In a survey of more than 100,000 high school students in 2004 by researchers at the University of Connecticut, 83% agree with the statement "People should be allowed to express unpopular opinions. " If 8 students are selected a random, what is the probability that at least 6 agree with the statement?

For any given event, the sum of probability of that event and the probability of its complement must equal one.

The complement of an event is the set of all outcomes in the sample space that are not in the event. The probability of the complement of an event is the probability that the event does not occur.

Therefore, if P(A) is the probability of an event A, then P(A') is the probability of the complement of A, and we have: P(A) + P(A') = 1

This is known as the complement rule of probability and is a fundamental principle in probability theory. It states that the sum of the probabilities of an event and its complement must equal one, which reflects the fact that either the event occurs or its complement occurs, but not both.

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Answer:

first one: 1300

Second one: 9.11

Third one : Sorry i dont have time rn to figure it out

Step-by-step explanation:

Answer :

Step-by-step explanation:

In the given figure,

We know that,

[tex] : \implies \rm\dfrac{P}{H}= sin \theta \\ [/tex]

where,

P is perpendicular (AC)

H is Hypotenuse (AB)

[tex]\theta[/tex] is 64°

Substituting the values,

[tex] : \implies \sf \dfrac{AC}{15} = sin \: 65\degree[/tex]

sin 65 = 0.9063 (approximately)

[tex]:\implies \sf \dfrac{AC}{15} = 0.9063 \\ [/tex]

[tex]:\implies \sf AC = 0.9063 \times 15 \\ [/tex]

[tex]:\implies \sf AC \approx 13.59 \\ [/tex]

Therefore, the length of side AC is 13.5 units

The value of x is 4cm and the breadth of the rectangle is 11cm and the side of the square is 9cm.

Let's begin by using the formula for the perimeter of a rectangle:

Perimeter of a rectangle = 2 * (length + breadth)

For the rectangle given in the problem, the length is 7 cm and the breadth is x+7 cm. Therefore, the perimeter of the rectangle can be expressed as:

2 * (7 cm + (x+7) cm) = 2 * (x+14) cm = 2x + 28 cm

For the square, the side length is x+5 cm. Therefore, the perimeter of the square can be expressed as:

4 * (x+5) cm = 4x + 20 cm

We are given that the perimeter of both shapes is the same. Therefore:

2x + 28 cm = 4x + 20 cm

Simplifying the equation by subtracting 2x from both sides, we get:

28 cm = 2x + 20 cm

Subtracting 20 cm from both sides, we get:

8 cm = 2x

Dividing both sides by 2, we get:

x = 4 cm

Therefore, the value of x is 4 cm.

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For the given system of equations there is no solution.

The given system of equations are -7x+7y=8 -----(i) and -14x+14y=14 -----(ii).

Multiply equation (i) by 2, we get

-14x+14y=16  -----(iii)

Subtract equation (ii) from equation (ii), we get

-14x+14y-(-14x+14y)=16-14

-14x+14y+14x-14y=2

0≠2

So, the is no solution

Therefore, for the given system of equations there is no solution.

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The length of the square whose area is given would be = 5cm.

The length of the square whose perimeter is given would be = 1m

For question a:

To calculate the length of a square when the area is given, the formula of area of square should be used.

That is ;

area of square = a²

area = 25

a = √25 = 5cm

For question b)

perimeter of square = 4a

perimeter = 4

a = 4/4 = 1m

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The graph of circle about the triangle is shown in figure.

Since, We knw that;

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

To circumscribe a circle about the triangle.

Now, We can graph the circle as shown in figure.

Which is circumscribe a circle about the triangle.

Thus, The correct figure is shown in figure.

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The dimensions of the rectangular field with the largest area are w = 600 feet and L = 1200 feet.

Let's denote the width of the rectangular field by w and its length by L.

Since the field borders a straight river, we only need to fence three sides of the rectangle, which gives us:

2w + L = 2400

Solving this equation for L, we get:

L = 2400 - 2w

Now, we want to find the dimensions of the field that will give us the largest possible area.

The area of a rectangle is given by A = wL. Substituting the expression for L from above, we get:

A = w(2400 - 2w)

= 2400w - 2[tex]w^2[/tex]

To find the maximum value of this function, we can take its derivative with respect to w and set it equal to zero:

dA/dw = 2400 - 4w = 0

Solving for w, we get w = 600.

