex]

[tex]86^2 = 7396[/tex]

Let us now see if the triangle fulfils the Pythagorean Theorem:

1936 + 5329 = 7265

We know the triangle is not obtuse because 7265 is less than 7396.

1936 + 7396 = 9332

We know the triangle is not acute because 9332 is greater than 5329.

5329 + 7396 = 12725

We know the triangle is obtuse because 12725 is greater than 7265 but less than 9332.

As a result, the triangle with sides 44, 73, and 86 is obtuse.

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The answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship. Snowfall, in particular, tends to decrease as temperatures rise. Covariance units are the product of the units of the two variables, which in this case are in2 and (degrees F)2, so covariance units are degree inches.

We are given the following details:

Correlation coefficient between December snowfall and temperature in Syracuse, New York: -0.5

December snowfall variation (S): 100 in2

Temperature variation in December (T): 25 (degrees F)2

We are asked to calculate the correlation between December snowfall and temperature in degrees inches.

Cov(S,T) can be calculated using the covariance formula:

Corr(S,T) = Cov(S,T) * sqrt(Var(S)) * sqrt(Var(T))

Plugging in the values from the problem yields:

Cov(S,T) = (-0.5) * sqrt(100 in2) * sqrt(25 (degrees F)2) = (-0.5) * 10 in * 5 degrees F = -25 degree inches

As a result, the answer is (a) -25. The covariance is negative, indicating that the December snowfall and temperature in Syracuse NY have an inverse relationship.

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6. The probability that Flight A will have a full flight is 0.4163.

7. The probability that all passengers who show up will have a seat on the flight is 0.5731.

8. The probability that Flight B will have exactly 68 customers show up is 0.0904.

9. The probability that all passengers that show up will have a seat on the flight is 0.9707.

6. If the airline chooses not to oversell flight A and sells exactly 96 tickets, the probability that it will have a full flight can be calculated using the binomial distribution. Let X be the number of passengers who show up for the flight.

Then, X follows a binomial distribution with n = 96 and p = 0.97 (since the probability that a passenger shows up is 1 - 0.03 = 0.97). Thus, the probability that all 96 passengers show up is:

P(X = 96) = (96 choose 96) × [tex]0.97^{96}[/tex] × [tex]0.03^0[/tex] = 0.4163

So, the probability that Flight A will have a full flight is 0.4163.

7. If the airline oversells Flight A with 99 tickets sold, the probability that all passengers who show up will have a seat on the flight (i.e. 3 or more no-shows) can be calculated using the binomial distribution again. Let Y be the number of no-shows for the flight. Then, Y follows a binomial distribution with n = 99 and p = 0.03. We want to find the probability that Y is greater than or equal to 3 (i.e. there are 3 or more no-shows), which can be calculated as:

P(Y >= 3) = 1 - P(Y <= 2) = 1 - ((99 choose 0) × [tex]0.03^0[/tex] × [tex]0.97^{99}[/tex] + (99 choose 1) × [tex]0.03^1[/tex] × [tex]0.97^{98}[/tex] + (99 choose 2) × [tex]0.03^2[/tex] × [tex]0.97^{97}[/tex]) = 0.5731

So, the probability that all passengers who show up will have a seat on the flight is 0.5731.

8. If the airline oversells Flight B with 70 tickets sold, the probability that the flight will have exactly 68 customers show up can be calculated using the binomial distribution with n = 70 and p = 0.98 (since the probability that a customer shows up is 1 - 0.02 = 0.98). Let Z be the number of customers who show up for the flight. Then, the probability that exactly 68 customers show up is:

P(Z = 68) = (70 choose 68) × [tex]0.98^{68}[/tex] × 0.02² = 0.0904

So, the probability that Flight B will have exactly 68 customers show up is 0.0904.

