Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes' are given below.
UVA (Pop.1): n1=87, ^p1=0.785
UVA (Pop.2): n2=85, ^p2=0.69
Find a 97.7% confidence interval for the difference p1−p2 of the population proportions.

Let's call the cost of the dryer "x".

We know from the problem that the washer costs $68 less than the dryer, so the cost of the washer would be "x - 68".

The problem also tells us that the combined cost of the washer and dryer is $782. So we can set up an equation:

x + (x - 68) = 782

Simplifying this equation, we get:

2x - 68 = 782

Adding 68 to both sides, we get:

2x = 850

Dividing both sides by 2, we get:

x = 425

So the dryer costs $425.

The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

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Answer:

D

Step-by-step explanation:

The roots of the given equation is real and equal.

Given , 5\(x^{2} \\\) - 10x+ k=0

The quadratic equation is b² - 4ac = 0

Here, a= 5, b= -10, c= k

substitute in b² - 4ac = 0

(-10)² - 4 * 5* k =0

100 - 20k =0 , let this be equation (1)

100 = 20k

k = \(\frac{100}{20}\)

k = 5.

now, substitute  k= 5 in equation (1)

100 -20k = 0

100 - 20*5 = 0

100 - 100 = 0

Therefore, the given equation is real and equal .

The correct question is 5x² - 10x + k =0

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Answer:

  a) 489.77 ft from friend

  b) 470.80 ft from cliff

Step-by-step explanation:

Given a man on a 135 ft cliff sees his friend at an angle of depression of 16°, you want to know the distance of the man from his friend, and the distance of the friend from the cliff.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

The 135 ft height of the cliff is modeled as the side of a right triangle that is opposite the angle of elevation from the friend to the top of the cliff. (See attachment 2.) That angle is the same as the angle of depression from the top of the cliff to the friend.

The hypotenuse of the triangle is the distance between the man and his friend. The side of the triangle adjacent to the friend is the distance to the cliff.

Using the above relations, we have ...

  sin(16°) = (cliff height)/(distance to friend)

  tan(16°) = (cliff height)/(distance to cliff)

Solving for the variables of interest gives ...

  distance to friend = (cliff height)/sin(16°) = (135 ft)/sin(16°) ≈ 489.77 ft

  distance to cliff = (cliff height)/tan(16°) = (135 ft)/tan(16°) ≈ 470.80 ft

The ma is 489.77 ft from his friend; the friend is 470.80 ft from the cliff.

__

Additional comment

The distances are given to more decimal places than necessary so you can round the answer as may be required.

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Answer: d= 412

i did 267+145 and that was 412 then i did 212-267 and got 145

a) The number of bacteria in the initial population is 34.

b) The exponential growth model is y = 34 * e^(kt)

Given data:

(a) To find the initial population, we can use the exponential growth formula:

y = A * e^(kt)

Where:

y = population at time t

A = initial population

k = growth rate

t = time

Given that there are 105 bacteria after 2 hours, so plug in these values into the formula:

105 = A * e^(k*2)

Similarly,  given that there are 325 bacteria after 4 hours:

325 = A * e^(k*4)

We now have a system of equations:

105 = A * e^(2k)

325 = A * e^(4k)

To solve for A, divide the second equation by the first equation:

325/105 = e^(4k)/e^(2k)

Simplifying further:

325/105 = e^(2k)

Taking the natural logarithm of both sides:

ln(325/105) = ln(e^(2k))

ln(325/105) = 2k

Solving for k:

k = 0.56493

Substitute it back into one of the original equations to solve for A. Let's use the first equation:

105 = A * e^(2k)

Substituting k = ln(325/105) / 2:

105 = A * e^(2 * ln(325/105) / 2)

Simplifying:

105 = A * (325/105)

A = 105 * (105/325)

A ≈ 34 (rounded to the nearest whole number)

Hence, the initial population is approximately 34 bacteria.

(b) Now that we have the initial population, A, and the growth rate, k, we can write the exponential growth model for the bacteria population:

y = 34 * e^(kt)

where t represents the time in hours.