Substituting this value back into the equation for L, we get:

L = 2400 - 2w = 1200

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Answer:

The finance charge can be calculated by adding up all the monthly payments and subtracting the original loan amount (in this case, $2,200):

Finance charge = 22 x $114.66 - $2,200

Finance charge = $2,524.52 - $2,200

Finance charge = $324.52

To calculate the amount of principal, we need to subtract the finance charge from the total amount borrowed:

Total amount borrowed = $2,200 + finance charge

Total amount borrowed = $2,200 + $324.52

Total amount borrowed = $2,524.52

Amount of principal = Total amount borrowed - Finance charge

Amount of principal = $2,524.52 - $324.52

Amount of principal = $2,200

Therefore, the amount of principal in this loan is $2,200.

Answer:  Therefore, the amount of principal is $1,070.80.

Step-by-step explanation:

To find the amount of principal, we need to first determine the total amount being financed, which is the difference between the purchase cost and the down payment:

Total amount financed = Purchase cost - Down payment

Total amount financed = $5,200 - $2,200

Total amount financed = $3,000

Next, we can use the formula for the present value of an annuity to calculate the amount of principal:

Present value of an annuity = Payment amount x (1 - (1 + interest rate)^(-number of payments))) / interest rate

Plugging in the given values, we get:

$114.66 = Payment amount

16% / 12 = 0.013333... = Interest rate per month

22 = Number of payments

Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...

Present value of an annuity = $2,004.20

Finally, we can subtract the finance charge from the present value of the annuity to get the amount of principal:

Amount of principal = Present value of annuity - Finance charge

Amount of principal = $2,004.20 - ($114.66 x 22)

Amount of principal = $2,004.20 - $2,522.52

Amount of principal = -$518.32

We get a negative value because the finance charge is greater than the present value of the annuity. Therefore, we need to adjust our calculation of the present value of the annuity.

If we assume that the finance charge is included in the total amount being financed, we can recalculate the present value of the annuity using a total amount financed of $3,518.32:

Present value of an annuity = $114.66 x (1 - (1 + 0.013333...)^(-22)) / 0.013333...

Present value of an annuity = $2,447.52

Then, we can subtract the finance charge from the total amount being financed to get the amount of principal:

Amount of principal = Total amount financed - Finance charge

Amount of principal = $3,518.32 - $2,447.52

Amount of principal = $1,070.80

Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.

Here,

let,

Pete is standing 4 feet away from a mirror on the ground.

Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.

We can say two triangles are formed are similar,

So if the mirror is 20 feet away from the base of the tree

After talkig the similarity theorem we get,

So x = 6*5

x = 30 feet.

The height of the mirror is 30 feet.

Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).

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complete question:

Pete is standing 4 feet away from a mirror on the ground. Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing. The two triangles formed are similar.

If the mirror is 20 feet away from the base of the tree

A.

22 feet

B.

19 feet

C.

13 feet

D.

30 feet

Actually, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y).

To see why, let's substitute y = 0 degrees into the expression:

sin(y)*tan(y) = cos(y)

sin(0)*tan(0) = cos(0)

0*tan(0) = 1

0 = 1

As we can see, the equation does not hold for y = 0 degrees. However, this does not make 0 degrees a counterexample, because 0 degrees is not in the domain of the tangent function.

The tangent function is undefined at odd multiples of 90 degrees (e.g. 90, 270, etc.), because at those angles the denominator of the tangent function becomes zero. Therefore, we cannot substitute y = 0 degrees into the expression sin(y)*tan(y) = cos(y), because it would result in division by zero.

In summary, 0 degrees is not a counterexample for the expression sin(y)*tan(y) = cos(y), because it is not in the domain of the tangent function.

a) The person that starts out with more money is: Julie.

b) Both people are depositing the same amount each month.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

George's amount starts out at $125, and increases by $50 each month, hence the function is:

G(x) = 125 + 50x.

Julie's amount starts out at $175, and increases by $50 each month, hence the function is:

G(x) = 175 + 50x.

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The proportions that can be used to find QR in the similar triangles are:

AB/PQ = BC/QR

5/10 = 3/QR

Sides of triangles that are similar usually have lengths that are proportional to each other.

Given that triangles ABC and PQR are similar to each other, their side lengths will be proportional, therefore:

AB/PQ = BC/QR = AC/PR.

Plugging in the given values from the image, we have:

5/10 = 3/QR

Therefore, the proportions we can use are:

AB/PQ = BC/QR

5/10 = 3/QR

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The probability that Sam is late to his final exam is 0.000008, or 0.0008%.