9. If the airline oversells Flight B with 72 tickets sold, the probability that all passengers who show up will have a seat on the flight can be calculated using the binomial distribution again. Let W be the number of no-shows for the flight. Then, W follows a binomial distribution with n = 72 and p = 0.02. We want to find the probability that W is less than or equal to 3, which can be calculated as:

P(W <= 3) = (72 choose 0) × [tex]0.02^0[/tex] × [tex]0.98^{72}[/tex] + (72 choose 1) × [tex]0.02^1[/tex] × [tex]0.98^{71}[/tex] + (72 choose 2) × [tex]0.02^2[/tex] × [tex]0.98^{70}[/tex] + (72 choose 3) × [tex]0.02^3[/tex] × [tex]0.98^{69}[/tex] = 0.9707.

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AB dotted line segment correctly represents the perpendicular bisector of line segment XY

A line is an infinitely long object with no width, depth, or curvature.

A perpendicular bisector can be defined as a line segment which bisects another line segment at 90 degrees.

In other words, a perpendicular bisector intersects another line segment at 90° and divides it into two equal parts.

In the given figure the XY is a straight line.

The perpendicular bisector to this line is AB.

Hence, AB dotted line segment correctly represents the perpendicular bisector of line segment XY

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Answer:

Step-by-step explanation:

Multiply x*x, then X*2, then -6*2, lastly -6*x. So in other words multiply all of the factors. pay close attention to the + and - negative signs.

Answer: [tex]x^{2}[/tex]+2x-6x+2x

Simplify: [tex]x^{2}[/tex]-4x+2x

(a) The max speed of Gregory is, [tex]v_{max} =\frac{32}{4} =8s[/tex]

(b) distance covered in additional z seconds is [tex]distance= 4zmeter[/tex]

(c)[tex]d(x)=30m+4(x-7s)[/tex]

Velocity is defined as the rate of change position of the object with respect to the time and frame of reference.

Gregory runs a 100-meter race. 5 seconds after the race started he is 30 meters from the starting line and reaches his max speed.

(a)The max speed covered by Gregory is ,

For constant speed, we know,

[tex]v=\frac{distance}{time taken}[/tex]

distance= 62m-30m=32m.

And the time take to reach 62m will be

time =9s-5s=4s

So, Gregory's max speed is,

[tex]v_{max} =\frac{32}{4} =8s[/tex]

(b) Suppose Gregory runs for an additional z seconds after reaching his max speed,

As the velocity of Gregory's is [tex]v_{max}[/tex], the distance covered by him is,

[tex]distance=v_{max}*zs[/tex]

[tex]distance= 4zmeter[/tex]

(c) At time 5+ z seconds the distance will be the30

meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:

[tex]distance=v_{max}*z+30\\distance=4\frac{m}{s} *z s[/tex]

At time x ( x greater or equal to 5 seconds) the distance will be the 30 meters he covers in the first part of the race plus the distance he traveled at constant speed. this is:

[tex]d(x)=30m+v_{max}*(x-5s)\\ d(x)=30m+4(x-7s)[/tex]

Hence,(a)The max speed of Gregory is, [tex]v_{max} =\frac{32}{4} =8s[/tex]

(b) distance covered in additional z seconds is [tex]distance= 4zmeter[/tex]

(c)[tex]d(x)=30m+4(x-7s)[/tex]

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Answer:

Tennis, a game of skill and grace,

A dance upon a court of green.

Racquets are partners in this space,

A symphony of motion seen.Each stroke a crescendo to the ear,

A harmony of speed and spin.

The ball, a fleeting, flashing sphere,

A fleeting moment to win.The court is life, a battlefield,

Of challenges and victories.

A test of strength, both heart and mind,

Of courage, skills, and agility.The net, a barrier, divides,

Two opponents in their quest.

A symbol of the tension that resides,

In every match, every test.But when the final point is served,

And winner takes the day.

The court transforms, a stage, preserved,

For celebration in its way.