Hence, the exponential equations are solved.

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Answer:

8.2

Step-by-step explanation:

The correct option is the third option, which states that 80 percent is being used as a hypothesis.

A hypothesis is a tentative assumption that is made to test a prediction. A hypothesis can be confirmed or refuted based on the results of an experiment.

In the given problem, Jim and Pam conducted an experiment to find out whether temperature affects learning.

20 rats were trained to press a lever in an operant chamber to obtain food pellets.

Jim and Pam estimated that 80 percent of all rats trained on this task in 70 degrees Fahrenheit temperature would emit more than one response per second.

Based on the information provided, 80 percent is being used as a hypothesis or predicted value that Jim and Pam had before conducting the experiment. Therefore, the correct option is the third option, which states that 80 percent is being used as a hypothesis. A hypothesis is a tentative assumption that is made to test a prediction. A hypothesis can be confirmed or refuted based on the results of an experiment.

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Answer:

1,5

Step-by-step explanation:

1,5 is located within the shaded region.

Answer:

Inline range: 2 ≤ n < 8

Interval range: [ - 2, 8 )

Loop: n = - 2; n < 8;

Step-by-step explanation:

The filled circle means inclusive while outlined circle means exclusive.

Answer:

-2 ≤ x > 8

Step-by-step explanation:

x = a possible number based on the diagram

the black-filled-in dot on the line above the number line indicated that it can either be '≤' or '≥'

the empty-not-filled-in dot means that it can be either '<' or '>'

the '≤' means x can be equal or greater to -2

and the '>' means that x must be less than 8

hope this helps!

The possible values of x for the given triangle ABC are 0.75<x<8.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Given that, m∠A < m∠B < m∠C.

a) From triangle ABC,

BC<AC<AB

2x+3<6x<5x+8

Now, 2x+3<6x

Subtract 2x on both the sides of an inequality, we get

3<4x

Divide 4 on both the sides of an inequality, we get

0.75<x

Here, 6x<5x+8

Subtract 5x on both the sides of an inequality, we get

x<8

So, possible values of x are 0.75<x<8

b) From triangle ABC,

BC<AC<AB

3x+1<4x+8<7x+2

Now, 3x+1<4x+8

Subtract 3x on both the sides of an inequality, we get

1<x+8

Subtract 8 on both the sides of an inequality, we get

-7<x

Here, 4x+8<7x+2

Subtract 4x on both the sides of an inequality, we get

8<3x+2

Subtract 2 on both the sides of an inequality, we get

6<3x

Divide 3 on both the sides of an inequality, we get

2<x

So, possible values of x are -7<x<2

Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.

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Two triangles are a square ，One Square Be 360º， Half of the square is 180º

Answer:

9 and 11

Step-by-step explanation:

Answer:

total 1 hour 15 mins

Step-by-step explanation:

3:45 - 5:00

lets count one by one

3:45 - 4:00 = 15 mins

4:00 - 5:00 = 1 hour

total 1 hour 15 mins

the larger the denominator compared to the numerator, the smaller the number, so:

So, let's choose the smallest number as a numerator, and the biggest numbers as a denominator:

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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Answer:

2.08 this is answer

Answer:

I'm sorry I really don't know I tried to figure it out but i couldn't im so sorry

Step-by-step explanation:

If Mike pitches a ridge tent. The tent is 16 yards wide and the slope of the tent measures 23 yards, the height of the tent is 28.07 cm

The solution for the height would be gotten with the Pythagorean theorem. The theorem states that in a right angled triangle the sum of the square on the hypotenuse is equal to the sum of the square of the two other sides of same triangle.

This is illustrated mathematically as

C² = A² + B²

where C is the height

A is the width in yards

B is the slope.

Then we have

C² = 16² + 23²

C = √785

C = 28.07 yards

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The series ∑=0infinity(3)2(2)! converges exactly to -9/2.