Let A be the event that the first alarm clock works, B be the event that the second alarm clock works, and C be the event that the third alarm clock works. Then, the probability that Sam is late to his final exam is given by:

P(Sam is late) = P(not A) * P(not B) * P(not C)

Since the alarm clocks work independently of each other, the probability that any one of them does not work is 1 - 0.98 = 0.02. Therefore:

P(Sam is late) = 0.02 x 0.02 x 0.02

P(Sam is late) = 0.000008

So, the probability that Sam is late to his final exam is 0.000008, or 0.0008% (rounded to three decimal places). This is a very small probability, indicating that it is highly unlikely that Sam will be late to his final exam if all three alarm clocks are working.

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Answer:

P= 29.389 ~ 29.4

Step-by-step explanation:

P= ns = 2rn sin(180/n)...... formula to find perimeter

p= 2(5)(5)sin(36)

p= 2(5)(5)sin(36)P= 50 ×0.5877

p= 2(5)(5)sin(36)P= 50 ×0.5877 P= 29.389 approximate to 29.4

The elephant can travel at a constant speed of 25 mph, while I can travel at a constant speed of 60 miles in 1/2 hour.

It's important to note that miles per hour (mph) is a unit of speed that measures how many miles an object can travel in one hour. In this scenario, the elephant can travel at a constant speed of 25 mph, meaning it can travel 25 miles in one hour. On the other hand, I can travel at a constant speed of 60 miles in 1/2 hour, which means I can travel 120 miles in one hour (since 1/2 hour is equal to 0.5 hours). Therefore, in terms of speed, I am faster than the elephant. However, it's important to keep in mind that speed isn't always the most important factor when it comes to transportation, as other variables such as distance, terrain, and mode of transportation can also play a role.

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The statement is true for any sets A and B.

The statement "A = A - B" is true if and only if every element of A is not an element of B.

The set A - B represents the elements that are in A but not in B. Therefore, A = A - B means that A contains no elements that are in B. In other words, A and B have no elements in common. This is equivalent to saying that every element of A is not an element of B.

Now, since A and B have no elements in common, it follows that B is a subset of A (i.e., B ⊂ A). This is because if an element is in B, it cannot be in A (as A contains no elements of B), and if an element is not in B, it must be in A. Similarly, since A contains no elements of B, it follows that 0 ≤ B ⊆ A. Moreover, since every element of A is not an element of B, it follows that 0 ≤ A ⊆ Bᶜ (the complement of B). Finally, since every set is a subset of itself, it follows that 0 ≤ ⊆ A.

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Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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There are 6,720 five-digit natural numbers that satisfy the given conditions.

First, we need to choose the leftmost digit which can be any odd digit from 1,3,5,7,9. This can be done in 5 ways.

Then we need to choose the second digit, which can be any even digit from 0,2,4,6,8, except the digit we already chose for the first place. This can be done in 4 ways.

For the third digit, we have 8 remaining digits (since we have used 2 digits already), out of which we can choose any one, giving us 8 choices.

Similarly, for the fourth digit, we have 7 remaining digits to choose from, and for the last digit, we have 6 remaining digits.

Therefore, the total number of such five-digit numbers is given by:

5 × 4 × 8 × 7 × 6 = 6,720

So there are 6,720 five-digit natural numbers that satisfy the given conditions.

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Angie earns $127.44 in interest over the 3-year period.

Angie has $1,062 in her savings account, and the bank pays 4% simple interest on savings. To calculate the interest she earns in 3 years, we need to use the simple interest formula, which is:

Simple Interest = Principal × Rate × Time

In this case, the principal (initial amount) is $1,062, the rate is 4% (or 0.04 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:

Simple Interest = $1,062 × 0.04 × 3

Next, we can calculate the interest:

Simple Interest = $1,062 × 0.04 × 3 = $127.44

So, Angie earns $127.44 in interest over the 3-year period.

In summary, when calculating simple interest, you multiply the principal (initial amount) by the interest rate and the length of time (in years) the money is in the account. In Angie's case, with $1,062 in her account and a 4% interest rate, she earns $127.44 in interest over 3 years.

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The value of x best corresponds to a y value of 1,783 is 12.7.

The given equation of a line is y=290x-1900.

Here, y=1783

Substitute y=1783 in y=290x-1900, we get

1783=290x-1900

290x=1783+1900

290x=3683

x=3683/290

x=12.7

Therefore, the value of x best corresponds to a y value of 1,783 is 12.7.