Step-by-step explanation:

Answer:

he would go to the barber shop 21 times in 2 years

Step-by-step explanation:

divide 4 by 52 and then multiply by 2

Answer:

26

Step-by-step explanation:

52÷4 = 13 times a year

therefore, for two years

13 × 2 = 26

Sarah spend $161.24 before two weeks.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

Sarah spends an average of $64.11 per week.

She spent $53.22 last week, and $64.11 this week.

As, 1 month = 4.34524 weeks

So, before two weeks she spends

64.11 = (64.11 + 53.22 +x )/ 4.34524

278.5733364 = 117.33 + x

x= 161.24

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Answer:

x=

Step-by-step explanation:

⅔x= 7x-1

2/3x=6

multiply both sides by 3/2

(3/2)(2/3x)= 6×3/2

x=

3x

x equals ur mom so udhdhddhehehrhrhrhrrruur mom is ur mome

The square root of zero is a counterexample of the statement, so it is false.

Here we have the following statement about square roots:

"the square root of a number will always have two outcomes One is positive and the other is negative."

This seems to be true because:

-2*-2 = 2*2 = 4

So √4 = 2 and -2

But, particularly the square root of zero is:

√0 = 0

So here we have only one outcome that is neither positive nor negative, then the statement is false.

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The derivation of the critical radius(r*) as  and critical saturation(S*) as  is explained below .

To derive the critical saturation ratio (S*) and critical radius (r*),

We  use calculus to find the maximum value of the saturation ratio for a given radius on the Kohler curve.

First, let us consider the equation for the saturation ratio, S, as a function of radius, r:

that is : S = 1 + ar²/3b  ;

where a and b are constants.

Next, we find the derivative of S with respect to r:

On differentiating Curve "S" with respect to "r" ;

⇒ dS/dr = 2ar/3b  ;

Equating the derivative = 0 , we can find the critical points:

⇒ dS/dr = 0 = 2ar/3b  ;

On Solving for r, we have ;

⇒ r* = √(3b/a)

Next , to find the critical saturation ratio(S*) , we substitute r* back into the original equation for S:

⇒ S* = 1 + ar²/3b = 1 + a×(3b/a)/3b = 1 + √(4a³/27b)

Therefore , the critical saturation ratio and critical radius are written as r* = √(3b/a)  and  S* = 1 + √(4a³/27b)  .

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The given question is incomplete , the complete question is

Using your calculus skills derive the equations for the critical saturation ratio and the critical radius. (Hint: the critical point on the Kohler curve represents a maximum value).

The equations you should end up with are as follows:

r* = √(3b/a) and S* = 1 + √(4a³/27b) Where r* is the critical radius and S* is the critical saturation ratio .

Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Step-by-step explanation:

d.) T distribution's mean=0 and standard deviation=1 is not true. Instead, the t distribution has a mean of 0 and a standard deviation that varies based on the sample size and degrees of freedom

The t distribution is not similar to the z distribution in terms of its standard deviation. Unlike the standard normal distribution (z distribution), which has a mean of 0 and a standard deviation of 1, the t distribution has a mean of 0, but its standard deviation varies depending on the sample size. Specifically, the t distribution has heavier tails than the z distribution, which means it has more spread in the distribution and more extreme values are more likely to occur.

The t distribution's mean=0 and standard deviation=1 is not true, hence the proper response is d. The t distribution, on the other hand, has a mean of zero and a standard deviation that varies according to the sample size and degrees of freedom.

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Answer:

13 3/4

Step-by-step explanation:

5+8 = 13

1/2 = 2/4

2/4+1/4 = 3/4

The problem is the multiplication with exponent or scientific notation kind of problem.

Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.

For example, 30,000 can be written as 3 × 10⁴.

Here, the problem is defined as multiplying the expression 5 × 10³ with some number to get the expression 5 × 10⁶.

Let x be the number that is multiplied.