We can write the series using the Maclaurin series for cos(x) as follows:

∑=0infinity^n(3^(2n))/(2n)! = cos(3i)

The Maclaurin series for cos(x) is:

cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...

Substituting x = 3i, we get:

cos(3i) = 1 - (3i)^2/2! + (3i)^4/4! - (3i)^6/6! + ...

Simplifying the powers of i, we get:

cos(3i) = 1 - 9/2! - i(3)^3/3! + i(3)^5/5! - ...

The imaginary part of cos(3i) is:

Im(cos(3i)) = -3^3/3! + 3^5/5! - ...

The series for the imaginary part is an alternating series with decreasing absolute values, so it converges by the Alternating Series Test. Therefore, the exact value of the series is the real part of cos(3i), which is:

Re(cos(3i)) = cosh(3) = (e^3 + e^-3)/2

Using a calculator or a computer program, we can evaluate cosh(3) and simplify to get:

cosh(3) = (e^3 + e^-3)/2 = (1/2)(e^6 + 1)/(e^3)

Therefore, the series ∑=0infinity(3)2(2)! converges exactly to -9/2.

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The probability of a randomly selected car weighing more than 4,000 pounds is 0.7175, the probability of a randomly selected car weighing less than 3,000 pounds is 0.2748, and the probability of a randomly selected car weighing between 2,800 and 4,500 pounds is 0.8187 - 0.2748 = 0.5449.

a. The probability of a randomly selected car weighing more than 4,000 pounds can be found using the standard normal distribution table. The z-score for 4,000 is (4,000 - 3,550) / 870 = 0.58. The probability of a randomly selected car weighing more than 4,000 pounds is 0.7175.

b. The probability of a randomly selected car weighing less than 3,000 pounds can be found using the standard normal distribution table. The z-score for 3,000 is (3,000 - 3,550) / 870 = -0.64. The probability of a randomly selected car weighing less than 3,000 pounds is 0.2748.

c. The probability of a randomly selected car weighing between 2,800 and 4,500 pounds can be found using the standard normal distribution table. The z-score for 2,800 is (2,800 - 3,550) / 870 = -0.94. The z-score for 4,500 is (4,500 - 3,550) / 870 = 1.04. The probability of a randomly selected car weighing between 2,800 and 4,500 pounds is 0.8187 - 0

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Answer:

  260 cm

Step-by-step explanation:

Each 1/00 of a meter is 1 cm, so 65/100 meters is 65 cm. If that is the length of paper required for 1 kite, then 4 times that length will be required for 4 kites.

__

The paper required for 4 kites is ...

  (65 cm) × 4 = 260 cm

Answer:

Area of rectangle = 150 cm

Step-by-step explanation:

Given the following data;

To find the area of the rectangle;

First of all, we would determine the dimensions (length and width) of the rectangle;

For length;

Length, L = 2x

For width;

Width, W = 3x

Mathematically, the perimeter of a rectangle is given by the formula;

P = 2(L + W)

50 = 2(2x + 3x)

50 = 2(5x)

50 = 10x

x = 50/10

x = 5

Length, L = 2x = 2 * 5 = 10 cm

Width, W = 3x = 3 * 5 = 15 cm

Now, we would find the area of the rectangle;

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = length * width

Area of rectangle = 10 * 15

Area of rectangle = 150 cm

Answer: 14 Adult tickets

Step-by-step explanation:

The equation for the total number of tickets would be

x+y=18

5x+3y=82

y=18-x

5x+3(18-x)=82

2x=28

x=14

x= Number of adult tickets

Answer:

Theoretical A - 20%

Experimental - 24%

Theoretical B - <

Step-by-step explanation:

The theoretical probability of choosing a card with the number 2 is:

1 out of 5 cards have the number 2, so the probability of choosing a card with the number 2 is 1/5 or 0.2, which is equal to 20%.

The experimental probability of choosing a card with the number 2 is:

Out of the 400 people surveyed, 96 chose the card labeled 2. So the experimental probability is 96/400 or 0.24, which is equal to 24%.

To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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