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The quadratic expression 4x^2 + 20x + 200 = 0 cannot be factored completely

From the question, we have the following parameters that can be used in our computation:

4x^2 + 20x + 200 = 0

Divide through the terms by 5

So, we have

x^2 + 5x + 50 = 0

Next, we check if the above expression has real roots using

D = b^2 - 4ac

So, we have

D = 5^2 - 4 * 1 * 50

Evaluate

D = -175

The above disciminant value is less than 0

This means that the equation has no real root and as such the equation cannot be factored

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The correct conclusion is to reject the null hypothesis (H0) and accept the alternative hypothesis (Ha) since the p-value (0.0139) is less than the level of significance (5%).

In hypothesis testing, the p-value is a measure of the strength of evidence against the null hypothesis.

In this case, the p-value is 0.0139, which means that the probability of observing a test statistic as extreme as the one obtained or more extreme, assuming the null hypothesis is true, is only 0.0139.

Since this value is less than the significance level of 5%, we reject the null hypothesis and accept the alternative hypothesis.

Therefore, we conclude that there is enough evidence to suggest that the true mean is greater than 10.

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The values of a and b in the sequence are 18 and 10, respectively.

To find the values of a and b in the sequence given, we can use the fact that the median is 18 and the mean is 17.

Since the median is 18, we know that a and b must be two numbers that are greater than or equal to 18. Since the sequence is numerically ordered, we can see that a must be 18 or greater.

We can also use the fact that the mean is 17 to find the sum of all the numbers in the sequence. We know that the sum of all the numbers in the sequence divided by the number of terms in the sequence must be equal to the mean. Since there are 10 terms in the sequence, we can write:

(7 + a + 12 + 15 + 17 + b + 20 + 22 + 24 + 25) / 10 = 17

Simplifying this expression, we get:

(142 + a + b) / 10 = 17

Multiplying both sides by 10, we get:

142 + a + b = 170

Subtracting 142 from both sides, we get:

a + b = 28

Now we know that a and b are two numbers greater than or equal to 18 that add up to 28. The only two numbers that satisfy this condition are 18 and 10.

Since the sequence is numerically ordered, we know that a must be greater than or equal to 18. Therefore, a = 18 and b = 10.

So, the values of a and b in the sequence are 18 and 10, respectively.

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The expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t

The cost to make one donut is $0.32.

Therefore, the cost to make one dozen donuts (12 donuts) is:

12 x $0.32 = $3.84

The cost of the cardboard for one box is $0.18 per square foot. Therefore, the cost of the cardboard for a box with surface area t (in square feet) is:

$0.18t

The total cost for one dozen donuts includes the cost to make the donuts and the cost of the box.

So, the expression to model the total cost for one dozen donuts, where t represents the total surface area of the box in square feet, is $3.84 + $0.18t

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The area of the vertical cross section of the cylinder is approximately 71.68 square units.

The circumference of a cylinder can be calculated using the formula:

C = 2πr

Where C is the circumference and r is the radius of the cylinder.

In this case, we know that the circumference is 30, so we can set up the equation:

30 = 2 * 3.14 * r

Dividing both sides of the equation by 2 * 3.14, we get:

r = 30 / (2 * 3.14)

r ≈ 4.777

The area of the vertical cross section of a cylinder is given by the formula:

A = πr^2

Substituting the value of r we found:

A = 3.14 * (4.777)^2

A ≈ 71.68

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We have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15. Since it can be expressed as a ratio of integers, we can conclude that it is rational.

To show that 3/5 + 2/3 is rational, we need to find a way to write it as a ratio of integers. To do this, we first need to find a common denominator for the two fractions. The least common multiple of 5 and 3 is 15, so we can rewrite the fractions as follows:

3/5 = 9/15

2/3 = 10/15

Now we can add the two fractions:

3/5 + 2/3 = 9/15 + 10/15

Combining the numerators, we get:

3/5 + 2/3 = 19/15

Therefore, we have expressed 3/5 + 2/3 as the ratio of two integers, 19 and 15.

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Answer:

 Rita's age = 3 years

Jane's age = 12 years

Step-by-step explanation:

Framing algebraic equations and solving:

          Let the age of Rita = x years

             Age of Jane = 4 times of Rita's age

                                   = 4*x

                                   = 4x

After 6 years,

   Jane's age = 4x + 6

     Rita's age = x + 6

Jane's age = twice of Rita's age

      4x + 6 = 2* (x + 6)

      4x + 6  = 2x + 12        {Distributive property}

Subtract 6 from both sides,

             4x = 2x + 12 - 6

            4x = 2x + 6

Subtract '2x' from both sides,

    4x - 2x = 6

            2x = 6

Divide both sides by 2,

              x = 6 ÷ 2

             x = 3

Rita's age = 3 years

Jane's age = 4 * 3

                  = 12 years