(5 × 10³) x = 5 × 10⁶

x = (5 × 10⁶) / (5 × 10³)

x = 10⁶ / 10³

x = 10⁶⁻³ = 10³

So here we are using the scientific notation to solve the whole problem and the answer itself is in the scientific notation.

Hence the given problem is a Multiplication of numbers in scientific notation kind of problem.

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Answer:

6/55

Step-by-step explanation:

2/5 ÷ 3 2/3

3 2/3 = 11/3

2/5 ÷ 11/3

= 2/5 x 3/11

= 6/55

So, the answer is 6/55

Answer:

37.8387 pounds of the 22% alloy copper and 13.1612 pounds of the 53% alloy copper must be used.

Step-by-step explanation:

Let x represent the amount of 22% copper needed.

Therefore, 51-x represents the amount of 53% copper needed.

Therefore, we can write

(22% * x) + (53% * (51-x)) = 30% * (51)

⇒0.22x + 0.53(51-x) = 0.3(51)

⇒ x = 37.8387

Thus, x =37.8387 and 51-x = 13.1612

a) Type of research hypothesis is tested in this study is causal RH

b) Type of design is being used in this study is non-experiment

c) Type of design is being used in this study is within-subjects design

d) No, the design used in this study cannot provide an appropriate test of the research hypothesis.

(a) The research hypothesis being tested in this study is a causal hypothesis. The company president believes that the type of music listened to can predict production line output.

(b) The type of design being used in this study is a non-experiment. The researcher is not manipulating the type of music listened to; instead, the plant is naturally exposed to either country or classical music.

(c) The design being used in this study is within-subjects design, as the same group of individuals is exposed to both types of music. It is also a repeated measures design, as the same individuals are measured twice (once under country music and once under classical music).

(d) No, the design used in this study cannot provide an appropriate test of the research hypothesis. Since the researcher is not manipulating the type of music listened to, it is possible that other variables could be affecting the production line output, such as different environmental conditions on each week, or different levels of motivation.

Therefore, it is difficult to determine if any differences in production line output are actually due to the type of music listened to. A true experiment with random assignment of workers to the two music conditions would provide a better test of the research hypothesis.

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Answer:

1. the lateral is 4.4 the total is 8.2

2. the lateral is 132 and the total is 41

The best definition of the term mirror line is "A mirror line is the line over which an object in the coordinate plane is reflected". So option A is correct.

A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.

Given options,

A. A mirror line is the line over which an object in the coordinate plane is reflected.

Yes this statement is according to definition of mirror line.

B. A mirror line is a line in the plane that is units away from the y-axis.

no its is not like that so it is incorrect option.

C. A mirror line is another name for the line of translation. no translation is a different concept so it also incorrect.

D. A mirror line is always a diagonal line in the plane that divides it into eight sections. it is also not correct.

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Answer:

80

Step-by-step explanation:

16/20 —> 80/100

or

16/20 = 8/10 = 80%

Answer:

y=-1

x=-1

Step-by-step explanation:

Answer: 58 degrees

Step-by-step explanation:

The probability of flipping heads, spinning an odd number, and then flipping tails is 1/8.

The probability of flipping heads, spinning an odd number, and then flipping tails is given by the product of the individual probabilities of each event.

The probability of flipping heads is 1/2,

the probability of spinning an odd number is 2/4 or 1/2, and

the probability of flipping tails is 1/2.

So, the probability of flipping heads, spinning an odd number, and then flipping tails is:

1/2 * 1/2 * 1/2 = 1/8

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On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = [tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667[/tex][tex]P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.[/tex]

16.67% probability = 0.1667

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The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The graph on the right shows the remaining life expectancy, E, in years for females of age x.

Then the average rate of change is given as,

Average rate = (32.8 - 24) / (60 - 50)

Average rate = 8.8 / 10

Average rate = 0.88

The average rate of change of life expectancy between the ages of 50 and 60 will be 0.88.

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